568 research outputs found
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. Modulo a mild
topological condition, we find a close connection between maximally flexible
networks and rank 1 matrices. The topological condition is H_1(X;Z)=0, where X
is the clique complex associated to the network's constraint graph; this
condition is generically satisfied for large random networks that are not
overly sparse. In order to prove our main results, we develop some
matrix-theoretic tools and present them in a self-contained section independent
of the neuroscience context.Comment: Accepted to Bulletin of Mathematical Biology, 11 July 201
Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration
This article deals with a viscoplastic material model of overstress type. The
model is based on a multiplicative decomposition of the deformation gradient
into elastic and inelastic part. An additional multiplicative decomposition of
inelastic part is used to describe a nonlinear kinematic hardening of
Armstrong-Frederick type.
Two implicit time-stepping methods are adopted for numerical integration of
evolution equations, such that the plastic incompressibility constraint is
exactly satisfied. The first method is based on the tensor exponential. The
second method is a modified Euler-Backward method. Special numerical tests show
that both approaches yield similar results even for finite inelastic
increments.
The basic features of the material response, predicted by the material model,
are illustrated with a series of numerical simulations.Comment: 29 pages, 7 figure
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. We then analyzed the activity of pyramidal neurons
in rat hippocampus, recorded while the animal was exploring a two-dimensional
environment, and confirmed that our method is able to detect geometric
organization using only the intrinsic pattern of neural correlations.
Remarkably, we found similar results during non-spatial behaviors such as wheel
running and REM sleep. This suggests that the geometric structure of
correlations is shaped by the underlying hippocampal circuits, and is not
merely a consequence of position coding. We propose that clique topology is a
powerful new tool for matrix analysis in biological settings, where the
relationship of observed quantities to more meaningful variables is often
nonlinear and unknown.Comment: 29 pages, 4 figures, 13 supplementary figures (last two authors
contributed equally
Diversity of emergent dynamics in competitive threshold-linear networks: a preliminary report
Threshold-linear networks consist of simple units interacting in the presence
of a threshold nonlinearity. Competitive threshold-linear networks have long
been known to exhibit multistability, where the activity of the network settles
into one of potentially many steady states. In this work, we find conditions
that guarantee the absence of steady states, while maintaining bounded
activity. These conditions lead us to define a combinatorial family of
competitive threshold-linear networks, parametrized by a simple directed graph.
By exploring this family, we discover that threshold-linear networks are
capable of displaying a surprisingly rich variety of nonlinear dynamics,
including limit cycles, quasiperiodic attractors, and chaos. In particular,
several types of nonlinear behaviors can co-exist in the same network. Our
mathematical results also enable us to engineer networks with multiple dynamic
patterns. Taken together, these theoretical and computational findings suggest
that threshold-linear networks may be a valuable tool for understanding the
relationship between network connectivity and emergent dynamics.Comment: 12 pages, 9 figures. Preliminary repor
Hippocampal representation of touch and sound guided behavior
Understanding the mechanisms by which sensory experiences are stored is a longstanding challenge for neuroscience. Previous work has described how the activity of neurons in the sensory cortex allows rats to discriminate the physical features of an object contacted with their whiskers. But to date there is no evidence about how neurons represent the behavioral significance of tactile stimuli, or how tactile events are encoded in memory. To investigate these issues, we recorded
single-unit firing and local field potentials from the CA1 region of hippocampus while rats performed a tactile task. On each trial, the rat touched a plate with its whiskers and, after identifying the texture of the plate, turned to the left or right to obtain its reward. Two textures were associated with each reward location. Over one-third of the sampled neurons encoded the identity of the texture: their firing differed for the two stimuli associated with the same reward location. Over 80 percent of the sampled neurons encoded the behavioral significance of the contacted texture: their firing differed according to the reward location with which it was associated. Texture and reward location signals were present continuously, from the moment of stimulus contact through the entire
period of reward collection. The local field potential power spectrum varied across the different phases of behavior, showing that signals of single-units were present within a sequence of different hippocampal states. The influence of location was examined by training rats to perform the same task in different positions within the room. The responses of neurons to a given stimulus in different locations were independent. This was not the case for reward location signals: neurons that carried a
signal in one location were more likely to carry a signal in the other location. In summary, during a touch-guided behavior, neurons of the CA1 region represent both non spatial (texture identity) and spatial (reward location) events. Additional experiments were carried out, on another set of rats, to generalize some of the above findings from the tactile to the auditory modality. On each trial, the rat leaned into the gap and heard one of four sounds which were distributed along a vowel continuum from "A" to "I". After identifying the sound, the rat turned to the left or right to obtain its reward. Two sounds were associated with each reward location, and the experiment was repeated on 2 platforms. As in the tactile task, more than 80 percent of neurons represented reward location and more than 25 percent of neurons represented the identity of the sound (the vowel). The role of context on the stimulus and reward location signals was the same as in the tactile experiments. Representations of sounds were independent across 2 platforms but the representations of reward location were not: neurons that carried a signal in one location were more likely to carry a signal in the other location. These responses were absent during passive listening to the sounds
К вопросу о методике расчета экономии от внедрения организационно-технических мероприятий в производство геологоразведочных работ
The combinatorial code and the graph rules of Dale networks
We describe the combinatorics of equilibria and steady states of neurons in
threshold-linear networks that satisfy the Dale's law. The combinatorial code
of a Dale network is characterized in terms of two conditions: (i) a condition
on the network connectivity graph, and (ii) a spectral condition on the
synaptic matrix. We find that in the weak coupling regime the combinatorial
code depends only on the connectivity graph, and not on the particulars of the
synaptic strengths. Moreover, we prove that the combinatorial code of a weakly
coupled network is a sublattice, and we provide a learning rule for encoding a
sublattice in a weakly coupled excitatory network. In the strong coupling
regime we prove that the combinatorial code of a generic Dale network is
intersection-complete and is therefore a convex code, as is common in some
sensory systems in the brain.Comment: 22 pages, 4 figures, added discussion section, corrected typos,
expanded the background on convex code
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