Related papers: LogLatt: A computational library for the calculus …
In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in…
Linear algebra routines are basic building blocks for the statistical software. In this paper we analyzed how can we can improve R performance for matrix computations. We benchmarked few matrix operations using the standard linear algebra…
Numerical simulations of quantum field theories on lattices serve as a fundamental tool for studying the non-perturbative regime of the theories, where analytic tools often fall short. Challenges arise when one takes the continuum limit or…
Braidlab is a Matlab package for analyzing data using braids. It was designed to be fast, so it can be used on relatively large problems. It uses the object-oriented features of Matlab to provide a class for braids on punctured disks and a…
We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to…
We introduce FunKit, a Mathematica package for the derivation and tracing of functional equations from arbitrary master equations. FunKit provides an expression vocabulary and a set of rules that allow for derivations in any given field…
This short paper presents a Wirtinger's-Calculus based load-flow methodology for power distribution grids. This approach allows to obtain an algorithm which works directly on the complex domain maintaining some useful symmetries and a…
Scientific legacy code in MATLAB/Octave not compatible with modernization of research workflows is vastly abundant throughout academic community. Performance of non-vectorized code written in MATLAB/Octave represents a major burden. A new…
We present methods for exploratory studies of molecular dynamics using MATLAB. Such methods are not suitable for large scale applications, but they can be used for developement and testing of new types of interactions and other aspects of…
The lattice Boltzmann method, after close to thirty years of presence in computational fluid dynamics has turned into a versatile, efficient and quite popular numerical tool for fluid flow simulations. The lattice Boltzmann method owes its…
While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
This paper is devoted to present the Mathematics Grammar Library, a system for multilingual mathematical text processing. We explain the context in which it originated, its current design and functionality and the current development goals.…
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small…
Logic gates can be written in terms of complex differential operators, where the inputs and outputs are holomorphic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection…
In many applications, such as physiology and finance, large time series data bases are to be analyzed requiring the computation of linear, nonlinear and other measures. Such measures have been developed and implemented in commercial and…
In many scientific fields like e.g. neuroscience, climatology or physics, complex relationships can be described most parsimoniously by nonlinear mechanics. Despite their relevance, many scientists still apply linear estimates in order to…
Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning…
Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…
Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…