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In the last few years, the importance of neoantigens in the development of personalized antitumor vaccines has increased remarkably. In order to study whether bioinformatic tools are effective in detecting neoantigens that generate an immune response, DNA samples from patients with cutaneous melanoma in different stages were obtained, resulting in a total of 6048 potential neoantigens gathered. Thereafter, the immunological responses generated by some of those neoantigens ex vivo were tested, using a vaccine designed by a new optimization approach and encapsulated in nanoparticles. Our bioinformatic analysis indicated that no differences were found between the number of neoantigens and that of non-mutated sequences detected as potential binders by IEDB tools. However, those tools were able to highlight neoantigens over non-mutated peptides in HLA-II recognition (p-value 0.03). However, neither HLA-I binding affinity (p-value 0.08) nor Class I immunogenicity values (p-value 0.96) indicated significant differences for the latter parameters. Subsequently, the new vaccine, using aggregative functions and combinatorial optimization, was designed. The six best neoantigens were selected and formulated into two nanoparticles, with which the immune response ex vivo was evaluated, demonstrating a specific activation of the immune response. This study reinforces the use of bioinformatic tools in vaccine development, as their usefulness is proven both in silico and ex vivo.

The inverse Galois problem wonders about the question whether any given finite group is isomorphic to the Galois group of a Galois extension. In this article, we will prove the Kronecker-Weber theorem, or in other words, that any abelian finite group is isomorphic to the Galois group of a Galois extension over Q: In this article, a number of concepts and brush-strokes of the necessary results to supportthis proof will be mentioned and presented: first, certain fundamental results of algebra, corresponding to polynomials and congruences; then, the fundamental definitions and theorems of Galois theory, and some notes of cyclotomic extensions; and finally, Kronecker-Weber theorem will be enunciated and proved, taking into account all the previous results.; Galoisen alderantzizko problema honetan datza: talde (finitu) bat emanda, Ga loisen hedadura bat ea existitzen den zehaztea, zeinentzat hedadura horri dagokion Galoisen taldea hasieran emandako taldearen isomorfoa baita. Artikulu honen helburua izango da Kro necker Weberren teorema frogatzea, edo, bestera esanda, edozein talde abeldar finitu Q-ren gai neko Galoisen hedadura baten Galoisen taldearen isomorfoa dela frogatzea. Artikulu honetan, froga horri eusteko beharrezkoak diren hainbat kontzeptu eta emaitzen pintzelkadak aipatuko eta aurkeztuko dira: hasteko, aljebraren oinarrizko zenbait emaitza, polinomioei eta kongruentziei dagozkionak, azalduko dira; gero, Galoisen teoriaren oinarrizko definizio eta teoremak eta heda dura ziklotomikoen inguruko apunte batzuk aurkeztuko dira; eta, azkenik, Kronecker -Weberren teorema enuntziatu eta frogatuko da, aurretik azaldutako emaitza guztiak aintzat harturik.

In this work we present a methodology of “learning by example” assisted by computers in the study of mathematics. We propose the use of mathematical computational packages to program applets aimed to solve mathematical problems. Each time the student runs the applet, a new random instance of the problem is generated, and he is guided, step by step to solve it. The student can repeat the process as many times as necessary until his knowledge is consolidated, by taking a more active role in the process after the first repetitions of several instances.

In this work we present the development and preliminary evaluation of several problem-based video podcasts addressed to students of the subject “Coding and Cryptography”. Specifically, this experiment has been carried out with the students of both the Bachelor’s degree in Mathematics and the Master’s degree of Mathematical Research and Modelling, Statistics and Computation, at the University of the Basque Country (UPV/EHU). Our results suggest that students found these complementary videos helpful for their learning process, indicating that this methodology could be appropriate for subjects treating complex concepts, such as those in the last years of degree or in master courses.

The main aim of this work is to describe the process by which some students, participating in a teaching experiment, recreate with guidance material and personal attendance some advanced concepts at the doctoral level. More precisely, the students deal with concepts related to pure abstract algebra, beginning with an exploration of the well known mathematical game of the Hanoi Towers on the three rods.

Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the ornessa measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.

Lan honek, nolabait ere, greziarrek aztertu eta garatu zuten marrazketa teknikoari mugak jartzea du helburutzat. Izan ere, erregela eta konpasa soilik erabiliz egin zitezkeen gauzak greziarrek ondo asko ezagutzen zituzten, baina ez zuten irizpiderik tresna hauekin egin ezin zitekeena aztertzeko. Horregatik, eraikuntza geometrikoak aztertzeko guk erabiliko dugun baliabidea oso modernoa izango da greziarrekin alderatuta: Galoisen teoria. Teoria honek eraikuntza geometrikoekin duen harremana izango da lan honen ardatz nagusia.

Duración (en horas): De 41 a 50 horas Destinatario: Estudiante, En el primer cuatrimestre del segundo curso del Grado de Matemáticas se imparte la asignatura obligatoria "Estructuras Algebraicas", cuyo conocimiento permite a los alumnos familiarizarse con los conceptos básicos de distintas estructuras algebraicas, y especialmente con la de "grupo". El estudio de este concepto y de sus propiedades se hace básicamente centrándonos en una diversidad muy amplia de ejemplos clásicos y no clásicos de grupos. Esta asignatura tiene una relación muy estrecha, entre otras, con las asignaturas "Ecuaciones Algebraicas" y "Algebra conmutativa" que se estudian en el tercer curso del Grado de Matemáticas. Se plantea desarrollar la metodología ABP en un 30% de la asignatura y en varios tipos de clases: magistrales, prácticas de aula y seminarios. A los alumnos el primer día de clase se les presenta un problema, llamado "el problema estructurante", cuyo estudio y análisis va a permitir que éstos de manera autónoma desarrollen las bases de la teoría de grupos, así como el crear algunos modelos teóricos de grupos del cubo de Rubik, como pueden ser los puzles. El principal objetivo no es ni mucho menos dar solución al cubo de Rubik, sino que valiéndonos de él, poder llegar a entender nociones básicas y propiedades de grupos, y de simetrías, entre otros. Los conocimientos tanto teóricos, como los procedimientos que se utilizarán para la interpretación de los resultados obtenidos serán siempre elaborados en equipo. Al finalizar el periodo del estudio del problema estructurante, los alumnos en equipo presentarán un informe que analice y dé respuesta a la siguiente pregunta: ¿cuánto de verdad hay en la leyenda, de que detrás del cubo de Rubik hay mucha matemática? En dicho informe se determinarán a su vez, los aspectos matemáticos desarrollados y tratados en el proceso, que han sido realmente válidos para dar una respuesta intuitiva a la pregunta formulada, así como las mayores carencias y dificultades con las que los alumnos se han encontrado a la hor

Hasteko, lehenengo Kapituluan Talde Teoriako oinarrizko kontzeptuak gogoratuko dira. Baita, garrantzi handia duen finituki sortuak diren talde abeldarren egitura teorema estudiatuko da. Memoria honen Bigarren Kapituluan, Sylow-en Teoremen ezagutza aztertuko da eta Sylow-en Teoremen ondorio interesgarri bat guztiz garatuta aurkeztuko da, aplikazio gisa. Orain, Hirugarren Kapituluan guretzat guztiz berria den gai bat aztertuko da: talde nilpotenteak, hain zuzen ere. Azkenik, lanaren Laugarren Kapitulua hiru zatitan banatuko da: alde batetik, talde ebazgarrien oinarriak, Pi-taldeak eta bukatzeko, talde ebazgarri finituen Hall-en Pi-azpitaldeak.