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model_full.pdf
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374
model_full.py
374
model_full.py
@ -85,11 +85,21 @@ def model_full(c1=10, mult_type='_multsorted2_', devs=['05'], save=True, end='al
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#################
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# power spectra data
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log = ''#'log'
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log = 'log'#'log'
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ylim_log = (-15, 3)
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nfft = 2 ** 13
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xlim_psd = [0, 300]
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DF1_desired, DF2_desired, fr, eod_fr, arrays_len = plt_data_full_model(c1, chose_score, detections, devs, dfs, end, grid[3], mult_type, sorted_on, alpha = [1,0.5], log = log,ylim_log = ylim_log, nfft = nfft, xlim_psd = xlim_psd)
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DF1_desired_orig = [133, 166]#33
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DF2_desired_orig = [-33, 53]#166
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#grid0 = gridspec.GridSpecFromSubplotSpec(len(DF1_desired_orig), 1, wspace=0.15, hspace=0.35,
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# subplot_spec=grid[1])
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DF1_desired, DF2_desired, fr, eod_fr, arrays_len = plt_data_full_model(c1, chose_score, detections, devs, dfs, end, grid[3], mult_type, sorted_on, DF2_desired = DF2_desired_orig, DF1_desired = DF1_desired_orig, alpha = [1, 0.5], log = log, ylim_log = ylim_log, nfft = nfft, xlim_psd = xlim_psd)
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#################
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@ -101,33 +111,91 @@ def model_full(c1=10, mult_type='_multsorted2_', devs=['05'], save=True, end='al
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subplot_spec=grid[2])
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fr_mult = fr / eod_fr
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multwise = False
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if multwise:
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DF1_frmult = np.abs((np.array(DF1_desired)-1)/fr_mult)
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DF2_frmult = np.abs((np.array(DF2_desired) - 1) / fr_mult)
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else:
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DF1_frmult = np.array(DF1_desired_orig)/fr
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DF2_frmult = np.array(DF2_desired_orig) / fr
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#embed()
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DF1_frmult[0] = 1
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print(DF1_frmult)
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print(DF2_frmult)
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#DF1_frmult[1] = 0.4
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#DF2_frmult[1] = 1.8
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#DF1_frmult[1] = 1.45
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#DF2_frmult[0] = 0.1
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#DF1_frmult[1] = 0.4
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#DF2_frmult[1] = 0.6
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ylim_log = (-35, 3)
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ylim_log = (-15, 3)
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#########################
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# punkte die zur zweiten Reihe gehören
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diagonal = 'line'
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combis = diagonal_points()
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freq1_ratio = 1 / 2
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freq2_ratio = 2 / 3 # 0.1
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# for combi in combis:
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diagonal = 'diagonal1' # 'vertical3'#'diagonal2'#'diagonal3'#'inside'#'horizontal'#'diagonal'#'vertical'#
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diagonal = 'test_data_cell_2022-01-05-aa-invivo-1'
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diagonal = 'diagonal1'
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# embed()
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freq1_ratio = combis[diagonal][0]
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freq2_ratio = combis[diagonal][1]
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diagonal = ''
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freq1_ratio = 1.17#0.25
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freq2_ratio = 0.37 # 0.1
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freq1_ratio = 1.2#0.25
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freq2_ratio = 0.7 # 0.1
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plus_q = 'plus' # 'minus'#'plus'##'minus'
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way = '' # 'mult'#'absolut'
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ways = ['mult_minimum_1', 'absolut', 'mult_env_3', 'mult_f1_3', 'mult_f2_3', 'mult_minimum_3', 'mult_env_1',
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'mult_f1_1', 'mult_f2_1', ]
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length = 1 # 5
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reshuffled = '' # ,
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alphas = [1,0.5]
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for g in range(len(DF1_desired)):
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axp = plt.subplot(grid0[g])
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fr = plt_model_full_model(axp, cells=[cell],trials_nr = arrays_len[g], add_pp=250, single_waves=['_SeveralSumWave_', ], cell_start=11,
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zeros='ones', several_peaks_nr = 3, alpha = alphas[g], log = log, nfft = nfft, freqs_mult1 = DF1_frmult[g], freqs_mult2 = DF2_frmult[g], xlim = [0, 170], a_f1s=[0.1], a_frs=[1], add_half=0, show=True)#01
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#
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old = False
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if old:
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fr = plt_model_full_model(axp, a_f1s=[0.03], af_2 = 0.1, cells=[cell],trials_nr = arrays_len[g], add_pp=250, single_waves=['_SeveralSumWave_', ], cell_start=11,
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zeros='ones', perc = 0.25, several_peaks_nr = 2, alpha = alphas[g], log = log, nfft = nfft, freqs_mult1 = DF1_frmult[g], freqs_mult2 = DF2_frmult[g], xlim = [0, 170], a_frs=[1], add_half=0, show=True)#01
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axes.append(axp)
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if g == 0:
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remove_xticks(axp)
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axp.set_xlabel('')
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axp.set_xlim(xlim_psd)
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if log == 'log':
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axp.set_ylim(ylim_log)
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else:
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fr = plt_model_full_model2(axp, dev_spikes='original', reshuffled=reshuffled, datapoints=50, limit=10.2,
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reshuffle=reshuffled, dev=0.0005, a_f1s=[0.15], af_2 = 0.15, trials_nr=arrays_len[g],
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stimulus_length=length, way=way, plus_q=plus_q, freq1_ratio=DF1_frmult[g],
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diagonal=diagonal, freq2_ratio=DF2_frmult[g], runs=5,nfft = nfft,
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cells=['2013-01-08-aa-invivo-1'],
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show=True, log = 'log', clip_on = True) # a_f1s=[0.02]"2012-12-13-an-invivo-1"
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axes.append(axp)
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if g == 0:
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remove_xticks(axp)
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axp.set_xlabel('')
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else:
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axp.set_xlabel('Frequency [Hz]')
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axp.set_xlim(xlim_psd)
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if log == 'log':
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axp.set_ylim(ylim_log)
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join_y(axes[1::])
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#.share
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@ -156,7 +224,7 @@ def model_full(c1=10, mult_type='_multsorted2_', devs=['05'], save=True, end='al
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save_visualization()
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def plt_model_full_model(axp, min=0.2, cells=[], alpha = 1, trials_nr = 15, add_pp=50,
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def plt_model_full_model(axp, min=0.2, cells=[], a_f2 = 0.1, perc = 0.05, alpha = 1, trials_nr = 15, add_pp=50,
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single_waves=['_SingleWave_', '_SeveralWave_', ], cell_start=13,
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zeros='zeros', several_peaks_nr = 2, a_f1s=[0, 0.005, 0.01, 0.05, 0.1, 0.2, ], a_frs=[1],
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add_half=0, log = 'log', xlim = [0, 350], freqs_mult1 = None, freqs_mult2 = None, show=False, nfft=int(2 ** 15), beat='', gain=1, us_name=''):
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@ -181,7 +249,7 @@ def plt_model_full_model(axp, min=0.2, cells=[], alpha = 1, trials_nr = 15, add_
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if single_wave == '_SingleWave_':
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a_f2s = [0] # , 0,0.2
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else:
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a_f2s = [0.1]
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a_f2s = [a_f2]
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for a_f2 in a_f2s:
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# 150
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@ -288,6 +356,8 @@ def plt_model_full_model(axp, min=0.2, cells=[], alpha = 1, trials_nr = 15, add_
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sampling_rate = 1 / deltat
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smoothed05 = gaussian_filter(spikes_mat, sigma=gaussian_intro() * sampling_rate)
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mat05 = np.mean(smoothed05, axis=0)
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beat1 = np.round(freq1 - eod_fr)[0]
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# if titles:
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# ax[0].set_title('a_f1 ' + str(a_f1), fontsize=fs)
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@ -297,6 +367,15 @@ def plt_model_full_model(axp, min=0.2, cells=[], alpha = 1, trials_nr = 15, add_
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beat1 = (freq1 - eod_fr)[0]
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beat2 = (freq2 - eod_fr)[0]
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test = False
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if test:
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ax = plt.subplot(1,1,1)
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ax.axvline(fr, color = 'blue')
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ax.axvline(beat1, color = 'green', linestyle = '-.')
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ax.axvline(beat2, color = 'purple', linestyle = '--')
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ax.plot(f, pp_mean)
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plt.show()
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#embed()
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nr = 2
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color_01, color_012, color01_2, color_02, color0_burst, color0 = colors_suscept_paper_dots()
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@ -355,7 +434,7 @@ def plt_model_full_model(axp, min=0.2, cells=[], alpha = 1, trials_nr = 15, add_
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axp, pp_mean, colors, f, add_log=2.5,
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text_extra=True, ha='center', rel='rel', rot=0, several_peaks=True,
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exact=False, texts_left=texts_left, add_texts=add_texts,several_peaks_nr=several_peaks_nr,
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rots=[0, 0, 0, 0,0], ms=14, alphas = [alpha]*len(colors), perc=0.05, log=log, clip_on=True) # True
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rots=[0, 0, 0, 0,0], ms=14, alphas = [alpha]*len(colors), perc=perc, log=log, clip_on=True) # True
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axp.plot(f, pp_mean, color='black', zorder=0) # 0.45
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axp.set_xlim(xlim)
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@ -372,9 +451,280 @@ def plt_model_full_model(axp, min=0.2, cells=[], alpha = 1, trials_nr = 15, add_
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axp.set_xlabel('Frequency [Hz]')
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return fr
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def plt_model_full_model2(ax, reshuffled='reshuffled',af_2 = 0.1, datapoints=1000, dev=0.0005, limit=10.2, a_f1s=[0.03],
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pdf=True, printing=False, plus_q='minus', freq1_ratio=1 / 2, diagonal='diagonal',
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freq2_ratio=2 / 3, way='absolut', stimulus_length=0.5, runs=1, trials_nr=500, cells=[],
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show=False, nfft=int(4096), beat='', nfft_for_morph=4096 * 4, gain=1,
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sampling_factors=[''],
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fish_receiver='Alepto', end_f1=4645,
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fish_emitter='Alepto',
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fish_jammer='Alepto', reshuffle='reshuffled',clip_on = True,
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redo_level='celllevel', step=10, zeros='zeros', corr='ratecorrrisidual',
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us_name='', dev_spikes='original', start_f1=20, log = '',plot=False):
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plot_style()
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model_cells = pd.read_csv(load_folder_name('calc_model_core') + "/models_big_fit_d_right.csv")
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if len(cells) < 1:
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cells = len(model_cells)
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#embed()
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for cell_here in cells:
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# sachen die ich variieren will
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###########################################
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single_waves = ['_SeveralWave_'] # , '_SingleWave_']
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####### VARY HERE
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for single_wave in single_waves:
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if single_wave == '_SingleWave_':
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a_f2s = [0] # , 0,0.2
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else:
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a_f2s = [af_2]
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for a_f2 in a_f2s:
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# ,0.05,0.01, 0.005, 0.1, 0.2] # 0.001,
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for a_f1 in a_f1s:
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a_frs = [1]
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titles_amp = ['base eodf'] # ,'baseline to Zero',]
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for a, a_fr in enumerate(a_frs):
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model_params = model_cells[model_cells['cell'] == cell_here].iloc[0]
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# model_params = model_cells.iloc[cell_nr]
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def plt_data_full_model(c1, chose_score, detections, devs, dfs, end, grid, mult_type, sorted_on, log = 'log', alpha = [], ylim_log = (-15, 3), nfft = 2 ** 13, xlim_psd = [0, 235]):
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# embed()
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eod_fr = model_params['EODf'] # .iloc[0]
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offset = model_params.pop('v_offset')
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cell = model_params.pop('cell')
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print(cell)
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SAM, adapt_offset, cell_recording, constant_reduction, damping, damping_type, dent_tau_change, exponential, f1, f2, fish_emitter, fish_receiver, fish_morph_harmonics_var, lower_tol, mimick, n, phase_right, phaseshift_fr, sampling_factor, upper_tol, zeros = default_model0()
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# in case you want a different sampling here we can adujust
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time_array, sampling, deltat = deltat_choice(model_params, sampling_factor, eod_fr,
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stimulus_length)
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# generate the eod_fish_r in the four mimick variants (copy, thunderfish, mimick, just sinus)
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eod_fish_r, deltat, eod_fr, time_array = eod_fish_r_generation(time_array, eod_fr, a_fr,
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stimulus_length, phaseshift_fr,
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cell_recording, zeros, mimick,
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sampling, fish_receiver, deltat,
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nfft, nfft_for_morph,
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fish_morph_harmonics_var=fish_morph_harmonics_var,
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beat=beat)
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sampling = 1 / deltat
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multiple = 0
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slope = 0
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add = 0
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plus = 0
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sig_val = (7, 1)
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variant = 'sinz'
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if exponential == '':
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v_exp = 1
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exp_tau = 0.001
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# prepare for adapting offset due to baseline modification
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baseline_with_wave_damping, baseline_without_wave = prepare_baseline_array(time_array, eod_fr,
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nfft_for_morph,
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phaseshift_fr,
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mimick, zeros,
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cell_recording,
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sampling,
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stimulus_length,
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fish_receiver,
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deltat, nfft,
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damping_type,
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damping, us_name,
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gain, beat=beat,
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fish_morph_harmonics_var=fish_morph_harmonics_var)
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spikes_base = [[]] * trials_nr
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color0 = 'green' # 'orange'
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color01 = 'blue'
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color02 = 'red'
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color012 = 'orange'
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color01_2 = 'purple'
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color01, color012, color01_2, color02, color0_burst, color0 = colors_suscept_paper_dots()
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#fig = plt.figure(figsize=(11.5, 5.4))
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# embed()
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for run in range(runs):
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print(run)
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t1 = time.time()
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for t in range(trials_nr):
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# get the baseline properties here
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# baseline_after,spikes_base,rate_adapted, rate_baseline_before, rate_baseline_after, np.array(spike_times), stimulus_power, v_dent_output[int(0.05 / deltat):-1], offset, v_mem_output
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stimulus = eod_fish_r
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stimulus_base = eod_fish_r
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if 'Zero' in titles_amp[a]:
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power_here = 'sinz' + '_' + zeros
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else:
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power_here = 'sinz'
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cvs, adapt_output, baseline_after_b, _, rate_adapted_b, rate_baseline_before_b, rate_baseline_after_b, \
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spikes_base[t], _, _, offset_new, _,noise_final = simulate(cell, offset, stimulus, f1,
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nr=n,
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power_variant=power_here,
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adapt_offset=adapt_offset,
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add=add, alpha=alpha,
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reshuffle=reshuffled,
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lower_tol=lower_tol,
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upper_tol=upper_tol,
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v_exp=v_exp, exp_tau=exp_tau,
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dent_tau_change=dent_tau_change,
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alter_taus=constant_reduction,
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exponential=exponential,
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exponential_mult=1,
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exponential_plus=plus,
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exponential_slope=slope,
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sig_val=sig_val, j=f2,
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deltat=deltat, t=t,
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**model_params)
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if t == 0:
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# here we record the changes in the offset due to the adaptation
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change_offset = offset - offset_new
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# and we subsequently reset the offset to be the new adapted for all subsequent trials
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offset = offset_new * 1
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if printing:
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print('Baseline time' + str(time.time() - t1))
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base_cut, mat_base = find_base_fr(spikes_base, deltat, stimulus_length, time_array, dev=dev)
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fr = np.mean(base_cut)
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if 'diagonal' in diagonal:
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two_third_fr = fr * freq2_ratio
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freq1_ratio = (1 - freq2_ratio)
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third_fr = fr * freq1_ratio
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else:
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two_third_fr = fr * freq2_ratio
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third_fr = fr * freq1_ratio
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if plus_q == 'minus':
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two_third_fr = -two_third_fr
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third_fr = -third_fr
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freqs2 = [eod_fr + two_third_fr] # , eod_fr - third_fr, two_third_fr,
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# third_fr,
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# two_third_eodf, eod_fr - two_third_eodf,
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# third_eodf, eod_fr - third_eodf, ]
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freqs1 = [
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eod_fr + third_fr] # , eod_fr - two_third_fr, third_fr,two_third_fr,third_eodf, eod_fr - third_eodf,two_third_eodf, eod_fr - two_third_eodf, ]
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#embed()
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sampling_rate = 1 / deltat
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base_cut, mat_base, smoothed0, mat0 = find_base_fr2(sampling_rate, spikes_base, deltat,
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stimulus_length, time_array, dev=dev)
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fr = np.mean(base_cut)
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frate, isis_diff = ISI_frequency(time_array, spikes_base[0], fill=0.0)
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isi = np.diff(spikes_base[0])
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cv0 = np.std(isi) / np.mean(isi)
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cv1 = np.std(frate) / np.mean(frate)
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for ff, freq1 in enumerate(freqs1):
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freq1 = [freq1]
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freq2 = [freqs2[ff]]
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# time_var = time.time()
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# if printing:
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# print(cell )
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# f_corr = create_beat_corr(np.array([freq1[f1]]), np.array([eod_fr]))
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# create the second eod_fish1 array analogous to the eod_fish_r array
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t1 = time.time()
|
||||
phaseshift_f1, phaseshift_f2 = get_phaseshifts(a_f1, a_f2, phase_right, phaseshift_fr)
|
||||
eod_fish1, time_fish_e = eod_fish_e_generation(time_array, a_f1, freq1, f1,
|
||||
nfft_for_morph, phaseshift_f1,
|
||||
cell_recording, fish_morph_harmonics_var,
|
||||
zeros, mimick, fish_emitter, sampling,
|
||||
stimulus_length, thistype='emitter')
|
||||
eod_fish2, time_fish_j = eod_fish_e_generation(time_array, a_f2, freq2, f2,
|
||||
nfft_for_morph, phaseshift_f2,
|
||||
cell_recording, fish_morph_harmonics_var,
|
||||
zeros, mimick, fish_jammer, sampling,
|
||||
stimulus_length, thistype='jammer')
|
||||
|
||||
eod_stimulus = eod_fish1 + eod_fish2
|
||||
|
||||
v_mems, offset_new, mat01, mat02, mat012, smoothed01, smoothed02, smoothed012, stimulus_01, stimulus_02, stimulus_012, mat05_01, spikes_01, mat05_02, spikes_02, mat05_012, spikes_012 = get_arrays_for_three(
|
||||
cell, a_f2, a_f1,
|
||||
SAM, eod_stimulus, eod_fish_r, freq2, eod_fish1, eod_fish_r,
|
||||
eod_fish2, stimulus_length,
|
||||
baseline_with_wave_damping, baseline_without_wave,
|
||||
offset, model_params, n, variant, t, adapt_offset,
|
||||
upper_tol, lower_tol, dent_tau_change, constant_reduction,
|
||||
exponential, plus, slope, add,
|
||||
deltat, alpha, sig_val, v_exp, exp_tau, f2,
|
||||
trials_nr, time_array,
|
||||
f1, freq1, damping_type,
|
||||
gain, eod_fr, damping, us_name, dev=dev, reshuffle=reshuffled)
|
||||
if printing:
|
||||
print('Generation process' + str(time.time() - t1))
|
||||
|
||||
|
||||
results_diff = pd.DataFrame()
|
||||
results_diff['f1'] = freq1
|
||||
results_diff['f2'] = freq2
|
||||
results_diff['f0'] = eod_fr
|
||||
|
||||
|
||||
if run == 0:
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
##################################
|
||||
# power spectrum
|
||||
# embed()
|
||||
if dev_spikes == 'original':
|
||||
nfft = 2 ** 15
|
||||
# embed()
|
||||
p0, p02, p01, p012, fs = calc_ps(nfft, [np.mean(mat012, axis=0)],
|
||||
[np.mean(mat01, axis=0)],
|
||||
[np.mean(mat02, axis=0)],
|
||||
[np.mean(mat0, axis=0)],
|
||||
test=False, sampling_rate=sampling_rate)
|
||||
|
||||
else:
|
||||
nfft = 2 ** 15
|
||||
p0, p02, p01, p012, fs = calc_ps(nfft, smoothed012,
|
||||
smoothed01, smoothed02, smoothed0,
|
||||
test=False, sampling_rate=sampling_rate)
|
||||
if log == 'log':
|
||||
p012 = 10 * np.log10(p012 / np.max(p012))
|
||||
# pp_mean = np.log
|
||||
p_arrays = [p012]
|
||||
for j in range(len(p_arrays)):
|
||||
sampling = 40000
|
||||
p0_means = []
|
||||
|
||||
for i in range(len(p0)):
|
||||
ax.plot(fs, p_arrays[j][i], color='grey')
|
||||
p0_mean = np.mean(p_arrays[j], axis=0)
|
||||
p0_means.append(p0_mean)
|
||||
ax.plot(fs, p0_mean, color='black') # plt_peaks(ax[0], p01, fs, 'orange')
|
||||
DF1 = np.abs(results_diff.f1.iloc[-1] - results_diff.f0.iloc[-1])
|
||||
DF2 = np.abs(results_diff.f2.iloc[-1] - results_diff.f0.iloc[-1])
|
||||
# embed()
|
||||
for p in range(len(p0_means)):
|
||||
freqs = [np.abs(DF1), np.abs(DF1 * 2),
|
||||
np.abs(DF2), np.abs(DF2 * 2),
|
||||
np.abs(np.abs(DF1) - np.abs(DF2)),
|
||||
np.abs(DF1) + np.abs(DF2), fr]
|
||||
colors = [color01, color01,color02, color02,
|
||||
color01_2, color012, color0]
|
||||
labels = ['DF1', 'DF1_H1', 'DF1_H3', 'DF1_H4', 'DF2', 'DF2_H1',
|
||||
'DF2_H2', 'DF2_H3', '|DF1-DF2|', '|DF1+DF2|', 'baseline']
|
||||
#embed()
|
||||
plt_peaks_several(labels, freqs, p0_means, 0, ax,
|
||||
p0_means[p], colors, fs, clip_on = clip_on, alpha=0.7)
|
||||
ax.set_xlim(0, 300)
|
||||
ax.set_ylim(0 - 20,
|
||||
np.max(np.max(p_arrays)) + 70) # np.min(np.min(p0_means))
|
||||
#if j == 0:
|
||||
# ax.legend(ncol=2)
|
||||
return fr
|
||||
|
||||
|
||||
|
||||
def plt_data_full_model(c1, chose_score, detections, devs, dfs, end, grid, mult_type, sorted_on, log = 'log', alpha = [],DF2_desired = [-33, -100], DF1_desired = [133, 66], ylim_log = (-15, 3), nfft = 2 ** 13, xlim_psd = [0, 235]):
|
||||
# mean_type = '_MeanTrialsIndexPhaseSort_Min0.25sExcluded_'
|
||||
extract = ''
|
||||
datasets, data_dir = find_all_dir_cells()
|
||||
@ -383,8 +733,8 @@ def plt_data_full_model(c1, chose_score, detections, devs, dfs, end, grid, mult_
|
||||
append_others = 'apend_others' # '#'apend_others'#'apend_others'#'apend_others'##'apend_others'
|
||||
autodefine = '_DFdesired_'
|
||||
autodefine = 'triangle_diagonal_fr' # ['triangle_fr', 'triangle_diagonal_fr', 'triangle_df2_fr','triangle_df2_eodf''triangle_df1_eodf', ] # ,'triangle_df2_fr''triangle_df1_fr','_triangle_diagonal__fr',]
|
||||
DF2_desired = [-33, -100] # 167(167, 133) (166, 249)
|
||||
DF1_desired = [133, 66] # (133, 265)167, -33) das ist ein komischer Punkt: (166,83)
|
||||
# 167(167, 133) (166, 249)
|
||||
# (133, 265)167, -33) das ist ein komischer Punkt: (166,83)
|
||||
#(66 / 166
|
||||
autodefine = '_dfchosen_closest_'
|
||||
autodefine = '_dfchosen_closest_first_'
|
||||
@ -667,7 +1017,7 @@ def plt_data_full_model(c1, chose_score, detections, devs, dfs, end, grid, mult_
|
||||
spikes_pure, time_array, range_plot=[3], names=names,
|
||||
ax01=ax00, clip_on = False, xlim_psd=xlim_psd, alphas = alphas, choice = choice, labels = labels, ylim_log=ylim_log, log=log, text_extra=False)
|
||||
# [arrays[-1]]arrays, ax00, ax_ps, cell, colors_p, f, [-1]grid0, group_mean, nfft, p_means, p_means_all, ps, row,spikes_pure, time_array,
|
||||
#embed()
|
||||
ax00.show_spines('lb')
|
||||
if gg == 0:
|
||||
ax00.legend(ncol=6, loc=(-1.22, 1.1))
|
||||
if gg != len(DF1_desired) - 1:
|
||||
|
||||
35895
model_full_05_012.csv
35895
model_full_05_012.csv
File diff suppressed because it is too large
Load Diff
37725
model_full_05_base_0.csv
37725
model_full_05_base_0.csv
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@ -1,89 +1,91 @@
|
||||
,0,1,2
|
||||
0,0.2650000001243047,0.36499999953786677,1.0800000001356338
|
||||
1,12.490000000523027,2.0399999999700587,13.605000000231678
|
||||
2,15.165000000249451,14.214999999812898,16.079999999553557
|
||||
3,16.790000000125758,16.989999999741592,17.78000000026369
|
||||
4,18.29000000043135,18.714999999820172,29.529999999928997
|
||||
5,30.140000000298926,29.014999999735778,31.079999999880975
|
||||
6,31.715000000528846,30.5899999999657,32.879999999883886
|
||||
7,45.34000000012139,32.24000000011995,46.180000000410665
|
||||
8,46.76500000050265,44.34000000003846,47.75499999973109
|
||||
9,48.29000000017669,47.264999999815814,49.32999999996101
|
||||
10,58.81499999986528,59.09000000031494,59.68000000043249
|
||||
11,60.34000000044881,60.614999999988974,61.23000000038447
|
||||
12,62.01499999997151,62.365000000345496,73.60499999972237
|
||||
13,75.58999999991767,75.66499999996277,76.47999999985333
|
||||
14,78.36499999984636,77.2400000001927,79.40499999963069
|
||||
15,89.01500000001516,80.51500000022325,88.7299999996205
|
||||
16,90.44000000039642,89.23999999990893,90.27999999957248
|
||||
17,92.14000000019706,90.74000000021452,103.62999999974565
|
||||
18,105.51499999973868,92.48999999966155,106.42999999995229
|
||||
19,106.96500000039788,104.31500000016068,109.52999999985624
|
||||
20,108.5399999997183,107.31499999986237,119.88000000032773
|
||||
21,119.11499999996278,119.1900000000079,121.4300000002797
|
||||
22,120.61500000026837,120.76500000023782,123.38000000013128
|
||||
23,135.59000000031784,122.43999999976052,136.5799999995463
|
||||
24,137.11499999999188,136.06500000026256,138.10500000012982
|
||||
25,138.6900000002218,137.56499999965865,148.804999999945
|
||||
26,149.41500000031493,149.3399999996019,150.40499999954338
|
||||
27,150.86500000006464,150.91499999983182,164.2549999998184
|
||||
28,165.81499999983617,152.4649999997838,166.6299999998475
|
||||
29,167.26500000049538,166.0150000003615,168.4800000004063
|
||||
30,168.76499999989147,167.5650000003135,178.72999999976602
|
||||
31,179.23999999993367,169.16499999991186,180.20499999979367
|
||||
32,180.71499999996132,179.4900000001054,181.7300000003772
|
||||
33,182.46500000031784,181.01499999977943,195.3800000002477
|
||||
34,196.14000000046627,182.63999999965574,196.8799999996438
|
||||
35,197.61500000049392,194.96500000025674,198.6300000000003
|
||||
36,199.06500000024363,197.76499999955388,209.00499999984024
|
||||
37,209.5150000000079,209.590000000053,210.45499999958994
|
||||
38,210.9150000001112,211.0900000003586,212.08000000037575
|
||||
39,212.71500000011412,212.73999999960336,225.6550000003219
|
||||
40,227.41499999983472,223.36499999949422,228.33000000004833
|
||||
41,228.94000000041825,226.48999999967612,230.13000000005124
|
||||
42,230.83999999971394,239.69000000000062,239.35499999983878
|
||||
43,240.86500000021016,241.21499999967466,241.80499999979222
|
||||
44,242.5150000003644,242.81500000018252,255.58000000014292
|
||||
45,256.13999999995696,254.9649999997474,257.13000000009487
|
||||
46,257.76499999983326,257.9650000003586,269.0549999998868
|
||||
47,259.31499999978524,269.86499999987257,270.5299999999144
|
||||
48,269.74000000018106,271.3149999996223,272.0049999999421
|
||||
49,271.18999999993076,272.99000000005447,284.4049999995579
|
||||
50,286.1399999997023,285.2149999995437,287.15500000011815
|
||||
51,287.6899999996543,287.9900000003819,288.82999999964085
|
||||
52,289.1649999996819,299.93999999954224,299.20500000039027
|
||||
53,299.69000000028,301.4149999995699,300.80499999998864
|
||||
54,301.21499999995405,303.01500000007775,302.3050000002942
|
||||
55,303.0400000002349,315.33999999976925,316.1050000000134
|
||||
56,316.26499999992785,318.1399999999759,318.6550000001691
|
||||
57,317.81499999987983,329.98999999984346,329.254999999782
|
||||
58,319.34000000046336,331.53999999979544,330.7050000004412
|
||||
59,330.1900000001272,333.21500000022763,332.2799999997616
|
||||
60,331.7400000000792,345.2899999998682,345.9299999996321
|
||||
61,346.36499999987547,348.1150000003528,348.7550000001167
|
||||
62,347.8399999999031,349.83999999952186,350.4800000001953
|
||||
63,349.3899999998551,360.1649999997154,360.75499999983293
|
||||
64,359.8649999998973,361.7149999996674,362.33000000006285
|
||||
65,361.3900000004808,363.66499999951895,375.905000000009
|
||||
66,363.1149999996499,376.91500000039935,377.42999999968305
|
||||
67,376.490000000101,378.41499999979544,379.22999999968596
|
||||
68,377.9900000004066,390.21500000001663,389.5549999998795
|
||||
69,379.6150000002829,391.73999999969067,390.98000000026076
|
||||
70,390.0650000000472,393.34000000019853,392.53000000021274
|
||||
71,391.5899999997212,405.6399999996121,406.2299999997296
|
||||
72,406.59000000004863,408.39000000017234,409.02999999993625
|
||||
73,408.0900000003542,410.1150000002509,410.7800000002928
|
||||
74,409.66499999967465,420.3899999998886,421.00500000028404
|
||||
75,420.13999999971685,421.93999999984055,422.50499999968014
|
||||
76,421.64000000002244,423.6900000001971,436.3050000003088
|
||||
77,423.2400000005303,437.16499999994096,437.9300000001851
|
||||
78,438.19000000030184,438.7649999995393,449.70500000012834
|
||||
79,439.7400000002538,450.4400000001898,451.2050000004339
|
||||
80,450.16499999974013,451.96499999986384,452.6799999995521
|
||||
81,451.7149999996921,453.6649999996645,464.87999999967286
|
||||
82,453.59000000052885,467.14000000031785,466.4800000001807
|
||||
83,466.96500000007046,468.63999999971395,469.4799999998824
|
||||
84,468.7900000003513,470.3399999995146,479.85499999972234
|
||||
85,480.34000000052157,480.61500000006174,481.2800000001036
|
||||
86,481.8150000005492,482.11500000036733,482.87999999970197
|
||||
87,483.4400000004255,483.8399999995364,
|
||||
,1,0
|
||||
0,2.355000000535088,15.005000000250956
|
||||
1,15.530000000581655,16.480000000278604
|
||||
2,17.055000000255692,18.205000000357185
|
||||
3,19.93000000038666,21.730000000438675
|
||||
4,21.555000000262968,34.605000000787925
|
||||
5,36.78000000036337,37.55500000084322
|
||||
6,38.23000000011308,39.18000000071953
|
||||
7,39.75500000069661,52.90500000051435
|
||||
8,56.05500000001558,55.705000000720986
|
||||
9,57.55500000032117,57.255000000672965
|
||||
10,59.07999999999521,58.75500000006906
|
||||
11,62.28000000010144,75.10500000085341
|
||||
12,75.73000000047688,76.6050000002495
|
||||
13,77.20500000050453,78.2800000006817
|
||||
14,80.17999999992827,93.25500000073117
|
||||
15,82.00500000020912,94.70500000048088
|
||||
16,95.35500000038229,97.68000000081412
|
||||
17,98.2550000007912,99.43000000026115
|
||||
18,99.90500000003595,115.63000000028734
|
||||
19,116.15500000061803,117.13000000059293
|
||||
20,117.65500000001413,118.68000000054491
|
||||
21,119.30500000016838,133.830000000721
|
||||
22,123.98000000030225,135.2800000004707
|
||||
23,135.68000000032117,136.78000000077628
|
||||
24,137.23000000027315,139.93000000032663
|
||||
25,140.1550000000505,154.7800000008054
|
||||
26,141.8800000001291,156.55500000053036
|
||||
27,155.33000000050453,159.3050000001811
|
||||
28,158.23000000000394,172.9050000004052
|
||||
29,159.8300000005118,175.93000000038484
|
||||
30,176.23000000003304,177.45500000005887
|
||||
31,177.73000000033863,179.155000000769
|
||||
32,179.329999999937,195.230000000315
|
||||
33,182.38000000019457,196.73000000062058
|
||||
34,195.78000000001413,199.85500000080248
|
||||
35,197.40499999989044,213.43000000074863
|
||||
36,200.38000000022367,214.90500000077628
|
||||
37,202.3050000007068,217.88000000020003
|
||||
38,217.08000000035173,219.73000000075882
|
||||
39,218.55500000037938,235.85500000086068
|
||||
40,220.1300000006093,237.32999999997884
|
||||
41,236.35500000000394,238.8800000008403
|
||||
42,237.88000000058747,254.08000000066278
|
||||
43,239.48000000018584,255.58000000005887
|
||||
44,244.27999999989044,257.0550000000865
|
||||
45,255.88000000061658,260.1800000002684
|
||||
46,257.48000000021494,274.95500000082285
|
||||
47,260.38000000062385,276.5550000004212
|
||||
48,262.1300000000709,278.2800000004998
|
||||
49,277.0800000007519,293.0300000007763
|
||||
50,278.5300000005016,296.0050000002
|
||||
51,280.05500000017565,297.555000000152
|
||||
52,296.4550000006064,299.15500000065987
|
||||
53,297.9550000000025,314.280000000558
|
||||
54,299.5300000002324,315.75500000058565
|
||||
55,314.7300000000549,317.1800000000574
|
||||
56,316.28000000000685,321.7300000006206
|
||||
57,317.85500000023677,333.7050000000589
|
||||
58,320.73000000036774,335.20500000036446
|
||||
59,335.579999999937,338.15500000041976
|
||||
60,337.1550000001669,339.88000000049834
|
||||
61,338.6550000004725,353.20500000039357
|
||||
62,340.30500000062676,356.20500000009525
|
||||
63,356.5300000000214,357.70500000040084
|
||||
64,358.0799999999734,374.55500000037756
|
||||
65,359.68000000048124,377.0549999999774
|
||||
66,362.93000000023386,380.23000000071517
|
||||
67,376.1050000002804,393.70500000045905
|
||||
68,377.7800000007126,395.2300000001331
|
||||
69,380.63000000056564,398.1800000001884
|
||||
70,395.73000000018584,399.78000000069625
|
||||
71,398.6050000003168,415.080000000721
|
||||
72,400.2300000001931,417.6299999999672
|
||||
73,415.35500000009125,419.255000000753
|
||||
74,416.8300000001189,434.3550000003732
|
||||
75,418.3300000004245,435.8050000001229
|
||||
76,422.8050000001538,437.28000000015055
|
||||
77,436.25500000052926,453.805000000152
|
||||
78,437.7800000002033,455.3050000004576
|
||||
79,440.70499999998066,458.23000000023495
|
||||
80,442.5300000002615,459.8050000004649
|
||||
81,455.955000000359,473.4800000006133
|
||||
82,458.80500000021203,476.3050000001884
|
||||
83,460.43000000008834,477.9300000000647
|
||||
84,476.8300000005191,479.53000000057256
|
||||
85,478.2800000002688,494.5550000002684
|
||||
86,479.8550000004987,495.9800000006497
|
||||
87,484.7800000006835,497.380000000753
|
||||
88,495.0800000005991,
|
||||
89,496.6300000005511,
|
||||
|
||||
|
@ -1,71 +1,72 @@
|
||||
,0,1,2
|
||||
0,4.547473508864641e-10,1.3500000000021828,0.024999999595820555
|
||||
1,8.550000000013824,7.600000000365981,6.4249999998082785
|
||||
2,17.475000000104046,13.34999999971842,12.799999999742795
|
||||
3,23.57499999970969,19.324999999753345,18.50000000035834
|
||||
4,32.475000000431464,31.424999999671854,21.724999999833017
|
||||
5,35.55000000005748,37.39999999970678,32.22500000015316
|
||||
6,42.02500000019427,43.50000000022192,39.62499999965985
|
||||
7,50.67499999995562,49.40000000033251,44.29999999979373
|
||||
8,56.72499999991487,58.42499999971551,54.6999999999116
|
||||
9,62.75000000050568,63.17499999977372,62.4000000000251
|
||||
10,71.72500000024229,73.45000000032087,69.70000000023902
|
||||
11,78.25000000002547,76.77499999999782,78.85000000010223
|
||||
12,86.74999999993815,87.39999999988868,84.87499999978354
|
||||
13,92.85000000045329,96.22499999977663,92.42500000004839
|
||||
14,104.7750000002452,102.4000000002161,99.87500000011096
|
||||
15,107.99999999971988,112.7000000001317,105.92500000007021
|
||||
16,116.95000000008804,118.77500000036889,115.1750000001357
|
||||
17,123.07499999997162,121.92499999991924,120.79999999991742
|
||||
18,129.00000000036016,133.6500000002161,125.54999999997563
|
||||
19,137.85000000052605,135.6250000003456,134.72500000011678
|
||||
20,147.2500000004402,142.90000000028158,142.0250000003307
|
||||
21,155.84999999964566,148.8750000003165,149.59999999996398
|
||||
22,157.70000000020445,160.8499999997548,157.17499999959728
|
||||
23,166.67499999994106,166.85000000006767,166.0999999996875
|
||||
24,174.07500000035725,172.90000000002692,172.32499999977335
|
||||
25,183.00000000044747,177.59999999952925,178.29999999980828
|
||||
26,184.9250000000211,185.02500000022337,184.30000000012114
|
||||
27,195.15000000001237,195.77499999968495,190.24999999987813
|
||||
28,202.72499999964566,198.60000000016953,197.9249999997137
|
||||
29,207.3249999998552,209.0499999999338,202.4499999999989
|
||||
30,219.62500000017826,215.20000000009532,211.4750000002914
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||||
31,225.10000000011132,225.62499999958163,217.27500000019973
|
||||
32,227.10000000051878,233.17499999984648,226.5250000002652
|
||||
33,237.40000000043437,238.0500000003849,235.47499999972388
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||||
34,245.0000000003456,245.32500000032087,241.69999999980973
|
||||
35,249.47500000007494,251.54999999949723,247.8750000002492
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||||
36,258.40000000016516,260.35000000001673,258.10000000024047
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||||
37,267.3250000002554,269.32499999975335,264.09999999964384
|
||||
38,273.8000000003922,272.5249999998596,271.62499999963075
|
||||
39,285.3250000002845,281.2749999998232,277.5000000003729
|
||||
40,286.9500000001608,289.00000000021464,286.7749999998068
|
||||
41,291.700000000219,294.999999999618,292.6749999999174
|
||||
42,303.52499999980864,299.5749999995496,301.60000000000764
|
||||
43,309.4750000004751,308.4249999997155,310.6499999996686
|
||||
44,314.12500000033106,320.42500000034124,316.5499999997792
|
||||
45,321.75000000052023,323.60000000016953,322.67499999966276
|
||||
46,327.82499999984793,332.47499999970387,328.5500000004049
|
||||
47,334.1000000004897,338.90000000019427,334.82500000013715
|
||||
48,342.52500000047803,346.1000000002059,346.7249999996511
|
||||
49,351.6999999997097,348.0500000000575,351.5749999999116
|
||||
50,355.10000000022046,358.1749999998465,358.8750000001255
|
||||
51,366.8750000001637,365.62499999990905,364.8249999998825
|
||||
52,372.7750000002743,374.5750000002772,375.62499999989996
|
||||
53,378.92500000043583,376.27500000007785,381.3750000001619
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||||
54,387.7500000003238,386.6000000002714,385.9999999997399
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||||
55,394.0749999997024,392.6249999999527,393.650000000207
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||||
56,400.04999999973734,401.67499999961365,399.4999999997617
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||||
57,408.7750000003325,408.125000000382,411.62499999995816
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||||
58,410.4499999998552,414.0249999995831,413.2499999998345
|
||||
59,420.95000000017535,422.874999999749,420.5999999996948
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||||
60,431.54999999978827,428.99999999963256,429.8750000000382
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||||
61,438.8500000000022,436.40000000004875,437.12499999969623
|
||||
62,442.25000000051296,442.4999999996544,444.6749999999611
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||||
63,452.64999999972133,453.0499999996209,452.1500000003016
|
||||
64,457.22499999965294,459.1249999998581,461.22500000024047
|
||||
65,463.25000000024374,465.32499999966603,467.17499999999745
|
||||
66,470.72499999967476,474.149999999554,473.37499999980537
|
||||
67,478.07500000044456,480.2500000000691,482.22499999997126
|
||||
68,487.0750000004591,488.9749999997548,486.90000000010514
|
||||
69,488.875000000462,490.87499999996,497.4000000004253
|
||||
,1,0
|
||||
0,0.09999999997489795,7.850000000416912
|
||||
1,8.849999999938518,16.800000000785076
|
||||
2,12.225000000171349,22.82500000046639
|
||||
3,21.175000000539512,28.925000000072032
|
||||
4,26.975000000447835,37.925000000086584
|
||||
5,36.25000000079126,45.37500000014916
|
||||
6,42.07500000006803,49.95000000008076
|
||||
7,48.150000000305226,59.0000000006512
|
||||
8,54.15000000061809,64.82500000083746
|
||||
9,63.10000000007676,75.42500000045038
|
||||
10,69.17500000031396,77.12500000025102
|
||||
11,75.22500000027321,87.60000000029322
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||||
12,81.15000000066175,95.0000000007094
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||||
13,93.05000000017571,101.05000000066866
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||||
14,96.27500000055988,107.25000000047658
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||||
15,105.12500000072578,115.97500000016225
|
||||
16,111.32500000053369,122.02500000012151
|
||||
17,120.22500000034597,131.02500000013606
|
||||
18,126.32499999995161,137.02500000044893
|
||||
19,133.9500000001408,143.07500000040818
|
||||
20,136.77500000062537,149.15000000064538
|
||||
21,145.72500000008404,158.32500000078653
|
||||
22,156.09999999992397,167.1000000001186
|
||||
23,162.17500000016116,173.15000000007785
|
||||
24,169.9000000005526,179.2000000000371
|
||||
25,174.22500000043328,185.15000000070359
|
||||
26,180.30000000067048,191.5250000006381
|
||||
27,189.25000000012915,203.07500000080836
|
||||
28,195.27500000071996,209.10000000048967
|
||||
29,203.0000000002019,216.67500000012296
|
||||
30,210.7499999999618,224.1000000008171
|
||||
31,219.27500000015243,230.02500000029613
|
||||
32,225.57500000016262,233.3000000003267
|
||||
33,234.27500000047985,242.2750000000633
|
||||
34,240.30000000016116,249.8500000006061
|
||||
35,246.32500000075197,255.72500000043874
|
||||
36,252.4250000003576,266.25000000012733
|
||||
37,258.5000000005948,275.22500000077343
|
||||
38,267.4750000003314,278.2250000004751
|
||||
39,276.475000000346,284.3000000007123
|
||||
40,282.5749999999516,290.4750000002423
|
||||
41,288.4250000004158,297.8250000001026
|
||||
42,294.5500000002994,308.32500000042273
|
||||
43,303.3499999999094,311.5500000008069
|
||||
44,306.45000000072287,317.225000000235
|
||||
45,315.5500000000302,329.4250000003558
|
||||
46,324.5750000003227,334.0000000002874
|
||||
47,330.7000000002063,339.8500000007516
|
||||
48,338.1750000005468,344.4250000006832
|
||||
49,344.05000000037944,354.9500000003718
|
||||
50,351.52500000071996,362.4250000007123
|
||||
51,357.6250000003256,371.375000000171
|
||||
52,366.4750000004915,376.0750000005828
|
||||
53,368.2750000004944,383.40000000016516
|
||||
54,378.6250000000564,389.6750000008069
|
||||
55,387.6500000003489,397.00000000038926
|
||||
56,393.6750000000302,407.47500000043146
|
||||
57,399.7500000002674,410.65000000025975
|
||||
58,411.4999999999327,419.45000000077926
|
||||
59,413.2250000000113,422.8250000001026
|
||||
60,423.5500000002048,433.05000000009386
|
||||
61,426.6750000003867,434.95000000029904
|
||||
62,435.6250000007549,446.5000000004693
|
||||
63,446.20000000008986,449.7000000005755
|
||||
64,451.200000000199,458.57500000010987
|
||||
65,459.6500000004653,464.7250000002714
|
||||
66,462.75000000036925,473.45000000086657
|
||||
67,471.8500000005861,479.6500000006745
|
||||
68,479.5000000001437,485.7250000000022
|
||||
69,485.4000000002543,494.85000000049695
|
||||
70,492.7500000001146,
|
||||
|
||||
|
@ -1,89 +1,76 @@
|
||||
,2,0,1
|
||||
0,9.325000000224463,2.4250000001302396,10.825000000111322
|
||||
1,10.749999999696229,9.550000000217551,12.424999999709689
|
||||
2,12.42500000012842,11.074999999891588,14.124999999510328
|
||||
3,24.37500000019827,12.725000000045839,26.02499999993379
|
||||
4,25.824999999947977,24.974999999813008,29.024999999635476
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||||
5,27.424999999546344,27.650000000448927,39.87500000020882
|
||||
6,39.79999999979373,38.60000000031505,41.39999999988286
|
||||
7,42.24999999974716,41.225000000395084,44.07499999960928
|
||||
8,44.00000000010368,43.100000000322325,56.02499999967913
|
||||
9,55.74999999976899,56.27500000036889,57.57499999963111
|
||||
10,57.32499999999891,57.80000000004293,59.29999999970969
|
||||
11,58.97500000015316,59.5749999997679,71.12500000020881
|
||||
12,70.94999999959145,71.3250000003427,72.75000000008512
|
||||
13,72.47500000017499,72.87500000029468,84.7750000000793
|
||||
14,84.67500000029577,83.94999999973152,86.32500000003128
|
||||
15,86.1999999999698,86.32499999976062,99.77499999949723
|
||||
16,89.17500000030304,88.0499999998392,101.27499999980282
|
||||
17,100.99999999989268,100.2000000003136,102.97499999960345
|
||||
18,102.62499999976899,103.05000000016662,115.05000000015352
|
||||
19,114.74999999996544,115.04999999988286,116.47499999962528
|
||||
20,116.19999999971515,116.5249999999105,119.57499999952924
|
||||
21,119.20000000032633,119.60000000044602,131.4250000003063
|
||||
22,131.0999999998403,130.22500000033688,133.07499999955107
|
||||
23,132.7249999997166,131.7500000000109,143.72499999971987
|
||||
24,144.77499999998872,145.1750000001084,146.42499999972424
|
||||
25,146.2750000002943,146.65000000013606,148.35000000020736
|
||||
26,148.05000000001928,148.1749999998101,161.47499999969804
|
||||
27,159.95000000044274,160.22500000008222,163.0750000002059
|
||||
28,161.44999999983884,161.65000000046348,173.70000000009676
|
||||
29,164.39999999989413,163.4500000004664,176.44999999974752
|
||||
30,176.2499999997617,175.30000000033397,178.1250000001797
|
||||
31,177.82499999999163,176.75000000008367,190.25000000037616
|
||||
32,179.52499999979227,178.4499999998843,191.74999999977226
|
||||
33,191.37499999965985,191.67500000048676,194.77499999975188
|
||||
34,193.00000000044565,193.22500000043874,206.62499999961946
|
||||
35,206.37499999998727,194.97499999988577,208.24999999949577
|
||||
36,207.8999999996613,206.82499999975335,220.44999999961655
|
||||
37,209.54999999981555,208.4749999999076,221.8749999999978
|
||||
38,221.45000000023902,220.49999999990177,223.6000000000764
|
||||
39,222.97499999991305,221.97499999992942,236.6749999999207
|
||||
40,224.65000000034524,225.24999999995998,238.22499999987267
|
||||
41,236.50000000021282,235.5000000002292,239.94999999995125
|
||||
42,238.12500000008913,237.3000000002321,250.52500000019572
|
||||
43,250.27499999965403,250.47500000027867,252.0750000001477
|
||||
44,251.74999999968168,251.9999999999527,265.4250000003209
|
||||
45,253.39999999983593,253.60000000046057,266.924999999717
|
||||
46,266.67500000008476,265.57499999989886,268.47499999966897
|
||||
47,268.2500000003147,267.1500000001288,280.7000000000677
|
||||
48,270.1499999996104,279.45000000045184,282.1499999998174
|
||||
49,280.3999999998796,281.99999999969805,285.07499999959475
|
||||
50,282.05000000003383,283.75000000005457,296.94999999974027
|
||||
51,296.64999999955216,295.90000000052896,298.62500000017246
|
||||
52,298.25000000006,297.39999999992506,310.52499999968643
|
||||
53,299.82500000028995,300.34999999998035,312.0749999996384
|
||||
54,311.7249999998039,310.7999999997446,313.89999999991926
|
||||
55,313.2749999997559,312.3499999996966,325.57499999966024
|
||||
56,314.9500000001881,325.9000000002743,327.10000000024377
|
||||
57,326.7749999997777,327.37500000030195,328.94999999989307
|
||||
58,328.35000000000764,339.57500000042273,342.07500000029324
|
||||
59,330.2500000002128,341.02500000017244,343.6250000002452
|
||||
60,341.89999999967586,343.92499999967185,345.2750000003995
|
||||
61,343.4749999999058,355.9250000002976,357.12500000026705
|
||||
62,345.24999999963075,357.4249999996937,358.7249999998654
|
||||
63,356.9749999999276,359.2249999996966,370.99999999991053
|
||||
64,358.4750000002332,370.94999999999345,372.5499999998625
|
||||
65,360.2000000003118,372.45000000029904,385.82500000011134
|
||||
66,371.99999999962347,374.1750000003776,387.32499999950744
|
||||
67,373.6499999997777,387.44999999971697,388.95000000029324
|
||||
68,385.8999999995449,389.0500000002248,400.92499999973154
|
||||
69,387.45000000040636,399.75000000004,402.3999999997592
|
||||
70,390.2000000000571,401.72500000016953,405.45000000001676
|
||||
71,402.124999999849,414.8000000000138,417.3250000001623
|
||||
72,403.6250000001546,416.24999999976353,418.87500000011426
|
||||
73,416.3000000000993,417.95000000047366,420.7999999996879
|
||||
74,418.57499999992615,429.92499999991196,432.39999999950453
|
||||
75,420.2749999997268,432.6249999999163,434.02500000029033
|
||||
76,432.17500000015025,435.7500000000982,446.17499999985523
|
||||
77,433.75000000038017,446.400000000267,447.7249999998072
|
||||
78,435.52500000010514,447.85000000001673,461.0749999999804
|
||||
79,447.22500000012406,460.0249999998596,462.550000000008
|
||||
80,448.85000000000036,461.52500000016516,464.17499999988434
|
||||
81,450.6500000000033,463.02500000047075,476.27499999980284
|
||||
82,462.32499999974425,476.350000000366,477.7499999998305
|
||||
83,463.89999999997417,477.87500000004,479.3250000000604
|
||||
84,465.6500000003307,491.42499999970823,
|
||||
85,477.37499999971806,492.8500000000895,
|
||||
86,478.9000000003016,494.50000000024374,
|
||||
87,480.85000000015316,,
|
||||
,0,1
|
||||
0,3.7000000006628397,0.8999999999021384
|
||||
1,6.925000000137516,8.125000000191722
|
||||
2,14.3250000005537,12.849999999971988
|
||||
3,20.250000000032742,18.875000000562796
|
||||
4,26.27500000062355,26.17500000077671
|
||||
5,36.87500000023647,30.800000000354704
|
||||
6,42.650000000776345,38.575000000392535
|
||||
7,44.35000000057698,48.825000000661746
|
||||
8,54.70000000013897,54.89999999998945
|
||||
9,60.825000000022555,60.75000000045365
|
||||
10,68.10000000086802,66.82500000069085
|
||||
11,73.05000000042128,73.17500000034742
|
||||
12,80.17500000050859,80.35000000008112
|
||||
13,84.95000000084474,86.37500000067193
|
||||
14,92.17500000022483,96.87500000008258
|
||||
15,100.00000000081855,102.8500000001175
|
||||
16,108.92499999999927,109.1000000004813
|
||||
17,115.05000000079235,116.37500000041727
|
||||
18,122.37500000037471,118.07500000021791
|
||||
19,130.07500000048822,128.37500000013353
|
||||
20,134.30000000016662,134.65000000077526
|
||||
21,140.30000000047949,140.4500000006836
|
||||
22,146.25000000023647,150.95000000009424
|
||||
23,152.37500000012005,152.92500000022375
|
||||
24,162.8250000007938,163.05000000001274
|
||||
25,164.57500000024083,170.57499999999965
|
||||
26,170.4000000004271,175.10000000028487
|
||||
27,176.40000000073996,182.5250000000695
|
||||
28,186.85000000050422,193.3000000007185
|
||||
29,188.60000000086075,199.00000000042456
|
||||
30,199.00000000006912,205.07500000066176
|
||||
31,205.02500000065993,211.14999999998946
|
||||
32,212.4750000007225,218.65000000060792
|
||||
33,218.42500000047949,224.70000000056717
|
||||
34,224.65000000056534,230.87500000009715
|
||||
35,234.95000000048094,241.10000000008841
|
||||
36,241.0000000004402,242.87500000072288
|
||||
37,248.42500000022483,253.1250000000826
|
||||
38,253.02500000043437,259.1500000006734
|
||||
39,259.2250000002423,265.1250000007083
|
||||
40,265.2000000002772,271.27499999996036
|
||||
41,272.4750000002132,283.1000000004595
|
||||
42,278.500000000804,284.75000000061374
|
||||
43,284.7500000002583,289.62500000024266
|
||||
44,290.6000000007225,295.52500000035326
|
||||
45,302.50000000023647,307.1750000007258
|
||||
46,307.12500000072396,309.12500000057736
|
||||
47,313.20000000005166,319.20000000071997
|
||||
48,320.65000000011423,320.80000000031833
|
||||
49,331.12500000015643,331.5500000006894
|
||||
50,332.625000000462,337.35000000059773
|
||||
51,340.45000000014625,343.32500000063266
|
||||
52,343.22500000007494,349.6500000000113
|
||||
53,352.4000000002161,355.5000000004755
|
||||
54,361.2000000007356,367.27500000041874
|
||||
55,368.80000000064683,368.94999999994144
|
||||
56,373.4000000008564,379.4500000002616
|
||||
57,379.27500000068903,385.4250000002965
|
||||
58,386.7250000007516,391.3750000000535
|
||||
59,397.35000000064247,397.525000000215
|
||||
60,403.35000000004584,403.57500000017427
|
||||
61,410.77500000073996,409.6250000001335
|
||||
62,416.7500000007749,415.6250000004464
|
||||
63,421.5000000008331,424.62500000046094
|
||||
64,428.8000000001375,433.4999999999953
|
||||
65,433.4750000002714,439.72500000008114
|
||||
66,440.75000000020736,445.70000000011606
|
||||
67,446.8500000007225,451.5250000003023
|
||||
68,457.4999999999818,459.2000000001379
|
||||
69,466.4750000006279,469.4500000004071
|
||||
70,470.8750000004329,475.45000000071997
|
||||
71,478.60000000082437,477.12500000024266
|
||||
72,481.47500000004584,487.4500000004362
|
||||
73,493.35000000019136,493.77500000072433
|
||||
74,494.9250000004213,
|
||||
|
||||
|
@ -1,78 +1,90 @@
|
||||
,1,0,2
|
||||
0,9.050000000165145,11.230000000265527,10.09999999954196
|
||||
1,10.54999999956124,18.6800000003281,19.250000000314667
|
||||
2,18.15000000038197,20.23000000028008,29.599999999876655
|
||||
3,19.675000000056006,29.330000000496902,31.275000000308847
|
||||
4,28.749999999994888,38.1799999997533,40.17500000012112
|
||||
5,37.67500000008511,39.82999999990755,47.72500000038597
|
||||
6,39.44999999981008,48.955000000402315,49.699999999605986
|
||||
7,49.62500000015496,50.52999999972274,59.82500000030447
|
||||
8,58.775000000018174,59.45499999981296,68.80000000004108
|
||||
9,60.32499999997015,68.48000000010546,70.45000000019533
|
||||
10,69.39999999990903,71.35500000023643,80.77500000038887
|
||||
11,71.05000000006328,79.17999999992065,82.44999999991157
|
||||
12,79.8000000000269,89.35500000026553,89.89999999997414
|
||||
13,88.82500000031939,91.02999999978823,98.92500000026664
|
||||
14,90.47499999956415,100.02999999980278,100.524999999865
|
||||
15,99.52500000013458,101.65499999967909,110.92499999998287
|
||||
16,109.89999999997451,112.10500000035285,119.89999999971948
|
||||
17,111.52499999985082,119.63000000033975,121.57500000015169
|
||||
18,119.02499999955978,128.60500000007636,129.42500000011387
|
||||
19,120.92499999976496,130.40500000007927,132.2250000003205
|
||||
20,129.49999999960198,140.67999999971693,140.99999999965257
|
||||
21,131.2999999996049,149.67999999973148,150.07499999959145
|
||||
22,141.9499999997737,151.22999999968346,159.17499999980828
|
||||
23,149.37499999955833,160.25499999997595,160.87499999960892
|
||||
24,152.12500000011858,161.9050000001302,169.92500000017935
|
||||
25,161.12500000013313,170.83000000022042,180.12499999989268
|
||||
26,168.67500000039797,179.9050000001593,181.77500000004693
|
||||
27,170.4749999994914,188.9300000004518,190.77500000006148
|
||||
28,180.7249999997606,192.15499999992647,192.3500000002914
|
||||
29,182.27499999971258,199.5799999997111,199.89999999964675
|
||||
30,191.22500000008074,201.45500000054784,210.2249999998403
|
||||
31,198.79999999971403,211.52999999978096,211.8499999997166
|
||||
32,200.37499999994395,220.5800000003514,219.4250000002594
|
||||
33,210.8249999997082,229.45499999988573,229.9000000003016
|
||||
34,212.62499999971112,230.95500000019132,231.5250000001779
|
||||
35,221.27500000038197,240.00499999985226,240.42499999999018
|
||||
36,230.39999999996724,241.68000000028445,242.29999999991742
|
||||
37,231.9999999995656,250.53000000045034,251.25000000028558
|
||||
38,241.09999999978243,259.5800000001113,260.19999999974425
|
||||
39,249.875000000024,261.1550000003412,269.1249999998345
|
||||
40,251.47499999962236,270.20500000000214,270.67499999978645
|
||||
41,260.4749999996369,279.17999999973875,279.57499999959873
|
||||
42,269.52500000020734,280.8800000004489,281.1249999995507
|
||||
43,272.55000000018697,291.20499999973293,290.35000000024775
|
||||
44,280.22500000002253,300.25500000030337,291.97500000012406
|
||||
45,281.80000000025245,301.85499999990174,300.4499999997588
|
||||
46,292.1249999995365,309.6550000002175,302.32499999968604
|
||||
47,293.7999999999687,319.8800000002088,311.17499999985193
|
||||
48,302.5999999995787,321.53000000036303,321.72499999981846
|
||||
49,311.6999999997955,330.32999999997304,330.6000000002623
|
||||
50,319.3249999999847,332.00500000040523,332.1500000002143
|
||||
51,323.7750000003456,342.3549999999672,334.10000000006585
|
||||
52,331.22499999949866,351.35499999998177,343.1499999997268
|
||||
53,338.9999999995365,353.0549999997824,350.550000000143
|
||||
54,341.8999999999454,362.0050000001506,360.82499999978063
|
||||
55,351.17500000028883,369.57999999978387,363.97500000024047
|
||||
56,359.8250000000502,371.25500000021606,371.29999999982283
|
||||
57,361.4999999995729,381.405000000283,380.2999999998374
|
||||
58,370.57499999951176,383.0799999998057,381.9249999997137
|
||||
59,379.59999999980425,392.1300000003761,392.4749999996802
|
||||
60,383.0999999996078,393.8550000004547,399.8750000000964
|
||||
61,390.3500000001753,401.3800000004416,401.4749999996948
|
||||
62,399.2000000003412,410.30500000053183,410.54999999963366
|
||||
63,409.5000000002568,420.6299999998159,412.00000000029286
|
||||
64,410.9500000000065,422.2050000000458,420.97500000002947
|
||||
65,421.49999999997306,431.3050000002626,422.6250000001837
|
||||
66,423.1500000001273,441.7050000003805,431.55000000027394
|
||||
67,432.02499999966165,443.4300000004591,433.1499999998723
|
||||
68,441.04999999995414,450.6800000001171,442.20000000044274
|
||||
69,442.72500000038633,452.3550000005493,451.1499999999014
|
||||
70,450.3000000000196,462.7800000000356,460.2249999998403
|
||||
71,459.4750000001608,470.5800000003514,461.8000000000702
|
||||
72,462.3250000000138,472.1050000000254,472.0999999999858
|
||||
73,471.2999999997504,481.25499999988864,479.82500000037726
|
||||
74,480.2500000001186,491.4300000002335,481.3500000000513
|
||||
75,481.80000000007055,500.47999999989446,490.52500000019245
|
||||
76,490.82500000036305,,
|
||||
,0,1
|
||||
0,2.21500000002689,0.6200000005089019
|
||||
1,12.515000000851984,13.89500000075774
|
||||
2,14.09000000017241,15.445000000709719
|
||||
3,15.66500000040233,17.020000000030144
|
||||
4,18.79000000058423,32.02000000035756
|
||||
5,32.16500000012584,33.52000000066315
|
||||
6,33.690000000709375,35.02000000005925
|
||||
7,36.59000000020879,37.970000000114545
|
||||
8,51.59000000053621,53.070000000644235
|
||||
9,53.16500000076613,54.57000000004033
|
||||
10,54.715000000718106,56.11999999999231
|
||||
11,57.61500000021752,59.34500000037648
|
||||
12,72.7650000003936,73.09500000044923
|
||||
13,75.56500000060024,75.54500000040267
|
||||
14,77.3899999999716,77.21999999992536
|
||||
15,92.36500000002107,92.42000000065732
|
||||
16,93.84000000004872,95.02000000045942
|
||||
17,96.6650000005333,96.64500000033573
|
||||
18,111.69000000022916,98.47000000061658
|
||||
19,113.29000000073702,113.19500000061512
|
||||
20,114.81500000041106,114.69500000001122
|
||||
21,117.76500000046636,116.29500000051908
|
||||
22,132.81500000044016,119.67000000075191
|
||||
23,134.31500000074575,134.170000000068
|
||||
24,135.86500000069773,135.72000000001998
|
||||
25,150.99000000059587,137.37000000017423
|
||||
26,153.6650000003223,152.3950000007796
|
||||
27,155.36500000012293,154.39500000027755
|
||||
28,157.16500000012584,156.72000000066026
|
||||
29,173.26500000085926,158.44500000073884
|
||||
30,174.7900000005333,173.42000000078832
|
||||
31,176.53999999998032,174.9700000007403
|
||||
32,192.8400000002088,176.52000000069228
|
||||
33,194.34000000051438,192.7950000006428
|
||||
34,195.81500000054203,194.2950000000389
|
||||
35,197.81500000004,195.87000000026882
|
||||
36,212.79000000008946,197.5950000003474
|
||||
37,215.31499999996723,212.44499999991666
|
||||
38,217.01500000067736,215.22000000075485
|
||||
39,232.09000000001961,216.94499999992394
|
||||
40,234.84000000057986,233.32000000007673
|
||||
41,236.4900000007341,234.84500000066026
|
||||
42,238.29000000073702,236.39500000061224
|
||||
43,252.99000000045763,251.5950000004347
|
||||
44,254.5400000004096,254.34500000008546
|
||||
45,256.26500000048816,256.07000000016404
|
||||
46,271.290000000184,258.0200000000156
|
||||
47,273.91500000026406,272.44500000031684
|
||||
48,275.6650000006206,274.0449999999152
|
||||
49,279.99000000050125,275.5950000007767
|
||||
50,293.5650000004474,278.42000000035176
|
||||
51,295.0150000001971,293.4200000006792
|
||||
52,296.6900000006293,294.97000000063116
|
||||
53,312.96500000057983,296.52000000058314
|
||||
54,314.4900000002539,311.8449999999763
|
||||
55,316.09000000076173,314.39500000013203
|
||||
56,317.76500000028443,316.0700000005642
|
||||
57,332.6650000004096,320.77000000006655
|
||||
58,334.16500000071517,332.5950000005657
|
||||
59,335.7900000005915,334.37000000029064
|
||||
60,340.0400000005478,338.5200000000447
|
||||
61,353.615000000494,353.4950000000942
|
||||
62,355.11500000079957,355.0200000006777
|
||||
63,356.9150000008025,356.59499999999815
|
||||
64,373.09000000055073,359.77000000073593
|
||||
65,374.61500000022477,373.14500000027755
|
||||
66,376.1900000004547,374.6950000002295
|
||||
67,391.61500000005014,376.5200000005104
|
||||
68,394.16500000020585,392.59500000005636
|
||||
69,395.8650000000065,394.1950000005642
|
||||
70,397.41500000086796,395.76999999988465
|
||||
71,412.3650000006395,400.39500000037214
|
||||
72,415.1400000005682,413.6200000000651
|
||||
73,416.79000000072244,415.195000000295
|
||||
74,433.16499999996574,416.8200000001713
|
||||
75,434.7150000008272,431.8700000001451
|
||||
76,436.2650000007792,433.44500000037505
|
||||
77,438.1150000004285,436.1950000000258
|
||||
78,452.865000000705,437.9450000003823
|
||||
79,454.34000000073263,452.7949999999516
|
||||
80,456.0150000002553,454.2950000002572
|
||||
81,472.3900000004081,455.79500000056277
|
||||
82,473.86500000043577,458.84499999991084
|
||||
83,475.3900000001098,473.8700000005162
|
||||
84,478.31500000079666,475.4200000004682
|
||||
85,493.2650000005682,476.9950000006981
|
||||
86,494.8400000007981,492.12000000059624
|
||||
87,496.4400000003965,494.72000000039833
|
||||
88,499.44000000009817,496.4450000004769
|
||||
|
||||
|
@ -520,7 +520,6 @@ Theoretical work shows that leaky-integrate-and-fire (LIF) model neurons show a
|
||||
\subsection*{Low-CV P-units exhibit nonlinear interactions} %frequency combinations withappearing when the input frequencies are related to \fbase{} are
|
||||
Second-order susceptibility is expected to be especially pronounced for low-CV cells \cite{Voronenko2017}. P-units fire action potentials probabilistically phase-locked to the self-generated EOD. Skipping of EOD cycles leads to the characteristic multimodal ISI distribution with maxima at integer multiples of the EOD period (\subfigrefb{fig:cells_suscept}{A}). In this example the ISI distribution has a CV of 0.2 which can be considered low among P-units\cite{Hladnik2023}. Spectral analysis of the baseline activity shows two major peaks, the first is located at the baseline firing rate (\fbase), the second is located at the discharge frequency of the electric organ (\feod{}) and is flanked by two smaller peaks at $\feod \pm \fbase{}$ (\subfigref{fig:cells_suscept}{B}). High-CV P-units do not exhibit pronounced nonlinearities (for more details see supplementary information: \nameref*{S1:highcvpunit} )
|
||||
|
||||
%
|
||||
|
||||
\begin{figure*}[!ht]
|
||||
\includegraphics[width=\columnwidth]{cells_suscept}
|
||||
@ -571,10 +570,11 @@ We calculated the second-order susceptibility surfaces at \fsum{} by extracting
|
||||
|
||||
%section \ref{intrinsicsplit_methods}).\figitem{A} Absolute value of the second-order susceptibility of an electrophysiologically recorded P-unit. RAM stimulus realizations $N=11$. Diagonal bands appear when the sum of the frequencies \fsum{} or the difference \fdiff{} is equal to \fbase{}. \figitem{B} The diagonals, that were present in \panel{A}, are complemented by vertical and horizontal lines when \fone{} or \ftwo{} are equal to \fbase{}. Note that the different scale of the second-order susceptibility is associated with the higher signal-to-ratio in case of 1 million repeats in \panel{B}.
|
||||
|
||||
The second-order susceptibility can also be calculated for the full matrix including negative frequency components of the respective spectra in \Eqnsref{eq:crosshigh} and (\ref{eq:susceptibility}). The resulting \suscept{} matrix is symmetric with respect to the origin and shows \suscept{} at \fsum{} in the upper-right and lower-left quadrants and \suscept{} for the differences \fdiff{} in the lower-right and upper-left quadrants \cite{Voronenko2017} (\figref{fig:model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \figref{fig:model_full} for the nonlinearity at \fsum{} and extend into the upper-left quadrant (representing \fdiff) fading out towards more negative $f_1$ frequencies. \suscept{} values at \fsum{} match the \fsum{} peak seen in \figref{fig:motivation}.
|
||||
The second-order susceptibility can also be calculated for the full matrix including negative frequency components of the respective spectra in \Eqnsref{eq:crosshigh} and (\ref{eq:susceptibility}). The resulting \suscept{} matrix is symmetric with respect to the origin and shows \suscept{} at \fsum{} in the upper-right and lower-left quadrants and \suscept{} for the differences \fdiff{} in the lower-right and upper-left quadrants \cite{Voronenko2017} (\subfigrefb{fig:model_full}{A}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \figref{fig:model_full} for the nonlinearity at \fsum{} and extend into the upper-left quadrant (representing \fdiff) fading out towards more negative $f_1$ frequencies. \suscept{} values at \fsum{} are present in the model with pure sine wave stimulation (\subfigrefb{fig:model_full}{B}, left) and match the \fsum{} peak seen in \figref{fig:motivation} that is also shown in (\subfigrefb{fig:model_full}{B}, right).
|
||||
|
||||
The smaller \fdiff{} power spectral peak observed during pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}) can be explained by the fading out horizontal line in the upper-left quadrant (\figrefb{fig:model_full}, \cite{Schlungbaum2023}). Even though the second-order susceptibilities here were estimated form data and models with an modulated (EOD) carrier (\figrefb{fig:model_full}) they are in good accordance with the second-order susceptibilities found in LIF models without a carrier\cite{Voronenko2017, Schlungbaum2023}.
|
||||
The smaller \fdiff{} power spectral peak observed during pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}, \subfigrefb{fig:model_full}{B}) can be explained by the fading out horizontal line in the upper-left quadrant (\figrefb{fig:model_full}, \cite{Schlungbaum2023}). Even though the second-order susceptibilities here were estimated form data and models with an modulated (EOD) carrier (\figrefb{fig:model_full}) they are in good accordance with the second-order susceptibilities found in LIF models without a carrier\cite{Voronenko2017, Schlungbaum2023}.
|
||||
|
||||
If two frequencies not part of the triangular structure are chosen with pure sine wave stimulation no nonlinearity peaks appear (\subfigrefb{fig:model_full}{C}). \notesr{Das sind toy Beispiele, die Powerspectren, da arbeite ich noch dran. Und auch an den Einheiten.}
|
||||
|
||||
\begin{figure*}[!ht]
|
||||
\includegraphics[width=\columnwidth]{data_overview_mod}
|
||||
|
||||
@ -520,7 +520,6 @@ Theoretical work shows that leaky-integrate-and-fire (LIF) model neurons show a
|
||||
\subsection*{Low-CV P-units exhibit nonlinear interactions} %frequency combinations withappearing when the input frequencies are related to \fbase{} are
|
||||
Second-order susceptibility is expected to be especially pronounced for low-CV cells \cite{Voronenko2017}. P-units fire action potentials probabilistically phase-locked to the self-generated EOD. Skipping of EOD cycles leads to the characteristic multimodal ISI distribution with maxima at integer multiples of the EOD period (\subfigrefb{fig:cells_suscept}{A}). In this example the ISI distribution has a CV of 0.2 which can be considered low among P-units\cite{Hladnik2023}. Spectral analysis of the baseline activity shows two major peaks, the first is located at the baseline firing rate (\fbase), the second is located at the discharge frequency of the electric organ (\feod{}) and is flanked by two smaller peaks at $\feod \pm \fbase{}$ (\subfigref{fig:cells_suscept}{B}). High-CV P-units do not exhibit pronounced nonlinearities (for more details see supplementary information: \nameref*{S1:highcvpunit} )
|
||||
|
||||
%
|
||||
|
||||
\begin{figure*}[!ht]
|
||||
\includegraphics[width=\columnwidth]{cells_suscept}
|
||||
@ -571,10 +570,11 @@ We calculated the second-order susceptibility surfaces at \fsum{} by extracting
|
||||
|
||||
%section \ref{intrinsicsplit_methods}).\figitem{A} Absolute value of the second-order susceptibility of an electrophysiologically recorded P-unit. RAM stimulus realizations $N=11$. Diagonal bands appear when the sum of the frequencies \fsum{} or the difference \fdiff{} is equal to \fbase{}. \figitem{B} The diagonals, that were present in \panel{A}, are complemented by vertical and horizontal lines when \fone{} or \ftwo{} are equal to \fbase{}. Note that the different scale of the second-order susceptibility is associated with the higher signal-to-ratio in case of 1 million repeats in \panel{B}.
|
||||
|
||||
The second-order susceptibility can also be calculated for the full matrix including negative frequency components of the respective spectra in \Eqnsref{eq:crosshigh} and (\ref{eq:susceptibility}). The resulting \suscept{} matrix is symmetric with respect to the origin and shows \suscept{} at \fsum{} in the upper-right and lower-left quadrants and \suscept{} for the differences \fdiff{} in the lower-right and upper-left quadrants \cite{Voronenko2017} (\figref{fig:model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \figref{fig:model_full} for the nonlinearity at \fsum{} and extend into the upper-left quadrant (representing \fdiff) fading out towards more negative $f_1$ frequencies. \suscept{} values at \fsum{} match the \fsum{} peak seen in \figref{fig:motivation}.
|
||||
The second-order susceptibility can also be calculated for the full matrix including negative frequency components of the respective spectra in \Eqnsref{eq:crosshigh} and (\ref{eq:susceptibility}). The resulting \suscept{} matrix is symmetric with respect to the origin and shows \suscept{} at \fsum{} in the upper-right and lower-left quadrants and \suscept{} for the differences \fdiff{} in the lower-right and upper-left quadrants \cite{Voronenko2017} (\subfigrefb{fig:model_full}{A}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \figref{fig:model_full} for the nonlinearity at \fsum{} and extend into the upper-left quadrant (representing \fdiff) fading out towards more negative $f_1$ frequencies. \suscept{} values at \fsum{} are present in the model with pure sine wave stimulation (\subfigrefb{fig:model_full}{B}, left) and match the \fsum{} peak seen in \figref{fig:motivation} that is also shown in (\subfigrefb{fig:model_full}{B}, right).
|
||||
|
||||
The smaller \fdiff{} power spectral peak observed during pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}) can be explained by the fading out horizontal line in the upper-left quadrant (\figrefb{fig:model_full}, \cite{Schlungbaum2023}). Even though the second-order susceptibilities here were estimated form data and models with an modulated (EOD) carrier (\figrefb{fig:model_full}) they are in good accordance with the second-order susceptibilities found in LIF models without a carrier\cite{Voronenko2017, Schlungbaum2023}.
|
||||
The smaller \fdiff{} power spectral peak observed during pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}, \subfigrefb{fig:model_full}{B}) can be explained by the fading out horizontal line in the upper-left quadrant (\figrefb{fig:model_full}, \cite{Schlungbaum2023}). Even though the second-order susceptibilities here were estimated form data and models with an modulated (EOD) carrier (\figrefb{fig:model_full}) they are in good accordance with the second-order susceptibilities found in LIF models without a carrier\cite{Voronenko2017, Schlungbaum2023}.
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If two frequencies not part of the triangular structure are chosen with pure sine wave stimulation no nonlinearity peaks appear (\subfigrefb{fig:model_full}{C}). \notesr{Das sind toy Beispiele, die Powerspectren, da arbeite ich noch dran. Und auch an den Einheiten.}
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\begin{figure*}[!ht]
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\includegraphics[width=\columnwidth]{data_overview_mod}
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