+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Using learning_mFISH branch of visual_behavior_analysis
+
+
+
+
+In [1]:
+
+
+
+
+
+
+import os
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+import seaborn as sns
+sns.set_context('notebook', font_scale=1.5, rc={'lines.markeredgewidth': 2})
+
+
+
+
+
+In [2]:
+
+
+
+
+
+
+%load_ext autoreload
+%autoreload 2
+
+%matplotlib inline
+
+
+
+
+
+In [3]:
+
+
+
+
+
+
+import visual_behavior.data_access.loading as loading
+
+
+
+
+
+get learning mFISH pilot data from lims¶
+
+
+
+
+
+In [4]:
+
+
+
+
+
+
+from allensdk.brain_observatory.behavior.behavior_project_cache import VisualBehaviorOphysProjectCache
+
+cache = VisualBehaviorOphysProjectCache.from_lims()
+
+
+
+
+
+In [5]:
+
+
+
+
+
+
+experiments_table = cache.get_ophys_experiment_table(passed_only=False)
+experiments_table = experiments_table[experiments_table.project_code=='LearningmFISHTask1A']
+
+
+
+
+
+In [6]:
+
+
+
+
+
+
+# what mice do we have?
+print(experiments_table.mouse_id.unique())
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+get behavior sessions for special mouse¶
+
+
+
+
+
+In [7]:
+
+
+
+
+
+
+behavior_sessions = cache.get_behavior_session_table()
+
+
+
+
+
+In [8]:
+
+
+
+
+
+
+mouse_id = '603892' # bestest GAD2 mouse
+
+# look at training history for this mouse
+mouse_beh_data = behavior_sessions[behavior_sessions.mouse_id==mouse_id].sort_values(by='date_of_acquisition')
+mouse_beh_data[['mouse_id', 'session_type', 'ophys_experiment_id', 'prior_exposures_to_image_set']]
+
+
+
+
+
+
+
+
+
+
+
+Out[8]:
+
+
+
+
+
+
+
+
+
+
+Get an ophys_experiment_id for one of the OPHYS_1_images_A sessions¶
+
+
+
+
+
+In [9]:
+
+
+
+
+
+
+experiment_ids = experiments_table[experiments_table.behavior_session_id==1156064616].index.values
+print(experiment_ids)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [10]:
+
+
+
+
+
+
+experiment_id = experiment_ids[0]
+
+
+
+
+
+load ophys dataset for this experiment¶
+
+
+
+
+
+In [11]:
+
+
+
+
+
+
+dataset = cache.get_behavior_ophys_experiment(experiment_id)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [12]:
+
+
+
+
+
+
+plt.imshow(dataset.max_projection, cmap='gray')
+
+
+
+
+
+
+
+
+
+
+
+Out[12]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [13]:
+
+
+
+
+
+
+plt.imshow(dataset.segmentation_mask_image, cmap='gray')
+
+
+
+
+
+
+
+
+
+
+
+Out[13]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [14]:
+
+
+
+
+
+
+dataset.dff_traces
+
+
+
+
+
+
+
+
+
+
+
+Out[14]:
+
+
+
+
+
+
+
+
+
+
+generate a dataframe of stimulus aligned traces for all cells in this dataset¶
+
+
+
+
+
+This VBA helper function calls core functions in mindscope_utilities, including mindscope_utilities.visual_behavior_ophys.data_formatting.get_stimulus_response_df and mindscope_utilities, including mindscope_utilities.visual_behavior_ophys.data_formatting.get_annotated_stimulus_presentations
+
+
+
+
+In [15]:
+
+
+
+
+
+
+stimulus_response_df = loading.get_stimulus_response_df(dataset, time_window=[-3, 3.1],
+ interpolate=True, output_sampling_rate=30,
+ data_type='dff', event_type='all')
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+stimulus_response_df contains the stimulus aligned trace for every cell, for every stimulus presentation in the session, in a defined time window around stimulus onset
+
+
+
+
+In [16]:
+
+
+
+
+
+
+stimulus_response_df.head()
+
+
+
+
+
+
+
+
+
+
+
+Out[16]:
+
+
+
+
+
+
+
+
+
+
+plot average response for a few conditions¶
+
+
+
+
+
+You can easily plot the population average response for all rows of the table (all stimulus conditions, all cells), or separating out just omissions or just changes
+ +
+
+
+
+
+average everything in stim_response_df¶
+
+
+
+
+
+In [17]:
+
+
+
+
+
+
+plt.plot(stimulus_response_df.trace_timestamps.mean(), stimulus_response_df.trace.mean())
+plt.xlabel('time relative to stimulus onset (s)')
+plt.ylabel('population response')
+
+
+
+
+
+
+
+
+
+
+
+Out[17]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+just image changes¶
+
+
+
+
+
+In [18]:
+
+
+
+
+
+
+# changes
+traces = stimulus_response_df[stimulus_response_df.is_change==True].trace.values
+timestamps = stimulus_response_df.trace_timestamps.values[0] # timestamps are shared across all rows
+plt.plot(timestamps, traces.mean())
+plt.xlabel('time after change (s)')
+plt.ylabel('population response')
+
+
+
+
+
+
+
+
+
+
+
+Out[18]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+across images¶
+
+
+
+
+
+In [19]:
+
+
+
+
+
+
+# for each image
+for image_name in stimulus_response_df.image_name.unique():
+ traces = stimulus_response_df[stimulus_response_df.image_name==image_name].trace.values
+ timestamps = stimulus_response_df.trace_timestamps.values[0] # timestamps are shared across all rows
+ plt.plot(timestamps, traces.mean(), label=image_name)
+plt.xlabel('time (s)')
+plt.ylabel('population response')
+plt.legend(bbox_to_anchor=(1,1))
+
+
+
+
+
+
+
+
+
+
+
+Out[19]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+There is a lot of metadata for each stimulus presentation
+ +
+
+
+
+
+In [20]:
+
+
+
+
+
+
+stimulus_response_df.keys()
+
+
+
+
+
+
+
+
+
+
+
+Out[20]:
+
+
+
+
+
+
+
+
+
+
+
+Plot population average for hit vs miss with sem¶
+
+
+
+
+
+In [21]:
+
+
+
+
+
+
+import visual_behavior.visualization.utils as utils
+
+
+
+
+
+In [22]:
+
+
+
+
+
+
+# hits vs. misses
+hit_traces = stimulus_response_df[(stimulus_response_df.is_change==True)&
+ (stimulus_response_df.licked==True)].trace.values
+miss_traces = stimulus_response_df[(stimulus_response_df.is_change==True)&
+ (stimulus_response_df.licked==False)].trace.values
+timestamps = stimulus_response_df.trace_timestamps.values[0] # timestamps are shared across all rows
+
+fig, ax = plt.subplots()
+ax = utils.plot_mean_trace(hit_traces, timestamps, legend_label='hit', color='g', xlim_seconds=[-2, 2], ax=ax)
+ax = utils.plot_mean_trace(miss_traces, timestamps, legend_label='miss', color='r', xlim_seconds=[-2, 2], ax=ax)
+ax = utils.plot_flashes_on_trace(ax, timestamps, change=True)
+ax.set_xlabel('time after change (s)')
+ax.set_ylabel('population response')
+
+
+
+
+
+
+
+
+
+
+
+Out[22]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+stimulus_response_df also works for behavior timeseries¶
+
+
+
+
+
+check the documentation for what data_type values are accepted
+
+
+
+
+In [23]:
+
+
+
+
+
+
+help(loading.get_stimulus_response_df)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+population average running speed for changes¶
+
+
+
+
+
+In [24]:
+
+
+
+
+
+
+# use a different data_type, and set event_type to just get changes
+running_traces = loading.get_stimulus_response_df(dataset, time_window=[-2, 2.1],
+ interpolate=True, output_sampling_rate=30,
+ data_type='running_speed', event_type='changes')
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [25]:
+
+
+
+
+
+
+fig, ax = plt.subplots()
+timestamps = running_traces.trace_timestamps.values[0]
+traces = running_traces.trace.values
+ax = utils.plot_mean_trace(traces, timestamps, xlim_seconds=[-2, 2.1], ax=ax)
+ax = utils.plot_flashes_on_trace(ax, timestamps, change=True)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+mean response dataframe¶
+
+
+
+
+
+Compute trial averaged responses for some set of conditions for one experiment¶
+
+
+
+
+
+In [26]:
+
+
+
+
+
+
+# lets look at the first day of novel images
+expts = experiments_table[(experiments_table.mouse_id==mouse_id)&
+ (experiments_table.prior_exposures_to_image_set==0)&
+ (experiments_table.session_type=='OPHYS_4_images_B')]
+
+expts
+
+
+
+
+
+
+
+
+
+
+
+Out[26]:
+
+
+
+
+
+
+
+
+
+
+In [27]:
+
+
+
+
+
+
+experiment_id = expts.index.values[0]
+
+expts.loc[experiment_id][['targeted_structure', 'imaging_depth', 'cre_line']]
+
+
+
+
+
+
+
+
+
+
+
+Out[27]:
+
+
+
+
+
+
+
+
+
+
+
+In [28]:
+
+
+
+
+
+
+# include invalid ROIs so it actually loads something
+dataset = loading.get_ophys_dataset(experiment_id)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [29]:
+
+
+
+
+
+
+dataset.dff_traces
+
+
+
+
+
+
+
+
+
+
+
+Out[29]:
+
+
+
+
+
+
+
+
+
+
+In [30]:
+
+
+
+
+
+
+# set all params here so they can be used later
+time_window = [-3, 3.1]
+interpolate = True
+output_sampling_rate = 30
+data_type = 'dff'
+event_type = 'changes'
+# get stimulus_response_df for changes, with annotated stimulus presentations columns
+stimulus_response_df = loading.get_stimulus_response_df(dataset, time_window=time_window,
+ interpolate=interpolate, output_sampling_rate=output_sampling_rate,
+ data_type=data_type, event_type=event_type)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+get average response dataframe, averaging over all changes presentations in 10 minute epochs in the session¶
+
+
+
+
+
+In [31]:
+
+
+
+
+
+
+df = stimulus_response_df.copy()
+
+
+
+
+
+In [32]:
+
+
+
+
+
+
+# check that 'epoch' column is in the dataframe so it can be used as a condition to group by
+df.keys()
+
+
+
+
+
+
+
+
+
+
+
+Out[32]:
+
+
+
+
+
+
+
+
+
+
+
+In [33]:
+
+
+
+
+
+
+import visual_behavior.ophys.response_analysis.utilities as ut
+
+
+
+
+
+In [34]:
+
+
+
+
+
+
+# get params for mean df creation from stimulus_response_df
+if 'response_window_duration' in df.keys():
+ response_window_duration = df.response_window_duration.values[0]
+output_sampling_rate = df.frame_rate.unique()[0]
+timestamps = df.trace_timestamps.values[0]
+window_around_timepoint_seconds = [timestamps[0], timestamps[-1]]
+
+# set conditions to average over
+conditions = ['cell_specimen_id', 'epoch']
+# use VBA get_mean_df function to average over trials defined by `conditions`
+# must use same time_window and frame rate as was used to create the stim_response_df
+mdf = ut.get_mean_df(df, conditions=conditions, frame_rate=output_sampling_rate,
+ time_window=time_window, response_window_duration=response_window_duration)
+# get rid of last epoch which doesnt have 10 full minutes in it
+epochs = np.sort(mdf.epoch.unique())
+mdf = mdf[mdf.epoch<epochs[-1]]
+
+
+
+
+
+In [35]:
+
+
+
+
+
+
+mdf.head(3)
+
+
+
+
+
+
+
+
+
+
+
+Out[35]:
+
+
+
+
+
+
+
+
+
+
+function to plot the average +/- sem trace for one cell¶
+
+
+
+
+
+In [36]:
+
+
+
+
+
+
+import visual_behavior.visualization.utils as utils
+
+
+
+
+
+In [37]:
+
+
+
+
+
+
+cell_specimen_id = mdf.cell_specimen_id.unique()[0]
+epochs = mdf.epoch.unique()
+colors = sns.color_palette('magma', len(epochs))
+fig, ax = plt.subplots()
+for i,epoch in enumerate(epochs):
+ cell_data = mdf[(mdf.cell_specimen_id==cell_specimen_id)&(mdf.epoch==epoch)]
+ ax = utils.plot_mean_trace_from_mean_df(cell_data, frame_rate=output_sampling_rate, color=colors[i],
+ legend_label=epoch, xlims=time_window, ax=ax)
+ ax = utils.plot_flashes_on_trace(ax, timestamps=cell_data.trace_timestamps.values[0], change=True)
+ax.legend(fontsize='x-small', title='epoch', title_fontsize='x-small', loc='upper left')
+ax.set_title('cell_specimen_id: '+str(cell_specimen_id))
+
+
+
+
+
+
+
+
+
+
+
+Out[37]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+
+
+
+
+
+Aggregate trial averaged responses for all session for one container¶
+
+
+
+
+
+In [39]:
+
+
+
+
+
+
+# get some container for special mouse
+mouse_data = experiments_table[experiments_table.mouse_id==mouse_id]
+container_id = mouse_data.ophys_container_id.unique()[0]
+experiment_ids = mouse_data[mouse_data.ophys_container_id==container_id].index.values
+print(len(experiment_ids))
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Note: this takes a while
+ +
+
+
+
+
+In [40]:
+
+
+
+
+
+
+# params for stim_response_df
+data_type = 'dff'
+event_type = 'changes'
+time_window = [-2, 2.1]
+interpolate = True
+output_sampling_rate = 30
+
+# conditions to average trials over
+conditions = ['cell_specimen_id', 'image_name']
+
+# loop through experients and aggregated trial averaged dfs
+big_mdf = pd.DataFrame()
+for experiment_id in experiment_ids:
+ try: # not all experiments load so need to to try except
+ print('expt_id:', experiment_id, ',', np.where(experiment_ids==experiment_id)[0][0], 'out of', len(experiment_ids))
+ # get dataset
+ dataset = loading.get_ophys_dataset(experiment_id)
+ # get stimulus_response_df
+ df = loading.get_stimulus_response_df(dataset, data_type=data_type, event_type=event_type, time_window=time_window,
+ interpolate=interpolate, output_sampling_rate=output_sampling_rate)
+ # get params for mean df creation from stimulus_response_df
+ if 'response_window_duration' in df.keys():
+ response_window_duration = df.response_window_duration.values[0]
+ output_sampling_rate = df.frame_rate.unique()[0]
+ timestamps = df.trace_timestamps.values[0]
+ window_around_timepoint_seconds = [timestamps[0], timestamps[-1]]
+ # get trial averaged response for conditions
+ mdf = ut.get_mean_df(df, conditions=conditions, frame_rate=output_sampling_rate,
+ time_window=time_window,
+ response_window_duration=response_window_duration)
+ # add experiment ID to be able to distinguish different sessions
+ mdf['ophys_experiment_id'] = experiment_id
+ # aggregate
+ big_mdf = pd.concat([big_mdf, mdf])
+ except Exception as e:
+ print(e)
+ print('problem for', experiment_id)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [45]:
+
+
+
+
+
+
+big_mdf.keys()
+
+
+
+
+
+
+
+
+
+
+
+Out[45]:
+
+
+
+
+
+
+
+
+
+
+
+In [46]:
+
+
+
+
+
+
+len(big_mdf)
+
+
+
+
+
+
+
+
+
+
+
+Out[46]:
+
+
+
+
+
+
+
+
+
+
+
+In [47]:
+
+
+
+
+
+
+big_mdf = big_mdf.merge(experiments_table, on='ophys_experiment_id')
+len(big_mdf)
+
+
+
+
+
+
+
+
+
+
+
+Out[47]:
+
+
+
+
+
+
+
+
+
+
+
+plot population average response for each image_name within each session_type¶
+
+
+
+
+
+In [48]:
+
+
+
+
+
+
+def condense_session_types(df):
+ df = df.copy()
+ df = df.reset_index()
+ for row in range(len(df)):
+ session_type = df.iloc[row].session_type
+ # all of Training 4 and 5 are basically the same
+ if session_type in ['TRAINING_4_images_A_training', 'TRAINING_5_images_A_epilogue', 'TRAINING_5_images_A_handoff_ready']:
+ df.at[row, 'session_type'] = 'TRAINING_4_images_A'
+ # for the first training session with images, remove the '10uL_reward bit'
+ elif session_type == 'TRAINING_3_images_A_10uL_reward':
+ df.at[row, 'session_type'] = 'TRAINING_3_images_A'
+ # otherwise, keep the same name
+ else:
+ pass
+ return df
+
+
+
+
+
+In [52]:
+
+
+
+
+
+
+big_mdf = condense_session_types(big_mdf)
+
+
+
+
+
+In [53]:
+
+
+
+
+
+
+import visual_behavior.visualization.ophys.platform_paper_figures as ppf
+
+
+
+
+
+In [55]:
+
+
+
+
+
+
+axes_column = 'session_type'
+hue_column = 'image_name'
+palette = sns.color_palette()
+
+ppf.plot_population_averages_for_conditions(big_mdf, data_type, event_type, axes_column, hue_column, palette=palette,
+ suptitle=None, horizontal=True, save_dir=None, folder=None)
+
+
+
+
+
+
+
+
+
+
+
+Out[55]:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+
+
+
+
+
+Aggregate trial averaged responses accross all sessions and all imaging planes for a given mouse¶
+
+
+
+
+
+In [215]:
+
+
+
+
+
+
+from visual_behavior.ophys.io.create_multi_session_df import get_multi_session_df
+
+
+
+
+
+This function will run the steps above iteratively for all sessions for the provided mouse_id and project code:
+ +* load dataset for each experiment
+* generate stimulus_response_df to get stimulus aligned traces
+* compute mean response dataframe averaged over the provided set of conditions
+* concatenate with all other sessions
+
+
+
+
+NOTE: this takes tens of minutes
+ +
+
+
+
+
+There is code to do this on the cluster in visual_behavior_analysis.scripts.run_create_multi_session_df.py
+
+
+
+
+In [216]:
+
+
+
+
+
+
+project_code = 'LearningmFISHTask1A'
+conditions = ['cell_specimen_id', 'image_name']
+data_type = 'dff'
+event_type = 'changes'
+
+multi_session_df = get_multi_session_df(project_code, mouse_id, conditions, data_type, event_type,
+ time_window=[-3, 3.1], interpolate=True, output_sampling_rate=30, response_window_duration=0.5)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+
+
+
+
+
+In [ ]:
+
+
+
+
+
+
+
+