669 research outputs found
Limit theorems for random point measures generated by cooperative sequential adsorption
We consider a finite sequence of random points in a finite domain of a
finite-dimensional Euclidean space. The points are sequentially allocated in
the domain according to a model of cooperative sequential adsorption. The main
peculiarity of the model is that the probability distribution of a point
depends on previously allocated points. We assume that the dependence vanishes
as the concentration of points tends to infinity. Under this assumption the law
of large numbers, the central limit theorem and Poisson approximation are
proved for the generated sequence of random point measures.Comment: 17 page
Optimization Under Uncertainty Using the Generalized Inverse Distribution Function
A framework for robust optimization under uncertainty based on the use of the
generalized inverse distribution function (GIDF), also called quantile
function, is here proposed. Compared to more classical approaches that rely on
the usage of statistical moments as deterministic attributes that define the
objectives of the optimization process, the inverse cumulative distribution
function allows for the use of all the possible information available in the
probabilistic domain. Furthermore, the use of a quantile based approach leads
naturally to a multi-objective methodology which allows an a-posteriori
selection of the candidate design based on risk/opportunity criteria defined by
the designer. Finally, the error on the estimation of the objectives due to the
resolution of the GIDF will be proven to be quantifiableComment: 20 pages, 25 figure
Model selection in High-Dimensions: A Quadratic-risk based approach
In this article we propose a general class of risk measures which can be used
for data based evaluation of parametric models. The loss function is defined as
generalized quadratic distance between the true density and the proposed model.
These distances are characterized by a simple quadratic form structure that is
adaptable through the choice of a nonnegative definite kernel and a bandwidth
parameter. Using asymptotic results for the quadratic distances we build a
quick-to-compute approximation for the risk function. Its derivation is
analogous to the Akaike Information Criterion (AIC), but unlike AIC, the
quadratic risk is a global comparison tool. The method does not require
resampling, a great advantage when point estimators are expensive to compute.
The method is illustrated using the problem of selecting the number of
components in a mixture model, where it is shown that, by using an appropriate
kernel, the method is computationally straightforward in arbitrarily high data
dimensions. In this same context it is shown that the method has some clear
advantages over AIC and BIC.Comment: Updated with reviewer suggestion
Stochastic Flux-Freezing and Magnetic Dynamo
We argue that magnetic flux-conservation in turbulent plasmas at high
magnetic Reynolds numbers neither holds in the conventional sense nor is
entirely broken, but instead is valid in a novel statistical sense associated
to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The
latter phenomenon is due to the explosive separation of particles undergoing
turbulent Richardson diffusion, which leads to a breakdown of Laplacian
determinism for classical dynamics. We discuss empirical evidence for
spontaneous stochasticity, including our own new numerical results. We then use
a Lagrangian path-integral approach to establish stochastic flux-freezing for
resistive hydromagnetic equations and to argue, based on the properties of
Richardson diffusion, that flux-conservation must remain stochastic at infinite
magnetic Reynolds number. As an important application of these results we
consider the kinematic, fluctuation dynamo in non-helical, incompressible
turbulence at unit magnetic Prandtl number. We present results on the
Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate
a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of
field-line motion is an essential ingredient of both. We finally consider
briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure
Pareto versus lognormal: a maximum entropy test
It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units
Finite size effects and the order of a phase transition in fragmenting nuclear systems
We discuss the implications of finite size effects on the determination of
the order of a phase transition which may occur in infinite systems. We
introduce a specific model to which we apply different tests. They are aimed to
characterise the smoothed transition observed in a finite system. We show that
the microcanonical ensemble may be a useful framework for the determination of
the nature of such transitions.Comment: LateX, 5 pages, 5 figures; Fig. 1 change
Minkowski distances and standardisation for clustering and classification of high dimensional data
There are many distance-based methods for classification and clustering, and
for data with a high number of dimensions and a lower number of observations,
processing distances is computationally advantageous compared to the raw data
matrix. Euclidean distances are used as a default for continuous multivariate
data, but there are alternatives. Here the so-called Minkowski distances,
(city block)-, (Euclidean)-, -, -, and maximum distances are
combined with different schemes of standardisation of the variables before
aggregating them. Boxplot transformation is proposed, a new transformation
method for a single variable that standardises the majority of observations but
brings outliers closer to the main bulk of the data. Distances are compared in
simulations for clustering by partitioning around medoids, complete and average
linkage, and classification by nearest neighbours, of data with a low number of
observations but high dimensionality. The -distance and the boxplot
transformation show good results.Comment: Preliminary version; final version to be published by Springer, using
Springer's svmult LATEX styl
Breakup Density in Spectator Fragmentation
Proton-proton correlations and correlations of protons, deuterons and tritons
with alpha particles from spectator decays following 197Au + 197Au collisions
at 1000 MeV per nucleon have been measured with two highly efficient detector
hodoscopes. The constructed correlation functions, interpreted within the
approximation of a simultaneous volume decay, indicate a moderate expansion and
low breakup densities, similar to assumptions made in statistical
multifragmentation models.
PACS numbers: 25.70.Pq, 21.65.+f, 25.70.Mn, 25.75.GzComment: 11 pages, LaTeX with 3 included figures; Also available from
http://www-kp3.gsi.de/www/kp3/aladin_publications.htm
Mass dependence of light nucleus production in ultrarelativistic heavy ion collisions
Light nuclei can be produced in the central reaction zone via coalescence in
relativistic heavy ion collisions. E864 at BNL has measured the production of
ten light nuclei with nuclear number of A=1 to A=7 at rapidity and
. Data were taken with a Au beam of momentum of 11.5 A
on a Pb or Pt target with different experimental settings. The
invariant yields show a striking exponential dependence on nuclear number with
a penalty factor of about 50 per additional nucleon. Detailed analysis reveals
that the production may depend on the spin factor of the nucleus and the
nuclear binding energy as well.Comment: (6 pages, 3 figures), some changes on text, references and figures'
lettering. To be published in PRL (13Dec1999
Tight Finite-Key Analysis for Quantum Cryptography
Despite enormous progress both in theoretical and experimental quantum
cryptography, the security of most current implementations of quantum key
distribution is still not established rigorously. One of the main problems is
that the security of the final key is highly dependent on the number, M, of
signals exchanged between the legitimate parties. While, in any practical
implementation, M is limited by the available resources, existing security
proofs are often only valid asymptotically for unrealistically large values of
M. Here, we demonstrate that this gap between theory and practice can be
overcome using a recently developed proof technique based on the uncertainty
relation for smooth entropies. Specifically, we consider a family of
Bennett-Brassard 1984 quantum key distribution protocols and show that security
against general attacks can be guaranteed already for moderate values of M.Comment: 11 pages, 2 figure
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