Neural field models with threshold noise

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches

The State of Research on Racial and Ethnic Discrimination in the Receipt of Health Care

https://ajph.aphapublications.org/doi/pdf/10.2105/AJPH.2012.30077

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times

The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions

Continuum neural field equations model the large scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounded domains. Neural field models do not require the specification of boundary conditions. Relatively little attention has been paid to the imposition of neural activity on the boundary, or to its role in inducing patterned states. Here we redress this imbalance by studying neural field models of Amari type (posed on one- and two-dimensional bounded domains) with Dirichlet boundary conditions. The Amari model has a Heaviside nonlinearity that allows for a description of localised solutions of the neural field with an interface dynamics. We show how to generalise this reduced but exact description by deriving a normal velocity rule for an interface that encapsulates boundary effects. The linear stability analysis of localised states in the interface dynamics is used to understand how spatially extended patterns may develop in the absence and presence of boundary conditions. Theoretical results for pattern formation are shown to be in excellent agreement with simulations of the full neural field model. Furthermore, a numerical scheme for the interface dynamics is introduced and used to probe the way in which a Dirichlet boundary condition can limit the growth of labyrinthine structures

NIA-AA Research Framework: Toward a Biological Definition of Alzheimer\u27s Disease

In 2011, the National Institute on Aging and Alzheimer\u27s Association created separate diagnostic recommendations for the preclinical, mild cognitive impairment, and dementia stages of Alzheimer\u27s disease. Scientific progress in the interim led to an initiative by the National Institute on Aging and Alzheimer\u27s Association to update and unify the 2011 guidelines. This unifying update is labeled a “research framework” because its intended use is for observational and interventional research, not routine clinical care. In the National Institute on Aging and Alzheimer\u27s Association Research Framework, Alzheimer\u27s disease (AD) is defined by its underlying pathologic processes that can be documented by postmortem examination or in vivo by biomarkers. The diagnosis is not based on the clinical consequences of the disease (i.e., symptoms/signs) in this research framework, which shifts the definition of AD in living people from a syndromal to a biological construct. The research framework focuses on the diagnosis of AD with biomarkers in living persons. Biomarkers are grouped into those of β amyloid deposition, pathologic tau, and neurodegeneration [AT(N)]. This ATN classification system groups different biomarkers (imaging and biofluids) by the pathologic process each measures. The AT(N) system is flexible in that new biomarkers can be added to the three existing AT(N) groups, and new biomarker groups beyond AT(N) can be added when they become available. We focus on AD as a continuum, and cognitive staging may be accomplished using continuous measures. However, we also outline two different categorical cognitive schemes for staging the severity of cognitive impairment: a scheme using three traditional syndromal categories and a six-stage numeric scheme. It is important to stress that this framework seeks to create a common language with which investigators can generate and test hypotheses about the interactions among different pathologic processes (denoted by biomarkers) and cognitive symptoms. We appreciate the concern that this biomarker-based research framework has the potential to be misused. Therefore, we emphasize, first, it is premature and inappropriate to use this research framework in general medical practice. Second, this research framework should not be used to restrict alternative approaches to hypothesis testing that do not use biomarkers. There will be situations where biomarkers are not available or requiring them would be counterproductive to the specific research goals (discussed in more detail later in the document). Thus, biomarker-based research should not be considered a template for all research into age-related cognitive impairment and dementia; rather, it should be applied when it is fit for the purpose of the specific research goals of a study. Importantly, this framework should be examined in diverse populations. Although it is possible that β-amyloid plaques and neurofibrillary tau deposits are not causal in AD pathogenesis, it is these abnormal protein deposits that define AD as a unique neurodegenerative diseaseamong different disorders that can lead to dementia. We envision that defining AD as a biological construct will enable a more accurate characterization and understanding of the sequence of events that lead to cognitive impairment that is associated with AD, as well as the multifactorial etiology of dementia. This approach also will enable a more precise approach to interventional trials where specific pathways can be targeted in the disease process and in the appropriate people

The limit to behavioral inertia and the power of default in voluntary contribution games

It is well documented that people are reluctant to switch from a default option. We experimentally test the robustness of this behavioral inertia in a collective decision-making setting by varying the default option type and the decision-making environment. We examine the impacts of automatic-participation and no-participation default options on subjects’ participation in a public goods provision and their contributions. Two variants of public goods game are employed: the linear and the threshold public goods games. The study shows the evidence of partial stickiness rather than complete stickiness of default options as indicated in empirical studies. Our experimental results square with the evidence of behavioral inertia only when the automatic-participation default is used. This default boosts contributions in the linear public goods game but not in the threshold public goods game. The evidence of partial stickiness is robust to the variation of the game employed, but the effect on contribution is sensitive to it

Search for the Decays B^0 -> D^{(*)+} D^{(*)-}

Using the CLEO-II data set we have searched for the Cabibbo-suppressed decays B^0 -> D^{(*)+} D^{(*)-}. For the decay B^0 -> D^{*+} D^{*-}, we observe one candidate signal event, with an expected background of 0.022 +/- 0.011 events. This yield corresponds to a branching fraction of Br(B^0 -> D^{*+} D^{*-}) = (5.3^{+7.1}_{-3.7}(stat) +/- 1.0(syst)) x 10^{-4} and an upper limit of Br(B^0 -> D^{*+} D^{*-}) D^{*\pm} D^\mp and B^0 -> D^+ D^-, no significant excess of signal above the expected background level is seen, and we calculate the 90% CL upper limits on the branching fractions to be Br(B^0 -> D^{*\pm} D^\mp) D^+ D^-) < 1.2 x 10^{-3}.Comment: 12 page postscript file also available through http://w4.lns.cornell.edu/public/CLNS, submitted to Physical Review Letter

ΛΛˉ\Lambda\bar{\Lambda} Production in Two-Photon Interactions at CLEO

Using the CLEO detector at the Cornell $e^+e^-$ storage ring, CESR, we study the two-photon production of $\Lambda \bar{\Lambda}$, making the first observation of $\gamma \gamma \to \Lambda \bar{\Lambda}$. We present the cross-section for $\gamma \gamma \to \Lambda \bar{\Lambda}$ as a function of the $\gamma \gamma$ center of mass energy and compare it to that predicted by the quark-diquark model.Comment: 10 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN