scholarly journals Markov Chain Abstractions of Electrochemical Reaction-Diffusion in Synaptic Transmission for Neuromorphic Computing

2021 ◽  
Vol 15 ◽  
Author(s):  
Margot Wagner ◽  
Thomas M. Bartol ◽  
Terrence J. Sejnowski ◽  
Gert Cauwenberghs
Keyword(s):  
Large Scale ◽  
Internal State ◽  
Reaction Diffusion ◽  
Space Representation ◽  
Chemical Synapse ◽  
Spatial And Temporal Scales ◽  
State Space Representation ◽  
Reaction Diffusion Model ◽  
Neuromorphic Hardware ◽  
The Brain

Progress in computational neuroscience toward understanding brain function is challenged both by the complexity of molecular-scale electrochemical interactions at the level of individual neurons and synapses and the dimensionality of network dynamics across the brain covering a vast range of spatial and temporal scales. Our work abstracts an existing highly detailed, biophysically realistic 3D reaction-diffusion model of a chemical synapse to a compact internal state space representation that maps onto parallel neuromorphic hardware for efficient emulation at a very large scale and offers near-equivalence in input-output dynamics while preserving biologically interpretable tunable parameters.

scholarly journals Towards Biophysically-Based Neuromorphic Computing at Scale: Markov Abstractions of Electrochemical Reaction-Diffusion in Synaptic Transmission

2020 ◽  
Author(s):  
Margot Wagner ◽  
Thomas M. Bartol ◽  
Terrence J. Sejnowski ◽  
Gert Cauwenberghs
Keyword(s):  
Large Scale ◽  
Internal State ◽  
Reaction Diffusion ◽  
Space Representation ◽  
Chemical Synapse ◽  
Spatial And Temporal Scales ◽  
State Space Representation ◽  
Reaction Diffusion Model ◽  
Neuromorphic Hardware ◽  
The Brain

ABSTRACTProgress in computational neuroscience towards understanding brain function is challenged both by the complexity of molecular-scale electrochemical interactions at the level of individual neurons and synapses, and the dimensionality of network dynamics across the brain covering a vast range of spatial and temporal scales. Our work abstracts the highly detailed, biophysically realistic 3D reaction-diffusion model of a chemical synapse to a compact internal state space representation that maps onto parallel neuromorphic hardware for efficient emulation on very large scale, and offers near-equivalence in input-output dynamics while preserving biologically interpretable tunable parameters.

scholarly journals Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bernard Girau ◽  
César Torres-Huitzil ◽  
Nikolaos Vlassopoulos ◽  
José Hugo Barrón-Zambrano
Keyword(s):  
Large Scale ◽  
Complex Dynamics ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Fpga Implementation ◽  
Cellular Slime Mold ◽  
Reaction Diffusion Model ◽  
Cellular Slime ◽  
Computational Resources ◽  
Embedded Implementation

We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of theDictyostelium discoideumcellular slime mold. The environment transmits information according to a reaction-diffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of self-organization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

scholarly journals System Modeling and Reliability Assessment of Microgrids: A Review

2021 ◽  
Vol 14 (1) ◽  
pp. 126
Author(s):  
Masood Ibni Nazir ◽  
Ikhlaq Hussain ◽  
Aijaz Ahmad ◽  
Irfan Khan ◽  
Ayan Mallik
Keyword(s):  
Solar Wind ◽  
Power System ◽  
Large Scale ◽  
System Modeling ◽  
Renewable Energy Sources ◽  
Biomass Energy ◽  
Space Representation ◽  
Small Scale ◽  
State Space Representation ◽  
Operating Modes

The world today is plagued with problems of increased transmission and distribution (T&D) losses leading to poor reliability due to power outages and an increase in the expenditure on electrical infrastructure. To address these concerns, technology has evolved to enable the integration of renewable energy sources (RESs) like solar, wind, diesel and biomass energy into small scale self-governing power system zones which are known as micro-grids (MGs). A de-centralised approach for modern power grid systems has led to an increased focus on distributed energy resources and demand response. MGs act as complete power system units albeit on a small scale. However, this does not prevent them from large operational sophistication allowing their independent functioning in both grid-connected and stand-alone modes. MGs provide greater reliability as compared to the entire system owing to the large amount of information secured from the bulk system. They comprise numerous sources like solar, wind, diesel along with storage devices and converters. Several modeling schemes have been devised to reduce the handling burden of large scale systems. This paper gives a detailed review of MGs and their architecture, state space representation of wind energy conversion systems & solar photovoltaic (PV) systems, operating modes and power management in a MG and its impact on a distribution network.

scholarly journals Reaction-Diffusion Model of PDGF-driven Recruitment in Experimental Glioblastoma

2016 ◽  
Author(s):  
Susan Christine Massey ◽  
Kristin Swanson
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Underlying Mechanism ◽  
Experimental Models ◽  
Platelet Derived Growth Factor ◽  
Reaction Diffusion Model ◽  
Large Numbers ◽  
Glial Progenitor Cells ◽  
The Brain ◽  
Glial Progenitor

Platelet-derived growth factor (PDGF) drives the formation of gliomas in an experimental animal model, which notably involves the recruitment of large numbers of glial progenitor cells (Assanah 2006). In order to understand the underlying mechanism, particularly what factors influence the degree of recruitment, and how varied amounts of PDGF would affect the gross characteristics and overall appearance of tumors in the brain, we adapted a reaction diffusion model of glioma, which has been used for analyzing clinical data, to model the interactions at play in these experimental models.

scholarly journals Automatic rational approximation and linearization of nonlinear eigenvalue problems

2021 ◽  
Author(s):  
Pieter Lietaert ◽  
Karl Meerbergen ◽  
Javier Pérez ◽  
Bart Vandereycken
Keyword(s):  
Rational Approximation ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Space Representation ◽  
Rational Approximations ◽  
Krylov Methods ◽  
Nonlinear Eigenvalue Problems ◽  
State Space Representation ◽  
Rational Polynomial ◽  
Nonlinear Eigenvalue

Abstract We present a method for solving nonlinear eigenvalue problems (NEPs) using rational approximation. The method uses the Antoulas–Anderson algorithm (AAA) of Nakatsukasa, Sète and Trefethen to approximate the NEP via a rational eigenvalue problem. A set-valued variant of the AAA algorithm is also presented for building low-degree rational approximations of NEPs with a large number of nonlinear functions. The rational approximation is embedded in the state-space representation of a rational polynomial by Su and Bai. This procedure perfectly fits the framework of the compact rational Krylov methods (CORK and TS-CORK), allowing solve large-scale NEPs to be efficiently solved. One advantage of our method, compared to related techniques such as NLEIGS and infinite Arnoldi, is that it automatically selects the poles and zeros of the rational approximations. Numerical examples show that the presented framework is competitive with NLEIGS and usually produces smaller linearizations with the same accuracy but with less effort for the user.

scholarly journals A macaque connectome for large-scale network simulations in TheVirtualBrain

2018 ◽  
Author(s):  
Kelly Shen ◽  
Gleb Bezgin ◽  
Michael Schirner ◽  
Petra Ritter ◽  
Stefan Everling ◽  
...  
Keyword(s):  
Resting State ◽  
Brain Function ◽  
Large Scale ◽  
Spatial And Temporal Scales ◽  
Multi Scale ◽  
Large Scale Network ◽  
Scale Network ◽  
Network Simulations ◽  
Dynamical Function ◽  
The Brain

AbstractModels of large-scale brain networks that are informed by the underlying anatomical connectivity contribute to our understanding of the mapping between the structure of the brain and its dynamical function. Connectome-based modelling is a promising approach to a more comprehensive understanding of brain function across spatial and temporal scales, but it must be constrained by multi-scale empirical data from animal models. Here we describe the construction of a macaque connectome for whole-cortex simulations in TheVirtualBrain, an open-source simulation platform. We take advantage of available axonal tract-tracing datasets and enhance the existing connectome data using diffusion-based tractography in macaques. We illustrate the utility of the connectome as an extension of TheVirtualBrain by simulating resting-state BOLD-fMRI data and fitting it to empirical resting-state data.

A MODEL OF THE FORMATION OF THE CEREBRAL CORTEX THROUGH A MIXED APPROACH OF REACTION DIFFUSION EQUATIONS AND MECHANICAL STRAIN

2012 ◽  
Vol 12 (05) ◽  
pp. 1250090
Author(s):  
DIEGO A GARZÓN-ALVARADO
Keyword(s):  
Cerebral Cortex ◽  
Mechanical Strain ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Model ◽  
Proposed Model ◽  
Mixed Approach ◽  
And Function ◽  
The Brain

During fetal development the morphology and function of the organs and tissues is determined. An example occurs with the formation of the cerebral cortex. On the external surface of the brain there are numerous folds (gyri, sulci, and fissures) that determine brain function. The exact cause for the formation of patterns of these folds is unknown. This article proposes a reaction-diffusion model in conjunction with a process of surface mechanical strain to explain the morphogenesis of the superficial structure of the brain.The model is solved using finite elements. There have been tests done on the formation of brain patterns through the reaction-diffusion equations with parameters in the space of Turing and by random mechanical strain. Several numerical examples have been developed that show an acceptable correlation between the results and clinical reality. With the model we can represent, qualitatively, the formation of the cerebral cortex by the proposed model. The model can approximate, and explain, lissencephaly and polymicrogyria, diseases that develop in the cerebral cortex and lead to medical complications to sufferers.

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