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In recent time there has been an increasing amount of interest in developing novel techniques for the generation of complex vector light beams. Amongst these, digital holography stands out as one of the most flexible and versatile with…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
We use a genetic algorithm to construct Hadamard Matrices. The initial population of random matrices is generated to have a balanced number of +1 and -1 entries in each column except the first column with all +1. Several fitness functions…
A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on…
Industrial robots are designed as general-purpose hardware with limited ability to adapt to changing task requirements or environments. Modular robots, on the other hand, offer flexibility and can be easily customized to suit diverse needs.…
The symbolic manipulation program FORM is specialized to handle very large algebraic expressions. Some specific features of its internal structure make FORM very well suited for parallelization. We have now two parallel versions of FORM,…
In this paper, we introduce an efficient algorithm for generating specific Hadamard rows, addressing the memory demands of pre-computing the entire matrix. Leveraging Sylvester's recursive construction, our method generates the required…
Efficient processing of tabular data is important in various industries, especially when working with datasets containing a large number of columns. Large language models (LLMs) have demonstrated their ability on several tasks through…
In this paper, we present techniques used to implement our portable vectorized library of C standard mathematical functions written entirely in C language. In order to make the library portable while maintaining good performance, intrinsic…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
Processing-in-memory (PIM) seeks to eliminate computation/memory data transfer using devices that support both storage and logic. Stateful logic techniques such as IMPLY, MAGIC and FELIX can perform logic gates within memristive crossbar…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
In~\cite{algorithmic} was given an algorithm that computes arithmetical structures on matrices. We use some of the ideas contained there to get an algorithm that computes arithmetical structures over dominated polynomials. A dominated…
Complex vector light modes, characterized by a non-uniform transverse polarization distribution, have pervaded a wide range of research fields. In this study, we propose a novel approach that enables the simultaneous generation of multiple…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
Imagination is the critical point in developing of realistic artificial intelligence (AI) systems. One way to approach imagination would be simulation of its properties and operations. We developed two models: AI-Brain Network Hierarchy of…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
Polynomial multiplication is a bottleneck in most of the public-key cryptography protocols, including Elliptic-curve cryptography and several of the post-quantum cryptography algorithms presently being studied. In this paper, we present a…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…