Related papers: Theory of processes
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian data analysis, like all data analysis, is an iterative process…
Building on the fundamental equation, this study revisits key thermodynamic concepts in a cohesive and innovative manner. It demonstrates the consistency of thermodynamic theory while addressing and clarifying common misconceptions and…
This paper presents an analytical taxonomy that can suitably describe, rather than simply classify, techniques for data presentation. Unlike previous works, we do not consider particular aspects of visualization techniques, but their…
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify…
The theory of actual causality, defined by Halpern and Pearl, and its quantitative measure - the degree of responsibility - was shown to be extremely useful in various areas of computer science due to a good match between the results it…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
In many different fields of science, it is useful to characterize physical states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
Context: The complexity of modern safety-critical systems in industries keep on increasing due to the rising number of features and functionalities. This calls for formal methods in order to entrust confidence in such systems. Nevertheless,…
The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory,…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…