536 research outputs found
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
Affine equivariant rank-weighted L-estimation of multivariate location
In the multivariate one-sample location model, we propose a class of flexible
robust, affine-equivariant L-estimators of location, for distributions invoking
affine-invariance of Mahalanobis distances of individual observations. An
involved iteration process for their computation is numerically illustrated.Comment: 16 pages, 4 figures, 6 table
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
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
Temperatures of Exploding Nuclei
Breakup temperatures in central collisions of 197Au + 197Au at bombarding
energies E/A = 50 to 200 MeV were determined with two methods. Isotope
temperatures, deduced from double ratios of hydrogen, helium, and lithium
isotopic yields, increase monotonically with bombarding energy from 5 MeV to 12
MeV, in qualitative agreement with a scenario of chemical freeze-out after
adiabatic expansion. Excited-state temperatures, derived from yield ratios of
states in 4He, 5Li, 6Li, and 8Be, are about 5 MeV, independent of the
projectile energy, and seem to reflect the internal temperature of fragments at
their final separation from the system.
PACS numbers: 25.70.Mn, 25.70.Pq, 25.75.-qComment: 10 pages, RevTeX with 4 included figures; Also available from
http://www-kp3.gsi.de/www/kp3/aladin_publications.htm
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
Thermal and Chemical Freeze-out in Spectator Fragmentation
Isotope temperatures from double ratios of hydrogen, helium, lithium,
beryllium, and carbon isotopic yields, and excited-state temperatures from
yield ratios of particle-unstable resonances in 4He, 5Li, and 8Be, were
determined for spectator fragmentation, following collisions of 197Au with
targets ranging from C to Au at incident energies of 600 and 1000 MeV per
nucleon. A deviation of the isotopic from the excited-state temperatures is
observed which coincides with the transition from residue formation to
multi-fragment production, suggesting a chemical freeze-out prior to thermal
freeze-out in bulk disintegrations.Comment: 14 pages, 10 figures, submitted to Phys. Rev. C, small changes as
suggested by the editors and referee
Detecting the start of an influenza outbreak using exponentially weighted moving average charts
Background. Influenza viruses cause seasonal outbreaks in temperate climates, usually during winter and early spring, and are endemic in tropical climates. The severity and length of influenza outbreaks vary from year to year. Quick and reliable detection of the start of an outbreak is needed to promote public health measures. Methods. We propose the use of an exponentially weighted moving average (EWMA) control chart of laboratory confirmed influenza counts to detect the start and end of influenza outbreaks. Results. The chart is shown to provide timely signals in an example application with seven years of data from Victoria, Australia. Conclusions. The EWMA control chart could be applied in other applications to quickly detect influenza outbreaks
Isospin influences on particle emission and critical phenomenon in nuclear dissociation
Features of particle emission and critical point behavior are investigated as
functions of the isospin of disassembling sources and temperature at a moderate
freeze-out density for medium-size Xe isotopes in the framework of isospin
dependent lattice gas model. Multiplicities of emitted light particles,
isotopic and isobaric ratios of light particles show the strong dependence on
the isospin of the dissociation source, but double ratios of light isotope
pairs and the critical temperature determined by the extreme values of some
critical observables are insensitive to the isospin of the systems. Values of
the power law parameter of cluster mass distribution, mean multiplicity of
intermediate mass fragments (), information entropy () and Campi's
second moment () also show a minor dependence on the isospin of Xe
isotopes at the critical point. In addition, the slopes of the average
multiplicites of the neutrons (), protons (), charged particles
(), and IMFs (), slopes of the largest fragment mass number
(), and the excitation energy per nucleon of the disassembling source
() to temperature are investigated as well as variances of the
distributions of , , , , and . It
is found that they can be taken as additional judgements to the critical
phenomena.Comment: 9 Pages, 8 figure
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