arXiv subjects

Kresimir Josic

Publications and source records attributed to Kresimir Josic.

16 recordsLinked to original sources

arXiv2026

Daring few, patient many: division of labor in decentralized foraging collectives

How do social animals make effective decisions in the absence of a leader? While coordination can improve accuracy, it also introduces delays as information propagates through the group. In changing environments, these delays can outweigh the benefits of globally coordinated decisions, even when local interactions remain tightly organized. This raises a key question: how can groups implement efficient collective decision-making without central coordination? We address this question using a collective foraging model in which individuals share information and rewards, but each must choose whether to bear the cost of exploring or to remain idle. We show that decentralized collectives can match the performance of centrally controlled groups through a division of labor: a small, heterogeneous subset explores even when expected rewards are negative, acquiring information to enable future foraging, while a coordinated majority forages only when expected rewards are positive. Information redundancy causes the optimal number of explorers to grow sublinearly with group size, so that larger groups need proportionally fewer explorers. The heterogeneity of the group is maximized at intermediate ecological pressures, but optimal groups are homogeneous when costs or fluctuations are extreme. Crucially, these group-level policies do not require central coordination, emerging instead from agents following simple threshold-based decision rules. We thus demonstrate a mechanism through which leaderless collectives can make effective decisions under uncertainty and show how ecological pressures can drive changes in the distribution of strategies employed by the group.

q-bio.PE↗

arXiv2020

Diversity Improves Speed and Accuracy in Social Networks

How does temporally structured private and social information shape collective decisions? To address this question we consider a network of rational agents who independently accumulate private evidence that triggers a decision upon reaching a threshold. When seen by the whole network, the first agent's choice initiates a wave of new decisions; later decisions have less impact. In heterogeneous networks, first decisions are made quickly by impulsive individuals who need little evidence to make a choice, but, even when wrong, can reveal the correct options to nearly everyone else. We conclude that groups comprised of diverse individuals can make more efficient decisions than homogenous ones.

physics.soc-ph↗

arXiv2018

Optimizing sequential decisions in the drift-diffusion model

To make decisions organisms often accumulate information across multiple timescales. However, most experimental and modeling studies of decision-making focus on sequences of independent trials. On the other hand, natural environments are characterized by long temporal correlations, and evidence used to make a present choice is often relevant to future decisions. To understand decision-making under these conditions we analyze how a model ideal observer accumulates evidence to freely make choices across a sequence of correlated trials. We use principles of probabilistic inference to show that an ideal observer incorporates information obtained on one trial as an initial bias on the next. This bias decreases the time, but not the accuracy of the next decision. Furthermore, in finite sequences of trials the rate of reward is maximized when the observer deliberates longer for early decisions, but responds more quickly towards the end of the sequence. Our model also explains experimentally observed patterns in decision times and choices, thus providing a mathematically principled foundation for evidence-accumulation models of sequential decisions.

q-bio.NC↗

arXiv2017

Evidence accumulation and change rate inference in dynamic environments

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an ideal observer model capable of inferring the present state of the environment along with its rate of change. Key to this computation is an update of the posterior probability of all possible changepoint counts. This computation can be challenging, as the number of possibilities grows rapidly with time. However, we show how the computations can be simplified in the continuum limit by a moment closure approximation. The resulting low-dimensional system can be used to infer the environmental state and change rate with accuracy comparable to the ideal observer. The approximate computations can be performed by a neural network model via a rate-correlation based plasticity rule. We thus show how optimal observers accumulate evidence in changing environments, and map this computation to reduced models which perform inference using plausible neural mechanisms.

q-bio.NC↗

arXiv2016

Loss of information in feedforward social networks

We consider model social networks in which information propagates directionally across layers of rational agents. Each agent makes a locally optimal estimate of the state of the world, and communicates this estimate to agents downstream. When agents receive information from the same source their estimates are correlated. We show that the resulting redundancy can lead to the loss of information about the state of the world across layers of the network, even when all agents have full knowledge of the network's structure. A simple algebraic condition identifies networks in which information loss occurs, and we show that all such networks must contain a particular network motif. We also study random networks asymptotically as the number of agents increases, and find a sharp transition in the probability of information loss at the point at which the number of agents in one layer exceeds the number in the previous layer.

stat.ME↗

arXiv2015

Stochastic models of evidence accumulation in changing environments

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information gained over an average environmental epoch. A plausible neural implementation of an optimal observer in a changing environment shows that, in contrast to previous models, neural populations representing alternate choices are coupled through excitation. Our work builds a bridge between statistical decision making in volatile environments and stochastic nonlinear dynamics.

q-bio.NC↗

arXiv2015

Networks that learn the precise timing of event sequences

Neuronal circuits can learn and replay firing patterns evoked by sequences of sensory stimuli. After training, a brief cue can trigger a spatiotemporal pattern of neural activity similar to that evoked by a learned stimulus sequence. Network models show that such sequence learning can occur through the shaping of feedforward excitatory connectivity via long term plasticity. Previous models describe how event order can be learned, but they typically do not explain how precise timing can be recalled. We propose a mechanism for learning both the order and precise timing of event sequences. In our recurrent network model, long term plasticity leads to the learning of the sequence, while short term facilitation enables temporally precise replay of events. Learned synaptic weights between populations determine the time necessary for one population to activate another. Long term plasticity adjusts these weights so that the trained event times are matched during playback. While we chose short term facilitation as a time-tracking process, we also demonstrate that other mechanisms, such as spike rate adaptation, can fulfill this role. We also analyze the impact of trial-to-trial variability, showing how observational errors as well as neuronal noise result in variability in learned event times. The dynamics of the playback process determine how stochasticity is inherited in learned sequence timings. Future experiments that characterize such variability can therefore shed light on the neural mechanisms of sequence learning.

q-bio.NC↗

arXiv2015

Visual Decisions in the Presence of Measurement and Stimulus Correlations

Humans and other animals base their decisions on noisy sensory input. Much work has therefore been devoted to understanding the computations that underly such decisions. The problem has been studied in a variety of tasks and with stimuli of differing complexity. However, the impact of correlations in sensory noise on perceptual judgments is not well understood. Here we examine how stimulus correlations together with correlations in sensory noise impact decision making. As an example, we consider the task of detecting the presence of a single or multiple targets amongst distractors. We assume that both the distractors and the observer's measurements of the stimuli are correlated. The computations of an optimal observer in this task are nontrivial, yet can be analyzed and understood intuitively. We find that when distractors are strongly correlated, measurement correlations can have a strong impact on performance. When distractor correlations are weak, measurement correlations have little impact, unless the number of stimuli is large. Correlations in neural responses to structured stimuli can therefore strongly impact perceptual judgments.

q-bio.NC↗

arXiv2013

Encoding certainty in bump attractors

Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit translational symmetry. Thus activity bumps are neutrally stable, and perturbations in position do not decay away. We extend previous work on bump attractors by constructing model networks capable of encoding the certainty or salience of a stimulus stored in memory. Such networks support bumps that are not only neutrally stable to perturbations in position, but also perturbations in amplitude. Possible bump solutions then lie on a two-dimensional attractor, determined by a continuum of positions and amplitudes. Such an attractor requires precisely balancing the strength of recurrent synaptic connections. The amplitude of activity bumps represents certainty, and is determined by the initial input to the system. Moreover, bumps with larger amplitudes are more robust to noise, and over time provide a more faithful representation of the stored stimulus. In networks with separate excitatory and inhibitory populations, generating bumps with a continuum of possible amplitudes, requires tuning the strength of inhibition to precisely cancel background excitation.

q-bio.NC↗

arXiv2013

Piecewise linear and Boolean models of chemical reaction networks

Models of biochemical networks are frequently high-dimensional and complex. Reduction methods that preserve important dynamical properties are therefore essential in their study. Interactions between the nodes in such networks are frequently modeled using a Hill function, $x^n/(J^n+x^n)$. Reduced ODEs and Boolean networks have been studied extensively when the exponent $n$ is large. However, the case of small constant $J$ appears in practice, but is not well understood. In this paper we provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. On the other hand, the simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in networks modeling a genetic switch and a genetic oscillator.

q-bio.MN↗

arXiv2012

Motif Statistics and Spike Correlations in Neuronal Networks

Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second-order motifs: diverging motifs, in which one cell provides input to two others, and chain motifs, in which two cells are connected via a third intermediary cell. Specifically, the prevalence of diverging and chain motifs tends to increase correlation. Our method is based on linear response theory, which enables us to express spiking statistics using linear algebra, and a resumming technique, which extrapolates from second order motifs to predict the overall effect of coupling on network correlation. Our motif-based results seek to isolate the effect of network architecture perturbatively from a known network state.

q-bio.NC↗

arXiv2010

Finite volume and asymptotic methods for stochastic neuron models with correlated inputs

We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein--Uhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation.

q-bio.NC↗

arXiv2009

Improved community structure detection using a modified fine tuning strategy

The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this unduely constrains their results, leading to a bias in the size of the communities they find and limiting their effectivness. To solve this problem, we propose adding a step to the existing algorithms that does not increase the order of their computational complexity. We show that, if this step is combined with a commonly used method, the identified constraint and resulting bias are removed, and its ability to find the optimal partitioning is improved. The effectiveness of this combined algorithm is also demonstrated by using it on real-world example networks. For a number of these examples, it achieves the best results of any known algorithm.

cs.CY↗

arXiv2008

Stimulus-dependent correlations and population codes

The magnitude of correlations between stimulus-driven responses of pairs of neurons can itself be stimulus-dependent. We examine how this dependence impacts the information carried by neural populations about the stimuli that drive them. Stimulus-dependent changes in correlations can both carry information directly and modulate the information separately carried by the firing rates and variances. We use Fisher information to quantify these effects and show that, although stimulus dependent correlations often carry little information directly, their modulatory effects on the overall information can be large. In particular, if the stimulus-dependence is such that correlations increase with stimulus-induced firing rates, this can significantly enhance the information of the population when the structure of correlations is determined solely by the stimulus. However, in the presence of additional strong spatial decay of correlations, such stimulus-dependence may have a negative impact. Opposite relationships hold when correlations decrease with firing rates.

q-bio.NC↗

arXiv2007

Universal properties of correlation transfer in integrate-and-fire neurons

One of the fundamental characteristics of a nonlinear system is how it transfers correlations in its inputs to correlations in its outputs. This is particularly important in the nervous system, where correlations between spiking neurons are prominent. Using linear response and asymptotic methods for pairs of unconnected integrate-and-fire (IF) neurons receiving white noise inputs, we show that this correlation transfer depends on the output spike firing rate in a strong, stereotyped manner, and is, surprisingly, almost independent of the interspike variance. For cells receiving heterogeneous inputs, we further show that correlation increases with the geometric mean spiking rate in the same stereotyped manner, greatly extending the generality of this relationship. We present an immediate consequence of this relationship for population coding via tuning curves.

q-bio.NC↗

arXiv1999

Dynamics of a Ring of Diffusively Coupled Lorenz Oscillators

We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a stable fixed state in arbitrarily large rings for a fixed coupling strength. This suggests that coherent behavior in networks of diffusively coupled systems may appear at a coupling strength that is independent of the size of the network.

cond-mat.stat-mech↗