Dynamics in Thompson's group F

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson’s group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

The Perception of the Elements in the Hindu Traditions

The essays in this volume, contributions to an international symposium at the University of Lausanne in June 1998, represent the perception of the elements as a framework for the history of religions (Maya Burger), exemplified by the Hindu traditions. Each element is treated by a specialist in a different academic field in order to bring out a variety of approaches important to the discipline of the history of religion. Ether (akasa) was assigned to philosophy (Wilhelm Halbfass), wind to the history of religion (Bettina Bäumer), fire to classical philology (Peter Schreiner), water to a specialist on Indian medicine (Arion Rosu) and earth to anthropology (Gabriella Eichinger Ferro-Luzzi, specializing on Tamil literature). Les articles du présent volume, issus d'un symposium international ayant eu lieu à l'Université de Lausanne en juin 1998, présentent la perception des éléments comme base de recherche de l'étude des religions (Maya Burger), exemplifiée à l'aide des traditions hindoues. Chaque élément est traité par un spécialiste d'une discipline académique particulière dans le but de souligner la variété des approches nécessaire à la discipline d'histoire des religions. L'éther (akasa) a été considéré sous l'angle de la philosophie (Wilhelm Halbfass), le vent sous celui de l'histoire des religions (Bettina Bäumer), le feu sous celui de la philologie classique (Peter Schreiner), l'eau par un spécialiste de la médecine indienne (Arion Rosu) et la terre sous l'angle de l'anthropologie (Gabriella Eichinger Ferro-Luzzi, se concentrant sur la littérature tamoule).

Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.

Classificació i importància dels elements paisatgístics del territori Tsimane' segons la percepció local

En aquesta tesis es presenten els resultats de la investigació duta a terme a les comunitats indígenes Tsimane’ de l’Amazònia boliviana. La investigació estudia la percepció dels indígenes sobre l’etnoclassificació del seu territori. S’estableix una clau de classificació i es determina la importància dels elements paisatgístics del territori Tsimane’ segons la percepció local. Aquesta informació permetrà integrar el coneixement local dins dels programes de desenvolupament integral i de planificació territorial en l’Amazònia Boliviana. L’estudi conclou que la població Tsimane’ classifica els elements paisatgístics del seu entorn en 89 taques conformades per una espècies arbòria dominant i que estan incloses en un o més dels nou paisatges identificats: Därsi Därä, Sajras, Sinues Ojñi’, Mayes, Múcúya, Tsäquis Därä, Cum, Tajñi’ i Jaman. A partir d’un anàlisi multicriteri s’ha determinat una importància total per cada paisatge segons els següents criteris d’importància: diversitat de taques, activitats econòmiques realitzables, presència espiritual, percepció individual i importància relativa segons els altres paisatges. Així doncs s’ha trobat que el paisatge més important és el Därsi Därä (bosc primari caracteritzat per un estrat arbori superior a 50 metres d’altura). També s’han analitzat les dades discernint segons el gènere de l’entrevistat i segons la proximitat de les comunitats estudiades a la ciutat més propera.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

The Perception of the Elements in the Hindu Traditions

The essays in this volume, contributions to an international symposium at the University of Lausanne in June 1998, represent the perception of the elements as a framework for the history of religions (Maya Burger), exemplified by the Hindu traditions. Each element is treated by a specialist in a different academic field in order to bring out a variety of approaches important to the discipline of the history of religion. Ether (akasa) was assigned to philosophy (Wilhelm Halbfass), wind to the history of religion (Bettina Bäumer), fire to classical philology (Peter Schreiner), water to a specialist on Indian medicine (Arion Rosu) and earth to anthropology (Gabriella Eichinger Ferro-Luzzi, specializing on Tamil literature). Les articles du présent volume, issus d'un symposium international ayant eu lieu à l'Université de Lausanne en juin 1998, présentent la perception des éléments comme base de recherche de l'étude des religions (Maya Burger), exemplifiée à l'aide des traditions hindoues. Chaque élément est traité par un spécialiste d'une discipline académique particulière dans le but de souligner la variété des approches nécessaire à la discipline d'histoire des religions. L'éther (akasa) a été considéré sous l'angle de la philosophie (Wilhelm Halbfass), le vent sous celui de l'histoire des religions (Bettina Bäumer), le feu sous celui de la philologie classique (Peter Schreiner), l'eau par un spécialiste de la médecine indienne (Arion Rosu) et la terre sous l'angle de l'anthropologie (Gabriella Eichinger Ferro-Luzzi, se concentrant sur la littérature tamoule).

Is the diagnostic yield of upper GI endoscopy improved by the use of explicit panel-based appropriateness criteria?

BACKGROUND: Increasing the appropriateness of use of upper gastrointestinal (GI) endoscopy is important to improve quality of care while at the same time containing costs. This study explored whether detailed explicit appropriateness criteria significantly improve the diagnostic yield of upper GI endoscopy. METHODS: Consecutive patients referred for upper GI endoscopy at 6 centers (1 university hospital, 2 district hospitals, 3 gastroenterology practices) were prospectively included over a 6-month period. After controlling for disease presentation and patient characteristics, the relationship between the appropriateness of upper GI endoscopy, as assessed by explicit Swiss criteria developed by the RAND/UCLA panel method, and the presence of relevant endoscopic lesions was analyzed. RESULTS: A total of 2088 patients (60% outpatients, 57% men) were included. Analysis was restricted to the 1681 patients referred for diagnostic upper GI endoscopy. Forty-six percent of upper GI endoscopies were judged to be appropriate, 15% uncertain, and 39% inappropriate by the explicit criteria. No cancer was found in upper GI endoscopies judged to be inappropriate. Upper GI endoscopies judged appropriate or uncertain yielded significantly more relevant lesions (60%) than did those judged to be inappropriate (37%; odds ratio 2.6: 95% CI [2.2, 3.2]). In multivariate analyses, the diagnostic yield of upper GI endoscopy was significantly influenced by appropriateness, patient gender and age, treatment setting, and symptoms. CONCLUSIONS: Upper GI endoscopies performed for appropriate indications resulted in detecting significantly more clinically relevant lesions than did those performed for inappropriate indications. In addition, no upper GI endoscopy that resulted in a diagnosis of cancer was judged to be inappropriate. The use of such criteria improves patient selection for upper GI endoscopy and can thus contribute to efforts aimed at enhancing the quality and efficiency of care. (Gastrointest Endosc 2000;52:333-41).

Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project.

We report the generation and analysis of functional data from multiple, diverse experiments performed on a targeted 1% of the human genome as part of the pilot phase of the ENCODE Project. These data have been further integrated and augmented by a number of evolutionary and computational analyses. Together, our results advance the collective knowledge about human genome function in several major areas. First, our studies provide convincing evidence that the genome is pervasively transcribed, such that the majority of its bases can be found in primary transcripts, including non-protein-coding transcripts, and those that extensively overlap one another. Second, systematic examination of transcriptional regulation has yielded new understanding about transcription start sites, including their relationship to specific regulatory sequences and features of chromatin accessibility and histone modification. Third, a more sophisticated view of chromatin structure has emerged, including its inter-relationship with DNA replication and transcriptional regulation. Finally, integration of these new sources of information, in particular with respect to mammalian evolution based on inter- and intra-species sequence comparisons, has yielded new mechanistic and evolutionary insights concerning the functional landscape of the human genome. Together, these studies are defining a path for pursuit of a more comprehensive characterization of human genome function.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

Explicit methods for Hilbert modular forms

We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.