CM points and weight 3=2 modular forms

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Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Job accessibility and employment probability

The objective of this paper is to estimate the impact of residential job accessibility on female employment probability in the metropolitan areas of Barcelona and Madrid. Following a “spatial mismatch” framework, we estimate a female employment probability equation where variables controlling for personal characteristics, residential segregation and employment potential on public transport network are included. Data used come from Microcensus 2001 of INE (National Institute of Statistics). The research focuses on the treatment of endogeneity problems and the measurement of accessibility variables. Our results show that low job accessibility in public transport negatively affects employment probability. The intensity of this effect tends to decrease with individual’s educational attainment. A higher degree of residential segregation also reduces job probability in a significant way..

A characterization of two weight norm inequalities for maximal singular integrals

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Two weight inequalities for discrete positive operators

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Two weight inequalities for maximal truncations of dyadic Calderón-Zygmund operators

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Chebyshev-type quadrature formulas for new weight classes

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Evaluating the probability and the impact of a failure in GMPLS based networks

In this paper, we define a new scheme to develop and evaluate protection strategies for building reliable GMPLS networks. This is based on what we have called the network protection degree (NPD). The NPD consists of an a priori evaluation, the failure sensibility degree (FSD), which provides the failure probability, and an a posteriori evaluation, the failure impact degree (FID), which determines the impact on the network in case of failure, in terms of packet loss and recovery time. Having mathematical formulated these components, experimental results demonstrate the benefits of the utilization of the NPD, when used to enhance some current QoS routing algorithms in order to offer a certain degree of protection

Estimation of the probability of congestion using Monte Carlo method in OPS networks

In networks with small buffers, such as optical packet switching based networks, the convolution approach is presented as one of the most accurate method used for the connection admission control. Admission control and resource management have been addressed in other works oriented to bursty traffic and ATM. This paper focuses on heterogeneous traffic in OPS based networks. Using heterogeneous traffic and bufferless networks the enhanced convolution approach is a good solution. However, both methods (CA and ECA) present a high computational cost for high number of connections. Two new mechanisms (UMCA and ISCA) based on Monte Carlo method are proposed to overcome this drawback. Simulation results show that our proposals achieve lower computational cost compared to enhanced convolution approach with an small stochastic error in the probability estimation

Probability distribution of the radionuclide half-lives

Power law distributions, a well-known model in the theory of real random variables, characterize a wide variety of natural and man made phenomena. The intensity of earthquakes, the word frequencies, the solar ares and the sizes of power outages are distributed according to a power law distribution. Recently, given the usage of power laws in the scientific community, several articles have been published criticizing the statistical methods used to estimate the power law behaviour and establishing new techniques to their estimation with proven reliability. The main object of the present study is to go in deep understanding of this kind of distribution and its analysis, and introduce the half-lives of the radioactive isotopes as a new candidate in the nature following a power law distribution, as well as a \canonical laboratory" to test statistical methods appropriate for long-tailed distributions.

Association between GIS-based exposure to urban air pollution during pregnancy and birth weight in the INMA Sabadell Cohort

Background: There is growing evidence that traffic-related air pollution reduces birth weight. Improving exposure assessment is a key issue to advance in this research area.Objective: We investigated the effect of prenatal exposure to traffic-related air pollution via geographic information system (GIS) models on birth weight in 570 newborns from the INMA (Environment and Childhood) Sabadell cohort.Methods: We estimated pregnancy and trimester-specific exposures to nitrogen dioxide and aromatic hydrocarbons [benzene, toluene, ethylbenzene, m/p-xylene, and o-xylene (BTEX)] by using temporally adjusted land-use regression (LUR) models. We built models for NO2 and BTEX using four and three 1-week measurement campaigns, respectively, at 57 locations. We assessed the relationship between prenatal air pollution exposure and birth weight with linear regression models. We performed sensitivity analyses considering time spent at home and time spent in nonresidential outdoor environments during pregnancy.Results: In the overall cohort, neither NO2 nor BTEX exposure was significantly associated with birth weight in any of the exposure periods. When considering only women who spent < 2 hr/day in nonresidential outdoor environments, the estimated reductions in birth weight associated with an interquartile range increase in BTEX exposure levels were 77 g [95% confidence interval (CI), 7–146 g] and 102 g (95% CI, 28–176 g) for exposures during the whole pregnancy and the second trimester, respectively. The effects of NO2 exposure were less clear in this subset.Conclusions: The association of BTEX with reduced birth weight underscores the negative role of vehicle exhaust pollutants in reproductive health. Time–activity patterns during pregnancy complement GIS-based models in exposure assessment.

Outage probability analysis for MRC in η-μ fading channels with co-channel interference

Exact closed-form expressions are obtained for the outage probability of maximal ratio combining in η-μ fadingchannels with antenna correlation and co-channel interference. The scenario considered in this work assumes the joint presence of background white Gaussian noise and independent Rayleigh-faded interferers with arbitrary powers. Outage probability results are obtained through an appropriate generalization of the moment-generating function of theη-μ fading distribution, for which new closed-form expressions are provided.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning