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Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…

We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we…

Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…

In this paper we focus on the study of the monotonicity properties of the residual and the past extropy as well as on some characterization problems. We then apply the derived results to analyze further stochastic aspects of order…

We introduce unbiased estimators for the Shannon entropy and the class number, in the situation that we are able to take sequences of independent samples of arbitrary length.

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…

This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become…

In this talk we discuss the possibility of constructing a fluctuation theory for structural glasses in the non-equilibrium aging state. After reviewing well known results in a toy model we discuss some of the key assumptions which support…

Using results from neurobiology on perceptual decision making and value-based decision making, the problem of decision making between lotteries is reformulated in an abstract space where uncertain prospects are mapped to corresponding…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

In this talk I will review some of the recent applications of the replica theory to glasses. I will firstly describe the basic assumptions and I will show that they can be considered as a precise reformulations of old ideas. The relation of…

The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…

Maximum entropy models are considered by many to be one of the most promising avenues of language modeling research. Unfortunately, long training times make maximum entropy research difficult. We present a novel speedup technique: we change…

In this paper, the variable wind power is incorporated into the dynamic model for long-term stability analysis. A theory-based method is proposed for power systems with wind power to conduct long-term stability analysis, which is able to…

A non-vanishing entropy production rate is one of the defining characteristics of any non-equilibrium system, and several techniques exist to determine this quantity directly from experimental data. The short-time inference scheme, derived…

It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…

We discuss a theoretical approach to structural glasses as they happen in real situations. Older ideas based on `configurational entropy', on `fictive temperatures' and on Edwards' `compactivity' are sharpened and unified in an out of…

Information theoretic quantities are extremely useful in discovering relationships between two or more data sets. One popular method---particularly for continuous systems---for estimating these quantities is the nearest neighbour…

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters…