The Factors of Graphs Abstract Agraph Gconsists of a non-null setVof objects called vertices together with a setEof objects callededges, the two sets having no common element. With each edge there are associated just two vertices, called its ends. Two or more edges may have the same pair ...
The mathematics of Peter L. Hammer (1936–2006): graphs, optimization, and Boolean modelsTrainsSchedulingOptimizationHeuristicsNo abstract is available for this item.doi:10.1007/s10479-011-0913-4Endre BorosYves CramaDominique de WerraPierre Hansen...
variety of operators and types. When applied to sparse adjacency matrices, these algebraic operations are equivalent to computations on graphs. GraphBLAS provides a powerful and expressive framework for creating graph algorithms based on the elegant mathematics of sparse matrix operations on a semiring....
Here, we use the Microsoft Academic Graph to study the bibliometric evolution of AI research and its related fields from 1950 to today. Although early AI researchers exhibited strong referencing behaviour towards philosophy, geography and art, modern AI research references mathematics and computer scienc...
We also thank the Mathematics Department of the Autonomous University of Madrid, SageMath, Inc., and Andrey Novoseltsev for providing the SageMathCell services running at https://sagecell.sagemath.org (used by AllenSPARQL). We would also like to express our sincere thanks to all researchers ...
In Section 2 we derive some basic properties of the interactive sum choice number, before providing upper bounds on the interactive sum choice number (and showing that these bounds improve on the sum choice number) for various families of graphs in Sections 3 Graphs that are sc-greedy, 4 ...
LLEMMA: AN OPEN LANGUAGE MODEL FOR MATHEMATICS; Zhangir Azerbayev et al Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models; Keming Lu et al Mixtral of Experts; Albert Q. Jiang et al DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language...
Large language models (LLMs) are artificial intelligence (AI) tools specifically trained to process and generate text. LLMs attracted substantial public attention after OpenAI’s ChatGPT was made publicly available in November 2022. LLMs can often answer
The role of teaching, learning, and assessment with digital technology has become increasingly prominent in mathematics education. This survey paper provid
The log-rank conjecture has a number of combinatorial interpretations, which will be the main focus of our paper. Lovász and Saks [12] observed (see also [13]) that this problem is closely related to bounding the chromatic number of graphs, whose adjacency matrix has bounded rank. Indeed,...