Related papers: Jumping champions and prime gaps using information…

A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…

We examine how the prior probability distribution of a sensory variable in the environment influences the optimal allocation of neurons and spikes in a population that represents that variable. We start with a conventional response model,…

An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…

This study proposes a framework that extends existing time-coding time-to-first-spike spiking neural network (SNN) models to allow processing information changing over time. We explain spike propagation through a model with multiple input…

This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated…

We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…

Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…

Frontier reasoning models are produced by posttraining base language models with reinforcement learning. Recent work has challenged this by showing that sampling from a sharpened version of the base model's distribution, a so-called power…

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error…

Spiking neural networks (SNNs) are brain-inspired models that enable energy-efficient implementation on neuromorphic hardware. However, the supervised training of SNNs remains a hard problem due to the discontinuity of the spiking neuron…

We speculate on the distribution of primes in exponentially growing, linear recurrence sequences $(u_n)_{n\geq 0}$ in the integers. By tweaking a heuristic which is successfully used to predict the number of prime values of polynomials, we…

Building upon the work of Chebyshev, Shannon and Kontoyiannis, it may be demonstrated that Chebyshev's asymptotic result: \begin{equation} \ln N \sim \sum_{p \leq N} \frac{1}{p} \cdot \ln p \end{equation} has a natural information-theoretic…

The problem of infering the top component of a noisy sample covariance matrix with prior information about the distribution of its entries is considered, in the framework of the spiked covariance model. Using the replica method of…

Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…

We introduce \emph{Information Topology}: a framework that unifies information theory and algebraic topology by treating \emph{cycle closure} as the primitive operation of inference. The starting point is the \emph{dot-cycle dichotomy},…

In an incomplete market underpinned by the trinomial model, we consider two investors : an ordinary agent whose decisions are driven by public information and an insider who possesses from the beginning a surplus of information encoded…

This paper deals with the problem of extracting the activity of individual neurons from multi-electrode recordings. Important aspects of this work are: 1) the sorting is done in two stages - a statistical model of the spikes from different…

We first provide a formula to calculate the probability of occurrence of different configurations (formation probabilities) in a generic free fermion system. We then study the scaling of these probabilities with respect to the size in the…

This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger (2002) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy…

Information encoding in the nervous system is supported through the precise spike-timings of neurons; however, an understanding of the underlying processes by which such representations are formed in the first place remains unclear. Here we…