相关论文: Streams and Lazy Evaluation Applied to Integrable …
The coupled nonlinear space fractional Ginzburg-Landau (CNLSFGL) equations with the fractional Laplacian have been widely used to model the dynamical processes in a fractal media with fractional dispersion. Due to the existence of…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
In this work we present an integrated computational pipeline involving several model order reduction techniques for industrial and applied mathematics, as emerging technology for product and/or process design procedures. Its data-driven…
Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…
As Large Language Models (LLMs) scale to million-token contexts, traditional Mechanistic Interpretability techniques for analyzing attention scale quadratically with context length, demanding terabytes of memory beyond 100,000 tokens. We…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
Studies in thermodynamics often require the reduction of some first or second order partial derivatives in terms of a smaller basic set. A simple algorithm to perform such a reduction is presented here, together with a review of earlier…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
Gradient-based analysis methods, such as saliency map visualizations and adversarial input perturbations, have found widespread use in interpreting neural NLP models due to their simplicity, flexibility, and most importantly, their…
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. Here we explore the methodology applied to the gap-tooth scheme in the equation-free approach of Kevrekidis in two…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
Large Language Models (LLMs) have demonstrated impressive reasoning capabilities but continue to struggle with arithmetic tasks. Prior works largely focus on outputs or prompting strategies, leaving the open question of the internal…
We develop a framework for computing two foundational analyses for concurrent higher-order programs: (control-)flow analysis (CFA) and may-happen-in-parallel analysis (MHP). We pay special attention to the unique challenges posed by the…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
The call-by-need lambda calculus provides an equational framework for reasoning syntactically about lazy evaluation. This paper examines its operational characteristics. By a series of reasoning steps, we systematically unpack the…
Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…
In this paper we present a differential semantics of Lazy AR Propagation (LARP) in discrete Bayesian networks. We describe how both single and multi dimensional partial derivatives of the evidence may easily be calculated from a junction…