32,042 research outputs found
On the Inversion of High Energy Proton
Inversion of the K-fold stochastic autoconvolution integral equation is an
elementary nonlinear problem, yet there are no de facto methods to solve it
with finite statistics. To fix this problem, we introduce a novel inverse
algorithm based on a combination of minimization of relative entropy, the Fast
Fourier Transform and a recursive version of Efron's bootstrap. This gives us
power to obtain new perspectives on non-perturbative high energy QCD, such as
probing the ab initio principles underlying the approximately negative binomial
distributions of observed charged particle final state multiplicities, related
to multiparton interactions, the fluctuating structure and profile of proton
and diffraction. As a proof-of-concept, we apply the algorithm to ALICE
proton-proton charged particle multiplicity measurements done at different
center-of-mass energies and fiducial pseudorapidity intervals at the LHC,
available on HEPData. A strong double peak structure emerges from the
inversion, barely visible without it.Comment: 29 pages, 10 figures, v2: extended analysis (re-projection ratios,
2D
Parameter Estimation of Social Forces in Crowd Dynamics Models via a Probabilistic Method
Focusing on a specific crowd dynamics situation, including real life
experiments and measurements, our paper targets a twofold aim: (1) we present a
Bayesian probabilistic method to estimate the value and the uncertainty (in the
form of a probability density function) of parameters in crowd dynamic models
from the experimental data; and (2) we introduce a fitness measure for the
models to classify a couple of model structures (forces) according to their
fitness to the experimental data, preparing the stage for a more general
model-selection and validation strategy inspired by probabilistic data
analysis. Finally, we review the essential aspects of our experimental setup
and measurement technique.Comment: 20 pages, 9 figure
Physics and application of photon number resolving detectors based on superconducting parallel nanowires
The Parallel Nanowire Detector (PND) is a photon number resolving (PNR)
detector which uses spatial multiplexing on a subwavelength scale to provide a
single electrical output proportional to the photon number. The basic structure
of the PND is the parallel connection of several NbN superconducting nanowires
(100 nm-wide, few nm-thick), folded in a meander pattern. PNDs were fabricated
on 3-4 nm thick NbN films grown on MgO (TS=400C) substrates by reactive
magnetron sputtering in an Ar/N2 gas mixture. The device performance was
characterized in terms of speed and sensitivity. PNDs showed a counting rate of
80 MHz and a pulse duration as low as 660ps full width at half maximum (FWHM).
Building the histograms of the photoresponse peak, no multiplication noise
buildup is observable. Electrical and optical equivalent models of the device
were developed in order to study its working principle, define design
guidelines, and develop an algorithm to estimate the photon number statistics
of an unknown light. In particular, the modeling provides novel insight of the
physical limit to the detection efficiency and to the reset time of these
detectors. The PND significantly outperforms existing PNR detectors in terms of
simplicity, sensitivity, speed, and multiplication noise
On nonparametric estimation of a mixing density via the predictive recursion algorithm
Nonparametric estimation of a mixing density based on observations from the
corresponding mixture is a challenging statistical problem. This paper surveys
the literature on a fast, recursive estimator based on the predictive recursion
algorithm. After introducing the algorithm and giving a few examples, I
summarize the available asymptotic convergence theory, describe an important
semiparametric extension, and highlight two interesting applications. I
conclude with a discussion of several recent developments in this area and some
open problems.Comment: 22 pages, 5 figures. Comments welcome at
https://www.researchers.one/article/2018-12-
Laplace Approximated EM Microarray Analysis: An Empirical Bayes Approach for Comparative Microarray Experiments
A two-groups mixed-effects model for the comparison of (normalized)
microarray data from two treatment groups is considered. Most competing
parametric methods that have appeared in the literature are obtained as special
cases or by minor modification of the proposed model. Approximate maximum
likelihood fitting is accomplished via a fast and scalable algorithm, which we
call LEMMA (Laplace approximated EM Microarray Analysis). The posterior odds of
treatment gene interactions, derived from the model, involve shrinkage
estimates of both the interactions and of the gene specific error variances.
Genes are classified as being associated with treatment based on the posterior
odds and the local false discovery rate (f.d.r.) with a fixed cutoff. Our
model-based approach also allows one to declare the non-null status of a gene
by controlling the false discovery rate (FDR). It is shown in a detailed
simulation study that the approach outperforms well-known competitors. We also
apply the proposed methodology to two previously analyzed microarray examples.
Extensions of the proposed method to paired treatments and multiple treatments
are also discussed.Comment: Published in at http://dx.doi.org/10.1214/10-STS339 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Dead Time Compensation for High-Flux Ranging
Dead time effects have been considered a major limitation for fast data
acquisition in various time-correlated single photon counting applications,
since a commonly adopted approach for dead time mitigation is to operate in the
low-flux regime where dead time effects can be ignored. Through the application
of lidar ranging, this work explores the empirical distribution of detection
times in the presence of dead time and demonstrates that an accurate
statistical model can result in reduced ranging error with shorter data
acquisition time when operating in the high-flux regime. Specifically, we show
that the empirical distribution of detection times converges to the stationary
distribution of a Markov chain. Depth estimation can then be performed by
passing the empirical distribution through a filter matched to the stationary
distribution. Moreover, based on the Markov chain model, we formulate the
recovery of arrival distribution from detection distribution as a nonlinear
inverse problem and solve it via provably convergent mathematical optimization.
By comparing per-detection Fisher information for depth estimation from high-
and low-flux detection time distributions, we provide an analytical basis for
possible improvement of ranging performance resulting from the presence of dead
time. Finally, we demonstrate the effectiveness of our formulation and
algorithm via simulations of lidar ranging.Comment: Revision with added estimation results, references, and figures, and
modified appendice
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