La correspondencia entre Robert Moray y Christiaan Huygens (1661-1669): encuentros y desencuentros en la promoción del conocimiento

Sir Robert Moray (1608/9-1673) fue un soldado, cortesano y "hombre de ciencia" escocés, que estuvo en el exilio durante el período de Oliver Cromwell. Poco después de su regreso a Inglaterra en 1660 y gracias en gran medida a su amistad con Carlos II, aparece vinculado al grupo que formará la Royal Society de Londres y será nombrado el primer presidente de la institución durante los primeros meses. Moray ha sido reconocido como una figura imprescindible para entender la consolidación de la Royal Society. Establece, además, una correspondencia muy importante con Christiaan Huygens, en donde aparecen tratados temas de gran relevancia en la década de 1660, tales como la determinación de la longitud en el mar mediante el uso del reloj de péndulo y la construcción y experimentación con la máquina neumática (emblema del proyecto experimental de Robert Boyle). En esta correspondencia aparecen reflejadas, así mismo, las tensiones sobre los problemas de prioridad en diferentes áreas de conocimiento. Una de estas agrias polémicas es la que enfrenta a James Gregory y a Huygens, que acabará con la relación epistolar entre Moray y el sabio holandés.

El reposo en agitación y el impulso de juego: algunas reflexiones sobre las teorías de B. Pascal y F. Schiller acerca del fracaso del proyecto humano

[spa] Revisar los Pensamientos de Pascal y las Cartas sobre la educación estética del hombre de Schiller constituye siempre un reto. Las teoríass de Pascal acerca del juego han sido analizadas fundamentalmente desde un punto de vista matemático, y pocas veces lo han sido desde un enfoque más antropológico y filosófico. El objetivo del presente artículo es reflexionar sobre sus papeles respectivos en la creación de un nuevo paradigma sobre el juego y leer cada uno de ellos a partir de las teorías del otro. Tal vez des este modo pueda probarse que ambos comparten un mismo proyecto irrealizable de lo humano. [eng] Reviewing the Thoughts by Pascal and the Letters on the Aesthetic Education of Man by Schiller is always a challenge. Pascal"s theories about play have been analyzed primarily from a mathematical point of view, and very few times have been examined from an anthropological and philosophical approach. The aim of this paper is to reflect on their respective roles in the creation of a new paradigm about play, and read each of them from the theories of the other. Perhaps in this way it might be proved that both share an unfeasible project about the human nature.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

Contribució de Pietro Mengoli al concepte de límit a través d'una teoria de les quasi proporcions

El treball de recerca que aquí es presenta és l’estudi dels tres primers "elementa" de la "Geometriae Speciosae Elementa" (Bolonya, 1659) de Pietro Mengoli (1625-1686), que fou possiblement el deixeble més original de Bonaventura Cavalieri (1598-1647). En aquesta obra Mengoli desenvolupa un nou mètode per calcular quadratures utilitzant una teoria numèrica anomenada de “quasi proporcions”. Mengoli fonamenta les quasi proporcions en la teoria de proporcions del llibre cinquè dels "Elements" d’Euclides, a la qual hi afegeix unes nocions originals: raó “quasi nul•la”, “quasi infinita” i “quasi un nombre”. Una exhaustiva anàlisi d’aquesta teoria demostra l’originalitat de l’obra de Mengoli tant pel que fa a la seva forma d’exposició com pel que fa al seu contingut.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Anàlisi de la controvèrsia L'Hôpital - Bernoulli

El 1696 el Marquès de L'Hôpital publicà el primer tractat sistemàtic sobre càlcul diferencial, l'"Analyse des infiniments petits", que es basava en les "Lectiones de calculo differentialium" de Johann Bernoulli. Però podem parlar d'aportacions originals per part de L'Hôpital? L'objectiu d'aquest treball de recerca és comparar el contingut i la forma de l'Analyse i de les Lectiones i detectar possibles influències d'altres autors per intentar, finalment, donar una resposta a aquesta qüestió.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

Green vs. Lempert functions: a minimal example

The Lempert function for a set of poles in a domain of Cn at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z, and majorizes the corresponding multi-pole pluricomplex Green function. Coman proved that both coincide in the case of sets of two poles in the unit ball. We give an example of a set of three poles in the unit ball where this equality fails.

La carta de poblament de Xodos : documentació, història i usos socials del català al País Valencià des de l'edat mitjana fins al segle XX

Edició filològica de la carta de poblament de Xodos (l'Alcalatén, País Valencià) a partir d'un manuscrit inèdit de 1625, conservat a la mateixa població. Inclou un estudi introductori que fa especial referència a aspectes relacionats amb la Història de la llengua catalana. Pretén aportar dades que reforcen la tesi que la catalanitat lingüística i l'adscripció dialectal de l'Alcalatén depenen, sobretot, de les repoblacions posteriors i no pas del repartiment territorial medieval; mostrar l'evolució del binomi llengua i poder en les relacions entre administradors i administrats al País Valencià; i estudiar els avanços i els retrocessos de l'ús públic del català.Altres objectius són: datar correctament la carta de poblament; relacionar l'ús de les llengües (aragonès, castellà, català i llatí) amb el context històric i sociocultural de cada època; il·lustrar la llarga presència del llatí en el llenguatge administratiu; i posar a l'abast del públic la documentació estudiada.

Prominent use of distal 5’ transcription start sites and discovery of a large number of additional exons in ENCODE regions

This report presents systematic empirical annotation of transcript products from 399 annotated protein-coding loci across the 1% of the human genome targeted by the Encyclopedia of DNA elements (ENCODE) pilot project using a combination of 5' rapid amplification of cDNA ends (RACE) and high-density resolution tiling arrays. We identified previously unannotated and often tissue- or cell-line-specific transcribed fragments (RACEfrags), both 5' distal to the annotated 5' terminus and internal to the annotated gene bounds for the vast majority (81.5%) of the tested genes. Half of the distal RACEfrags span large segments of genomic sequences away from the main portion of the coding transcript and often overlap with the upstream-annotated gene(s). Notably, at least 20% of the resultant novel transcripts have changes in their open reading frames (ORFs), most of them fusing ORFs of adjacent transcripts. A significant fraction of distal RACEfrags show expression levels comparable to those of known exons of the same locus, suggesting that they are not part of very minority splice forms. These results have significant implications concerning (1) our current understanding of the architecture of protein-coding genes; (2) our views on locations of regulatory regions in the genome; and (3) the interpretation of sequence polymorphisms mapping to regions hitherto considered to be "noncoding," ultimately relating to the identification of disease-related sequence alterations.

GENCODE: producing a reference annotation for ENCODE

Background: The GENCODE consortium was formed to identify and map all protein-coding genes within the ENCODE regions. This was achieved by a combination of initial manualannotation by the HAVANA team, experimental validation by the GENCODE consortium and a refinement of the annotation based on these experimental results.Results: The GENCODE gene features are divided into eight different categories of which onlythe first two (known and novel coding sequence) are confidently predicted to be protein-codinggenes. 5’ rapid amplification of cDNA ends (RACE) and RT-PCR were used to experimentallyverify the initial annotation. Of the 420 coding loci tested, 229 RACE products have beensequenced. They supported 5’ extensions of 30 loci and new splice variants in 50 loci. In addition,46 loci without evidence for a coding sequence were validated, consisting of 31 novel and 15putative transcripts. We assessed the comprehensiveness of the GENCODE annotation byattempting to validate all the predicted exon boundaries outside the GENCODE annotation. Outof 1,215 tested in a subset of the ENCODE regions, 14 novel exon pairs were validated, only twoof them in intergenic regions.Conclusions: In total, 487 loci, of which 434 are coding, have been annotated as part of theGENCODE reference set available from the UCSC browser. Comparison of GENCODEannotation with RefSeq and ENSEMBL show only 40% of GENCODE exons are contained withinthe two sets, which is a reflection of the high number of alternative splice forms with uniqueexons annotated. Over 50% of coding loci have been experimentally verified by 5’ RACE forEGASP and the GENCODE collaboration is continuing to refine its annotation of 1% humangenome with the aid of experimental validation.

Gene finding in the chicken genome

Background: Despite the continuous production of genome sequence for a number of organisms,reliable, comprehensive, and cost effective gene prediction remains problematic. This is particularlytrue for genomes for which there is not a large collection of known gene sequences, such as therecently published chicken genome. We used the chicken sequence to test comparative andhomology-based gene-finding methods followed by experimental validation as an effective genomeannotation method.Results: We performed experimental evaluation by RT-PCR of three different computational genefinders, Ensembl, SGP2 and TWINSCAN, applied to the chicken genome. A Venn diagram wascomputed and each component of it was evaluated. The results showed that de novo comparativemethods can identify up to about 700 chicken genes with no previous evidence of expression, andcan correctly extend about 40% of homology-based predictions at the 5' end.Conclusions: De novo comparative gene prediction followed by experimental verification iseffective at enhancing the annotation of the newly sequenced genomes provided by standardhomology-based methods.

Speed Dating y el mercado de solteros

Encontrar tu media naranja ocupa recursos, es un hecho crucial en el ser humano ser capaz de optimizarlos y hacer una elección que, como demostraremos, es racional aunque parezca que el amor sea ilógico.Considerando los posibles candidatos parte de la oferta y/o la demanda, los economistas crean modelos para explicar un mercadomatrimonial en el que la base de estudio son los clientes de Speed Dating, un sistema de citas rápidas. Siendo ésta la base principal,nuestro objetivo es realizar un proyecto en el que seamos capaces de establecer un prototipo de cliente, tanto femenino como masculino observando los posibles sesgos que tal población pueda mostrar para estudios de inferencia estadística sobre la población de los solteros.Las diferencias entre sexos son una motivación esencial, preguntarnos si puede marcar una diferencia en el punto de partida también. Éstas y demás preguntas las resolveremos en las siguientes páginas, ¿sabéis que en realidad nos unen más aspectos que el estado civil?, ¿no essospechoso que seamos aparentemente tan iguales?Si realmente la guerra de sexos existe aquí demostramos que avanzamos en aras de la igualdad: Los solteros del Speed Dating tienen altos niveles de estudios, dedican su tiempo de ocio a actividades culturales y de entretenimiento y disponen de una mentalidad abierta.La paz es posible pero no deja de implicar la incertidumbre sobre si una diferencia es positiva o negativa, cuestiones morales a parte. Si los candidatos de un sexo determinado superan al contrario, es lógico que, al haber mayor competencia busquen la diferenciación como ventaja comparativa para acceder a mejores términos de comercio, así que si no existe tal diferencia puede ser por dos motivos: realmente la igualdad impera en la sociedad como estudios sociológicos determinan, resaltando la homogamia, concepto propio de un mercado matrimonial “sin restricciones” o quizás, la heterogamia en las uniones está quedando en segundo lado, perdiendo en términos de apertura social.