Related papers: Bi-capacities -- Part II: the Choquet integral

Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring. We show that imposing symmetry…

Complementarity among species with different traits is one of the basic processes affecting biodiversity, defined as the number of species in the ecosystem. We present here a soluble model ecosystem in which the species are characterized by…

The debate around the interpretability of attention mechanisms is centered on whether attention scores can be used as a proxy for the relative amounts of signal carried by sub-components of data. We propose to study the interpretability of…

This paper studies n-player games where players beliefs about their opponents behaviour are capacities (fuzzy measures, non-additive probabilities). The concept of an equilibrium under uncertainty was introduced by J.Dow and S.Werlang…

Bipartite experiments arise in various fields, in which the treatments are randomized over one set of units, while the outcomes are measured over another separate set of units. However, existing methods often rely on strong model…

Relational structures are emerging as ubiquitous mathematical machinery in the semantics of open systems of various kinds. Cartesian bicategories are a well-known categorical algebra of relations that has proved especially useful in recent…

Inquisitive modal logic, InqML, in its epistemic incarnation, extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. We use the natural notion of…

Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connected colimits and limits in the starting category become…

Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…

The educability model is a computational model that has been recently proposed to describe the cognitive capability that makes humans unique among existing biological species on Earth in being able to create advanced civilizations.…

Phenomena involving multiple scattering, despite having attracted considerable attention in physics for decades, continue to generate unexpected and counterintuitive behaviours prompting further studies. For optical scattering, the memory…

We introduce the notion of a bicollapsible 2-complex. This allows us to generalize the hyperbolicity of one-relator groups with torsion to a broader class of groups with presentations whose relators are proper powers. We also prove that…

In the same way decomposition spaces, also known as unital 2-Segal spaces, have incidence (co)algebras, and certain relative decomposition spaces have incidence (co)modules, we identify the structures that have incidence bi(co)modules: they…

Perceptual multistability, observed across species and sensory modalities, offers valuable insights into numerous cognitive functions and dysfunctions. For instance, differences in temporal dynamics and information integration during…

Bidirectional devices are devices for which the roles of the input and output ports can be exchanged. Mathematically, these devices are described by bistochastic quantum channels, namely completely positive linear maps that are both…

Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units.…

In this paper the theory of semi-bounded rationality is proposed as an extension of the theory of bounded rationality. In particular, it is proposed that a decision making process involves two components and these are the correlation…

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…

This paper proposes a definition of what it means for one system description language to encode another one, thereby enabling an ordering of system description languages with respect to expressive power. I compare the proposed definition…

We show that a normalized capacity $\nu: \mathcal{P}(\mathbf{N})\to \mathbf{R}$ is invariant with respect to an ideal $\mathcal{I}$ on $\mathbf{N}$ if and only if it can be represented as a Choquet average of $\{0,1\}$-valued finitely…