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We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. The construction is achieved via a categorical approach that…
This paper studies the problem of modeling complex domains of actions and change within high-level action description languages. We investigate two main issues of concern: (a) can we represent complex domains that capture together different…
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the…
In the present work we redefine and generalize the action principle for dissipative systems proposed by Riewe by fixing the mathematical inconsistencies present in the original approach. In order to formulate a quadratic Lagrangian for…
The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we…
We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
In clinical research and clinical decision-making, it is important to know if a study changes or only supports the current standards of care for specific disease management. We define such a change as transformative and a support as…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
In reinforcement learning, different reward functions can be equivalent in terms of the optimal policies they induce. A particularly well-known and important example is potential shaping, a class of functions that can be added to any reward…
This paper introduces a proof calculus for real-analytic differential-algebraic dynamic logic, enabling correct transformations of differential-algebraic equations. Applications include index reductions from differential-algebraic equations…
By adhering to the dictum, "No causation without manipulation (treatment, intervention)", cause and effect data analysis represents changes in observed data in terms of changes in the causal factors. When causal factors are not amenable for…
Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between…
The exploration-exploitation trade-off is central to the description of adaptive behaviour in fields ranging from machine learning, to biology, to economics. While many approaches have been taken, one approach to solving this trade-off has…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…
We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive…
The score function estimator is widely used for estimating gradients of stochastic objectives in stochastic computation graphs (SCG), eg, in reinforcement learning and meta-learning. While deriving the first-order gradient estimators by…
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…