ATTRACTOR-BASED MODELS FOR SEQUENCES AND PATTERN GENERATION IN NEURAL CIRCUITS.

Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion [51]. There is also substantial evidence that the brain encodes memories and processes information via of neural activity. In this dissertation, we are focused on the general problem of how neural circuits encode rhythmic activity, as in central pattern generators (CPGs), as well as the encoding of sequences.

On open and closed convex codes.

Neural codes serve as a language for neurons in the brain. () which arise from the pattern of intersections of collections of open (or closed) convex sets in Euclidean space, are of particular relevance to neuroscience. Not every code is open or closed convex, however, and the combinatorial properties of a code that determine its realization by such sets are still poorly understood.

Clique topology reveals intrinsic geometric structure in neural correlations.

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries.

A no-go theorem for one-layer feedforward networks.

It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain the set of possible response patterns, thereby shaping the neural code. This implies the existence of neural codes that cannot arise solely from feedforward processing. We set out to find such codes in the context of one-layer feedforward networks and identified a large class of combinatorial codes that indeed cannot be shaped by the feedforward architecture alone.

Encoding binary neural codes in networks of threshold-linear neurons.

Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded patterns is still poorly understood. Here we consider this problem for networks of threshold-linear neurons whose computational function is to learn and store a set of binary patterns (e.

The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes.

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code.

Combinatorial neural codes from a mathematical coding theory perspective.

Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical coding theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes).

Short-Term Facilitation may Stabilize Parametric Working Memory Trace.

Networks with continuous set of attractors are considered to be a paradigmatic model for parametric working memory (WM), but require fine tuning of connections and are thus structurally unstable. Here we analyzed the network with ring attractor, where connections are not perfectly tuned and the activity state therefore drifts in the absence of the stabilizing stimulus. We derive an analytical expression for the drift dynamics and conclude that the network cannot function as WM for a period of several seconds, a typical delay time in monkey memory experiments.

Flexible memory networks.

Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network's connectivity matrix.

Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus.

Hippocampal neurons can display reliable and long-lasting sequences of transient firing patterns, even in the absence of changing external stimuli. We suggest that time-keeping is an important function of these sequences, and propose a network mechanism for their generation. We show that sequences of neuronal assemblies recorded from rat hippocampal CA1 pyramidal cells can reliably predict elapsed time (15-20 s) during wheel running with a precision of 0.

Effects of adult-generated granule cells on coordinated network activity in the dentate gyrus.

Throughout the adult life of most mammals, new neurons are continuously generated in the dentate gyrus of the hippocampal formation. Recent work has documented specific cognitive deficits after elimination of adult hippocampal neurogenesis in rodents, suggesting that these neurons may contribute to information processing in hippocampal circuits. Young adult-born neurons exhibit enhanced excitability and have altered capacity for synaptic plasticity in hippocampal slice preparations in vitro.

How do neurons work together? Lessons from auditory cortex.

Recordings of single neurons have yielded great insights into the way acoustic stimuli are represented in auditory cortex. However, any one neuron functions as part of a population whose combined activity underlies cortical information processing. Here we review some results obtained by recording simultaneously from auditory cortical populations and individual morphologically identified neurons, in urethane-anesthetized and unanesthetized passively listening rats.

A simple model of cortical dynamics explains variability and state dependence of sensory responses in urethane-anesthetized auditory cortex.

The responses of neocortical cells to sensory stimuli are variable and state dependent. It has been hypothesized that intrinsic cortical dynamics play an important role in trial-to-trial variability; the precise nature of this dependence, however, is poorly understood. We show here that in auditory cortex of urethane-anesthetized rats, population responses to click stimuli can be quantitatively predicted on a trial-by-trial basis by a simple dynamical system model estimated from spontaneous activity immediately preceding stimulus presentation.

Cell groups reveal structure of stimulus space.

An important task of the brain is to represent the outside world. It is unclear how the brain may do this, however, as it can only rely on neural responses and has no independent access to external stimuli in order to "decode" what those responses mean. We investigate what can be learned about a space of stimuli using only the action potentials (spikes) of cells with stereotyped -- but unknown -- receptive fields.

Internally generated cell assembly sequences in the rat hippocampus.

A long-standing conjecture in neuroscience is that aspects of cognition depend on the brain's ability to self-generate sequential neuronal activity. We found that reliably and continually changing cell assemblies in the rat hippocampus appeared not only during spatial navigation but also in the absence of changing environmental or body-derived inputs. During the delay period of a memory task, each moment in time was characterized by the activity of a particular assembly of neurons.

Pattern capacity of a perceptron for sparse discrimination.

We evaluate the capacity and performance of a perceptron discriminator operating in a highly sparse regime where classic perceptron results do not apply. The perceptron is constructed to respond to a specified set of q stimuli, with only statistical information provided about other stimuli to which it is not supposed to respond. We compute the probability of both false-positive and false-negative errors and determine the capacity of the system for not responding to nonselected stimuli and for responding to selected stimuli in the presence of noise.

Theta-mediated dynamics of spatial information in hippocampus.

In rodent hippocampus, neuronal activity is organized by a 6-10 Hz theta oscillation. The spike timing of hippocampal pyramidal cells with respect to the theta rhythm correlates with an animal's position in space. This correlation has been suggested to indicate an explicit temporal code for position.

Valuations for spike train prediction.

The ultimate product of an electrophysiology experiment is often a decision on which biological hypothesis or model best explains the observed data. We outline a paradigm designed for comparison of different models, which we refer to as spike train prediction. A key ingredient of this paradigm is a prediction quality valuation that estimates how close a predicted conditional intensity function is to an actual observed spike train.