Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

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.

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Una aproximació al pensament algebraic a l'Espanya del segle XVI: estudi del manuscrit 2294 de la Biblioteca de la Universitat de Salamanca

Aquest treball analitza el “Tratado y libro de arte mayor o álgebra” que forma part del manuscrit 2294 de la Biblioteca de la Universitat de Salamanca, datat el 1590. El seu autor és Diego Pérez de Mesa. L’objectiu d’aquest estudi és aportar nous elements que ajudin a entendre quin era l’estatus de l’àlgebra a la Península Ibèrica en un segle que va ser clau en el seu desenvolupament. Primer es descriu el manuscrit i després es reflexiona sobre les seves aportacions a la matemàtica, mostrant algunes característiques originals d’aquesta àlgebra enfront d’altres àlgebres de la Península Ibèrica del segle XVI.

Validity, reliability and responsiveness of the French language translation of the Western Ontario Shoulder Instability Index (WOSI).

BACKGROUND: The WOSI (Western Ontario Shoulder Instability Index) is a self-administered quality of life questionnaire designed to be used as a primary outcome measure in clinical trials on shoulder instability, as well as to measure the effect of an intervention on any particular patient. It is validated and is reliable and sensitive. As it is designed to measure subjective outcome, it is important that translation should be methodologically rigorous, as it is subject to both linguistic and cultural interpretation. OBJECTIVE: To produce a French language version of the WOSI that is culturally adapted to both European and North American French-speaking populations. MATERIALS AND METHODS: A validated protocol was used to create a French language WOSI questionnaire (WOSI-Fr) that would be culturally acceptable for both European and North American French-speaking populations. Reliability and responsiveness analyses were carried out, and the WOSI-Fr was compared to the F-QuickDASH-D/S (Disability of the Arm, Shoulder and Hand-French translation), and Walch-Duplay scores. RESULTS: A French language version of the WOSI (WOSI-Fr) was accepted by a multinational committee. The WOSI-Fr was then validated using a total of 144 native French-speaking subjects from Canada and Switzerland. Comparison of results on two WOSI-Fr questionnaires completed at a mean interval of 16 days showed that the WOSI-Fr had strong reliability, with a Pearson and interclass correlation of r=0.85 (P=0.01) and ICC=0.84 [95% CI=0.78-0.88]. Responsiveness, at a mean 378.9 days after surgical intervention, showed strong correlation with that of the F-QuickDASH-D/S, with r=0.67 (P<0.01). Moreover, a standardized response means analysis to calculate effect size for both the WOSI-Fr and the F-QuickDASH-D/S showed that the WOSI-Fr had a significantly greater ability to detect change (SRM 1.55 versus 0.87 for the WOSI-Fr and F-QuickDASH-D/S respectively, P<0.01). The WOSI-Fr showed fair correlation with the Walch-Duplay. DISCUSSION: A French-language translation of the WOSI questionnaire was created and validated for use in both Canadian and Swiss French-speaking populations. This questionnaire will facilitate outcome assessment in French-speaking settings, collaboration in multinational studies and comparison between studies performed in different countries. TYPE OF STUDY: Multicenter cohort study. LEVEL OF EVIDENCE: II.

Comprehensive Expression Analyses of Neural Cell-Type-Specific miRNAs Identify New Determinants of the Specification and Maintenance of Neuronal Phenotypes.

MicroRNAs (miRNAs) have been shown to play important roles in both brain development and the regulation of adult neural cell functions. However, a systematic analysis of brain miRNA functions has been hindered by a lack of comprehensive information regarding the distribution of miRNAs in neuronal versus glial cells. To address this issue, we performed microarray analyses of miRNA expression in the four principal cell types of the CNS (neurons, astrocytes, oligodendrocytes, and microglia) using primary cultures from postnatal d 1 rat cortex. These analyses revealed that neural miRNA expression is highly cell-type specific, with 116 of the 351 miRNAs examined being differentially expressed fivefold or more across the four cell types. We also demonstrate that individual neuron-enriched or neuron-diminished RNAs had a significant impact on the specification of neuronal phenotype: overexpression of the neuron-enriched miRNAs miR-376a and miR-434 increased the differentiation of neural stem cells into neurons, whereas the opposite effect was observed for the glia-enriched miRNAs miR-223, miR-146a, miR-19, and miR-32. In addition, glia-enriched miRNAs were shown to inhibit aberrant glial expression of neuronal proteins and phenotypes, as exemplified by miR-146a, which inhibited neuroligin 1-dependent synaptogenesis. This study identifies new nervous system functions of specific miRNAs, reveals the global extent to which the brain may use differential miRNA expression to regulate neural cell-type-specific phenotypes, and provides an important data resource that defines the compartmentalization of brain miRNAs across different cell types.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Native language, spoken language, translation and trade

We construct new series for common native language and common spoken language for 195 countries, which we use together with series for common official language and linguis-tic proximity in order to draw inferences about (1) the aggregate impact of all linguistic factors on bilateral trade, (2) whether the linguistic influences come from ethnicity and trust or ease of communication, and (3) in so far they come from ease of communication, to what extent trans-lation and interpreters play a role. The results show that the impact of linguistic factors, all together, is at least twice as great as the usual dummy variable for common language, resting on official language, would say. In addition, ease of communication is far more important than ethnicity and trust. Further, so far as ease of communication is at work, translation and inter-preters are extremely important. Finally, ethnicity and trust come into play largely because of immigrants and their influence is otherwise difficult to detect.

Native language, spoken language, translation and trade

We construct new series for common native language and common spoken language for 195 countries, which we use together with series for common official language and linguis-tic proximity in order to draw inferences about (1) the aggregate impact of all linguistic factors on bilateral trade, (2) whether the linguistic influences come from ethnicity and trust or ease of communication, and (3) in so far they come from ease of communication, to what extent trans-lation and interpreters play a role. The results show that the impact of linguistic factors, all together, is at least twice as great as the usual dummy variable for common language, resting on official language, would say. In addition, ease of communication is far more important than ethnicity and trust. Further, so far as ease of communication is at work, translation and inter-preters are extremely important. Finally, ethnicity and trust come into play largely because of immigrants and their influence is otherwise difficult to detect.

A Framework for Analyzing Language and Welfare

The paper proposes a general model that will encompass trade and social benefits of a common language, a preference for a variety of languages, the fundamental role of translators, an emotional attachment to maternal language, and the threat that globalization poses to the vast majority of languages. With respect to people’s emotional attachment, the model considers minorities to suffer losses from the subordinate status of their language. In addition, the model treats the threat to minority language as coming from the failure of the parents in the minority to transmit their maternal language (durably) to their children. Some familiar results occur. In particular, we encounter the usual social inefficiencies of decentralized solutions to language learning when the sole benefits of the learning are communicative benefits (though translation intervenes). However, these social inefficiencies assume a totally different air when the con-sumer gains of variety are brought in. One fundamental aim of the paper is to bring together contributions to the economics of language from labor economics, network externalities and international trade that are typically treated separately.