SCRaMbLE_simulation_chr_len_events_easy.py

from SCRaMbLE_simulation_3 import force_SCRaMLE_lin_cir
from SCRaMbLE_simulation_3 import force_SCRaMLE_lin_cir_events
from comparison_sol import LoxP_unit_count_Dict_list
from comparison_sol import NG50_calculator
from comparison_sol import essential_ratio_calculator
from comparison_sol import half_life
from SCRaMbLE_simulation_chr_len_events_store2 import plot_chr_len
from SCRaMbLE_simulation_chr_len_events_store2 import plot_chr_len_median
from work_parallel_functions import sum_within_list
from work_parallel_functions import standard_deviation_from_points_parallel
#from Mapping_coverage_MM import calculate_LU_CN_percentage
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import random
import statistics

# SCRaMbLEs a synthetic chromosome and outputs chr_len, L_unique, LG50
def SCRaMbLE_SIM_length(syn_chr, events=15, simulations=100, essential=[], CEN=[], circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1]):
    chr_len = [[] for _ in range(simulations)]
    L_unique = [[] for _ in range(simulations)]
    LG50 = [[] for _ in range(simulations)]
    chr_len_SD = [0]    # The first value is always 0
    L_unique_SD = [0]
    LG50_SD = [0]
    # Percentiles or Quartiles.
    chr_len_Q1 = [len(syn_chr)]
    chr_len_Q2 = [len(syn_chr)]   # Median
    chr_len_Q3 = [len(syn_chr)]
    L_unique_Q1 = [len(syn_chr)]
    L_unique_Q2 = [len(syn_chr)]
    L_unique_Q3 = [len(syn_chr)]
    LG50_Q1, LG50_Q2, LG50_Q3 = [len(syn_chr)/2], [len(syn_chr)/2], [len(syn_chr)/2]

    # Count the events type
    Events = [[] for _ in range(simulations)]
    # Calculate the ratio of essential LUs
    essential_ratio = [[] for _ in range(simulations)]

    for s in range(simulations):
        print(s)
        SCRaMbLEd = syn_chr[:]
        for _ in range(events):
            # Perform SCRaMbLE on the synthetic chromosome
            #SCRaMbLEd = force_SCRaMLE_lin_cir(SCRaMbLEd, Number_events=1, essential=essential, circular=circular, mu=mu, sigma=sigma, CEN=CEN, force=force, probability=probability)
            chr_events = force_SCRaMLE_lin_cir_events(SCRaMbLEd, Number_events=1, essential=essential, circular=circular, mu=mu, sigma=sigma, CEN=CEN, force=force, probability=probability, event_type=True)
            #print(chr_events)
            SCRaMbLEd = chr_events[0]
            if chr_events[1] != []:
                Events[s].append(chr_events[1][0])
            else:
                Events[s].append("NULL")
            # Get some statistics about the SCRaMbLEd chromosome
            NG50 = NG50_calculator(SCRaMbLEd)
            chr_len[s].append(len(SCRaMbLEd))
            L_unique[s].append(NG50[1])
            LG50[s].append(NG50[3])
            essential_ratio[s].append(essential_ratio_calculator(chromosome=SCRaMbLEd, essential=essential))
    # Calculate the standard deviation
    for s in range(events):
        CHR_L = [sim_L[s] for sim_L in chr_len]
        unique_L = [sim_L[s] for sim_L in L_unique]
        LG50_L = [sim_L[s] for sim_L in LG50]
        chr_len_SD.append(statistics.stdev(CHR_L))
        L_unique_SD.append(statistics.stdev(unique_L))
        LG50_SD.append(statistics.stdev(LG50_L))
        chr_len_Q1.append(np.percentile(CHR_L, 25))
        chr_len_Q2.append(np.percentile(CHR_L, 50))
        chr_len_Q3.append(np.percentile(CHR_L, 75))
        L_unique_Q1.append(np.percentile(unique_L, 25))
        L_unique_Q2.append(np.percentile(unique_L, 50))
        L_unique_Q3.append(np.percentile(unique_L, 75))
        LG50_Q1.append(np.percentile(LG50_L, 25))
        LG50_Q2.append(np.percentile(LG50_L, 50))
        LG50_Q3.append(np.percentile(LG50_L, 75))

    chr_len_Q1_Q2_Q3 = [chr_len_Q1, chr_len_Q2, chr_len_Q3]
    L_unique_Q1_Q2_Q3 = [L_unique_Q1, L_unique_Q2, L_unique_Q3]
    LG50_Q1_Q2_Q3 = [LG50_Q1, LG50_Q2, LG50_Q3]

    print("chr_len =", len(chr_len), np.percentile(chr_len, 50))#, chr_len)
    #print("L_unique =", L_unique)
    #print("LG50 =", LG50)
    print("chr_len_SD =", len(chr_len_SD), np.percentile(chr_len, 50))#, chr_len_SD)
    #print("L_unique_SD =", L_unique_SD)
    #print("LG50_SD =", LG50_SD)
    #print("chr_len_Q1 =", chr_len_Q1)
    print("chr_len_Q1_Q2_Q3 =", len(chr_len_Q1), "=", np.percentile(chr_len_Q1, 50), np.percentile(chr_len_Q2, 50), np.percentile(chr_len_Q3, 50))
    #print("Events =", Events)
    # How many chromosomes reached the length of zero?
    last_chr_len = [sim[-1] for sim in chr_len]
    last_chr_len_zero = last_chr_len.count(0)
    print("last_chr_len_zero =", 100 * last_chr_len_zero / simulations, "%")
    return chr_len, L_unique, LG50, chr_len_SD, L_unique_SD, LG50_SD, Events, essential_ratio, chr_len_Q1_Q2_Q3, L_unique_Q1_Q2_Q3, LG50_Q1_Q2_Q3

def plot_SCRaMbLE_chr_len(syn_chr, events=15, simulations=100, essential=[], CEN=[], circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1], file_name="", SD=False):
    # SCRaMbLE the chromosome and generate chr_len, L_unique, LG50
    S = SCRaMbLE_SIM_length(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=circular, mu=mu, sigma=sigma, force=force, probability=probability)
    chr_len = S[0]
    L_unique = S[1]
    LG50 = S[2]
    #chr_len_Q1, chr_len_Q2, chr_len_Q3 = S[6], S[7], S[8]
    chr_len_Q1_Q2_Q3 = S[8]
    L_unique_Q1_Q2_Q3 = S[9]
    LG50_Q1_Q2_Q3 = S[10]

    # Count SCRaMbLE events types
    Events = S[6]
    DELs = [0 for _ in range(events)]
    INVs = [0 for _ in range(events)]
    DUPs = [0 for _ in range(events)]
    for Sim in Events:
        for E in range(len(Sim)):
            if Sim[E] == "DEL":
                DELs[E] += 1
            if Sim[E] == "INV":
                INVs[E] += 1
            if Sim[E] == "DUP":
                DUPs[E] += 1
    # Convert the number of SEs into percentages
    DELs = [e/simulations for e in DELs]
    INVs = [e/simulations for e in INVs]
    DUPs = [e/simulations for e in DUPs]
    # Calculate the ratio of essential LUs
    essential_ratio = S[7]

    if SD == True:
        chr_len_SD = S[3]
        L_unique_SD = S[4]
        LG50_SD = S[5]
    else:
        chr_len_SD = []
        L_unique_SD = []
        LG50_SD = []

    # List of time points
    SCRaMbLEd_events = list(range(0, events+1, 1))  # +1 because we record also the initial value

    # If you want to plot all the SCRaMbLE chromosomes
    #plot_chr_len(SCRaMbLEd_events[1:], chr_len, L_unique=L_unique, LG50=LG50, num_essential=len(essential), simulations=simulations, file_name="")

    # Put together all the simulations
    chr_len_L = sum_within_list(chr_len)
    L_unique_L = sum_within_list(L_unique)
    LG50_L = sum_within_list(LG50)
    essential_ratio_L = sum_within_list(essential_ratio)

    # Add the first value
    NG50 = NG50_calculator(syn_chr)
    chr_len_L.insert(0, len(syn_chr)*simulations)
    L_unique_L.insert(0, NG50[0]*simulations)
    LG50_L.insert(0, NG50[3]*simulations)
    #essential_ratio_L.insert(0, 0.5*simulations)

    # Divide for the number of simulations. You can use also the function divide_by_sim in work_parallel_functions
    chr_len_L = [x / simulations for x in chr_len_L]
    L_unique_L = [x / simulations for x in L_unique_L]
    LG50_L = [x / simulations for x in LG50_L]
    essential_ratio_L = [x / simulations for x in essential_ratio_L]
    print("chr_len_L =", chr_len_L)
    print("chr_len_Q2 =", chr_len_Q1_Q2_Q3[1])
    #print("L_unique_L =", L_unique_L)
    #print("LG50_L =", LG50_L)
    #print("DELs =", DELs)
    #print("INVs =", INVs)
    #print("DUPs =", DUPs)

    # Plot the results
    plot_chr_len(SCRaMbLEd_events, chr_len_L, L_unique=L_unique_L, LG50=LG50_L, num_essential=len(essential), simulations=simulations, circular=circular, probability=probability, file_name=file_name, SD_chr_len=chr_len_SD, SD_L_unique=L_unique_SD, SD_LG50=LG50_SD)
    plot_chr_len_median(SCRaMbLEd_events, chr_len_Q1_Q2_Q3, L_unique=L_unique_Q1_Q2_Q3, LG50=LG50_Q1_Q2_Q3, num_essential=len(essential), simulations=simulations, circular=circular, probability=probability, file_name=file_name)

    # plot the frequencies of the SCRaMbLE events types
    plt.figure(figsize=(7, 3.5), dpi=300)
    # Font size
    SMALL_SIZE = 8
    MEDIUM_SIZE = 9
    BIGGER_SIZE = 10
    plt.rc('font', size=SMALL_SIZE)  # controls default text sizes
    plt.rc('axes', titlesize=SMALL_SIZE)  # fontsize of the axes title
    plt.rc('axes', labelsize=MEDIUM_SIZE)  # fontsize of the x and y labels
    plt.rc('xtick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('ytick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('legend', fontsize=SMALL_SIZE)  # legend fontsize
    plt.rc('figure', titlesize=MEDIUM_SIZE)  # fontsize of the figure title
    plt.rcParams['lines.linewidth'] = 0.65

    #print(len(SCRaMbLEd_events), len(DELs))
    plt.ylim(0, 1)
    plt.plot(SCRaMbLEd_events[1:], DELs, label="DELs", linewidth=0.7)
    plt.plot(SCRaMbLEd_events[1:], INVs, label="INVs", linewidth=0.7)
    plt.plot(SCRaMbLEd_events[1:], DUPs, label="DUPs", linewidth=0.7)
    plt.plot(SCRaMbLEd_events[1:], essential_ratio_L, label="essential ratio")  # linewidth=0.65
    plt.ylabel("Percentage of event type over " + str(simulations) + " simulations")
    plt.xlabel("SCRaMbLEd events")
    plt.title("Frequencies of SCRaMbLE event types", fontsize=9)
    plt.legend(fontsize=8)
    # These are some information to add to the saved files.
    # Create a random seed to save the image
    random_seed = str(random.random())[2:6]
    if circular:    # record if the chromosome is linear or circular
        lin_cir = "c"
    else:
        lin_cir = "l"
    probability_str = ""    # record the probabilities of each event
    for i in probability:
        probability_str = probability_str + str(i)
    file_name1 = "SCRaMbLE_chr_len/SCRaMbLE_events_types_" + lin_cir + "_events_" + str(SCRaMbLEd_events[-1]) + "_sim_" + str(simulations) + "_P" + probability_str + "_" + file_name + random_seed
    plt.savefig(file_name1 + ".png", dpi=300, bbox_inches='tight')
    plt.savefig(file_name1 + ".svg", format="svg", dpi=300, bbox_inches='tight')
    plt.show()
    plt.close()
    return None

# I split the function plot_SCRaMbLE_chr_len in two pieces
def mean_SCRaMbLE_chr_len(syn_chr, events=15, simulations=100, essential=[], CEN=[], circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1], file_name="", num_essential=0):
    if num_essential != 0:
        num_essential = 10
        essential = sorted(random.sample(syn_chr, k=num_essential))
    # Generate the chr len
    S = SCRaMbLE_SIM_length(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=circular, mu=mu, sigma=sigma, force=force, probability=probability)
    chr_len = S[0]
    L_unique = S[1]
    LG50 = S[2]

    # If you want to plot all the SCRaMbLE chromosomes
    #plot_chr_len(SCRaMbLEd_events, chr_len, L_unique=L_unique, LG50=LG50, num_essential=len(essential), simulations=simulations, file_name="")

    # Put together all the simulations
    chr_len_L = sum_within_list(chr_len)
    L_unique_L = sum_within_list(L_unique)
    LG50_L = sum_within_list(LG50)

    # Add the first value
    NG50 = NG50_calculator(syn_chr)
    chr_len_L.insert(0, len(syn_chr)*simulations)
    L_unique_L.insert(0, NG50[0]*simulations)
    LG50_L.insert(0, NG50[3]*simulations)

    # Divide for the number of simulations. You can use also the function divide_by_sim in work_parallel_functions
    chr_len_L = [x / simulations for x in chr_len_L]
    L_unique_L = [x / simulations for x in L_unique_L]
    LG50_L = [x / simulations for x in LG50_L]
    #print("half_life chr_len_L =", half_life(chr_len_L))
    #print("half_life L_unique_L =", half_life(L_unique_L, minus_constant=len(essential)))
    #print("half_life LG50_L =", half_life(LG50_L))
    return chr_len_L, L_unique_L, LG50_L


def plot_mean_SCRaMbLE_chr_len(syn_chr, events=15, simulations=100, essential=[], CEN=[], circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1], file_name=""):
    A_result = mean_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=circular, mu=mu, sigma=sigma, force=force, probability=probability)

    # List of time points
    SCRaMbLEd_events = list(range(0, events + 1, 1))  # +1 because we record also the initial value

    # Plot the results
    plot_chr_len(SCRaMbLEd_events, chr_len=A_result[0], L_unique=A_result[1], LG50=A_result[2], num_essential=len(essential), simulations=simulations, circular=circular, probability=probability, file_name=file_name)
    return None

# This function plots the chromosome length over a SCRaMbLE evolution using different initial chromosome length.
def chr_len_range_SCRaMbLE(events=15, simulations=100, essential=[], CEN=[], circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1], file_name=""):

    #chr_len_range = list(range(25, 201, 25))
    chr_len_range = list(range(25, 226, 50))
    # chr_len_range = [25, 50, 75, 100, 125, 150, 175, 200]
    # chr_len_range = [25, 75, 125, 175, 225]
    print("chr_len_range =", chr_len_range)

    chr_len_multi = []
    L_unique_multi = []
    LG50_multi = []
    half_life_L_unique_L_multi = []
    for i in chr_len_range:
        print("Chr len =", i)
        # Create the chromosomes
        SYN_CHR = list(range(1, i, 1))
        # Use this if you want to chose the essential LUs at random
        num_essential = 10
        essential = sorted(random.sample(SYN_CHR, k=num_essential))
        A_result = mean_SCRaMbLE_chr_len(SYN_CHR, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=circular, mu=mu, sigma=sigma, force=force, probability=probability, file_name=file_name, num_essential=10)
        chr_len_multi.append(A_result[0])
        L_unique_multi.append(A_result[1])
        LG50_multi.append(A_result[2])
        print(i, "half_life chr_len_L =", half_life(A_result[0]))
        print(i, "half_life L_unique_L =", half_life(A_result[1], minus_constant=num_essential))
        # print(i, "half_life LG50_L =", half_life(A_result[2]))
        half_life_L_unique_L_multi.append(half_life(A_result[1], minus_constant=num_essential))
        print()

    # List of time points
    SCRaMbLEd_events = list(range(0, events + 1, 1))  # +1 because we record also the initial value

    # plot the results
    plt.figure(figsize=(7, 3.5), dpi=300)

    # Font size
    SMALL_SIZE = 8
    MEDIUM_SIZE = 9
    BIGGER_SIZE = 10
    plt.rc('font', size=SMALL_SIZE)  # controls default text sizes
    plt.rc('axes', titlesize=SMALL_SIZE)  # fontsize of the axes title
    plt.rc('axes', labelsize=MEDIUM_SIZE)  # fontsize of the x and y labels
    plt.rc('xtick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('ytick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('legend', fontsize=SMALL_SIZE)  # legend fontsize
    plt.rc('figure', titlesize=MEDIUM_SIZE)  # fontsize of the figure title
    plt.rcParams['lines.linewidth'] = 0.65

    plt.ylabel("Chr length mean over " + str(simulations) + " simulations")
    plt.xlabel("SCRaMbLEd events")
    plt.title("Chr length over SCRaMbLE events", fontsize=9)

    #plt.plot(0, 0, label="Chr len", color="tab:blue")
    plt.plot(0, 0, label="No. unique LUs", color="C1")
    # plt.plot(0,0, label="LG50", color="tab:green")
    #Labels = ["Chr = 25", "Chr = 50", "Chr = 75", "Chr = 100", "Chr = 125", "Chr = 150", "Chr = 175", "Chr = 200"]
    Labels = ["Chr len = 25 LUs", "Chr len = 75 LUs", "Chr len = 125 LUs", "Chr len = 175 LUs", "Chr len = 225 LUs"]
    colours = ["C0", "C2", "C3", "C4", "C5"]
    #Labels, colours = [], []
    #for i in range(len(chr_len_range)):
    #    Labels.append("Chr len = " + str(chr_len_range[i]) + " LUs")
    #    colours.append("C" + str(i))

    for i in range(len(chr_len_multi)):
        plt.plot(SCRaMbLEd_events, chr_len_multi[i], color=colours[i], label=Labels[i])
        # plt.errorbar(SCRaMbLEd_events, chr_len[i], yerr=SD_chr_len, elinewidth=0.1)
        if L_unique_multi != [[]]:
            plt.plot(SCRaMbLEd_events, L_unique_multi[i], color="C1")   # color="cornflowerblue"
        #if LG50 != [[]]:
        #    plt.plot(SCRaMbLEd_events, LG50[i], label="LG50", color="tab:green")
    plt.hlines(num_essential, 0, SCRaMbLEd_events[-1], colors="red", linestyle=":", label="No. essential LUs")
    plt.legend(fontsize=8)
    #plt.yscale('log', base=2)
    # Plot the half-life of non-essential LUs
    for i in range(len(chr_len_range)):
        print("half_life_L_unique_L_multi =", chr_len_range[i], half_life_L_unique_L_multi[i])
        # plt.hlines(chr_len_range[i]/2, 0, SCRaMbLEd_events[-1], colors="grey", linestyle=":", alpha=0.5)
        # plt.hlines(chr_len_range[i]/4, 0, SCRaMbLEd_events[-1], colors="blue", linestyle=":", alpha=0.5)
        if half_life_L_unique_L_multi[i] != []:
            half = chr_len_range[i] - (chr_len_range[i] - num_essential) / 2
            #plt.hlines(half, 0, half_life_L_unique_L_multi[i][0], colors="grey", linestyle=":", alpha=0.5)
            plt.scatter(half_life_L_unique_L_multi[i][0], half, s=5, color="black")
    # These are some information to add to the saved files.
    # Create a random seed to save the image
    random_seed = str(random.random())[2:6]
    if circular:  # record if the chromosome is linear or circular
        lin_cir = "c"
    else:
        lin_cir = "l"
    probability_str = ""  # record the probabilities of each event
    for i in probability:
        probability_str = probability_str + str(i)

    file_name = "SCRaMbLE_chr_len/chr_length_" + lin_cir + "_events_" + str(SCRaMbLEd_events[-1]) + "_sim_" + str(simulations) + "_P" + probability_str + "_" + file_name + random_seed
    plt.savefig(file_name + ".png", dpi=300, bbox_inches='tight')
    plt.savefig(file_name + ".svg", format="svg", dpi=300, bbox_inches='tight')
    plt.show()
    plt.close()
    return None

# This function plots the chromosome length over a SCRaMbLE evolution using different number of essential LUs.
def chr_len_essential_range_SCRaMbLE(syn_chr=50, events=15, simulations=100, CEN=[], circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1], file_name=""):

    essential_range = list(range(0, 51, 10))
    # essential_range = [0, 10, 20, 30, 40, 50]
    print("essential_range =", essential_range)

    chr_len_multi = []
    L_unique_multi = []
    LG50_multi = []

    for ESSE in essential_range:
        print("num essential =", ESSE)
        if ESSE == 0:
            essential = []
        else:
            essential = sorted(random.sample(syn_chr, k=ESSE))
        A_result = mean_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=circular, mu=mu, sigma=sigma, force=force, probability=probability, file_name=file_name)
        chr_len_multi.append(A_result[0])
        L_unique_multi.append(A_result[1])
        LG50_multi.append(A_result[2])

    # List of time points
    SCRaMbLEd_events = list(range(0, events + 1, 1))  # +1 because we record also the initial value

    # plot the results
    plt.figure(figsize=(7, 3.5), dpi=300)

    # Font size
    SMALL_SIZE = 8
    MEDIUM_SIZE = 9
    BIGGER_SIZE = 10
    plt.rc('font', size=SMALL_SIZE)  # controls default text sizes
    plt.rc('axes', titlesize=SMALL_SIZE)  # fontsize of the axes title
    plt.rc('axes', labelsize=MEDIUM_SIZE)  # fontsize of the x and y labels
    plt.rc('xtick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('ytick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('legend', fontsize=SMALL_SIZE)  # legend fontsize
    plt.rc('figure', titlesize=MEDIUM_SIZE)  # fontsize of the figure title
    plt.rcParams['lines.linewidth'] = 0.65

    plt.ylabel("Chr length mean over " + str(simulations) + " simulations")
    plt.xlabel("SCRaMbLEd events")
    plt.title("Chr length over SCRaMbLE events")

    Labels = ["# essential LUs = 0", "# essential LUs = 10", "# essential LUs = 20", "# essential LUs = 30", "# essential LUs = 40", "# essential LUs = 50"]

    for i in range(len(chr_len_multi)):
        plt.plot(SCRaMbLEd_events, chr_len_multi[i], label=Labels[i])
        # if L_unique != [[]]:
        #    plt.plot(SCRaMbLEd_events, L_unique[i], color="cornflowerblue")
    plt.legend(fontsize=8)
    # These are some information to add to the saved files.
    # Create a random seed to save the image
    random_seed = str(random.random())[2:6]
    if circular:  # record if the chromosome is linear or circular
        lin_cir = "c"
    else:
        lin_cir = "l"
    probability_str = ""  # record the probabilities of each event
    for i in probability:
        probability_str = probability_str + str(i)
    file_name = "SCRaMbLE_chr_len/chr_length_" + lin_cir + "_events_" + str(SCRaMbLEd_events[-1]) + "_sim_" + str(simulations) + "_P" + probability_str + "_" + file_name + random_seed
    plt.savefig(file_name + ".png", dpi=300, bbox_inches='tight')
    plt.savefig(file_name + ".svg", format="svg", dpi=300, bbox_inches='tight')
    plt.show()
    plt.close()
    return None

# This function plots the chromosome length over a SCRaMbLE evolution using different probabilities of deletions and duplications.
def chr_len_probabilities_range_SCRaMbLE(syn_chr=50, events=15, simulations=100, essential=[], CEN=[], circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1], file_name="", LOG=True):

    probabilities_range = [[0,4,4,1], [0,4,4,2], [0,4,4,4], [0,4,4,8], [0,4,4,16]]

    chr_len_multi = []
    L_unique_multi = []
    LG50_multi = []

    for PROB in probabilities_range:
        print("Probability =", PROB)
        A_result = mean_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=circular, mu=mu, sigma=sigma, force=force, probability=PROB, file_name=file_name)
        chr_len_multi.append(A_result[0])
        L_unique_multi.append(A_result[1])
        LG50_multi.append(A_result[2])

    # List of time points
    SCRaMbLEd_events = list(range(0, events + 1, 1))  # +1 because we record also the initial value

    # plot the results
    plt.figure(figsize=(7, 3.5), dpi=300)

    # Font size
    SMALL_SIZE = 8
    MEDIUM_SIZE = 9
    BIGGER_SIZE = 10
    plt.rc('font', size=SMALL_SIZE)  # controls default text sizes
    plt.rc('axes', titlesize=SMALL_SIZE)  # fontsize of the axes title
    plt.rc('axes', labelsize=MEDIUM_SIZE)  # fontsize of the x and y labels
    plt.rc('xtick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('ytick', labelsize=SMALL_SIZE)  # fontsize of the tick labels
    plt.rc('legend', fontsize=SMALL_SIZE)  # legend fontsize
    plt.rc('figure', titlesize=MEDIUM_SIZE)  # fontsize of the figure title
    plt.rcParams['lines.linewidth'] = 0.65

    plt.ylabel("Chr length mean over " + str(simulations) + " simulations")
    plt.xlabel("SCRaMbLEd events")
    plt.title("Chr length over SCRaMbLE events", fontsize=9)

    #Labels = ["P(Del)/P(Dup) = 4", "P(Del)/P(Dup) = 2", "P(Del)/P(Dup) = 1", "P(Del)/P(Dup) = 1/2", "P(Del)/P(Dup) = 1/4"]
    Labels = ["$P_{DEL}/P_{DUP} = 4$", "$P_{DEL}/P_{DUP} = 2$", "$P_{DEL}/P_{DUP} = 1$", "$P_{DEL}/P_{DUP} = 1/2$", "$P_{DEL}/P_{DUP} = 1/4$"]

    for i in range(len(chr_len_multi)):
        plt.plot(SCRaMbLEd_events, chr_len_multi[i], label=Labels[i])
        # if L_unique != [[]]:
        #    plt.plot(SCRaMbLEd_events, L_unique[i], color="cornflowerblue")
    plt.hlines(num_essential, 0, SCRaMbLEd_events[-1], colors="red", linestyle=":", label="No. essential LUs")
    plt.legend(fontsize=8)
    # These are some information to add to the saved files.
    # Create a random seed to save the image
    random_seed = str(random.random())[2:6]
    if circular:  # record if the chromosome is linear or circular
        lin_cir = "c"
    else:
        lin_cir = "l"
    probability_str = ""  # record the probabilities of each event
    for i in probability:
        probability_str = probability_str + str(i)
    log_id = ""
    if LOG:
        plt.yscale('log')
        log_id = "_log"
    file_name = "SCRaMbLE_chr_len/chr_length_" + lin_cir + "_events_" + str(SCRaMbLEd_events[-1]) + "_sim_" + str(simulations) + "_P" + probability_str + "_" + file_name + random_seed + log_id
    plt.savefig(file_name + ".png", dpi=300, bbox_inches="tight")
    plt.savefig(file_name + ".svg", format="svg", dpi=300, bbox_inches="tight")
    plt.show()
    plt.close()
    return None

# test the code
if __name__ == "__main__":

    import os
    # Create the folder where the output will be created
    if not os.path.exists("SCRaMbLE_chr_len"):
        os.makedirs("SCRaMbLE_chr_len")

    # Test the chromosome length evolution under SCRaMbLE evolution
    syn_chr = list(range(1, 45, 1))
    essential = [2, 7, 9, 10, 12, 20]
    #essential = [2, 7, 9, 10, 12, 19, 20, 24]  # LUs 19 and 24 are not essential but required for fast growth. Deletion of LU 6 can also generate some slow growth phenotype.
    #num_essential = 10
    #essential = sorted(random.sample(syn_chr, k=num_essential))
    #print("essential =", essential)
    CEN = [2]
    events = 1000
    simulations = 1000
    plot_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=True, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1], SD=True)

    # Try a different chromosome with 100 LUs
    syn_chr = list(range(1, 101, 1))
    events = 750
    #plot_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=False, mu=0, sigma=10, force=True, probability=[0, 4, 4, 1], SD=True)
    num_essential = 5
    essential = sorted(random.sample(syn_chr, k=num_essential))
    CEN_random = [essential[round(len(essential)/2)]]
    print("essential =", essential, CEN_random)
    #plot_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN_random, circular=False, mu=0, sigma=10, force=True, probability=[0, 4, 4, 1], SD=True)

    #plot_mean_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1])

    # Test the impact of initial chromosome length on the chromosome length during SCRaMbLE evolution
    num_essential = 10
    simulations = 50
    # I set the essential LUs at random inside the function
    #essential = sorted(random.sample(syn_chr, k=num_essential))
    #essential = sorted(random.sample(range(1, 26), k=num_essential))
    events = 1000
    #chr_len_range_SCRaMbLE(events=events, simulations=simulations, essential=essential, CEN=CEN, circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1])
    half_life_L_unique_L_multi = [101, 78, 95, 84, 96]  # Average = 90.8 +- 9.47100839404126
    #print("half_life_L_unique_L_multi =", half_life_L_unique_L_multi, statistics.mean(half_life_L_unique_L_multi), "+-", statistics.stdev(half_life_L_unique_L_multi))
    # chr_len_essential_range_SCRaMbLE
    syn_chr = list(range(1, 51, 1))
    #chr_len_essential_range_SCRaMbLE(syn_chr, events=events, simulations=simulations, CEN=CEN, circular=False, mu=0, sigma=10, force=True, probability=[0, 2, 2, 1])

    # Test the impact of SCRaMbLE event type probabilities on the chromosome length during SCRaMbLE evolution
    syn_chr = list(range(1, 51, 1))
    num_essential = 10
    events = 250
    simulations = 100
    essential = sorted(random.sample(syn_chr, k=num_essential))
    #chr_len_probabilities_range_SCRaMbLE(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=False, mu=0, sigma=10, force=True, LOG=False)

    # Neutral Evolution. Zero essential LUs
    syn_chr = list(range(1, 101, 1))
    essential = []
    CEN = []
    events = 1000
    simulations = 200
    #plot_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=False, mu=0, sigma=10, force=True, probability=[0, 10, 10, 9], SD=True)
    simulations = 200
    #plot_SCRaMbLE_chr_len(syn_chr, events=events, simulations=simulations, essential=essential, CEN=CEN, circular=False, mu=0, sigma=10, force=True, probability=[0, 10, 10, 11], SD=True)

    # probability = [0, 10, 10, 9]  = [0, 34.48, 34.48, 31.03]. Pdel/Pdup = 34.48/31.03 = 1.111
    # probability = [0, 10, 10, 11] = [0, 32.25, 32.25, 35.48]. Pdel/Pdup = 32.25/35.48 = 0.909


    """
    25
chr_len = 200 40.0
chr_len_SD = 1001 40.0
chr_len_Q1_Q2_Q3 = 1001 = 28.0 40.0 57.0
last_chr_len_zero = 0.0 %
[24.0, 24.985, 26.395, 27.615, 28.405, 28.93, 29.525, 30.34, 31.87, 32.565, 32.99, 33.405, 34.59, 35.295, 36.115, 36.555, 36.7, 37.095, 37.385, 37.875, 38.595, 38.43, 38.865, 39.375, 40.035, 39.585, 39.715, 40.645, 40.585, 41.62, 42.23, 43.215, 43.7, 44.08, 44.095, 44.055, 44.075, 44.095, 44.635, 45.375, 46.06, 45.51, 46.245, 45.54, 45.68, 46.325, 45.98, 46.165, 46.565, 46.93, 47.29, 47.34, 46.885, 46.94, 47.22, 47.45, 47.09, 47.35, 47.795, 48.055, 48.345, 48.855, 48.77, 48.565, 49.25, 49.705, 49.555, 49.5, 49.705, 49.365, 49.02, 49.075, 49.045, 48.885, 48.91, 49.68, 49.46, 49.01, 48.68, 49.155, 48.77, 49.565, 49.66, 49.13, 49.53, 49.575, 50.15, 50.755, 50.71, 50.76, 50.2, 50.205, 50.485, 50.295, 49.955, 49.87, 50.195, 50.655, 50.66, 50.6, 50.82, 51.02, 50.615, 50.09, 50.11, 49.96, 50.3, 50.435, 49.38, 49.555, 49.69, 50.11, 49.65, 49.7, 49.48, 49.17, 48.89, 49.255, 48.86, 48.16, 47.97, 47.99, 48.165, 48.07, 48.165, 48.005, 48.07, 48.135, 48.16, 48.2, 48.365, 48.34, 47.71, 46.89, 47.63, 47.41, 48.2, 48.38, 48.5, 48.12, 48.245, 48.055, 48.57, 48.72, 48.495, 48.17, 49.025, 49.38, 49.245, 49.025, 49.665, 49.54, 49.33, 48.985, 49.235, 48.89, 48.98, 49.27, 49.41, 48.935, 49.31, 49.615, 49.84, 49.55, 49.34, 49.49, 50.05, 49.455, 49.375, 49.04, 48.53, 48.6, 48.52, 48.365, 48.365, 48.39, 48.95, 48.585, 48.535, 49.33, 49.615, 49.94, 50.385, 50.87, 51.01, 51.775, 51.29, 51.445, 51.575, 51.785, 52.08, 51.805, 51.4, 50.83, 50.475, 49.87, 49.82, 49.98, 50.375, 49.705, 49.225, 49.595, 49.475, 49.285, 49.22, 49.765, 50.015, 49.835, 49.98, 49.98, 50.235, 49.765, 50.245, 50.265, 50.145, 50.27, 50.76, 50.545, 50.645, 50.5, 50.19, 50.745, 50.9, 50.935, 50.955, 50.93, 50.575, 50.805, 50.79, 50.675, 50.875, 50.57, 50.61, 50.32, 50.82, 50.505, 50.73, 50.685, 50.92, 49.905, 49.1, 49.71, 49.53, 48.74, 48.285, 48.85, 48.53, 48.625, 48.365, 48.645, 48.175, 47.67, 47.69, 47.25, 47.32, 46.775, 46.96, 47.345, 47.795, 47.885, 48.17, 49.06, 49.075, 48.635, 48.85, 48.825, 48.825, 48.975, 48.555, 49.365, 49.4, 49.5, 49.38, 49.75, 49.52, 49.06, 49.07, 49.105, 49.035, 49.105, 49.88, 49.455, 49.56, 49.915, 50.03, 50.02, 50.025, 49.835, 49.48, 48.785, 49.2, 48.285, 48.62, 48.66, 47.73, 47.89, 47.72, 47.58, 47.43, 47.01, 47.19, 47.11, 47.155, 47.215, 46.76, 46.9, 46.7, 46.68, 46.54, 47.015, 47.29, 47.56, 47.54, 47.105, 47.535, 47.54, 47.37, 47.405, 48.555, 49.275, 49.63, 49.745, 49.56, 49.66, 50.015, 49.66, 49.93, 50.01, 50.605, 50.405, 50.57, 50.595, 50.685, 50.61, 50.69, 50.685, 50.73, 50.69, 50.195, 50.34, 50.13, 49.855, 49.685, 50.325, 50.31, 50.61, 50.27, 50.16, 50.65, 50.58, 51.11, 50.92, 50.65, 50.74, 50.98, 50.49, 50.475, 50.58, 50.87, 50.61, 50.365, 49.97, 50.385, 50.175, 50.225, 49.92, 50.395, 50.075, 50.375, 50.555, 50.755, 50.915, 51.405, 51.395, 51.02, 50.575, 50.005, 50.665, 50.215, 50.09, 49.785, 50.11, 50.05, 49.735, 49.305, 48.435, 48.955, 48.82, 48.815, 47.99, 47.865, 48.21, 48.21, 48.515, 48.145, 47.98, 48.515, 48.57, 48.35, 47.93, 47.675, 48.155, 48.545, 48.77, 49.02, 48.695, 48.92, 48.99, 49.42, 49.385, 49.58, 49.4, 49.265, 49.455, 49.725, 48.895, 49.145, 49.26, 48.945, 48.88, 49.09, 48.5, 48.465, 48.26, 48.495, 48.87, 48.665, 48.24, 48.265, 47.8, 48.235, 47.895, 48.28, 48.345, 48.89, 48.685, 48.55, 48.75, 48.635, 48.73, 49.19, 49.105, 49.18, 49.335, 49.42, 49.43, 49.165, 49.495, 49.43, 49.46, 49.41, 49.605, 49.51, 48.91, 49.035, 49.145, 48.77, 48.25, 48.195, 48.48, 48.17, 47.98, 47.215, 47.22, 47.465, 47.82, 47.765, 47.9, 48.29, 48.395, 47.52, 46.87, 46.71, 46.85, 46.805, 47.08, 47.305, 47.03, 47.01, 46.765, 46.695, 47.155, 46.935, 47.22, 46.78, 46.625, 46.43, 46.08, 46.26, 46.05, 46.135, 46.42, 46.065, 46.055, 45.85, 46.425, 46.815, 46.605, 46.345, 45.955, 46.025, 46.0, 46.195, 45.785, 45.61, 45.35, 45.68, 46.08, 45.98, 46.655, 46.88, 47.27, 47.235, 47.37, 47.355, 47.625, 47.6, 47.115, 47.475, 46.92, 47.02, 46.31, 46.675, 46.425, 46.155, 46.57, 46.915, 46.76, 46.66, 47.08, 47.295, 47.38, 47.285, 47.23, 47.1, 46.715, 46.765, 47.175, 47.18, 46.885, 47.05, 47.42, 47.585, 47.635, 48.21, 48.17, 48.56, 49.175, 49.01, 48.85, 48.29, 48.625, 48.795, 48.22, 48.58, 47.815, 47.6, 47.515, 47.56, 46.835, 46.565, 46.46, 46.325, 46.025, 46.8, 46.63, 46.285, 45.66, 45.625, 45.075, 44.975, 44.71, 45.065, 44.77, 44.72, 44.765, 44.83, 45.325, 45.25, 44.52, 44.895, 45.335, 45.28, 45.99, 45.895, 45.78, 45.27, 45.515, 45.71, 45.225, 44.91, 45.01, 45.5, 45.125, 45.465, 44.965, 45.375, 44.295, 44.575, 44.695, 44.58, 43.855, 43.66, 43.935, 44.015, 43.56, 43.685, 43.735, 43.79, 43.6, 43.965, 44.085, 43.945, 43.535, 43.605, 43.76, 43.32, 43.29, 43.49, 43.49, 43.395, 43.035, 42.435, 42.685, 42.535, 42.655, 42.37, 42.355, 42.435, 42.13, 41.52, 41.455, 41.51, 41.835, 41.765, 41.545, 41.795, 42.295, 41.77, 41.365, 41.93, 41.355, 41.35, 40.905, 40.465, 40.515, 40.455, 40.385, 40.67, 40.92, 41.06, 40.88, 41.015, 41.165, 41.26, 41.345, 41.975, 42.015, 41.745, 42.235, 42.07, 42.095, 42.005, 41.58, 41.645, 41.705, 41.275, 40.27, 40.56, 40.55, 40.455, 40.615, 40.09, 40.1, 39.505, 39.385, 39.135, 39.29, 39.73, 40.365, 40.645, 40.31, 40.15, 40.115, 39.905, 39.865, 39.645, 39.745, 39.84, 39.755, 39.54, 40.065, 39.84, 39.9, 40.455, 40.565, 40.255, 40.875, 40.53, 40.88, 40.93, 40.535, 40.625, 40.935, 40.545, 40.295, 40.705, 40.44, 39.815, 39.695, 39.69, 39.68, 39.225, 39.42, 39.26, 39.945, 40.205, 40.35, 40.335, 40.925, 40.885, 40.97, 41.375, 41.675, 41.795, 41.75, 41.77, 41.42, 41.365, 41.85, 41.745, 41.825, 41.75, 41.69, 41.505, 41.665, 41.81, 42.085, 42.155, 41.75, 41.92, 41.245, 41.325, 41.545, 41.99, 41.98, 42.155, 41.525, 41.88, 41.49, 41.425, 41.81, 41.38, 41.215, 41.75, 42.01, 42.045, 41.68, 42.155, 41.75, 42.165, 41.1, 41.63, 40.885, 40.825, 40.925, 40.165, 40.205, 40.335, 39.77, 40.27, 40.3, 40.475, 40.655, 40.645, 40.225, 40.48, 40.525, 41.66, 41.605, 41.5, 41.63, 41.7, 41.615, 41.6, 41.48, 41.565, 41.28, 40.895, 40.81, 40.68, 40.445, 39.895, 39.84, 39.485, 39.25, 39.83, 40.055, 40.095, 40.395, 40.63, 40.6, 40.73, 41.29, 40.99, 40.905, 40.65, 40.705, 40.835, 40.55, 40.93, 41.05, 40.98, 40.775, 41.005, 41.16, 41.045, 40.965, 41.14, 40.785, 40.22, 40.015, 40.06, 40.5, 40.45, 40.37, 40.19, 40.255, 39.745, 39.835, 40.18, 39.98, 40.17, 40.49, 40.75, 40.725, 40.595, 41.165, 40.58, 40.065, 40.19, 40.34, 39.73, 39.84, 40.225, 40.24, 40.105, 40.5, 40.555, 40.905, 41.06, 41.405, 41.22, 41.12, 41.62, 41.265, 40.975, 40.99, 41.06, 41.215, 41.01, 40.95, 41.015, 41.205, 41.195, 41.62, 41.715, 42.13, 42.33, 42.25, 42.31, 42.715, 42.65, 42.605, 42.635, 42.325, 42.375, 42.8, 42.135, 42.28, 41.835, 42.275, 42.665, 42.645, 42.325, 42.275, 42.11, 41.885, 42.195, 42.71, 42.96, 43.425, 42.57, 42.84, 43.185, 43.085, 42.525, 42.09, 41.91, 41.62, 41.415, 40.66, 40.25, 40.055, 40.5, 40.175, 40.09, 40.205, 40.305, 40.71, 40.78, 40.61, 40.71, 40.49, 40.3, 40.565, 40.7, 40.625, 40.555, 40.23, 40.275, 40.455, 39.77, 39.665, 39.92, 39.595, 39.98, 40.155, 39.84, 39.93, 40.055, 40.19, 39.74, 39.425, 39.11, 39.385, 39.905, 40.435, 40.425, 40.275, 39.87, 40.195, 40.045, 40.55, 40.915, 41.35, 40.995, 41.185, 41.465, 41.72, 42.24, 42.165, 41.89, 41.66, 41.615, 41.725, 41.145, 41.52, 41.425, 41.81, 41.335, 41.095, 41.355, 40.84, 40.89, 41.05, 41.395, 41.225, 41.495, 41.755, 41.92, 41.865, 42.45, 42.255, 42.145, 42.025, 41.885, 41.675, 41.185, 40.89, 41.61, 41.525, 41.25, 41.6, 41.465, 40.96, 40.45, 39.735, 39.925, 40.16, 39.795, 39.675, 39.74, 39.88, 40.255, 39.885, 40.095, 39.675, 39.975, 39.57, 39.64]
25 half_life chr_len_L = []
[24.0, 23.79, 23.65, 23.565, 23.45, 23.36, 23.215, 23.09, 23.04, 22.9, 22.75, 22.61, 22.515, 22.4, 22.285, 22.14, 22.035, 21.92, 21.765, 21.605, 21.55, 21.46, 21.395, 21.335, 21.275, 21.195, 21.15, 21.11, 21.035, 20.96, 20.905, 20.885, 20.79, 20.725, 20.66, 20.6, 20.525, 20.395, 20.3, 20.225, 20.145, 20.04, 19.985, 19.93, 19.875, 19.83, 19.8, 19.755, 19.705, 19.665, 19.585, 19.54, 19.445, 19.39, 19.345, 19.295, 19.2, 19.13, 19.08, 19.02, 18.94, 18.895, 18.84, 18.8, 18.75, 18.675, 18.645, 18.58, 18.515, 18.46, 18.4, 18.325, 18.285, 18.24, 18.185, 18.11, 18.06, 18.03, 17.975, 17.95, 17.9, 17.865, 17.825, 17.755, 17.715, 17.66, 17.635, 17.605, 17.565, 17.52, 17.46, 17.415, 17.365, 17.32, 17.29, 17.25, 17.22, 17.16, 17.105, 17.065, 17.01, 16.98, 16.945, 16.91, 16.865, 16.82, 16.79, 16.775, 16.725, 16.69, 16.635, 16.615, 16.555, 16.535, 16.53, 16.465, 16.395, 16.36, 16.315, 16.285, 16.245, 16.22, 16.175, 16.15, 16.105, 16.055, 16.03, 15.98, 15.95, 15.915, 15.885, 15.855, 15.755, 15.7, 15.675, 15.655, 15.64, 15.595, 15.575, 15.53, 15.495, 15.46, 15.44, 15.405, 15.36, 15.33, 15.305, 15.275, 15.235, 15.215, 15.195, 15.16, 15.11, 15.09, 15.07, 15.045, 15.01, 15.0, 14.98, 14.94, 14.91, 14.895, 14.865, 14.84, 14.805, 14.785, 14.765, 14.73, 14.7, 14.665, 14.645, 14.62, 14.59, 14.575, 14.56, 14.54, 14.535, 14.505, 14.485, 14.485, 14.465, 14.465, 14.455, 14.415, 14.395, 14.37, 14.33, 14.32, 14.285, 14.25, 14.225, 14.22, 14.185, 14.16, 14.135, 14.115, 14.11, 14.09, 14.085, 14.065, 14.04, 14.02, 14.005, 14.0, 13.98, 13.97, 13.955, 13.935, 13.92, 13.91, 13.885, 13.875, 13.875, 13.865, 13.85, 13.845, 13.84, 13.83, 13.815, 13.805, 13.79, 13.765, 13.755, 13.75, 13.725, 13.715, 13.71, 13.695, 13.69, 13.66, 13.66, 13.65, 13.645, 13.64, 13.62, 13.605, 13.6, 13.58, 13.575, 13.56, 13.56, 13.545, 13.54, 13.505, 13.495, 13.495, 13.49, 13.47, 13.465, 13.445, 13.405, 13.38, 13.36, 13.35, 13.335, 13.305, 13.295, 13.28, 13.255, 13.23, 13.23, 13.21, 13.2, 13.195, 13.185, 13.18, 13.175, 13.13, 13.095, 13.085, 13.075, 13.065, 13.065, 13.055, 13.045, 13.035, 13.015, 13.0, 12.995, 12.995, 12.985, 12.97, 12.97, 12.965, 12.935, 12.91, 12.89, 12.855, 12.855, 12.84, 12.83, 12.83, 12.825, 12.815, 12.815, 12.815, 12.81, 12.795, 12.77, 12.765, 12.75, 12.73, 12.71, 12.7, 12.695, 12.685, 12.685, 12.685, 12.67, 12.665, 12.65, 12.635, 12.615, 12.595, 12.59, 12.575, 12.57, 12.555, 12.55, 12.54, 12.535, 12.52, 12.515, 12.51, 12.49, 12.46, 12.44, 12.44, 12.44, 12.435, 12.43, 12.42, 12.41, 12.4, 12.385, 12.37, 12.35, 12.34, 12.335, 12.335, 12.325, 12.315, 12.315, 12.31, 12.31, 12.3, 12.29, 12.29, 12.275, 12.27, 12.27, 12.27, 12.26, 12.255, 12.245, 12.24, 12.23, 12.215, 12.205, 12.19, 12.185, 12.18, 12.17, 12.155, 12.155, 12.14, 12.14, 12.13, 12.12, 12.1, 12.1, 12.095, 12.09, 12.09, 12.085, 12.085, 12.085, 12.08, 12.065, 12.065, 12.065, 12.045, 12.045, 12.04, 12.035, 12.035, 12.025, 12.01, 12.0, 11.99, 11.98, 11.975, 11.965, 11.96, 11.955, 11.94, 11.94, 11.925, 11.92, 11.915, 11.915, 11.905, 11.9, 11.895, 11.885, 11.875, 11.87, 11.865, 11.86, 11.855, 11.845, 11.835, 11.835, 11.82, 11.805, 11.795, 11.79, 11.775, 11.755, 11.75, 11.75, 11.74, 11.74, 11.72, 11.715, 11.71, 11.705, 11.695, 11.69, 11.68, 11.67, 11.67, 11.66, 11.66, 11.65, 11.65, 11.645, 11.64, 11.635, 11.635, 11.625, 11.625, 11.62, 11.62, 11.62, 11.605, 11.595, 11.585, 11.58, 11.58, 11.575, 11.57, 11.56, 11.56, 11.545, 11.53, 11.51, 11.5, 11.48, 11.475, 11.475, 11.475, 11.46, 11.46, 11.45, 11.45, 11.45, 11.45, 11.45, 11.45, 11.45, 11.445, 11.435, 11.435, 11.43, 11.425, 11.425, 11.415, 11.4, 11.4, 11.395, 11.39, 11.38, 11.38, 11.375, 11.365, 11.355, 11.345, 11.34, 11.335, 11.33, 11.325, 11.325, 11.32, 11.32, 11.315, 11.31, 11.305, 11.3, 11.3, 11.29, 11.285, 11.28, 11.275, 11.26, 11.255, 11.255, 11.255, 11.25, 11.245, 11.24, 11.235, 11.23, 11.22, 11.22, 11.22, 11.22, 11.22, 11.22, 11.21, 11.2, 11.195, 11.19, 11.185, 11.185, 11.185, 11.185, 11.185, 11.185, 11.175, 11.175, 11.175, 11.16, 11.16, 11.15, 11.15, 11.135, 11.125, 11.115, 11.11, 11.105, 11.105, 11.105, 11.1, 11.1, 11.1, 11.1, 11.095, 11.09, 11.09, 11.08, 11.075, 11.07, 11.065, 11.065, 11.06, 11.055, 11.055, 11.055, 11.05, 11.045, 11.035, 11.035, 11.035, 11.03, 11.02, 11.02, 11.01, 11.01, 11.0, 11.0, 10.99, 10.99, 10.98, 10.97, 10.97, 10.965, 10.96, 10.955, 10.955, 10.95, 10.95, 10.945, 10.945, 10.92, 10.92, 10.92, 10.915, 10.915, 10.905, 10.895, 10.89, 10.885, 10.88, 10.88, 10.88, 10.88, 10.88, 10.87, 10.87, 10.87, 10.87, 10.86, 10.86, 10.86, 10.855, 10.855, 10.855, 10.855, 10.84, 10.84, 10.84, 10.835, 10.83, 10.825, 10.825, 10.82, 10.815, 10.81, 10.805, 10.805, 10.805, 10.805, 10.805, 10.805, 10.8, 10.8, 10.8, 10.8, 10.795, 10.785, 10.785, 10.77, 10.765, 10.765, 10.76, 10.76, 10.76, 10.75, 10.745, 10.745, 10.745, 10.745, 10.745, 10.74, 10.74, 10.735, 10.735, 10.73, 10.725, 10.72, 10.72, 10.715, 10.715, 10.715, 10.715, 10.715, 10.71, 10.705, 10.7, 10.7, 10.695, 10.695, 10.695, 10.695, 10.695, 10.69, 10.685, 10.68, 10.68, 10.68, 10.68, 10.67, 10.67, 10.665, 10.665, 10.665, 10.665, 10.655, 10.655, 10.645, 10.63, 10.63, 10.63, 10.63, 10.63, 10.63, 10.62, 10.62, 10.62, 10.62, 10.62, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.61, 10.605, 10.605, 10.605, 10.595, 10.59, 10.59, 10.59, 10.59, 10.59, 10.59, 10.59, 10.585, 10.575, 10.575, 10.57, 10.57, 10.555, 10.55, 10.55, 10.54, 10.54, 10.54, 10.535, 10.535, 10.525, 10.525, 10.525, 10.525, 10.525, 10.525, 10.525, 10.52, 10.52, 10.52, 10.52, 10.52, 10.52, 10.52, 10.52, 10.515, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.505, 10.505, 10.505, 10.505, 10.505, 10.505, 10.495, 10.495, 10.495, 10.49, 10.49, 10.49, 10.49, 10.49, 10.485, 10.485, 10.485, 10.48, 10.48, 10.48, 10.475, 10.475, 10.475, 10.47, 10.47, 10.465, 10.465, 10.465, 10.46, 10.46, 10.46, 10.46, 10.455, 10.455, 10.45, 10.445, 10.445, 10.445, 10.44, 10.44, 10.435, 10.435, 10.43, 10.43, 10.43, 10.43, 10.42, 10.42, 10.42, 10.42, 10.42, 10.42, 10.42, 10.42, 10.415, 10.41, 10.41, 10.405, 10.405, 10.405, 10.395, 10.395, 10.39, 10.385, 10.38, 10.375, 10.375, 10.37, 10.37, 10.37, 10.36, 10.36, 10.36, 10.355, 10.355, 10.345, 10.345, 10.345, 10.34, 10.34, 10.335, 10.335, 10.335, 10.33, 10.33, 10.33, 10.33, 10.32, 10.32, 10.32, 10.315, 10.31, 10.31, 10.305, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.295, 10.29, 10.29, 10.29, 10.29, 10.285, 10.285, 10.285, 10.285, 10.285, 10.285, 10.285, 10.285, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.275, 10.275, 10.27, 10.27, 10.27, 10.27, 10.27, 10.27, 10.27, 10.27, 10.265, 10.265, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.24, 10.24, 10.24, 10.24, 10.24, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235]
25 half_life L_unique_L = [101, 244, 419, 598, 792]
[24.0, 23.79, 23.65, 23.565, 23.45, 23.36, 23.215, 23.09, 23.04, 22.9, 22.75, 22.61, 22.515, 22.4, 22.285, 22.14, 22.035, 21.92, 21.765, 21.605, 21.55, 21.46, 21.395, 21.335, 21.275, 21.195, 21.15, 21.11, 21.035, 20.96, 20.905, 20.885, 20.79, 20.725, 20.66, 20.6, 20.525, 20.395, 20.3, 20.225, 20.145, 20.04, 19.985, 19.93, 19.875, 19.83, 19.8, 19.755, 19.705, 19.665, 19.585, 19.54, 19.445, 19.39, 19.345, 19.295, 19.2, 19.13, 19.08, 19.02, 18.94, 18.895, 18.84, 18.8, 18.75, 18.675, 18.645, 18.58, 18.515, 18.46, 18.4, 18.325, 18.285, 18.24, 18.185, 18.11, 18.06, 18.03, 17.975, 17.95, 17.9, 17.865, 17.825, 17.755, 17.715, 17.66, 17.635, 17.605, 17.565, 17.52, 17.46, 17.415, 17.365, 17.32, 17.29, 17.25, 17.22, 17.16, 17.105, 17.065, 17.01, 16.98, 16.945, 16.91, 16.865, 16.82, 16.79, 16.775, 16.725, 16.69, 16.635, 16.615, 16.555, 16.535, 16.53, 16.465, 16.395, 16.36, 16.315, 16.285, 16.245, 16.22, 16.175, 16.15, 16.105, 16.055, 16.03, 15.98, 15.95, 15.915, 15.885, 15.855, 15.755, 15.7, 15.675, 15.655, 15.64, 15.595, 15.575, 15.53, 15.495, 15.46, 15.44, 15.405, 15.36, 15.33, 15.305, 15.275, 15.235, 15.215, 15.195, 15.16, 15.11, 15.09, 15.07, 15.045, 15.01, 15.0, 14.98, 14.94, 14.91, 14.895, 14.865, 14.84, 14.805, 14.785, 14.765, 14.73, 14.7, 14.665, 14.645, 14.62, 14.59, 14.575, 14.56, 14.54, 14.535, 14.505, 14.485, 14.485, 14.465, 14.465, 14.455, 14.415, 14.395, 14.37, 14.33, 14.32, 14.285, 14.25, 14.225, 14.22, 14.185, 14.16, 14.135, 14.115, 14.11, 14.09, 14.085, 14.065, 14.04, 14.02, 14.005, 14.0, 13.98, 13.97, 13.955, 13.935, 13.92, 13.91, 13.885, 13.875, 13.875, 13.865, 13.85, 13.845, 13.84, 13.83, 13.815, 13.805, 13.79, 13.765, 13.755, 13.75, 13.725, 13.715, 13.71, 13.695, 13.69, 13.66, 13.66, 13.65, 13.645, 13.64, 13.62, 13.605, 13.6, 13.58, 13.575, 13.56, 13.56, 13.545, 13.54, 13.505, 13.495, 13.495, 13.49, 13.47, 13.465, 13.445, 13.405, 13.38, 13.36, 13.35, 13.335, 13.305, 13.295, 13.28, 13.255, 13.23, 13.23, 13.21, 13.2, 13.195, 13.185, 13.18, 13.175, 13.13, 13.095, 13.085, 13.075, 13.065, 13.065, 13.055, 13.045, 13.035, 13.015, 13.0, 12.995, 12.995, 12.985, 12.97, 12.97, 12.965, 12.935, 12.91, 12.89, 12.855, 12.855, 12.84, 12.83, 12.83, 12.825, 12.815, 12.815, 12.815, 12.81, 12.795, 12.77, 12.765, 12.75, 12.73, 12.71, 12.7, 12.695, 12.685, 12.685, 12.685, 12.67, 12.665, 12.65, 12.635, 12.615, 12.595, 12.59, 12.575, 12.57, 12.555, 12.55, 12.54, 12.535, 12.52, 12.515, 12.51, 12.49, 12.46, 12.44, 12.44, 12.44, 12.435, 12.43, 12.42, 12.41, 12.4, 12.385, 12.37, 12.35, 12.34, 12.335, 12.335, 12.325, 12.315, 12.315, 12.31, 12.31, 12.3, 12.29, 12.29, 12.275, 12.27, 12.27, 12.27, 12.26, 12.255, 12.245, 12.24, 12.23, 12.215, 12.205, 12.19, 12.185, 12.18, 12.17, 12.155, 12.155, 12.14, 12.14, 12.13, 12.12, 12.1, 12.1, 12.095, 12.09, 12.09, 12.085, 12.085, 12.085, 12.08, 12.065, 12.065, 12.065, 12.045, 12.045, 12.04, 12.035, 12.035, 12.025, 12.01, 12.0, 11.99, 11.98, 11.975, 11.965, 11.96, 11.955, 11.94, 11.94, 11.925, 11.92, 11.915, 11.915, 11.905, 11.9, 11.895, 11.885, 11.875, 11.87, 11.865, 11.86, 11.855, 11.845, 11.835, 11.835, 11.82, 11.805, 11.795, 11.79, 11.775, 11.755, 11.75, 11.75, 11.74, 11.74, 11.72, 11.715, 11.71, 11.705, 11.695, 11.69, 11.68, 11.67, 11.67, 11.66, 11.66, 11.65, 11.65, 11.645, 11.64, 11.635, 11.635, 11.625, 11.625, 11.62, 11.62, 11.62, 11.605, 11.595, 11.585, 11.58, 11.58, 11.575, 11.57, 11.56, 11.56, 11.545, 11.53, 11.51, 11.5, 11.48, 11.475, 11.475, 11.475, 11.46, 11.46, 11.45, 11.45, 11.45, 11.45, 11.45, 11.45, 11.45, 11.445, 11.435, 11.435, 11.43, 11.425, 11.425, 11.415, 11.4, 11.4, 11.395, 11.39, 11.38, 11.38, 11.375, 11.365, 11.355, 11.345, 11.34, 11.335, 11.33, 11.325, 11.325, 11.32, 11.32, 11.315, 11.31, 11.305, 11.3, 11.3, 11.29, 11.285, 11.28, 11.275, 11.26, 11.255, 11.255, 11.255, 11.25, 11.245, 11.24, 11.235, 11.23, 11.22, 11.22, 11.22, 11.22, 11.22, 11.22, 11.21, 11.2, 11.195, 11.19, 11.185, 11.185, 11.185, 11.185, 11.185, 11.185, 11.175, 11.175, 11.175, 11.16, 11.16, 11.15, 11.15, 11.135, 11.125, 11.115, 11.11, 11.105, 11.105, 11.105, 11.1, 11.1, 11.1, 11.1, 11.095, 11.09, 11.09, 11.08, 11.075, 11.07, 11.065, 11.065, 11.06, 11.055, 11.055, 11.055, 11.05, 11.045, 11.035, 11.035, 11.035, 11.03, 11.02, 11.02, 11.01, 11.01, 11.0, 11.0, 10.99, 10.99, 10.98, 10.97, 10.97, 10.965, 10.96, 10.955, 10.955, 10.95, 10.95, 10.945, 10.945, 10.92, 10.92, 10.92, 10.915, 10.915, 10.905, 10.895, 10.89, 10.885, 10.88, 10.88, 10.88, 10.88, 10.88, 10.87, 10.87, 10.87, 10.87, 10.86, 10.86, 10.86, 10.855, 10.855, 10.855, 10.855, 10.84, 10.84, 10.84, 10.835, 10.83, 10.825, 10.825, 10.82, 10.815, 10.81, 10.805, 10.805, 10.805, 10.805, 10.805, 10.805, 10.8, 10.8, 10.8, 10.8, 10.795, 10.785, 10.785, 10.77, 10.765, 10.765, 10.76, 10.76, 10.76, 10.75, 10.745, 10.745, 10.745, 10.745, 10.745, 10.74, 10.74, 10.735, 10.735, 10.73, 10.725, 10.72, 10.72, 10.715, 10.715, 10.715, 10.715, 10.715, 10.71, 10.705, 10.7, 10.7, 10.695, 10.695, 10.695, 10.695, 10.695, 10.69, 10.685, 10.68, 10.68, 10.68, 10.68, 10.67, 10.67, 10.665, 10.665, 10.665, 10.665, 10.655, 10.655, 10.645, 10.63, 10.63, 10.63, 10.63, 10.63, 10.63, 10.62, 10.62, 10.62, 10.62, 10.62, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.615, 10.61, 10.605, 10.605, 10.605, 10.595, 10.59, 10.59, 10.59, 10.59, 10.59, 10.59, 10.59, 10.585, 10.575, 10.575, 10.57, 10.57, 10.555, 10.55, 10.55, 10.54, 10.54, 10.54, 10.535, 10.535, 10.525, 10.525, 10.525, 10.525, 10.525, 10.525, 10.525, 10.52, 10.52, 10.52, 10.52, 10.52, 10.52, 10.52, 10.52, 10.515, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.51, 10.505, 10.505, 10.505, 10.505, 10.505, 10.505, 10.495, 10.495, 10.495, 10.49, 10.49, 10.49, 10.49, 10.49, 10.485, 10.485, 10.485, 10.48, 10.48, 10.48, 10.475, 10.475, 10.475, 10.47, 10.47, 10.465, 10.465, 10.465, 10.46, 10.46, 10.46, 10.46, 10.455, 10.455, 10.45, 10.445, 10.445, 10.445, 10.44, 10.44, 10.435, 10.435, 10.43, 10.43, 10.43, 10.43, 10.42, 10.42, 10.42, 10.42, 10.42, 10.42, 10.42, 10.42, 10.415, 10.41, 10.41, 10.405, 10.405, 10.405, 10.395, 10.395, 10.39, 10.385, 10.38, 10.375, 10.375, 10.37, 10.37, 10.37, 10.36, 10.36, 10.36, 10.355, 10.355, 10.345, 10.345, 10.345, 10.34, 10.34, 10.335, 10.335, 10.335, 10.33, 10.33, 10.33, 10.33, 10.32, 10.32, 10.32, 10.315, 10.31, 10.31, 10.305, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.295, 10.29, 10.29, 10.29, 10.29, 10.285, 10.285, 10.285, 10.285, 10.285, 10.285, 10.285, 10.285, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.28, 10.275, 10.275, 10.27, 10.27, 10.27, 10.27, 10.27, 10.27, 10.27, 10.27, 10.265, 10.265, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.26, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.255, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.25, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.245, 10.24, 10.24, 10.24, 10.24, 10.24, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235, 10.235]

    
    75
chr_len = 200 58.0
chr_len_SD = 1001 58.0
chr_len_Q1_Q2_Q3 = 1001 = 39.0 53.0 74.0
last_chr_len_zero = 0.0 %
[74.0, 74.575, 74.89, 75.235, 76.125, 76.885, 77.04, 77.3, 77.695, 78.465, 78.93, 79.505, 79.85, 80.31, 80.735, 81.39, 81.755, 81.94, 81.75, 81.975, 82.88, 82.715, 83.405, 83.49, 83.84, 83.945, 83.73, 83.92, 84.07, 84.065, 84.41, 84.635, 84.93, 85.105, 84.995, 84.6, 84.615, 84.38, 84.785, 84.895, 85.99, 86.35, 86.945, 86.735, 87.68, 87.63, 87.455, 87.18, 87.3, 87.05, 87.58, 87.605, 87.965, 88.205, 87.625, 87.78, 88.645, 89.225, 89.21, 89.64, 89.52, 89.995, 89.87, 89.15, 88.765, 89.665, 89.66, 89.525, 88.83, 88.235, 88.835, 88.59, 88.695, 88.68, 88.54, 89.12, 89.17, 89.275, 89.195, 89.2, 88.655, 88.34, 88.02, 87.47, 86.825, 86.37, 86.69, 86.765, 86.905, 86.61, 86.405, 87.205, 87.855, 87.9, 87.78, 87.855, 88.205, 87.83, 88.23, 88.475, 88.825, 87.79, 88.08, 87.425, 87.455, 88.415, 88.545, 87.91, 88.175, 87.455, 87.075, 87.36, 88.12, 88.37, 87.815, 87.915, 87.675, 87.74, 88.385, 88.205, 88.115, 87.145, 87.975, 87.795, 88.04, 87.885, 87.88, 87.96, 88.015, 87.915, 87.795, 87.985, 87.86, 87.765, 87.505, 88.19, 87.65, 87.865, 88.685, 88.115, 87.725, 87.945, 87.74, 87.77, 87.67, 87.25, 87.135, 86.475, 85.895, 86.695, 86.085, 86.545, 85.835, 84.97, 85.525, 84.65, 85.29, 85.04, 84.595, 84.8, 84.425, 85.11, 84.79, 84.965, 84.145, 84.005, 83.225, 83.83, 83.975, 83.845, 83.94, 84.61, 84.685, 85.085, 84.765, 84.495, 84.23, 84.5, 83.765, 83.525, 83.845, 83.28, 82.745, 82.79, 82.645, 83.12, 82.705, 82.65, 83.29, 82.635, 81.655, 81.69, 81.675, 81.26, 81.775, 81.11, 81.225, 81.09, 81.605, 81.52, 81.1, 80.805, 80.675, 80.29, 79.995, 79.41, 78.34, 78.07, 77.72, 77.89, 77.83, 78.115, 78.68, 78.945, 78.8, 78.995, 78.705, 78.41, 78.515, 78.96, 78.59, 78.22, 77.895, 77.98, 78.025, 78.37, 79.185, 78.335, 78.98, 78.495, 77.54, 77.08, 77.2, 76.88, 76.51, 76.325, 76.26, 76.22, 76.235, 76.1, 75.89, 75.595, 75.755, 75.675, 76.02, 74.93, 75.145, 75.855, 75.635, 75.815, 75.925, 76.205, 76.565, 76.58, 76.345, 76.145, 75.8, 75.335, 75.81, 75.72, 75.7, 74.87, 74.865, 75.29, 74.76, 74.95, 74.91, 74.685, 74.24, 74.28, 73.905, 74.335, 73.98, 74.12, 73.08, 72.42, 72.575, 71.675, 71.42, 71.175, 70.665, 70.155, 70.225, 69.66, 69.62, 68.98, 68.56, 68.465, 69.045, 69.475, 69.78, 69.195, 69.29, 70.07, 70.085, 69.705, 69.96, 69.745, 69.22, 69.46, 70.055, 70.64, 70.835, 71.15, 70.57, 69.84, 70.225, 69.845, 70.645, 71.005, 70.655, 70.62, 69.75, 69.815, 69.945, 69.705, 69.29, 69.49, 69.395, 68.65, 69.39, 68.385, 68.33, 67.295, 67.49, 67.09, 67.425, 67.53, 67.89, 68.465, 68.1, 67.485, 66.36, 66.3, 66.745, 67.305, 67.305, 67.21, 66.975, 67.18, 67.15, 67.325, 67.005, 67.085, 66.725, 66.905, 66.45, 66.47, 66.015, 66.295, 65.95, 65.815, 65.93, 66.18, 66.0, 66.29, 66.19, 66.71, 66.8, 66.53, 66.36, 66.255, 66.38, 66.745, 67.48, 66.675, 66.28, 66.76, 65.98, 66.615, 66.815, 66.785, 66.725, 66.21, 65.87, 65.63, 64.97, 64.65, 64.805, 64.825, 64.65, 64.57, 64.11, 63.525, 63.16, 63.08, 62.605, 62.51, 62.72, 62.92, 62.85, 62.785, 62.995, 63.395, 63.255, 62.775, 62.73, 62.845, 62.89, 62.205, 62.28, 61.61, 61.31, 61.92, 61.705, 61.785, 61.79, 61.775, 61.445, 61.645, 62.08, 62.06, 62.215, 62.835, 63.11, 62.655, 63.09, 62.94, 63.42, 64.18, 64.26, 64.11, 64.265, 64.78, 65.155, 64.755, 64.645, 64.455, 63.93, 62.91, 62.84, 62.735, 62.64, 62.54, 62.12, 62.505, 62.135, 62.06, 61.72, 61.8, 62.06, 62.055, 61.455, 61.55, 61.815, 61.49, 61.28, 60.7, 60.545, 60.925, 60.51, 59.885, 59.755, 59.15, 59.44, 59.165, 58.935, 58.655, 58.415, 58.77, 58.735, 59.27, 59.46, 59.67, 59.5, 59.505, 59.39, 59.99, 59.855, 60.04, 60.29, 60.13, 60.38, 60.83, 61.625, 61.65, 61.62, 61.28, 61.155, 61.16, 61.045, 60.995, 60.525, 60.37, 60.71, 60.33, 60.285, 59.77, 59.995, 59.75, 59.54, 59.69, 59.845, 59.71, 59.87, 59.85, 59.665, 59.78, 59.795, 59.905, 60.165, 59.765, 59.445, 59.8, 59.7, 59.745, 59.69, 59.17, 58.89, 58.555, 58.145, 58.385, 58.52, 57.96, 58.31, 58.38, 58.32, 58.35, 57.88, 57.82, 57.535, 57.715, 57.68, 57.305, 57.305, 57.085, 56.835, 56.64, 56.515, 56.7, 56.945, 56.68, 56.62, 56.28, 56.52, 55.88, 55.71, 55.91, 56.22, 56.43, 56.805, 56.115, 56.06, 55.58, 55.325, 55.03, 55.09, 55.325, 55.1, 55.055, 55.33, 55.96, 56.065, 55.92, 55.685, 56.27, 55.93, 55.825, 55.885, 56.51, 56.835, 57.255, 56.815, 56.96, 56.485, 57.14, 57.355, 57.51, 57.185, 57.625, 57.74, 57.69, 57.575, 57.79, 57.835, 57.015, 57.065, 57.175, 56.945, 57.14, 56.6, 56.18, 56.25, 56.81, 56.51, 56.805, 57.405, 57.495, 57.425, 57.5, 57.445, 57.675, 57.27, 56.845, 56.65, 56.18, 55.495, 55.395, 55.14, 54.69, 54.85, 55.01, 54.45, 54.105, 54.48, 54.635, 54.61, 54.04, 52.935, 53.07, 52.88, 53.195, 53.69, 53.525, 53.065, 52.47, 52.325, 52.48, 52.39, 52.43, 51.955, 51.6, 51.11, 51.485, 51.745, 52.385, 51.915, 52.425, 51.745, 51.495, 51.01, 51.34, 51.195, 50.885, 51.325, 51.2, 51.09, 50.92, 50.82, 50.75, 50.715, 50.45, 50.395, 50.31, 50.275, 50.03, 49.595, 49.52, 49.97, 50.48, 51.055, 50.875, 51.36, 51.72, 51.49, 51.78, 52.17, 51.93, 52.49, 51.93, 52.095, 52.07, 51.775, 51.675, 51.605, 51.875, 51.515, 51.55, 51.68, 51.93, 52.515, 51.8, 51.63, 51.74, 51.7, 51.575, 51.99, 51.68, 51.545, 51.0, 51.7, 52.04, 51.98, 52.015, 52.12, 51.86, 52.02, 52.42, 52.78, 52.21, 51.795, 52.18, 51.9, 50.86, 50.92, 51.445, 52.22, 52.455, 52.03, 51.81, 51.4, 51.135, 51.495, 51.525, 51.495, 51.43, 51.72, 51.9, 51.515, 51.375, 52.03, 51.85, 52.3, 52.23, 52.135, 51.96, 52.135, 52.385, 52.325, 52.125, 52.44, 51.98, 51.96, 51.81, 51.78, 51.59, 51.75, 51.875, 51.805, 52.565, 52.5, 53.04, 53.61, 52.85, 53.48, 54.05, 53.5, 53.81, 54.22, 54.355, 53.93, 53.77, 53.51, 53.525, 53.315, 52.975, 52.94, 52.615, 52.98, 52.975, 53.155, 53.345, 53.025, 53.23, 53.335, 53.67, 54.4, 54.28, 53.82, 53.16, 52.945, 53.315, 53.335, 52.45, 51.565, 51.505, 52.38, 52.015, 52.37, 51.825, 51.87, 51.825, 52.205, 52.55, 52.05, 51.765, 51.825, 51.58, 51.175, 51.965, 51.955, 52.39, 53.115, 52.47, 52.285, 52.295, 52.175, 52.28, 52.05, 51.93, 51.775, 51.95, 51.565, 50.985, 51.31, 51.365, 51.595, 51.27, 50.85, 50.8, 51.36, 51.455, 50.665, 50.81, 50.36, 50.435, 50.3, 50.275, 50.765, 50.81, 50.43, 50.38, 50.83, 50.825, 51.0, 51.36, 51.24, 50.955, 50.775, 51.145, 50.67, 50.27, 50.125, 50.175, 50.495, 51.205, 51.415, 51.605, 51.39, 51.1, 51.475, 51.62, 51.105, 51.52, 51.52, 51.25, 50.995, 50.805, 50.79, 50.155, 50.165, 50.27, 50.125, 50.21, 50.27, 50.38, 50.745, 50.65, 49.865, 50.135, 50.185, 50.665, 50.625, 50.625, 50.535, 50.815, 50.68, 51.14, 51.11, 50.9, 51.225, 51.21, 50.605, 50.69, 50.445, 50.19, 50.55, 49.825, 49.805, 50.17, 50.09, 50.535, 50.445, 50.29, 50.33, 49.915, 49.935, 49.805, 49.575, 49.52, 49.475, 49.825, 49.83, 49.53, 49.205, 49.0, 48.945, 49.125, 48.775, 48.33, 47.82, 47.48, 47.585, 47.985, 48.59, 48.785, 49.02, 49.145, 49.505, 49.43, 49.185, 49.075, 48.66, 48.67, 49.0, 49.195, 49.475, 49.18, 48.825, 49.195, 49.14, 48.925, 48.775, 48.5, 48.745, 49.06, 49.29, 49.375, 48.99, 49.16, 48.765, 48.365, 48.095, 48.325, 48.625, 48.49, 48.215, 48.51, 48.86, 48.585, 48.645, 48.56, 48.505, 48.845, 48.5, 48.395, 48.565, 47.935, 47.65, 47.715, 47.9, 48.105, 48.53, 48.535, 48.115, 47.67, 47.68, 47.23, 47.695, 48.0, 48.12, 47.935, 48.04, 47.975, 47.64, 47.325, 47.705, 47.885, 47.53, 46.945, 47.065, 46.64, 46.995, 47.315, 46.825, 47.375, 47.62, 47.285, 47.175, 47.41, 47.065, 46.825, 46.97, 47.03, 47.18, 47.28, 47.175, 47.77, 48.325, 48.265, 48.005, 48.195, 47.835, 47.725, 47.91, 47.775, 47.83, 47.68, 48.45, 48.955, 48.765, 48.42, 47.88, 47.86, 47.51, 47.355, 47.845, 47.695, 48.0, 47.905, 47.86]
75 half_life chr_len_L = []
[74.0, 73.04, 71.92, 70.65, 69.48, 68.795, 67.875, 67.185, 66.39, 65.835, 65.155, 64.785, 64.085, 63.52, 62.94, 62.455, 61.885, 61.315, 60.665, 60.305, 59.98, 59.485, 58.935, 58.55, 58.015, 57.53, 57.135, 56.795, 56.22, 55.58, 55.17, 54.845, 54.535, 54.165, 53.865, 53.51, 53.175, 52.73, 52.365, 52.07, 51.85, 51.485, 51.175, 50.76, 50.48, 50.13, 49.66, 49.385, 49.18, 48.785, 48.57, 48.31, 48.025, 47.765, 47.355, 47.105, 46.94, 46.63, 46.375, 46.205, 45.985, 45.78, 45.56, 45.415, 45.105, 44.87, 44.695, 44.505, 44.315, 44.005, 43.725, 43.46, 43.315, 43.015, 42.74, 42.48, 42.315, 42.16, 41.89, 41.715, 41.57, 41.355, 41.195, 41.0, 40.84, 40.63, 40.44, 40.21, 40.06, 39.89, 39.675, 39.495, 39.35, 39.19, 39.055, 38.925, 38.79, 38.61, 38.465, 38.345, 38.19, 37.95, 37.785, 37.555, 37.47, 37.34, 37.165, 36.965, 36.77, 36.565, 36.445, 36.29, 36.23, 36.14, 36.005, 35.865, 35.725, 35.55, 35.38, 35.31, 35.18, 35.065, 34.97, 34.855, 34.745, 34.595, 34.51, 34.38, 34.285, 34.155, 34.06, 33.95, 33.815, 33.645, 33.585, 33.495, 33.37, 33.205, 33.105, 32.97, 32.9, 32.785, 32.72, 32.66, 32.55, 32.41, 32.32, 32.2, 32.06, 31.945, 31.825, 31.775, 31.655, 31.54, 31.425, 31.275, 31.21, 31.125, 30.98, 30.815, 30.7, 30.59, 30.475, 30.385, 30.245, 30.15, 30.01, 29.87, 29.785, 29.685, 29.605, 29.555, 29.46, 29.385, 29.31, 29.18, 29.09, 29.03, 28.94, 28.875, 28.79, 28.655, 28.615, 28.505, 28.4, 28.315, 28.195, 28.095, 27.995, 27.92, 27.825, 27.755, 27.695, 27.64, 27.56, 27.475, 27.43, 27.355, 27.27, 27.215, 27.155, 27.025, 26.92, 26.825, 26.78, 26.7, 26.595, 26.555, 26.46, 26.435, 26.315, 26.235, 26.17, 26.12, 26.045, 26.005, 25.93, 25.885, 25.785, 25.68, 25.595, 25.545, 25.505, 25.44, 25.41, 25.405, 25.375, 25.3, 25.26, 25.2, 25.125, 25.055, 25.015, 24.915, 24.845, 24.775, 24.72, 24.68, 24.655, 24.565, 24.515, 24.43, 24.34, 24.3, 24.265, 24.225, 24.16, 24.105, 24.04, 23.99, 23.955, 23.915, 23.88, 23.775, 23.705, 23.68, 23.57, 23.51, 23.465, 23.435, 23.395, 23.355, 23.31, 23.255, 23.14, 23.095, 23.035, 22.98, 22.935, 22.905, 22.885, 22.83, 22.77, 22.745, 22.665, 22.575, 22.535, 22.455, 22.405, 22.375, 22.305, 22.265, 22.23, 22.175, 22.12, 22.065, 21.995, 21.92, 21.895, 21.855, 21.805, 21.74, 21.72, 21.675, 21.615, 21.56, 21.485, 21.43, 21.405, 21.33, 21.285, 21.22, 21.17, 21.15, 21.14, 21.095, 21.025, 20.985, 20.93, 20.895, 20.81, 20.75, 20.705, 20.655, 20.605, 20.58, 20.53, 20.485, 20.44, 20.415, 20.4, 20.33, 20.31, 20.245, 20.195, 20.105, 20.07, 20.025, 19.975, 19.915, 19.895, 19.85, 19.8, 19.79, 19.755, 19.72, 19.685, 19.675, 19.625, 19.61, 19.58, 19.535, 19.49, 19.475, 19.43, 19.395, 19.36, 19.335, 19.26, 19.215, 19.145, 19.125, 19.1, 19.055, 19.005, 18.985, 18.96, 18.925, 18.89, 18.855, 18.805, 18.79, 18.775, 18.745, 18.715, 18.695, 18.66, 18.625, 18.575, 18.55, 18.53, 18.525, 18.505, 18.48, 18.45, 18.42, 18.375, 18.345, 18.31, 18.3, 18.26, 18.235, 18.21, 18.165, 18.145, 18.145, 18.13, 18.11, 18.08, 18.065, 18.045, 18.02, 18.0, 17.985, 17.955, 17.93, 17.91, 17.9, 17.84, 17.8, 17.78, 17.75, 17.715, 17.68, 17.645, 17.635, 17.62, 17.59, 17.565, 17.55, 17.54, 17.52, 17.51, 17.485, 17.455, 17.43, 17.415, 17.395, 17.36, 17.34, 17.33, 17.315, 17.28, 17.26, 17.235, 17.225, 17.185, 17.155, 17.115, 17.08, 17.07, 17.06, 17.04, 17.025, 17.015, 16.98, 16.965, 16.96, 16.94, 16.925, 16.895, 16.87, 16.84, 16.83, 16.795, 16.78, 16.77, 16.735, 16.705, 16.69, 16.67, 16.605, 16.57, 16.55, 16.525, 16.51, 16.47, 16.445, 16.405, 16.4, 16.4, 16.39, 16.385, 16.38, 16.37, 16.345, 16.335, 16.325, 16.29, 16.28, 16.265, 16.25, 16.235, 16.21, 16.205, 16.19, 16.165, 16.155, 16.15, 16.15, 16.145, 16.11, 16.095, 16.07, 16.06, 16.045, 16.03, 15.985, 15.97, 15.945, 15.93, 15.915, 15.915, 15.905, 15.885, 15.87, 15.845, 15.81, 15.8, 15.79, 15.78, 15.75, 15.735, 15.695, 15.68, 15.645, 15.63, 15.595, 15.565, 15.55, 15.535, 15.525, 15.495, 15.47, 15.47, 15.46, 15.45, 15.415, 15.395, 15.39, 15.365, 15.355, 15.34, 15.32, 15.305, 15.27, 15.23, 15.22, 15.2, 15.185, 15.145, 15.13, 15.115, 15.08, 15.07, 15.055, 15.045, 15.03, 15.02, 15.01, 14.99, 14.97, 14.955, 14.94, 14.92, 14.9, 14.865, 14.86, 14.845, 14.82, 14.805, 14.79, 14.765, 14.765, 14.76, 14.75, 14.735, 14.73, 14.72, 14.71, 14.7, 14.695, 14.685, 14.67, 14.655, 14.635, 14.63, 14.63, 14.61, 14.61, 14.595, 14.595, 14.58, 14.565, 14.555, 14.525, 14.525, 14.5, 14.475, 14.47, 14.46, 14.43, 14.425, 14.425, 14.41, 14.4, 14.385, 14.36, 14.35, 14.35, 14.345, 14.335, 14.325, 14.325, 14.3, 14.29, 14.27, 14.245, 14.23, 14.22, 14.21, 14.205, 14.2, 14.19, 14.17, 14.165, 14.15, 14.14, 14.115, 14.115, 14.085, 14.07, 14.065, 14.05, 14.04, 14.03, 14.015, 14.0, 14.0, 13.985, 13.98, 13.975, 13.955, 13.94, 13.94, 13.925, 13.92, 13.92, 13.905, 13.88, 13.875, 13.87, 13.845, 13.84, 13.835, 13.83, 13.82, 13.815, 13.81, 13.805, 13.805, 13.8, 13.79, 13.79, 13.775, 13.76, 13.755, 13.735, 13.735, 13.735, 13.725, 13.71, 13.71, 13.705, 13.705, 13.695, 13.69, 13.67, 13.665, 13.665, 13.665, 13.665, 13.66, 13.66, 13.645, 13.64, 13.63, 13.625, 13.61, 13.6, 13.595, 13.595, 13.585, 13.58, 13.565, 13.565, 13.555, 13.55, 13.54, 13.535, 13.525, 13.515, 13.51, 13.51, 13.505, 13.5, 13.5, 13.495, 13.485, 13.485, 13.47, 13.46, 13.455, 13.445, 13.44, 13.43, 13.42, 13.415, 13.395, 13.395, 13.375, 13.37, 13.37, 13.365, 13.36, 13.355, 13.35, 13.345, 13.34, 13.34, 13.33, 13.32, 13.3, 13.29, 13.275, 13.275, 13.275, 13.27, 13.265, 13.255, 13.245, 13.235, 13.235, 13.225, 13.225, 13.215, 13.205, 13.2, 13.195, 13.19, 13.18, 13.175, 13.175, 13.16, 13.16, 13.155, 13.135, 13.13, 13.115, 13.11, 13.095, 13.085, 13.08, 13.08, 13.075, 13.075, 13.07, 13.07, 13.05, 13.05, 13.05, 13.035, 13.03, 13.03, 13.025, 13.02, 13.015, 13.01, 13.005, 13.005, 12.985, 12.98, 12.97, 12.95, 12.94, 12.93, 12.925, 12.92, 12.91, 12.91, 12.905, 12.905, 12.9, 12.9, 12.9, 12.895, 12.89, 12.89, 12.89, 12.885, 12.88, 12.87, 12.87, 12.86, 12.85, 12.85, 12.845, 12.84, 12.835, 12.835, 12.825, 12.82, 12.815, 12.815, 12.815, 12.8, 12.785, 12.78, 12.775, 12.765, 12.765, 12.745, 12.735, 12.725, 12.72, 12.715, 12.71, 12.7, 12.7, 12.695, 12.685, 12.685, 12.685, 12.675, 12.665, 12.66, 12.66, 12.655, 12.655, 12.65, 12.635, 12.635, 12.63, 12.63, 12.625, 12.625, 12.62, 12.61, 12.61, 12.605, 12.6, 12.6, 12.59, 12.58, 12.575, 12.57, 12.57, 12.56, 12.555, 12.535, 12.53, 12.52, 12.5, 12.5, 12.5, 12.49, 12.49, 12.485, 12.47, 12.46, 12.455, 12.425, 12.425, 12.41, 12.41, 12.4, 12.4, 12.39, 12.385, 12.375, 12.37, 12.37, 12.37, 12.36, 12.345, 12.345, 12.34, 12.33, 12.32, 12.315, 12.31, 12.31, 12.31, 12.295, 12.295, 12.295, 12.295, 12.285, 12.285, 12.285, 12.28, 12.28, 12.27, 12.25, 12.245, 12.24, 12.235, 12.235, 12.23, 12.23, 12.225, 12.22, 12.215, 12.215, 12.215, 12.215, 12.21, 12.205, 12.2, 12.2, 12.19, 12.19, 12.19, 12.18, 12.175, 12.17, 12.17, 12.165, 12.165, 12.165, 12.165, 12.165, 12.155, 12.15, 12.145, 12.135, 12.135, 12.135, 12.13, 12.125, 12.12, 12.105, 12.095, 12.09, 12.085, 12.085, 12.08, 12.08, 12.075, 12.075, 12.075, 12.055, 12.055, 12.055, 12.055, 12.055, 12.05, 12.05, 12.04, 12.04, 12.04, 12.035, 12.035, 12.035, 12.025, 12.015, 12.015, 12.015, 12.015, 12.01, 12.01, 12.01, 12.005, 12.0, 11.995, 11.995, 11.99, 11.985, 11.98, 11.975, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.96, 11.96, 11.95, 11.95, 11.945, 11.94, 11.94, 11.935, 11.935, 11.935, 11.93, 11.93, 11.93, 11.92, 11.92, 11.915, 11.91, 11.905, 11.9, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895]
75 half_life L_unique_L = [78, 216, 392, 617, 953]
[74.0, 73.04, 71.92, 70.65, 69.48, 68.795, 67.875, 67.185, 66.39, 65.835, 65.155, 64.785, 64.085, 63.52, 62.94, 62.455, 61.885, 61.315, 60.665, 60.305, 59.98, 59.485, 58.935, 58.55, 58.015, 57.53, 57.135, 56.795, 56.22, 55.58, 55.17, 54.845, 54.535, 54.165, 53.865, 53.51, 53.175, 52.73, 52.365, 52.07, 51.85, 51.485, 51.175, 50.76, 50.48, 50.13, 49.66, 49.385, 49.18, 48.785, 48.57, 48.31, 48.025, 47.765, 47.355, 47.105, 46.94, 46.63, 46.375, 46.205, 45.985, 45.78, 45.56, 45.415, 45.105, 44.87, 44.695, 44.505, 44.315, 44.005, 43.725, 43.46, 43.315, 43.015, 42.74, 42.48, 42.315, 42.16, 41.89, 41.715, 41.57, 41.355, 41.195, 41.0, 40.84, 40.63, 40.44, 40.21, 40.06, 39.89, 39.675, 39.495, 39.35, 39.19, 39.055, 38.925, 38.79, 38.61, 38.465, 38.345, 38.19, 37.95, 37.785, 37.555, 37.47, 37.34, 37.165, 36.965, 36.77, 36.565, 36.445, 36.29, 36.23, 36.14, 36.005, 35.865, 35.725, 35.55, 35.38, 35.31, 35.18, 35.065, 34.97, 34.855, 34.745, 34.595, 34.51, 34.38, 34.285, 34.155, 34.06, 33.95, 33.815, 33.645, 33.585, 33.495, 33.37, 33.205, 33.105, 32.97, 32.9, 32.785, 32.72, 32.66, 32.55, 32.41, 32.32, 32.2, 32.06, 31.945, 31.825, 31.775, 31.655, 31.54, 31.425, 31.275, 31.21, 31.125, 30.98, 30.815, 30.7, 30.59, 30.475, 30.385, 30.245, 30.15, 30.01, 29.87, 29.785, 29.685, 29.605, 29.555, 29.46, 29.385, 29.31, 29.18, 29.09, 29.03, 28.94, 28.875, 28.79, 28.655, 28.615, 28.505, 28.4, 28.315, 28.195, 28.095, 27.995, 27.92, 27.825, 27.755, 27.695, 27.64, 27.56, 27.475, 27.43, 27.355, 27.27, 27.215, 27.155, 27.025, 26.92, 26.825, 26.78, 26.7, 26.595, 26.555, 26.46, 26.435, 26.315, 26.235, 26.17, 26.12, 26.045, 26.005, 25.93, 25.885, 25.785, 25.68, 25.595, 25.545, 25.505, 25.44, 25.41, 25.405, 25.375, 25.3, 25.26, 25.2, 25.125, 25.055, 25.015, 24.915, 24.845, 24.775, 24.72, 24.68, 24.655, 24.565, 24.515, 24.43, 24.34, 24.3, 24.265, 24.225, 24.16, 24.105, 24.04, 23.99, 23.955, 23.915, 23.88, 23.775, 23.705, 23.68, 23.57, 23.51, 23.465, 23.435, 23.395, 23.355, 23.31, 23.255, 23.14, 23.095, 23.035, 22.98, 22.935, 22.905, 22.885, 22.83, 22.77, 22.745, 22.665, 22.575, 22.535, 22.455, 22.405, 22.375, 22.305, 22.265, 22.23, 22.175, 22.12, 22.065, 21.995, 21.92, 21.895, 21.855, 21.805, 21.74, 21.72, 21.675, 21.615, 21.56, 21.485, 21.43, 21.405, 21.33, 21.285, 21.22, 21.17, 21.15, 21.14, 21.095, 21.025, 20.985, 20.93, 20.895, 20.81, 20.75, 20.705, 20.655, 20.605, 20.58, 20.53, 20.485, 20.44, 20.415, 20.4, 20.33, 20.31, 20.245, 20.195, 20.105, 20.07, 20.025, 19.975, 19.915, 19.895, 19.85, 19.8, 19.79, 19.755, 19.72, 19.685, 19.675, 19.625, 19.61, 19.58, 19.535, 19.49, 19.475, 19.43, 19.395, 19.36, 19.335, 19.26, 19.215, 19.145, 19.125, 19.1, 19.055, 19.005, 18.985, 18.96, 18.925, 18.89, 18.855, 18.805, 18.79, 18.775, 18.745, 18.715, 18.695, 18.66, 18.625, 18.575, 18.55, 18.53, 18.525, 18.505, 18.48, 18.45, 18.42, 18.375, 18.345, 18.31, 18.3, 18.26, 18.235, 18.21, 18.165, 18.145, 18.145, 18.13, 18.11, 18.08, 18.065, 18.045, 18.02, 18.0, 17.985, 17.955, 17.93, 17.91, 17.9, 17.84, 17.8, 17.78, 17.75, 17.715, 17.68, 17.645, 17.635, 17.62, 17.59, 17.565, 17.55, 17.54, 17.52, 17.51, 17.485, 17.455, 17.43, 17.415, 17.395, 17.36, 17.34, 17.33, 17.315, 17.28, 17.26, 17.235, 17.225, 17.185, 17.155, 17.115, 17.08, 17.07, 17.06, 17.04, 17.025, 17.015, 16.98, 16.965, 16.96, 16.94, 16.925, 16.895, 16.87, 16.84, 16.83, 16.795, 16.78, 16.77, 16.735, 16.705, 16.69, 16.67, 16.605, 16.57, 16.55, 16.525, 16.51, 16.47, 16.445, 16.405, 16.4, 16.4, 16.39, 16.385, 16.38, 16.37, 16.345, 16.335, 16.325, 16.29, 16.28, 16.265, 16.25, 16.235, 16.21, 16.205, 16.19, 16.165, 16.155, 16.15, 16.15, 16.145, 16.11, 16.095, 16.07, 16.06, 16.045, 16.03, 15.985, 15.97, 15.945, 15.93, 15.915, 15.915, 15.905, 15.885, 15.87, 15.845, 15.81, 15.8, 15.79, 15.78, 15.75, 15.735, 15.695, 15.68, 15.645, 15.63, 15.595, 15.565, 15.55, 15.535, 15.525, 15.495, 15.47, 15.47, 15.46, 15.45, 15.415, 15.395, 15.39, 15.365, 15.355, 15.34, 15.32, 15.305, 15.27, 15.23, 15.22, 15.2, 15.185, 15.145, 15.13, 15.115, 15.08, 15.07, 15.055, 15.045, 15.03, 15.02, 15.01, 14.99, 14.97, 14.955, 14.94, 14.92, 14.9, 14.865, 14.86, 14.845, 14.82, 14.805, 14.79, 14.765, 14.765, 14.76, 14.75, 14.735, 14.73, 14.72, 14.71, 14.7, 14.695, 14.685, 14.67, 14.655, 14.635, 14.63, 14.63, 14.61, 14.61, 14.595, 14.595, 14.58, 14.565, 14.555, 14.525, 14.525, 14.5, 14.475, 14.47, 14.46, 14.43, 14.425, 14.425, 14.41, 14.4, 14.385, 14.36, 14.35, 14.35, 14.345, 14.335, 14.325, 14.325, 14.3, 14.29, 14.27, 14.245, 14.23, 14.22, 14.21, 14.205, 14.2, 14.19, 14.17, 14.165, 14.15, 14.14, 14.115, 14.115, 14.085, 14.07, 14.065, 14.05, 14.04, 14.03, 14.015, 14.0, 14.0, 13.985, 13.98, 13.975, 13.955, 13.94, 13.94, 13.925, 13.92, 13.92, 13.905, 13.88, 13.875, 13.87, 13.845, 13.84, 13.835, 13.83, 13.82, 13.815, 13.81, 13.805, 13.805, 13.8, 13.79, 13.79, 13.775, 13.76, 13.755, 13.735, 13.735, 13.735, 13.725, 13.71, 13.71, 13.705, 13.705, 13.695, 13.69, 13.67, 13.665, 13.665, 13.665, 13.665, 13.66, 13.66, 13.645, 13.64, 13.63, 13.625, 13.61, 13.6, 13.595, 13.595, 13.585, 13.58, 13.565, 13.565, 13.555, 13.55, 13.54, 13.535, 13.525, 13.515, 13.51, 13.51, 13.505, 13.5, 13.5, 13.495, 13.485, 13.485, 13.47, 13.46, 13.455, 13.445, 13.44, 13.43, 13.42, 13.415, 13.395, 13.395, 13.375, 13.37, 13.37, 13.365, 13.36, 13.355, 13.35, 13.345, 13.34, 13.34, 13.33, 13.32, 13.3, 13.29, 13.275, 13.275, 13.275, 13.27, 13.265, 13.255, 13.245, 13.235, 13.235, 13.225, 13.225, 13.215, 13.205, 13.2, 13.195, 13.19, 13.18, 13.175, 13.175, 13.16, 13.16, 13.155, 13.135, 13.13, 13.115, 13.11, 13.095, 13.085, 13.08, 13.08, 13.075, 13.075, 13.07, 13.07, 13.05, 13.05, 13.05, 13.035, 13.03, 13.03, 13.025, 13.02, 13.015, 13.01, 13.005, 13.005, 12.985, 12.98, 12.97, 12.95, 12.94, 12.93, 12.925, 12.92, 12.91, 12.91, 12.905, 12.905, 12.9, 12.9, 12.9, 12.895, 12.89, 12.89, 12.89, 12.885, 12.88, 12.87, 12.87, 12.86, 12.85, 12.85, 12.845, 12.84, 12.835, 12.835, 12.825, 12.82, 12.815, 12.815, 12.815, 12.8, 12.785, 12.78, 12.775, 12.765, 12.765, 12.745, 12.735, 12.725, 12.72, 12.715, 12.71, 12.7, 12.7, 12.695, 12.685, 12.685, 12.685, 12.675, 12.665, 12.66, 12.66, 12.655, 12.655, 12.65, 12.635, 12.635, 12.63, 12.63, 12.625, 12.625, 12.62, 12.61, 12.61, 12.605, 12.6, 12.6, 12.59, 12.58, 12.575, 12.57, 12.57, 12.56, 12.555, 12.535, 12.53, 12.52, 12.5, 12.5, 12.5, 12.49, 12.49, 12.485, 12.47, 12.46, 12.455, 12.425, 12.425, 12.41, 12.41, 12.4, 12.4, 12.39, 12.385, 12.375, 12.37, 12.37, 12.37, 12.36, 12.345, 12.345, 12.34, 12.33, 12.32, 12.315, 12.31, 12.31, 12.31, 12.295, 12.295, 12.295, 12.295, 12.285, 12.285, 12.285, 12.28, 12.28, 12.27, 12.25, 12.245, 12.24, 12.235, 12.235, 12.23, 12.23, 12.225, 12.22, 12.215, 12.215, 12.215, 12.215, 12.21, 12.205, 12.2, 12.2, 12.19, 12.19, 12.19, 12.18, 12.175, 12.17, 12.17, 12.165, 12.165, 12.165, 12.165, 12.165, 12.155, 12.15, 12.145, 12.135, 12.135, 12.135, 12.13, 12.125, 12.12, 12.105, 12.095, 12.09, 12.085, 12.085, 12.08, 12.08, 12.075, 12.075, 12.075, 12.055, 12.055, 12.055, 12.055, 12.055, 12.05, 12.05, 12.04, 12.04, 12.04, 12.035, 12.035, 12.035, 12.025, 12.015, 12.015, 12.015, 12.015, 12.01, 12.01, 12.01, 12.005, 12.0, 11.995, 11.995, 11.99, 11.985, 11.98, 11.975, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.965, 11.96, 11.96, 11.95, 11.95, 11.945, 11.94, 11.94, 11.935, 11.935, 11.935, 11.93, 11.93, 11.93, 11.92, 11.92, 11.915, 11.91, 11.905, 11.9, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895, 11.895]


    125
chr_len = 200 67.0
chr_len_SD = 1001 67.0
chr_len_Q1_Q2_Q3 = 1001 = 42.75 59.0 80.0
last_chr_len_zero = 0.0 %
[124.0, 124.685, 124.935, 125.585, 126.4, 126.455, 126.69, 126.97, 127.435, 128.28, 129.12, 129.685, 128.98, 128.825, 129.555, 130.035, 130.085, 129.995, 130.1, 130.595, 130.58, 131.78, 131.995, 132.43, 132.79, 132.965, 133.055, 132.875, 132.735, 132.51, 132.67, 133.505, 132.9, 133.28, 133.555, 133.145, 133.185, 132.75, 132.485, 132.425, 131.905, 131.345, 130.995, 131.255, 131.84, 131.77, 132.575, 132.545, 132.025, 131.9, 132.03, 132.5, 133.075, 132.01, 132.11, 131.845, 131.35, 131.68, 131.86, 131.445, 130.8, 129.96, 129.985, 129.55, 129.25, 129.865, 129.87, 129.88, 130.335, 129.895, 129.975, 129.445, 129.01, 128.065, 128.125, 128.12, 127.365, 127.44, 128.13, 127.76, 127.295, 127.22, 127.735, 127.345, 126.53, 126.015, 125.335, 124.785, 124.895, 125.11, 124.56, 124.495, 124.595, 124.49, 125.15, 125.295, 124.805, 124.82, 124.075, 123.315, 123.04, 123.06, 122.49, 121.955, 121.53, 120.925, 120.505, 119.88, 119.36, 119.34, 119.06, 119.035, 119.525, 119.155, 119.33, 119.715, 119.095, 119.25, 119.765, 119.605, 119.01, 119.38, 118.975, 118.04, 116.94, 116.395, 115.735, 115.215, 115.28, 115.12, 115.265, 114.49, 114.73, 114.315, 113.975, 113.76, 113.175, 113.395, 113.25, 113.475, 113.21, 113.13, 112.66, 111.82, 111.6, 111.51, 111.19, 110.225, 110.12, 109.68, 110.05, 110.475, 109.76, 109.515, 109.14, 108.915, 108.715, 108.81, 109.29, 109.47, 108.7, 108.125, 106.87, 106.78, 106.21, 105.95, 104.265, 104.445, 104.68, 103.965, 103.47, 104.005, 104.475, 103.835, 104.19, 104.395, 104.26, 103.705, 103.56, 102.27, 102.33, 102.185, 102.565, 102.595, 103.015, 102.655, 102.415, 102.02, 101.895, 102.38, 102.64, 103.055, 103.295, 103.465, 103.49, 103.125, 103.0, 103.525, 103.805, 103.53, 103.295, 103.14, 102.985, 102.55, 101.805, 101.405, 101.05, 100.565, 100.59, 100.315, 100.165, 100.41, 99.015, 99.395, 99.505, 98.685, 98.435, 98.08, 98.085, 97.945, 97.895, 98.44, 97.92, 97.715, 98.415, 98.31, 97.85, 97.67, 97.685, 97.745, 97.45, 97.42, 97.16, 98.07, 97.89, 98.145, 97.635, 97.23, 96.705, 96.445, 96.43, 96.32, 96.66, 96.32, 96.485, 96.03, 96.645, 95.63, 94.59, 94.525, 95.51, 95.14, 94.76, 94.61, 94.875, 94.345, 94.385, 93.955, 94.2, 93.875, 93.28, 92.61, 92.955, 92.795, 92.685, 92.175, 92.055, 92.2, 92.195, 92.07, 91.855, 91.31, 91.29, 90.825, 90.15, 89.89, 89.595, 89.73, 89.825, 89.74, 89.56, 88.93, 88.345, 88.38, 88.455, 88.675, 88.615, 88.355, 88.27, 88.03, 88.075, 87.83, 87.85, 88.07, 88.045, 87.61, 87.18, 86.995, 87.32, 87.195, 86.995, 87.5, 87.64, 86.98, 87.38, 87.32, 87.29, 87.085, 87.185, 87.38, 86.525, 86.725, 86.595, 86.505, 86.46, 86.83, 86.74, 86.365, 86.33, 85.53, 85.715, 85.76, 85.365, 85.615, 85.73, 85.745, 86.205, 85.81, 85.575, 85.505, 84.975, 84.89, 84.38, 84.39, 83.56, 83.33, 83.55, 83.495, 83.675, 83.3, 83.48, 83.45, 82.885, 82.595, 82.64, 82.225, 82.845, 82.355, 81.84, 82.42, 82.135, 82.325, 82.385, 81.695, 81.805, 81.535, 81.005, 80.545, 80.315, 80.495, 80.54, 81.03, 80.8, 80.785, 79.94, 79.955, 79.815, 79.64, 79.49, 79.83, 80.02, 79.485, 79.215, 79.355, 78.695, 78.43, 78.87, 78.27, 78.19, 77.715, 78.355, 77.51, 77.81, 77.635, 76.935, 76.62, 75.75, 75.295, 74.345, 74.645, 75.24, 75.125, 75.225, 76.185, 76.915, 76.53, 76.655, 76.775, 76.95, 76.895, 77.07, 76.39, 75.56, 75.565, 75.005, 75.435, 75.6, 75.465, 75.11, 75.08, 75.02, 74.775, 74.765, 74.675, 74.185, 73.11, 73.1, 72.935, 72.6, 72.44, 72.61, 72.395, 72.78, 72.23, 72.28, 72.005, 72.4, 72.715, 72.845, 72.775, 72.38, 71.795, 71.445, 71.98, 72.105, 71.655, 70.87, 70.83, 70.93, 70.255, 69.655, 69.5, 69.295, 69.085, 69.41, 69.59, 68.64, 68.6, 68.68, 68.6, 68.245, 67.315, 66.66, 66.82, 66.745, 67.155, 67.42, 66.23, 66.005, 65.685, 66.235, 66.205, 65.715, 65.33, 64.875, 65.245, 65.695, 64.87, 64.135, 64.185, 64.15, 63.835, 63.87, 64.285, 64.25, 64.715, 64.58, 64.72, 64.805, 64.445, 64.925, 65.13, 65.02, 65.185, 65.075, 64.89, 64.945, 64.66, 64.905, 64.845, 64.39, 64.42, 64.06, 64.16, 64.86, 64.79, 63.835, 63.955, 63.69, 63.66, 63.17, 63.65, 63.38, 64.08, 64.15, 64.14, 65.31, 66.2, 66.58, 66.795, 66.62, 66.745, 66.32, 66.075, 65.795, 65.225, 66.24, 66.04, 65.31, 65.735, 65.725, 65.725, 65.69, 65.3, 64.485, 64.5, 64.02, 63.77, 63.98, 63.94, 63.89, 63.775, 63.295, 63.325, 63.91, 63.095, 62.76, 63.145, 62.95, 63.22, 63.935, 63.73, 64.035, 64.23, 64.595, 64.3, 64.455, 64.14, 63.46, 63.505, 63.145, 62.79, 63.33, 62.725, 63.02, 62.72, 62.245, 62.055, 62.025, 61.635, 61.25, 61.005, 61.295, 61.1, 61.44, 61.26, 61.46, 61.37, 61.105, 61.055, 61.125, 61.18, 60.965, 61.63, 61.73, 61.675, 61.43, 60.845, 61.26, 61.025, 60.465, 60.095, 60.29, 60.53, 60.365, 59.56, 59.465, 59.96, 59.595, 59.085, 58.735, 58.45, 58.345, 58.88, 59.685, 58.925, 58.34, 58.76, 58.625, 59.275, 59.14, 58.985, 59.085, 58.96, 58.63, 58.515, 59.03, 59.875, 59.695, 59.765, 59.31, 59.51, 59.955, 59.625, 59.315, 59.265, 59.12, 59.065, 59.285, 58.855, 58.535, 59.125, 59.205, 58.765, 58.755, 58.135, 58.2, 58.43, 58.06, 58.49, 58.415, 58.0, 58.23, 58.13, 58.29, 58.3, 58.08, 57.905, 57.895, 58.35, 58.27, 59.115, 59.18, 58.93, 59.08, 59.0, 58.8, 58.34, 58.235, 58.265, 57.67, 57.905, 57.685, 57.13, 57.14, 57.585, 57.895, 58.45, 58.38, 58.31, 58.925, 58.58, 58.115, 58.505, 58.56, 58.06, 58.235, 58.49, 58.615, 58.305, 57.475, 57.97, 57.56, 57.31, 57.735, 58.045, 58.15, 57.94, 58.515, 58.175, 58.505, 58.37, 58.215, 57.955, 58.23, 57.8, 56.935, 57.245, 56.84, 56.62, 56.47, 56.09, 56.13, 56.185, 56.445, 56.815, 56.36, 56.45, 56.63, 56.885, 57.235, 57.395, 57.48, 57.97, 57.665, 57.88, 58.115, 58.14, 57.9, 57.805, 57.86, 57.855, 57.86, 57.67, 58.105, 57.285, 57.67, 57.535, 57.19, 56.82, 56.935, 56.61, 56.675, 56.28, 56.375, 56.455, 56.29, 56.635, 56.665, 56.325, 56.255, 56.93, 57.3, 57.495, 56.995, 57.205, 58.08, 57.875, 57.69, 56.85, 56.385, 56.225, 56.08, 56.27, 55.99, 55.615, 55.625, 55.74, 56.3, 55.86, 55.89, 55.68, 55.14, 55.01, 54.84, 54.075, 53.565, 53.845, 53.75, 53.69, 54.3, 54.12, 54.34, 54.595, 55.04, 55.035, 54.915, 54.35, 54.56, 54.25, 54.715, 55.1, 54.735, 53.8, 53.685, 54.2, 53.945, 54.225, 53.85, 53.845, 53.875, 54.005, 54.01, 53.79, 53.745, 54.155, 54.22, 53.64, 53.23, 53.195, 53.065, 53.03, 53.15, 53.06, 52.805, 52.86, 53.65, 53.22, 52.85, 53.515, 53.84, 53.58, 53.33, 53.54, 53.53, 53.71, 53.98, 53.85, 53.6, 53.625, 53.56, 53.7, 53.65, 53.41, 52.705, 52.36, 52.255, 52.025, 52.645, 52.505, 52.575, 52.5, 52.715, 53.04, 53.02, 52.19, 51.845, 52.24, 52.435, 51.545, 51.425, 51.4, 51.11, 51.215, 50.835, 50.68, 51.105, 50.585, 50.915, 50.975, 51.11, 51.435, 51.17, 51.145, 51.4, 50.92, 51.36, 51.295, 51.565, 51.395, 50.705, 51.085, 50.775, 50.225, 50.12, 50.305, 50.48, 50.455, 50.4, 50.855, 50.625, 50.575, 50.49, 50.685, 50.775, 51.12, 51.57, 51.155, 51.2, 50.705, 50.635, 50.475, 50.555, 51.15, 51.315, 51.765, 50.975, 51.525, 51.55, 51.085, 50.6, 50.7, 50.69, 50.24, 50.13, 50.27, 50.07, 50.475, 50.765, 50.62, 51.17, 49.9, 50.19, 49.875, 49.81, 49.68, 49.71, 48.985, 48.945, 48.775, 48.91, 48.26, 48.435, 48.555, 48.365, 48.46, 48.305, 48.12, 48.08, 48.57, 48.91, 49.555, 49.42, 49.47, 50.175, 50.25, 50.41, 50.365, 50.36, 50.86, 50.645, 50.67, 50.355, 50.29, 50.67, 50.98, 51.25, 50.87, 50.84, 51.07, 51.115, 50.895, 50.93, 50.835, 50.425, 50.29, 50.58, 50.05, 50.44, 50.36, 50.405, 51.115, 50.79, 51.055, 51.105, 51.18, 50.345, 50.0, 50.94, 51.29, 50.81, 50.545, 50.565, 50.37, 50.425, 50.065, 50.04, 50.695, 50.53, 50.695, 50.41, 50.0, 50.35, 49.55, 49.3, 49.65, 49.485, 49.47, 49.61, 49.37, 49.695, 50.285, 50.43, 50.44, 49.815, 50.055, 50.86, 50.385, 50.465, 49.87, 50.145, 50.45, 50.765, 50.75, 51.25, 51.98, 52.21, 52.175, 52.53, 51.86, 51.38, 51.095, 51.155, 51.075, 51.055, 51.0, 51.525, 51.425, 51.62, 51.495, 51.165]
125 half_life chr_len_L = [559]
[124.0, 122.78, 121.325, 120.45, 119.675, 118.365, 117.06, 115.84, 114.865, 114.005, 113.09, 112.13, 110.845, 109.82, 109.1, 108.29, 107.385, 106.51, 105.78, 104.86, 104.055, 103.545, 103.01, 102.335, 101.42, 100.915, 100.19, 99.42, 98.635, 97.975, 97.46, 96.925, 96.075, 95.39, 94.975, 94.4, 93.84, 93.29, 92.635, 92.095, 91.595, 91.075, 90.41, 90.01, 89.5, 89.035, 88.71, 88.2, 87.52, 86.925, 86.375, 86.105, 85.58, 84.98, 84.45, 83.785, 83.21, 82.78, 82.365, 81.81, 81.34, 80.92, 80.465, 79.925, 79.465, 79.125, 78.71, 78.395, 78.055, 77.465, 77.14, 76.55, 76.14, 75.425, 74.825, 74.505, 74.06, 73.585, 73.255, 72.755, 72.225, 71.84, 71.53, 71.13, 70.765, 70.42, 69.995, 69.53, 69.085, 68.7, 68.42, 68.1, 67.795, 67.475, 67.115, 66.775, 66.36, 66.025, 65.735, 65.275, 64.98, 64.705, 64.395, 64.14, 63.935, 63.52, 63.17, 62.81, 62.52, 62.2, 61.91, 61.55, 61.195, 60.93, 60.725, 60.445, 60.07, 59.695, 59.48, 59.18, 58.73, 58.57, 58.335, 57.935, 57.56, 57.305, 57.0, 56.735, 56.495, 56.115, 55.85, 55.585, 55.285, 54.865, 54.535, 54.25, 54.0, 53.785, 53.565, 53.33, 53.02, 52.695, 52.44, 52.235, 52.035, 51.72, 51.41, 51.14, 50.8, 50.63, 50.43, 50.335, 50.12, 49.92, 49.785, 49.565, 49.285, 49.105, 48.935, 48.71, 48.48, 48.315, 48.02, 47.84, 47.59, 47.375, 47.09, 46.825, 46.625, 46.43, 46.25, 46.065, 45.895, 45.68, 45.55, 45.415, 45.25, 45.05, 44.845, 44.545, 44.405, 44.115, 43.855, 43.695, 43.51, 43.375, 43.155, 42.885, 42.72, 42.65, 42.475, 42.35, 42.215, 42.06, 41.905, 41.775, 41.545, 41.355, 41.2, 41.005, 40.89, 40.715, 40.565, 40.395, 40.21, 40.08, 39.835, 39.68, 39.52, 39.325, 39.155, 39.06, 38.82, 38.755, 38.645, 38.45, 38.31, 38.21, 38.08, 37.935, 37.79, 37.7, 37.55, 37.435, 37.31, 37.225, 37.11, 36.985, 36.925, 36.83, 36.66, 36.53, 36.445, 36.355, 36.13, 36.0, 35.91, 35.75, 35.65, 35.525, 35.415, 35.32, 35.23, 35.115, 34.92, 34.77, 34.65, 34.53, 34.34, 34.205, 34.11, 33.98, 33.865, 33.76, 33.68, 33.55, 33.475, 33.335, 33.285, 33.18, 33.055, 32.925, 32.855, 32.745, 32.62, 32.49, 32.435, 32.345, 32.26, 32.165, 32.055, 31.985, 31.885, 31.835, 31.69, 31.585, 31.485, 31.385, 31.27, 31.205, 31.105, 31.02, 30.935, 30.87, 30.8, 30.695, 30.6, 30.54, 30.47, 30.33, 30.265, 30.195, 30.08, 30.005, 29.92, 29.775, 29.675, 29.585, 29.52, 29.41, 29.31, 29.205, 29.155, 29.05, 28.995, 28.945, 28.85, 28.78, 28.705, 28.67, 28.565, 28.515, 28.445, 28.39, 28.335, 28.27, 28.23, 28.18, 28.11, 28.01, 27.94, 27.88, 27.84, 27.755, 27.705, 27.615, 27.575, 27.44, 27.375, 27.32, 27.235, 27.15, 27.08, 27.02, 26.93, 26.845, 26.765, 26.7, 26.61, 26.535, 26.485, 26.45, 26.35, 26.285, 26.16, 26.105, 26.06, 26.01, 25.955, 25.865, 25.805, 25.76, 25.705, 25.665, 25.62, 25.555, 25.52, 25.46, 25.37, 25.34, 25.295, 25.225, 25.16, 25.13, 25.04, 24.985, 24.94, 24.85, 24.8, 24.72, 24.69, 24.615, 24.555, 24.505, 24.42, 24.37, 24.305, 24.27, 24.195, 24.14, 24.115, 24.07, 24.0, 23.965, 23.9, 23.84, 23.72, 23.63, 23.525, 23.465, 23.43, 23.385, 23.34, 23.25, 23.185, 23.15, 23.105, 23.025, 22.985, 22.945, 22.895, 22.815, 22.78, 22.715, 22.65, 22.61, 22.53, 22.475, 22.435, 22.4, 22.325, 22.28, 22.26, 22.215, 22.17, 22.125, 22.095, 22.025, 21.99, 21.935, 21.89, 21.83, 21.735, 21.69, 21.66, 21.59, 21.54, 21.49, 21.435, 21.355, 21.335, 21.275, 21.22, 21.165, 21.14, 21.075, 21.01, 20.96, 20.915, 20.84, 20.815, 20.775, 20.74, 20.65, 20.605, 20.57, 20.52, 20.49, 20.445, 20.405, 20.36, 20.305, 20.255, 20.195, 20.16, 20.12, 20.07, 20.02, 19.965, 19.935, 19.9, 19.88, 19.855, 19.795, 19.745, 19.72, 19.685, 19.655, 19.605, 19.545, 19.52, 19.43, 19.36, 19.325, 19.3, 19.265, 19.24, 19.2, 19.165, 19.15, 19.13, 19.09, 19.04, 19.035, 18.995, 18.98, 18.93, 18.905, 18.875, 18.845, 18.795, 18.77, 18.73, 18.695, 18.66, 18.64, 18.63, 18.595, 18.565, 18.545, 18.51, 18.475, 18.43, 18.38, 18.355, 18.34, 18.34, 18.315, 18.305, 18.275, 18.245, 18.225, 18.215, 18.205, 18.19, 18.165, 18.14, 18.105, 18.09, 18.07, 18.05, 18.045, 18.02, 17.995, 17.96, 17.945, 17.91, 17.875, 17.855, 17.83, 17.815, 17.785, 17.76, 17.73, 17.7, 17.665, 17.62, 17.595, 17.575, 17.555, 17.525, 17.505, 17.48, 17.465, 17.46, 17.445, 17.43, 17.385, 17.35, 17.31, 17.255, 17.205, 17.19, 17.145, 17.13, 17.115, 17.095, 17.075, 17.05, 17.035, 17.02, 17.005, 16.985, 16.96, 16.93, 16.9, 16.875, 16.825, 16.78, 16.755, 16.745, 16.735, 16.715, 16.7, 16.685, 16.67, 16.665, 16.645, 16.605, 16.59, 16.575, 16.555, 16.55, 16.535, 16.5, 16.44, 16.43, 16.405, 16.39, 16.35, 16.325, 16.31, 16.305, 16.295, 16.275, 16.24, 16.22, 16.215, 16.18, 16.16, 16.145, 16.135, 16.11, 16.095, 16.06, 16.03, 16.015, 16.015, 16.005, 15.985, 15.97, 15.955, 15.935, 15.92, 15.9, 15.88, 15.87, 15.85, 15.835, 15.795, 15.755, 15.745, 15.735, 15.72, 15.705, 15.675, 15.65, 15.63, 15.62, 15.615, 15.61, 15.595, 15.585, 15.57, 15.56, 15.53, 15.5, 15.48, 15.48, 15.46, 15.445, 15.435, 15.43, 15.425, 15.42, 15.41, 15.39, 15.38, 15.375, 15.365, 15.335, 15.325, 15.315, 15.3, 15.29, 15.275, 15.255, 15.25, 15.225, 15.21, 15.195, 15.18, 15.16, 15.145, 15.135, 15.125, 15.12, 15.11, 15.085, 15.075, 15.06, 15.035, 15.01, 15.005, 15.005, 15.0, 14.97, 14.955, 14.935, 14.93, 14.92, 14.9, 14.89, 14.88, 14.86, 14.845, 14.84, 14.82, 14.8, 14.785, 14.78, 14.775, 14.77, 14.755, 14.73, 14.71, 14.68, 14.67, 14.655, 14.645, 14.645, 14.645, 14.64, 14.635, 14.62, 14.605, 14.59, 14.59, 14.585, 14.58, 14.57, 14.555, 14.55, 14.53, 14.52, 14.51, 14.485, 14.47, 14.46, 14.44, 14.43, 14.4, 14.395, 14.385, 14.37, 14.355, 14.345, 14.33, 14.33, 14.33, 14.32, 14.31, 14.295, 14.295, 14.275, 14.265, 14.255, 14.25, 14.22, 14.215, 14.21, 14.195, 14.195, 14.185, 14.155, 14.155, 14.14, 14.13, 14.11, 14.095, 14.095, 14.09, 14.075, 14.07, 14.06, 14.045, 14.04, 14.04, 14.03, 14.025, 14.025, 14.025, 14.015, 14.005, 13.995, 13.99, 13.985, 13.95, 13.945, 13.94, 13.925, 13.925, 13.9, 13.89, 13.875, 13.865, 13.855, 13.85, 13.84, 13.84, 13.83, 13.83, 13.815, 13.81, 13.795, 13.78, 13.775, 13.77, 13.76, 13.745, 13.74, 13.725, 13.725, 13.72, 13.71, 13.695, 13.69, 13.68, 13.665, 13.655, 13.645, 13.64, 13.625, 13.605, 13.585, 13.58, 13.58, 13.57, 13.56, 13.555, 13.55, 13.525, 13.515, 13.505, 13.48, 13.47, 13.465, 13.465, 13.465, 13.455, 13.45, 13.445, 13.44, 13.43, 13.43, 13.42, 13.41, 13.385, 13.38, 13.365, 13.36, 13.355, 13.345, 13.34, 13.33, 13.325, 13.32, 13.31, 13.29, 13.285, 13.275, 13.27, 13.25, 13.245, 13.24, 13.23, 13.225, 13.22, 13.2, 13.19, 13.17, 13.17, 13.165, 13.165, 13.165, 13.16, 13.155, 13.15, 13.145, 13.135, 13.11, 13.105, 13.105, 13.105, 13.1, 13.1, 13.095, 13.095, 13.09, 13.075, 13.07, 13.05, 13.05, 13.045, 13.035, 13.015, 12.99, 12.99, 12.98, 12.965, 12.965, 12.955, 12.94, 12.93, 12.92, 12.915, 12.89, 12.885, 12.885, 12.88, 12.875, 12.875, 12.875, 12.87, 12.85, 12.835, 12.835, 12.82, 12.82, 12.81, 12.8, 12.795, 12.775, 12.77, 12.755, 12.75, 12.745, 12.745, 12.745, 12.73, 12.725, 12.725, 12.72, 12.715, 12.71, 12.71, 12.71, 12.7, 12.7, 12.695, 12.685, 12.685, 12.68, 12.675, 12.675, 12.655, 12.65, 12.645, 12.635, 12.635, 12.635, 12.635, 12.635, 12.625, 12.625, 12.62, 12.61, 12.605, 12.605, 12.6, 12.595, 12.595, 12.585, 12.575, 12.575, 12.575, 12.565, 12.56, 12.555, 12.555, 12.555, 12.55, 12.545, 12.545, 12.54, 12.53, 12.52, 12.52, 12.52, 12.515, 12.51, 12.505, 12.5, 12.49, 12.49, 12.485, 12.465, 12.465, 12.455, 12.455, 12.445, 12.44, 12.44, 12.44, 12.44, 12.435, 12.43, 12.425, 12.42, 12.42, 12.41, 12.41, 12.41, 12.405, 12.4, 12.4, 12.4, 12.395, 12.395, 12.395, 12.395, 12.39, 12.385, 12.385, 12.385, 12.38, 12.38, 12.365, 12.365, 12.36, 12.355]
125 half_life L_unique_L = [95, 215, 378, 555, 808]
[124.0, 122.78, 121.325, 120.45, 119.675, 118.365, 117.06, 115.84, 114.865, 114.005, 113.09, 112.13, 110.845, 109.82, 109.1, 108.29, 107.385, 106.51, 105.78, 104.86, 104.055, 103.545, 103.01, 102.335, 101.42, 100.915, 100.19, 99.42, 98.635, 97.975, 97.46, 96.925, 96.075, 95.39, 94.975, 94.4, 93.84, 93.29, 92.635, 92.095, 91.595, 91.075, 90.41, 90.01, 89.5, 89.035, 88.71, 88.2, 87.52, 86.925, 86.375, 86.105, 85.58, 84.98, 84.45, 83.785, 83.21, 82.78, 82.365, 81.81, 81.34, 80.92, 80.465, 79.925, 79.465, 79.125, 78.71, 78.395, 78.055, 77.465, 77.14, 76.55, 76.14, 75.425, 74.825, 74.505, 74.06, 73.585, 73.255, 72.755, 72.225, 71.84, 71.53, 71.13, 70.765, 70.42, 69.995, 69.53, 69.085, 68.7, 68.42, 68.1, 67.795, 67.475, 67.115, 66.775, 66.36, 66.025, 65.735, 65.275, 64.98, 64.705, 64.395, 64.14, 63.935, 63.52, 63.17, 62.81, 62.52, 62.2, 61.91, 61.55, 61.195, 60.93, 60.725, 60.445, 60.07, 59.695, 59.48, 59.18, 58.73, 58.57, 58.335, 57.935, 57.56, 57.305, 57.0, 56.735, 56.495, 56.115, 55.85, 55.585, 55.285, 54.865, 54.535, 54.25, 54.0, 53.785, 53.565, 53.33, 53.02, 52.695, 52.44, 52.235, 52.035, 51.72, 51.41, 51.14, 50.8, 50.63, 50.43, 50.335, 50.12, 49.92, 49.785, 49.565, 49.285, 49.105, 48.935, 48.71, 48.48, 48.315, 48.02, 47.84, 47.59, 47.375, 47.09, 46.825, 46.625, 46.43, 46.25, 46.065, 45.895, 45.68, 45.55, 45.415, 45.25, 45.05, 44.845, 44.545, 44.405, 44.115, 43.855, 43.695, 43.51, 43.375, 43.155, 42.885, 42.72, 42.65, 42.475, 42.35, 42.215, 42.06, 41.905, 41.775, 41.545, 41.355, 41.2, 41.005, 40.89, 40.715, 40.565, 40.395, 40.21, 40.08, 39.835, 39.68, 39.52, 39.325, 39.155, 39.06, 38.82, 38.755, 38.645, 38.45, 38.31, 38.21, 38.08, 37.935, 37.79, 37.7, 37.55, 37.435, 37.31, 37.225, 37.11, 36.985, 36.925, 36.83, 36.66, 36.53, 36.445, 36.355, 36.13, 36.0, 35.91, 35.75, 35.65, 35.525, 35.415, 35.32, 35.23, 35.115, 34.92, 34.77, 34.65, 34.53, 34.34, 34.205, 34.11, 33.98, 33.865, 33.76, 33.68, 33.55, 33.475, 33.335, 33.285, 33.18, 33.055, 32.925, 32.855, 32.745, 32.62, 32.49, 32.435, 32.345, 32.26, 32.165, 32.055, 31.985, 31.885, 31.835, 31.69, 31.585, 31.485, 31.385, 31.27, 31.205, 31.105, 31.02, 30.935, 30.87, 30.8, 30.695, 30.6, 30.54, 30.47, 30.33, 30.265, 30.195, 30.08, 30.005, 29.92, 29.775, 29.675, 29.585, 29.52, 29.41, 29.31, 29.205, 29.155, 29.05, 28.995, 28.945, 28.85, 28.78, 28.705, 28.67, 28.565, 28.515, 28.445, 28.39, 28.335, 28.27, 28.23, 28.18, 28.11, 28.01, 27.94, 27.88, 27.84, 27.755, 27.705, 27.615, 27.575, 27.44, 27.375, 27.32, 27.235, 27.15, 27.08, 27.02, 26.93, 26.845, 26.765, 26.7, 26.61, 26.535, 26.485, 26.45, 26.35, 26.285, 26.16, 26.105, 26.06, 26.01, 25.955, 25.865, 25.805, 25.76, 25.705, 25.665, 25.62, 25.555, 25.52, 25.46, 25.37, 25.34, 25.295, 25.225, 25.16, 25.13, 25.04, 24.985, 24.94, 24.85, 24.8, 24.72, 24.69, 24.615, 24.555, 24.505, 24.42, 24.37, 24.305, 24.27, 24.195, 24.14, 24.115, 24.07, 24.0, 23.965, 23.9, 23.84, 23.72, 23.63, 23.525, 23.465, 23.43, 23.385, 23.34, 23.25, 23.185, 23.15, 23.105, 23.025, 22.985, 22.945, 22.895, 22.815, 22.78, 22.715, 22.65, 22.61, 22.53, 22.475, 22.435, 22.4, 22.325, 22.28, 22.26, 22.215, 22.17, 22.125, 22.095, 22.025, 21.99, 21.935, 21.89, 21.83, 21.735, 21.69, 21.66, 21.59, 21.54, 21.49, 21.435, 21.355, 21.335, 21.275, 21.22, 21.165, 21.14, 21.075, 21.01, 20.96, 20.915, 20.84, 20.815, 20.775, 20.74, 20.65, 20.605, 20.57, 20.52, 20.49, 20.445, 20.405, 20.36, 20.305, 20.255, 20.195, 20.16, 20.12, 20.07, 20.02, 19.965, 19.935, 19.9, 19.88, 19.855, 19.795, 19.745, 19.72, 19.685, 19.655, 19.605, 19.545, 19.52, 19.43, 19.36, 19.325, 19.3, 19.265, 19.24, 19.2, 19.165, 19.15, 19.13, 19.09, 19.04, 19.035, 18.995, 18.98, 18.93, 18.905, 18.875, 18.845, 18.795, 18.77, 18.73, 18.695, 18.66, 18.64, 18.63, 18.595, 18.565, 18.545, 18.51, 18.475, 18.43, 18.38, 18.355, 18.34, 18.34, 18.315, 18.305, 18.275, 18.245, 18.225, 18.215, 18.205, 18.19, 18.165, 18.14, 18.105, 18.09, 18.07, 18.05, 18.045, 18.02, 17.995, 17.96, 17.945, 17.91, 17.875, 17.855, 17.83, 17.815, 17.785, 17.76, 17.73, 17.7, 17.665, 17.62, 17.595, 17.575, 17.555, 17.525, 17.505, 17.48, 17.465, 17.46, 17.445, 17.43, 17.385, 17.35, 17.31, 17.255, 17.205, 17.19, 17.145, 17.13, 17.115, 17.095, 17.075, 17.05, 17.035, 17.02, 17.005, 16.985, 16.96, 16.93, 16.9, 16.875, 16.825, 16.78, 16.755, 16.745, 16.735, 16.715, 16.7, 16.685, 16.67, 16.665, 16.645, 16.605, 16.59, 16.575, 16.555, 16.55, 16.535, 16.5, 16.44, 16.43, 16.405, 16.39, 16.35, 16.325, 16.31, 16.305, 16.295, 16.275, 16.24, 16.22, 16.215, 16.18, 16.16, 16.145, 16.135, 16.11, 16.095, 16.06, 16.03, 16.015, 16.015, 16.005, 15.985, 15.97, 15.955, 15.935, 15.92, 15.9, 15.88, 15.87, 15.85, 15.835, 15.795, 15.755, 15.745, 15.735, 15.72, 15.705, 15.675, 15.65, 15.63, 15.62, 15.615, 15.61, 15.595, 15.585, 15.57, 15.56, 15.53, 15.5, 15.48, 15.48, 15.46, 15.445, 15.435, 15.43, 15.425, 15.42, 15.41, 15.39, 15.38, 15.375, 15.365, 15.335, 15.325, 15.315, 15.3, 15.29, 15.275, 15.255, 15.25, 15.225, 15.21, 15.195, 15.18, 15.16, 15.145, 15.135, 15.125, 15.12, 15.11, 15.085, 15.075, 15.06, 15.035, 15.01, 15.005, 15.005, 15.0, 14.97, 14.955, 14.935, 14.93, 14.92, 14.9, 14.89, 14.88, 14.86, 14.845, 14.84, 14.82, 14.8, 14.785, 14.78, 14.775, 14.77, 14.755, 14.73, 14.71, 14.68, 14.67, 14.655, 14.645, 14.645, 14.645, 14.64, 14.635, 14.62, 14.605, 14.59, 14.59, 14.585, 14.58, 14.57, 14.555, 14.55, 14.53, 14.52, 14.51, 14.485, 14.47, 14.46, 14.44, 14.43, 14.4, 14.395, 14.385, 14.37, 14.355, 14.345, 14.33, 14.33, 14.33, 14.32, 14.31, 14.295, 14.295, 14.275, 14.265, 14.255, 14.25, 14.22, 14.215, 14.21, 14.195, 14.195, 14.185, 14.155, 14.155, 14.14, 14.13, 14.11, 14.095, 14.095, 14.09, 14.075, 14.07, 14.06, 14.045, 14.04, 14.04, 14.03, 14.025, 14.025, 14.025, 14.015, 14.005, 13.995, 13.99, 13.985, 13.95, 13.945, 13.94, 13.925, 13.925, 13.9, 13.89, 13.875, 13.865, 13.855, 13.85, 13.84, 13.84, 13.83, 13.83, 13.815, 13.81, 13.795, 13.78, 13.775, 13.77, 13.76, 13.745, 13.74, 13.725, 13.725, 13.72, 13.71, 13.695, 13.69, 13.68, 13.665, 13.655, 13.645, 13.64, 13.625, 13.605, 13.585, 13.58, 13.58, 13.57, 13.56, 13.555, 13.55, 13.525, 13.515, 13.505, 13.48, 13.47, 13.465, 13.465, 13.465, 13.455, 13.45, 13.445, 13.44, 13.43, 13.43, 13.42, 13.41, 13.385, 13.38, 13.365, 13.36, 13.355, 13.345, 13.34, 13.33, 13.325, 13.32, 13.31, 13.29, 13.285, 13.275, 13.27, 13.25, 13.245, 13.24, 13.23, 13.225, 13.22, 13.2, 13.19, 13.17, 13.17, 13.165, 13.165, 13.165, 13.16, 13.155, 13.15, 13.145, 13.135, 13.11, 13.105, 13.105, 13.105, 13.1, 13.1, 13.095, 13.095, 13.09, 13.075, 13.07, 13.05, 13.05, 13.045, 13.035, 13.015, 12.99, 12.99, 12.98, 12.965, 12.965, 12.955, 12.94, 12.93, 12.92, 12.915, 12.89, 12.885, 12.885, 12.88, 12.875, 12.875, 12.875, 12.87, 12.85, 12.835, 12.835, 12.82, 12.82, 12.81, 12.8, 12.795, 12.775, 12.77, 12.755, 12.75, 12.745, 12.745, 12.745, 12.73, 12.725, 12.725, 12.72, 12.715, 12.71, 12.71, 12.71, 12.7, 12.7, 12.695, 12.685, 12.685, 12.68, 12.675, 12.675, 12.655, 12.65, 12.645, 12.635, 12.635, 12.635, 12.635, 12.635, 12.625, 12.625, 12.62, 12.61, 12.605, 12.605, 12.6, 12.595, 12.595, 12.585, 12.575, 12.575, 12.575, 12.565, 12.56, 12.555, 12.555, 12.555, 12.55, 12.545, 12.545, 12.54, 12.53, 12.52, 12.52, 12.52, 12.515, 12.51, 12.505, 12.5, 12.49, 12.49, 12.485, 12.465, 12.465, 12.455, 12.455, 12.445, 12.44, 12.44, 12.44, 12.44, 12.435, 12.43, 12.425, 12.42, 12.42, 12.41, 12.41, 12.41, 12.405, 12.4, 12.4, 12.4, 12.395, 12.395, 12.395, 12.395, 12.39, 12.385, 12.385, 12.385, 12.38, 12.38, 12.365, 12.365, 12.36, 12.355]

    
    175
chr_len = 200 74.0
chr_len_SD = 1001 74.0
chr_len_Q1_Q2_Q3 = 1001 = 44.0 63.0 88.25
last_chr_len_zero = 0.0 %
[174.0, 173.085, 172.84, 172.52, 172.485, 172.53, 172.335, 171.565, 171.3, 171.51, 171.075, 170.87, 169.5, 169.085, 168.68, 168.26, 167.82, 167.3, 167.685, 167.73, 167.565, 167.405, 167.65, 166.515, 166.105, 166.735, 166.29, 166.32, 166.75, 166.19, 167.145, 166.475, 166.135, 166.025, 165.915, 164.92, 164.665, 164.515, 164.33, 164.085, 163.485, 163.08, 162.995, 162.46, 163.49, 163.13, 162.615, 163.165, 162.225, 162.145, 161.805, 161.02, 160.59, 160.39, 160.035, 160.1, 158.95, 158.4, 158.675, 158.735, 158.57, 158.275, 157.61, 158.18, 156.51, 156.64, 155.925, 156.865, 156.535, 156.215, 155.93, 155.355, 155.355, 155.215, 154.77, 154.36, 154.74, 154.86, 154.785, 154.77, 154.715, 154.715, 153.845, 153.455, 153.535, 153.34, 153.41, 152.91, 152.71, 152.09, 151.64, 151.855, 151.12, 150.235, 150.19, 150.005, 149.66, 149.74, 149.065, 148.65, 149.225, 149.185, 148.395, 147.37, 147.045, 146.715, 146.54, 146.23, 145.945, 146.36, 146.15, 146.725, 146.58, 146.61, 146.48, 146.57, 146.14, 146.1, 145.42, 145.57, 145.25, 144.855, 144.5, 144.455, 144.01, 143.255, 143.385, 142.665, 141.725, 140.105, 139.975, 140.085, 139.295, 138.785, 138.525, 138.21, 138.725, 138.1, 137.68, 137.36, 137.745, 137.515, 137.33, 137.395, 137.0, 137.075, 136.46, 135.695, 135.215, 135.005, 134.48, 133.28, 132.305, 132.075, 132.64, 132.97, 133.145, 131.95, 132.29, 132.26, 132.39, 132.305, 131.715, 131.31, 131.28, 130.78, 130.265, 129.68, 130.585, 130.125, 129.0, 129.545, 130.035, 129.735, 129.39, 129.46, 128.695, 128.63, 127.535, 127.66, 127.44, 126.92, 126.705, 125.84, 125.355, 125.745, 124.925, 124.46, 124.075, 123.14, 122.165, 121.85, 121.92, 121.475, 121.95, 121.305, 120.56, 120.48, 120.14, 120.075, 120.26, 119.305, 118.87, 118.435, 117.97, 118.38, 117.39, 117.81, 117.65, 117.19, 116.575, 116.17, 115.88, 116.365, 116.22, 115.54, 114.595, 115.05, 115.19, 115.455, 115.435, 115.19, 114.745, 114.775, 114.5, 114.62, 114.71, 115.065, 114.545, 114.145, 114.575, 114.535, 113.71, 113.08, 112.35, 111.92, 112.47, 111.715, 111.765, 111.14, 111.015, 111.38, 110.665, 110.315, 110.255, 110.02, 109.535, 109.735, 109.625, 109.86, 109.415, 109.245, 109.09, 109.735, 109.525, 108.955, 108.2, 108.095, 107.715, 107.5, 107.55, 106.93, 107.015, 106.78, 106.295, 106.455, 106.09, 105.735, 105.355, 105.085, 105.16, 104.985, 103.81, 103.705, 102.94, 102.165, 101.76, 101.57, 101.715, 101.655, 101.17, 100.91, 100.72, 99.85, 100.765, 101.585, 101.99, 101.625, 100.98, 102.17, 102.165, 102.26, 101.55, 100.805, 100.47, 100.035, 99.17, 99.2, 98.675, 98.115, 97.36, 97.2, 96.835, 97.18, 97.835, 97.825, 98.155, 98.03, 97.68, 96.92, 96.835, 97.505, 97.465, 97.3, 97.395, 96.6, 95.69, 95.815, 95.98, 96.095, 95.56, 95.04, 94.375, 94.685, 94.775, 95.305, 94.835, 95.545, 96.01, 95.635, 95.21, 94.975, 94.39, 93.645, 94.045, 93.675, 92.92, 92.435, 92.105, 92.015, 92.13, 92.24, 91.57, 91.385, 91.17, 90.755, 90.755, 90.92, 90.705, 90.275, 89.755, 89.525, 89.88, 89.505, 89.58, 89.455, 90.335, 90.165, 89.905, 90.19, 89.795, 89.03, 88.33, 87.855, 88.05, 87.57, 87.565, 86.84, 86.865, 87.11, 87.07, 86.435, 85.92, 85.64, 85.61, 84.86, 84.805, 84.84, 84.425, 84.455, 84.4, 84.075, 84.01, 83.53, 84.105, 83.37, 83.385, 82.995, 83.14, 82.925, 81.96, 81.815, 81.575, 81.815, 81.655, 81.715, 81.78, 81.475, 81.485, 81.585, 81.34, 80.875, 81.355, 80.75, 79.94, 80.325, 80.105, 80.215, 79.72, 79.575, 79.33, 79.48, 80.15, 80.23, 80.58, 79.75, 80.14, 79.865, 80.04, 79.805, 79.305, 78.605, 78.91, 78.76, 78.435, 78.175, 77.86, 77.325, 77.35, 77.0, 77.23, 77.465, 77.385, 77.14, 77.485, 77.665, 77.45, 77.13, 76.79, 76.75, 76.505, 76.66, 76.675, 76.49, 76.505, 76.315, 76.01, 76.26, 75.96, 76.215, 75.77, 75.345, 74.81, 74.83, 74.135, 73.95, 73.68, 73.715, 73.455, 73.315, 73.35, 73.44, 73.09, 73.015, 73.425, 73.565, 73.09, 72.8, 72.05, 71.87, 72.085, 72.05, 72.125, 72.04, 71.445, 71.765, 71.96, 71.415, 71.335, 70.515, 70.64, 70.12, 70.61, 71.315, 71.38, 71.285, 71.02, 70.775, 70.555, 70.77, 70.55, 70.305, 70.945, 71.34, 71.425, 71.57, 71.495, 71.95, 72.01, 71.4, 71.345, 71.275, 71.22, 71.095, 71.39, 71.34, 71.21, 71.0, 71.045, 70.66, 70.62, 70.665, 70.95, 71.51, 71.385, 70.51, 71.055, 71.15, 70.68, 71.075, 70.72, 69.79, 70.045, 70.02, 69.78, 69.615, 69.595, 68.85, 69.12, 69.125, 69.495, 69.15, 69.405, 69.865, 69.765, 70.285, 70.185, 69.475, 69.595, 69.15, 68.915, 68.93, 69.095, 69.09, 69.695, 69.56, 69.475, 69.36, 68.76, 68.555, 69.05, 69.145, 69.305, 69.45, 69.165, 69.285, 69.42, 68.615, 68.295, 68.63, 68.57, 69.235, 68.625, 68.715, 68.415, 68.81, 69.09, 69.22, 68.865, 68.845, 68.505, 68.455, 68.575, 68.45, 67.785, 67.795, 67.69, 67.45, 67.195, 66.51, 66.73, 66.315, 66.485, 66.68, 66.74, 66.865, 66.265, 66.375, 65.975, 66.78, 66.04, 66.19, 66.43, 67.07, 67.36, 67.37, 67.955, 67.54, 66.835, 67.02, 67.08, 66.985, 66.12, 65.95, 65.465, 65.23, 65.225, 65.745, 65.515, 65.42, 65.1, 64.815, 64.685, 64.59, 64.7, 64.585, 64.9, 65.205, 65.745, 66.015, 66.14, 66.27, 65.94, 65.485, 66.315, 66.32, 66.085, 65.07, 65.395, 65.84, 65.72, 65.43, 66.285, 66.14, 65.755, 66.35, 66.165, 66.385, 66.71, 66.16, 66.475, 66.46, 66.03, 65.9, 66.11, 65.835, 65.6, 65.565, 65.175, 64.62, 63.67, 63.81, 64.145, 63.36, 63.645, 63.99, 63.35, 62.45, 62.875, 61.72, 61.135, 60.99, 60.525, 60.35, 60.455, 60.765, 61.125, 61.71, 61.9, 61.78, 61.205, 60.92, 60.505, 60.61, 60.075, 59.395, 58.935, 58.975, 58.93, 59.055, 59.345, 59.815, 60.095, 60.48, 60.095, 59.84, 60.07, 59.98, 59.975, 60.08, 59.97, 59.68, 60.135, 60.21, 59.46, 58.935, 58.88, 58.655, 58.75, 58.83, 58.635, 58.205, 58.34, 58.615, 58.725, 58.35, 57.93, 57.365, 57.49, 57.075, 56.35, 56.605, 56.605, 56.98, 57.185, 56.895, 56.97, 56.735, 56.72, 56.63, 56.26, 56.0, 56.19, 56.635, 56.695, 56.36, 56.52, 56.475, 56.8, 56.72, 56.54, 57.34, 57.64, 57.25, 57.29, 57.96, 58.01, 57.7, 58.11, 58.19, 58.79, 58.62, 58.385, 57.825, 57.945, 57.67, 58.01, 58.14, 58.33, 58.345, 58.315, 58.485, 58.54, 57.965, 57.99, 57.92, 57.83, 57.01, 57.37, 57.12, 56.965, 57.12, 57.29, 56.595, 56.77, 56.73, 56.35, 56.295, 56.2, 56.64, 56.28, 56.44, 56.49, 56.025, 55.885, 56.125, 56.255, 56.16, 56.49, 56.745, 56.955, 56.665, 56.285, 55.66, 56.25, 56.675, 56.565, 57.185, 57.285, 56.635, 56.66, 56.095, 55.855, 55.945, 55.935, 56.27, 56.59, 56.815, 57.68, 57.66, 57.575, 57.395, 56.86, 57.23, 57.38, 56.915, 57.085, 56.905, 57.0, 57.11, 57.565, 56.975, 56.61, 56.47, 57.0, 57.015, 56.545, 56.55, 56.675, 56.745, 56.715, 56.185, 55.96, 55.775, 55.23, 55.025, 55.22, 55.205, 54.955, 54.775, 54.36, 54.23, 53.805, 54.0, 54.155, 53.975, 53.705, 54.665, 53.98, 54.205, 54.305, 53.45, 53.45, 53.825, 53.44, 53.765, 53.675, 53.04, 52.715, 52.84, 52.415, 52.89, 53.21, 52.68, 52.855, 53.14, 52.96, 53.485, 53.735, 53.565, 54.24, 54.065, 54.065, 54.125, 54.77, 54.085, 53.88, 53.555, 53.17, 53.83, 53.525, 53.85, 54.4, 54.4, 54.45, 54.38, 54.66, 54.63, 55.23, 55.02, 54.605, 54.24, 54.115, 53.69, 53.69, 53.205, 53.24, 53.26, 52.575, 52.81, 52.76, 52.76, 52.355, 52.51, 52.585, 52.355, 52.345, 52.63, 52.585, 52.435, 51.91, 51.675, 51.97, 51.875, 51.775, 52.225, 51.87, 52.17, 52.805, 53.06, 52.79, 51.895, 52.14, 51.815, 51.865, 52.425, 52.83, 52.785, 52.88, 52.975, 53.325, 53.515, 54.075, 53.77, 54.54, 54.11, 54.12, 54.16, 53.895, 53.23, 53.255, 53.62, 53.2, 53.76, 53.82, 53.845, 53.51, 53.435, 53.31, 52.355, 52.18, 53.36, 52.96, 52.79, 52.975, 52.93, 52.795, 52.475, 52.6, 52.78, 53.005, 53.02, 52.605, 52.58, 52.54, 52.435, 52.73, 52.465, 52.75, 52.325, 52.195, 51.5, 51.415, 50.725, 50.93, 50.495, 50.02, 49.84, 50.045, 50.58, 50.22, 50.915, 50.6, 51.02, 50.27, 51.0, 51.24, 51.835, 52.07, 52.68, 52.4, 51.955, 51.52, 51.665, 51.835, 51.93, 51.925, 51.97, 51.78, 51.765, 50.895, 50.995, 51.135, 51.045, 51.835, 52.175, 52.365, 51.77, 51.365, 51.435, 51.625]
175 half_life chr_len_L = [367]
[174.0, 171.74, 170.075, 168.345, 166.83, 165.55, 163.825, 161.82, 159.81, 158.57, 156.9, 155.11, 153.34, 152.135, 150.36, 148.745, 147.005, 145.695, 144.49, 143.35, 141.855, 140.545, 139.295, 138.05, 136.875, 135.84, 134.78, 133.865, 133.13, 132.075, 131.455, 130.515, 129.47, 128.66, 127.915, 126.81, 126.0, 125.295, 124.495, 123.495, 122.53, 121.5, 120.33, 119.345, 118.76, 117.64, 116.635, 115.85, 114.685, 113.97, 113.065, 112.205, 111.31, 110.59, 109.66, 109.075, 108.375, 107.475, 107.12, 106.46, 105.56, 104.985, 104.425, 103.845, 102.795, 102.335, 101.5, 101.0, 100.35, 99.845, 99.3, 98.79, 98.285, 97.7, 97.125, 96.635, 96.225, 95.57, 94.98, 94.465, 93.96, 93.495, 92.93, 92.38, 91.815, 91.285, 90.875, 90.29, 89.89, 89.3, 88.56, 88.245, 87.63, 87.07, 86.64, 86.22, 85.655, 85.17, 84.645, 84.28, 83.97, 83.525, 83.095, 82.5, 82.055, 81.445, 80.985, 80.595, 80.095, 79.685, 79.325, 79.08, 78.695, 78.375, 78.02, 77.66, 77.27, 76.9, 76.585, 76.27, 75.865, 75.495, 75.165, 74.64, 74.11, 73.78, 73.475, 73.02, 72.595, 72.155, 71.675, 71.385, 70.93, 70.52, 70.2, 69.79, 69.4, 69.04, 68.66, 68.35, 68.065, 67.74, 67.355, 67.09, 66.79, 66.57, 66.24, 65.865, 65.62, 65.275, 65.075, 64.725, 64.465, 63.97, 63.75, 63.37, 63.12, 62.805, 62.475, 62.195, 61.9, 61.59, 61.385, 61.195, 60.96, 60.55, 60.23, 59.87, 59.705, 59.505, 59.27, 59.08, 58.935, 58.725, 58.485, 58.33, 58.055, 57.78, 57.435, 57.185, 57.065, 56.675, 56.46, 56.26, 56.02, 55.805, 55.59, 55.375, 55.03, 54.815, 54.495, 54.235, 54.01, 53.8, 53.62, 53.38, 53.195, 52.995, 52.8, 52.64, 52.465, 52.11, 51.965, 51.75, 51.54, 51.415, 51.265, 51.08, 50.89, 50.64, 50.365, 50.04, 49.76, 49.52, 49.4, 49.18, 48.975, 48.825, 48.68, 48.485, 48.33, 48.15, 47.905, 47.57, 47.42, 47.295, 47.07, 46.935, 46.795, 46.675, 46.51, 46.275, 46.17, 46.02, 45.83, 45.65, 45.555, 45.4, 45.29, 45.185, 45.05, 44.87, 44.64, 44.42, 44.24, 44.07, 43.975, 43.785, 43.63, 43.495, 43.29, 43.125, 43.0, 42.86, 42.725, 42.555, 42.365, 42.255, 42.14, 42.0, 41.86, 41.635, 41.54, 41.38, 41.195, 41.075, 40.87, 40.75, 40.62, 40.485, 40.345, 40.23, 40.1, 39.975, 39.83, 39.68, 39.57, 39.44, 39.35, 39.22, 39.025, 38.88, 38.68, 38.53, 38.44, 38.3, 38.245, 38.12, 37.995, 37.91, 37.83, 37.72, 37.56, 37.445, 37.26, 37.13, 37.04, 36.945, 36.835, 36.615, 36.43, 36.295, 36.16, 36.07, 36.0, 35.915, 35.755, 35.62, 35.48, 35.3, 35.165, 35.055, 34.945, 34.795, 34.67, 34.575, 34.465, 34.395, 34.285, 34.175, 34.065, 33.95, 33.84, 33.765, 33.71, 33.645, 33.525, 33.475, 33.38, 33.21, 33.11, 33.035, 32.93, 32.805, 32.69, 32.595, 32.515, 32.41, 32.29, 32.175, 32.145, 32.01, 31.9, 31.84, 31.715, 31.64, 31.57, 31.48, 31.4, 31.275, 31.15, 31.03, 30.875, 30.805, 30.745, 30.645, 30.585, 30.485, 30.4, 30.34, 30.2, 30.085, 30.02, 29.92, 29.82, 29.73, 29.675, 29.58, 29.505, 29.43, 29.315, 29.235, 29.125, 29.035, 28.94, 28.875, 28.755, 28.685, 28.625, 28.555, 28.465, 28.41, 28.35, 28.25, 28.205, 28.105, 28.015, 27.92, 27.825, 27.755, 27.72, 27.65, 27.595, 27.56, 27.46, 27.37, 27.335, 27.29, 27.225, 27.13, 27.065, 27.0, 26.945, 26.86, 26.81, 26.71, 26.62, 26.535, 26.45, 26.375, 26.325, 26.275, 26.22, 26.15, 26.06, 26.0, 25.945, 25.84, 25.775, 25.675, 25.58, 25.51, 25.46, 25.41, 25.335, 25.27, 25.185, 25.13, 25.09, 25.01, 24.965, 24.92, 24.855, 24.8, 24.75, 24.655, 24.57, 24.51, 24.43, 24.31, 24.25, 24.215, 24.165, 24.115, 24.04, 23.985, 23.91, 23.88, 23.795, 23.755, 23.68, 23.645, 23.595, 23.57, 23.54, 23.485, 23.405, 23.315, 23.3, 23.26, 23.15, 23.085, 23.02, 22.98, 22.93, 22.885, 22.82, 22.805, 22.75, 22.7, 22.655, 22.595, 22.53, 22.485, 22.425, 22.365, 22.345, 22.295, 22.265, 22.165, 22.12, 22.035, 21.98, 21.945, 21.905, 21.895, 21.84, 21.79, 21.73, 21.655, 21.635, 21.585, 21.555, 21.515, 21.47, 21.425, 21.41, 21.355, 21.305, 21.26, 21.23, 21.19, 21.07, 21.02, 20.965, 20.925, 20.895, 20.86, 20.84, 20.8, 20.765, 20.73, 20.705, 20.675, 20.65, 20.595, 20.555, 20.535, 20.47, 20.45, 20.39, 20.33, 20.265, 20.235, 20.215, 20.165, 20.13, 20.07, 20.045, 20.035, 19.995, 19.97, 19.945, 19.925, 19.885, 19.83, 19.81, 19.735, 19.69, 19.675, 19.63, 19.605, 19.6, 19.545, 19.535, 19.525, 19.49, 19.46, 19.43, 19.41, 19.39, 19.37, 19.35, 19.3, 19.265, 19.22, 19.2, 19.175, 19.135, 19.11, 19.08, 19.07, 19.05, 19.01, 18.975, 18.935, 18.905, 18.88, 18.855, 18.84, 18.825, 18.82, 18.815, 18.795, 18.75, 18.73, 18.71, 18.675, 18.645, 18.62, 18.575, 18.545, 18.5, 18.495, 18.48, 18.45, 18.43, 18.41, 18.39, 18.37, 18.355, 18.34, 18.32, 18.315, 18.3, 18.27, 18.26, 18.24, 18.215, 18.205, 18.17, 18.155, 18.095, 18.065, 18.055, 17.995, 17.975, 17.965, 17.94, 17.91, 17.89, 17.865, 17.84, 17.83, 17.81, 17.77, 17.745, 17.715, 17.695, 17.675, 17.66, 17.635, 17.635, 17.59, 17.58, 17.55, 17.525, 17.505, 17.485, 17.48, 17.43, 17.425, 17.415, 17.39, 17.37, 17.325, 17.305, 17.29, 17.285, 17.27, 17.225, 17.21, 17.18, 17.165, 17.135, 17.105, 17.065, 17.06, 17.05, 17.015, 17.0, 16.975, 16.965, 16.895, 16.88, 16.865, 16.84, 16.8, 16.8, 16.78, 16.74, 16.725, 16.715, 16.685, 16.665, 16.65, 16.63, 16.61, 16.595, 16.58, 16.57, 16.55, 16.53, 16.515, 16.48, 16.465, 16.43, 16.405, 16.365, 16.345, 16.325, 16.315, 16.27, 16.25, 16.215, 16.185, 16.185, 16.18, 16.175, 16.16, 16.14, 16.105, 16.065, 16.05, 16.035, 16.03, 15.985, 15.94, 15.915, 15.895, 15.885, 15.875, 15.85, 15.84, 15.805, 15.795, 15.77, 15.76, 15.745, 15.725, 15.7, 15.67, 15.66, 15.655, 15.64, 15.615, 15.605, 15.585, 15.575, 15.555, 15.53, 15.52, 15.505, 15.49, 15.47, 15.42, 15.42, 15.41, 15.4, 15.385, 15.375, 15.37, 15.335, 15.31, 15.29, 15.285, 15.27, 15.26, 15.24, 15.235, 15.225, 15.18, 15.17, 15.16, 15.145, 15.125, 15.115, 15.095, 15.08, 15.06, 15.04, 14.995, 14.97, 14.965, 14.96, 14.93, 14.915, 14.885, 14.865, 14.835, 14.81, 14.79, 14.77, 14.77, 14.76, 14.755, 14.75, 14.74, 14.715, 14.715, 14.695, 14.68, 14.655, 14.65, 14.63, 14.62, 14.61, 14.605, 14.595, 14.58, 14.58, 14.57, 14.56, 14.55, 14.525, 14.515, 14.495, 14.485, 14.47, 14.46, 14.43, 14.385, 14.385, 14.365, 14.355, 14.35, 14.34, 14.335, 14.335, 14.33, 14.32, 14.31, 14.285, 14.26, 14.24, 14.23, 14.225, 14.225, 14.215, 14.21, 14.205, 14.195, 14.185, 14.175, 14.175, 14.175, 14.165, 14.155, 14.15, 14.13, 14.12, 14.11, 14.075, 14.06, 14.05, 14.035, 14.03, 14.015, 14.015, 13.995, 13.99, 13.965, 13.96, 13.955, 13.94, 13.935, 13.915, 13.915, 13.905, 13.89, 13.89, 13.88, 13.87, 13.855, 13.85, 13.825, 13.795, 13.79, 13.78, 13.75, 13.74, 13.725, 13.715, 13.715, 13.705, 13.695, 13.695, 13.695, 13.665, 13.65, 13.64, 13.62, 13.62, 13.61, 13.58, 13.58, 13.57, 13.565, 13.56, 13.56, 13.545, 13.535, 13.525, 13.515, 13.495, 13.49, 13.49, 13.49, 13.48, 13.475, 13.475, 13.455, 13.445, 13.44, 13.435, 13.415, 13.415, 13.415, 13.415, 13.415, 13.41, 13.39, 13.375, 13.375, 13.365, 13.355, 13.35, 13.335, 13.33, 13.33, 13.32, 13.315, 13.305, 13.3, 13.295, 13.295, 13.285, 13.275, 13.27, 13.265, 13.26, 13.26, 13.24, 13.24, 13.225, 13.215, 13.21, 13.205, 13.19, 13.18, 13.175, 13.165, 13.15, 13.135, 13.125, 13.12, 13.115, 13.115, 13.105, 13.095, 13.095, 13.09, 13.085, 13.085, 13.075, 13.075, 13.06, 13.06, 13.05, 13.045, 13.04, 13.035, 13.03, 13.02, 13.01, 13.01, 13.005, 13.0, 12.985, 12.985, 12.97, 12.96, 12.96, 12.955, 12.955, 12.955, 12.95, 12.945, 12.935, 12.925, 12.92, 12.92, 12.915, 12.91, 12.9, 12.9, 12.895, 12.88, 12.875, 12.875, 12.87, 12.86, 12.85, 12.835, 12.835, 12.835, 12.825, 12.82, 12.815, 12.81, 12.795, 12.785, 12.78, 12.78, 12.775, 12.775, 12.77, 12.765, 12.76, 12.755, 12.75, 12.75, 12.75, 12.75, 12.74, 12.735, 12.73, 12.73, 12.725, 12.71, 12.705]
175 half_life L_unique_L = [84, 208, 357, 523, 745]
[174.0, 171.74, 170.075, 168.345, 166.83, 165.55, 163.825, 161.82, 159.81, 158.57, 156.9, 155.11, 153.34, 152.135, 150.36, 148.745, 147.005, 145.695, 144.49, 143.35, 141.855, 140.545, 139.295, 138.05, 136.875, 135.84, 134.78, 133.865, 133.13, 132.075, 131.455, 130.515, 129.47, 128.66, 127.915, 126.81, 126.0, 125.295, 124.495, 123.495, 122.53, 121.5, 120.33, 119.345, 118.76, 117.64, 116.635, 115.85, 114.685, 113.97, 113.065, 112.205, 111.31, 110.59, 109.66, 109.075, 108.375, 107.475, 107.12, 106.46, 105.56, 104.985, 104.425, 103.845, 102.795, 102.335, 101.5, 101.0, 100.35, 99.845, 99.3, 98.79, 98.285, 97.7, 97.125, 96.635, 96.225, 95.57, 94.98, 94.465, 93.96, 93.495, 92.93, 92.38, 91.815, 91.285, 90.875, 90.29, 89.89, 89.3, 88.56, 88.245, 87.63, 87.07, 86.64, 86.22, 85.655, 85.17, 84.645, 84.28, 83.97, 83.525, 83.095, 82.5, 82.055, 81.445, 80.985, 80.595, 80.095, 79.685, 79.325, 79.08, 78.695, 78.375, 78.02, 77.66, 77.27, 76.9, 76.585, 76.27, 75.865, 75.495, 75.165, 74.64, 74.11, 73.78, 73.475, 73.02, 72.595, 72.155, 71.675, 71.385, 70.93, 70.52, 70.2, 69.79, 69.4, 69.04, 68.66, 68.35, 68.065, 67.74, 67.355, 67.09, 66.79, 66.57, 66.24, 65.865, 65.62, 65.275, 65.075, 64.725, 64.465, 63.97, 63.75, 63.37, 63.12, 62.805, 62.475, 62.195, 61.9, 61.59, 61.385, 61.195, 60.96, 60.55, 60.23, 59.87, 59.705, 59.505, 59.27, 59.08, 58.935, 58.725, 58.485, 58.33, 58.055, 57.78, 57.435, 57.185, 57.065, 56.675, 56.46, 56.26, 56.02, 55.805, 55.59, 55.375, 55.03, 54.815, 54.495, 54.235, 54.01, 53.8, 53.62, 53.38, 53.195, 52.995, 52.8, 52.64, 52.465, 52.11, 51.965, 51.75, 51.54, 51.415, 51.265, 51.08, 50.89, 50.64, 50.365, 50.04, 49.76, 49.52, 49.4, 49.18, 48.975, 48.825, 48.68, 48.485, 48.33, 48.15, 47.905, 47.57, 47.42, 47.295, 47.07, 46.935, 46.795, 46.675, 46.51, 46.275, 46.17, 46.02, 45.83, 45.65, 45.555, 45.4, 45.29, 45.185, 45.05, 44.87, 44.64, 44.42, 44.24, 44.07, 43.975, 43.785, 43.63, 43.495, 43.29, 43.125, 43.0, 42.86, 42.725, 42.555, 42.365, 42.255, 42.14, 42.0, 41.86, 41.635, 41.54, 41.38, 41.195, 41.075, 40.87, 40.75, 40.62, 40.485, 40.345, 40.23, 40.1, 39.975, 39.83, 39.68, 39.57, 39.44, 39.35, 39.22, 39.025, 38.88, 38.68, 38.53, 38.44, 38.3, 38.245, 38.12, 37.995, 37.91, 37.83, 37.72, 37.56, 37.445, 37.26, 37.13, 37.04, 36.945, 36.835, 36.615, 36.43, 36.295, 36.16, 36.07, 36.0, 35.915, 35.755, 35.62, 35.48, 35.3, 35.165, 35.055, 34.945, 34.795, 34.67, 34.575, 34.465, 34.395, 34.285, 34.175, 34.065, 33.95, 33.84, 33.765, 33.71, 33.645, 33.525, 33.475, 33.38, 33.21, 33.11, 33.035, 32.93, 32.805, 32.69, 32.595, 32.515, 32.41, 32.29, 32.175, 32.145, 32.01, 31.9, 31.84, 31.715, 31.64, 31.57, 31.48, 31.4, 31.275, 31.15, 31.03, 30.875, 30.805, 30.745, 30.645, 30.585, 30.485, 30.4, 30.34, 30.2, 30.085, 30.02, 29.92, 29.82, 29.73, 29.675, 29.58, 29.505, 29.43, 29.315, 29.235, 29.125, 29.035, 28.94, 28.875, 28.755, 28.685, 28.625, 28.555, 28.465, 28.41, 28.35, 28.25, 28.205, 28.105, 28.015, 27.92, 27.825, 27.755, 27.72, 27.65, 27.595, 27.56, 27.46, 27.37, 27.335, 27.29, 27.225, 27.13, 27.065, 27.0, 26.945, 26.86, 26.81, 26.71, 26.62, 26.535, 26.45, 26.375, 26.325, 26.275, 26.22, 26.15, 26.06, 26.0, 25.945, 25.84, 25.775, 25.675, 25.58, 25.51, 25.46, 25.41, 25.335, 25.27, 25.185, 25.13, 25.09, 25.01, 24.965, 24.92, 24.855, 24.8, 24.75, 24.655, 24.57, 24.51, 24.43, 24.31, 24.25, 24.215, 24.165, 24.115, 24.04, 23.985, 23.91, 23.88, 23.795, 23.755, 23.68, 23.645, 23.595, 23.57, 23.54, 23.485, 23.405, 23.315, 23.3, 23.26, 23.15, 23.085, 23.02, 22.98, 22.93, 22.885, 22.82, 22.805, 22.75, 22.7, 22.655, 22.595, 22.53, 22.485, 22.425, 22.365, 22.345, 22.295, 22.265, 22.165, 22.12, 22.035, 21.98, 21.945, 21.905, 21.895, 21.84, 21.79, 21.73, 21.655, 21.635, 21.585, 21.555, 21.515, 21.47, 21.425, 21.41, 21.355, 21.305, 21.26, 21.23, 21.19, 21.07, 21.02, 20.965, 20.925, 20.895, 20.86, 20.84, 20.8, 20.765, 20.73, 20.705, 20.675, 20.65, 20.595, 20.555, 20.535, 20.47, 20.45, 20.39, 20.33, 20.265, 20.235, 20.215, 20.165, 20.13, 20.07, 20.045, 20.035, 19.995, 19.97, 19.945, 19.925, 19.885, 19.83, 19.81, 19.735, 19.69, 19.675, 19.63, 19.605, 19.6, 19.545, 19.535, 19.525, 19.49, 19.46, 19.43, 19.41, 19.39, 19.37, 19.35, 19.3, 19.265, 19.22, 19.2, 19.175, 19.135, 19.11, 19.08, 19.07, 19.05, 19.01, 18.975, 18.935, 18.905, 18.88, 18.855, 18.84, 18.825, 18.82, 18.815, 18.795, 18.75, 18.73, 18.71, 18.675, 18.645, 18.62, 18.575, 18.545, 18.5, 18.495, 18.48, 18.45, 18.43, 18.41, 18.39, 18.37, 18.355, 18.34, 18.32, 18.315, 18.3, 18.27, 18.26, 18.24, 18.215, 18.205, 18.17, 18.155, 18.095, 18.065, 18.055, 17.995, 17.975, 17.965, 17.94, 17.91, 17.89, 17.865, 17.84, 17.83, 17.81, 17.77, 17.745, 17.715, 17.695, 17.675, 17.66, 17.635, 17.635, 17.59, 17.58, 17.55, 17.525, 17.505, 17.485, 17.48, 17.43, 17.425, 17.415, 17.39, 17.37, 17.325, 17.305, 17.29, 17.285, 17.27, 17.225, 17.21, 17.18, 17.165, 17.135, 17.105, 17.065, 17.06, 17.05, 17.015, 17.0, 16.975, 16.965, 16.895, 16.88, 16.865, 16.84, 16.8, 16.8, 16.78, 16.74, 16.725, 16.715, 16.685, 16.665, 16.65, 16.63, 16.61, 16.595, 16.58, 16.57, 16.55, 16.53, 16.515, 16.48, 16.465, 16.43, 16.405, 16.365, 16.345, 16.325, 16.315, 16.27, 16.25, 16.215, 16.185, 16.185, 16.18, 16.175, 16.16, 16.14, 16.105, 16.065, 16.05, 16.035, 16.03, 15.985, 15.94, 15.915, 15.895, 15.885, 15.875, 15.85, 15.84, 15.805, 15.795, 15.77, 15.76, 15.745, 15.725, 15.7, 15.67, 15.66, 15.655, 15.64, 15.615, 15.605, 15.585, 15.575, 15.555, 15.53, 15.52, 15.505, 15.49, 15.47, 15.42, 15.42, 15.41, 15.4, 15.385, 15.375, 15.37, 15.335, 15.31, 15.29, 15.285, 15.27, 15.26, 15.24, 15.235, 15.225, 15.18, 15.17, 15.16, 15.145, 15.125, 15.115, 15.095, 15.08, 15.06, 15.04, 14.995, 14.97, 14.965, 14.96, 14.93, 14.915, 14.885, 14.865, 14.835, 14.81, 14.79, 14.77, 14.77, 14.76, 14.755, 14.75, 14.74, 14.715, 14.715, 14.695, 14.68, 14.655, 14.65, 14.63, 14.62, 14.61, 14.605, 14.595, 14.58, 14.58, 14.57, 14.56, 14.55, 14.525, 14.515, 14.495, 14.485, 14.47, 14.46, 14.43, 14.385, 14.385, 14.365, 14.355, 14.35, 14.34, 14.335, 14.335, 14.33, 14.32, 14.31, 14.285, 14.26, 14.24, 14.23, 14.225, 14.225, 14.215, 14.21, 14.205, 14.195, 14.185, 14.175, 14.175, 14.175, 14.165, 14.155, 14.15, 14.13, 14.12, 14.11, 14.075, 14.06, 14.05, 14.035, 14.03, 14.015, 14.015, 13.995, 13.99, 13.965, 13.96, 13.955, 13.94, 13.935, 13.915, 13.915, 13.905, 13.89, 13.89, 13.88, 13.87, 13.855, 13.85, 13.825, 13.795, 13.79, 13.78, 13.75, 13.74, 13.725, 13.715, 13.715, 13.705, 13.695, 13.695, 13.695, 13.665, 13.65, 13.64, 13.62, 13.62, 13.61, 13.58, 13.58, 13.57, 13.565, 13.56, 13.56, 13.545, 13.535, 13.525, 13.515, 13.495, 13.49, 13.49, 13.49, 13.48, 13.475, 13.475, 13.455, 13.445, 13.44, 13.435, 13.415, 13.415, 13.415, 13.415, 13.415, 13.41, 13.39, 13.375, 13.375, 13.365, 13.355, 13.35, 13.335, 13.33, 13.33, 13.32, 13.315, 13.305, 13.3, 13.295, 13.295, 13.285, 13.275, 13.27, 13.265, 13.26, 13.26, 13.24, 13.24, 13.225, 13.215, 13.21, 13.205, 13.19, 13.18, 13.175, 13.165, 13.15, 13.135, 13.125, 13.12, 13.115, 13.115, 13.105, 13.095, 13.095, 13.09, 13.085, 13.085, 13.075, 13.075, 13.06, 13.06, 13.05, 13.045, 13.04, 13.035, 13.03, 13.02, 13.01, 13.01, 13.005, 13.0, 12.985, 12.985, 12.97, 12.96, 12.96, 12.955, 12.955, 12.955, 12.95, 12.945, 12.935, 12.925, 12.92, 12.92, 12.915, 12.91, 12.9, 12.9, 12.895, 12.88, 12.875, 12.875, 12.87, 12.86, 12.85, 12.835, 12.835, 12.835, 12.825, 12.82, 12.815, 12.81, 12.795, 12.785, 12.78, 12.78, 12.775, 12.775, 12.77, 12.765, 12.76, 12.755, 12.75, 12.75, 12.75, 12.75, 12.74, 12.735, 12.73, 12.73, 12.725, 12.71, 12.705]

    
    225
chr_len = 200 83.0
chr_len_SD = 1001 83.0
chr_len_Q1_Q2_Q3 = 1001 = 54.5 76.5 99.25
last_chr_len_zero = 0.0 %
[224.0, 224.275, 224.295, 224.08, 224.14, 224.33, 224.14, 223.79, 223.38, 223.565, 222.81, 222.66, 223.11, 222.11, 221.44, 220.82, 220.39, 219.77, 220.065, 220.305, 219.92, 219.135, 217.86, 218.325, 218.14, 218.31, 218.13, 218.11, 217.605, 217.31, 217.14, 216.275, 215.895, 216.32, 216.095, 215.625, 215.18, 214.805, 214.39, 214.16, 214.3, 214.07, 214.02, 212.79, 212.41, 212.05, 210.905, 210.065, 210.045, 209.425, 209.06, 208.32, 207.03, 207.15, 206.67, 206.14, 205.555, 205.24, 205.27, 204.725, 204.54, 203.41, 202.83, 202.08, 201.62, 201.155, 200.76, 200.705, 200.915, 200.49, 199.185, 198.85, 198.72, 198.815, 198.47, 198.29, 198.14, 197.57, 196.825, 195.795, 195.64, 194.94, 194.95, 194.445, 194.52, 193.925, 193.635, 192.545, 193.025, 192.175, 191.53, 191.08, 190.31, 190.16, 190.365, 190.605, 189.92, 190.445, 189.5, 188.99, 189.005, 188.83, 187.72, 187.5, 187.28, 186.415, 185.705, 185.045, 183.945, 183.77, 183.16, 183.15, 182.34, 182.665, 182.03, 182.395, 181.86, 182.255, 181.925, 181.645, 180.915, 180.23, 180.03, 179.555, 178.71, 178.02, 177.355, 176.855, 176.08, 176.39, 176.715, 176.095, 175.675, 175.99, 175.765, 175.44, 174.405, 174.125, 173.515, 173.62, 172.91, 172.595, 172.815, 172.34, 172.065, 170.83, 169.615, 168.885, 168.075, 166.775, 167.44, 167.09, 167.025, 167.17, 167.03, 166.24, 165.23, 163.265, 162.855, 163.035, 162.315, 161.445, 160.765, 160.115, 160.515, 160.525, 160.28, 160.435, 160.45, 160.56, 161.255, 160.895, 160.375, 160.475, 161.235, 160.685, 160.13, 159.42, 158.775, 158.5, 157.635, 157.745, 157.925, 157.41, 156.61, 155.785, 155.375, 155.02, 154.59, 153.27, 154.095, 153.81, 153.855, 153.14, 152.96, 152.645, 152.64, 152.02, 151.4, 150.85, 150.715, 149.92, 149.115, 148.705, 147.97, 147.84, 147.48, 147.285, 146.71, 145.91, 145.65, 145.665, 145.58, 145.285, 144.66, 144.065, 143.645, 143.6, 143.605, 143.375, 143.69, 143.415, 143.14, 143.215, 142.685, 141.22, 139.95, 140.15, 139.61, 138.855, 138.98, 137.31, 135.985, 135.97, 135.405, 136.16, 136.655, 135.98, 135.425, 134.82, 134.55, 133.975, 133.41, 133.195, 133.0, 132.13, 131.755, 131.435, 131.37, 131.085, 130.62, 130.415, 129.545, 128.445, 127.56, 127.495, 126.875, 125.915, 126.075, 126.145, 124.755, 125.335, 125.18, 124.385, 124.33, 124.04, 123.675, 123.805, 122.875, 122.91, 122.46, 122.405, 122.03, 121.865, 121.275, 121.065, 120.755, 120.55, 120.465, 120.59, 119.5, 118.72, 118.315, 117.91, 117.63, 117.8, 117.42, 117.18, 115.83, 115.515, 115.03, 115.15, 114.77, 114.495, 114.68, 114.355, 113.89, 113.38, 112.965, 112.49, 112.405, 111.74, 112.14, 111.635, 111.65, 111.21, 111.065, 111.33, 110.965, 110.25, 110.295, 110.36, 110.675, 110.395, 110.465, 109.91, 109.365, 109.19, 108.325, 107.585, 107.295, 107.35, 107.41, 107.755, 108.455, 107.44, 107.135, 106.355, 105.85, 105.8, 105.595, 106.07, 105.015, 104.79, 104.825, 104.91, 104.595, 104.215, 103.77, 103.705, 103.775, 103.645, 103.265, 103.32, 103.93, 103.86, 103.945, 104.0, 103.145, 102.85, 102.715, 102.435, 102.37, 102.475, 102.0, 101.71, 101.48, 101.15, 101.15, 100.385, 100.525, 100.48, 100.205, 99.72, 99.505, 99.76, 99.655, 99.255, 99.61, 99.26, 99.12, 98.58, 98.29, 98.2, 97.58, 97.35, 97.795, 97.565, 97.01, 97.07, 96.63, 97.065, 96.895, 96.755, 96.6, 96.675, 96.555, 96.665, 97.02, 97.045, 96.39, 96.515, 95.97, 96.01, 95.815, 95.465, 95.185, 95.535, 95.14, 94.885, 94.765, 95.67, 95.29, 95.135, 95.01, 95.135, 94.92, 94.735, 93.4, 92.775, 91.95, 91.97, 91.385, 90.52, 90.26, 90.61, 89.675, 88.875, 89.1, 88.79, 88.6, 88.43, 88.3, 88.245, 88.555, 88.71, 88.575, 88.85, 88.945, 88.79, 89.23, 89.215, 89.435, 89.785, 90.085, 89.55, 89.065, 88.71, 88.075, 88.09, 88.775, 89.32, 89.115, 89.615, 89.57, 89.07, 88.635, 88.175, 87.72, 87.275, 87.195, 86.96, 86.98, 87.1, 86.945, 86.29, 85.87, 86.405, 85.93, 86.275, 86.225, 86.475, 85.94, 86.17, 86.625, 86.595, 86.77, 86.905, 87.19, 87.2, 86.09, 85.805, 86.22, 85.835, 86.19, 86.005, 85.945, 85.7, 85.31, 85.155, 84.715, 84.995, 85.005, 85.16, 85.205, 85.365, 85.29, 84.715, 84.165, 83.39, 83.39, 83.19, 82.985, 83.125, 83.835, 83.31, 82.955, 83.34, 83.675, 83.205, 82.525, 82.195, 81.8, 81.405, 81.27, 81.765, 81.445, 81.2, 80.485, 79.77, 79.86, 79.115, 78.975, 78.535, 77.91, 78.205, 78.62, 79.395, 78.575, 78.59, 78.7, 79.775, 79.555, 79.21, 79.09, 78.74, 78.15, 78.05, 77.79, 77.725, 76.825, 76.165, 76.775, 76.455, 76.285, 76.025, 76.03, 75.53, 75.395, 75.395, 75.185, 75.155, 74.59, 74.375, 74.715, 74.65, 74.765, 74.84, 74.84, 75.26, 75.04, 74.905, 75.29, 75.925, 75.45, 75.055, 75.22, 75.485, 75.375, 75.175, 75.585, 75.45, 75.915, 75.755, 75.445, 75.0, 74.22, 73.885, 73.485, 74.18, 74.46, 74.43, 74.355, 74.255, 74.49, 73.91, 74.165, 73.95, 73.685, 73.75, 73.825, 73.395, 73.035, 73.045, 73.005, 72.635, 72.3, 72.59, 72.81, 73.14, 72.685, 72.295, 71.905, 72.035, 71.795, 71.87, 72.03, 72.16, 71.645, 70.94, 70.35, 70.83, 70.77, 70.84, 71.39, 70.385, 70.215, 70.255, 70.38, 69.8, 70.375, 70.42, 70.025, 69.42, 69.385, 69.755, 69.765, 69.475, 69.55, 69.7, 70.59, 70.715, 70.47, 70.36, 69.465, 69.525, 69.145, 69.7, 69.98, 69.66, 69.92, 70.415, 70.2, 69.7, 69.345, 69.375, 68.945, 68.5, 68.29, 68.62, 68.68, 69.335, 69.235, 68.84, 68.275, 68.125, 68.09, 68.205, 68.665, 68.635, 68.38, 68.225, 68.395, 68.91, 69.245, 68.65, 68.245, 67.87, 67.635, 67.245, 66.72, 66.65, 66.45, 66.31, 66.575, 66.8, 66.485, 66.555, 65.8, 65.745, 65.32, 65.63, 66.075, 66.175, 66.07, 66.1, 66.165, 66.76, 66.94, 66.8, 66.39, 65.795, 65.93, 65.785, 65.5, 65.325, 65.335, 65.43, 65.085, 65.555, 64.48, 64.445, 65.035, 65.325, 65.07, 65.31, 65.25, 65.615, 65.735, 65.745, 64.935, 65.25, 65.525, 65.345, 65.265, 64.44, 64.355, 64.54, 63.55, 62.925, 63.28, 63.125, 63.42, 62.93, 62.945, 62.485, 62.67, 62.255, 62.575, 62.84, 62.11, 62.075, 62.03, 62.12, 61.88, 62.085, 62.135, 61.985, 61.49, 61.685, 61.825, 62.135, 62.42, 63.09, 63.215, 63.47, 63.755, 63.57, 63.92, 63.79, 63.605, 63.845, 63.71, 63.755, 63.6, 63.8, 63.565, 62.9, 62.69, 62.65, 62.59, 62.04, 62.14, 62.265, 62.105, 62.27, 62.645, 63.01, 62.98, 63.105, 63.105, 62.845, 62.545, 62.875, 62.82, 62.67, 62.85, 62.435, 63.385, 62.965, 62.975, 62.42, 62.215, 62.195, 61.995, 62.78, 62.365, 61.995, 62.0, 61.95, 61.17, 60.96, 61.26, 61.15, 61.4, 60.935, 60.765, 60.535, 59.8, 59.205, 59.255, 58.7, 58.53, 58.53, 58.185, 58.02, 58.125, 58.325, 57.81, 57.825, 58.06, 58.085, 57.735, 57.59, 57.735, 58.175, 58.44, 58.2, 57.555, 57.21, 57.48, 57.945, 57.525, 57.34, 56.85, 56.92, 57.21, 57.53, 57.1, 57.105, 57.0, 56.59, 56.675, 57.245, 57.26, 57.65, 57.41, 57.04, 56.715, 56.785, 56.365, 56.55, 56.6, 56.515, 56.305, 56.785, 57.15, 56.775, 56.845, 56.935, 56.5, 56.585, 57.0, 57.135, 57.27, 56.965, 56.795, 56.44, 56.33, 56.32, 56.38, 56.415, 56.13, 56.4, 56.655, 56.095, 55.82, 55.77, 55.875, 56.115, 55.955, 56.41, 56.57, 56.45, 56.42, 56.06, 56.195, 56.585, 56.64, 56.79, 56.49, 56.31, 56.305, 56.345, 56.11, 56.185, 56.125, 55.85, 55.95, 56.25, 56.15, 56.315, 56.35, 56.03, 55.505, 54.83, 54.72, 54.53, 54.34, 54.515, 54.875, 54.94, 54.675, 54.735, 54.91, 54.965, 55.65, 55.175, 54.355, 54.305, 53.46, 53.655, 53.11, 53.365, 53.435, 53.185, 53.545, 52.93, 52.83, 52.56, 52.65, 53.045, 52.77, 52.81, 52.7, 53.085, 52.77, 52.95, 52.745, 52.965, 52.71, 52.755, 52.79, 52.905, 53.335, 53.415, 53.02, 53.29, 53.03, 53.315, 53.86, 54.28, 53.995, 54.155, 54.78, 54.505, 54.145, 54.045, 53.985, 53.99, 54.35, 54.12, 53.01, 52.765, 53.11, 52.95, 52.965, 53.22, 52.99, 53.08, 53.27, 53.06, 53.23, 53.315, 53.48, 53.345, 53.705, 54.14, 54.21, 54.07, 53.82, 54.01, 54.355, 54.105, 54.355, 54.51, 54.115, 53.62, 53.34, 52.575, 52.645, 52.295, 51.995, 52.3, 51.865, 51.505, 51.875, 51.585, 51.455, 51.8, 51.675, 51.43, 51.025, 51.355, 50.64, 50.96, 51.09, 50.61, 50.605, 50.505, 50.715, 51.215, 51.62, 51.39, 51.95, 51.775, 51.605, 51.995, 52.03, 52.055, 52.545]
225 half_life chr_len_L = [301, 856]
[224.0, 221.91, 220.175, 218.51, 216.74, 214.975, 213.29, 211.4, 209.565, 208.055, 206.1, 204.555, 203.24, 201.6, 199.785, 197.58, 196.075, 194.21, 192.78, 191.725, 190.39, 188.83, 187.505, 186.35, 185.07, 183.995, 183.005, 181.615, 180.185, 178.9, 177.73, 176.11, 174.87, 173.94, 172.92, 171.65, 170.095, 169.095, 167.99, 166.715, 165.48, 164.69, 163.72, 162.68, 161.445, 160.19, 158.52, 157.315, 156.365, 155.4, 154.205, 153.355, 152.105, 150.985, 149.985, 148.995, 148.08, 147.265, 146.53, 145.15, 144.205, 143.26, 142.39, 141.375, 140.565, 139.8, 139.12, 138.21, 137.395, 136.565, 135.685, 135.125, 134.445, 133.78, 132.785, 131.965, 131.095, 130.27, 129.26, 128.335, 127.7, 126.885, 126.305, 125.66, 124.975, 124.21, 123.56, 122.67, 122.175, 121.24, 120.325, 119.53, 118.75, 118.195, 117.54, 117.1, 116.49, 116.07, 115.335, 114.745, 114.165, 113.59, 112.935, 112.295, 111.635, 111.03, 110.59, 110.1, 109.49, 108.935, 108.09, 107.35, 106.805, 106.295, 105.63, 105.035, 104.46, 104.1, 103.53, 103.08, 102.54, 101.98, 101.515, 101.02, 100.415, 99.805, 99.185, 98.87, 98.295, 97.905, 97.64, 97.115, 96.815, 96.335, 95.755, 95.4, 94.8, 94.335, 93.87, 93.42, 92.87, 92.455, 91.945, 91.495, 91.035, 90.44, 90.085, 89.66, 89.14, 88.59, 88.185, 87.825, 87.52, 87.015, 86.655, 86.25, 85.835, 85.28, 84.825, 84.555, 84.13, 83.69, 83.32, 82.88, 82.595, 82.125, 81.735, 81.475, 81.18, 80.84, 80.395, 79.97, 79.655, 79.225, 78.875, 78.535, 78.285, 77.99, 77.595, 77.14, 76.695, 76.37, 76.035, 75.75, 75.515, 75.075, 74.58, 74.195, 73.82, 73.355, 73.0, 72.8, 72.525, 72.19, 71.895, 71.625, 71.23, 70.93, 70.515, 70.105, 69.7, 69.405, 69.175, 68.89, 68.585, 68.33, 68.115, 67.965, 67.575, 67.32, 67.085, 66.87, 66.615, 66.28, 66.01, 65.705, 65.33, 65.15, 64.905, 64.67, 64.335, 64.135, 63.89, 63.64, 63.33, 62.92, 62.53, 62.295, 61.995, 61.765, 61.5, 61.265, 60.895, 60.61, 60.23, 59.925, 59.595, 59.33, 59.07, 58.775, 58.555, 58.33, 58.175, 57.97, 57.845, 57.58, 57.255, 57.045, 56.8, 56.55, 56.36, 56.115, 55.94, 55.69, 55.44, 55.185, 54.945, 54.705, 54.48, 54.28, 54.03, 53.705, 53.47, 53.245, 52.98, 52.75, 52.54, 52.355, 52.11, 51.965, 51.75, 51.59, 51.34, 51.115, 50.885, 50.71, 50.595, 50.355, 50.19, 50.055, 49.83, 49.615, 49.4, 49.185, 49.055, 48.845, 48.665, 48.525, 48.27, 48.15, 47.925, 47.725, 47.535, 47.375, 47.155, 46.965, 46.83, 46.64, 46.475, 46.26, 46.045, 45.84, 45.69, 45.6, 45.48, 45.255, 45.075, 44.885, 44.73, 44.585, 44.48, 44.355, 44.235, 44.005, 43.87, 43.77, 43.595, 43.475, 43.145, 42.965, 42.74, 42.6, 42.48, 42.31, 42.15, 41.995, 41.86, 41.715, 41.535, 41.4, 41.275, 41.095, 40.95, 40.765, 40.555, 40.42, 40.25, 40.08, 39.935, 39.76, 39.64, 39.475, 39.34, 39.175, 39.12, 38.97, 38.855, 38.725, 38.57, 38.505, 38.385, 38.29, 38.125, 38.03, 37.875, 37.71, 37.52, 37.375, 37.28, 37.165, 37.1, 36.94, 36.855, 36.695, 36.58, 36.475, 36.4, 36.27, 36.12, 36.01, 35.905, 35.78, 35.63, 35.49, 35.335, 35.24, 35.16, 35.08, 34.955, 34.84, 34.6, 34.535, 34.415, 34.325, 34.21, 34.11, 33.99, 33.87, 33.785, 33.66, 33.59, 33.51, 33.415, 33.305, 33.155, 33.095, 33.005, 32.915, 32.79, 32.66, 32.555, 32.525, 32.42, 32.365, 32.3, 32.215, 32.105, 31.995, 31.865, 31.76, 31.655, 31.555, 31.46, 31.335, 31.27, 31.195, 31.055, 30.925, 30.805, 30.76, 30.675, 30.515, 30.43, 30.33, 30.24, 30.11, 30.025, 29.925, 29.825, 29.745, 29.71, 29.65, 29.57, 29.455, 29.395, 29.33, 29.255, 29.2, 29.14, 29.065, 29.01, 28.935, 28.875, 28.775, 28.675, 28.595, 28.58, 28.515, 28.475, 28.41, 28.35, 28.285, 28.22, 28.115, 28.03, 27.945, 27.88, 27.85, 27.785, 27.73, 27.645, 27.58, 27.51, 27.435, 27.385, 27.335, 27.285, 27.195, 27.115, 27.06, 26.975, 26.925, 26.845, 26.8, 26.745, 26.715, 26.635, 26.6, 26.58, 26.48, 26.445, 26.405, 26.36, 26.305, 26.275, 26.225, 26.16, 26.065, 25.97, 25.93, 25.895, 25.85, 25.815, 25.725, 25.685, 25.615, 25.565, 25.51, 25.47, 25.4, 25.34, 25.295, 25.225, 25.17, 25.095, 25.04, 25.0, 24.94, 24.835, 24.77, 24.695, 24.655, 24.615, 24.58, 24.505, 24.41, 24.37, 24.34, 24.235, 24.135, 24.08, 24.04, 24.005, 23.925, 23.875, 23.825, 23.785, 23.725, 23.655, 23.55, 23.46, 23.415, 23.335, 23.265, 23.225, 23.185, 23.105, 23.07, 23.02, 22.955, 22.9, 22.845, 22.81, 22.785, 22.73, 22.68, 22.635, 22.56, 22.49, 22.45, 22.41, 22.385, 22.335, 22.3, 22.26, 22.225, 22.19, 22.15, 22.12, 22.065, 21.99, 21.985, 21.935, 21.905, 21.865, 21.825, 21.77, 21.69, 21.665, 21.625, 21.565, 21.515, 21.485, 21.445, 21.425, 21.375, 21.35, 21.305, 21.255, 21.22, 21.185, 21.145, 21.13, 21.085, 21.05, 21.005, 20.945, 20.905, 20.875, 20.825, 20.8, 20.73, 20.72, 20.685, 20.66, 20.64, 20.62, 20.585, 20.54, 20.51, 20.47, 20.43, 20.4, 20.37, 20.32, 20.255, 20.225, 20.21, 20.165, 20.13, 20.1, 20.045, 19.985, 19.92, 19.855, 19.83, 19.79, 19.76, 19.705, 19.675, 19.65, 19.62, 19.59, 19.565, 19.525, 19.51, 19.455, 19.43, 19.41, 19.37, 19.345, 19.33, 19.29, 19.265, 19.205, 19.17, 19.125, 19.085, 19.055, 19.035, 19.01, 18.97, 18.93, 18.895, 18.875, 18.86, 18.835, 18.815, 18.79, 18.74, 18.715, 18.69, 18.645, 18.63, 18.605, 18.545, 18.525, 18.43, 18.42, 18.4, 18.37, 18.355, 18.315, 18.295, 18.28, 18.235, 18.21, 18.18, 18.165, 18.11, 18.095, 18.055, 18.025, 18.005, 17.98, 17.965, 17.95, 17.925, 17.895, 17.87, 17.85, 17.835, 17.83, 17.8, 17.765, 17.7, 17.645, 17.63, 17.585, 17.555, 17.53, 17.49, 17.435, 17.42, 17.415, 17.405, 17.405, 17.4, 17.37, 17.355, 17.31, 17.295, 17.285, 17.255, 17.235, 17.21, 17.2, 17.195, 17.145, 17.12, 17.115, 17.085, 17.065, 17.045, 17.015, 16.97, 16.945, 16.915, 16.905, 16.88, 16.855, 16.83, 16.82, 16.805, 16.755, 16.75, 16.705, 16.68, 16.655, 16.64, 16.625, 16.595, 16.54, 16.51, 16.495, 16.49, 16.475, 16.45, 16.445, 16.44, 16.41, 16.39, 16.365, 16.345, 16.33, 16.315, 16.285, 16.27, 16.265, 16.265, 16.245, 16.195, 16.175, 16.165, 16.14, 16.125, 16.11, 16.085, 16.08, 16.075, 16.05, 16.035, 16.02, 16.01, 16.01, 16.0, 15.99, 15.97, 15.96, 15.95, 15.935, 15.915, 15.915, 15.9, 15.88, 15.86, 15.82, 15.79, 15.755, 15.73, 15.71, 15.675, 15.66, 15.63, 15.6, 15.58, 15.545, 15.505, 15.49, 15.485, 15.465, 15.45, 15.445, 15.435, 15.415, 15.41, 15.39, 15.355, 15.35, 15.325, 15.325, 15.3, 15.285, 15.265, 15.24, 15.22, 15.2, 15.19, 15.185, 15.17, 15.155, 15.15, 15.12, 15.105, 15.085, 15.06, 15.05, 15.04, 15.015, 15.0, 14.99, 14.975, 14.965, 14.94, 14.925, 14.92, 14.9, 14.89, 14.87, 14.87, 14.85, 14.845, 14.83, 14.83, 14.8, 14.79, 14.785, 14.775, 14.755, 14.745, 14.74, 14.725, 14.695, 14.665, 14.655, 14.64, 14.64, 14.615, 14.595, 14.585, 14.575, 14.565, 14.56, 14.545, 14.535, 14.51, 14.5, 14.49, 14.48, 14.475, 14.46, 14.455, 14.435, 14.41, 14.38, 14.365, 14.36, 14.35, 14.345, 14.335, 14.325, 14.32, 14.315, 14.31, 14.305, 14.285, 14.285, 14.275, 14.255, 14.25, 14.24, 14.225, 14.215, 14.205, 14.185, 14.18, 14.175, 14.145, 14.14, 14.13, 14.12, 14.1, 14.1, 14.09, 14.075, 14.055, 14.045, 14.045, 14.04, 13.995, 13.99, 13.975, 13.96, 13.95, 13.93, 13.92, 13.915, 13.915, 13.885, 13.86, 13.855, 13.835, 13.83, 13.825, 13.82, 13.815, 13.81, 13.81, 13.795, 13.79, 13.775, 13.77, 13.765, 13.755, 13.745, 13.74, 13.73, 13.72, 13.715, 13.705, 13.7, 13.7, 13.695, 13.695, 13.68, 13.67, 13.67, 13.665, 13.64, 13.625, 13.62, 13.61, 13.605, 13.6, 13.585, 13.57, 13.56, 13.555, 13.55, 13.55, 13.535, 13.53, 13.525, 13.51, 13.5, 13.49, 13.485, 13.475, 13.465, 13.455, 13.45, 13.425, 13.415, 13.415, 13.415, 13.41, 13.38, 13.365, 13.355, 13.345, 13.34, 13.32, 13.3, 13.3, 13.3, 13.295, 13.28, 13.27, 13.27, 13.27, 13.25, 13.245, 13.23, 13.22, 13.205, 13.19, 13.185, 13.18, 13.17, 13.15, 13.15, 13.14, 13.13, 13.13, 13.13, 13.12, 13.105, 13.105, 13.1, 13.09, 13.09]
225 half_life L_unique_L = [96, 224, 363, 532, 727, 970]
[224.0, 221.91, 220.175, 218.51, 216.74, 214.975, 213.29, 211.4, 209.565, 208.055, 206.1, 204.555, 203.24, 201.6, 199.785, 197.58, 196.075, 194.21, 192.78, 191.725, 190.39, 188.83, 187.505, 186.35, 185.07, 183.995, 183.005, 181.615, 180.185, 178.9, 177.73, 176.11, 174.87, 173.94, 172.92, 171.65, 170.095, 169.095, 167.99, 166.715, 165.48, 164.69, 163.72, 162.68, 161.445, 160.19, 158.52, 157.315, 156.365, 155.4, 154.205, 153.355, 152.105, 150.985, 149.985, 148.995, 148.08, 147.265, 146.53, 145.15, 144.205, 143.26, 142.39, 141.375, 140.565, 139.8, 139.12, 138.21, 137.395, 136.565, 135.685, 135.125, 134.445, 133.78, 132.785, 131.965, 131.095, 130.27, 129.26, 128.335, 127.7, 126.885, 126.305, 125.66, 124.975, 124.21, 123.56, 122.67, 122.175, 121.24, 120.325, 119.53, 118.75, 118.195, 117.54, 117.1, 116.49, 116.07, 115.335, 114.745, 114.165, 113.59, 112.935, 112.295, 111.635, 111.03, 110.59, 110.1, 109.49, 108.935, 108.09, 107.35, 106.805, 106.295, 105.63, 105.035, 104.46, 104.1, 103.53, 103.08, 102.54, 101.98, 101.515, 101.02, 100.415, 99.805, 99.185, 98.87, 98.295, 97.905, 97.64, 97.115, 96.815, 96.335, 95.755, 95.4, 94.8, 94.335, 93.87, 93.42, 92.87, 92.455, 91.945, 91.495, 91.035, 90.44, 90.085, 89.66, 89.14, 88.59, 88.185, 87.825, 87.52, 87.015, 86.655, 86.25, 85.835, 85.28, 84.825, 84.555, 84.13, 83.69, 83.32, 82.88, 82.595, 82.125, 81.735, 81.475, 81.18, 80.84, 80.395, 79.97, 79.655, 79.225, 78.875, 78.535, 78.285, 77.99, 77.595, 77.14, 76.695, 76.37, 76.035, 75.75, 75.515, 75.075, 74.58, 74.195, 73.82, 73.355, 73.0, 72.8, 72.525, 72.19, 71.895, 71.625, 71.23, 70.93, 70.515, 70.105, 69.7, 69.405, 69.175, 68.89, 68.585, 68.33, 68.115, 67.965, 67.575, 67.32, 67.085, 66.87, 66.615, 66.28, 66.01, 65.705, 65.33, 65.15, 64.905, 64.67, 64.335, 64.135, 63.89, 63.64, 63.33, 62.92, 62.53, 62.295, 61.995, 61.765, 61.5, 61.265, 60.895, 60.61, 60.23, 59.925, 59.595, 59.33, 59.07, 58.775, 58.555, 58.33, 58.175, 57.97, 57.845, 57.58, 57.255, 57.045, 56.8, 56.55, 56.36, 56.115, 55.94, 55.69, 55.44, 55.185, 54.945, 54.705, 54.48, 54.28, 54.03, 53.705, 53.47, 53.245, 52.98, 52.75, 52.54, 52.355, 52.11, 51.965, 51.75, 51.59, 51.34, 51.115, 50.885, 50.71, 50.595, 50.355, 50.19, 50.055, 49.83, 49.615, 49.4, 49.185, 49.055, 48.845, 48.665, 48.525, 48.27, 48.15, 47.925, 47.725, 47.535, 47.375, 47.155, 46.965, 46.83, 46.64, 46.475, 46.26, 46.045, 45.84, 45.69, 45.6, 45.48, 45.255, 45.075, 44.885, 44.73, 44.585, 44.48, 44.355, 44.235, 44.005, 43.87, 43.77, 43.595, 43.475, 43.145, 42.965, 42.74, 42.6, 42.48, 42.31, 42.15, 41.995, 41.86, 41.715, 41.535, 41.4, 41.275, 41.095, 40.95, 40.765, 40.555, 40.42, 40.25, 40.08, 39.935, 39.76, 39.64, 39.475, 39.34, 39.175, 39.12, 38.97, 38.855, 38.725, 38.57, 38.505, 38.385, 38.29, 38.125, 38.03, 37.875, 37.71, 37.52, 37.375, 37.28, 37.165, 37.1, 36.94, 36.855, 36.695, 36.58, 36.475, 36.4, 36.27, 36.12, 36.01, 35.905, 35.78, 35.63, 35.49, 35.335, 35.24, 35.16, 35.08, 34.955, 34.84, 34.6, 34.535, 34.415, 34.325, 34.21, 34.11, 33.99, 33.87, 33.785, 33.66, 33.59, 33.51, 33.415, 33.305, 33.155, 33.095, 33.005, 32.915, 32.79, 32.66, 32.555, 32.525, 32.42, 32.365, 32.3, 32.215, 32.105, 31.995, 31.865, 31.76, 31.655, 31.555, 31.46, 31.335, 31.27, 31.195, 31.055, 30.925, 30.805, 30.76, 30.675, 30.515, 30.43, 30.33, 30.24, 30.11, 30.025, 29.925, 29.825, 29.745, 29.71, 29.65, 29.57, 29.455, 29.395, 29.33, 29.255, 29.2, 29.14, 29.065, 29.01, 28.935, 28.875, 28.775, 28.675, 28.595, 28.58, 28.515, 28.475, 28.41, 28.35, 28.285, 28.22, 28.115, 28.03, 27.945, 27.88, 27.85, 27.785, 27.73, 27.645, 27.58, 27.51, 27.435, 27.385, 27.335, 27.285, 27.195, 27.115, 27.06, 26.975, 26.925, 26.845, 26.8, 26.745, 26.715, 26.635, 26.6, 26.58, 26.48, 26.445, 26.405, 26.36, 26.305, 26.275, 26.225, 26.16, 26.065, 25.97, 25.93, 25.895, 25.85, 25.815, 25.725, 25.685, 25.615, 25.565, 25.51, 25.47, 25.4, 25.34, 25.295, 25.225, 25.17, 25.095, 25.04, 25.0, 24.94, 24.835, 24.77, 24.695, 24.655, 24.615, 24.58, 24.505, 24.41, 24.37, 24.34, 24.235, 24.135, 24.08, 24.04, 24.005, 23.925, 23.875, 23.825, 23.785, 23.725, 23.655, 23.55, 23.46, 23.415, 23.335, 23.265, 23.225, 23.185, 23.105, 23.07, 23.02, 22.955, 22.9, 22.845, 22.81, 22.785, 22.73, 22.68, 22.635, 22.56, 22.49, 22.45, 22.41, 22.385, 22.335, 22.3, 22.26, 22.225, 22.19, 22.15, 22.12, 22.065, 21.99, 21.985, 21.935, 21.905, 21.865, 21.825, 21.77, 21.69, 21.665, 21.625, 21.565, 21.515, 21.485, 21.445, 21.425, 21.375, 21.35, 21.305, 21.255, 21.22, 21.185, 21.145, 21.13, 21.085, 21.05, 21.005, 20.945, 20.905, 20.875, 20.825, 20.8, 20.73, 20.72, 20.685, 20.66, 20.64, 20.62, 20.585, 20.54, 20.51, 20.47, 20.43, 20.4, 20.37, 20.32, 20.255, 20.225, 20.21, 20.165, 20.13, 20.1, 20.045, 19.985, 19.92, 19.855, 19.83, 19.79, 19.76, 19.705, 19.675, 19.65, 19.62, 19.59, 19.565, 19.525, 19.51, 19.455, 19.43, 19.41, 19.37, 19.345, 19.33, 19.29, 19.265, 19.205, 19.17, 19.125, 19.085, 19.055, 19.035, 19.01, 18.97, 18.93, 18.895, 18.875, 18.86, 18.835, 18.815, 18.79, 18.74, 18.715, 18.69, 18.645, 18.63, 18.605, 18.545, 18.525, 18.43, 18.42, 18.4, 18.37, 18.355, 18.315, 18.295, 18.28, 18.235, 18.21, 18.18, 18.165, 18.11, 18.095, 18.055, 18.025, 18.005, 17.98, 17.965, 17.95, 17.925, 17.895, 17.87, 17.85, 17.835, 17.83, 17.8, 17.765, 17.7, 17.645, 17.63, 17.585, 17.555, 17.53, 17.49, 17.435, 17.42, 17.415, 17.405, 17.405, 17.4, 17.37, 17.355, 17.31, 17.295, 17.285, 17.255, 17.235, 17.21, 17.2, 17.195, 17.145, 17.12, 17.115, 17.085, 17.065, 17.045, 17.015, 16.97, 16.945, 16.915, 16.905, 16.88, 16.855, 16.83, 16.82, 16.805, 16.755, 16.75, 16.705, 16.68, 16.655, 16.64, 16.625, 16.595, 16.54, 16.51, 16.495, 16.49, 16.475, 16.45, 16.445, 16.44, 16.41, 16.39, 16.365, 16.345, 16.33, 16.315, 16.285, 16.27, 16.265, 16.265, 16.245, 16.195, 16.175, 16.165, 16.14, 16.125, 16.11, 16.085, 16.08, 16.075, 16.05, 16.035, 16.02, 16.01, 16.01, 16.0, 15.99, 15.97, 15.96, 15.95, 15.935, 15.915, 15.915, 15.9, 15.88, 15.86, 15.82, 15.79, 15.755, 15.73, 15.71, 15.675, 15.66, 15.63, 15.6, 15.58, 15.545, 15.505, 15.49, 15.485, 15.465, 15.45, 15.445, 15.435, 15.415, 15.41, 15.39, 15.355, 15.35, 15.325, 15.325, 15.3, 15.285, 15.265, 15.24, 15.22, 15.2, 15.19, 15.185, 15.17, 15.155, 15.15, 15.12, 15.105, 15.085, 15.06, 15.05, 15.04, 15.015, 15.0, 14.99, 14.975, 14.965, 14.94, 14.925, 14.92, 14.9, 14.89, 14.87, 14.87, 14.85, 14.845, 14.83, 14.83, 14.8, 14.79, 14.785, 14.775, 14.755, 14.745, 14.74, 14.725, 14.695, 14.665, 14.655, 14.64, 14.64, 14.615, 14.595, 14.585, 14.575, 14.565, 14.56, 14.545, 14.535, 14.51, 14.5, 14.49, 14.48, 14.475, 14.46, 14.455, 14.435, 14.41, 14.38, 14.365, 14.36, 14.35, 14.345, 14.335, 14.325, 14.32, 14.315, 14.31, 14.305, 14.285, 14.285, 14.275, 14.255, 14.25, 14.24, 14.225, 14.215, 14.205, 14.185, 14.18, 14.175, 14.145, 14.14, 14.13, 14.12, 14.1, 14.1, 14.09, 14.075, 14.055, 14.045, 14.045, 14.04, 13.995, 13.99, 13.975, 13.96, 13.95, 13.93, 13.92, 13.915, 13.915, 13.885, 13.86, 13.855, 13.835, 13.83, 13.825, 13.82, 13.815, 13.81, 13.81, 13.795, 13.79, 13.775, 13.77, 13.765, 13.755, 13.745, 13.74, 13.73, 13.72, 13.715, 13.705, 13.7, 13.7, 13.695, 13.695, 13.68, 13.67, 13.67, 13.665, 13.64, 13.625, 13.62, 13.61, 13.605, 13.6, 13.585, 13.57, 13.56, 13.555, 13.55, 13.55, 13.535, 13.53, 13.525, 13.51, 13.5, 13.49, 13.485, 13.475, 13.465, 13.455, 13.45, 13.425, 13.415, 13.415, 13.415, 13.41, 13.38, 13.365, 13.355, 13.345, 13.34, 13.32, 13.3, 13.3, 13.3, 13.295, 13.28, 13.27, 13.27, 13.27, 13.25, 13.245, 13.23, 13.22, 13.205, 13.19, 13.185, 13.18, 13.17, 13.15, 13.15, 13.14, 13.13, 13.13, 13.13, 13.12, 13.105, 13.105, 13.1, 13.09, 13.09]



half_life_L_unique_L_multi = 25 [101, 244, 419, 598, 792]
half_life_L_unique_L_multi = 75 [78, 216, 392, 617, 953]
half_life_L_unique_L_multi = 125 [95, 215, 378, 555, 808]
half_life_L_unique_L_multi = 175 [84, 208, 357, 523, 745]
half_life_L_unique_L_multi = 225 [96, 224, 363, 532, 727, 970]
    """