80,384 research outputs found

    Queues and risk processes with dependencies

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    We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential distributions introduced in [12]. In this setting, we obtain the steady state waiting time distribution and we show that the classical relation between the steady state waiting time and the workload distributions re- mains valid when the independence assumption is relaxed. We also prove duality results with the ruin functions in an ordinary and a delayed ruin process. These extend several known dualities between queueing and risk models in the independent case. Finally we show that there exist stochastic order relations between the waiting times under various instances of correlation

    Bose-Einstein correlations for Levy stable source distributions

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    The peak of the two-particle Bose-Einstein correlation functions has a very interesting structure. It is often believed to have a multivariate Gaussian form. We show here that for the class of stable distributions, characterized by the index of stability 0<α≤20 < \alpha \le 2, the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of α=2\alpha = 2. We give examples for the Bose-Einstein correlation functions for univariate as well as multivariate stable distributions, and check the model against two-particle correlation data.Comment: 30 pages, 1 figure, an important misprint in former eqs. (37-38) and other minor misprints are corrected, citations update

    SKIRT: the design of a suite of input models for Monte Carlo radiative transfer simulations

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    The Monte Carlo method is the most popular technique to perform radiative transfer simulations in a general 3D geometry. The algorithms behind and acceleration techniques for Monte Carlo radiative transfer are discussed extensively in the literature, and many different Monte Carlo codes are publicly available. On the contrary, the design of a suite of components that can be used for the distribution of sources and sinks in radiative transfer codes has received very little attention. The availability of such models, with different degrees of complexity, has many benefits. For example, they can serve as toy models to test new physical ingredients, or as parameterised models for inverse radiative transfer fitting. For 3D Monte Carlo codes, this requires algorithms to efficiently generate random positions from 3D density distributions. We describe the design of a flexible suite of components for the Monte Carlo radiative transfer code SKIRT. The design is based on a combination of basic building blocks (which can be either analytical toy models or numerical models defined on grids or a set of particles) and the extensive use of decorators that combine and alter these building blocks to more complex structures. For a number of decorators, e.g. those that add spiral structure or clumpiness, we provide a detailed description of the algorithms that can be used to generate random positions. Advantages of this decorator-based design include code transparency, the avoidance of code duplication, and an increase in code maintainability. Moreover, since decorators can be chained without problems, very complex models can easily be constructed out of simple building blocks. Finally, based on a number of test simulations, we demonstrate that our design using customised random position generators is superior to a simpler design based on a generic black-box random position generator.Comment: 15 pages, 4 figures, accepted for publication in Astronomy and Computin

    Recent advances in directional statistics

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    Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

    Enhancing the significance of gravitational wave bursts through signal classification

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    The quest to observe gravitational waves challenges our ability to discriminate signals from detector noise. This issue is especially relevant for transient gravitational waves searches with a robust eyes wide open approach, the so called all- sky burst searches. Here we show how signal classification methods inspired by broad astrophysical characteristics can be implemented in all-sky burst searches preserving their generality. In our case study, we apply a multivariate analyses based on artificial neural networks to classify waves emitted in compact binary coalescences. We enhance by orders of magnitude the significance of signals belonging to this broad astrophysical class against the noise background. Alternatively, at a given level of mis-classification of noise events, we can detect about 1/4 more of the total signal population. We also show that a more general strategy of signal classification can actually be performed, by testing the ability of artificial neural networks in discriminating different signal classes. The possible impact on future observations by the LIGO-Virgo network of detectors is discussed by analysing recoloured noise from previous LIGO-Virgo data with coherent WaveBurst, one of the flagship pipelines dedicated to all-sky searches for transient gravitational waves
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