arXiv subjects

Kevin K. Lin

Publications and source records attributed to Kevin K. Lin.

At least 19 recordsLinked to original sources

arXiv2026

Mostly-monocular responses and other visual functions in a multiscale network model of Macaque V1

Visual signals from the two eyes merge gradually as they pass through the primary visual cortex (V1). Here we use a computational model of Macaque V1 to study the first stage of this integration along the magnocellular pathway, in layer 4C$\alpha$, aiming to infer neuroanatomical origins of binocular response. It is known that neurons in layer 4C$\alpha$ are predominantly monocular, though some do exhibit varying degrees of binocularity. We find (1) the emergence of narrow binocular strips along borders of ocular dominance columns (ODC), a finding that aligns with experiments; (2) most consistent with data is when $10-30\%$ of interactions near ODC boundaries are cross-columnar; and (3) feedback from layer 6 is largely monocular. These results were obtained through systematic hypothesis testing using a multiscale model that is orders of magnitude faster than its biologically-detailed predecessors. We propose that multiscale modeling can be an effective tool for bridging anatomy and function.

q-bio.NC↗

arXiv2025

Numerical study of high-dimensional covariance estimation and localization for data assimilation

Covariance localization is a critical component of ensemble-based data assimilation (DA) and many current localization schemes simply dampen correlations as a function of distance. Increases in computational resources, broadening scope of application for DA, and advances in general statistical methodology raise the question as to whether alternative localization methods may improve ensemble DA relative to current schemes. We carefully explore this issue by comparing distance based localization with alternative covariance localization techniques, partially those taken from the statistical literature. The comparison is done on test problems that we designed to challenge distance-based localization, including joint state-parameter estimation in a modified Lorenz '96 model and state estimation in a two-layer quasi-geostrophic model. Across all sets of experiments, we find that while localization of any kind (with rare exceptions) can lead to significant reductions in error, traditional, distance-based localization generally leads to the largest error reduction. More general localization schemes can sometimes lead to greater error reduction, though the impacts may only be marginal and may require more tuning and/or prior information.

physics.data-an↗

arXiv2024

Examining the Link Between Peroxiredoxin Proteins and Mutually Exclusive Transcription Factor Activation With a Mathematical Model

Oxidative stress is a fundamental stimulus to which eukaryotic cells respond via many channels. Among these channels are both protein systems that process oxidative stress, such as the 2-Cys peroxiredoxin-thioredoxin system (PTRS), as well as changes in transcriptional activity that target outcomes such as growth, damage control and repair, or cell death. Recent work has revealed connections between the PTRS and temporal phases of transcriptional activity involving famous transcription factors like p53 and FOXO1. To examine potential mechanisms for these connections, we implement an existing dynamical systems mathematical model for the PTRS. We hypothesize that dose-dependent hyperoxidation events enact ultrasensitive switches by which the PTRS can categorize stress severity and activate appropriate transcriptional responses. Using numerical simulations of the PTRS in human cells, we provide a proof of principle for staggered, switchlike hyperoxidation of peroxiredoxins (Prx) as well as an underlying mechanism requiring simultaneous signaling by Prx I and II. Then, we use our model to make testable predictions about individual Prx knockouts as well as the affinity for hydrogen peroxide of Prx across oxidation states. This study provides direction for future experimental work and sheds light into the mechanisms underlying oxidative stress response in human cells.

q-bio.BM↗

arXiv2021

A data-informed mean-field approach to mapping of cortical parameter landscapes

Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a "biologically plausible" region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simple geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space.

q-bio.NC↗

arXiv2019

Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typically exhibits memory effects. Recent work has found a variety of data-driven model reduction methods to be effective for representing such non-Markovian dynamics, but their scope and dynamical underpinning remain incompletely understood. Here, we study data-driven model reduction from a dynamical systems perspective. For both chaotic and randomly-forced systems, we show the problem can be naturally formulated within the framework of Koopman operators and the Mori-Zwanzig projection operator formalism. We give a heuristic derivation of a NARMAX (Nonlinear Auto-Regressive Moving Average with eXogenous input) model from an underlying dynamical model. The derivation is based on a simple construction we call Wiener projection, which links Mori-Zwanzig theory to both NARMAX and to classical Wiener filtering. We apply these ideas to the Kuramoto-Sivashinsky model of spatiotemporal chaos and a viscous Burgers equation with stochastic forcing.

math.NA↗

arXiv2017

Symmetrized importance samplers for stochastic differential equations

We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of our importance sampling schemes when the noise is not too large. We demonstrate that this is indeed the case for a number of linear and nonlinear examples. Potential applications, e.g., data assimilation, are discussed.

math.NA↗

arXiv2016

Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems

We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations, which are then discretized for numerical solution. The second is discrete in time, where one directly infers a discrete-time model in the form of a nonlinear autoregression moving average model. The comparison is performed in a special case where the observations are known to have been obtained from a hypoelliptic stochastic differential equation. We show that the discrete-time approach has better predictive skills, especially when the data are relatively sparse in time. We discuss open questions as well as the broader significance of the results.

math.NA↗

arXiv2014

Small-noise analysis and symmetrization of implicit Monte Carlo samplers

Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algo- rithms that leads to improved (implicit) sampling schemes at a rel- atively small additional cost. Computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.

math.NA↗

arXiv2014

Control Theory and Experimental Design in Diffusion Processes

This paper considers the problem of designing time-dependent, real-time control policies for controllable nonlinear diffusion processes, with the goal of obtaining maximally-informative observations about parameters of interest. More precisely, we maximize the expected Fisher information for the parameter obtained over the duration of the experiment, conditional on observations made up to that time. We propose to accomplish this with a two-step strategy: when the full state vector of the diffusion process is observable continuously, we formulate this as an optimal control problem and apply numerical techniques from stochastic optimal control to solve it. When observations are incomplete, infrequent, or noisy, we propose using standard filtering techniques to first estimate the state of the system, then apply the optimal control policy using the posterior expectation of the state. We assess the effectiveness of these methods in 3 situations: a paradigmatic bistable model from statistical physics, a model of action potential generation in neurons, and a model of a simple ecological system.

stat.ME↗

arXiv2013

Chaos and reliability in balanced spiking networks with temporal drive

Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in different initial states, will the system entrain to the signal in a repeatable way? Reliability is of particular interest in neuroscience, where large, complex networks of excitatory and inhibitory cells are ubiquitous. These networks are known to autonomously produce strongly chaotic dynamics - an obvious threat to reliability. Here, we show that such chaos persists in the presence of weak and strong stimuli, but that even in the presence of chaos, intermittent periods of highly reliable spiking often coexist with unreliable activity. We elucidate the local dynamical mechanisms involved in this intermittent reliability, and investigate the relationship between this phenomenon and certain time-dependent attractors arising from the dynamics. A conclusion is that chaotic dynamics do not have to be an obstacle to precise spike responses, a fact with implications for signal coding in large networks.

nlin.CD↗

arXiv2012

Limitations of perturbative techniques in the analysis of rhythms and oscillations

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, based on the infinitesimal phase response curve (PRC), is shown to give different predictions than the full model. Shear-induced chaos, i.e., chaotic behavior that results from the amplification of small perturbations by underlying shear, is missed entirely by the PRC. We show also that the presence of "sticky" phase-space structures tend to cause perturbative techniques to overestimate the frequencies and regularity of the oscillations. The phenomena we describe can all be observed in a simple 2D neuron model, which we choose for illustration as the PRC is widely used in mathematical neuroscience.

q-bio.NC↗

arXiv2010

Dynamics of Periodically-kicked Oscillators

We review some recent results surrounding a general mechanism for producing chaotic behavior in periodically-kicked oscillators. The key geometric ideas are illustrated via a simple linear shear model.

math.DS↗

arXiv2010

Nonequilibrium Steady States for Certain Hamiltonian Models

We report the results of a numerical study of nonequilibrium steady states for a class of Hamiltonian models. In these models of coupled matter-energy transport, particles exchange energy through collisions with pinned-down rotating disks. In [Commun. Math. Phys. 262 (2006)], Eckmann and Young studied 1D chains and showed that certain simple formulas give excellent approximations of energy and particle density profiles. Keeping the basic mode of interaction in [Eckmann-Young], we extend their prediction scheme to a number of new settings: 2D systems on different lattices, driven by a variety of boundary (heat bath) conditions including the use of thermostats. Particle-conserving models of the same type are shown to behave similarly. The second half of this paper examines memory and finite-size effects, which appear to impact only minimally the profiles of the models tested in [Eckmann-Young]. We demonstrate that these effects can be significant or insignificant depending on the local geometry. Dynamical mechanisms are proposed, and in the case of directional bias in particle trajectories due to memory, correction schemes are derived and shown to give accurate predictions.

cond-mat.stat-mech↗

arXiv2008

Coupling Control Variates for Markov Chain Monte Carlo

We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.

math.NA↗

arXiv2008

Reliability of Layered Neural Oscillator Networks

We study the reliability of large networks of coupled neural oscillators in response to fluctuating stimuli. Reliability means that a stimulus elicits essentially identical responses upon repeated presentations. We view the problem on two scales: neuronal reliability, which concerns the repeatability of spike times of individual neurons embedded within a network, and pooled-response reliability, which addresses the repeatability of the total synaptic output from the network. We find that individual embedded neurons can be reliable or unreliable depending on network conditions, whereas pooled responses of sufficiently large networks are mostly reliable. We study also the effects of noise, and find that some types affect reliability more seriously than others.

q-bio.NC↗

arXiv2007

Reliability of Coupled Oscillators I: Two-Oscillator Systems

This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial condition. Our main result is that both reliable and unreliable behaviors occur in this network for broad ranges of coupling strengths, even though individual oscillators are always reliable when uncoupled. A new finding is that at low input amplitudes, the system is highly susceptible to unreliable responses when the feedforward and feedback couplings are roughly comparable. A geometric explanation based on shear-induced chaos at the onset of phase-locking is proposed.

nlin.CD↗

arXiv2007

Reliability of Coupled Oscillators II: Larger Networks

We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In this paper, we extend previous results on two-cell networks to larger systems. The first issue that arises is chaos in the absence of inputs, which we demonstrate and interpret in terms of reliability. We give a mathematical analysis of networks that can be decomposed into modules connected by an acyclic graph. For this class of networks, we show how to localize the source of unreliability, and address questions concerning downstream propagation of unreliability once it is produced.

nlin.CD↗

arXiv2007

Shear-Induced Chaos

Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out some numerical studies of shear-induced chaos. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times, and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed.

math.DS↗