A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of "observables", thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

Prediction of peptide and protein propensity for amyloid formation

Understanding which peptides and proteins have the potential to undergo amyloid formation and what driving forces are responsible for amyloid-like fiber formation and stabilization remains limited. This is mainly because proteins that can undergo structural changes, which lead to amyloid formation, are quite diverse and share no obvious sequence or structural homology, despite the structural similarity found in the fibrils. To address these issues, a novel approach based on recursive feature selection and feed-forward neural networks was undertaken to identify key features highly correlated with the self-assembly problem. This approach allowed the identification of seven physicochemical and biochemical properties of the amino acids highly associated with the self-assembly of peptides and proteins into amyloid-like fibrils (normalized frequency of β-sheet, normalized frequency of β-sheet from LG, weights for β-sheet at the window position of 1, isoelectric point, atom-based hydrophobic moment, helix termination parameter at position j+1 and ΔGº values for peptides extrapolated in 0 M urea). Moreover, these features enabled the development of a new predictor (available at http://cran.r-project.org/web/packages/appnn/index.html) capable of accurately and reliably predicting the amyloidogenic propensity from the polypeptide sequence alone with a prediction accuracy of 84.9 % against an external validation dataset of sequences with experimental in vitro, evidence of amyloid formation

Search for R-parity Violating Supersymmetry in Dimuon and Four-Jets Channel

We present results of a search for R-parity-violating decay of the neutralino chi_1^0, taken to be the Lightest Supersymmetric Particle. It is assumed that this decay proceeds through one of the lepton-number violating couplings lambda-prime_2jk (j=1,2; k=1,2,3). This search is based on 77.5 pb-1 of data, collected by the D0 experiment at the Fermilab Tevatron in ppbar collisions at a center of mass energy of 1.8 TeV in 1992-1995.Comment: 10 pages, 3 figure

A Quasi-Model-Independent Search for New Physics at Large Transverse Momentum

We apply a quasi-model-independent strategy ("Sleuth") to search for new high p_T physics in approximately 100 pb^-1 of ppbar collisions at sqrt(s) = 1.8 TeV collected by the DZero experiment during 1992-1996 at the Fermilab Tevatron. Over thirty-two e mu X, W+jets-like, Z+jets-like, and 3(lepton/photon)X exclusive final states are systematically analyzed for hints of physics beyond the standard model. Simultaneous sensitivity to a variety of models predicting new phenomena at the electroweak scale is demonstrated by testing the method on a particular signature in each set of final states. No evidence of new high p_T physics is observed in the course of this search, and we find that 89% of an ensemble of hypothetical similar experimental runs would have produced a final state with a candidate signal more interesting than the most interesting observed in these data.Comment: 28 pages, 17 figures. Submitted to Physical Review

Central carbon metabolism in the progression of mammary carcinoma

There is a growing belief that the metabolic program of breast tumor cells could be a therapeutic target. Yet, without detailed information on central carbon metabolism in breast tumors it is impossible to know which metabolic pathways to target, and how their inhibition might influence different stages of breast tumor progression. Here we perform the first comprehensive profiling of central metabolism in the MCF10 model of mammary carcinoma, where the steps of breast tumor progression (transformation, tumorigenicity and metastasis) can all be examined in the context of the same genetic background. The metabolism of [U-13C]-glucose by a series of progressively more aggressive MCF10 cell lines was tracked by 2D NMR and mass spectrometry. From this analysis the flux of carbon through distinct metabolic reactions was quantified by isotopomer modeling. The results indicate widespread changes to central metabolism upon cellular transformation including increased carbon flux through the pentose phosphate pathway (PPP), the TCA cycle, as well as increased synthesis of glutamate, glutathione and fatty acids (including elongation and desaturation). The de novo synthesis of glycine increased upon transformation as well as at each subsequent step of breast tumor cell progression. Interestingly, the major metabolic shift in metastatic cells is a large increase in the de novo synthesis of proline. This work provides the first comprehensive view of changes to central metabolism as a result of breast tumor progression

Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at s√=8 TeV with ATLAS

Measurements of fiducial and differential cross sections are presented for Higgs boson production in proton-proton collisions at a centre-of-mass energy of s√=8 TeV. The analysis is performed in the H → γγ decay channel using 20.3 fb−1 of data recorded by the ATLAS experiment at the CERN Large Hadron Collider. The signal is extracted using a fit to the diphoton invariant mass spectrum assuming that the width of the resonance is much smaller than the experimental resolution. The signal yields are corrected for the effects of detector inefficiency and resolution. The pp → H → γγ fiducial cross section is measured to be 43.2 ±9.4(stat.) − 2.9 + 3.2 (syst.) ±1.2(lumi)fb for a Higgs boson of mass 125.4GeV decaying to two isolated photons that have transverse momentum greater than 35% and 25% of the diphoton invariant mass and each with absolute pseudorapidity less than 2.37. Four additional fiducial cross sections and two cross-section limits are presented in phase space regions that test the theoretical modelling of different Higgs boson production mechanisms, or are sensitive to physics beyond the Standard Model. Differential cross sections are also presented, as a function of variables related to the diphoton kinematics and the jet activity produced in the Higgs boson events. The observed spectra are statistically limited but broadly in line with the theoretical expectations

Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13