arXiv subjects

Jose M. Betancourt

Publications and source records attributed to Jose M. Betancourt.

5 recordsLinked to original sources

arXiv2026

On the Information Required for Feedback Control

Biological systems across scales, along with many engineering problems, must control noisy systems with limited information. Here we study information-limited feedback control of stochastic systems to achieve target steady states, and derive a lower bound on the information rate from controlled system to controller. This framework allows us to obtain performance-information Pareto frontiers for wide-ranging control problems with limited information. For systems with state-independent passive dynamics, the bound is saturated by an explicit optimal control protocol which probabilistically time-reverses the passive dynamics. We showcase these results through applications to nonlinear particle localization, microbial navigation, and experimentally realized information engines.

cond-mat.stat-mech↗

arXiv2026

Discrete turn strategies emerge in information-limited navigation

Navigation up a smooth sensory gradient is one of the simplest behavioural tasks, and some organisms solve it by making continuous adjustments to their course. Bacteria instead employ a variety of discrete strategies, including run and tumble motion, direction reversals, and turns by specific angles. Here we ask what drives the choice of these strategies, framing the problem as maximising up-gradient speed with a given amount of sensory information per unit time. We find that, without directional information on which way to turn, behavioural strategies that take discrete actions perform better than gradual steering. As the amount of information is increased, we see a series of transitions between optimal strategies, including a shift from direction reversals to fully re-orienting tumbles. Among more complex re-orientation strategies, we show that discrete turn angles are best, and observe transitions in the number of angles employed by the optimal strategy. More broadly, such emergent simplicity in behaviour is a tractable example of a widespread phenomenon in which biology chooses a discrete solution, despite the underlying physics being continuous.

physics.bio-ph↗

arXiv2026

Thermal fluctuations set fundamental limits on ion channel function

Voltage-gated ion channels are essential for propagating signals in neurons. Each channel senses the local membrane potential created by nearby ions. Fluctuations in these ions introduce two fundamental noise sources: (i) shot noise, from the discreteness of ionic charge, and (ii) Johnson-Nyquist noise, from long-wavelength thermal fluctuations of the electric field. We show that, for an individual channel, shot noise dominates and sets an intrinsic limit to voltage sensing. On the $10$ $μ$s timescales relevant to channel gating, this limit corresponds to an accuracy of about $10$ mV -- close to measured channel sensitivities. When signals from many channels are aggregated, Johnson-Nyquist noise eventually overtakes shot noise and bounds the total information that can be sensed from the environment. This transition occurs at an ion channel density of $< 1$ channel/$μ$m$^2$ for slow signals and around $10^2-10^4$ channels/$μ$m$^2$ for signals with $10$ $μ$s timescales, both of which are within the range of experimentally-measured densities for somas and axon initial segments, respectively. These results provide design principles for single-channel architecture and collective sensing and suggest that neuronal computation is ultimately constrained by thermal fluctuations.

physics.bio-ph↗

arXiv2025

The Strength of Local Structures in Decentralized Network Formation

I study dynamic network formation games in which agents meet stochastically and form links based on their valuation of the network. I show that these games can be represented in terms of the values agents assign to network sub-structures. Particularly, this characterizes potential games as those where all participants in a structure value it equally. When valuations are restricted to a finite set of repeated sub-structures, or motifs, the model exhibits phase transitions: small changes in motif values cause discontinuous shifts in network density.

econ.TH↗

arXiv2025

Tractability and Phase Transitions in Endogenous Network Formation

The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network formation process can be found in closed form, and is given by a Gibbs measure. For conservative processes, the stationary distribution of a certain class of models can be characterized for an arbitrarily large number of players. In this limit, the statistical properties of the model can exhibit phase transitions: discontinuous changes as a response to continuous changes in model parameters.

econ.TH↗