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Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…
Regina is a software package for studying 3-manifold triangulations and normal surfaces. It includes a graphical user interface and Python bindings, and also supports angle structures, census enumeration, combinatorial recognition of…
PieceWise Affine (PWA) approximations for nonlinear functions have been extensively used for tractable, computationally efficient control of nonlinear systems. However, reaching a desired approximation accuracy without prior information…
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…
Many parallel algorithms use at least linear auxiliary space in the size of the input to enable computations to be done independently without conflicts. Unfortunately, this extra space can be prohibitive for memory-limited machines,…
In this paper, we apply the Logistic PCA (LPCA) as a dimensionality reduction tool for visualizing patterns and characterizing the relevance of mathematics abilities from a given population measured by a large-scale assessment. We establish…
Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the…
The dual Youla method for closed loop identification is known to have several practically important merits. Namely, it provides an accurate plant model irrespective of noise models, and fits inherently to handle unstable plants by using…
Rational Tracer (Ratracer) is a tool to simplify complicated arithmetic expressions using modular arithmetics and rational function reconstruction, with the main idea of separating the construction of expressions (via tracing, i.e.…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
Nonlinear expressions are often approximated by piecewise affine (PWA) functions to simplify analysis or reduce computational costs. To reduce computational complexity, multivariate functions can be represented as compositions of functions…
Franka Emika robots have gained significant popularity in research and education due to their exceptional versatility and advanced capabilities. This work introduces panda-py - a Python interface and framework designed to empower Franka…
This study introduces AyutthayaAlpha, an advanced transformer-based machine learning model designed for the transliteration of Thai proper names into Latin script. Our system achieves state-of-the-art performance with 82.32% first-token…
Learning tabula rasa, that is without any prior knowledge, is the prevalent workflow in reinforcement learning (RL) research. However, RL systems, when applied to large-scale settings, rarely operate tabula rasa. Such large-scale systems…
Runge-Kutta methods are a popular class of numerical methods for solving ordinary differential equations. Every Runge-Kutta method is characterized by two basic parameters: its order, which measures the accuracy of the solution it produces,…
Parikh (tree) automata are an expressive and yet computationally well-behaved extension of finite automata -- they allow to increment a number of counters during their computations, which are finally tested by a semilinear constraint. In…
Large language models (LLMs) demonstrate strong task-specific capabilities through fine-tuning, but merging multiple fine-tuned models often leads to degraded performance due to overlapping instruction-following components. Task Arithmetic…
We present a comprehensive computational study of a class of linear system solvers, called {\it Triangle Algorithm} (TA) and {\it Centering Triangle Algorithm} (CTA), developed by Kalantari \cite{kalantari23}. The algorithms compute an…