299 research outputs found
Well-Posedness for Semi-Relativistic Hartree Equations of Critical Type
We prove local and global well-posedness for semi-relativistic, nonlinear
Schr\"odinger equations with
initial data in , . Here is a critical
Hartree nonlinearity that corresponds to Coulomb or Yukawa type
self-interactions. For focusing , which arise in the quantum theory of
boson stars, we derive a sufficient condition for global-in-time existence in
terms of a solitary wave ground state. Our proof of well-posedness does not
rely on Strichartz type estimates, and it enables us to add external potentials
of a general class.Comment: 18 pages; replaced with revised version; remark and reference on blow
up adde
A Centre-Stable Manifold for the Focussing Cubic NLS in
Consider the focussing cubic nonlinear Schr\"odinger equation in : It admits special solutions of the form
, where is a Schwartz function and a positive
() solution of The space of
all such solutions, together with those obtained from them by rescaling and
applying phase and Galilean coordinate changes, called standing waves, is the
eight-dimensional manifold that consists of functions of the form . We prove that any solution starting
sufficiently close to a standing wave in the norm and situated on a certain codimension-one local
Lipschitz manifold exists globally in time and converges to a point on the
manifold of standing waves. Furthermore, we show that \mc N is invariant
under the Hamiltonian flow, locally in time, and is a centre-stable manifold in
the sense of Bates, Jones. The proof is based on the modulation method
introduced by Soffer and Weinstein for the -subcritical case and adapted
by Schlag to the -supercritical case. An important part of the proof is
the Keel-Tao endpoint Strichartz estimate in for the nonselfadjoint
Schr\"odinger operator obtained by linearizing around a standing wave solution.Comment: 56 page
Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
We study the long-time behavior of small solutions of the initial-value problem for the generalized Korteweg-de Vries equation [part]tu + [part]x3u + [part]xF(u) = 0 (gKdV) u(x, 0) = g(x). For the case where F(w)=|w|s, with s > (1/4)(23 - [radical sign]57) [approximate] 3.8625, our results imply that if ||g||L11 + ||g||L22 is sufficiently small then supr(1 + |t|)1/3||u(t)||L[infinity] D[alpha]F(u)||Lp and products ||D[alpha](fg)||Lp, 0 p < [infinity].Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29171/1/0000217.pd
MRLocus: Identifying causal genes mediating a trait through Bayesian estimation of allelic heterogeneity
Expression quantitative trait loci (eQTL) studies are used to understand the regulatory function of non-coding genome-wide association study (GWAS) risk loci, but colocalization alone does not demonstrate a causal relationship of gene expression affecting a trait. Evidence for mediation, that perturbation of gene expression in a given tissue or developmental context will induce a change in the downstream GWAS trait, can be provided by two-sample Mendelian Randomization (MR). Here, we introduce a new statistical method, MRLocus, for Bayesian estimation of the gene-to-trait effect from eQTL and GWAS summary data for loci with evidence of allelic heterogeneity, that is, containing multiple causal variants. MRLocus makes use of a colocalization step applied to each nearly-LD-independent eQTL, followed by an MR analysis step across eQTLs. Additionally, our method involves estimation of the extent of allelic heterogeneity through a dispersion parameter, indicating variable mediation effects from each individual eQTL on the downstream trait. Our method is evaluated against other state-of-the-art methods for estimation of the gene-to-trait mediation effect, using an existing simulation framework. In simulation, MRLocus often has the highest accuracy among competing methods, and in each case provides more accurate estimation of uncertainty as assessed through interval coverage. MRLocus is then applied to five candidate causal genes for mediation of particular GWAS traits, where gene-to-trait effects are concordant with those previously reported. We find that MRLocusâs estimation of the causal effect across eQTLs within a locus provides useful information for determining how perturbation of gene expression or individual regulatory elements will affect downstream traits. The MRLocus method is implemented as an R package available at https://mikelove.github.io/ mrlocus
Electromagnetic transition form factors and dilepton decay rates of nucleon resonances
Relativistic, kinematically complete phenomenological expressions for the
dilepton decay rates of nucleon resonances with arbitrary spin and parity are
derived in terms of the magnetic, electric, and Coulomb transition form
factors. The dilepton decay rates of the nucleon resonances with masses below 2
GeV are estimated using the extended vector meson dominance model for the
transition form factors. The model provides a unified description of the photo-
and electroproduction data, the vector meson decays, and the dilepton decays of
the nucleon resonances. The constraints on the transition form factors from the
quark counting rules are taken into account. The parameters of the model are
fixed by fitting the available photo- and electroproduction data and using
results of the multichannel partial-wave analysis of the scattering.
Where experimental data are not available, predictions of the non-relativistic
quark models are used as an input. The vector meson coupling constants of the
magnetic, electric, and Coulomb types are determined. The dilepton widths and
the dilepton spectra from decays of nucleon resonances with masses below 2 GeV
are calculated.Comment: An error in the code is found and fixed. Numerical results for the
spin-half nucleon resonances changed. A few misprints are removed from the
text. 56 pages including 7 tables and 27 eps figures, REVTe
Contemporary integrative taxonomy for sexually deprived protists: A case study of Trachelomonas (Euglenaceae) from western Ukraine
As many other protist groups, euglenophytes are prone to false identification based solely on morphology because of a limited amount of morphological features and cryptic speciation. One of the supposedly completely asexual groups within the freshwater phototrophic representatives of euglenophytes is Trachelomonas , capable of forming an inorganic shell around its cell (i.e., the lorica). The International Code of Nomenclature for algae, fungi, and plants regulates the taxonomy not only of flowering plants, but explicitly also of phototrophic protists, and provides powerful tools to resolve various taxonomic challenges. To exemplify some of the problems and potential solutions, a number of Trachelomonas strains were collected from the muddy, lakeârich region of Dobrostany and cultivated under stable laboratory conditions. Being a type locality of 58 unclarified Trachelomonas names, this region in western Ukraine is of great taxonomic importance. Based on light and electron microscopy, and on RAxML and MrBayes phylogenetics using multiple loci and a representative taxon sample, a detailed description of investigated strains and their systematic placement is provided. Morphologically, the strains differed slightly but consistently in minute characters such as size, lorica shape and ornamentation. The presently most comprehensive molecular tree of the Euglenaceae indicated to the existence of at least five different species present in the newly investigated samples, although they were collected from localities in very close vicinity to each other and at the same date. Based on morphological comparisons with type illustrations of species validly described 100 or more years ago, biological material was used to epitypify three names of Trachelomonas , eternally linking morphology with reliable genetic information. This taxonomic application is one of the powerful methods to clarify ambiguous scientific names, which has particular importance in characterâpoor protists such as the euglenophytes
Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV
Results are presented from a search for a W' boson using a dataset
corresponding to 5.0 inverse femtobarns of integrated luminosity collected
during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV.
The W' boson is modeled as a heavy W boson, but different scenarios for the
couplings to fermions are considered, involving both left-handed and
right-handed chiral projections of the fermions, as well as an arbitrary
mixture of the two. The search is performed in the decay channel W' to t b,
leading to a final state signature with a single lepton (e, mu), missing
transverse energy, and jets, at least one of which is tagged as a b-jet. A W'
boson that couples to fermions with the same coupling constant as the W, but to
the right-handed rather than left-handed chiral projections, is excluded for
masses below 1.85 TeV at the 95% confidence level. For the first time using LHC
data, constraints on the W' gauge coupling for a set of left- and right-handed
coupling combinations have been placed. These results represent a significant
improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe
Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV
A search for a Higgs boson decaying into two photons is described. The
analysis is performed using a dataset recorded by the CMS experiment at the LHC
from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an
integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross
section of the standard model Higgs boson decaying to two photons. The expected
exclusion limit at 95% confidence level is between 1.4 and 2.4 times the
standard model cross section in the mass range between 110 and 150 GeV. The
analysis of the data excludes, at 95% confidence level, the standard model
Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The
largest excess of events above the expected standard model background is
observed for a Higgs boson mass hypothesis of 124 GeV with a local significance
of 3.1 sigma. The global significance of observing an excess with a local
significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is
estimated to be 1.8 sigma. More data are required to ascertain the origin of
this excess.Comment: Submitted to Physics Letters
Measurement of the Lambda(b) cross section and the anti-Lambda(b) to Lambda(b) ratio with Lambda(b) to J/Psi Lambda decays in pp collisions at sqrt(s) = 7 TeV
The Lambda(b) differential production cross section and the cross section
ratio anti-Lambda(b)/Lambda(b) are measured as functions of transverse momentum
pt(Lambda(b)) and rapidity abs(y(Lambda(b))) in pp collisions at sqrt(s) = 7
TeV using data collected by the CMS experiment at the LHC. The measurements are
based on Lambda(b) decays reconstructed in the exclusive final state J/Psi
Lambda, with the subsequent decays J/Psi to an opposite-sign muon pair and
Lambda to proton pion, using a data sample corresponding to an integrated
luminosity of 1.9 inverse femtobarns. The product of the cross section times
the branching ratio for Lambda(b) to J/Psi Lambda versus pt(Lambda(b)) falls
faster than that of b mesons. The measured value of the cross section times the
branching ratio for pt(Lambda(b)) > 10 GeV and abs(y(Lambda(b))) < 2.0 is 1.06
+/- 0.06 +/- 0.12 nb, and the integrated cross section ratio for
anti-Lambda(b)/Lambda(b) is 1.02 +/- 0.07 +/- 0.09, where the uncertainties are
statistical and systematic, respectively.Comment: Submitted to Physics Letters
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