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In specific motifs of three recurrently connected neurons with probabilistic response, the spontaneous information flux, defined as the mutual information between subsequent states, has been shown to increase by adding ongoing white noise…

Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…

Many quantum information tasks rely on entanglement, which is used as a resource, for example, to enable efficient and secure communication. Typically, noise, accompanied by loss of entanglement, reduces the efficiency of quantum protocols.…

This paper focuses on the maximal distribution on sublinear expectation space and introduces a new type of random fields with the maximally distributed finite-dimensional distribution. The corresponding spatial maximally distributed white…

This paper considers a sequential estimation and sensor scheduling problem in the presence of multiple communication channels. As opposed to the classical remote estimation problem that involves one perfect (noiseless) channel and one…

It often is emphasized that gene expression is noisy. A seemingly contradictory view is that control mechanisms have been optimized to squeeze as much information as possible out of a limited number of molecules. Here we revisit these…

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting.…

Life relies on the efficient performance of molecular codes, which relate symbols and meanings via error-prone molecular recognition. We describe how optimizing a code to withstand the impact of molecular recognition noise may be…

We study the stochastic resonance (SR) of a flexible polymer surmounting a bistable-potential barrier. Due to the flexibility that can enhance crossing rate and change chain conformations at the barrier, the SR behaviors manifest many…

We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition…

It is known that under fixed-rate information constraints, adaptive quantizers can be used to stabilize an open-loop-unstable linear system on $\mathbb{R}^n$ driven by unbounded noise. These adaptive schemes can be designed so that they…

Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features in the presence of noise are lacking. Here, we provide very…

We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…

Tight lower and upper bounds on the ratio of relative entropies of two probability distributions with respect to a common third one are established, where the three distributions are collinear in the standard $(n-1)$-simplex. These bounds…

In this article, we investigate the stochastic resonance (SR) effect in a finite array of noisy bistable systems with nearest-neighbor coupling driven by a weak time-periodic driving force. The array is characterized by a collective…

We revisit the problem of searching for gravitational waves from inspiralling compact binaries in Gaussian coloured noise. For binaries with quasicircular orbits and non-precessing component spins, considering dominant mode emission only,…

An appealing new principle for neural population codes is that correlations among neurons organize neural activity patterns into a discrete set of clusters, which can each be viewed as a noise-robust population "codeword". Previous studies…

One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…

Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such…