Related papers: dxo: A System for Relational Algebra and Different…

A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…

We present a miniKanren-based type inferencer for an educational programming language with first-class functions, S-expressions, and pattern-matching. The language itself is untyped which adds a certain specificity to the problem and…

We introduce DISTAL, a compiler for dense tensor algebra that targets modern distributed and heterogeneous systems. DISTAL lets users independently describe how tensors and computation map onto target machines through separate format and…

A completely integrable nonlinear partial differential equation (PDE) can be associated with a system of linear PDEs in an auxiliary function whose compatibility requires that the original PDE is satisfied. This associated system is called…

Recent advances in diffusion language models (DLMs) have presented a promising alternative to traditional autoregressive large language models (LLMs). However, DLMs still lag behind LLMs in reasoning performance, especially as the number of…

Direct Preference Optimization (DPO) aligns language models using pairwise preference comparisons, offering a simple and effective alternative to Reinforcement Learning (RL) from human feedback. However, in many practical settings, training…

We present an implementation of the relational programming language miniKanren as a set of combinators and syntax extensions for OCaml. The key feature of our approach is polymorphic unification, which can be used to unify data structures…

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…

Direct preference optimization (DPO) is a successful fine-tuning strategy for aligning large language models with human preferences without the need to train a reward model or employ reinforcement learning. DPO, as originally formulated,…

In this paper, we propose a framework to extract the algebra of the transformations of worlds from the perspective of an agent. As a starting point, we use our framework to reproduce the symmetry-based representations from the…

We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…

This is the second in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…

Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…

The survey is devoted to algebraic structures related to integrable ODEs and evolution PDEs. A description of Lax representations is given in terms of vector space decomposition of loop algebras into a direct sum of Taylor series and a…

A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…

In in this paper we show how using D.A. it is found a simple change of variables (c.v.) that brings us to obtain differential equations simpler than the original one. In a pedagogical way (at least we try to do that) and in order to make…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…

Background: Computational analysis of next-generation sequencing data is outpaced by data generation in many cases. In one such case, paired-end reads can be produced from the Illumina sequencing method faster than they can be overlapped by…

In this work we present useful techniques and possible enhancements when applying an Algorithmic Differentiation (AD) tool to the linear algebra library Eigen using our in-house AD by overloading (AD-O) tool dco/c++ as a case study. After…