Related papers: The Category-Theoretic Arithmetic of Information
We propose an information-theoretic framework to measure narratives, providing a formalism to understand pivotal moments, cliffhangers, and plot twists. This approach offers creatives and AI researchers tools to analyse and benchmark human-…
Several mathematical ideas have been investigated for Quantitative Information Flow. Information theory, probability, guessability are the main ideas in most proposals. They aim to quantify how much information is leaked, how likely is to…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
Category theory has been recently used as a tool for constructing and modeling an information flow framework. Here, we show that the flow of information can be described using preradicals. We prove that preradicals generalize the notion of…
We propose categories of $1$-dimensional and multi-dimensional quantum walks. In the categories, an object is a quantum walk, and a morphism is an intertwining operator between two quantum walks. The new framework enables us to discuss…
We characterize the statistical bootstrap for the estimation of information-theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately,…
Identifying the origin of nonequilibrium characteristics in a generic interacting system having multiple degrees of freedom is a challenging task. In this context, information theoretic measures such as mutual information and related…
In this paper we consider an information theoretic approach for the accounting classification process. We propose a matrix formalism and an algorithm for calculations of information theoretic measures associated to accounting…
We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the statistics are information statistics…
We give a non-technical introduction of the basic concepts of Quantum Information Theory along the distinction between possible and impossible machines. We then proceed to describe the mathematical framework of Quantum Information Theory.…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
A variety of idealized models of communication systems exist, and all may have something in common. Starting with Shannons communication model and ending with the OSI model, this paper presents progressively more advanced forms of modeling…
We expose the information flow capabilities of pure bipartite entanglement as a theorem -- which embodies the exact statement on the `seemingly acausal flow of information' in protocols such as teleportation. We use this theorem to…
The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…
This thesis (defended 10/07/2019) develops a theory of networks of hybrid open systems and morphisms. It builds upon a framework of networks of continuous-time open systems as product and interconnection. We work out categorical notions for…
We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…