Probabilistic and analytic aspects of Boolean functions

This thesis will focus on the study of Boolean functions. In point of fact, they can be represented with a Fourier expansion and many of the definitions and results for these functions can be rewritten in terms of the Fourier coefficients. The definition of Boolean functions is simple, this implies that they have a natural interpretation and hence have applications in many areas of scientific research. Specifically, in this thesis we will see applications in Social Choice Theory, Theoretical Computer Science and Combinatorics. For the first area, we will see and prove with Fourier analysis Arrow's theorem and KKL theorem in order to show that it is not possible to define a perfect voting election system from an ethical standpoint. Additionally, we will translate the proof presented by Arrow for his own theorem in terms of mathematical language. The work for the second application will follow the steps to prove Sensitivity Conjecture which, although it has remained unsolved for 30 years, Huang has presented a brilliant short proof in a paper published at Annals of Mathematics very recently (2019). For the last area we will present the strange phenomena of thresholds in Random Graph properties and we will show Margulis-Russo Formula to study this event in terms of Boolean functions Fourier analysis

Numerical simulation of sea waves and their impact against breakwaters for assessing coastal protection systems

Aquest treball estudia la propagació d’ones i la seva interacció amb estructures sòlides utilitzant un innovador mètode numèric, el Particle Finite Element Method (PFEM). Un mètode numèric és un model de simulació equivalent a un físic capaç de recrear la realitat. Per validar el mètode numèric a l’àrea d’aplicació, aquest projecte compara els resultats obtinguts en PFEM amb resultats experimentals d’anàlisis a laboratoris. També els compara amb resultats d’un altre mètode numèric, el Eulerià Finite Element Method (FEM). Per fer-ho, quatre diferents anàlisis es duen a terme. Els dos primers estudiant el cas d’ones solitàries, el tercer estudia un tren d’ones i el Quart analitza un tren d’ones que impacta amb un trencaonades.Este trabajo estudia la propagación de olas y su interacción con estructuras sólidas usando un innovador método numérico, el Particle Finite Element Method (PFEM). Un método numérico es un modelo de simulación equivalente a uno físico capaz de recrear la realidad. Para validar el método numérico en el área de aplicación, este proyecto compara los resultados obtenidos en PFEM con resultados experimentales de análisis en laboratorios. También los compara con resultados de otro método numérico, el Euleriano Finite Element Method (FEM). Para hacerlo, cuatro diferentes análisis se llevan a cabo. Los dos primeros estudian el caso de olas solitarias, el tercero estudia un tren de olas y el cuarto analiza un tren de olas que impacta en un rompeolas.This work studies water waves propagation and their interaction with solid structures using an innovative numerical method, the Particle Finite Element Method (PFEM). A numerical method is a simulation model equivalent to a physical one able of simulating reality. To validate the numerical method in the given area of application, this project compares the results obtained by PFEM with experimental results from laboratory analysis. It also compares the results with the ones conducted with another numerical method, the Eulerian Finite Element Method (FEM). To do so, four different analyses are performed. The first two analyse the case of solitary waves, the third analyse a wave train and the fourth anayse a wave train that impacts with a breakwater

Aplicació de la química analítica a l'estudi de vidres antics

Aquest es un recull (amb 42 referències) d'articles sobre 1'aplicació de l'anàlisi química a l'estudi de vidres antics. Després d'examinar l'estructura i composició del vidre citem les tècniques utilitzades en la datació del vidre, els processor d'alteració química que pateixen els vidres per causa d'agents externs i els mètodes actuals emprats per a la seva anàlisi qualitativa i quantitativa. Finalment, comentem els mètodes de determinació de l'origen geogràfic dels vidres. Els vidres medievals són els més estudiats degut a la seva importància artística.This is a review (with 42 references) about the chemical analysis application in the study of the ancient glasses. After the examine the glass structure and composition, we appoint the techniques used for glass dating, the processes of the chemical alteration of the glass caused by externs agents and the actual methods used to determine their qualitative and quantitative anlysis. At last, we appoint the methods of geographic source determination of the glass. The medieval glasses are the most studied ones due to their artistic importance

Ricard Lamote de Grignon i l'Orquestra Simfònica de Girona

Después de diversas iniciativas ciudadanas de principios del s. XX, en 1929 se creó la Orquestra Simfònica de Girona, ligada en cierto modo a l'Associació de Música, fundada en 1922; fue su presidente Josep M. Dalmau i Casademont, quien logró crear la orquesta. Su primer director fue Ismael Granero, músico de la guarnición militar de Girona; desde la primavera de 1932 se hizo cargo de la dirección Ricard Lamote de Grignon, que imprimió un ritmo creciente de calidad interpretativa y variedad de repertorio, con numerosas primeras audiciones y estrenos. La vida de la orquesta terminó en 1937, debido a la Guerra Civil. (F.B.B.)À la suite d'initiatives diverses entreprises dans la ville au début du XXè siècle, l'Orchestre Symphonique de Gérone est créée en 1929, liée d'une certaine façon à l'Associació de Música, fondée en 1922; son président, Josep M. Dalmau i Casademont est le fondateur de cet orchestre. Son premier directeur est Ismael Granero, musicien de la garnison militaire de Gérone; au printemps 1932, la direction est à la charge de Ricard Lamote de Grignon à qui l'on doit le rythme croissant de la qualité de ses interprétations et la variété du répertoire, ainsi que de nombreuses premières auditions et inaugurations. La vie de l'orchestre s'achève en 1937 en raison de la guerre civile. (F.B.B.)After numerous grassroots initiatives at the beginning of the 20th century, in 1929 the Symphonyc Orchestra of Girona was founded, linked to a certain degree to the l'Associació de Música, founded in 1922, whose president Josep M. Dalmau i Casademont, set up the orchestra. Its first conductor was Ismael Granero, a musician from the Girona military establishment. From the spring of 1932, the conductor was Ricard Lamote de Grignon, who imposed on the orchestra an increasing degree of interpretational quality and variety of repertoire, with numerous first performances. The life of the orchestra ended in 1937, due to the civil war. (F.B.B.)Nach verschiedenen Bürgerinitiativen am Anfang des 20. Jahrhunderts wurde 1929 das Sinfonieorchester von Girona gegründet, welches sich auf gewisser Weise an den 1922 gegründeten l'Associació de Música (Musikverband) bindet; sein Vorsitzender war Josep M. Dalmau i Casademont, dem es gelang, das Orchester zu gründen. Sein erster Dirigent war Ismael Granero, Musik aus der Militärgarnison von Girona; ab Frühling 1932 wurde es dann von Ricard Lamote de Grignon dirigiert, der einen steigenden Rhythmus von darstellender Qualität und Vielfalt im Repertoire mit zahlreichen ersten Konzerten und Premieren. Das Orchesterleben endete 1937 aufgrund des Bürgerkrieges. (F.B.B.

2,2′,2′′,2′′′-[Pyridine-2,6-diylbis(methyl­ene­nitrilo)]tetra­ethanol

In the crystal structure of the title compound C15H27N3O4, the mol­ecule is located on a twofold axis and the asymmetric unit contains one half-mol­ecule, with one N and one C atom lying on the rotation axis. The pyridine ring is the hydrogen-bond acceptor, while two hydroxyl O atoms act as hydrogen-bond donors in intra­molecular O—H⋯N and intermolecular O—H⋯N and O—H⋯O hydrogen bonds, thereby forming a closed hydrogen-bonded cage

The Zinc-Dependent Protease Activity of the Botulinum Neurotoxins

The botulinum neurotoxins (BoNT, serotypes A-G) are some of the most toxic proteins known and are the causative agents of botulism. Following exposure, the neurotoxin binds and enters peripheral cholinergic nerve endings and specifically and selectively cleaves one or more SNARE proteins to produce flaccid paralysis. This review centers on the kinetics of the Zn-dependent proteolytic activities of these neurotoxins, and briefly describes inhibitors, activators and factors underlying persistence of toxin action. Some of the structural, enzymatic and inhibitor data that are discussed here are available at the botulinum neurotoxin resource, BotDB (http://botdb.abcc.ncifcrf.gov)

Oxidative stress induced by the Fe2+/ascorbic acid system or model ischemia in vitro: effect of carvedilol and pyridoindole antioxidant SMe1EC2 in young and adult rat brain tissue

New effective strategies and new highly effective neuroprotective agents are being searched for the therapy of human stroke and cerebral ischemia. The compound SMe1EC2 is a new derivative of stobadine, with enhanced antioxidant properties compared to the maternal drug. Carvedilol, a non-selective beta-blocker, possesses besides its cardioprotective and vasculoprotective properties also an antioxidant effect. We compared the effect of carvedilol and SMe1EC2, antioxidants with a similar chemical structure, in two experimental models of oxidative stress in young and adult rat brain tissue. SMe1EC2 was found to improve the resistance of hippocampal neurons to ischemia in vitro in young and even in 18-month-old rats and inhibited formation of protein carbonyl groups induced by the Fe2+/ascorbic acid pro-oxidative system in brain cortex homogenates of young rats. Carvedilol exerted a protective effect only in the hippocampus of 2-month-old rats and that at the concentration 10-times higher than did SMe1EC2. The inhibitory effect of carvedilol on protein carbonyl formation induced by the pro-oxidative system was not proved in the cortex of either young or adult rats. An increased baseline level of the content of protein carbonyl groups in the adult versus young rat brain cortex confirmed age-related changes in neuronal tissue and may be due to increased production of reactive oxygen species and low antioxidant defense mechanisms in the adult rat brain. The results revealed the new pyridoindole SMe1EC2 to be more effective than carvedilol in neuroprotection of rat brain tissue in both experimental models involving oxidative stress