Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

From deep seated slope deformation to rock avalanche: Destabilization and transportation models of the Sierre landslide (Switzerland)

Sackung is a widespread post-glacial morphological feature affecting Alpine mountains and creating characteristic geomorphological expression that can be detected from topography. Over long time evolution, internal deformation can lead to the formation of rapidly moving phenomena such as a rock-slide or rock avalanche. In this study, a detailed description of the Sierre rock-avalanche (SW Switzerland) is presented. This convex-shaped postglacial instability is one of the larger rock-avalanche in the Alps, involving more than 1.5 billion m3 with a run-out distance of about 14 km and extremely low Fahrböschung angle. This study presents comprehensive analyses of the structural and geological characteristics leading to the development of the Sierre rock-avalanche. In particular, by combining field observations, digital elevation model analyses and numerical modelling, the strong influence of both ductile and brittle tectonic structures on the failure mechanism and on the failure surface geometry is highlighted. The detection of pre-failure deformation indicates that the development of the rock avalanche corresponds to the last evolutionary stage of a pre-existing deep seated gravitational slope instability. These analyses accompanied by the dating and the characterization of rock avalanche deposits, allow the proposal of a destabilization model that clarifies the different phases leading to the development of the Sierre rock avalanche.

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

Redox dysregulation and oxidative stress in schizophrenia: genetic and functional anomalies of glutathione synthesis in patients and experimental models involving GABA interneurons and NMDA receptors

Objective: Converging evidence speak in favor of an abnormal susceptibility to oxidative stress in schizophrenia. A decreased level of glutathione (GSH), the principal non-protein antioxidant and redox regulator, was observed both in cerebrospinal-fluid and prefrontal cortex of schizophrenia patients (Do et al., 2000). Results: Schizophrenia patients have an abnormal GSH synthesis most likely of genetic origin: Two independent case-control studies showed a significant association between schizophrenia and a GAG trinucleotide repeat (TNR) polymorphism in the GSH key synthesizing enzyme glutamate-cysteine-ligase (GCL) catalytic subunit (GCLC) gene. The most common TNR genotype 7/7 was more frequent in controls, whereas the rarest TNR genotype 8/8 was three times more frequent in patients. The disease-associated genotypes correlated with a decrease in GCLC protein expression, GCL activity and GSH content. Such a redox dysregulation during development could underlie the structural and functional anomalies in connectivity: In experimental models, GSH deficit induced anomalies similar to those observed in patients. (a) morphology: In animal models with GSH deficit during the development we observed in prefrontal cortex a decreased dendritic spines density in pyramidal cells and an abnormal development of parvalbumine (but not of calretinine) immunoreactive GABA interneurones in anterior cingulate cortex. (b) physiology: GSH depletion in hippocampal slices induces NMDA receptors hypofunction and an impairment of long term potentiation. In addition, GSH deficit affected the modulation of dopamine on NMDA-induced Ca 2+ response in cultured cortical neurons. While dopamine enhanced NMDA responses in control neurons, it depressed NMDA responses in GSH-depleted neurons. Antagonist of D2-, but not D1-receptors, prevented this depression, a mechanism contributing to the efficacy of antipsychotics. The redox sensitive ryanodine receptors and L-type calcium channels underlie these observations. (c) cognition: Developing rats with low [GSH] and high dopamine lead deficit in olfactory integration and in object recognition which appears earlier in males that females, in analogy to the delay of the psychosis onset between man and woman. Conclusion: These clinical and experimental evidence, combined with the favorable outcome of a clinical trial with N-Acetyl Cysteine, a GSH precursor, on both the negative symptoms (Berk et al., submitted) and the mismatch negativity in an auditory oddball paradigm supported the proposal that a GSH synthesis impairment of genetic origin represent, among other factors, one major risk factor in schizophrenia.

Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Epidemic models with an infected-infectious period

The introduction of an infective-infectious period on the geographic spread of epidemics is considered in two different models. The classical evolution equations arising in the literature are generalized and the existence of epidemic wave fronts is revised. The asymptotic speed is obtained and improves previous results for the Black Death plague

PSyscal: disseny i implementació d'un sistema paral·lel per al calibratge automàtic de models P-Sistema

Es tracta d'un projecte que proposa una aplicació per al calibratge automàtic de models P-sistema. Per a fer-ho primer es farà un estudi sobre els models P-sistema i el procediment seguit pels investigadors per desenvolupar aquest tipus de models. Es desenvoluparà una primera solució sèrie per al problema, i s'analitzaran els seus punts febles. Seguidament es proposarà una versió paral·lela que millori significativament el temps d'execució, tot mantenint una alta eficiència i escalabilitat.

Disseny i implementació d'una API en Python per el processament de models de poblacions simulats mitjançant PlinguaCore

En aquest projecte, tractarem de crear una aplicació que ens permeti d'una forma ràpida i eficient, el processament dels resultats obtinguts per un eina de simulació d'ecosistemes naturals anomenada PlinguaCore .L'objectiu d'aquest tractament és doble. En primer lloc, dissenyar una API que ens permeti de forma eficient processar la gran quantitat de dades generades per simulador d'ecosistemes PlinguaCore. En segon lloc, fer que aquesta API es pugui integrar en altres aplicacions, tant de tractament de dades, com de cal·libració dels models.

Predictions from information-theoretical models of nonequilibrium radiation

The radiation distribution function used by Domínguez and Jou [Phys. Rev. E 51, 158 (1995)] has been recently modified by Domínguez-Cascante and Faraudo [Phys. Rev. E 54, 6933 (1996)]. However, in these studies neither distribution was written in terms of directly measurable quantities. Here a solution to this problem is presented, and we also propose an experiment that may make it possible to determine the distribution function of nonequilibrium radiation experimentally. The results derived do not depend on a specific distribution function for the matter content of the system

Redox dysregulation in the pathophysiology of schizophrenia and bipolar disorder: insights from animal models.

Abstract Significance: Schizophrenia (SZ) and bipolar disorder (BD) are classified as two distinct diseases. However, accumulating evidence shows that both disorders share genetic, pathological, and epidemiological characteristics. Based on genetic and functional findings, redox dysregulation due to an imbalance between pro-oxidants and antioxidant defense mechanisms has been proposed as a risk factor contributing to their pathophysiology. Recent Advances: Altered antioxidant systems and signs of increased oxidative stress are observed in peripheral tissues and brains of SZ and BD patients, including abnormal prefrontal levels of glutathione (GSH), the major cellular redox regulator and antioxidant. Here we review experimental data from rodent models demonstrating that permanent as well as transient GSH deficit results in behavioral, morphological, electrophysiological, and neurochemical alterations analogous to pathologies observed in patients. Mice with GSH deficit display increased stress reactivity, altered social behavior, impaired prepulse inhibition, and exaggerated locomotor responses to psychostimulant injection. These behavioral changes are accompanied by N-methyl-D-aspartate receptor hypofunction, elevated glutamate levels, impairment of parvalbumin GABA interneurons, abnormal neuronal synchronization, altered dopamine neurotransmission, and deficient myelination. Critical Issues: Treatment with the GSH precursor and antioxidant N-acetylcysteine normalizes some of those deficits in mice, but also improves SZ and BD symptoms when given as adjunct to antipsychotic medication. Future Directions: These data demonstrate the usefulness of GSH-deficient rodent models to identify the mechanisms by which a redox imbalance could contribute to the development of SZ and BD pathophysiologies, and to develop novel therapeutic approaches based on antioxidant and redox regulator compounds. Antioxid. Redox Signal. 18, 1428-1443.

Protective and Aggravating Effects of Nlrp3 Inflammasome Activation in IBD Models: Influence of Genetic and Environmental Factors.

Background: Inflammatory bowel disease (IBD) is characterized by chronic intestinal inflammation due to dysregulation of the mucosal immune system. The cytokines IL-1β and IL-18 appear early in intestinal inflammation and their pro-forms are processed via the caspase-1-activating multiprotein complex, the Nlrp3 inflammasome. Previously, we reported that the uptake of dextran sodium sulfate (DSS) by macrophages activates the Nlrp3 inflammasome and that Nlrp3(-/-) mice are protected in the acute DSS colitis model. Of note, other groups have reported opposing effects in regards to DSS susceptibility in Nlrp3(-/-) mice. Recently, mice lacking inflammasomes were found to develop a distinct intestinal microflora. Methods: To reconcile the contradicting observations, we investigated the role of Nlrp3 deficiency in two different IBD models: acute DSS colitis and TNBS (2,4,6-trinitrobenzene sulfonic acid)-induced colitis. In addition, we investigated the impact of the intestinal flora on disease severity by performing cohousing experiments of wild-type and Nlrp3(-/-) mice, as well as by antibiotic treatment. Results: Nlrp3(-/-) mice treated with either DSS or TNBS exhibited attenuated colitis and lower mortality. This protective effect correlated with an increased frequency of CD103+ lamina propria dendritic cells expressing a tolerogenic phenotype in Nlrp3(-/-) mice in steady state conditions. Interestingly, after cohousing, Nlrp3(-/-) mice were as susceptible as wild-type mice, indicating that transmission of endogenous bacterial flora between the two mouse strains might increase susceptibility of Nlrp3(-/-) mice towards DSS-induced colitis. Accordingly, treatment with antibiotics almost completely prevented colitis in the DSS model. Conclusions: The composition of the intestinal microflora significantly influences disease severity in IBD models comparing wild-type and Nlrp3(-/-) mice. This observation may - at least in part - explain contradictory results concerning the role of the inflammasome in different labs. Further studies are required to define the role of the Nlrp3 inflammasome in noninflamed mucosa under steady state conditions and in IBD.

Establishment of animal models to analyze the kinetics and distribution of human tumor antigen-specific CD8⁺ T cells.

Many patients develop tumor antigen-specific T cell responses detectable in peripheral blood mononuclear cells (PBMCs) following cancer vaccine. However, measurable tumor regression is observed in a limited number of patients receiving cancer vaccines. There is a need to re-evaluate systemically the immune responses induced by cancer vaccines. Here, we established animal models targeting two human cancer/testis antigens, NY-ESO-1 and MAGE-A4. Cytotoxic T lymphocyte (CTL) epitopes of these antigens were investigated by immunizing BALB/c mice with plasmids encoding the entire sequences of NY-ESO-1 or MAGE-A4. CD8(+) T cells specific for NY-ESO-1 or MAGE-A4 were able to be detected by ELISPOT assays using antigen presenting cells pulsed with overlapping peptides covering the whole protein, indicating the high immunogenicity of these antigens in mice. Truncation of these peptides revealed that NY-ESO-1-specific CD8(+) T cells recognized D(d)-restricted 8mer peptides, NY-ESO-181-88. MAGE-A4-specific CD8(+) T cells recognized D(d)-restricted 9mer peptides, MAGE-A4265-273. MHC/peptide tetramers allowed us to analyze the kinetics and distribution of the antigen-specific immune responses, and we found that stronger antigen-specific CD8(+) T cell responses were required for more effective anti-tumor activity. Taken together, these animal models are valuable for evaluation of immune responses and optimization of the efficacy of cancer vaccines.