Related papers: Logical, Metric, and Algorithmic Characterisations…
We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system we propose a new definition of multiplication between distributions, and we check that this definition can be…
As the title suggests, this is the third paper in a series addressing bilevel optimization problems that are governed by the Kantorovich problem of optimal transport. These tasks can be reformulated as mathematical problems with…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
We consider symmetric multi-marginal Kantorovich optimal transport problems on finite state spaces with uniform-marginal constraint. These problems consist of minimizing a linear objective function over a high-dimensional polytope, here…
Drawing (a multiset of) coloured balls from an urn is one of the most basic models in discrete probability theory. Three modes of drawing are commonly distinguished: multinomial (draw-replace), hypergeometric (draw-delete), and Polya…
We study optimal transport between probability measures supported on the same finite metric space, where the ground cost is a distance induced by a weighted connected graph. Building on recent work showing that the resulting Kantorovich…
We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of…
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…
The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in…
Linear transfers between probability distributions were introduced in [5,6] in order to extend the theory of optimal mass transportation while preserving the important duality established by Kantorovich. It is shown here that $\{0,…
Many results in probability (most famously, Strassen's theorem on stochastic domination), characterize some relationship between probability distributions in terms of the existence of a particular structured coupling between them. Optimal…
Behavioural distances generally offer more fine-grained means of comparing quantitative systems than two-valued behavioural equivalences. They often relate to quantitative modalities, which generate quantitative modal logics that…
This paper is concerned with an optimization problem governed by the Kantorovich optimal transportation problem. This gives rise to a bilevel optimization problem, which can be reformulated as a mathematical problem with complementarity…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
In this paper the factorization method is used in order to obtain the eigenvalues and eigenfunctions of a quantum particle confined in a one-dimensional infinite well. The output results from the mentioned approach allows us to explore an…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
This research includes the study of some positive sampling Kantorovich operators (SK operators) and their convergence properties. A comprehensive analysis of both local and global approximation properties is presented using sampling…
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…
Probabilistic automata (PA), also known as probabilistic nondeterministic labelled transition systems, combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…