Related papers: Polynomiogram: An Integrated Framework for Root Vi…

The subject of Polynomiography deals with algorithmic visualization of polynomial equations, having many applications in STEM and art, see [Kal04]. Here we consider the polynomiography of the partial sums of the exponential series. While…

This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…

To bridge the gap between artists and non-specialists, we present a unified framework, Neural-Polyptych, to facilitate the creation of expansive, high-resolution paintings by seamlessly incorporating interactive hand-drawn sketches with…

Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…

Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers into an ontological knowledge graph. Through an in-depth structural analysis, we have calculated node degrees, identified…

Whilst there are perhaps only a few scientific methods, there seem to be almost as many artistic methods as there are artists. Artistic processes appear to inhabit the highest order of open-endedness. To begin to understand some of the…

Generative art merges creativity with computation, using algorithms to produce aesthetic works. This paper introduces Samila, a Python-based generative art library that employs mathematical functions and randomness to create visually…

Generative art systems often involve high-dimensional and complex parameter spaces in which aesthetically compelling outputs occupy only small, fragmented regions. Because of this combinatorial explosion, artists typically rely on extensive…

Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with…

The roots of any polynomial of degree m with integer coefficients, can be computed by manipulation of sequences made from 2m distinct symbols and counting the different symbols in the sequences. This method requires only 'primitive'…

Creating and understanding art has long been a hallmark of human ability. When presented with finished digital artwork, professional graphic artists can intuitively deconstruct and replicate it using various drawing tools, such as the line…

Student appreciation of a function is enhanced by understanding the graphical representation of that function. From the real graph of a polynomial, students can identify real-valued solutions to polynomial equations that correspond to the…

Recent advancements in Generative Artificial Intelligence (GenAI) have significantly enhanced the capabilities of both image generation and editing. However, current approaches often treat these tasks separately, leading to inefficiencies…

Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…

There are two classes of generative art approaches: neural, where a deep model is trained to generate samples from a data distribution, and symbolic or algorithmic, where an artist designs the primary parameters and an autonomous system…

We propose a new framework for the recognition of online handwritten graphics. Three main features of the framework are its ability to treat symbol and structural level information in an integrated way, its flexibility with respect to…

Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…

Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…

Recently there has been increasing interest in developing and deploying deep graph learning algorithms for many tasks, such as fraud detection and recommender systems. Albeit, there is a limited number of publicly available graph-structured…