Journal of Mathematical Neuroscience最新文献_第6页

The Dynamics of Networks of Identical Theta Neurons. 相同θ神经元网络的动力学。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2018-02-05 DOI: 10.1186/s13408-018-0059-7

Carlo R Laing

引用次数: 32

Kernel Reconstruction for Delayed Neural Field Equations. 延迟神经场方程的核重构。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2018-02-05 DOI: 10.1186/s13408-018-0058-8

Jehan Alswaihli, Roland Potthast, Ingo Bojak, Douglas Saddy, Axel Hutt

{"title":"Kernel Reconstruction for Delayed Neural Field Equations.","authors":"Jehan Alswaihli, Roland Potthast, Ingo Bojak, Douglas Saddy, Axel Hutt","doi":"10.1186/s13408-018-0058-8","DOIUrl":"https://doi.org/10.1186/s13408-018-0058-8","url":null,"abstract":"Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues.In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Fréchet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":"8 1","pages":"3"},"PeriodicalIF":2.3,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-018-0058-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35794081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli. 基于脉冲时间的复杂细胞稀疏功能识别与视觉刺激解码。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2018-01-18 DOI: 10.1186/s13408-017-0057-1

Aurel A Lazar, Nikul H Ukani, Yiyin Zhou

引用次数: 2

Robust Exponential Memory in Hopfield Networks. Hopfield网络中的鲁棒指数记忆。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2018-01-16 DOI: 10.1186/s13408-017-0056-2

Christopher J Hillar, Ngoc M Tran

{"title":"Robust Exponential Memory in Hopfield Networks.","authors":"Christopher J Hillar, Ngoc M Tran","doi":"10.1186/s13408-017-0056-2","DOIUrl":"https://doi.org/10.1186/s13408-017-0056-2","url":null,"abstract":"The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically coupled McCulloch-Pitts binary neurons interact to perform emergent computation. Although previous researchers have explored the potential of this network to solve combinatorial optimization problems or store reoccurring activity patterns as attractors of its deterministic dynamics, a basic open problem is to design a family of Hopfield networks with a number of noise-tolerant memories that grows exponentially with neural population size. Here, we discover such networks by minimizing probability flow, a recently proposed objective for estimating parameters in discrete maximum entropy models. By descending the gradient of the convex probability flow, our networks adapt synaptic weights to achieve robust exponential storage, even when presented with vanishingly small numbers of training patterns. In addition to providing a new set of low-density error-correcting codes that achieve Shannon's noisy channel bound, these networks also efficiently solve a variant of the hidden clique problem in computer science, opening new avenues for real-world applications of computational models originating from biology.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":"8 1","pages":"1"},"PeriodicalIF":2.3,"publicationDate":"2018-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-017-0056-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35743400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 20

A Rate-Reduced Neuron Model for Complex Spiking Behavior. 复杂尖峰行为的速率降低神经元模型。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-12-11 DOI: 10.1186/s13408-017-0055-3

Koen Dijkstra, Yuri A Kuznetsov, Michel J A M van Putten, Stephan A van Gils

引用次数: 1

Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations. 神经场方程行波解的有限尺寸效应。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-12-01 Epub Date: 2017-07-06 DOI: 10.1186/s13408-017-0048-2

Eva Lang, Wilhelm Stannat

引用次数: 6

Fast-Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes. 高协维奇点展开中的快慢爆发子和类的超慢跃迁。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-12-01 Epub Date: 2017-07-25 DOI: 10.1186/s13408-017-0050-8

Maria Luisa Saggio, Andreas Spiegler, Christophe Bernard, Viktor K Jirsa

{"title":"Fast-Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes.","authors":"Maria Luisa Saggio, Andreas Spiegler, Christophe Bernard, Viktor K Jirsa","doi":"10.1186/s13408-017-0050-8","DOIUrl":"https://doi.org/10.1186/s13408-017-0050-8","url":null,"abstract":"Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system. In this work, we propose a model that, appropriately tuned, can display several types of bursting behaviors. The model contains two subsystems acting at different time scales. For the fast subsystem we use the planar unfolding of a high codimension singularity. In its bifurcation diagram, we locate paths that underlie the right sequence of bifurcations necessary for bursting. The slow subsystem steers the fast one back and forth along these paths leading to bursting behavior. The model is able to produce almost all the classes of bursting predicted for systems with a planar fast subsystem. Transitions between classes can be obtained through an ultra-slow modulation of the model's parameters. A detailed exploration of the parameter space allows predicting possible transitions. This provides a single framework to understand the coexistence of diverse bursting patterns in physical and biological systems or in models.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":"7 1","pages":"7"},"PeriodicalIF":2.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-017-0050-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35200488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 60

Timescales and Mechanisms of Sigh-Like Bursting and Spiking in Models of Rhythmic Respiratory Neurons. 节律性呼吸神经元模型中叹息样爆发和尖峰的时间尺度和机制。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-12-01 Epub Date: 2017-06-06 DOI: 10.1186/s13408-017-0045-5

Yangyang Wang, Jonathan E Rubin

{"title":"Timescales and Mechanisms of Sigh-Like Bursting and Spiking in Models of Rhythmic Respiratory Neurons.","authors":"Yangyang Wang, Jonathan E Rubin","doi":"10.1186/s13408-017-0045-5","DOIUrl":"https://doi.org/10.1186/s13408-017-0045-5","url":null,"abstract":"Neural networks generate a variety of rhythmic activity patterns, often involving different timescales. One example arises in the respiratory network in the pre-Bötzinger complex of the mammalian brainstem, which can generate the eupneic rhythm associated with normal respiration as well as recurrent low-frequency, large-amplitude bursts associated with sighing. Two competing hypotheses have been proposed to explain sigh generation: the recruitment of a neuronal population distinct from the eupneic rhythm-generating subpopulation or the reconfiguration of activity within a single population. Here, we consider two recent computational models, one of which represents each of the hypotheses. We use methods of dynamical systems theory, such as fast-slow decomposition, averaging, and bifurcation analysis, to understand the multiple-timescale mechanisms underlying sigh generation in each model. In the course of our analysis, we discover that a third timescale is required to generate sighs in both models. Furthermore, we identify the similarities of the underlying mechanisms in the two models and the aspects in which they differ.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":"7 1","pages":"3"},"PeriodicalIF":2.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-017-0045-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35068732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

How Adaptation Makes Low Firing Rates Robust. 适应性如何使低射击率变得稳健。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-12-01 Epub Date: 2017-06-24 DOI: 10.1186/s13408-017-0047-3

Arthur S Sherman, Joon Ha

{"title":"How Adaptation Makes Low Firing Rates Robust.","authors":"Arthur S Sherman, Joon Ha","doi":"10.1186/s13408-017-0047-3","DOIUrl":"https://doi.org/10.1186/s13408-017-0047-3","url":null,"abstract":"Low frequency firing is modeled by Type 1 neurons with a SNIC, but, because of the vertical slope of the square-root-like f-I curve, low f only occurs over a narrow range of I. When an adaptive current is added, however, the f-I curve is linearized, and low f occurs robustly over a large I range. Ermentrout (Neural Comput. 10(7):1721-1729, 1998) showed that this feature of adaptation paradoxically arises from the SNIC that is responsible for the vertical slope. We show, using a simplified Hindmarsh-Rose neuron with negative feedback acting directly on the adaptation current, that whereas a SNIC contributes to linearization, in practice linearization over a large interval may require strong adaptation strength. We also find that a type 2 neuron with threshold generated by a Hopf bifurcation can also show linearization if adaptation strength is strong. Thus, a SNIC is not necessary. More fundamental than a SNIC is stretching the steep region near threshold, which stems from sufficiently strong adaptation, though a SNIC contributes if present. In a more realistic conductance-based model, Morris-Lecar, with negative feedback acting on the adaptation conductance, an additional assumption that the driving force of the adaptation current is independent of I is needed. If this holds, strong adaptive conductance is both necessary and sufficient for linearization of f-I curves of type 2 f-I curves.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":"7 1","pages":"4"},"PeriodicalIF":2.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-017-0047-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35118764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Regularization of Ill-Posed Point Neuron Models. 病态点神经元模型的正则化。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-12-01 Epub Date: 2017-07-14 DOI: 10.1186/s13408-017-0049-1

Bjørn Fredrik Nielsen

{"title":"Regularization of Ill-Posed Point Neuron Models.","authors":"Bjørn Fredrik Nielsen","doi":"10.1186/s13408-017-0049-1","DOIUrl":"https://doi.org/10.1186/s13408-017-0049-1","url":null,"abstract":"Point neuron models with a Heaviside firing rate function can be ill-posed. That is, the initial-condition-to-solution map might become discontinuous in finite time. If a Lipschitz continuous but steep firing rate function is employed, then standard ODE theory implies that such models are well-posed and can thus, approximately, be solved with finite precision arithmetic. We investigate whether the solution of this well-posed model converges to a solution of the ill-posed limit problem as the steepness parameter of the firing rate function tends to infinity. Our argument employs the Arzelà-Ascoli theorem and also yields the existence of a solution of the limit problem. However, we only obtain convergence of a subsequence of the regularized solutions. This is consistent with the fact that models with a Heaviside firing rate function can have several solutions, as we show. Our analysis assumes that the vector-valued limit function v, provided by the Arzelà-Ascoli theorem, is threshold simple: That is, the set containing the times when one or more of the component functions of v equal the threshold value for firing, has zero Lebesgue measure. If this assumption does not hold, we argue that the regularized solutions may not converge to a solution of the limit problem with a Heaviside firing function.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":"7 1","pages":"6"},"PeriodicalIF":2.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-017-0049-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35168391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3