608,821 research outputs found
Multi-Instantons and Multi-Cuts
We discuss various aspects of multi-instanton configurations in generic
multi-cut matrix models. Explicit formulae are presented in the two-cut case
and, in particular, we obtain general formulae for multi-instanton amplitudes
in the one-cut matrix model case as a degeneration of the two-cut case. These
formulae show that the instanton gas is ultra-dilute, due to the repulsion
among the matrix model eigenvalues. We exemplify and test our general results
in the cubic matrix model, where multi-instanton amplitudes can be also
computed with orthogonal polynomials. As an application, we derive general
expressions for multi-instanton contributions in two-dimensional quantum
gravity, verifying them by computing the instanton corrections to the string
equation. The resulting amplitudes can be interpreted as regularized partition
functions for multiple ZZ-branes, which take into full account their
back-reaction on the target geometry. Finally, we also derive structural
properties of the trans-series solution to the Painleve I equation.Comment: 34 pages, 3 figures, JHEP3.cls; v2: added references, minor changes;
v3: added 1 reference, more minor changes, final version for JMP; v4: more
typos correcte
Robust testing in generalized linear models by sign-flipping score contributions
Generalized linear models are often misspecified due to overdispersion,
heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood
methods for testing in misspecified models often do not provide satisfactory
type-I error rate control. We provide a novel semi-parametric test, based on
sign-flipping individual score contributions. The tested parameter is allowed
to be multi-dimensional and even high-dimensional. Our test is often robust
against the mentioned forms of misspecification and provides better type-I
error control than its competitors. When nuisance parameters are estimated, our
basic test becomes conservative. We show how to take nuisance estimation into
account to obtain an asymptotically exact test. Our proposed test is
asymptotically equivalent to its parametric counterpart.Comment: To appear in Journal of the Royal Statistical Society: Series B
(Methodology). Early view version (2020
COMPOSITE NONPARAMETRIC TESTS IN HIGH DIMENSION
This dissertation focuses on the problem of making high-dimensional inference for two or more groups. High-dimensional means both the sample size (n) and dimension (p) tend to infinity, possibly at different rates. Classical approaches for group comparisons fail in the high-dimensional situation, in the sense that they have incorrect sizes and low powers. Much has been done in recent years to overcome these problems. However, these recent works make restrictive assumptions in terms of the number of treatments to be compared and/or the distribution of the data. This research aims to (1) propose and investigate refined small-sample approaches for high-dimension data in the multi-group setting (2) propose and study a fully-nonparametric approach, and (3) conduct an extensive comparison of the proposed methods with some existing ones in a simulation.
When treatment effects can meaningfully be formulated in terms of means, a semiparametric approach under equal and unequal covariance assumptions is investigated. Composites of F-type statistics are used to construct two tests. One test is a moderate-p version – the test statistic is centered by asymptotic mean – and the other test is a large-p version asymptotic-expansion based finite-sample correction for the mean of the test statistic. These tests do not make any distributional assumptions and, therefore, they are nonparametric in a way. The theory for the tests only requires mild assumptions to regulate the dependence. Simulation results show that, for moderately small samples, the large-p version yields substantial gain in the size with a small power tradeoff.
In some situations mean-based inference is not appropriate, for example, for data that is in ordinal scale or heavy tailed. For these situations, a high-dimensional fully-nonparametric test is proposed. In the two-sample situation, a composite of a Wilcoxon-Mann-Whitney type test is investigated. Assumptions needed are weaker than those in the semiparametric approach. Numerical comparisons with the moderate-p version of the semiparametric approach show that the nonparametric test has very similar size but achieves superior power, especially for skewed data with some amount of dependence between variables.
Finally, we conduct an extensive simulation to compare our proposed methods with other nonparametric test and rank transformation methods. A wide spectrum of simulation settings is considered. These simulation settings include a variety of heavy tailed and skewed data distributions, homoscedastic and heteroscedastic covariance structures, various amounts of dependence and choices of tuning (smoothing window) parameter for the asymptotic variance estimators. The fully-nonparametric and the rank transformation methods behave similarly in terms of type I and type II errors. However, the two approaches fundamentally differ in their hypotheses. Although there are no formal mathematical proofs for the rank transformations, they have a tendency to provide immunity against effects of outliers. From a theoretical standpoint, our nonparametric method essentially uses variable-by-variable ranking which naturally arises from estimating the nonparametric effect of interest. As a result of this, our method is invariant against application of any monotone marginal transformations. For a more practical comparison, real-data from an Encephalogram (EEG) experiment is analyzed
A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics
We describe a new Godunov algorithm for relativistic magnetohydrodynamics
(RMHD) that combines a simple, unsplit second order accurate integrator with
the constrained transport (CT) method for enforcing the solenoidal constraint
on the magnetic field. A variety of approximate Riemann solvers are implemented
to compute the fluxes of the conserved variables. The methods are tested with a
comprehensive suite of multidimensional problems. These tests have helped us
develop a hierarchy of correction steps that are applied when the integration
algorithm predicts unphysical states due to errors in the fluxes, or errors in
the inversion between conserved and primitive variables. Although used
exceedingly rarely, these corrections dramatically improve the stability of the
algorithm. We present preliminary results from the application of these
algorithms to two problems in RMHD: the propagation of supersonic magnetized
jets, and the amplification of magnetic field by turbulence driven by the
relativistic Kelvin-Helmholtz instability (KHI). Both of these applications
reveal important differences between the results computed with Riemann solvers
that adopt different approximations for the fluxes. For example, we show that
use of Riemann solvers which include both contact and rotational
discontinuities can increase the strength of the magnetic field within the
cocoon by a factor of ten in simulations of RMHD jets, and can increase the
spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a
factor of 2. This increase in accuracy far outweighs the associated increase in
computational cost. Our RMHD scheme is publicly available as part of the Athena
code.Comment: 75 pages, 28 figures, accepted for publication in ApJS. Version with
high resolution figures available from
http://jila.colorado.edu/~krb3u/Athena_SR/rmhd_method_paper.pd
CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
We present a program that implements the OPP reduction method to extract the
coefficients of the one-loop scalar integrals from a user defined
(sub)-amplitude or Feynman Diagram, as well as the rational terms coming from
the 4-dimensional part of the numerator. The rational pieces coming from the
epsilon-dimensional part of the numerator are treated as an external input, and
can be computed with the help of dedicated tree-level like Feynman rules.
Possible numerical instabilities are dealt with the help of arbitrary
precision routines, that activate only when needed.Comment: Version published in JHE
Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers
In this paper we use the genuinely multidimensional HLL Riemann solvers
recently developed by Balsara et al. to construct a new class of
computationally efficient high order Lagrangian ADER-WENO one-step ALE finite
volume schemes on unstructured triangular meshes. A nonlinear WENO
reconstruction operator allows the algorithm to achieve high order of accuracy
in space, while high order of accuracy in time is obtained by the use of an
ADER time-stepping technique based on a local space-time Galerkin predictor.
The multidimensional HLL and HLLC Riemann solvers operate at each vertex of the
grid, considering the entire Voronoi neighborhood of each node and allows for
larger time steps than conventional one-dimensional Riemann solvers. The
results produced by the multidimensional Riemann solver are then used twice in
our one-step ALE algorithm: first, as a node solver that assigns a unique
velocity vector to each vertex, in order to preserve the continuity of the
computational mesh; second, as a building block for genuinely multidimensional
numerical flux evaluation that allows the scheme to run with larger time steps
compared to conventional finite volume schemes that use classical
one-dimensional Riemann solvers in normal direction. A rezoning step may be
necessary in order to overcome element overlapping or crossing-over. We apply
the method presented in this article to two systems of hyperbolic conservation
laws, namely the Euler equations of compressible gas dynamics and the equations
of ideal classical magneto-hydrodynamics (MHD). Convergence studies up to
fourth order of accuracy in space and time have been carried out. Several
numerical test problems have been solved to validate the new approach
Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis
Factor analysis aims to determine latent factors, or traits, which summarize
a given data set. Inter-battery factor analysis extends this notion to multiple
views of the data. In this paper we show how a nonlinear, nonparametric version
of these models can be recovered through the Gaussian process latent variable
model. This gives us a flexible formalism for multi-view learning where the
latent variables can be used both for exploratory purposes and for learning
representations that enable efficient inference for ambiguous estimation tasks.
Learning is performed in a Bayesian manner through the formulation of a
variational compression scheme which gives a rigorous lower bound on the log
likelihood. Our Bayesian framework provides strong regularization during
training, allowing the structure of the latent space to be determined
efficiently and automatically. We demonstrate this by producing the first (to
our knowledge) published results of learning from dozens of views, even when
data is scarce. We further show experimental results on several different types
of multi-view data sets and for different kinds of tasks, including exploratory
data analysis, generation, ambiguity modelling through latent priors and
classification.Comment: 49 pages including appendi
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