Related papers: Stochastic time-evolution, information geometry an…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
We reformulate models in epidemiology and population dynamics in terms of probability distributions. This allows us to construct the Fisher information, which we interpret as the metric of a one-dimensional differentiable manifold. For…
Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
Understanding the temporal dependence of precipitation is key to improving weather predictability and developing efficient stochastic rainfall models. We introduce an information-theoretic approach to quantify memory effects in discrete…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
Stochastic time-varying optimization is an integral part of learning in which the shape of the function changes over time in a non-deterministic manner. This paper considers multiple models of stochastic time variation and analyzes the…
Quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information will flow from the environments to…
We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale. Compared to the deterministic case and as far as we work in $L^2$, the…
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age"…
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…
The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we…
Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution…
The efficient sensing of weak environmental perturbations via special degeneracies called exceptional points in non-Hermitian systems has gained enormous traction in the last few decades. However, in contrast to the extensive literature on…
The electronic local density of states of solids, if normalized correctly, represents the probability density that the electron at a specific position has a particular energy. Because this probability density can vary in space in disordered…