Related papers: Coalgebraic Behavioral Metrics
Hilbert space structure is assumed as a valid geometric description for neurodynamics, i.e., for applying any kind of quantum formalism in brain dynamics. The orientation selectivity of the neurons is used as a justification to construct a…
Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the…
We study coalgebraic modal logic to characterise behavioural equivalence in the presence of side effects, i.e., when coalgebras live in a (co)Kleisli or an Eilenberg-Moore category. Our aim is to develop a general framework based on indexed…
We study general geometric properties of cone spaces, and we apply them on the Hellinger--Kantorovich space $(\mathcal{M}(X),\mathsf{H\hspace{-0.25em} K}_{\alpha,\beta}).$ We exploit a two-parameter scaling property of the…
Collective behavior in animals has long been modeled through self-propelled particle models, which reproduce striking group-level phenomena through abstract interaction forces. Yet these models are fundamentally descriptive: they leave open…
We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov's theorem) or…
In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of…
We introduce a generalization of the bisimulation game that finds distinguishing Hennessy-Milner logic formulas from every finitary, subformula-closed language in van Glabbeek's linear-time--branching-time spectrum between two finite-state…
Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have…
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on earlier work that obtains Hennessy-Milner theorems as corollaries…
Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…
Living systems display complex behaviors driven by physical forces as well as decision-making. Hydrodynamic theories hold promise for simplified universal descriptions of socially-generated collective behaviors. However, the construction of…
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…
This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base…
A popular approach to solving large probabilistic systems relies on aggregating states based on a measure of similarity. Many approaches in the literature are heuristic. A number of recent methods rely instead on metrics based on the notion…
The belief construction is a fundamental technique for transforming partially observable systems to fully observable ones while preserving the relevant semantics. It plays a central role in the analysis of partially observable systems, in…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…