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Gasoline blending scheduling uses resource allocation and operation sequencing to meet a refinery's production requirements. The presence of nonlinearity, integer constraints, and a large number of decision variables adds complexity to this…
Fork algebras are an extension of relation algebras obtained by extending the set of logical symbols with a binary operator called fork. This class of algebras was introduced by Haeberer and Veloso in the early 90's aiming at enriching…
Direct Preference Optimization (DPO) has emerged as a predominant alignment method for diffusion models, facilitating off-policy training without explicit reward modeling. However, its reliance on large-scale, high-quality human preference…
Mathematical physics problems are often formulated using differential oprators of vector analysis - invariant operators of first order, namely, divergence, gradient and rotor operators. In approximate solution of such problems it is natural…
We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE which provides…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
The biharmonic operator plays a central role in a wide array of physical models, notably in elasticity theory and the streamfunction formulation of the Navier-Stokes equations. The need for corresponding numerical simulations has led, in…
We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential operators. Our approach is quite straightforward…
This paper introduces semi-ring dictionaries, a powerful class of compositional and purely functional collections that subsume other collection types such as sets, multisets, arrays, vectors, and matrices. We developed SDQL, a statically…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
In this note, we construct and study an algebraic system similar to the natural numbers, but with noncommutative addition. The addition we introduce is a binary operation that commutes with itself in the sense of N. Durov. Neverheless, the…
Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints.…
Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple…
The multiplicative and additive compounds of a matrix have important applications in geometry, linear algebra, and the analysis of dynamical systems. In particular, the $k$-compounds allow to build a $k$-compound dynamical system that…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
Diffusion language models (DLMs) enable parallel, order-agnostic generation with iterative refinement, offering a flexible alternative to autoregressive large language models (LLMs). However, adapting reinforcement learning (RL) fine-tuning…
Learning options that allow agents to exhibit temporally higher order behavior has proven to be useful in increasing exploration, reducing sample complexity and for various transfer scenarios. Deep Discovery of Options (DDO) is a generative…
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal…
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…