Optimization of coefficients of lists of polynomials by evolutionary algorithms

We here discuss the optimization of coefficients of lists of polynomials using evolutionary computation. The given polynomials have 5 variables, namely t, a1, a2, a3, a4, and integer coefficients. The goal is to find integer values i, with i 2 {1, 2, 3, 4}, substituting ai such that, after crossing out the gcd (greatest common divisor) of all coefficients of the polynomials, the resulting integers are minimized in absolute value. Evolution strategies, a special class of heuristic, evolutionary algorithms, are here used for solving this problem. In this paper we describe this approach in detail and analyze test results achieved for two benchmark problem instances; we also show a visual analysis of the fitness landscapes of these problem instancesMinisterio de Ciencia e Innovació

Moore-Penrose approach in the Hough transform framework

Maria-Laura Torrente is a member of GNAMPA - Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni of INDAM. J.R. Sendra is member of the Research Group ASYNACS (Ref.CT-CE2019/683).Let F(x, a) be a real polynomial in two sets of variables, x and a, that is linear with respect to one of the variable sets, say a. In this paper, we deal with two of the main steps of the Hough transform framework for the pattern recognition technique to detect loci in images. More precisely, we present an algorithmic process, based on the Moore–Penrose pseudo-inverse, to provide a region of analysis in the parameter space. In addition, we state an upper bound for the sampling distance of the discretization of the parameter space region.Agencia Estatal de Investigació

Optimization of coefficients of lists of polynomials by evolutionary algorithms

We here discuss the optimization of coefficients of lists of polynomials using evolutionary computation. The given polynomials have 5 variables, namely t, a1, a2, a3, a4, and integer coefficients. The goal is to find integer values i, with i 2 {1, 2, 3, 4}, substituting ai such that, after crossing out the gcd (greatest common divisor) of all coefficients of the polynomials, the resulting integers are minimized in absolute value. Evolution strategies, a special class of heuristic, evolutionary algorithms, are here used for solving this problem. In this paper we describe this approach in detail and analyze test results achieved for two benchmark problem instances; we also show a visual analysis of the fitness landscapes of these problem instancesThe authors thank Franz Winkler at the Research Institute for Symbolic Computation, Johannes Kepler University Linz, for his advice. R. Sendra is partially supported by the Spanish Ministerio de Economía y Competitividad under the project MTM2011-25816-C02-01 and is a member of the Research Group ASYNACS (Ref. CCEE2011/R34). The authors also thanks members of the Heuristic and Evolutionary Algorithms Laboratory as well as of the Bioinformatics Research Group, University of Applied Sciences Upper Austria, for their comments

Fitness landscape analysis in the optimization of coefficients of curve parametrizations

Este documento se considera que es una ponencia de congresos en lugar de un capítulo de libro.Computer Aided Systems Theory - EUROCAST 2017, 19-24 February, Las Palmas de Gran Canaria, Spain.J.R. Sendra is member of the Research Group ASYNACS (Ref.CT-CE2019/683)Parametric representations of geometric objects, such as curves or surfaces, may have unnecessarily huge integer coefficients. Our goal is to search for an alternative parametric representation of the same object with significantly smaller integer coefficients. We have developed and implemented an evolutionary algorithm that is able to find solutions to this problem in an efficient as well as robust way. In this paper we analyze the fitness landscapes associated with this evolutionary algorithm. We here discuss the use of three different strategies that are used to evaluate and order partial solutions. These orderings lead to different landscapes of combinations of partial solutions in which the optimal solutions are searched. We see that the choice of this ordering strategy has a huge inuence on the characteristics of the resulting landscapes, which are in this paper analyzed using a set of metrics, and also on the quality of the solutions that can be found by the subsequent evolutionary search.Ministerio de Economía y CompetitividadEuropean Regional Development FundAustrian Research Promotion Agenc

Algebraic linearizations of matrix polynomials

We show how to construct linearizations of matrix polynomials za(z)d0+c0, a(z)b(z), a(z) +b(z)(when deg (b(z))<deg (a(z))), and za(z)d0b(z) +c0from linearizations of the component parts, a(z)and b(z). This allows the extension to matrix polynomials of a new companion matrix construction.Ministerio de Economía y CompetitividadEuropean Regional Development Fund (ERDF)Part of this work was developed while R.M.Corless was visiting the University of Alcalá, in the frame of the project Giner de los Rios. We acknowledge the support of the Ontario Graduate Institution, the National Science & Engineering Research Council of Canada, the University of Alcalá, the Rotman Institute of Philosophy, the Ontario Research Centre of Computer Algebra, and Western Univ

Upper Hessenberg and Toeplitz Bohemians

We also acknowledge the support of the Ontario Graduate Institution, The National Science & Engineering Research Council of Canada, the University of Alcala, the Rotman Institute of Philosophy, the Ontario Research Centre of Computer Algebra, and Western University. Part of this work was developed while R. M. Corless was visiting the University of Alcala, in the frame of the project Giner de los Rios. J.R. Sendra is member of the Research Group ASYNACS (Ref. CT-CE2019/683).A set of matrices with entries from a fixed finite population P is called “Bohemian”. The mnemonic comes from BOunded HEight Matrix of Integers, BOHEMI, and although the population P need not be solely made up of integers, it frequently is. In this paper we look at Bohemians, specifically those with population {−1,0,+1} and sometimes other populations, for instance {0,1,i,−1,−i}. More, we specialize the matrices to be upper Hessenberg Bohemian. We then study the characteristic polynomials of these matrices, and their height, that is the infinity norm of the vector of monomial basis coefficients. Focusing on only those matrices whose characteristic polynomials have maximal height allows us to explicitly identify these polynomials and give useful bounds on their height, and conjecture an accurate asymptotic formula. The lower bound for the maximal characteristic height is exponential in the order of the matrix; in contrast, the height of the matrices remains constant. We give theorems about the number of normal matrices and the number of stable matrices in these families.Agencia Estatal de Investigació

The “Alluvial Mesovoid Shallow Substratum”, a new subterranean habitat

Received: April 5, 2013; Accepted: August 23, 2013; Published: October 4, 2013In this paper we describe a new type of subterranean habitat associated with dry watercourses in the Eastern Iberian Peninsula, the “Alluvial Mesovoid Shallow Substratum” (alluvial MSS). Historical observations and data from field sampling specially designed to study MSS fauna in the streambeds of temporary watercourses support the description of this new habitat. To conduct the sampling, 16 subterranean sampling devices were placed in a region of Eastern Spain. The traps were operated for 12 months and temperature and relative humidity data were recorded to characterise the habitat. A large number of species was captured, many of which belonged to the arthropod group, with marked hygrophilous, geophilic, lucifugous and mesothermal habits. In addition, there was also a substantial number of species showing markedly ripicolous traits. The results confirm that the network of spaces which forms in alluvial deposits of temporary watercourses merits the category of habitat, and here we propose the name of “alluvial MSS”. The “alluvial MSS” may be covered or not by a layer of soil, is extremely damp, provides a buffer against above ground temperatures and is aphotic. In addition, compared to other types of MSS, it is a very unstable habitat. It is possible that the “alluvial MSS” may be found in other areas of the world with strongly seasonal climatic regimes, and could play an important role as a biogeographic corridor and as a refuge from climatic changes.The Spanish Ministry of Science and Innovation for funded this research project (CGL2010-19924) and the Ministry of Education and Science programme "Juan de la Cierva". This research Project (CGL2010-19924) was funded by the Spanish Ministry of Science and Innovation.The Ministry of Education and Science programme "Juan de la Cierva" funded the research activity of one of the authors (A. J-V.).Peer reviewe

El nuevo paradigma de la industria 4.0 y su aplicación a la industria agroalimentaria

El concepto Industria 4.0 se corresponde con el nuevo paradigma de la industria digitalizada e interconectada. El desarrollo tecnológico que estamos viviendo permite fabricar con un nivel de valor agregado cada vez más alto, y el sector agroalimentario no es una excepción en este nuevo escenario. Se han planteado tres líneas de trabajo para desarrollar durante la investigación planificador de la demanda, mantenimiento predictivo y gestión energética inteligente. Para ello se plantearán una serie de hipótesis que se validarán mediante su aplicación en las instalaciones que Procavi tiene en su planta de Marchena. Centrándonos en la industria agroalimentaria se analizará las nuevas oportunidades y retos, evolucionar del nuevo paradigma industrial.The Industry 4.0 concept corresponds to the new paradigm of the digitalized and interconnected industry. The technological development that can currently be manufactured with a level of added value at the same time, and the agri-food sector is no exception in this new scenario. The current technological development allows manufactured with a high level of added value, and the agri-food sector is no exception in this new scenario. Three lines of work have been proposed for the development during the investigation, the demand planner, the predictive maintenance and the intelligent energy management. To this end, a series of hypotheses will be proposed that will be validated through their application in the facilities that Procavi has in Marchena. Focusing on the agri-food industry, we analyze the new opportunities and challenges, evolution of the new industrial paradigm.Plan Propio de la Universidad de Sevilla Proyecto: 2017/0000096