Synchrony on Networks

Below are my initial impressions about the project. These are just a sketch, and open to change!

Useful Tools

The Enthought Scientific Python package is here.

One of the key texts in theoretical / computational neuroscience is Dayan and Abbott's Theoretical Neuroscience. I just uploaded the first chapter of this book onto my dropbox's public folder. You can get it following this link.

To Do

Put your email here, or if you'd rather not have your email address online, email me at ddarmon at math dot umd dot edu and I'll put together a mailing list. I'll email out a Dropbox link with some preliminary code and some sample data.

Elisa elisa.omodei@gmail.com Luíño luis.seoane@upf.edu Cesar cesar7@gmail.com Regina Reginaram76@yahoo.es Jody jjwright49@me.com Cheryl che.abundo@gmail.com

Read Aram et al.'s paper.

Play around with the code in the Dropbox folder, especially generate_poisson.py. This script generates samples from an inhomogeneous Poisson process.

Basic (Toy) Model

Throughout, I'll use the word 'spike' interchangeably with 'tweet.'

The basic skeleton is based off of the paper by Aram et al. We consider a network of users which we'll model as a graph with a vertex for each user and an edge denoting a connection between each user. For Twitter data, these edges might indicate follower/followee relationships. Directedness of these edges is an open question. This gives us the basic structural model.

The dynamics occurring on top of this network will take the form of coupled inhomogeneous Poisson processes. That is, each vertex will have a Poisson process on top of it, and the rate of the process will depend on the behavior of the other nodes connected to it. An inhomogeneous Poisson process model is a common (though very rough) approximation of neural behavior. It captures the notion of 'completely random.'

Aram's model sets the instantaneous rate of each user to be a (constant) base rate, plus terms that depend on the behavior of the neighbors of a given user (if a neighbor has recently tweeted, and the user is dynamically connected to that user, they are more likely to tweet). The constant base rate is open to change.

Community Detection

A standard approach to finding communities within a network is to look at the network structure alone. We attempt to partition the nodes in the network such that there are many more edges within a community than between communities. A popular method for doing this is the fast-greedy algorithm developed by Clauset, Newman, and Moore.

Another algorithm developed by some colleagues from Granada.

Two algorithms to detect modularity across snapshots

• Nature Paper 1
• Science Paper 2

Toy Network

One of our first tasks is to design a reasonable (small) network to run the toy model on top of. This network should presumably have apparent community structure, and then we can design on top of this a weighted network that incorporates the notion of dynamical community. These weights would essentially correspond to the weights in Equation 4 of Aram et al.' paper. One option for designing realistic network structure is to use a small network within the Twitter network I have available.

Tweet-Triggered Average ;)

I am trying to get a nice summary of Spike Triggered Average from Dayan&Abbott's book. By now I leave here the wikipedia site for it, where the idea is more or less clear. In the first chapters of Dayan&Abbott's book you can also find very basics about Poisson processes and such. I will upload it soon!

Written at the top, but I write it again: we just got ready the first chapter of the Dayan & Abbott book on Theoretical Neuroscience. Just use this link to get it from my dropbox. It is not like you need to learn it by heart, but the techniques used there (spike-triggered average and many others) seem very useful to me for our current problem. I believe we can make use of them.

What about a meeting? I (Luíño) will be busy tomorrow with the physics lab and the discussion about History (anyone is invited, by the way, at 8:00 pm), but what about meeting on Tuesday?

Meeting on Tuesday sounds like a great idea. If anyone is available and would like to meet Monday during the lab time, I'm available. Hopefully once more people sign up for the Google Group, we can send these sort of organizational things through that.

I made a brief script you can get here from my dropbox. Also, I wrote a very short report (File:BriefReport ITI.pdf) outlining the results, in case you wish to take a look. -- Luíño

I updated the scripts a little bit. Now it is possible to produce autocorrelation plots of the tweets of single users. To advance in the direction of Tweet-Triggered Average more detailed data sets will be needed, but I think the idea remains feasible. -- Luíño