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## On the Impact of Lepton PDFs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this paper we discuss the effect of the complete leading-order QED
corrections to the DGLAP equations in the perturbative evolution of parton
distribution functions (PDFs). This requires the extension of the purely QCD
DGLAP evolution, including a PDF for the photons and, consistently, also for
the charged leptons $e^{\pm}$, $\mu^\pm$ and $\tau^\pm$. We present the
implementation of the QED-corrected DGLAP evolution in the presence of photon
and lepton PDFs in the APFEL program and, by means of different assumptions for
the initial scale PDFs, we produce for the first time PDF sets containing
charged lepton distributions. We also present phenomenological studies that aim
to assess the impact of the presence of lepton PDFs in the proton for some
relevant SM (and BSM) processes at the LHC at 13 TeV and the FCC-hh at 100 TeV.
The impact of the photon PDF is also outlined for those processes.; Comment: 32 pages, 19 figures, matches published version in JHEP

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## Do your volatility smiles take care of extreme events?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/10/2010
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In the Black-Scholes context we consider the probability distribution
function (PDF) of financial returns implied by volatility smile and we study
the relation between the decay of its tails and the fitting parameters of the
smile. We show that, considering a scaling law derived from data, it is
possible to get a new fitting procedure of the volatility smile that considers
also the exponential decay of the real PDF of returns observed in the financial
markets. Our study finds application in the Risk Management activities where
the tails characterization of financial returns PDF has a central role for the
risk estimation.

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## Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The likelihood calculation of a vast number of particles is the computational
bottleneck for the particle filter in applications where the observation
information is rich. For fast computing the likelihood of particles, a
numerical fitting approach is proposed to construct the Likelihood Probability
Density Function (Li-PDF) by using a comparably small number of so-called
fulcrums. The likelihood of particles is thereby analytically inferred,
explicitly or implicitly, based on the Li-PDF instead of directly computed by
utilizing the observation, which can significantly reduce the computation and
enables real time filtering. The proposed approach guarantees the estimation
quality when an appropriate fitting function and properly distributed fulcrums
are used. The details for construction of the fitting function and fulcrums are
addressed respectively in detail. In particular, to deal with multivariate
fitting, the nonparametric kernel density estimator is presented which is
flexible and convenient for implicit Li-PDF implementation. Simulation
comparison with a variety of existing approaches on a benchmark 1-dimensional
model and multi-dimensional robot localization and visual tracking demonstrate
the validity of our approach.; Comment: 42 pages...

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## Turbulent-Like Behavior of Seismic Time Series

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/02/2009
Português

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We report on a novel stochastic analysis of seismic time series for the
Earth's vertical velocity, by using methods originally developed for complex
hierarchical systems, and in particular for turbulent flows. Analysis of the
fluctuations of the detrended increments of the series reveals a pronounced
change of the shapes of the probability density functions (PDF) of the series'
increments. Before and close to an earthquake the shape of the PDF and the
long-range correlation in the increments both manifest significant changes. For
a moderate or large-size earthquake the typical time at which the PDF undergoes
the transition from a Gaussian to a non-Gaussian is about 5-10 hours. Thus, the
transition represents a new precursor for detecting such earthquakes.; Comment: 12 pages, 5 figures

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## Dynamics of a tracer granular particle as a non-equilibrium Markov process

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/09/2005
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The dynamics of a tracer particle in a stationary driven granular gas is
investigated. We show how to transform the linear Boltzmann equation describing
the dynamics of the tracer into a master equation for a continuous Markov
process. The transition rates depend upon the stationary velocity distribution
of the gas. When the gas has a Gaussian velocity probability distribution
function (pdf), the stationary velocity pdf of the tracer is Gaussian with a
lower temperature and satisfies detailed balance for any value of the
restitution coefficient $\alpha$. As soon as the velocity pdf of the gas
departs from the Gaussian form, detailed balance is violated. This
non-equilibrium state can be characterized in terms of a Lebowitz-Spohn action
functional $W(\tau)$ defined over trajectories of time duration $\tau$. We
discuss the properties of this functional and of a similar functional
$\bar{W}(\tau)$ which differs from the first for a term which is non-extensive
in time. On the one hand we show that in numerical experiments, i.e. at finite
times $\tau$, the two functionals have different fluctuations and $\bar{W}$
always satisfies an Evans-Searles-like symmetry. On the other hand we cannot
observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC)
relation...

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## Tail-Constraining Stochastic Linear-Quadratic Control: Large Deviation and Statistical Physics Approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Standard definition of the stochastic Risk-Sensitive Linear-Quadratic (RS-LQ)
control depends on the risk parameter, which is normally left to be set
exogenously. We reconsider the classical approach and suggest two alternatives
resolving the spurious freedom naturally. One approach consists in seeking for
the minimum of the tail of the Probability Distribution Function (PDF) of the
cost functional at some large fixed value. Another option suggests to minimize
the expectation value of the cost functional under constraint on the value of
the PDF tail. Under assumption of the resulting control stability, both
problems are reduced to static optimizations over stationary control matrix.
The solutions are illustrated on the examples of scalar and 1d chain (string)
systems. Large Deviation self-similar asymptotic of the cost functional PDF is
analyzed.; Comment: 11 pages

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## Path probability density functions for semi-Markovian random walks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/06/2007
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#Mathematical Physics#Physics - Biological Physics#Quantitative Biology - Other Quantitative Biology

In random walks, the path representation of the Green's function is an
infinite sum over the length of path probability density functions (PDFs). Here
we derive and solve, in Laplace space, the recursion relation for the n order
path PDF for any arbitrarily inhomogeneous semi-Markovian random walk in a
one-dimensional (1D) chain of L states. The recursion relation relates the n
order path PDF to L/2 (round towards zero for an odd L) shorter path PDFs, and
has n independent coefficients that obey a universal formula. The z transform
of the recursion relation straightforwardly gives the generating function for
path PDFs, from which we obtain the Green's function of the random walk, and
derive an explicit expression for any path PDF of the random walk. These
expressions give the most detailed description of arbitrarily inhomogeneous
semi-Markovian random walks in 1D.

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## Statistics of energy dissipation in a quantum dot operating in the cotunneling regime

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/06/2014
Português

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At Coulomb blockade valleys inelastic cotunneling processes generate
particle-hole excitations in quantum dots (QDs), and lead to energy
dissipation. We have analyzed the probability distribution function (PDF) of
energy dissipated in a QD due to such processes during a given time interval.
We obtained analytically the cumulant generating function, and extracted the
average, variance and Fano factor. The latter diverges as $T^3/(eV)^2$ at bias
$eV$ smaller than the temperature $T$, and reaches the value $3 eV / 5$ in the
opposite limit. The PDF is further studied numerically. As expected, Crooks
fluctuation relation is not fulfilled by the PDF. Our results can be verified
experimentally utilizing transport measurements of charge.; Comment: 5 pages, 3 figures

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## The PDF4LHC Working Group Interim Report

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/01/2011
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This document is intended as a study of benchmark cross sections at the LHC
(at 7 TeV) at NLO using modern parton distribution functions currently
available from the 6 PDF fitting groups that have participated in this
exercise. It also contains a succinct user guide to the computation of PDFs,
uncertainties and correlations using available PDF sets.
A companion note, also submitted to the archive, provides an interim summary
of the current recommendations of the PDF4LHC working group for the use of
parton distribution functions and of PDF uncertainties at the LHC, for cross
section and cross section uncertainty calculations.; Comment: 35 pages

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## QC Paulinesia

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/07/2004
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My goal in producing this document was to create a collection of qubit
circuit identities that are used in Quantum Computing. Mathematicians and
Physicists may consider it as being analogous to a Table of Integrals or a
Mathematical Handbook such as Gradshteyn-Ryzhik or Abramowitz-Stegun. Computer
Programmers may think of it as a scrapbook of code snippets that are elegant,
instructive, well documented, and useful. Electronics experts may view it as a
compendium of circuits for performing a large assortment of tasks. The vast
majority of the circuit identities collected in this work were not discovered
for the first time by me, and I take no credit for discovering them. In
producing this document, I am acting as a collector, not as a discoverer.; Comment: 45 pages (files: 1 .tex, 2 .sty, 2 .eps) A nicer pdf version, with
better figure resolution than the arxiv pdf, can be found at
www.ar-tiste.com/PaulinesiaVer1.pdf

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## Quantum Computation Based Probability Density Function Estimation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/09/2004
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Signal processing techniques will lean on blind methods in the near future,
where no redundant, resource allocating information will be transmitted through
the channel. To achieve a proper decision, however, it is essential to know at
least the probability density function (pdf), which to estimate is classically
a time consumption and/or less accurate hard task, that may make decisions to
fail. This paper describes the design of a quantum assisted pdf estimation
method also by an example, which promises to achieve the exact pdf by proper
setting of parameters in a very fast way.; Comment: 5 pages, 3 figures, will be published by International Journal of
Quantum Information

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## Accurate Modeling of Weak Lensing with the sGL Method

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We revise and extend the stochastic approach to cumulative weak lensing
(hereafter the sGL method) first introduced in Ref. [1]. Here we include a
realistic halo mass function and density profiles to model the distribution of
mass between and within galaxies, galaxy groups and galaxy clusters. We also
introduce a modeling of the filamentary large-scale structures and a method to
embed halos into these structures. We show that the sGL method naturally
reproduces the weak lensing results for the Millennium Simulation. The strength
of the sGL method is that a numerical code based on it can compute the lensing
probability distribution function for a given inhomogeneous model universe in a
few seconds. This makes it a useful tool to study how lensing depends on
cosmological parameters and its impact on observations. The method can also be
used to simulate the effect of a wide array of systematic biases on the
observable PDF. As an example we show how simple selection effects may reduce
the variance of observed PDF, which could possibly mask opposite effects from
very large scale structures. We also show how a JDEM-like survey could
constrain the lensing PDF relative to a given cosmological model. The updated
turboGL code is available at turboGL.org.; Comment: PRD style: 20 pages...

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## Methods of exploring energy diffusion in lattices with finite temperature

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/06/2011
Português

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We discuss two methods for exploring energy diffusion in lattices with finite
temperature in this paper. The first one is the energy-kick (EK) method. To
apply this method, one adds an external energy kick to a particle in the
lattice, and tracks its evolution by evolving the kicked system. The second one
is the fluctuation-correlation (FC) method. The formula for calculating the
probability density function (PDF) using the canonical ensemble is slightly
revised and extended to the microcanonical ensemble. We show that the FC method
has advantages over the EK method theoretically and technically. Theoretically,
the PDF obtained by the FC method reveals the diffusion processes of the inner
energy while the PDF obtained by the EK method represents that of the kick
energy. The diffusion processes of the inner energy and the external energy
added to the system, i.e., the kick energy, may be different quantitatively and
even qualitatively depending on models. To show these facts, we study not only
the equilibrium systems but also the stationary nonequilibrium systems.
Examples showing that the inner energy and the kick energy may have different
diffusion behavior are reported in both cases. The technical advantage enables
us to study the long-time diffusion processes and thus avoids the finite-time
effect.; Comment: 10 pages;7figure

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## Generalized Rejection Sampling Schemes and Applications in Signal Processing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/04/2009
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Bayesian methods and their implementations by means of sophisticated Monte
Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters,
have become very popular in signal processing over the last years. However, in
many problems of practical interest these techniques demand procedures for
sampling from probability distributions with non-standard forms, hence we are
often brought back to the consideration of fundamental simulation algorithms,
such as rejection sampling (RS). Unfortunately, the use of RS techniques
demands the calculation of tight upper bounds for the ratio of the target
probability density function (pdf) over the proposal density from which
candidate samples are drawn. Except for the class of log-concave target pdf's,
for which an efficient algorithm exists, there are no general methods to
analytically determine this bound, which has to be derived from scratch for
each specific case. In this paper, we introduce new schemes for (a) obtaining
upper bounds for likelihood functions and (b) adaptively computing proposal
densities that approximate the target pdf closely. The former class of methods
provides the tools to easily sample from a posteriori probability distributions
(that appear very often in signal processing problems) by drawing candidates
from the prior distribution. However...

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## On the Gap and Time Interval between the First Two Maxima of Long Random Walks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Condensed Matter - Statistical Mechanics#Condensed Matter - Disordered Systems and Neural Networks#Mathematics - Probability

In the context of order statistics of discrete time random walks (RW), we
investigate the statistics of the gap, $G_n$, and the number of time steps,
$L_n$, between the two highest positions of a Markovian one-dimensional random
walker, starting from $x_0 = 0$, after $n$ time steps (taking the $x$-axis
vertical). The jumps $\eta_i = x_i - x_{i-1}$ are independent and identically
distributed random variables drawn from a symmetric probability distribution
function (PDF), $f(\eta)$, the Fourier transform of which has the small $k$
behavior $1 - \hat f(k) \propto |k|^\mu$, with $0 < \mu \leq 2$. For $\mu=2$,
the variance of the jump distribution is finite and the RW (properly scaled)
converges to a Brownian motion. For $0<\mu<2$, the RW is a L\'evy flight of
index $\mu$. We show that the joint PDF of $G_n$ and $L_n$ converges to a well
defined stationary bi-variate distribution $p(g,l)$ as the RW duration $n$ goes
to infinity. We present a thorough analytical study of the limiting joint
distribution $p(g,l)$, as well as of its associated marginals $p_{\rm gap}(g)$
and $p_{\rm time}(l)$, revealing a rich variety of behaviors depending on the
tail of $f(\eta)$ (from slow decreasing algebraic tail to fast decreasing
super-exponential tail). We also address the problem for a random bridge where
the RW starts and ends at the origin after $n$ time steps. We show that in the
large $n$ limit...

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## Disentangling electroweak effects in Z-boson production

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/05/2014
Português

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Parton distributions with QED corrections open new scenarios for high
precision physics. We recall the need for accurate and improved predictions
which keeps into account higher order QCD corrections together with electroweak
effects. We study predictions obtained with the improved Born approximation and
the $G_{\mu}$ scheme by using two public codes: DYNNLO and HORACE. We focus our
attention on the Drell-Yan Z-boson invariant mass distribution at low- and
high-mass regions, recently measured by the ATLAS experiment and we estimate
the impact of each component of the final prediction. We show that electroweak
corrections are larger than PDF uncertainties for modern PDF sets and therefore
such corrections are necessary to improve the extraction of future PDF sets.; Comment: 5 pages, 4 figures, to appear in the proceedings of the Les
Rencontres de Physique de la Vall\'ee d'Aoste, La Thuile 2014

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## Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/03/2010
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Dispersion of a passive scalar from concentrated sources in fully developed
turbulent channel flow is studied with the probability density function (PDF)
method. The joint PDF of velocity, turbulent frequency and scalar concentration
is represented by a large number of Lagrangian particles. A stochastic
near-wall PDF model combines the generalized Langevin model of Haworth & Pope
with Durbin's method of elliptic relaxation to provide a mathematically exact
treatment of convective and viscous transport with a non-local representation
of the near-wall Reynolds stress anisotropy. The presence of walls is
incorporated through the imposition of no-slip and impermeability conditions on
particles without the use of damping or wall-functions. Information on the
turbulent timescale is supplied by the gamma-distribution model of van Slooten
et al. Two different micromixing models are compared that incorporate the
effect of small scale mixing on the transported scalar: the widely used
interaction by exchange with the mean (IEM) and the interaction by exchange
with the conditional mean (IECM) model. Single-point velocity and concentration
statistics are compared to direct numerical simulation and experimental data at
Re_\tau=1080 based on the friction velocity and the channel half width. The
joint model accurately reproduces a wide variety of conditional and
unconditional statistics in both physical and composition space.; Comment: Accepted in Physics of Fluids...

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## Galactic Substructure and Direct Detection of Dark Matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We study the effects of substructure in the Galactic halo on direct detection
of dark matter, on searches for energetic neutrinos from WIMP annihilation in
the Sun and Earth, and on the enhancement in the WIMP annihilation rate in the
halo. Our central result is a probability distribution function (PDF) P(\rho)
for the local dark-matter density. This distribution must be taken into account
when using null dark-matter searches to constrain the properties of dark-matter
candidates. We take two approaches to calculating the PDF. The first is an
analytic model that capitalizes on the scale-invariant nature of the
structure--formation hierarchy in order to address early stages in the
hierarchy (very small scales; high densities). Our second approach uses
simulation-inspired results to describe the PDF that arises from lower-density
larger-scale substructures which formed in more recent stages in the merger
hierarchy. The distributions are skew positive, and they peak at densities
lower than the mean density. The local dark-matter density may be as small as
1/10th the canonical value of ~ 0.4 GeV/cm^3, but it is probably no less than
0.2 GeV/cm^3.; Comment: 11 pages, 3 figures, Replaced with version accepted for publication
in Phys. Rev. D

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## The Observed Probability Distribution Function, Power Spectrum, and Correlation Function of the Transmitted Flux in the Lyman-alpha Forest

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/11/1999
Português

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A sample of eight quasars observed at high resolution and signal-to-noise is
used to determine the probability distribution function (PDF), the power
spectrum, and the correlation function of the transmitted flux in the \lya
forest, in three redshift bins centered at z=2.41, 3.00, and 3.89. All the
results are presented in tabular form, with full error covariance matrices to
allow for comparisons with any numerical simulations and with other data sets.
The observations are compared with a numerical simulation of the \lya forest of
a Lambda-CDM model with Omega=0.4, known to agree with other large-scale
structure observational constraints. There is excellent agreement for the PDF,
if the mean transmitted flux is adjusted to match the observations. A small
difference between the observed and predicted PDF is found at high fluxes and
low redshift, which may be due to the uncertain effects of fitting the spectral
continuum. Using the numerical simulation, we show how the flux power spectrum
can be used to recover the initial power spectrum of density fluctuations. From
our sample of eight quasars, we measure the amplitude of the mass power
spectrum to correspond to a linear variance per unit ln(k) of
$\Delta^2_\rho(k)=0.72\pm0.09$ at k=0.04(km/s)^{-1} and z=3...

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## Capacity of a Class of State-Dependent Orthogonal Relay Channels

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The class of orthogonal relay channels in which the orthogonal channels
connecting the source terminal to the relay and the destination, and the relay
to the destination, depend on a state sequence, is considered. It is assumed
that the state sequence is fully known at the destination while it is not known
at the source or the relay. The capacity of this class of relay channels is
characterized, and shown to be achieved by the partial
decode-compress-and-forward (pDCF) scheme. Then the capacity of certain binary
and Gaussian state-dependent orthogonal relay channels are studied in detail,
and it is shown that the compress-and-forward (CF) and
partial-decode-and-forward (pDF) schemes are suboptimal in general. To the best
of our knowledge, this is the first single relay channel model for which the
capacity is achieved by pDCF, while pDF and CF schemes are both suboptimal.
Furthermore, it is shown that the capacity of the considered class of
state-dependent orthogonal relay channels is in general below the cut-set
bound. The conditions under which pDF or CF suffices to meet the cut-set bound,
and hence, achieve the capacity, are also derived.; Comment: This paper has been accepted by IEEE Transactions on Information
Theory

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