Related papers: On the information-theoretic structure of distribu…
Scientific datasets often arise from multiple independent mechanisms such as spatial, categorical or structural effects, whose combined influence obscures their individual contributions. We introduce DIVIDE, a framework that disentangles…
Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the…
What is the role of coherence in determining the distribution of work done on a quantum system? We approach this question from an operational perspective and consider a setup in which the internal energy of a closed system is recorded by a…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…
We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…
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…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
Understanding the applicability and limitations of electronic-structure methods needs careful and efficient comparison with accurate reference data. Knowledge of the quality and errors of electronic-structure calculations is crucial to…
In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…
We consider three types of entities for quantum measurements. In order of generality, these types are: observables, instruments and measurement models. If $\alpha$ and $\beta$ are entities, we define what it means for $\alpha$ to be a part…
Complexity measures in the context of the Integrated Information Theory of consciousness try to quantify the strength of the causal connections between different neurons. This is done by minimizing the KL-divergence between a full system…
The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $\mu(E)$ to every (suitably regular) set $E$ of histories. Even though $\mu(E)$ cannot in general be interpreted as the expectation value…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
This paper presents a communication efficient distributed algorithm, $\mathcal{CIRFE}$ of the \emph{consensus}+\emph{innovations} type, to estimate a high-dimensional parameter in a multi-agent network, in which each agent is interested in…
Identifying groups that share common features among datasets through clustering analysis is a typical problem in many fields of science, particularly in post-omics and systems biology research. In respect of this, quantifying how a measure…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and…