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We consider the problem of information compression from high dimensional data. Where many studies consider the problem of compression by non-invertible transformations, we emphasize the importance of invertible compression. We introduce new…
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general types of model, corresponding to whether the reference process…
Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as…
Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$…
Using the square-root map p-->\sqrt{p} a probability density function p can be represented as a point of the unit sphere S in the Hilbert space of square-integrable functions. If the density function depends smoothly on a set of parameters,…
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input…
Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the…
We consider a sequential decision making task where we are not allowed to evaluate parameters that violate an a priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown constraint and allow…
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique,…
The authors have recently defined the R\'enyi information dimension rate $d(\{X_t\})$ of a stationary stochastic process $\{X_t,\,t\in\mathbb{Z}\}$ as the entropy rate of the uniformly-quantized process divided by minus the logarithm of the…
The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on…
We have a lot of relation to the encoding and the Theory of Information, when considering thinking. This is a natural process and, at once, the complex thing we investigate. This always was a challenge - to understand how our mind works,…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
Pinning down a precise understanding of information flow within physical interactions remains a central concern to fields like stochastic thermodynamics and quantum information science. In both spheres a careful accounting of bits (or…
Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information…
Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Computing expected information gain (EIG) from prior to posterior (equivalently, mutual information between candidate observations and model parameters or other quantities of interest) is a fundamental challenge in Bayesian optimal…