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Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Analyzing large datasets to select optimal features is one of the most important research areas in machine learning and data mining. This feature selection procedure involves dimensionality reduction which is crucial in enhancing the…
Computer-aided design (CAD) is a way to digitally create 2D drawings and 3D models of real-world products. Traditional CAD typically relies on hand-drawing by experts or modifications of existing library files, which doesn't allow for rapid…
Local geometry-controllable computer-aided design (CAD) generation aims to modify local parts of CAD models automatically, enhancing design efficiency. It also ensures that the shapes of newly generated local parts follow user-specific…
Digital Geometry software should reflect the generality of the underlying mathe- matics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital geometry data structures and…
Trimming techniques are efficient ways to generate complex geometries in Computer-Aided Design(CAD). In this paper, an improved isogeometric analysis(IGA) method for trimmed geometries is proposed. We will show that the proposed method…
We propose GANCoder, an automatic programming approach based on Generative Adversarial Networks (GAN), which can generate the same functional and logical programming language codes conditioned on the given natural language utterances. The…
Conformal Geometric Algebra (CGA) is a framework that allows the representation of objects, such as points, planes and spheres, and deformations, such as translations, rotations and dilations as uniform vectors, called multivectors. In this…
Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a technique…
We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic…
In information retrieval research; Genetic Algorithms (GA) can be used to find global solutions in many difficult problems. This study used different similarity measures (Dice, Inner Product) in the VSM, for each similarity measure we…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
One of the biggest challenges in the research of generative adversarial networks (GANs) is assessing the quality of generated samples and detecting various levels of mode collapse. In this work, we construct a novel measure of performance…
Statistical design of experiments is widely used in scientific and industrial investigations. A generalized minimum aberration (GMA) orthogonal array is optimum under the well-established, so-called GMA criterion, and such an array can…
We present a method for automatically building diagrams for olympiad-level geometry problems and implement our approach in a new open-source software tool, the Geometry Model Builder (GMB). Central to our method is a new domain-specific…
This paper presents an optimization technique for the multi-pass face milling process. Genetic algorithm (GA) is used to obtain the optimum cutting parameters by minimizing the unit production cost for a given amount of material removal.…
We present a Python package together with a practical guide for the implementation of a lightweight diversity-enhanced genetic algorithm (GA) approach for the exploration of multi-dimensional parameter spaces. Searching a parameter space…
We extend coded distributed computing over finite fields to allow the number of workers to be larger than the field size. We give codes that work for fully general matrix multiplication and show that in this case we serendipitously have…
Genetic algorithms are considered as an original way to solve problems, probably because of their generality and of their "blind" nature. But GAs are also unusual since the features of many implementations (among all that could be thought…
Algebraic-geometric codes on Garcia-Stichtenoth family of curves are used to construct the asymptotically good quantum codes.