Conditions for wave trains in spiking neural networks

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and uniqueness of different types of waves or bumps of activity using neural-field models, phenomenological coarse-grained descriptions of neural-network dynamics. But it remains unclear how these insights can be transferred to more biologically realistic networks of spiking neurons, where individual neurons fire irregularly. Here, we employ mean-field theory to reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with distance-dependent connectivity to an effective neural-field model. In contrast to existing phenomenological descriptions, the dynamics in this neural-field model depends on the mean and the variance in the synaptic input, both determining the amplitude and the temporal structure of the resulting effective coupling kernel. For the neural-field model we employ liner stability analysis to derive conditions for the existence of spatial and temporal oscillations and wave trains, that is, temporally and spatially periodic traveling waves. We first prove that wave trains cannot occur in a single homogeneous population of neurons, irrespective of the form of distance dependence of the connection probability. Compatible with the architecture of cortical neural networks, wave trains emerge in two-population networks of excitatory and inhibitory neurons as a combination of delay-induced temporal oscillations and spatial oscillations due to distance-dependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neural-field model and numerical simulations of both networks of nonlinear rate-based units and networks of LIF neurons.Comment: 36 pages, 8 figures, 4 table

Simulation and Theory of Large-Scale Cortical Networks

Cerebral cortex is composed of intricate networks of neurons. These neuronal networks are strongly interconnected: every neuron receives, on average, input from thousands or more presynaptic neurons. In fact, to support such a number of connections, a majority of the volume in the cortical gray matter is filled by axons and dendrites. Besides the networks, neurons themselves are also highly complex. They possess an elaborate spatial structure and support various types of active processes and nonlinearities. In the face of such complexity, it seems necessary to abstract away some of the details and to investigate simplified models. In this thesis, such simplified models of neuronal networks are examined on varying levels of abstraction. Neurons are modeled as point neurons, both rate-based and spike-based, and networks are modeled as block-structured random networks. Crucially, on this level of abstraction, the models are still amenable to analytical treatment using the framework of dynamical mean-field theory. The main focus of this thesis is to leverage the analytical tractability of random networks of point neurons in order to relate the network structure, and the neuron parameters, to the dynamics of the neurons—in physics parlance, to bridge across the scales from neurons to networks. More concretely, four different models are investigated: 1) fully connected feedforward networks and vanilla recurrent networks of rate neurons; 2) block-structured networks of rate neurons in continuous time; 3) block-structured networks of spiking neurons; and 4) a multi-scale, data-based network of spiking neurons. We consider the first class of models in the light of Bayesian supervised learning and compute their kernel in the infinite-size limit. In the second class of models, we connect dynamical mean-field theory with large-deviation theory, calculate beyond mean-field fluctuations, and perform parameter inference. For the third class of models, we develop a theory for the autocorrelation time of the neurons. Lastly, we consolidate data across multiple modalities into a layer- and population-resolved model of human cortex and compare its activity with cortical recordings. In two detours from the investigation of these four network models, we examine the distribution of neuron densities in cerebral cortex and present a software toolbox for mean-field analyses of spiking networks

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)

Modélisation mathématique de la dépression synaptique et des périodes réfractaires pour le Quantron

RÉSUMÉ : La reconnaissance de formes est un mécanisme omniprésent dans le cerveau humain. Dans le cas des ordinateurs, ce mécanisme est plus complexe et plus lourd à effectuer. Des modèles de réseaux de neurones artificiels (RNA) ont été développés afin de pallier aux limites des machines. Le Quantron, dont le potentiel à générer des formes hautement non-linéaires a été démontré, est cependant incapable de produire des formes entièrement convexes. L’idée de raffiner le modèle du Quantron en y ajoutant des considérations biologiques est explorée. La dépression synaptique et les périodes réfractaires servent de tremplin pour ce raffinement, dans le but d’augmenter le potentiel de reconnaissance du Quantron. L’influence de la dépression synaptique est testée en développant trois modèles différents. Le premier modèle correspond à une dépression très brusque. Le deuxième modèle représente une dépression plus lisse. Le troisième modèle se rapproche encore plus de la réalité. Ces modèles ont amené une variabilité inhibitrice importante pour les frontières de séparation. Ils ont également permis d’obtenir des formes convexes presque circulaires (îlots). L’ajout de périodes réfractaires a également été étudié en développant trois modèles supplémentaires. Ceux-ci ont montré que la contribution aux frontières de séparation des périodes réfractaires, sous formes de processus stochastique, est significative, mais peu ciblée. En combinant ces deux notions biologiques on a pu montrer, notamment grâce aux propriétés excitatrices et inhibitrices des périodes réfractaires, ainsi qu’à travers la capacité de filtre fréquentiel de la dépression, que le nouveau Quantron ainsi créé peut générer, pour la première fois, des îlots convexes en utilisant très peu de paramètres.----------ABSTRACT : Pattern recognition is a ubiquitous mechanism of the human brain. For computers, this mechanism is more complex and computationally harder to perform. Artificial neural networks have been developed to overcome the limits of machines. The Quantron, whose potential to generate highly non-linear forms has been demonstrated, is however unable to produce forms entirely convex. The idea of creating a more sophisticated Quantron model by adding biological considerations is explored. Synaptic depression and refractory periods serve as a springboard to this sophistication, in order to enhance the recognition potential of the Quantron. Effects of synaptic depression are tested by developing three different models. The first model corresponds to an abrupt depression. The second model represents a smoother depression. The third model represents reality even more closely. The three models have provided major inhibitory variability to the decision boundaries. They were able to obtain convex forms nearly circular (“island-shaped”). The insertion of refractory period has also been studied by developing three additional models. They showed that contribution to decision boundaries with refractory periods, as stochastic process, is significant, but lacks focus. By joining these two biological notions, it has been shown, especially through excitatory and inhibitory properties of the refractory periods, as well as through the frequency filter capability of the depression, that the new created Quantron could generate, for the first time, convex islands using very few parameters

Exploring the potential of brain-inspired computing

The gap between brains and computers regarding both their cognitive capability and power efficiency is remarkably huge. Brains process information massively in parallel and its constituents are intrinsically self-organizing, while in digital computers the execution of instructions is deterministic and rather serial. The recent progress in the development of dedicated hardware systems implementing physical models of neurons and synapses enables to efficiently emulate spiking neural networks. In this work, we verify the design and explore the potential for brain-inspired computing of such an analog neuromorphic system, called Spikey. We demonstrate the versatility of this highly configurable substrate by the implementation of a rich repertoire of network models, including models for signal propagation and enhancement, general purpose classifiers, cortical models and decorrelating feedback systems. Network emulations on Spikey are highly accelerated and consume less than 1 nJ per synaptic transmission. The Spikey system, hence, outperforms modern desktop computers in terms of fast and efficient network simulations closing the gap to brains. During this thesis the stability, performance and user-friendliness of the Spikey system was improved integrating it into the neuroscientific tool chain and making it available for the community. The implementation of networks suitable to solve everyday tasks, like object or speech recognition, qualifies this technology to be an alternative to conventional computers. Considering the compactness, computational capability and power efficiency, neuromorphic systems may qualify as a valuable complement to classical computation

A stochastic model of malaria transmission

Malaria models have evolved since Ross and Macdonald. By using an agent-based stochastic model we have looked into di erent aspects of disease transmission: 1. Gametocytemia phase transition between epidemic stability and disease elimination, and the potential bene t of combining gametocidal agents and ivermectin. 2. Heterogeneity promotes disease spreading. 3. Disease supression from the combined use of ivermectin and primaquine. 4. Utility of Hurst exponent and Shannon entropy in malaria forecasting. Results and conclusion: Malaria transmission was simulated with a computational agent-based model assuming a small African village. We have con rmed gametocytemia as a critical factor in disease transmission, revealing an abrupt phase transition between epidemic stability and disease elimination [326]. We have also found that synergism between gametocidal agents (primaquine) and ivermectin (a selective Anophelocide drug a ecting parasite maturation after mosquito infection) could e ectively suppress human-to-mosquito disease transmission [326]. We have found that heterogeneity ampli es disease transmission (roughly three times in our model). Different aspects of heterogeneity were analyzed such as human migration, mosquito density, and rainfall [327]. We have con rmed the potential bene t of suppressing heterogeneity-induced disease transmission with the use of gametocidal agents and ivermectin. Hurst exponent has been used in hydrology and in the stock market. No previous evidence of its application to infectious theory has been found. Yet, our data suggests that Hurst exponent and information entropy could be useful in malaria forecasting [328]. Our results support the combined use of gametocidal agents (primaquine or methylene blue) and ivermectin as part of an integrated approach to malaria.Os modelos de malária são úteis desde Ross e Macdonald. Através de um modelo estocástico de agente, foram analisados vários aspectos da transmissão da malária: 1. A existência de uma transição de fase entre estabilidade e eliminação da doença em função da gametocitemia. 2. O uso combinado de fármacos gametocidas e ivermectina na redução da transmissão. 3. O papel da heterogeneidadena propagação da malária. 4. A utilidade do expoente de Hurst e da entropia de Shannon na previão da malária. Resultados e conclusões: Foi utilizado um modelo computacional de agente com simulação da transmissão de malária numa pequena aldeia africana. Confirmámos a gametocitemia como um factor crítico na propagação da malária demonstrando uma transição abrupta de fase entre estabilidade epidémica e eliminação da doença. No nosso modelo foi demonstrado que na presença de heterogeneidade a transmissão de malária pode sofrer uma amplificação significativa, de aproximadamente três vezes. Foram analisados diferentes aspectos da heterogeneidade tais como a migração humana, a densidade vectorial e a precipitação sazonal. Foi confirmado o potencial benefício de supressão da transmissão da malária na presença de heterogeneidade com a utilização de fármacos gametocidas (primaquina) e ivermectina. O expoente de Hurst tem sido aplicado com sucesso nas áreas da hidrologia e do mercado bolsista. Não houve até agora evidência da sua aplicação à área da infecciologia. No entanto, os dados apresentados sugerem a sua utilidade, a par da entropia de Shannon, na previsão da incidência da malária. Foi demonstrado que o uso combinado de agentes gametocidas (primaquina ou azul de metileno) e ivermectina pode constituir uma abordagem eficaz na prevenção da malári

Brain Computations and Connectivity [2nd edition]

This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations. Brain Computations and Connectivity is about how the brain works. In order to understand this, it is essential to know what is computed by different brain systems; and how the computations are performed. The aim of this book is to elucidate what is computed in different brain systems; and to describe current biologically plausible computational approaches and models of how each of these brain systems computes. Understanding the brain in this way has enormous potential for understanding ourselves better in health and in disease. Potential applications of this understanding are to the treatment of the brain in disease; and to artificial intelligence which will benefit from knowledge of how the brain performs many of its extraordinarily impressive functions. This book is pioneering in taking this approach to brain function: to consider what is computed by many of our brain systems; and how it is computed, and updates by much new evidence including the connectivity of the human brain the earlier book: Rolls (2021) Brain Computations: What and How, Oxford University Press. Brain Computations and Connectivity will be of interest to all scientists interested in brain function and how the brain works, whether they are from neuroscience, or from medical sciences including neurology and psychiatry, or from the area of computational science including machine learning and artificial intelligence, or from areas such as theoretical physics

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

Life Sciences Program Tasks and Bibliography for FY 1996

This document includes information on all peer reviewed projects funded by the Office of Life and Microgravity Sciences and Applications, Life Sciences Division during fiscal year 1996. This document will be published annually and made available to scientists in the space life sciences field both as a hard copy and as an interactive Internet web page