Existence and Stability of Standing Pulses in Neural Networks: II Stability

We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear gain function. When two standing single-pulse solutions coexist, the small pulse is unstable, and the large pulse is stable. The large single-pulse is bistable with the ``all-off'' state. This bistable localized activity may have strong implications for the mechanism underlying working memory. We show that dimple pulses have similar stability properties to large pulses but double pulses are unstable.Comment: 31 pages, 16 figures, submitted to SIAM Journal on Applied Dynamical System

Symmetry-breaking transitions in networks of nonlinear circuit elements

We investigate a nonlinear circuit consisting of N tunnel diodes in series, which shows close similarities to a semiconductor superlattice or to a neural network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like system. The tunnel diodes are coupled globally through a load resistor. We find complex bifurcation scenarios with symmetry-breaking transitions that generate multiple fixed points off the synchronization manifold. We show that multiply degenerate zero-eigenvalue bifurcations occur, which lead to multistable current branches, and that these bifurcations are also degenerate with a Hopf bifurcation. These predicted scenarios of multiple branches and degenerate bifurcations are also found experimentally.Comment: 32 pages, 11 figures, 7 movies available as ancillary file

Network Amplification of Local Fluctuations Causes High Spike Rate Variability, Fractal Firing Patterns and Oscillatory Local Field Potentials

We investigate a model for neural activity in a two-dimensional sheet of leaky integrate-and-fire neurons with feedback connectivity consisting of local excitation and surround inhibition. Each neuron receives stochastic input from an external source, independent in space and time. As recently suggested by Softky and Koch (1992, 1993), independent stochastic input alone cannot explain the high interspike interval variability exhibited by cortical neurons in behaving monkeys. We show that high variability can be obtained due to the amplification of correlated fluctuations in a recurrent network. Furthermore, the cross-correlation functions have a dual structure, with a sharp peak on top of a much broader hill. This is due to the inhibitory and excitatory feedback connections, which cause "hotspots" of neural activity to form within the network. These localized patterns of excitation appear as clusters or stripes that coalesce, disintegrate, or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters. The synaptic current impinging upon a single neuron shows large fluctuations at many time scales, leading to a large coefficient of variation (C_V) for the interspike interval statistics. The power spectrum associated with single units shows a 1/f decay for small frequencies and is flat at higher frequencies, while the power spectrum of the spiking activity averaged over many cells—equivalent to the local field potential—shows no 1/f decay but a prominent peak around 40 Hz, in agreement with data recorded from cat and monkey cortex (Gray et al. 1990; Eckhorn et al. 1993). Firing rates exhibit self-similarity between 20 and 800 msec, resulting in 1/f-like noise, consistent with the fractal nature of neural spike trains (Teich 1992)

Information processing in a midbrain visual pathway

Visual information is processed in brain via the intricate interactions between neurons. We investigated a midbrain visual pathway: optic tectum and its isthmic nucleus) that is motion sensitive and is thought as part of attentional system. We determined the physiological properties of individual neurons as well as their synaptic connections with intracellular recordings. We reproduced the center-surround receptive field structure of tectal neurons in a dynamical recurrent feedback loop. We reveal in a computational model that the anti-topographic inhibitory feedback could mediate competitive stimulus selection in a complex visual scene. We also investigated the dynamics of the competitive selection in a rate model. The isthmotectal feedback loop gates the information transfer from tectum to thalamic rotundus. We discussed the role of a localized feedback projection in contributing to the gating mechanisms with both experimental and numerical approaches. We further discussed the dynamics of the isthmotectal system by considering the propagation delays between different components. We conclude that the isthmotectal system is involved in attention-like competitive stimulus selection and control the information coding in the motion sensitive SGC-I neurons by modulating the retino-tectal synaptic transmission

Adaptive map alignment in the superior colliculus of the barn owl: a neuromorphic implementation

Adaptation is one of the basic phenomena of biology, while adaptability is an important feature for neural network. Young barn owl can well adapt its visual and auditory integration to the environmental change, such as prism wearing. At first, a mathematical model is introduced by the related study in biological experiment. The model well explained the mechanism of the sensory map realignment through axongenesis and synaptogenesis. Simulation results of this model are consistent with the biological data. Thereafter, to test the model’s application in hardware, the model is implemented into a robot. Visual and auditory signals are acquired by the sensors of the robot and transferred back to PC through bluetooth. Results of the robot experiment are presented, which shows the SC model allowing the robot to adjust visual and auditory integration to counteract the effects of a prism. Finally, based on the model, a silicon Superior Colliculus is designed in VLSI circuit and fabricated. Performance of the fabricated chip has shown the synaptogenesis and axogenesis can be emulated in VLSI circuit. The circuit of neural model provides a new method to update signals and reconfigure the switch network (the chip has an automatic reconfigurable network which is used to correct the disparity between signals). The chip is also the first Superior Colliculus VLSI circuit to emulate the sensory map realignment

Attractors, memory and perception

In this Thesis, the first three introductory chapters are devoted to the review of literature on contextual perception, its neural basis and network modeling of memory. In chapter 4, the first two sections give the definition of our model; and the next two sections, 4.3 and 4.4, report the original work of mine on retrieval properties of different network structures and network dynamics underlying the response to ambiguous patterns, respectively. The reported work in chapter 5 has been done in collaboration with Prof Bharathi Jagadeesh in University of Washington, and is already published in the journal \u201dCerebral Cortex\u201d. In this collaboration, Yan Liu, from the group in Seattle, carried out the recording experiments and I did the data analysis and network simulations. Chapter 6, which represents a network model for \u201dpriming\u201d and \u201dadaptation aftereffect\u201d is done by me. The works reported in 4.3, 4.5, and the whole chapter 6 are in preparation for publication

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

Localist representation can improve efficiency for detection and counting

Almost all representations have both distributed and localist aspects, depending upon what properties of the data are being considered. With noisy data, features represented in a localist way can be detected very efficiently, and in binary representations they can be counted more efficiently than those represented in a distributed way. Brains operate in noisy environments, so the localist representation of behaviourally important events is advantageous, and fits what has been found experimentally. Distributed representations require more neurons to perform as efficiently, but they do have greater versatility