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The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional geometrical domain in the tensor train format; secondly, to develop a new algorithm…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…
Image-based experiments can yield many thousands of individual measurements describing each object of interest, such as cells in microscopy screens. CellProfiler Analyst is a free, open-source software package designed for the exploration…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
Pre-trained language models (LMs) are currently integral to many natural language processing systems. Although multilingual LMs were also introduced to serve many languages, these have limitations such as being costly at inference time and…
We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…
We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six.…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…
Equations of motion for a classical 3d discrete model, whose auxialiary system is a linear system, are investigated. The Lagrangian form of the equations of motion is derived. The Lagrangian variables are a triplet of "tau functions". The…
We present Elvet, a Python package for solving differential equations and variational problems using machine learning methods. Elvet can deal with any system of coupled ordinary or partial differential equations with arbitrary initial and…
We present VitaLLM, a mixed precision accelerator that enables ternary weight large language models to run efficiently on edge devices. The design combines two compute cores, a multiplier free TINT core for ternary-INT projections and a…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
This article introduces HYLU, a hybrid parallel LU factorization-based general-purpose solver designed for efficiently solving sparse linear systems (Ax=b) on multi-core shared-memory architectures. The key technical feature of HYLU is the…
Three-dimensional medical image data and computer-aided decision making, particularly using deep learning, are becoming increasingly important in the medical field. To aid in these developments we introduce PR3DICTR: Platform for Research…
The equations for the critical points of the action functional defined by a Lagrangian depending on higher-order derivatives of admissible curves on a Lie algebroid are found. The relation with Euler-Poincar\'e and Lagrange Poincar\'e type…