4,574 research outputs found
A new approach for sizing trials with composite binary endpoints using anticipated marginal values and accounting for the correlation between components
Composite binary endpoints are increasingly used as primary endpoints in
clinical trials. When designing a trial, it is crucial to determine the
appropriate sample size for testing the statistical differences between
treatment groups for the primary endpoint. As shown in this work, when using a
composite binary endpoint to size a trial, one needs to specify the event rates
and the effect sizes of the composite components as well as the correlation
between them. In practice, the marginal parameters of the components can be
obtained from previous studies or pilot trials, however, the correlation is
often not previously reported and thus usually unknown. We first show that the
sample size for composite binary endpoints is strongly dependent on the
correlation and, second, that slight deviations in the prior information on the
marginal parameters may result in underpowered trials for achieving the study
objectives at a pre-specified significance level. We propose a general strategy
for calculating the required sample size when the correlation is not specified,
and accounting for uncertainty in the marginal parameter values. We present the
web platform CompARE to characterize composite endpoints and to calculate the
sample size just as we propose in this paper. We evaluate the performance of
the proposal with a simulation study, and illustrate it by means of a real case
study using CompARE
Duplications of the critical Rubinstein-Taybi deletion region on chromosome 16p13.3 cause a novel recognisable syndrome
Background The introduction of molecular karyotyping technologies facilitated the identification of specific genetic disorders associated with imbalances of certain genomic regions. A detailed phenotypic delineation of interstitial 16p13.3 duplications is hampered by the scarcity of such patients.
Objectives To delineate the phenotypic spectrum associated with interstitial 16p13.3 duplications, and perform a genotype-phenotype analysis.
Results The present report describes the genotypic and phenotypic delineation of nine submicroscopic interstitial 16p13.3 duplications. The critically duplicated region encompasses a single gene, CREBBP, which is mutated or deleted in Rubinstein-Taybi syndrome. In 10 out of the 12 hitherto described probands, the duplication arose de novo.
Conclusions Interstitial 16p13.3 duplications have a recognizable phenotype, characterized by normal to moderately retarded mental development, normal growth, mild arthrogryposis, frequently small and proximally implanted thumbs and characteristic facial features. Occasionally, developmental defects of the heart, genitalia, palate or the eyes are observed. The frequent de novo occurrence of 16p13.3 duplications demonstrates the reduced reproductive fitness associated with this genotype. Inheritance of the duplication from a clinically normal parent in two cases indicates that the associated phenotype is incompletely penetrant
Lectures on Linear Stability of Rotating Black Holes
These lecture notes are concerned with linear stability of the non-extreme
Kerr geometry under perturbations of general spin. After a brief review of the
Kerr black hole and its symmetries, we describe these symmetries by Killing
fields and work out the connection to conservation laws. The Penrose process
and superradiance effects are discussed. Decay results on the long-time
behavior of Dirac waves are outlined. It is explained schematically how the
Maxwell equations and the equations for linearized gravitational waves can be
decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky
equation can be fully separated to a system of coupled ordinary differential
equations. Linear stability of the non-extreme Kerr black hole is stated as a
pointwise decay result for solutions of the Cauchy problem for the Teukolsky
equation. The stability proof is outlined, with an emphasis on the underlying
ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in
July 2018, minor improvements (published version
Some remarks on a new exotic spacetime for time travel by free fall
This work is essentially a review of a new spacetime model with closed causal
curves, recently presented in another paper (Class. Quantum Grav.
\textbf{35}(16) (2018), 165003). The spacetime at issue is topologically
trivial, free of curvature singularities, and even time and space orientable.
Besides summarizing previous results on causal geodesics, tidal accelerations
and violations of the energy conditions, here redshift/blueshift effects and
the Hawking-Ellis classification of the stress-energy tensor are examined.Comment: 17 pages, 9 figures. Submitted as a contribution to the proceedings
of "DOMOSCHOOL - International Alpine School of Mathematics and Physics,
Domodossola 2018". Possible text overlaps with my previous work
arXiv:1803.08214, of which this is essentially a review. Additional results
concerning redshift/blueshift effects and the classification of the
stress-energy tensor are presented her
Initial/boundary-value problems of tumor growth within a host tissue
This paper concerns multiphase models of tumor growth in interaction with a
surrounding tissue, taking into account also the interplay with diffusible
nutrients feeding the cells. Models specialize in nonlinear systems of possibly
degenerate parabolic equations, which include phenomenological terms related to
specific cell functions. The paper discusses general modeling guidelines for
such terms, as well as for initial and boundary conditions, aiming at both
biological consistency and mathematical robustness of the resulting problems.
Particularly, it addresses some qualitative properties such as a priori
nonnegativity, boundedness, and uniqueness of the solutions. Existence of the
solutions is studied in the one-dimensional time-independent case.Comment: 30 pages, 5 figure
Tamari Lattices and the symmetric Thompson monoid
We investigate the connection between Tamari lattices and the Thompson group
F, summarized in the fact that F is a group of fractions for a certain monoid
F+sym whose Cayley graph includes all Tamari lattices. Under this
correspondence, the Tamari lattice operations are the counterparts of the least
common multiple and greatest common divisor operations in F+sym. As an
application, we show that, for every n, there exists a length l chain in the
nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page
Stable non-uniform black strings below the critical dimension
The higher-dimensional vacuum Einstein equation admits translationally
non-uniform black string solutions. It has been argued that infinitesimally
non-uniform black strings should be unstable in 13 or fewer dimensions and
otherwise stable. We construct numerically non-uniform black string solutions
in 11, 12, 13, 14 and 15 dimensions. Their stability is investigated using
local Penrose inequalities. Weakly non-uniform solutions behave as expected.
However, in 12 and 13 dimensions, strongly non-uniform solutions appear to be
stable and can have greater horizon area than a uniform string of the same
mass. In 14 and 15 dimensions all non-uniform black strings appear to be
stable.Comment: 26 pages, 11 figures. V2: reference added, matches published versio
Reverse mathematics of matroids
Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract related reverse mathematics results. In particular, we show that the existence of bases for vector spaces of bounded dimension is equivalent to the induction scheme for \Sigma^0_2 formulas
Missing Features Reconstruction Using a Wasserstein Generative Adversarial Imputation Network
Missing data is one of the most common preprocessing problems. In this paper,
we experimentally research the use of generative and non-generative models for
feature reconstruction. Variational Autoencoder with Arbitrary Conditioning
(VAEAC) and Generative Adversarial Imputation Network (GAIN) were researched as
representatives of generative models, while the denoising autoencoder (DAE)
represented non-generative models. Performance of the models is compared to
traditional methods k-nearest neighbors (k-NN) and Multiple Imputation by
Chained Equations (MICE). Moreover, we introduce WGAIN as the Wasserstein
modification of GAIN, which turns out to be the best imputation model when the
degree of missingness is less than or equal to 30%. Experiments were performed
on real-world and artificial datasets with continuous features where different
percentages of features, varying from 10% to 50%, were missing. Evaluation of
algorithms was done by measuring the accuracy of the classification model
previously trained on the uncorrupted dataset. The results show that GAIN and
especially WGAIN are the best imputers regardless of the conditions. In
general, they outperform or are comparative to MICE, k-NN, DAE, and VAEAC.Comment: Preprint of the conference paper (ICCS 2020), part of the Lecture
Notes in Computer Scienc
R-mode oscillations and rocket effect in rotating superfluid neutron stars. I. Formalism
We derive the hydrodynamical equations of r-mode oscillations in neutron
stars in presence of a novel damping mechanism related to particle number
changing processes. The change in the number densities of the various species
leads to new dissipative terms in the equations which are responsible of the
{\it rocket effect}. We employ a two-fluid model, with one fluid consisting of
the charged components, while the second fluid consists of superfluid neutrons.
We consider two different kind of r-mode oscillations, one associated with
comoving displacements, and the second one associated with countermoving, out
of phase, displacements.Comment: 10 page
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