ICMS

Mar 23, 2009 - Mar 25, 2009

Royal Society of Edinburgh, 22-26 George Street, Edinburgh

Organisers

Name	Institution
Coombes, Stephen	University of Nottingham
Timofeeva, Yulia	University of Warwick

 

Training Workshop Organiser
Dr Mark van Rossum, University of Edinburgh

This is the second annual meeting of the UK Mathematical Neuroscience Network. The network is focussed on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviour in the applied neurosciences. This three-day conference will provide an overview of the current state of research in mathematical approaches to neuroscience, bringing together both physical and life scientists. Drawing together the field in this way will allow for a critical discussion of the relevant experimental facts and of various mathematical methods and techniques that have been successfully applied to date. Importantly, it will draw attention to, and help develop, those pieces of mathematical theory which are likely to be relevant to future studies of the brain.

The meeting will consist of invited speakers, core members and registered participants. In addition, the schedule will allow for a number of poster presentations.

This event is sponsored by the EPSRC via the UK Mathematical Neuroscience Network

Invited speakers

Michael Breakspear
Carson Chow
Geoff Goodhill
Vincent Hakim
Viktor Jirsa
Carlo Laing
Peter Latham
Andre Longtin
Stefano Panzeri
David Pinto
Horacio Rotstein
Andrey Shilnikov
Dan Tranchina
Krasimira Tsaneva-Atanasova
Carl Van Vreeswijk
Thomas Wennekers

Arrangements

Participation
This workshop is now full.
Invited speakers will receive an e-mail invitation.

Venue
The meeting will be held at the the Royal Society of Edinburgh, 22-26 George Street, Edinburgh, EH2 2PQ. The Conference Room is equipped with an OHP, data projector and flipchart.

Registration
Registration will take place from 08.45 - 09.30, on Monday 23 March, in the foyer of the Royal Society of Edinburgh.

Registration fee
There is a registration fee of 80.00 GBP for this meeting. This fee can be paid in advance by credit/debit card using this form.

Meals and Refreshments
Morning and afternoon refreshments will be provided at the venue.

A Conference Dinner will take place on Tuesday 24 March at 19.00.

Accommodation
Participants are asked to make their own accommodation arrangements. A list of Edinburgh accommodation of various sorts and prices is available here .

Financial Assistance
Some financial assistance is available to assist graduate students who attend BOTH the training workshop and the conference.. Applicants should provide a brief résumé including degrees and at least one recommendation letter explaining their suitability for the activity. The résumé and letter should be e-mailed to Irene Moore. Students requesting financial support will be notified by 6 February 2009.

Training Workshop
A one-day training workshop for PhD students and post-docs entitled “An introduction to Mathematical Neuroscience” will take place prior to the meeting on Sunday 22 March at the University of Edinburgh. This will be organised by Mark van Rossum and will comprise a series of 'primer' lectures designed to introduce the concepts that will be covered in the main conference.

The workshop will run from 12.30 until 17.15 on Sunday 22 March in Room G07, Informatics Forum, 10 Crichton Street, University of Edinburgh. Click here for directions.

 

Programme

Sunday 22 March - Training Workshop

Please note that the training workshop will take place in a different venue from the main workshop.

12.30 - 12.45	Introduction by Steve Coombes and Mark van Rossum
12.45 - 13.45	Carson Chow (National Institutes of Health) Path integral methods for solving stochastic equations
13.45 - 14.45	Steve Coombes (University of Nottingham) Dynamical models: from neural microcircuits to cortical regions
14.45 - 15.15	Break
15.15 - 16.15	Rasmus Peterson (University of Manchester) Decoding neuronal activity
16.15 - 17.15	Peter Ashwin (University of Exeter) Dynamical modelling of systems of coupled oscillators
	Beer and pizza

Monday 23 March - Main Workshop

09.00 - 10.30	Registration and coffee
10.30 - 10.45	Welcome
10.45 - 11.30	Geoff Goodhill (University of Queensland) A Bayesian model predicts the response of axons to molecular gradients
11.30 - 12.15	Krasimira Tsaneva-Atanasova (University of Bristol) Bursting in neuroendocrine cells
12.15 - 14.00	Lunch
14.00 - 14.45	Horacio Rotstein ( New Jersey Institute of Technology) The dynamic transition from theta to hyper-excitable (gamma) rhythmic activity in medial entorhinal cortex layer II stellate cells
14.45 - 15.30	Andrey Shilnikov (Georgia State University) Multistability in models of center pattern generators
15.30 - 16.15	Coffee/tea
16.15 - 17.00	Vincent Hakim (CNRS and Ecole Normale Superieure) Neurons in networks: stochastic dynamics, correlations, oscillations and all that.
18.00 - 19.30	Poster session and wine reception at ICMS, 14 India Street, Edinburgh EH3 6EZ map

Tuesday 24 March

09.15 - 10.00	Andre Longtin ( University of Ottawa) Driven recurrent sensory networks and plasticity
10.00 - 10.45	Coffee/tea
10.45 - 11.30	Peter Latham ( University College London) The spatial correlational structure in strongly coupled networks: an analytic approach
11.30 - 12.15	Daniel Tranchina (New York University) Modeling synaptic input event times as a general modulated renewal process within a population density framework: consequences for statistics and dynamics of the spike train output
12.15 - 14.00	Lunch
14.00 - 14.45	Stefano Panzeri ( Italian Institute of Technology) Phase-of-firing coding in sensory cortex
14.45 - 15.30	David Pinto (University of Rochester) Ictogenesis: The dynamics of epileptic initiation
15.30 - 16.15	Coffee/tea
16.15 - 17.00	Carson Chow (National Institutes of Health) Generalized activity equations for neural networks
17.00 - 17.45	Thomas Wennekers (University of Plymouth) On the natural hierarchical composition of cliques in cell assemblies
19.00	Workshop dinner - Howies, 29 Waterloo Place, Edinburgh map

Wednesday 25 March

09.00 - 09.45	Carl van Vreeswijk (CNRS) On the cumulants of stationary stochastic point processes
09.45 - 10.30	Carlo Laing (Massey University) Dimension reduction in neural models: an example – binocular rivalry
10.30 - 11.00	Coffee/tea
11.00 - 11.45	Micheal Breakspear (University of New South Wales ) Multistability and non-diffusivity in large scale spontaneous cortical activity
11.45 - 12.30	Viktor Jirsa (CNRS) Noise during rest enables the exploration of the brain’s dynamic repertoire

 

Presentations:

Presentation Details
Breakspear, Michael
Multistability and non-diffusivity in large scale spontaneous cortical activity
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It is widely assumed that the brain is a complex system par-excellence, hence exhibiting all the hallmarks of a self organising system such as nonlinearity, multistability, coherency and non-diffusivity. Surprisingly, at least at the very large-scale of cortical dynamics, there is little empirical evidence to support this and hence most computational and methodological frameworks for healthy brain activity have proceeded very reasonably from a purely linear/diffusive perspective. By studying the temporal fluctuations of power in resting state EEG, we show that whilst these simple assumptions hold true at some temporal scales, there is strong evidence for bistability and non-diffusivity in key brain rhythms. Bistability is manifest as non-classic bursting between high and low amplitude modes in the alpha rhythm. Non-diffusivity is expressed through the apperance of irregular extremal events in beta rhythm power fluctuations. Whilst there is a good conceptual framework for understanding bistability in cortical dynamics, the implications of the extremal events presents a challenge to existing computational frameworks.
Chow, Carson
Generalized activity equations for neural networks
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Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate while leaving out higher order statistics like correlations between firing. A stochastic theory of neural networks which includes statistics at all orders was recently formulated. I will describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations, i.e. they depend only upon the mean and specific correlations of interest, without an ad hoc criterion for doing so. I will show in an example of an all-to-all connected network how the system of generalized activity equations captures phenomena missed by the mean fieldrate equations alone.
Goodhill, Geoff
A Bayesian model predicts the response of axons to molecular gradients
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Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. First, we develop a Bayesian "ideal observer" analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. We find experimentally that a measurable response can be seen to gradients as shallow as 1 molecule per millimetre, a degree of sensitivity much higher than previously reported for any chemotacting system. Together these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be employed by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.
Hakim, Vincent
Neurons in networks: stochastic dynamics, correlations, oscillations and all that.
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I will introduce basic quantities that are useful to analyse the dynamics of large neuronal networks, explain how they can be computed for simple model neurons and show their usefulness for describing experimental results, taking recent data on cerebellar cell networks as an example.
Jirsa, Viktor
Noise during rest enables the exploration of the brain’s dynamic repertoire
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Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1–100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, ,0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space–time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.
Laing, Carlo
Dimension reduction in neural models: an example – binocular rivalry
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Binocular rivalry occurs when two very different images are presented to the two eyes. Previous models for this phenomenon have been either phenomenological rate models or more realistic spiking neuron models. Few attempts have been made to derive the former type of model from the latter. We give such a derivation, using data-mining techniques to automatically extract appropriate variables for a low-dimensional description.
Latham, Peter
The spatial correlational structure in strongly coupled networks: an analytic approach
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Determining the correlational structure in large neuronal networks is critical for understanding everything from information storage to network dynamics to computing to learning. Historically, the main approach has been experimental, but the amount of data required to accurately assess correlations scales very badly with the number of neurons. An alternative approach is to directly compute the correlations as a function of network connectivity and single neuron properties. So far this computational approach has been applied solely to weakly connected networks - networks in which the connection strength is inversely proportional to the number of connections per neuron [Ginzburg and Sompolinsky, PRE, 50:3171-3191, 1994; Ganguli, COSYNE, 2006; Beck, Bejjanki and Pouget, submitted]. Here we consider the much more realistic regime in which there is strong, but random, background connectivity, and weak, structured connectivity. Using a simple model, we find an analytic expression that relates correlations to the connectivity matrix. Our main result is that the background connectivity, which is random and therefore does not play a major computational role, can have a large effect on the correlational structure. This makes it hard to relate measured correlations to the part of the connectivity matrix we care about - the structured part.
Longtin, Andre
Driven recurrent sensory networks and plasticity
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All senses feature a flow of neural activity from the first transduction stage to increasingly deeper nuclei in the brain. They also feature a reverse flow from deeper structures back to more peripheral structures. The role of this dominant sensory feedback is not well understood. The circuitry of sensory processes in the absence of inputs supports a variety of neural behaviors such as equilibria, oscillations in time and/or space. We present recent results on the effect of random spatiotemporal inputs on such networks, focussing on the role of correlations in these inputs in exciting specific behaviors. In particular, we consider what the role of ON and OFF cells may be in this respect. We find a host of novel dynamical behaviors when such cells are, as in many senses, implicated in distributed delayed feedback loops. We finally consider how plasticity is likely to affect these behaviors. We show that general combinations of facilitation and depression play little role in transferring information about steady state sensory inputs, at least in the feedforward direction, but that the mean firing rate can powerfully gate information flow.
Panzeri, Stefano
Phase-of-firing coding in sensory cortex
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I will present some recent evidence that neurons in priamry visual and auditory cortices encode information about natural visual or auditory stimuli in terms of spike timing relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. I will also describe the potential computational advantages of representing information in terms of phase of firing. These advantages are 1) higher information content than spike counts 2) ability to represent information about several effective stimuli in an easily decodable format 3) robustness to sensory noise. This is a joint work with Nikos Logothetis, Christop Kayser and Marcelo Montemurro.
Pinto, David
Ictogenesis: The dynamic of epileptic seizure onset
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David J Pinto PhD*1,2, Sally P. Duarte, M.Eng.1, Sneha Narayanan2 1 Department of Neurobiology and Anatomy, 2 Department of Biomedical Engineering, University of Rochester School of Medicine, Rochester, NY Rather than a single phenomenon, epileptic activity in the brain consists of a sequence of events – onset, propagation, and termination. Each component can be understood both biologically and mathematically as distinct and independent dynamic processes. Of the three steps, one could argue that understanding the onset, or ictogenesis, of epilepsy is of primary importance. That is, if we can understand and control how epileptic seizures begin, we may be able to find a means to stop them even before they start. Intuitively, ictogenesis is easy to understand. A group of errant neurons become active and recruits activity in other neurons until the neuronal network reaches some threshold and explodes into uncontrolled activity. Describing the same process with mathematical rigor is more problematic. What do we mean by “network threshold”? How does one describe an unstable manifold in a network of spiking neurons? Does the relevant dynamic variable depend on the number of active neurons or on the temporal pattern of activity between them? In this presentation, we describe our initial steps toward answering these questions. We will present data from an experimental model of epilepsy using brain slices. These data provide clues for understanding the biology of a network-based unstable manifold separating the rest state from epileptiform activity. We then frame the problem of ictogenesis mathematically using three strategies. First, we will present results from large-scale network models that capture the ictogenic process observed experimentally. Next, we will present a reduced model that illustrates how we can relate biological data to a linear stability analysis of network threshold. Finally, we propose the use of the Globally Coupled Map (GCM) framework as a vehicle for a full stability analysis of activity in a network of spiking neurons.
Rotstein, Horacio
The dynamic mechanism of abrupt transition to hyperexcitable (epileptic) activity in medial entorhinal cortex layer II stellate cells
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This talk concerns the biophysical mechanism underlying the transition from the theta (4 - 12 Hz) to a hyperexcitable frequency regime in medial entorhinal cortex (MEC) layer II stellate cells (SCs) as a result of recurrent excitatory connectivity among latter and lack of enough inhibitory regulation. The existence of recurrent (excitatory) connections among SCs in slices of MEC was recently uncovered by Kumar et al (J. Neuroscie., 27:1239-1246, 2007). They also show that these connections are "similar" in control and pilocarpine-treated (epileptic) tissue while recurrent inhibitory circuits are reduced in the latter as compared to the former. In this talk we present a biophysical (conductance based) model that reproduces the experimental findings. We show that hyperexcitability can be obtained not only as the result of reduced synaptic inhibition but also as a result of increased synaptic excitation in the absence of inhibition. In addition, we show that this transition is abrupt as the maximal synaptic conductance increases through a critical value. Using dynamical systems techniques, we explain the mechanism underlying these phenomena. We set forward the hypothesis that SCs have intrinsic dynamic properties that endow them with the ability to display both theta and hyperexcitable spiking activity. The "choice'" of voltage time scale made by the cell depends on a combination of the network excitatory and inhibitory synaptic currents.
Shilnikov, Andrey
Multistability in models of center pattern generators
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We study polyrhythmic dynamics in inhibitory-excitatory models of central pattern generators controlling various locomotive behaviors of animals. We discuss the multistability of inhibitory networks that results in polyrhythmicity of its emergent synchronous behaviors. The pacemaker determining the specific rhythm of a motif was found to be a cell with the longest duty cycle. We analyze various configurations of the motifs and describe the universal mechanisms for synergetics of the bursting patterns.
Tranchina, Daniel
Modeling synaptic input event times as a general modulated renewal process within a population density framework: consequences for statistics and dynamics of the spike train output
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In the probability density function (PDF) approach to neural network modeling, a common simplifying assumption is that a Poisson process governs the arrival times of postsynaptic events. This ignores temporal correlations that can have important physiological consequences with respect to synchrony of population activity (Cateau and Reyes, 2006). A less restrictive assumption that captures input correlations is that the synaptic event times comprise a general modulated renewal process. Extending PDF methods appropriately for the integrate-and-fire neuron model with instantaneous synaptic kinetics gives 2 state variables: membrane voltage, v, and time since last synaptic input event, s. Between input events, v decays towards rest, while s evolves with unit velocity. Upon arrival of a synaptic event, v undergoes a jump of random size, and s is reset to zero. The hazard function, h(s,t), plays a central role; it gives the probability per unit time of a synaptic input event at time t, given elapsed time s since the last event. We study how regularity of the synaptic input affects statistics of the spike-train output: spike rate; PDF and coefficient of variation of the inter-spike interval; and the autocorrelation function of the spike train. We discuss the relevance to neural network simulations.
Tsaneva-Atanasova, Krasimira
Bursting in neuroendocrine cells
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Many secretory cells such as neurons that secrete neurotransmitters or gland cells that secrete hormones exhibit prolonged action potential or plateau-bursting behaviour. Although regulated by the interplay between voltage gated calcium channels and calcium sensitive potassium channels the bursting patterns that these cells exhibit could be vastly diverse. For example, in the case of beta-cell (square-wave or fold-homoclinic) bursting relies on the existence of a supercritical Hopf bifurcation in the fast subsystem while somatotroph or inner ear hair cells plateau-bursting requires fold-subHopf structure. We study the transition between those two types of bursting and show that it could be accounted for by a single physiologically plausible control parameter. Some theoretical as well as experimental implications of this result will be discussed.
van Vreeswijk, Carl
On the Cumulants of Stationary Stochastic Point Processes.
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60 years ago W.L. Smith showed that for large time windows, T, the cumulants of the spike count distribution all increase linearly with T, and how the prefactor for the k-th cumulant can be expressed in the first k moments of the inter-spike interval (ISI) distribution. This is a very useful result for the analysis of spike statistics, if neuronal activity is well approximated by a renewal process. But, particularly for neurons with spike adaptation, this is often not the case. Here one should consider stochastic point processes that allow for serial correlations. For such processes only results for the first two cumulants have previously been reported. I will show that in such processes the cumulants of the spike count distribution also grow linearly with T and how these can be expressed in the moments of ISI distribution and the correlations between ISIs. I will further discuss some applications of the theory.
Wennekers, Thomas
On the natural hierarchical composition of cliques in cell assemblies
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Hebbian cell assemblies can be formalised as sets of tightly connected cells in auto- and hetero-associative memories. Direct evidence for such "cliques" has recently been obtained in multiple-unit recordings from rat hippocampal neurons. These experiments suggest a hierarchical organisation where cliques are embedded in each other such that larger cliques represent less specific stimulus conditions. We here suggest an interpretation stating that the firing patterns may not just reflect nested categories but a lattice of concepts about stimulus-response mappings in the sense of formal concept analysis, an applied branch of set theory. We present an implementation of formal concept lattices in bidirectional associative memories that in contrast to previous work satisfies Dale's principle and uses balanced excitation and inhibition. Inhibitory cells have fixed, non-plastic synapses even if the model learns new concepts. As an extreme case a single global inhibitory cell is enough that controls the total level of activation. The excitatory cells can further learn incrementally using a Hebbian coincidence learning rule. Implications of the model for retrieval in auto-associative memories are further outlined. Overall the model is well suited for representing hierarchical compositional relationships between entities in the form of correlated patterns in technical cognitive systems and potentially the brain.

Participants

Name	Institution
Adhikari, Mohit	University of Bristol
Ahmadi, Mandana	University College London
Aksenova, Tetiana	Thematic Network for Advanced Research, Grenoble
Ashwin, Peter	University of Exeter
Avila Akerberg, Oscar	McGill University
Barbieri, Francesca	Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS)
Baroni, Fabiano	Universidad Autónoma de Madrid
Barrett, David	University College London
Basalyga, Gleb	University of Plymouth
Benjamin, Oscar	University of Bristol
Billings, Guy	University College London
Borisyuk, Roman	University of Plymouth
Breakspear, Michael	University of New South Wales
Buckwar, Evelyn	Heriot-Watt University
Chik, David	University of Plymouth
Chow, Carson	National Institutes of Health
Coombes, Stephen	University of Nottingham
Crofts, Jonathan	University of Strathclyde
De Wilde, Philippe	Heriot-Watt University
Etminani, Mahsa	Iran University Of Medical Sciences
Fox, Charles	University of Sheffield
Gardner, Robert	University of Warwick
Gheorghe, Ana Maria	University of Nottingham
Goodhill, Geoff	University of Queensland
Gucwa, Ilona	Max Planck Institute for Mathematics in the Sciences
Hakim, Vincent	CNRS and Ecole Normale Superieure
Hennig, Matthias	University of Edinburgh
Holden, Richard	University of Leicester
Ince, Robin	University of Manchester
Jirsa, Viktor	Theoretical Neuroscience Group (CNRS), ISM
Kanitscheider, Ingmar	Institute for Theoretical Physics Amsterdam
Laing, Carlo	Massey University
Lajoie, Guillaume	University of Washington
Langdon, Angela	University of New South Wales
Latham, Peter	University College London
Laudanski, Jonathan	University of Nottingham
Lepora, Nathan	University of Sheffield
Lerchner, Alexander	University College London
Longtin, Andre	University of Ottawa
Lord, Gabriel	Heriot-Watt University
Malik, Naveed	University of Warwick
Marin, Boris	Universidade de São Paulo
Marten, Frank	University of Bristol
Masud, Mohammad	University of Plymouth
Michalareas, George	University of Glasgow
Montemurro, Marcelo	University of Manchester
Muller, Eilif	EPFL
Nowacki, Jakub	University of Bristol
O'Donnell, Cian	University of Edinburgh
Panzeri, Stefano	Italian Institute of Technology
Petersen, Rasmus	University of Manchester
Pinto, David	University of Rochester
Puggioni, Paolo	CERN
Riedler, Martin	Heriot-Watt University
Rotstein, Horacio	New Jersey Institute of Technology
Saal, Hannes	University of Edinburgh
Schmidt, Helmut	University of Nottingham
Schulz, David	University College London
Series, Peggy	University of Edinburgh
Shilnikov, Andrey	Georgia State University
Taxidis, Jiannis	University of Nottingham
Teriakidis, Adrianna	University of Edinburgh
Terry, John	University of Bristol
Thul, Rüdiger	University of Nottingham
Timofeeva, Yulia	University of Warwick
Tranchina, Daniel	New York University
Trenado, Carlos	Saarland University Hospital
Tsaneva-Atanasova, Krasimira	University of Bristol
van Rossum, Mark	University of Edinburgh
van Vreeswijk, Carl	CNRS
Vladimirskiy, Boris	University of Bern
Wennekers, Thomas	University of Plymouth
Wessnitzer, Jan	University of Edinburgh
Williamson, Ross	University College London