Introduction to the Maple Power Tool Intpakx

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented. (C) 2011 Elsevier B.V. All rights reserved.

Incorporating variable peak -to -daily ratios in the equilibrium traffic assignment procedure of the Florida Standard Urban Transportation Modeling Structure (FSUTMS)

The standard highway assignment model in the Florida Standard Urban Transportation Modeling Structure (FSUTMS) is based on the equilibrium traffic assignment method. This method involves running several iterations of all-or-nothing capacity-restraint assignment with an adjustment of travel time to reflect delays encountered in the associated iteration. The iterative link time adjustment process is accomplished through the Bureau of Public Roads (BPR) volume-delay equation. Since FSUTMS' traffic assignment procedure outputs daily volumes, and the input capacities are given in hourly volumes, it is necessary to convert the hourly capacities to their daily equivalents when computing the volume-to-capacity ratios used in the BPR function. The conversion is accomplished by dividing the hourly capacity by a factor called the peak-to-daily ratio, or referred to as CONFAC in FSUTMS. The ratio is computed as the highest hourly volume of a day divided by the corresponding total daily volume. ^ While several studies have indicated that CONFAC is a decreasing function of the level of congestion, a constant value is used for each facility type in the current version of FSUTMS. This ignores the different congestion level associated with each roadway and is believed to be one of the culprits of traffic assignment errors. Traffic counts data from across the state of Florida were used to calibrate CONFACs as a function of a congestion measure using the weighted least squares method. The calibrated functions were then implemented in FSUTMS through a procedure that takes advantage of the iterative nature of FSUTMS' equilibrium assignment method. ^ The assignment results based on constant and variable CONFACs were then compared against the ground counts for three selected networks. It was found that the accuracy from the two assignments was not significantly different, that the hypothesized improvement in assignment results from the variable CONFAC model was not empirically evident. It was recognized that many other factors beyond the scope and control of this study could contribute to this finding. It was recommended that further studies focus on the use of the variable CONFAC model with recalibrated parameters for the BPR function and/or with other forms of volume-delay functions. ^

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Finite-temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential that is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak-coupling Gross-Pitaevskii regime to the strong-coupling, fermionic Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center.

Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

SCANNERS: constraining the phase diagram of a complex scalar singlet at the LHC

We present the first version of a new tool to scan the parameter space of generic scalar potentials, SCANNERS (Coimbra et al., SCANNERS project., 2013). The main goal of SCANNERS is to help distinguish between different patterns of symmetry breaking for each scalar potential. In this work we use it to investigate the possibility of excluding regions of the phase diagram of several versions of a complex singlet extension of the Standard Model, with future LHC results. We find that if another scalar is found, one can exclude a phase with a dark matter candidate in definite regions of the parameter space, while predicting whether a third scalar to be found must be lighter or heavier. The first version of the code is publicly available and contains various generic core routines for tree level vacuum stability analysis, as well as implementations of collider bounds, dark matter constraints, electroweak precision constraints and tree level unitarity.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Primary Disorders of Neurotransmitter Metabolism: Experience of a Tertiary Center

Neurotransmitter diseases are a group of inherited disorders attributable to a disturbance of neurotransmitter metabolism. Biogenic amines are neurotransmitters with multiple roles including psychomotor function, hormone secretion, cardiovascular, respiratory and gastrointestinal control, sleep mechanisms, body temperature and pain. Given the multiple functions of monoamines, disorders of their metabolism comprise a wide spectrum of manifestations, with motor dysfunction being the most prominent clinical feature. Methods: Case review of 12 patients from 4 families, with primary disorders of biogenic amine metabolism. Results: Aromatic L-amino acid decarboxylase deficiency (4 patients from 2 families), and GTP-cyclohydrolase (8 patients from 2 families) were the two diseases identified. Age at first symptoms varied between 2 months and 6 years. Developmental delay was present in all cases except 2 patients with GTP cyclohydrolase deficiency. The combination of axial hypotonia and limb dystonia was also frequent. Children with aromatic L-amino acid decarboxylase deficiency exhibited temperature instability, oculogyric crisis and disturbances of sleep. The index case of one family with GTP cyclohydrolase deficiency presented with Parkinsonism (bradykinesia, rigidity and hypomimia). Analysis of neurotransmitters and their metabolites in CSF was crucial for the identification of index cases. Response to therapy was variable but in general unsatisfactory except in a family with GTP cyclohydrolase deficiency. Conclusions: These disorders should be considered in the differential diagnosis of paediatric neurodegenerative diseases, in order to allow an adequate therapeutic trial that can favor prognosis.

Plasmacytoid dendritic cells: one-trick ponies or workhorses of the immune system?

Plasmacytoid dendritic cells (pDCs) were first described as interferon-producing cells and, for many years, their overlapping characteristics with both lymphocytes and classical dendritic cells (cDCs) created confusion over their exact ontogeny. In this Viewpoint article, Nature Reviews Immunology asks five leaders in the field to discuss their thoughts on the development and functions of pDCs--do these cells serve mainly as a major source of type I interferons or do they also make other important contributions to immune responses?

On the configuration of Herman rings of meromorphic functions

We prove some results concerning the possible configuration s of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period a nd give a sufficient condition for a configuration to be realizable.

Linking landscape- and population ecology for large population management modelling: the case of Ibex (capra ibex) in Switzerland

La biologie de la conservation est communément associée à la protection de petites populations menacées d?extinction. Pourtant, il peut également être nécessaire de soumettre à gestion des populations surabondantes ou susceptibles d?une trop grande expansion, dans le but de prévenir les effets néfastes de la surpopulation. Du fait des différences tant quantitatives que qualitatives entre protection des petites populations et contrôle des grandes, il est nécessaire de disposer de modèles et de méthodes distinctes. L?objectif de ce travail a été de développer des modèles prédictifs de la dynamique des grandes populations, ainsi que des logiciels permettant de calculer les paramètres de ces modèles et de tester des scénarios de gestion. Le cas du Bouquetin des Alpes (Capra ibex ibex) - en forte expansion en Suisse depuis sa réintroduction au début du XXème siècle - servit d?exemple. Cette tâche fut accomplie en trois étapes : En premier lieu, un modèle de dynamique locale, spécifique au Bouquetin, fut développé : le modèle sous-jacent - structuré en classes d?âge et de sexe - est basé sur une matrice de Leslie à laquelle ont été ajoutées la densité-dépendance, la stochasticité environnementale et la chasse de régulation. Ce modèle fut implémenté dans un logiciel d?aide à la gestion - nommé SIM-Ibex - permettant la maintenance de données de recensements, l?estimation automatisée des paramètres, ainsi que l?ajustement et la simulation de stratégies de régulation. Mais la dynamique d?une population est influencée non seulement par des facteurs démographiques, mais aussi par la dispersion et la colonisation de nouveaux espaces. Il est donc nécessaire de pouvoir modéliser tant la qualité de l?habitat que les obstacles à la dispersion. Une collection de logiciels - nommée Biomapper - fut donc développée. Son module central est basé sur l?Analyse Factorielle de la Niche Ecologique (ENFA) dont le principe est de calculer des facteurs de marginalité et de spécialisation de la niche écologique à partir de prédicteurs environnementaux et de données d?observation de l?espèce. Tous les modules de Biomapper sont liés aux Systèmes d?Information Géographiques (SIG) ; ils couvrent toutes les opérations d?importation des données, préparation des prédicteurs, ENFA et calcul de la carte de qualité d?habitat, validation et traitement des résultats ; un module permet également de cartographier les barrières et les corridors de dispersion. Le domaine d?application de l?ENFA fut exploré par le biais d?une distribution d?espèce virtuelle. La comparaison à une méthode couramment utilisée pour construire des cartes de qualité d?habitat, le Modèle Linéaire Généralisé (GLM), montra qu?elle était particulièrement adaptée pour les espèces cryptiques ou en cours d?expansion. Les informations sur la démographie et le paysage furent finalement fusionnées en un modèle global. Une approche basée sur un automate cellulaire fut choisie, tant pour satisfaire aux contraintes du réalisme de la modélisation du paysage qu?à celles imposées par les grandes populations : la zone d?étude est modélisée par un pavage de cellules hexagonales, chacune caractérisée par des propriétés - une capacité de soutien et six taux d?imperméabilité quantifiant les échanges entre cellules adjacentes - et une variable, la densité de la population. Cette dernière varie en fonction de la reproduction et de la survie locale, ainsi que de la dispersion, sous l?influence de la densité-dépendance et de la stochasticité. Un logiciel - nommé HexaSpace - fut développé pour accomplir deux fonctions : 1° Calibrer l?automate sur la base de modèles de dynamique (par ex. calculés par SIM-Ibex) et d?une carte de qualité d?habitat (par ex. calculée par Biomapper). 2° Faire tourner des simulations. Il permet d?étudier l?expansion d?une espèce envahisseuse dans un paysage complexe composé de zones de qualité diverses et comportant des obstacles à la dispersion. Ce modèle fut appliqué à l?histoire de la réintroduction du Bouquetin dans les Alpes bernoises (Suisse). SIM-Ibex est actuellement utilisé par les gestionnaires de la faune et par les inspecteurs du gouvernement pour préparer et contrôler les plans de tir. Biomapper a été appliqué à plusieurs espèces (tant végétales qu?animales) à travers le Monde. De même, même si HexaSpace fut initialement conçu pour des espèces animales terrestres, il pourrait aisément être étndu à la propagation de plantes ou à la dispersion d?animaux volants. Ces logiciels étant conçus pour, à partir de données brutes, construire un modèle réaliste complexe, et du fait qu?ils sont dotés d?une interface d?utilisation intuitive, ils sont susceptibles de nombreuses applications en biologie de la conservation. En outre, ces approches peuvent également s?appliquer à des questions théoriques dans les domaines de l?écologie des populations et du paysage.<br/><br/>Conservation biology is commonly associated to small and endangered population protection. Nevertheless, large or potentially large populations may also need human management to prevent negative effects of overpopulation. As there are both qualitative and quantitative differences between small population protection and large population controlling, distinct methods and models are needed. The aim of this work was to develop theoretical models to predict large population dynamics, as well as computer tools to assess the parameters of these models and to test management scenarios. The alpine Ibex (Capra ibex ibex) - which experienced a spectacular increase since its reintroduction in Switzerland at the beginning of the 20th century - was used as paradigm species. This task was achieved in three steps: A local population dynamics model was first developed specifically for Ibex: the underlying age- and sex-structured model is based on a Leslie matrix approach with addition of density-dependence, environmental stochasticity and culling. This model was implemented into a management-support software - named SIM-Ibex - allowing census data maintenance, parameter automated assessment and culling strategies tuning and simulating. However population dynamics is driven not only by demographic factors, but also by dispersal and colonisation of new areas. Habitat suitability and obstacles modelling had therefore to be addressed. Thus, a software package - named Biomapper - was developed. Its central module is based on the Ecological Niche Factor Analysis (ENFA) whose principle is to compute niche marginality and specialisation factors from a set of environmental predictors and species presence data. All Biomapper modules are linked to Geographic Information Systems (GIS); they cover all operations of data importation, predictor preparation, ENFA and habitat suitability map computation, results validation and further processing; a module also allows mapping of dispersal barriers and corridors. ENFA application domain was then explored by means of a simulated species distribution. It was compared to a common habitat suitability assessing method, the Generalised Linear Model (GLM), and was proven better suited for spreading or cryptic species. Demography and landscape informations were finally merged into a global model. To cope with landscape realism and technical constraints of large population modelling, a cellular automaton approach was chosen: the study area is modelled by a lattice of hexagonal cells, each one characterised by a few fixed properties - a carrying capacity and six impermeability rates quantifying exchanges between adjacent cells - and one variable, population density. The later varies according to local reproduction/survival and dispersal dynamics, modified by density-dependence and stochasticity. A software - named HexaSpace - was developed, which achieves two functions: 1° Calibrating the automaton on the base of local population dynamics models (e.g., computed by SIM-Ibex) and a habitat suitability map (e.g. computed by Biomapper). 2° Running simulations. It allows studying the spreading of an invading species across a complex landscape made of variously suitable areas and dispersal barriers. This model was applied to the history of Ibex reintroduction in Bernese Alps (Switzerland). SIM-Ibex is now used by governmental wildlife managers to prepare and verify culling plans. Biomapper has been applied to several species (both plants and animals) all around the World. In the same way, whilst HexaSpace was originally designed for terrestrial animal species, it could be easily extended to model plant propagation or flying animals dispersal. As these softwares were designed to proceed from low-level data to build a complex realistic model and as they benefit from an intuitive user-interface, they may have many conservation applications. Moreover, theoretical questions in the fields of population and landscape ecology might also be addressed by these approaches.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Jumps in the Volatility of Financial Markets.

Recent work suggests that the conditional variance of financial returns may exhibit sudden jumps. This paper extends a non-parametric procedure to detect discontinuities in otherwise continuous functions of a random variable developed by Delgado and Hidalgo (1996) to higher conditional moments, in particular the conditional variance. Simulation results show that the procedure provides reasonable estimates of the number and location of jumps. This procedure detects several jumps in the conditional variance of daily returns on the S&P 500 index.

Characterization of polycystin-1 in ADPKD pathogenetic mechanism : biogenesis and functional implications by genetic approaches in mouse

La polykystose rénale autosomique dominante (ADPKD) est une des maladies génétiques les plus communes. ADPKD se manifeste le plus souvent au stade adulte par la présence de kystes rénaux, et bien souvent de kystes hépatiques, avec une progression très variable. ADPKD mène à une insuffisance rénale: les seuls recours sont la dialyse puis la transplantation rénale. Les mutations dispersées sur les gènes PKD1 (majoritairement; la protéine polycystine-1, PC1) et PKD2 (la protéine polycystine-2, PC2) sont responsables de l’ADPKD. Le mécanisme pathogénétique de perte de fonction (LOF) et donc d’un effet récessif cellulaire est évoqué comme causatif de l’ADPKD. LOF est en effet supporté par les modèles murins d’inactivation de gènes PKD1/PKD2, qui développent de kystes, quoique in utéro et avec une rapidité impressionnante dans les reins mais pas dans le foie. Malgré de nombreuses études in vitro, le rôle de PC1/PC2 membranaire/ciliaire reste plutôt hypothétique et contexte-dépendant. Ces études ont associé PC1/PC2 à une panoplie de voies de signalisation et ont souligné une complexité structurelle et fonctionnelle exceptionnelle, dont l’implication a été testée notamment chez les modèles de LOF. Toutefois, les observations patho-cellulaires chez l’humain dont une expression soutenue, voire augmentée, de PKD1/PC1 et l’absence de phénotypes extrarénaux particuliers remet en question l’exclusivité du mécanisme de LOF. Il était donc primordial 1) d’éclaircir le mécanisme pathogénétique, 2) de générer des outils in vivo authentiques d’ADPKD en terme d’initiation et de progression de la maladie et 3) de mieux connaitre les fonctions des PC1/PC2 indispensables pour une translation clinique adéquate. Cette thèse aborde tous ces points. Tout d’abord, nous avons démontré qu’une augmentation de PKD1 endogène sauvage, tout comme chez l’humain, est pathogénétique en générant et caractérisant en détail un modèle murin transgénique de Pkd1 (Pkd1TAG). Ce modèle reproduit non seulement les caractéristiques humaines rénales, associées aux défauts du cil primaire, mais aussi extrarénales comme les kystes hépatiques. La sévérité du phénotype corrèle avec le niveau d’expression de Pkd1 ce qui supporte fortement un modèle de dosage. Dans un deuxième temps, nous avons démontré par les études de complémentations génétiques que ces deux organes reposent sur une balance du clivage GPS de Pc1, une modification post-traductionelle typique des aGPCR, et dont l’activité et l’abondance semblent strictement contrôlées. De plus, nous avons caractérisé extensivement la biogénèse de Pc1 et de ses dérivés in vivo générés suite au clivage GPS. Nous avons identifié une toute nouvelle forme et prédominante à la membrane, la forme Pc1deN, en plus de confirmer deux fragments N- et C-terminal de Pc1 (NTF et CTF, respectivement) qui eux s’associent de manière non-covalente. Nous avons démontré de façon importante que le trafic de Pc1deN i.e., une forme NTF détachée du CTF, est toutefois dépendant de l’intégrité du fragment CTF in vivo. Par la suite, nous avons généré un premier modèle humanisant une mutation PKD1 non-sens tronquée au niveau du domaine NTF(E3043X) en la reproduisant chez une souris transgénique (Pkd1extra). Structurellement, cette mutation, qui mimique la forme Pc1deN, s’est également avérée causative de PKD. Le modèle Pkd1extra a permis entre autre de postuler l’existence d’une cross-interaction entre différentes formes de Pc1. De plus, nos deux modèles murins sont tous les deux associés à des niveaux altérés de c-Myc et Pc2, et soutiennent une implication réelle de ces derniers dans l’ADPKD tou comme une interaction fonctionnelle entre les polycystines. Finalement, nous avons démontré un chevauchement significatif entre l’ADPKD et le dommage rénal aigüe (ischémie/AKI) dont une expression augmentée de Pc1 et Pc2 mais aussi une stimulation de plusieurs facteurs cystogéniques tel que la tubérine, la β-caténine et l’oncogène c-Myc. Nos études ont donc apporté des évidences cruciales sur la contribution du gène dosage dans l’ADPKD. Nous avons développé deux modèles murins qui serviront d’outil pour l’analyse de la pathologie humaine ainsi que pour la validation préclinique ADPKD. L’identification d’une nouvelle forme de Pc1 ajoute un niveau de complexité supplémentaire expliquant en partie une capacité de régulation de plusieurs voies de signalisation par Pc1. Nos résultats nous amènent à proposer de nouvelles approches thérapeutiques: d’une part, le ciblage de CTF i.e., de style chaperonne, et d’autre part le ciblage de modulateurs intracellulaires (c-Myc, Pc2, Hif1α). Ensemble, nos travaux sont d’une importance primordiale du point de vue informatif et pratique pour un avancement vers une thérapie contre l’ADPKD. Le partage de voies communes entre AKI et ADPKD ouvre la voie aux approches thérapeutiques parallèles pour un traitement assurément beaucoup plus rapide.