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analysis:course-w16:week16 [2016/02/28 21:08]
mvdm [Co-activation: concept and overall workflow]
analysis:course-w16:week16 [2016/03/01 09:50]
eirvine [Steps 5-7: Get co-activation probabilities]
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 ~~DISCUSSION~~ ~~DISCUSSION~~
- 
-:!: **UNDER CONSTRUCTION,​ PLEASE DO NOT USE YET** :!: 
  
 ===== Pairwise co-occurrence ===== ===== Pairwise co-occurrence =====
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   * Learn to think about possible ensemble firing patterns and ways to characterize them   * Learn to think about possible ensemble firing patterns and ways to characterize them
 +  * Implement, in detail, an analysis of pairwise co-occurrence during putative "​replay"​ events
   * Apply a permutation test (shuffle) to determine levels of chance (independent) co-occurrence   * Apply a permutation test (shuffle) to determine levels of chance (independent) co-occurrence
  
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 Shown schematically are three putative SWRs, associated with a "​forward"​ replay (cells active in same order as experienced),​ an indeterminate replay (no order detectable; may be a replay of some different experience from which we do not know the correct place cell order), and a "​reverse"​ replay. Shown schematically are three putative SWRs, associated with a "​forward"​ replay (cells active in same order as experienced),​ an indeterminate replay (no order detectable; may be a replay of some different experience from which we do not know the correct place cell order), and a "​reverse"​ replay.
  
-Suppose we want to quantify how much a rat is recalling a certain ​location ​trajectory ("​experience"​). We could identify how many times certain trajectories are replayed, like the left trajectory or the right trajectory along arms of a T-maze. There are a few ways of doing this, including co-activation analysis, sequence analysis, and decoding. This module will cover co-activation analysis.+Suppose we want to quantify how much a rat is recalling a certain trajectory ("​experience"​). We could identify how many times certain trajectories are replayed, like the left trajectory or the right trajectory along arms of a T-maze. There are a few ways of doing this, including co-activation analysis, sequence analysis, and decoding. This module will cover co-activation analysis.
  
 Overview of sharp wave-ripple associated spiking activity analyses: Overview of sharp wave-ripple associated spiking activity analyses:
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 ==== Co-activation:​ concept and overall workflow ====  ==== Co-activation:​ concept and overall workflow ==== 
  
-Co-activation or co-occurrence analysis allows us to examine the content of "​replay"​ without direct reference to the field order of place cells in the environment. By grouping place cells into categories such as "​left-arm place cells" and "​right-arm place cells" we can ask if left cells are significantly more active together than right cells, which would suggest that the rat may have been recalling the left arm more frequently than the right arm.+Co-activation or co-occurrence analysis allows us to examine the content of "​replay"​ without direct reference to the field order of place cells in the environment ​(Cheng and Frank, 2008). By grouping place cells into categories such as "​left-arm place cells" and "​right-arm place cells" we can ask if left cells are significantly more active together than right cells, which would suggest that the rat may have been recalling the left arm more frequently than the right arm.
  
 {{ :​analysis:​course-w16:​cc_schematic1.png?​nolink&​300 |}} {{ :​analysis:​course-w16:​cc_schematic1.png?​nolink&​300 |}}
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   - **Get z-scored coactivity for cell pairs**: are the cell pairs co-active at greater than chance levels? (If the cells are firing randomly, we still expect them to co-occur to some degree)   - **Get z-scored coactivity for cell pairs**: are the cell pairs co-active at greater than chance levels? (If the cells are firing randomly, we still expect them to co-occur to some degree)
  
 +This module will first take you through how existing code accomplishes these steps. Then, the final section implements a basic version of the same analysis from scratch, so that you can get to know the guts of the analysis and build on it yourself.
 ==== Step-by-step ==== ==== Step-by-step ====
  
 === Setup and data loading === === Setup and data loading ===
  
-First, make sure you do a ''​git pull''​ as usual, and get the data. We'll be using session ''​R064-2015-04-22''​. You'll also need to include the ''​tasks\Alyssa-Tmaze''​ and ''​tasks\ReplayAnalysis''​ folders in your path.+First, make sure you do a ''​git pull''​ as usual, and get the data. We'll be using session ''​R064-2015-04-22''​. You'll also need to include the ''​tasks\Alyssa-Tmaze''​ and ''​tasks\Replay_Analysis''​ folders in your path.
  
 Then, we load the data: Then, we load the data:
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 </​code>​ </​code>​
  
-=== Generating candidate events ===+=== Step 1: Generating candidate events ===
  
-This was covered ​in Module 6. You can use your own code for detecting sharp wave-ripples (SWRs), or the code below (just make sure your variable is called ​evt):+Detecting putative sharp-wave ripple events based on thresholding power in a certain frequency band was introduced ​in [[analysis:​course-w16:​week6|Module 6]]. You can use your own code for detecting sharp wave-ripples (SWRs), or the code below (just make sure your variable ​containing detected intervals ​is called ​''​evt''​):
  
 <code matlab> <code matlab>
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 evt = TSDtoIV(cfg,​SWR);​ % evt is the set of candidate events evt = TSDtoIV(cfg,​SWR);​ % evt is the set of candidate events
  
-clearvars -except evt ExpKeys+clearvars -except ​S pos evt ExpKeys
 </​code>​ </​code>​
 +
 +:!: Make sure that the filter above performed as expected. In particular, if the %%FieldTrip%% version of ''​filtfilt()''​ takes precedence in your path over the matlab builtin version, this could fail!
  
 Normally there is a lot more that goes on during candidate detection, such as the elimination of events that occur when the rat is moving too quickly, and but we will keep it simple for now. Normally there is a lot more that goes on during candidate detection, such as the elimination of events that occur when the rat is moving too quickly, and but we will keep it simple for now.
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 ☛ What other steps can you think of that may improve the detection of candidate SWR events? Scan the Methods sections of a few replay papers to see how they do it. ☛ What other steps can you think of that may improve the detection of candidate SWR events? Scan the Methods sections of a few replay papers to see how they do it.
  
-=== Estimating place fields === +=== Step 2: Estimating place fields === 
  
 The basics of estimating tuning curves are covered [[analysis:​course-w16:​week10|here]]. Place cells can fire locally (in-field, when the rat is inside the place field) and non-locally (out-out-field,​ e.g. when the rat is at rest but recalling a previously experienced trajectory). Replay is an example of non-local firing, and it occurs during periods of quiescence. Since non-local firing can affect estimates of place field location, we exclude times when the rat was moving too slowly: The basics of estimating tuning curves are covered [[analysis:​course-w16:​week10|here]]. Place cells can fire locally (in-field, when the rat is inside the place field) and non-locally (out-out-field,​ e.g. when the rat is at rest but recalling a previously experienced trajectory). Replay is an example of non-local firing, and it occurs during periods of quiescence. Since non-local firing can affect estimates of place field location, we exclude times when the rat was moving too slowly:
  
 <code matlab> <code matlab>
-% Get his linear speed: 
 linspeed = getLinSpd([],​pos);​ % linear speed linspeed = getLinSpd([],​pos);​ % linear speed
  
 % Threshold speed % Threshold speed
 cfg = []; cfg.method = '​raw';​ cfg.operation = '>';​ cfg.threshold = 3.5; % speed limit in cm/sec cfg = []; cfg.method = '​raw';​ cfg.operation = '>';​ cfg.threshold = 3.5; % speed limit in cm/sec
-iv_fast = TSDtoIV(cfg,​linspeed);​ % intervals with speed above thresh+iv_fast = TSDtoIV(cfg,​linspeed);​ % only keep intervals with speed above thresh
  
 % Restrict data so it includes fast intervals only % Restrict data so it includes fast intervals only
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   * Red and blue circles depict hypothetical locations of some place fields.   * Red and blue circles depict hypothetical locations of some place fields.
  
-Our goal is to group the place cells into left and right categories, so we need to look at how cells were spiking when the rat went left or right. However, it’s not quite this simple because the rat often chose one arm far more often than the other, so we need to make sure we’re estimating place fields for the two groups with the same amount of position data. Let’s cheat by using an existing function called ''​GetMatchedTrials'':​+Our goal is to group the place cells into left and right categories, so we need to look at how cells were spiking when the rat went left or right. However, it’s not quite this simple because the rat often chose one arm far more often than the other, so we need to make sure we’re estimating place fields for the two groups with the same amount of position data. Let’s cheat by using an existing function called ''​GetMatchedTrials()'':​
  
 <code matlab> <code matlab>
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 </​code>​ </​code>​
  
-Right now the position data exists in two dimensions (the horizontal plane), but it’s simpler to think of the data in one dimension, existing from the bottom of the Tmaze out to the end of either the left or right arm. To do this, we linearize the position data onto the left and right trajectories. Coordinates defining linear trajectories exist already in metadata, but they are in units of pixels so we need to standardize them to have a bin size in centimeters:​+Right now the position data exists in two dimensions (the horizontal plane), but it’s simpler to think of the data in one dimension, existing from the bottom of the Tmaze out to the end of either the left or right arm. To do this, we linearize the position data onto the left and right trajectories. Coordinates defining linear trajectories exist already in ''​metadata''​, but they are in units of pixels so we need to standardize them to have a bin size in centimeters:​
  
 <code matlab> <code matlab>
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 ☛ Why do we say place fields are "​estimated"​ instead of, say, obtained or computed? ☛ Why do we say place fields are "​estimated"​ instead of, say, obtained or computed?
  
-=== Categorizing place cells ===+=== Step 3: Categorizing place cells === 
 + 
 +So far, we have place fields (PF) for all cells that were active during left or right traversals of the track, including cells that were active on the central arm and cells that were active on both arms. We need to keep cells that were responsive to a single arm of the track. 
 + 
 +To exclude central arm cells, we can select cells with fields that are located beyond the choice point: 
 + 
 +<code matlab>​ 
 +% Linearize choice point so that it exists in the same units as the 
 +% linearized position data: 
 +chp_tsd = tsd(0,​metadata.coord.chp_cm,​{'​x','​y'​});​ % make choice point useable by cobebase functions 
 +cfg = []; cfg.Coord = coord.L; 
 +chp.L = LinearizePos(cfg,​chp_tsd);​ % the exact chp for L or R differs depending on the coord 
 +cfg.Coord = coord.R; 
 +chp.R = LinearizePos(cfg,​chp_tsd);​ 
 + 
 +% Get indices for cells with fields after the choice point 
 +fields.L = PF.L.field_template_idx(PF.L.field_loc > chp.L.data(1));​ 
 +fields.R = PF.R.field_template_idx(PF.R.field_loc > chp.R.data(1));​ 
 +</​code>​ 
 + 
 +The ''​fields''​ struct contains indices of the cells that were not active on the central arm. However, we still need to account for some cells having fields on multiple arms: 
 + 
 +<code matlab>​ 
 +% Remove cells that are active on both arms 
 +[~,​remove.L,​remove.R] = intersect(fields.L,​fields.R);​ % intersect tells us which of the indices are common to both groups 
 +fields.L(remove.L) = []; 
 +fields.R(remove.R) = []; 
 +</​code>​ 
 + 
 +As a last step, we need to make sure that each cell appears only once in the list (if a cell has multiple fields on the same arm, we don’t want to keep multiple copies of that cell in our analysis):​ 
 + 
 +<code matlab>​ 
 +% Some cells have double place fields on the arms, so they are present 
 +% twice in the list of cells. Remove them. 
 +fields.L = unique(fields.L);​ 
 +fields.R = unique(fields.R);​ 
 +</​code>​ 
 + 
 +(Aside: The function ''​unique()''​ returns sorted output, so the cells will no longer be ordered according to field location like they are when output from ''​MakeTC()''​. This is not an issue for co-occurrence analysis, but is for sequence analysis.) 
 + 
 +Now that we have the indices describing which cells have fields on the left or right arm only, we can select them from our original spike train: 
 + 
 +<code matlab>​ 
 +% Select place cells using the indices in the fields struct 
 +% Note that we're indexing into the *original* non-restricted collection of 
 +% spiketrains 
 +S_arm.L = SelectTS([],​S,​fields.L);​ 
 +S_arm.R = SelectTS([],​S,​fields.R);​ 
 +</​code>​ 
 + 
 +As you can see from the command line output of ''​SelectTS()'',​ not many cells of the original 178 are left after this operation! 
 +=== Step 4: Make a Q-matrix === 
 + 
 +A Q-matrix is organized such at each row represents a neural unit and each column represents a candidate that units are potentially active in. Thus, each element of the Q-matrix is a count of the number of spikes emitted by the corresponding neural unit in the corresponding time bin. Below, we'll use an existing function, but it is not much more than a wrapped version of the built-in fuction ''​histc()'':​ 
 + 
 +<code matlab>​ 
 +% There is an existing function that makes a Q-matrix from spiketrains and 
 +% candidate intervals 
 +cfg = []; 
 +cfg.win = 0.1; % In seconds, the binsize for containing spikes. i.e. the interval boundaries are redrawn to all have length 100 ms. If empty [], the exact candidate boundaries are used 
 +Q.L = MakeQfromS2(cfg,​S_arm.L,​evt);​ 
 +Q.R = MakeQfromS2(cfg,​S_arm.R,​evt);​ 
 +</​code>​ 
 + 
 +This Q-matrix contains the number of times each uniquely left-arm place cell spiked during candidate, or sharp wave-ripple,​ events. 
 + 
 +Consider column 7 (i.e. event 7) for the "​left"​ cells (''​Q.L.data(:,​7)''​):​ cell 1 spiked three twice, and cells 11 and 12 spiked once. These left arm cells co-occurred during the same candidate interval. This matrix is the basis for all subsequent analysis steps, much in the same way that a slightly different Q-matrix is the basis for the [[analysis:​course-w16:​week10|decoding analysis]] covered earlier. 
 + 
 +=== Steps 5-7: Get co-activation probabilities === 
 + 
 +There is an existing function in the codebase that does steps 5-7. We'll run it, plot the results, and then look at what's going on internally. 
 + 
 +<code matlab>​ 
 +cfg = []; 
 +cfg.nShuffle = 1000; 
 +cfg.useMask = 1; 
 +cfg.outputFormat = '​vectorU';​ 
 +CC.L = CoOccurQ2(cfg,​Q.L);​ 
 +CC.R = CoOccurQ2(cfg,​Q.R);​ 
 +</​code>​ 
 + 
 +== Step 5 results: Cell participation during candidate events (''​p0''​) == 
 + 
 +Overall, are left cells more active during candidates than right cells? If so, this means they are more likely to co-occur by chance: 
 + 
 +<code matlab>​ 
 +% Make a bar plot 
 +p0_data = [nanmean(CC.L.p0) nanmean(CC.R.p0)];​ 
 +colors = flipud(linspecer(2));​ % get some colors for plotting 
 +location = [1 3]; % where on the x-axis to place the bars 
 + 
 +figure; 
 +for iBar = 1:​length(p0_data) 
 +   ​bar(location(iBar),​p0_data(iBar),'​FaceColor',​colors(iBar,:​),'​EdgeColor','​none'​);​ 
 +            hold on  
 +end 
 + 
 +set(gca,'​XLim',​[location(1)-1 location(2)+1],'​XTick',​location,'​XTickLabel',​{'​L'​ '​R'​});​ xlabel('​Field location'​) 
 +ylabel({'​Proportion of';'​SWRs active'​}) 
 +title('​Activation probability (p0)'​) 
 +</​code>​ 
 + 
 +== Step 6 results: Joint probability for cell pairs in the same group (''​p3''​) == 
 + 
 + 
 +The frequency of pairs of cells firing together during candidate events (the coactivity, or co-occurrence,​ of cell pairs): 
 + 
 +<code matlab>​ 
 +% Make a bar plot 
 +p3_data = [nanmean(CC.L.p3) nanmean(CC.R.p3)];​ 
 +colors = flipud(linspecer(2));​ % get some colors for plotting 
 +location = [1 3]; % where on the x-axis to place the bars 
 + 
 +figure; 
 +for iBar = 1:​length(p3_data) 
 +   ​bar(location(iBar),​p3_data(iBar),'​FaceColor',​colors(iBar,:​),'​EdgeColor','​none'​);​ 
 +            hold on  
 +end 
 + 
 +set(gca,'​XLim',​[location(1)-1 location(2)+1],'​XTick',​location,'​XTickLabel',​{'​L'​ '​R'​});​ xlabel('​Field location'​) 
 +ylabel({'​Cell pair'; 'joint probability'​}) 
 +title('​Observed coactivity (p3)'​) 
 +</​code>​ 
 + 
 +== Step 7: Z-score coactivity (''​p4''​) == 
 + 
 +Are cells co-occurring more often than expected by chance? 
 + 
 +<code matlab>​ 
 +% Make a bar plot 
 +p4_data = [nanmean(CC.L.p4) nanmean(CC.R.p4)];​ 
 +colors = flipud(linspecer(2));​ % get some colors for plotting 
 +location = [1 3]; % where on the x-axis to place the bars 
 + 
 +figure; 
 +for iBar = 1:​length(p4_data) 
 +   ​bar(location(iBar),​p4_data(iBar),'​FaceColor',​colors(iBar,:​),'​EdgeColor','​none'​);​ 
 +            hold on  
 +end 
 + 
 +set(gca,'​XLim',​[location(1)-1 location(2)+1],'​XTick',​location,'​XTickLabel',​{'​L'​ '​R'​});​ xlabel('​Field location'​) 
 +ylabel({'​SWR coactivation';​ '​Z-score'​}) 
 +title('​Coactivation above chance levels (p4)'​) 
 +</​code>​ 
 + 
 +A neat way of plotting all of these in one figure is: 
 + 
 +<code matlab>​ 
 +%% Plot everything in one figure using a loop 
 + 
 +p_list = {'​p0','​p3','​p4'​};​ 
 +titles = {'​Activation probability (p0)','​Observed coactivity (p3)','​Coactivation above chance levels (p4)'​};​ 
 +ylabels = {{'​Proportion of';'​SWRs active'​},​{'​Cell pair'; 'joint probability'​},​{'​SWR coactivation';​ '​Z-score'​}};​ 
 +arms = {'​L','​R'​};​ 
 +colors = flipud(linspecer(2));​ 
 +location = [1 2.5]; 
 + 
 +figure; 
 +for iP = length(p_list):​-1:​1 
 +     
 +    p_data(iP,​1:​2) = [nanmean(CC.L.(p_list{iP})) nanmean(CC.R.(p_list{iP}))];​ 
 +         
 +    h(iP) = subplot(1,​3,​iP);​ 
 +    for iBar = 1:​length(arms) 
 +     
 +        bar(location(iBar),​p_data(iP,​iBar),'​FaceColor',​colors(iBar,:​),'​EdgeColor','​none'​) 
 +        hold on 
 +         
 +        title(titles{iP}) 
 +        ylabel(ylabels{iP}) 
 +        xlabel('​Field location'​) 
 +    end 
 +end 
 + 
 +set(h,'​XLim',​[location(1)-1 location(2)+1],'​XTick',​location,'​XTickLabel',​{'​L'​ '​R'​});​ 
 +set(h,'​PlotBoxAspectRatio',​[1 1 1]); maximize 
 +</​code>​ 
 + 
 +This gives something like: 
 + 
 +{{ :​analysis:​course-w16:​cooccur_results.png?​nolink&​600 |}} 
 + 
 +It looks like his right cell pairs are more co-active than his left cell pairs, relative to shuffled co-coccurrence,​ suggesting that there may be more right trajectories replayed compared to left trajectories. 
 + 
 +Note: in interpreting results like the above, it is important to consider what asymmetries may be present in the neural and behavioral data that could account for any differences. We used the function ''​GetMatchedTrials()''​ earlier to create a fair comparison between left and right from a behavioral sampling perspective,​ but that doesn'​t change the fact that behaviorally,​ the animal experienced the right trajectory more often than the left: 
 + 
 +<code matlab>​ 
 +fprintf('​Number of left trials: %d\n',​length(metadata.taskvars.trial_iv_L.tstart)) 
 +fprintf('​Number of right trials: %d\n',​length(metadata.taskvars.trial_iv_R.tstart)) 
 +</​code>​ 
 + 
 +==== Implementing a basic co-occurrence analysis from scratch ==== 
 + 
 +In this section, we will implement a simple version of coactivation analysis, where we don't care how many times a cell spiked during a given candidate event, only whether it spiked or not. Since our Q matrix contains spike counts, we convert the Q matrix to binary with 1's indicating that a cell was active in a candidate bin and 0's indicating that it wasn'​t:​ 
 + 
 +<code matlab>​ 
 +% Pull some Q data out of the collector struct. Let's work with just the 
 +% left cells for these examples: 
 +Q_binary = Q.L.data; 
 + 
 +% First exclude counts > 0 
 +Q_binary(Q_binary > 1) = 1; 
 +</​code>​ 
 + 
 +== Calculating p0 == 
 + 
 +This is a one-liner:​ 
 + 
 +<code matlab>​ 
 +% Get expected co-occurrence under independence assumption 
 +p0 = nanmean(Q_binary,​2);​ % fraction of bins each cell participates in individually 
 + 
 +% this is the same as nansum(Q_binary,​2)./​length(evt.tstart) 
 +% Fraction of bins active is equal to the sum of candidate bins the cell was 
 +% active in divided by the total number of candidates 
 + 
 +% Plot results 
 +figure; bar(1, nanmean(p0),'​facecolor',​colors(1,:​));​ set(gca,'​xlim',​[0 2],'​ylim',​get(gca,'​ylim'​)*1.3) 
 +</​code>​ 
 + 
 +== Calculating p3 == 
 + 
 +<code matlab>​ 
 +% Get observed co-occurrences 
 +nCells = size(Q_binary,​1);​ 
 +p3 = nan(nCells);​ 
 +for iI = 1:nCells 
 +    for iJ = 1:nCells 
 +    
 +        p3(iI,iJ) = nanmean(Q_binary(iI,:​).*Q_binary(iJ,:​));​ 
 +         
 +    end 
 +end 
 +p3(logical(eye(size(p3)))) = NaN; % probability of cell co-occurring with itself is not defined 
 +</​code>​ 
 + 
 +p3 is a symmetrical matrix that is nCells x nCells in dimension. The co-occurrence of cells 1 and 2, for example, can be seen in (row 1, column 2 ) and (row 2, column 1). 
 +Note the diagonal of NaNs: this is because it doesn’t make sense asking about a cell’s co-occurrence with itself, so we exclude these values from the set. 
 + 
 +Since p3 is symmetrical,​ it has multiple copies of the same measure. We can keep one copy by extracting either the upper or lower triangular parts of the matrix: 
 + 
 +<code matlab>​ 
 +keep = triu(ones(nCells),​1);​ % get indices of values we want to keep (the 1 means we're discarding the diagonal) 
 +p3_upper = p3(find(keep));​ 
 +% now p3 is a vector and contains only one copy of each co-occurrence value 
 + 
 +% Plot results 
 +figure; bar(1, nanmean(p3_upper),'​facecolor',​colors(1,:​));​ set(gca,'​xlim',​[0 2],'​ylim',​get(gca,'​ylim'​)*1.3) 
 +</​code>​ 
 + 
 +== Calculating p4 == 
 + 
 +It's possible that co-occurrence values in p3 are expected by chance alone: if one set of cells (left or right) is more chatty overall and active in a higher proportion of candidate events, we would expect them to co-occur more often.  
 +What we can do to check if the co-occurrences are similar to chance is to randomly shuffle the values within each row, and compare the shuffled co-occurrences with the observed co-occurrences and get a z-score. This will tell us if observed co-occurrences (p3) occur at a higher rate than expected by chance. The number of shuffles for accurate estimates of chance co-occurrence is at least 10,000. But a lower number reduces the time required for computation and is a close enough approximation for these purposes: 
 + 
 +<code matlab>​ 
 +nShuffles = 1000; 
 + 
 +shuf_p4 = nan(nShuffles,​nCells,​nCells);​ 
 +nBins = size(Q_binary,​2);​ 
 + 
 +for iShuf = 1:​nShuffles 
 +     
 +    % permute Q-matrix 
 +    Q_shuffle = Q_binary; 
 +    for iCell = 1:nCells 
 +        Q_shuffle(iCell,:​) = Q_shuffle(iCell,​randperm(nBins));​ % this step using randperm mixes the contents of each row horizontally 
 +    end 
 +     
 +    % now compute shuffled co-occurrences 
 +    for iI = 1:nCells 
 +        for iJ = 1:nCells 
 +             
 +            shuf_p4(iShuf,​iI,​iJ) = nanmean(Q_shuffle(iI,:​).*Q_shuffle(iJ,:​));​ % shuf_p4 is the shuffled co-occurrences and is a 3-dimensional array 
 +             
 +        end 
 +    end % of loop over cell pairs 
 +     
 +end % of loop over shuffles 
 + 
 +% z-score coactivity 
 +p4 = nan(nCells);​ 
 + 
 +for iI = 1:nCells 
 +    for iJ = 1:nCells 
 +         
 +        p4(iI,iJ) = (p3(iI,​iJ)-nanmean(sq(shuf_p4(:,​iI,​iJ))))./​nanstd(sq(shuf_p4(:,​iI,​iJ)));​ 
 +         
 +    end 
 +end % of loop over cell pairs 
 + 
 +% p4 is a symmetrical matrix like p3, so let's keep half of it: 
 +p4_upper = p4(find(keep));​ 
 +figure; bar(1, nanmean(p4_upper),'​facecolor',​colors(1,:​));​ set(gca,'​xlim',​[0 2],'​ylim',​get(gca,'​ylim'​)*1.3) 
 +</​code>​ 
 + 
 +This shuffling procedure is an example of **resampling**:​ we create a number of different data sets based on some rearrangement of the original data. In this case, the specific resampling is a shuffle or permutation,​ which breaks any relationship between neurons (because we shuffle each neuron independently) and therefore functions as a control for the amount of co-occurrence we expect by chance (i.e. if the neurons were independently active). In general, a major advantage of resampling methods is that they preserve aspects of the underlying distribution -- in this case, of spike counts -- and make no particular assumptions about its shape, whereas many parametric statistical tests require data to be e.g. normally distributed.
  
 ==== Challenges ==== ==== Challenges ====
  
 ★ Why don't we just look at single-cell activation? Under what conditions would the results from that be the same, or different, from pairwise co-occurrence?​ ★ Why don't we just look at single-cell activation? Under what conditions would the results from that be the same, or different, from pairwise co-occurrence?​
 +
 +★ Comment on the choice of bins used in constructing the Q-matrix. It it reasonable to assume that SWR events are always 100ms in length? Modify the code to use the actual length of SWR events. Is the resampling statistic still doing the right thing in this case?
 +
 +★ Implement co-occurrence analysis on your own data.
  
 ==== Credits ==== ==== Credits ====
  
 This module was developed by [[https://​github.com/​aacarey | Alyssa Carey]]. This module was developed by [[https://​github.com/​aacarey | Alyssa Carey]].
analysis/course-w16/week16.txt · Last modified: 2018/07/07 10:19 (external edit)