1,720,973 research outputs found
Constructing Hadamard matrices using binary codes
Full text linkIn this paper is presented a very efficient method for constructing Hadamard matrices, using binary code products. We will construct such matrices using the scalar production of two vectors and the tensor production of Hadamard matrices. This method is based on the representation of the natural number as a binary code which takes only two values 0 or 1. Such a method of generating Hadamard matrices can be used in practice to generate different codes, in telecommunication systems, to correct blocked codes, but also in science as for example in Boolean algebra
Generating Arithmetic and Geometric Sequences in Java: A Mathematical Approach
No full textThis paper demonstrates how mathematical sequences, particularly arithmetic and geometric sequences, can be implemented in programming using Java arrays. In mathematics, sequences are ordered sets of numbers following a specific pattern, whereas in computer science, these sequences can be implemented as arrays. The main goal is to show the similarities between mathematics and programming. A simple Java program generates arithmetic and geometric arrays automatically, allowing students to visualize patterns and understand how to apply mathematical principles in code. This paper explains the process of writing the Java program and provides examples of output arrays. This approach solidifies the understanding of sequences while providing concrete programming experience. By combining theory and practical implementation, students can see the direct application of mathematics in computer science. The method used is simple and suitable for educational purposes or further exploration in computational contexts
Machine Learning and its impact on everyday life
No full textThis study focuses on Machine Learning technology and its use in everyday life. In this paper, we will analyze the historical development of Machine Learning technology, its key components, and its applications in daily life, particularly in the fields of healthcare, education, its role as a personal assistant and the implementation of recommendations and predictions in various applications. Furthermore, we will explore the need for Machine Learning in the business world and the risk associated with data usage in this context. Finally, we will examine the latest trends in Machine Learning development and the future possibilities for its use in various life domains. This analysis will be beneficial in understanding the functionality of Machine Learning in the background together with the risks and opportunities of Machine Learning in this rapidly evolving technological landscape
Geometry of Complexity in Mathematics and Computing Fractals
No full textFractals are structures that reveal infinitely complex patterns yet are surprisingly simple. They emerge as objects defined by recursion and they capture the idea of selfsimilarity. Beyond visual appeal, fractals also carry deep mathematical significance, bridging geometry, analysis and chaos theory. They challenge the very concept of dimension, expanding the understanding of geometry that exists beyond the Euclidean limits. In computer science, algorithms for generating these fractals rely on recursion, iteration and complex numbers. As coding provides a base for fractals to show how mathematical beauty can be showcased in the digital world, in generating landscapes, textures, organic forms and realism. These however not being the only functions but also supports data compression, image recognition, and modeling of chaotic systems. They stand as a powerful intersection between abstract theory and applied computation, embodying the synergy of math and computer science. Their paradoxical nature is part of their allure. On one hand, they are born from equations that can be written in a few lines. On the other, they give rise to visuals so complex and alive that they seem beyond calculation. In this sense, fractals appear less like human inventions and more like discoveries of a hidden order already woven into nature itself. Fractals remain both familiar and alien glimpses of infinity that we can generate but never fully grasp. As we look closer, we find they are not only art and not only mathematics, but a bridge between the two, pointing toward patterns that seem to echo across science, technology, and even philosophy
Incidence matrix and some of its applications in graph theory
Full text linkIn this paper we will focus mainly on some basic concepts and definitions regarding incidence matrices and some examples of their application in graph theory. To give their clearest definition of the incidence matrix, we will first give the meaning of the incidence structure, then through it to define the incidence matrix. The structure of incidence is called the ordered triplet S=(P,B,I), where P∩B=ϕ, I⊆P×B and P,B while, are two non-empty sets and I a relation in between them, such that I⊂P×B. We call the elements of P community dots and we will mark them in lower case letters of, and we will call B the elements of the community blocks or lines and we will mark them in uppercase letters. Like any double bond, between two finite sets the incidence I bond of a finite structure S=(P,B,I) has the bond matrix, which we call the incidence matrix. The incidence matrix A represents a reflection of P×B→0,1, that is (p,X)⟶1, if p I X and (p,X)⟶0, if and is denoted A=aijvxb. If G is a graph with n vertices, m edges and without self-loops. The incidence matrix A of G is an n×m matrix A=(aij) whose n rows correspond to the n vertices and the m columns correspond to m edges such that
A=aij={1, if jth edge mj is incident on the ith vertex 0, otherwise
Incidence matrices have a great application in many fields of science such as:
telecommunications, coding theory, graph theory, etc
USING THE INTERNET OF THINGS IN PERSONAL HEALTH
Full text linkWith the increase in development of technology and with the evolution of the Internet, a wide network was created, which is composed of devices with different sizes and multiple functions, known as Internet of Things ( IoT). Internet of Things has found high usability in different industry sectors, like:military sector, aerial, educational, medical and in many other sectors. It had a great influence in the medical sector, by making the process of monitoring medical data easier, medication management, diagnosis of diseases, saving and better analysis of the data, and reducing patients expenses. These monitoring devices like smartphones, smartwatches, glucose and oxygen monitors, have applications that collect patient data in real time, afterwards the data is shown to the users. They use different sensors to monitor metrics like heartbeats, quality and longevity of sleep, burned calories and many more. The potential for future development of Internet of Things in the personal health aspect is really high, also including here mental health which will be discussed in this thesis
Matrix Operations Underlying the Transformer Models
No full textThis paper explores the mathematical principles underlying the transformer model, an architecture that is driving the advancement of artificial intelligence (AI). While older processing models like Recurrent Neural Networks and Long Short-Term Memory Networks struggled with long range dependencies and parallel computations, transformers overcome these challenges through self attention and parallelism. The core of this architecture lies matrix operations, specifically matrix multiplication and the dot product, which allow transformers to capture relationships across sequences.This paper first walks us through the traditional sequential models, then outlines the encoder, decoder and encoder-decoder variations that define the modern transformer architecture. We then focus on Query, Key and Value matrices within the attention mechanism, and illustrating the computation of attention using embedding vectors and weight matrices through a concrete example.By focusing on the linear algebra underlying transformer models, this paper shows how mathematical operations ensure efficiency and performance in natural language processing (NLP) and beyond. Understanding these fundamental mathematical principles clarifies how transformers work and provides insight into the future of AI
A Comparative Analysis of Mathematical Domains and Computer Network Domains
No full textThe connection between mathematics and computer science is essential for advancing the knowledge and technologies that shape our digital world. Mathematics provides foundational concepts in many areas of computer science, enabling the development of modern technology. This paper explores the similarities and differences between the concept of domain in mathematics and computer networks. While both fields use the term domain to indicate fundamental ideas, the contexts and applications vary significantly. In mathematics, domains refer to specific sets of values essential for analyzing functions and discovering patterns. In contrast, in computer networks, domains serve as organizational frameworks that manage resources and facilitate communication. Through a detailed examination, this analysis clarifies how these terms, although homonymous, reflect distinct conceptual frameworks. By highlighting these differences, we gain valuable insights into their respective roles and importance across various disciplines
Applied cryptography with python
No full textCryptography is a key aspect of information security and provides data security. This paper aims to provide a better understanding of cryptography and its application with Python through real life examples. It covers the basics of cryptography, containing information about symmetric and asymmetric encryption methods. Throughout the paper we dive into different encryption methods, from simple to more complex, starting with the Caesar Cipher that has been used by people ever since ancient times, the Reverse Cipher which is one of the simplest encryption methods, all the way to implementing a RSA Algorithm using Python’s cryptography library, always providing knowledge over each of their pros and cons. We’re going to tackle the advanced encryption methods using the cryp-tography library, specifically the “Fernet” class. This paper showcases the real-world applications of cryptography in modern systems like secure communication between devices and hashing techniques for password encryption, high-lighting the importance of cryptography in protecting sensitive information
CinemaVerse
No full textThe concept of the project is the software that enables the online purchase of tickets for the movies that customers want to watch. The software is intended to be part of a cinema which offers a wide range of films and events such as: the CINEPLEX cinema in Kosovo or the ABC cinema in Pristina. Within this software the user will be able to view information about any movie that is showing that he wants, the information will be of this type: name, genre, price and trailer of the movie. Movies will be categorized by genres (action, comedy, horror, etc.), so the user will be able to search for movies according to their favorite genre. Cinemas will also be able to host events in their spaces, these will be seen by site users and they will be able to buy tickets (if available) to go to that specific event. Events can be such as birthday parties, film fairs, replays of old films, etc.
The main goal of CinemaVerse is to facilitate and not waste the time of customers to watch the list of films that are available in all cinemas in Kosovo
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