Related papers: Kantorovich Functors and Characteristic Logics for…
Simulations and bisimulations are ubiquitous in the study of concurrent systems and modal logics of various types. Besides classical relational transition systems, relevant system types include, for instance, probabilistic, weighted,…
In this paper, we explore lifting Markov Decision Processes (MDPs) to the space of probability measures and consider the so-called measurized MDPs: deterministic processes where states are probability measures on the original state space,…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
We estimate the rate of convergence for the Kantorovich (or Wasserstein) distance between empirical measures of i.i.d. random variables associated with the Laguerre model of order $\alpha$ on $(0,\infty)^N$ and their common law, which is…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
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…
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize…
We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii)…
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…
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…
Recent research in image and video recognition indicates that many visual processes can be thought of as being generated by a time-varying generative model. A nearby descriptive model for visual processes is thus a statistical distribution…
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…
By subjecting a dynamical system to a series of short pulses and varying several time delays we can obtain multidimensional characteristic measures of the system. Multidimensional Kullback-Leibler response function (KLRF), which are based…
It has been argued by Shepard that there is a robust psychological law that relates the distance between a pair of items in psychological space and the probability that they will be confused with each other. Specifically, the probability of…
We discuss the cosmology of axion-scalar systems in asymptotic limits of type IIB/F-theory flux compactifications. These results allow us to test a putative extension of the Distance Conjecture in a dynamical setting, which posits that…
The distributed and continuous representations used by neural networks are at odds with representations employed in linguistics, which are typically symbolic. Vector quantization has been proposed as a way to induce discrete neural…
Complex systems, such as brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often challenging. We propose using a…
Like notions of process equivalence, behavioural preorders on processes come in many flavours, ranging from fine-grained comparisons such as ready simulation to coarse-grained ones such as trace inclusion. Often, such behavioural preorders…
Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…
Large language models (LLMs) increasingly exhibit human-like patterns of pragmatic and social reasoning. This paper addresses two related questions: do LLMs approximate human social meaning not only qualitatively but also quantitatively,…