arXiv subjects

Braden A. W. Brinkman

Publications and source records attributed to Braden A. W. Brinkman.

7 recordsLinked to original sources

arXiv2025

Responses to transient perturbation can distinguish intrinsic from latent criticality in spiking neural populations

The critical brain hypothesis posits that neural circuitry operates near criticality to reap the computational benefits of accessing a wide range of timescales. The theory of critical phenomena generally predicts heavy-tailed (power-law) correlations in space and time near criticality, but it has been argued that in the brain such correlations could be inherited from ``latent variables,'' such as external sensory signals that are not directly observed when recording from neural circuitry. Distinguishing whether heavy-tailed correlations in neural activity are intrinsically generated within a neural circuit or are driven by unobserved latent variables is crucial for properly interpreting circuit functions. We argue that measuring neural responses to sudden perturbative inputs, rather than correlations in ongoing activity, can disambiguate these cases. We demonstrate this approach in a model of stochastic spiking neuron populations receiving external latent input that can be tuned to a critical state. We propose a scaling theory for the covariance and response functions of the spiking network, which we validate with simulations. We end by discussing how our approach might generalize to models of neural populations with more realistic biophysical details.

q-bio.NC↗

arXiv2025

Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes

The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical phenomena explain how systems tuned to a critical point display scale invariance due to fluctuations in activity spanning a wide range of time or spatial scales. In the brain this scale invariance has been hypothesized to have several computational benefits, including increased collective sensitivity to changes in input and robust propagation of information across a circuit. However, our theoretical understanding of critical phenomena in neural circuitry is limited because standard renormalization group methods apply to systems with either highly organized or completely random connections. Connections between neurons lie between these extremes, and may be either excitatory (positive) or inhibitory (negative), but not both. In this work we develop a renormalization group method that applies to models of spiking neural populations with some realistic biological constraints on connectivity, and derive a scaling theory for the statistics of neural activity when the population is tuned to a critical point. We show that the scaling theories differ for models of in vitro versus in vivo circuits -- they belong to different "universality classes" -- and that both may exhibit "anomalous" scaling at a critical balance of inhibition and excitation. We verify our theoretical results on simulations of neural activity data, and discuss how our scaling theory can be further extended and applied to real neural data.

q-bio.NC↗

arXiv2024

Metastability in networks of nonlinear stochastic integrate-and-fire neurons

Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant bombardment of information. How these collective patterns of activity depend on single-neuron properties is often unclear. Single-neuron recordings have shown that individual neurons' responses to inputs are nonlinear, which prevents a straightforward extrapolation from single neuron features to emergent collective states. Here, we use a field-theoretic formulation of a stochastic leaky integrate-and-fire model to study the impact of single-neuron nonlinearities on macroscopic network activity. In this model, a neuron integrates spiking output from other neurons in its membrane voltage and emits spikes stochastically with an intensity depending on the membrane voltage, after which the voltage resets. We show that the interplay between nonlinear spike intensity functions and membrane potential resets can i) give rise to metastable active firing rate states in recurrent networks, and ii) can enhance or suppress mean firing rates and membrane potentials in the same or paradoxically opposite directions.

q-bio.NC↗

arXiv2023

Applications of information geometry to spiking neural network behavior

The space of possible behaviors complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is a prominent example of a biological system with complex behaviors. The number of possible patterns of spikes emitted by a local brain circuit is combinatorially large, though the brain may not make use of all of them. Understanding which of these possible patterns are actually used by the brain, and how those sets of patterns change as properties of neural circuitry change is a major goal in neuroscience. Recently, tools from information geometry have been used to study embeddings of probabilistic models onto a hierarchy of model manifolds that encode how model behaviors change as a function of their parameters, giving a quantitative notion of "distances" between model behaviors. We apply this method to a network model of excitatory and inhibitory neural populations to understand how the competition between membrane and synaptic response timescales shapes the network's information geometry. The hyperbolic embedding allows us to identify the statistical parameters to which the model behavior is most sensitive, and demonstrate how the ranking of these coordinates changes with the balance of excitation and inhibition in the network.

q-bio.NC↗

arXiv2022

Metastable dynamics of neural circuits and networks

Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of patterns, which emerge spontaneously or in response to incoming activity produced by sensory inputs. In this Review, we focus on neural dynamics that is best understood as a sequence of repeated activations of a number of discrete hidden states. These transiently occupied states are termed "metastable" and have been linked to important sensory and cognitive functions. In the rodent gustatory cortex, for instance, metastable dynamics have been associated with stimulus coding, with states of expectation, and with decision making. In frontal, parietal, and motor areas of macaques, metastable activity has been related to behavioral performance, choice behavior, task difficulty, and attention. In this article, we review the experimental evidence for neural metastable dynamics together with theoretical approaches to the study of metastable activity in neural circuits. These approaches include (i) a theoretical framework based on non-equilibrium statistical physics for network dynamics; (ii) statistical approaches to extract information about metastable states from a variety of neural signals; and (iii) recent neural network approaches, informed by experimental results, to model the emergence of metastable dynamics. By discussing these topics, we aim to provide a cohesive view of how transitions between different states of activity may provide the neural underpinnings for essential functions such as perception, memory, expectation, or decision making, and more generally, how the study of metastable neural activity may advance our understanding of neural circuit function in health and disease.

q-bio.NC↗

arXiv2017

Predicting how and when hidden neurons skew measured synaptic interactions

A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the "hidden" portion of the network. To properly interpret neural data and determine how biological structure gives rise to neural circuit function, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron $r'$ to a post-synaptic neuron $r$ can be decomposed into a sum of the true interaction from $r'$ to $r$ plus corrections from every directed path from $r'$ to $r$ through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have---or do not have---major effects on reshaping the interactions among observed neurons. As a particular example of interest, we derive a formula for the impact of hidden units in random networks with "strong" coupling---connection weights that scale with $1/\sqrt{N}$, where $N$ is the network size, precisely the scaling observed in recent experiments. With this quantitative relationship between measured and true interactions, we can study how network properties shape effective interactions, which properties are relevant for neural computations, and how to manipulate effective interactions.

q-bio.NC↗

arXiv2008

Temperature Dependence of Interlayer Magnetoresistance in Anisotropic Layered Metals

Studies of interlayer transport in layered metals have generally made use of zero temperature conductivity expressions to analyze angle-dependent magnetoresistance oscillations (AMRO). However, recent high temperature AMRO experiments have been performed in a regime where the inclusion of finite temperature effects may be required for a quantitative description of the resistivity. We calculate the interlayer conductivity in a layered metal with anisotropic Fermi surface properties allowing for finite temperature effects. We find that resistance maxima are modified by thermal effects much more strongly than resistance minima. We also use our expressions to calculate the interlayer resistivity appropriate to recent AMRO experiments in an overdoped cuprate which led to the conclusion that there is an anisotropic, linear in temperature contribution to the scattering rate and find that this conclusion is robust.

cond-mat.str-el↗