Complex Nonlinear Neural Dynamics Workshop Abstracts

 

Peter Andras

Department of Psychology

University of Newcastle

Newcastle upon Tyne, UK

 

Advantages of Chaos

 

There are several proposals about how information encoding works in nervous systems (e.g., spike rate, population activity, spatio-temporal activity patterns). Encoding with spatio-temporal patterns leads to the question of what kind of dynamic attractors in the space of spatio-temporal patterns are better fitted to encode large amounts of information. Here we show that chaotic spatio-temporal pattern attractors are able to encode more information than other types of attractors.

 

 

 

Amir Assadi

Department of Mathematics

University of Wisconsin

Madison, WI

 

Neuronal Dynamics and Sparse Coding In The Anterior Cingulate Cortex

 

A novel multi-scale temporal analysis of multi-electrode spike recording from the anterior cingulate cortex reveals sparse coding by local circuits of neurons. We propose an architecture for synaptic organization of the anterior cingulate cortex based on well-known biological principles such as Hebbian learning and the sparse coding hypothesis to model cortical information processing of pain in accordance with experimental results.

 

 

 

Paul Bressloff

Department of Mathematics

University of Utah

Salt Lake City, UT

 

The functional geometry of local and horizontal connections in a dynamical model of V1

 

A dynamical model of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the geometry of local and long-range horizontal connections. Each hypercolumn is modeled as a network of interacting excitatory and inhibitory neural populations with orientation and spatial frequency preferences organized around a pair of pinwheels. The pinwheels are arranged on a planar lattice, reflecting the crystalline-like structure of cortex. Local interactions within a hypercolumn generate orientation and spatial frequency tuning curves, which are modulated by horizontal connections between different hypercolumns on the lattice. The symmetry properties of the local and long-range connections play an important role in determining the types of spontaneous and stimulus-evoked activity patterns that can arise in cortex.

 

 

 

Giampaolo D’Alessandro

Department of Mathematics

University of Southampton

Southampton, UK

 

Analysis of patch clamp recordings in the hippocampus of rats

 

We have measured the excitatory and inhibitory inputs to local inter-neurons in slices of the hippocampus of rats and have analysed them using linear and nonlinear techniques.  The analysis suggests that most of the signals arriving to the inter-neurons are random, even though in a few cases a periodic and stable activity could also be detected.  The detection of synchronous events in dual cell recordings has allowed us to establish that the randomness of the incoming signals is not due to the superposition of many fairly regular inputs.

 

 

 

David DeMaris

IBM Microelectronics Division

Austin, TX

 

Coding and Computation with Densities in Coupled Chaotic Maps

 

Theory and applications have emerged over the last decade suggesting the utility of coding and computation using population statistics (densities) of evolving spatio-temporal networks of chaotic recurrent units.  Results in recognition of 3D objects and other spatial processing problems are reviewed. Related theoretical concepts, including symbolic dynamics and dynamical recognizers,  periodic densities, and clustering via Markov relaxation are discussed.  With density coding, the dynamical recognizer framework developed for small recurrent networks is extended to support more general representation spaces.

 

 

 

Thomas Ferree

Dynamic Neuroimaging Laboratory

Department of Radiology

University of California

San Francisco, CA

 

Scaling behavior and global brain states in human EEG

 

EEG and MEG measure the collective behavior of large populations of cortical pyramidal neurons.  Using the technique of detrended fluctuation analysis to study the dynamics across temporal scales, we have found that human resting EEG typically exhibits power-law scaling behavior in two temporal ranges.  Such scaling behavior in complex systems is often interpreted as a signature of self-organized criticality.  Extending this analysis to 128 electrode channels, we find that the moments of the distributions of the scaling exponents also exhibit power-law behavior.  This gives rise to a putative physiological definition of global brain state.  As a form of data reduction, it facilitates comparison across subjects.  We present here two clinical applications of this approach.  First, we show that the scaling exponents reflect brain state changes due to anaesthesia.  Second, we compare the global brain state of 18 normal subjects against 10 subjects with acute ischemic stroke, and find nearly perfect separation of the two groups.

 

 

 

Walter J. Freeman

Department of Molecular & Cell Biology

University of California

Berkeley, CA

 

Bridging the gap between microscopic neurons and macroscopic brain with mesoscopic nonlinear neurodynamics

 

Brain systems operate on many levels of organization, each with its own scales of time and space.  Dynamics is applicable to every level, from the atomic to the molecular, and from macromolecular organelles to the neurons into which they are incorporated.  In turn the neurons form populations; they form systems, and so on to an embodied brain interacting intentionally with its environment.  Each level is "macroscopic" to the one below it and "microscopic" to the one above it.  Among the most difficult tasks are those of conceiving and describing the exchanges between levels, seeing that the scales of time and distance are incommensurate, and that causal inference is far more ambiguous between than within levels.  That holds for the relation of action potentials recorded from microelectrodes to whole brain activity seen with fMRI and PET.   A new recourse is to conceive, identify and model an intervening "mesoscopic" level, at which is found local self-organizing neural populations.  Their characteristic activities consist of steady-state, uncorrelated, background action potentials and EEG dendritic activity.  The contribution that mesoscopic neurodynamics can make is to gain better understanding of self-organizing "wave packets" in primary sensory areas. These packets are manifested in spatially distributed, amplitude-modulated (AM), aperiodic, spatially coherent carrier waves.  The formation of these "AM patterns" by wave packets is governed by a landscape of nonconvergent attractors that are formed by prior learning and stored in each sensory cortex.  The access to each attractor on presentation of the relevant conditioned stimulus is by a 1st order phase transition, making perception a creative act of neural masses.  The pattern requires a high level of synaptic interaction in cortex that reduces the degrees of freedom and dimensionality of cortical populations.  Hence the transition is comparable to a phase transition of a vapor to a liquid.  A conditioned stimulus elicits clouds of action potentials in sensory cortex like water molecules in steam.  They are condensed in the formation of an AM pattern like the formation of a scintillating rain drop.  The AM pattern is read out through divergent-convergent pathways that perform a spatial integral transform, an essential step toward forming macroscopic perceptions through global brain dynamics.

 

 

 

Mathew V. Jones

Department of Physiology

University of Wisconsin-Madison

Madison, WI  

 

Synaptic communication in the presence of noise

 

A neuron receives its input via thousands of noisy synapses, each activated by variable presynaptic spiketrains. How can neural representations remain stable despite relying on such unreliable transmission channels? Several theories address the issue of stability in the presence of noise, but little experimental data concerning the impact of noise is available at the level of individual neurons and synapses. We present experimental studies of the effects of natural synaptic noise on spiketrains of granule cells in hippocampal slices. We use biophysically realistic synaptic conductance injections that mimic input from many excitatory and inhibitory neurons, including experimentally measured fluctuations in timing, amplitude and kinetics. Methods of synaptic stimulus reconstruction and classification of preferred stimuli are also explored. We find that a) natural synaptic noise does not prevent precise spike timing (< 2 ms), b) feedforward inhibition favors sparse but precise and reliable time-coding, c) efficient rate- and/or time-based coding probably operates in a temporally sparse input regime and d) even in the presence of natural synaptic noise, granule cells are sensitive to temporal correlations among as few as 4 presynaptic neurons, on a background of 96 uncorrelated competing inputs. Future directions will involve an information-theoretic analysis of stimulus selectivity and the effects of feedback inhibition on selectivity and coding efficiency.

 

 

 

Leslie M. Kay

Department of Psychology

Institute for Mind and Biology

University of Chicago

Chicago, IL

 

Fast behavioral state changes and their influences on system dynamics

 

Many analyses of system dynamics rely on long periods of relatively  stationary activity as measured by neural signals.  Dynamical models of perceptual systems should take into account the extreme nonstationarity of behavior and not rely on stationary states, which usually represent habituation, attentive waiting or even seizures.  Psychological or behavioral states can be fleeting, lasting on the order of one second or less.  Olfactory-guided behavior displays rapid successions of behavioural states, often changing from one sniff to the next. The neural correlates of these changes are represented in the wide-ranging changes in the frequency and coherence characteristics of the local field potential as well as the firing properties of individual neurons in the olfactory bulb.   They may be induced by changes in motor behavior, neuromodulatory release, momentary centrifugal control of peripheral sensory brain regions or all of these.

 

 

 

Robert Kozma

Division of Computer Science

Department of Mathematical Sciences

University of Memphis

Memphis, TN

 

Neuropercolation model of spatio-temporal neurodynamics

 

We study aperiodic brain activity observed in cortical EEG measurements. The experiments indicate the presence of complex spatio-temporal dynamics in various cortical areas. In our approach, the basal state of cortical dynamics is considered a high-dimensional chaotic

attractor. Sensory inputs induce phase transitions and the dynamics is constrained to an attractor wing (i.e., the recalled memory pattern). The mathematical theory of random graphs and percolation processes provides a very powerful tool to understand and interprete these

findings. In the neuropercolation model we describe the behavior of the neuropil, the filamentous texture of neural tissue, as a random cellular automata. Neural populations stem ontogenetically in embryos from aggregates of neurons that grow axons and dendrites and form synaptic connections of steadily increasing density. At some threshold the density allows neurons to transmit more pulses than they receive, so that an aggregate undergoes a state transition from a zero point attractor to a non-zero point attractor, thereby becoming a population. First order phase transitions are described in the neuropercolation model, using various order parameters.

 

 

 

William B. Levy

Department of Neurosurgery

University of Virginia

Charlottesville, VA

 

Improving Learning on a Nonlinear Task by Adding Random Fluctuations

 

We hypothesize the hippocampus is a random recoding device and that such random recoding allows the hippocampus to solve problems on which other brain regions have failed. Adding biologically sensible random fluctuations improves the performance of this hippocampal model for problems such as transverse patterning and transitive inference.

 

 

 

Steven J. Schiff

Krasnow Institute for Advanced Study

Department of Psychology

George Mason University

Fairfax, VA

 

Detecting weak neuronal interactions - are linear techniques better?

 

There has been considerable theoretical work on nonlinear functional relationships between coupled systems over the past 2 decades. There are clear theoretical examples where a nonlinear method is required to detect such interactions. Although several biological examples have been studied with such tools, validation of the results is always problematic. Here we present a theoretical framework for approaching such systems, and present evidence why linear methods may be critical for analysis of neuronal systems.

 

 

 

Thomas P. Sutula

Detling Professor and Chair, Department of Neurology

Director, Center for Neuroscience

University of Wisconsin,

Madison, WI

 

The changing brain: Plasticity of neural circuits in development, memory, and epilepsy

 

The nervous system, once regarded as complex and static, is now recognized to possess extraordinary capacity for modification and adaptation. The capacity for modification or “brain plasticity” plays a major role in development, learning and memory, behavior, and many diseases. The brain undergoes active growth processes throughout life in adaptive response to all sorts of new experiences.   Neural circuits also undergo modification in response to injury and a variety of pathological processes including epilepsy, a common neurological disorder that afflicts more than 1% of the population.  Epilepsy is defined by recurring brief episodes of neural synchronization accompanied by abnormal behaviors or seizures.  There is now abundant evidence that seizures predictably modify the developing and adult hippocampus and dentate gyrus, a region of brain that plays a role in learning, memory, and epilepsy.  Brief seizures that disrupt normal behavior for only tens of seconds induce an evolving sequence of long-lasting structural and functional alterations involving all levels of biological organization in neural circuits, from gene transcription to behavior.  At the molecular and cellular level, seizures induce alterations in transcription, receptor proteins, neuronal death, and axon sprouting which rearranges synaptic connectivity and increases recurrent excitation in the dentate gyrus.  At the systems level, these seizure-induced alterations have adverse consequences that include memory disturbances, decreases in inhibition, reduction in the normal filtering properties of the dentate gyrus, and increased susceptibility to additional seizures (kindling).  Study of these seizure-induced cellular alterations in experimental models provides an opportunity to assess how subtle but cumulative neuronal alterations may contribute to emergent network effects in complex systems such as hippocampal circuitry, and also provides potential targets for novel therapeutic intervention.