Research

Quasiregular dynamics

thesamovar — Mon, 31 May 2010 12:47:44 +0100

With Alastair Fletcher, I wrote some code for producing images of Mandelbrot and Julia sets for quasiregular mappings. A paper on this is currently in review, and can be accessed from arxiv.org. The code used to generate the images can be downloaded from the zip file below, including a description of how it works. The code requires Python 2.5/6 and Numpy.

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qr_dynamics.zip	8.78 KB

Neuroscience

thesamovar — Sun, 28 Jan 2007 18:46:20 +0000

I am a postdoctoral researcher in the field of theoretical neuroscience. I'm currently a member of the Equipe Audition, part of the Laboratoire Psychologie de la Perception, in the Département d'Etudes Cognitives (DEC), Ecole Normale Supérieure (ENS), France. I'm funded by Spikehear, a European Research Council grant.

Research Interests

I am interested in neural mechanisms underlying computations performed by the brain. In particular, I'm interested in understanding spike-timing based codes and computation. At the moment, I'm trying to understand how neural synchrony can be used to perform sound localisation (see below).

Projects

Brian

"Brian" is a software package for simulating spiking neural networks. Specifically, it is a package for the Python programming language providing functions and classes designed to make writing simulations of neural networks as easy and flexible as possible. See Brian's web page.

The most recent release of Brian added the model fitting toolbox for automatic fitting of spiking neuron models to electrophysiological recordings. For the next releases, we are focussing on a new library, Brian Hears, for auditory modelling, and on running Brian on GPU chips (inexpensive massively parallel processors available in consumer graphics cards).

Sound localisation

Sound localisation is the ability of many animals to determine to a greater or lesser degree of accuracy the direction from which a sound is coming. I am working on a neural model of this ability using synchrony, coincidence detection, and spike-timing dependent plasticity. The hope is that this will throw light on the computations performed by real brains (in particular, localisation not just in the horizontal plane), learning (in particular, to account for our ability to learn to localise sounds after a change in head or ear shape such as happens during development), and also provide effective new algorithms to localise sounds in the presence of distractors, noise, reverberations, etc.

Publications

Goodman, D. F. M., & Brette, R. (2010). Learning to localise sounds with spiking neural networks. NIPS (accepted) [provisional pdf]
Goodman, D. F. M. (2010). Code generation: a strategy for neural network simulators. Neuroinformatics (accepted) [provisional pdf]
Rossant, C, Goodman, D. F. M, Platkiewicz, J, & Brette, R. (2010). Automatic fitting of spiking neuron models to electrophysiological recordings. Frontiers in Neuroinformatics. doi:10.3389/neuro.11.002.2010
Goodman, D. F. M, & Brette, R. (2009). The Brian simulator. Frontiers in Neuroscience 3(2), doi:10.3389/neuro.01.026.2009
Brette, R., & Goodman, D. (2009). Brian: a simple and flexible simulator for spiking neural networks. The Neuromorphic Engineer. doi: 10.2417/1200906.1659
Goodman, D., & Brette, R. (2008). Brian: a simulator for spiking neural networks in Python. Frontiers in Neuroinformatics, 2(5), doi:10.3389/neuro.11.005.2008.

Presentations and Posters

Spotlight presentation of poster on "Learning to localise sounds with spiking neural networks" at NIPS, Vancouver (December 2010)
Co-author of presentation given by Cyrille Rossant on “Playdoh: a lightweight Python library for distributed computation and optimisation” at EuroSciPy (July 2010)
Tutorial on Brian (via Skype) at Telluride in Colorado (July 2010)
Talk on "Computation with spikes" at Mathematical Neuroscience, Edinburgh (April 2010)
Poster on sound localisation at Mathematical Neuroscience, Edinburgh (April 2010)
Tutorial on Python and Brian at Neurocomp in Bordeaux, France (September 2009)
Tutorial on Python and Brian at the Python in neuroscience workshop at CNS, Berlin (July 2009)
Poster on sound localisation at CNS, Berlin (July 2009)
Presentation on Brian at the Gatsby computational neuroscience unit, London (July 2009)
Presentation on sound localisation at The Ear Institute, London (July 2009)
Presentation on sound localisation at CerCo , Toulouse, France (Jan 2009)
Presentation on Brian at software interoperability workshop at CNS, Portland OR, USA (July 2008)
Poster on Brian at CNS, Portland OR, USA (July 2008)
Tutorial on Brian at "Using Python in computational neuroscience" workshop in Freiburg, Germany (June 2008)
Presentation on Brian at Visiontrain meeting in Malmo, Sweden (May 2008)
Presentation on Brian at Facets CodeJam 2 in Gif-sur-Yvette, France (May 2008)
Poster on Brian at the Mathematical Neuroscience Meeting in Edinburgh, Scotland (March 2008)

Other

Reviewer for Frontiers in Neuroinformatics, Neural Computation and the Journal of Computational Neuroscience.
Designed the front cover of the May 2010 issue of Neuron (right, click for higher resolution version), featuring Agus et al.'s "Rapid Formation of Robust Auditory Memories: Insights from Noise".

The twisting boundary of the Maskit slice

thesamovar — Wed, 22 Nov 2006 05:36:31 +0000

I am currently working on a paper, based on chapter 5 of my thesis, which I intend to submit to the journal Experimental Mathematics. This paper will present the numerical evidence I gathered during my PhD for the conjectures that the boundary of the Maskit slice is twisting (spiralling infinitely) almost everywhere, and has Hausdorff dimension less than 1.25.

You can download the current version as a PDF (~0.5MB).

Attachment	Size
twisting.pdf	511.25 KB

Maskit

thesamovar — Sun, 15 Oct 2006 04:22:43 +0100

I wrote some software to draw pictures of the Maskit slice, including pleating rays. It allows you to zoom in as far as numerical precision allows, and it has a nice graphical interface (illustrated below). If you're interested in how it works, take a look here. You can export the pictures as postscript files or into Mathematica. You can also export to binary or ASCII format, but I haven't provided any documentation on these. The software runs on Windows, and requires DirectX (which should be installed on almost all versions of Windows now). If you want to try to compile and run this on Linux, let me know. It is possible, but it takes a bit of work and since each version of Linux is different I can't provide a precompiled version. You can download the software here (360k) as a zipped folder.

Maskit software screenshot

Attachment	Size
maskit-distrib.zip	358.92 KB

Programs

thesamovar — Sun, 15 Oct 2006 04:16:49 +0100

As part of my thesis, I wrote some software to draw pictures of the Maskit slice. If you only want to produce pictures of the Maskit slice, you should use the graphical version of this software. The Mathematica notebooks from my thesis can be downloaded here (zipped folder, 40k). Some of these notebooks will work on their own (including all of the algorithms chapter notebook), but some of them require datasets produced by the C++ software. These files are approximately 120MB and too large to include on this webpage, but you can generate them yourself with the C++ software. You can download the C++ source code only distribution here (37k), or with Windows executable files here (161k). I have tested the source code on MS Visual C++ and gcc/Linux. This version of the software only includes the command line version of the software. You can download the graphical version of this software, but compiling this version from the source code is quite complicated. Email me if you want to try this.

Attachment	Size
mathematica-nodata.zip	39.61 KB
hyperbolic-noexe.zip	36.83 KB
hyperbolic.zip	160.22 KB

Spirals in the boundary of quasifuchsian space

thesamovar — Sun, 15 Oct 2006 04:12:40 +0100

My paper Spirals in the boundary of slices of quasifuchsian space was published by the Journal of Conformal Geometry and Dynamics. The abstract reads:

We prove that the Bers and Maskit slices of the quasifuchsian space of a once punctured torus have a dense, uncountable set of points in their boundaries about which the boundary spirals infinitely.

You can download my version (slightly different to the published version) in PDF format (340k).

Below is a series of zooms into the Maskit slice, clockwise from top left to bottom right, illustrating the phenomenon of spirals in the boundary of the Maskit slice.

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spirals.pdf	339.63 KB

Thesis

thesamovar — Sun, 15 Oct 2006 03:26:49 +0100

My PhD thesis is entitled Boundaries of slices of quasifuchsian space. As well as the results from my paper it has some conjectural results about the boundary of the Maskit and Bers slices. On the basis of very strong numerical evidence, I conjecture that the boundary spirals infinitely almost everywhere and that the Hausdorff dimension of the Maskit slice is less than 1.25 (and more likely to be closer to 1.05). You can download it in PDF (1.8MB) format only. The computer programs that come with are available on this page. In order to save some trees, the version on this page is a single spaced version with small margins, unlike the printed version which is double spaced with large margins. In order to save space on my webpage, this version doesn't have the highest quality versions of some of the figures produced by David Wright. If you're interested, email me or him.

Below is a series of zooms into the Maskit slice, clockwise from top left to bottom right, illustrating the phenomenon of spirals in the boundary of the Maskit slice.

Attachment	Size
thesis.pdf	1.76 MB