Oinarrizko estatistika: R praktikak

228 p.Zalantza barik, arlo anitzetan agertzen den interes handiko irakasgaia da Estatistika. Are gehiago, jakintza-arlo guztietan hartzen da aintzat: Zientziak, Osasun Zientziak, Ingeniaritza eta Arkitektura, Gizarte eta Lege Zientziak, eta Giza Zientziak, hain zuzen ere. Gaur egun, gauza jakina da ezinbestekoa dela softwarea erabiltzea heziketa-prozesuan. Ikasmaterial honetan, Estatistika lantzeko hamazazpi praktika adierazten dira R programaren bidez. R da analisi estatistiko eta grafikoetara bideraturiko programa eta programazio-hizkuntza. Proiektua irekia eta doan banatzen dena da (GNU General Public Licence deritzon litzentziak ezarritako irizpideen arabera), eta Linux, Windows eta Macintosh sistemetarako aurki daiteke. Aucland Unibertsitateko Ross Ihaka eta Robert Gentleman irakasleek sortu zuten 1992. urtean; egun, R-ren Garapenerako Talde Nuklear (“R Development Core Team” ingelesez) izenarekin ezagutzen diren estatistikan aditu batzuk, “developers” deritzenak, arduratzen dira programaren banaketaz eta garapenaz. Gero eta maizago erabiltzen ari den programa da, bai irakaskuntza-mailan (ASA saria jaso du), bai ikerkuntzarako, eta bai enpresa-arloan ere. Izan ere, R edozein erabiltzailek heda dezake haiek sortutako pakete edo eraskinen bidez. Ikasmaterial hau idazteko momentuan, eskuragai dauden pakete kopurua ia ia 10.000koa da, bere hazkundea esponentziala izanik. Programaren inguruko hasierako ikaskuntza/ezagutza fasea gainditu ostean, R-ren erabilera erraza da. Gainera, Rcmdr paketea instalatuz, interfaze grafiko bat erabiltzeko aukera dugu, programa komertzialen itxura lortuz. EHUko Medikuntza Fakultateko José Ramón Ruedari eta Borja Santosi esker eskuragarri dugu, egun, Rcmdr paketearen euskarazko bertsio bat, eta, ikasmaterial honetan, bertsio hori erabiliko dugu

Sudokoa: denbora-pasa edo zientzia?

Testu honetan, sudoku munduaren atea zabaldu nahi dugu, bai jokua fenomeno modura ikusita, bai eta jokuak Zientzarekin eta bereziki Programazio Matematikoa, Konbinatoria eta Talde Teoria arloekin duen loturaren aldetik. Zein ote da jokoaren konplexutasun konputazionala? Ekuazio-sistema sinple baten bidez adieraz ote daiteke sudokua? Zenbat denbora beharko du programa batek sudoku bat ebazteko? Ba al dago munduan zailena den sudoku bat? Zenbat soluzio daude? Ezagutzen da beharrezkoa den sarrera kopuru gutxienezkoa? Galdera hauek erantzuten saiatuko gara, gaur egungo logikan oinarritutako denbora-pasa honen zaletasunean eta ikerkuntza mailan sortutako interesari erreparatuz

Matematika diskretua

172 p.Aurkibidea: I) Konbinatoria: 1. Oinarrizko konbinatoria. 2. Konbinazio-identitateak. 3. Funtzio sortzaileak eta errepikapenak. 4. Zenbait zenbaki-familia garrantzitsu. II) Grafo-teoria: 5. Grafo-teoria. III) Ariketak: A. Zenbait ariketaren ebazpenak. B. Ariketen zenbakizko soluzioak. IV) Bibliografia

Matematika diskretua

172 p.Aurkibidea: I) Konbinatoria: 1. Oinarrizko konbinatoria. 2. Konbinazio-identitateak. 3. Funtzio sortzaileak eta errepikapenak. 4. Zenbait zenbaki-familia garrantzitsu. II) Grafo-teoria: 5. Grafo-teoria. III) Ariketak: A. Zenbait ariketaren ebazpenak. B. Ariketen zenbakizko soluzioak. IV) Bibliografia

A note on the implementation of the BFC-MSMIP algorithm in C++ by using COIN-OR as an optimization engine

The aim of this technical report is to present some detailed explanations in order to help to understand and use the algorithm Branch and Fix Coordination for solving MultiStage Mixed Integer Problems (BFC- MSMIP). We have developed an algorithmic approach implemented in a C++ experimental code that uses the optimization engine COmputational INfrastructure for Operations Research (COIN-OR) for solving the auxiliary linear and mixed 0-1 submodels. Now, we give the computational and implementational descrip- tion in order to use this open optimization software not only in the implementation of our procedure but also in similar schemes to be developed by the users.nonanticipativity constraints, cluster partitioning, COIN-OR library, branch-and-fix coordination, multi-stage stochastic mixed 0-1 programming

A parallelizable algorithmic framework for solving large scale multi-stage stochastic mixed 0-1 problems under uncertainty

Preprint submitted to Computers & Operations Researchmulti-stage stochastic mixed 0-1 optimization, nonsymmetric scenario trees, implicit and explicit nonanticipativity constraints, splitting variable and compact representations, scenario cluster partitioning

A mathematical analysis of EDAs with distance-based exponential models

Estimation of Distribution Algorithms have been successfully used to solve permutation-based Combinatorial Optimization Problems. In this case, the algorithms use probabilistic models specifically designed for codifying probability distributions over permutation spaces. One class of these probability models are distance-based exponential models, and one example of this class is the Mallows model. In spite of its practical success, the theoretical analysis of Estimation of Distribution Algorithms for permutation-based Combinatorial Optimization Problems has not been developed as extensively as it has been for binary problems. With this motivation, this paper presents a first mathematical analysis of the convergence behavior of Estimation of Distribution Algorithms based on Mallows models. The model removes the randomness of the algorithm in order to associate a dynamical system to it. Several scenarios of increasing complexity with different fitness functions and initial probability distributions are analyzed. The obtained results show: a) the strong dependence of the final results on the initial population, and b) the possibility to converge to non-degenerate distributions even in very simple scenarios, which has not been reported before in the literature.This research has been partially supported by Spanish Ministry of Science and Innovation through the projects PID2019-104966GB-I00/AEI/10.13039/501100011033, PID2019-104933GB-I00/AEI/10.13039/501100011033, PID2019-106453GA-I00/AEI/10.13039/501100011033 and BCAM Severo Ochoa accreditation SEV-2017-0718; and by the Basque Government through the program BERC 2022-2025 and the projects IT1504-22 and IT1494-22; and by UPV/EHU through the project GIU20/054. Imanol holds a grant from the Department of Education of the Basque Government (PRE_2021_2_0224). Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

Symmetrical Motifs in Young Children’s Drawings: A Study on Their Representations of Plant Life

Young children love drawing; this is without question. Besides that, drawings are also of interest to scholars and educators, since they seem to provide food for thought regarding children's conceptual development during their early education. Different approaches are taken when it comes to analysing children's drawings but insufficient attention has been given to the issue of the spontaneous depictions of symmetrical motifs in young children's drawings. This pictorial phenomena might not go unnoticed by parents and teachers but the fact is that the scientific community has no reliable data regarding how children under 8 naturally draw symmetrical patterns to express themselves graphically. Accordingly, the present study analyses 116 drawings undertaken by children between 4 and 7 on a well-known natural issue in early childhood such as plant life. Pictorial motifs displaying both cyclic and dihedral symmetries were found in the pictorial sample under examination and the data gathered is put in perspective with the gender and educational level variables. The results of the study show that symmetry, particularly, dihedral symmetry, is a very common pictorial practice in the sample and, also, that the occurrence of symmetrical motifs displays a relationship with the independent variables considered in the study.This study was funded by the University of the Basque Country (PES17/39)

Children’s Pictorial Expression of Plant Life and Its Connection with School-Based Greenness

Previous research highlights the positive influence that experiences in nature have on children’s physical, emotional and conceptual development. There is also evidence that indicates that the availability of green areas on school grounds is associated with pupils’ better academic performance as well as with their comprehension of wildlife. This study examines the drawings that 152 children completed with the objective of expressing their understanding of the plant world. Approximately half of the drawings were depicted by children that attend a school with green areas within the school site as well as in the surrounding area. The remaining half of the sample includes the illustrations that children attending an educational centre with, virtually, no green areas within the school premises or in the immediate vicinity. Notwithstanding the fact that the two schools involved in the study belong to a similar social context and they are relatively close to each other, the results show relevant differences between the drawings by the two groups compared, in terms of the pictorial content and the utilisation of colour. The results are discussed in light of the growing number of studies that emphasise the positive impact that close contact with nature has on children’s everyday life at school.This research was funded by the University of the Basque Country through the projects PPGA20/05, GIU20/054 and PES20/4