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Parametric computer-aided design (CAD) is the dominant paradigm in mechanical engineering for physical design. Distinguished by relational geometry, parametric CAD models begin as two-dimensional sketches consisting of geometric primitives…
Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…
We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most…
Matlab is very widely used in scientific computing, but Matlab computational efficiency is lower than C language program. In order to improve the computing speed, some toolbox can use GPU to accelerate the computation. This paper describes…
In this paper we introduce the responsive graphical user interface (ReGUI) approach to creating applications, and demonstrate how this approach can be implemented in MATLAB. The same general technique can be used in other programming…
MATLAB has emerged as one of the languages most commonly used by scientists and engineers for technical computing, with ~1,000,000 users worldwide. The compute intensive nature of technical computing means that many MATLAB users have codes…
The aim of this work is to define and implement an extended C++ language to support the SIMD programming paradigm. The C++ programming language has been extended to express all the potentiality of an abstract SIMD machine consisting of a…
Integrating artificial intelligence (AI) into software engineering can transform traditional practices by enhancing efficiency, accuracy, and innovation. This study explores using ChatGPT, an advanced AI language model, to enhance UML class…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
PENLAB is an open source software package for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these. It is written entirely in MATLAB. PENLAB is a young brother of our code PENNON \cite{pennon}…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
Matlab is one of the most widely used mathematical computing environments in technical computing. It has an interactive environment which provides high performance computing (HPC) procedures and easy to use. Parallel computing with Matlab…
Automatic Differentiation (AD) is instrumental for science and industry. It is a tool to evaluate the derivative of a function specified through a computer program. The range of AD application domain spans from Machine Learning to Robotics…
Geometric Semantic Genetic Programming (GSGP) is a state-of-the-art machine learning method based on evolutionary computation. GSGP performs search operations directly at the level of program semantics, which can be done more efficiently…
The optimal design of compounds through manipulating properties at the molecular level is often the key to considerable scientific advances and improved process systems performance. This paper highlights key trends, challenges, and…
We introduce qclab++, a light-weight, fully-templated C++ package for GPU-accelerated quantum circuit simulations. The code offers a high degree of portability as it has no external dependencies and the GPU kernels are generated through…
Large language models (LLMs) have recently demonstrated their potential in clinical applications, providing valuable medical knowledge and advice. For example, a large dialog LLM like ChatGPT has successfully passed part of the US medical…
LaTeX is a free document preparation system that handles the typesetting of mathematical expressions smoothly and elegantly. It has become the standard format for creating and publishing research articles in mathematics and many scientific…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…