Related papers: Cartesian Difference Categories: Extended Report
Following an idea of A. Berenstein, we define a commutor for the category of crystals of a finite dimensional complex reductive Lie algebra. We show that this endows the category of crystals with the structure of a coboundary category.…
This paper generalizes the changes-in-changes (CIC) model to handle discrete treatments with more than two categories, extending the binary case of Athey and Imbens (2006). While the original CIC model is well-suited for binary treatments,…
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…
This paper describes how to define and work with differential equations in the abstract setting of tangent categories. The key notion is that of a curve object which is, for differential geometry, the structural analogue of a natural number…
Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives…
In this paper we present a comprehensive view of prominent causal discovery algorithms, categorized into two main categories (1) assuming acyclic and no latent variables, and (2) allowing both cycles and latent variables, along with…
We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
In this paper, we prove that given a differential graded category C and B a full differential graded subcategory closed under coproducts, there is a canonical recollement of differential graded categories, for which we use enriched…
Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly…
We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…
We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four…
Lagrangian descriptors (LDs) based on the arc length of orbits previously demonstrated their utility in delineating structures governing the dynamics. Recently, a chaos indicator based on the second derivatives of the LDs, referred to as…
We consider conditional transition systems, that model software product lines with upgrades, in a coalgebraic setting. By using Birkhoff's duality for distributive lattices, we derive two equivalent Kleisli categories in which these…
Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this…
It is shown that some class of differential inclusions has solutions that are defined and bounded for all real values of independent variable. Applications to dynamics are considered.
Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from…
An attempt is made to quantitatively demonstrate the difference between a complex adaptive combat model and conventional combat models. The work shows that complex adaptive models may give rise to "turbulent" dynamics, which emerge once the…
A relevant category is a symmetric monoidal closed category with a diagonal natural transformation that satisfies some coherence conditions. Every cartesian closed category is a relevant category in this sense. The denomination 'relevant'…