Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Informaticology: combining Computer Science, Data Science, and Fiction Science

Motivated by an intention to remedy current complications with Dutch terminology concerning informatics, the term informaticology is positioned to denote an academic counterpart of informatics where informatics is conceived of as a container for a coherent family of practical disciplines ranging from computer engineering and software engineering to network technology, data center management, information technology, and information management in a broad sense. Informaticology escapes from the limitations of instrumental objectives and the perspective of usage that both restrict the scope of informatics. That is achieved by including fiction science in informaticology and by ranking fiction science on equal terms with computer science and data science, and framing (the study of) game design, evelopment, assessment and distribution, ranging from serious gaming to entertainment gaming, as a chapter of fiction science. A suggestion for the scope of fiction science is specified in some detail. In order to illustrate the coherence of informaticology thus conceived, a potential application of fiction to the ontology of instruction sequences and to software quality assessment is sketched, thereby highlighting a possible role of fiction (science) within informaticology but outside gaming

Bio-Mathematics- a Special Reference To Matrices

Mathematics is one of the oldest organized disciplines of human knowledge with a continuous line of development spanning 5000 years or more. It originated from human curiosity and is an endless enterprise.   Mathematics is known as the “Queen of all Sciences’ as it provides solution techniques & increases the potentials of other disciplines like Physics, Chemistry, Biology, etc. In this era of scientific, industrial and I.T revolution, due attention to mathematics is essential for the progress of the world.   Mathematics permeates biology. However mathematics in biology is appreciated only when biologists start reading & doing research. Even today there are only a few mathematicians who are knowledgeable in biology & very few biologists know mathematics.   Mathematical biology is emerging very rapidly for today traditional academic boundaries require interdisciplinary approaches. Biological concepts and models are becoming more quantitative. For a progressive and fruitful research career in biology one must have requisite knowledge of biology, mathematics, and computer science. A conscious effort to learn the necessary mathematics via biological applications is the need of the hour.   Mathematical biology is an interdisciplinary scientific research field with a range of mathematical applications in biology, biotechnology, medicine etc.; Matrices, Linear algebra, Abstract algebra, Calculus, Differential equations, Graph theory, Statistics, Probability, Operations Research are some areas of Mathematics most commonly applied in Biology.

From Cbits to Qbits: Teaching computer scientists quantum mechanics

A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory. Although the article as a whole addresses teachers of physics, well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.Comment: 19 pages, no figures. Submitted to the American Journal of Physic

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science