Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session V34: Focus Session: Nonlinear Dynamics of Neuronal Systems |
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Sponsoring Units: DBP GSNP Chair: Peter Jung, Ohio University Room: Colorado Convention Center 404 |
Thursday, March 8, 2007 11:15AM - 11:51AM |
V34.00001: Dynamics and pattern formation of synaptic learning: Why do we profit from slow learning? Invited Speaker: J. Leo van Hemmen Neuronal dynamics is the dynamics of the brain. It is highly nonlinear because neurons are elements responding to a membrane potential that needs to exceed a threshold in order to generate an action potential or `spike'. Neuronal dynamics occurs on at least two different levels: that of the neurons themselves (on a millisecond timescale) and a much slower one at the synapses, where learning takes place. Synapses are situated on a neuron, receive spikes emitted by other neurons, and are located at the end of an axon transmitting spikes with a finite delay. This talk will concentrate on many fascinating questions such as: What do synaptic representations (maps) of the outside sensory world look like, how do they develop as a consequence of synaptic learning, and is their development compatible with chaos or is it governed by totally different principles? In so doing, we focus on universal principles underlying both the rich diversity of neuronal dynamics of many interacting neurons and the corresponding, adiabatic, learning dynamics at the synapses in conjunction with pattern formation in large systems of synapses. The timescale of the latter is, in general, at least five orders of magnitude slower than that of the neurons. Not only does this ``slow'' synaptic learning lead to an adiabatic principle and, hence, to analytical insight into the learning process itself but it also allows for robustness of learning as compared to the much more fragile neuronal dynamics. [Preview Abstract] |
Thursday, March 8, 2007 11:51AM - 12:03PM |
V34.00002: Synchronized dynamics of cortical neurons with time-delay feedback Alexandra Landsman, Ira Schwartz The dynamics of three mutually delay coupled cortical neurons are explored. When coupled in a line, delays introduce correlations in the time series at the time-scale of the delay. The middle neuron leads the outer ones by the delay time, while the end neurons are synchronized with zero lag times. Synchronization is found to be highly dependent on the synaptic time constant, with faster synapses increasing both the degree of synchronization and the firing rate. Analysis shows that pre-synaptic input during the inter-spike interval stabilizes the synchronous state, even for arbitrarily weak coupling, and independent of the initial phase. The finding may be of significance to synchronization of large groups of cells in the cortex that are spatially distanced from each other. [Preview Abstract] |
Thursday, March 8, 2007 12:03PM - 12:15PM |
V34.00003: Eye-Target Synchrony and Attention R. Contreras, R. Kolster, S. Basu, H. U. Voss, J. Ghajar, M. Suh, S. Bahar Eye-target synchrony is critical during smooth pursuit. We apply stochastic phase synchronization to human pursuit of a moving target, in both normal and mild traumatic brain injured (TBI) subjects. Smooth pursuit utilizes the same neural networks used by attention. To test whether smooth pursuit is modulated by attention, subjects tracked a target while loaded with tasks involving working memory. Preliminary results suggest that additional cognitive load increases normal subjects' performance, while the effect is reversed in TBI patients. We correlate these results with eye-target synchrony. Additionally, we correlate eye-target synchrony with frequency of target motion, and discuss how the range of frequencies for optimal synchrony depends on the shift from attentional to automatic-response time scales. Synchrony deficits in TBI patients can be correlated with specific regions of brain damage imaged with diffusion tensor imaging (DTI). [Preview Abstract] |
Thursday, March 8, 2007 12:15PM - 12:27PM |
V34.00004: Complex patterns of synchrony in networks undergoing exogenous drive Jack Waddell, Michal Zochowski It has been established that various exogenous oscillatory drives modulate neural activity (and potentially information processing) in the brain. We explore the effect of an exogenous drive on the spatio-temporal pattern formation of a network of coupled non-identical R\"{o}ssler oscillators. We investigate the formation and properties of the phase locked states, dependent on the network properties as well as those of the external drive. We have found that such drive has a complex effect on the pattern formation in the network, depending on the coupling strength between the oscillators, drive strength as well as its frequency relative to the oscillators. [Preview Abstract] |
Thursday, March 8, 2007 12:27PM - 12:39PM |
V34.00005: Measurements of synchronization between interacting networks in a model of focal epilepsy S. Feldt, H. Osterhage, F. Mormann, K. Lehnertz, M. Zochowski We use a simple model of two interacting networks of neurons to explain a seemingly paradoxical result observed in epileptic patients indicating that the level of phase synchrony drops below normal levels during the preictal state. We show that the transition from the interictal to preictal and then to ictal state may be divided into separate dynamical regimes: the formation of slow oscillatory activity observed during the normal (interictal) period, structureless activity during the preictal period when the two networks have different properties, and bursting dynamics driven by the network corresponding to the focus. We thus hypothesize that the beginning of the preictal period marks the beginning of the transition of the focal network from normal activity towards seizing and compare our results to measurements of the preictal length in human patients. [Preview Abstract] |
Thursday, March 8, 2007 12:39PM - 12:51PM |
V34.00006: Structural network heterogeneities and network dynamics: a possible dynamical mechanism for hippocampal memory reactivation. Piotr Jablonski, Gina Poe, Michal Zochowski The hippocampus has the capacity for reactivating recently acquired memories and it is hypothesized that one of the functions of sleep reactivation is the facilitation of consolidation of novel memory traces. The dynamic and network processes underlying such a reactivation remain, however, unknown. We show that such a reactivation characterized by local, self-sustained activity of a network region may be an inherent property of the recurrent excitatory-inhibitory network with a heterogeneous structure. The entry into the reactivation phase is mediated through a physiologically feasible regulation of global excitability and external input sources, while the reactivated component of the network is formed through induced network heterogeneities during learning. We show that structural changes needed for robust reactivation of a given network region are well within known physiological parameters. [Preview Abstract] |
Thursday, March 8, 2007 12:51PM - 1:03PM |
V34.00007: Processing of odor stimuli by neuronal network models of the olfactory bulb Stuart Wick, Martin Wiechert, Hermann Riecke, Rainer Friedrich The space of perceptable odors is high-dimensional and its representation in the various brain structures is still poorly understood. We focus on the olfactory bulb, which constitutes the first processing stage for odor stimuli after they have been sensed by receptor neurons. Experimentally it is found that the correlations between the outputs of the bulb are significantly reduced relative to those of the corresponding inputs, thus enhancing the discriminability of similar odors. We have generated a firing-rate-based network model with parameters derived from experimental data that reproduces decorrelation. Here we use this model to investigate the dependence of stimulus representations on odor concentration. We address the possibility of a change in perceived odor identity with changing concentration and the dependence of odor discriminability on odor concentration. We interpret some of our results within a simple mean-field model for the neural activity. [Preview Abstract] |
Thursday, March 8, 2007 1:03PM - 1:15PM |
V34.00008: The dynamics of temporal ordering in driven integrate-and-fire-neurons. Jan Engelbrecht, Renato Mirollo Spike-timing neural codes involve the development of some kind of temporal order (synchrony) between a neuron's spike times and timing features in either the stimulus, local field potentials or the average activity in a population of synchronizing neurons. In order to explore the dynamics of temporal ordering we study an integrate-and-fire neuron with a (small) oscillatory component in its input. Tuning the frustration due to the interplay between the neuron's natural firing time and the oscillatory rhythm's period, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics controlled by a correlation time that diverges at phase boundaries -- quite analogous to diverging correlation lengths in equilibrium phase transitions. Our results can be understood in terms on an extension of the theory of circle maps. In addition, they address how fast synchronous behavior can emerge in biological or artificial neural networks. [Preview Abstract] |
Thursday, March 8, 2007 1:15PM - 1:27PM |
V34.00009: Rocking the boat: Auditory localization of ground-borne vibrations in snakes J. Leo van Hemmen Experiments [1] have shown that sand-dwelling desert snakes can localize prey in the absence of visual, chemosensory, and infrared cues. Instead, prey-generated surface waves traveling along the substrate surface provide the necessary information for a snake to estimate the stimulus position. The snake's inner ear is mechanically coupled to the lower jaw through a lever construction. Moreover, the left and right jaws in snakes are only loosely linked, thus providing the possibility of detecting surface vibrations and locating a stimulus through interaural time differences. Using the theory of floating bodies as an approximation of a snake jaw resting on a sandy substrate, we explicitly calculate [2] the response of the lower jaw to incoming surface waves and show that the sensitivity of the snake ear suffices to allow prey localization on the basis of interaural time-of-arrival differences. Refs.: [1] B.A. Young and M. Morain, J. Exp. Biol. \textbf{205} (2002) 661; [2] P. Friedel, B.A. Young, and J.L. van Hemmen, TU Munich preprint (2007). [Preview Abstract] |
Thursday, March 8, 2007 1:27PM - 1:39PM |
V34.00010: Two-dimensional encoding and adaptation in the songbird auditory forebrain Tatyana Sharpee, Katherine Nagel, Allison Doupe Neural adaptation is crucial for many auditory tasks, such as speech recognition, where robust performance is achieved over a wide range of signal-to-noise ratios and in the presence of 1/f- type noise. While faithful high-rate sampling can work well in the presence of noise which is largely uncorrelated between successive signal samples, alternative strategies might be needed to achieve reliable performance in the presence of strongly correlated noise. We studied how neurons in songbird auditory forebrain region (field L) encode temporal modulations of the amplitude of band-limited sounds using an information- theoretic method for finding relevant stimulus dimensions [1]. We robustly found that neurons in field L perform temporal processing based on simultaneous sampling of locally smoothed values of log-amplitude and its time-derivative. Either one of the two stimulus features could play the dominant role in neural response. We conclude with a theoretical explanation for the optimality of such signal processing strategies in situations where noise and signals have comparable correlation times. [1] T. Sharpee, N.C. Rust, W. Bialek, Neural. Computation 16, 223 (2004). [Preview Abstract] |
Thursday, March 8, 2007 1:39PM - 1:51PM |
V34.00011: Astrocytes optimize synaptic fidelity Suhita Nadkarni, Peter Jung, Herbert Levine Most neuronal synapses in the central nervous system are enwrapped by an astrocytic process. This relation allows the astrocyte to listen to and feed back to the synapse and to regulate synaptic transmission. We combine a tested mathematical model for the Ca$^{2+}$ response of the synaptic astrocyte and presynaptic feedback with a detailed model for vesicle release of neurotransmitter at active zones. The predicted Ca$^{2+}$ dependence of the presynaptic synaptic vesicle release compares favorably for several types of synapses, including the Calyx of Held. We hypothesize that the feedback regulation of the astrocyte onto the presynaptic terminal {\it optimizes} the fidelity of the synapse in terms of information transmission. [Preview Abstract] |
Thursday, March 8, 2007 1:51PM - 2:03PM |
V34.00012: Dynamical analysis of Bayesian inference models and its relation to connectionist neural network models for the Eriksen task Yuan Liu, Angela Yu, Philip Holmes We analyze Bayesian compatibility bias and spatial uncertainly models for the two-alternative forced choice Eriksen task, in which subjects must correctly identify a central stimulus and disregard flankers that may or may not be compatible with it. We simplify the models, deriving linear, uncoupled, discrete dynamical systems and their continuum limits: stochastic differential equations. Analytical solutions of these allow us to describe how posterior probabilities and psychometric functions depend upon parameters. We compare our results with numerical simulations of original inference models and show that agreement is good enough for them to be useful in parameterizing such models. Our analysis also reveals that Bayesian updating is closely related to a simple drift diffusion process that can be derived from neural network models. [Preview Abstract] |
Thursday, March 8, 2007 2:03PM - 2:15PM |
V34.00013: Walking at stability's edge John Milton, David Nichols, Adam Coleman, Coury Clemens, Annie Nguyentat, Ami Radunskaya During self-paced human walking, the variability in inter- stride intervals exhibit fractal dynamics characterized by long--range correlations having a power-law decay with exponent $\alpha$. We used diffusion fluctuation analysis (DFA) to estimate $\alpha$ as a function of the roughness of the walking surface for eight (8) healthy subjects (1200-1400 inter- stride intervals for each walking surface). For each subject the highest $\alpha$ (mean 0.96, range 0.88- 1.10) occured for walking on a running track and $\alpha$ was $15-20\%$ lower for walking on either a relatively smoother (tennis hard court) or a rougher (dirt path) surface. These observations are captured by a stochastic discrete time cubic map: $I_{i+1}=a(\xi_i)I_i - bI^3_i + \eta_i$, where $I_i$ is the $i$--th inter--stride time, $a(\xi_i)=a_o (\xi) + \xi_i$ describes parametric, colored noise where $a_0(\xi)$ is a constant that depends on surface roughness and $\xi_i$ is colored noise with mean zero, $\eta_i$ is low--intensity additive white noise, and $b$ is a constant. As the roughness, and hence $a_0(\xi)$, of the walking surface increases, the fluctuations in the inter--stride interval are predicted to obey a power law whose exponent changes non-monotonically: the highest values of $\alpha$ determined with DFA occur when $a_0(\xi)$ is close to the deterministic stability boundary $a=1$. Thus the neural control of walking appears to involve a dynamical system tuned close to the edge of stability subjected to the effects of parametric noise. [Preview Abstract] |
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