Department of Psychology
University of Newcastle
Newcastle upon Tyne, UK
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.
Department of Mathematics
University of Wisconsin
Madison, WI
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.
Department
of Mathematics
University
of Utah
Salt
Lake City, UT
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.
Department
of Mathematics
University
of Southampton
Southampton,
UK
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.
IBM
Microelectronics Division
Austin,
TX
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.
Dynamic Neuroimaging Laboratory
Department of Radiology
University of California
San Francisco, CA
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.
Department
of Molecular & Cell Biology
University
of California
Berkeley,
CA
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.
Department of Physiology
University of Wisconsin-Madison
Madison, WI
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.
Department
of Psychology
Institute
for Mind and Biology
University
of Chicago
Chicago,
IL
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.
Division
of Computer Science
Department
of Mathematical Sciences
University
of Memphis
Memphis,
TN
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.
Department
of Neurosurgery
University
of Virginia
Charlottesville,
VA
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.
Krasnow Institute for Advanced Study
Department of Psychology
George Mason University
Fairfax, VA
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.
Detling Professor and Chair,
Department of Neurology
Director, Center for Neuroscience
University of Wisconsin,
Madison, WI
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.