On Sudakov's type decomposition of transference plans with norm costs

We consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost \d{\cdot}\min \bigg\{ \int \d{\mathtt T(x) - x} d\mu(x), \ \mathtt T : \R^d \to \R^d, \ \nu = \mathtt T_\# \mu \bigg\},with $\mu$, $\nu$ probability measures in $\R^d$ and $\mu$ absolutely continuous w.r.t. \LL. The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in Z_\a\times\R^d, where \{Z_\a\}_{\a\in\A} \subset \R^d are disjoint regions such that the construction of an optimal map \mathtt T_\a : Z_\a \to \R^d is simpler than in the original problem, and then to obtain $\mathtt T$ by piecing together the maps \mathtt T_\a. When the norm \d{\cdot} is strictly convex \cite{sudak}, the sets Z_\a are a family of $1$-dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map \mathtt T_\a is straightforward provided one can show that the disintegration of \LL (and thus of $\mu$) on such segments is absolutely continuous w.r.t. the $1$-dimensional Hausdorff measure \cite{Car:strictly}. When the norm \d{\cdot} is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions \{Z_\a\}_{\a\in\A} on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper we show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set Z_\a and then in $\R^d$. The strategy is sufficiently powerful to be applied to other optimal transportation problems. The analysis requires \begin{enumerate}\item the study of the transportation problem on directed locally affine partitions \{Z\ka,C\ka\}_{k,\a} of $\R^d$, i.e. sets Z\ka \subset \R^d which are relatively open in their $k$-dimensional affine hull and on which the transport occurs only along directions belonging to a cone C\ka;\item the proof of the absolute continuity w.r.t. the suitable $k$-dimensional Hausdorff measure of the disintegration of \LL on these directed locally affine partitions;\item the definition of cyclically connected sets w.r.t. a family of transportation plans with finite cone costs;\item the proof of the existence of cyclically connected directed locally affine partitions for transport problems with cost functions which are indicator functions of cones and no potentials can be constructed. \end{enumerate

The Measurement Process in Local Quantum Theory and the EPR Paradox

We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account: 1. the finite and non zero time duration T of the interaction between the observed system and the microscopic part of the measurement apparatus; 2. the finite space size R of that apparatus; 3. the fact that the macroscopic part of the measurement apparatus, having the role of amplifying the effect of that interaction to a macroscopic scale, is composed by a very large but finite number N of particles. The conventional picture of the measurement, as an instantaneous action turning a pure state into a mixture, arises only in the limit in which N and R tend to infinity, and T tends to 0. We sketch here a proposed scheme, which still ought to be made mathematically precise in order to analyse its implications and to test it in specific models, where we argue that in Quantum Field Theory this picture should apply to the unique time evolution expressing the dynamics of a given theory, and should comply with the Principle of Locality. We comment on the Einstein Podolski Rosen thought experiment (partly modifying the discussion on this point in an earlier version of this note), reformulated here only in terms of local observables (rather than global ones, as one particle or polarisation observables). The local picture of the measurement process helps to make it clear that there is no conflict with the Principle of Locality.Comment: 18 page

The effects of related experiments

The effects of the experiment itself upon the obtained results and, especially, the influence of a large number of experiments are extensively discussed in the literature. We show that the important factor that stands at the basis of these effects is that the involved experiments are related and not independent and detached from each other. This relationship takes, as shown here, different forms for different situations and is found in entirely different physical regimes such as the quantum and classical ones.Comment: 27 pages, 6 figures, 1 table. One figure removed. Some former text has been rewritten in compact and clearer way. Also the title change

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

Search for chargino-neutralino production with mass splittings near the electroweak scale in three-lepton final states in √s=13 TeV pp collisions with the ATLAS detector

A search for supersymmetry through the pair production of electroweakinos with mass splittings near the electroweak scale and decaying via on-shell W and Z bosons is presented for a three-lepton final state. The analyzed proton-proton collision data taken at a center-of-mass energy of √s=13  TeV were collected between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 139  fb−1. A search, emulating the recursive jigsaw reconstruction technique with easily reproducible laboratory-frame variables, is performed. The two excesses observed in the 2015–2016 data recursive jigsaw analysis in the low-mass three-lepton phase space are reproduced. Results with the full data set are in agreement with the Standard Model expectations. They are interpreted to set exclusion limits at the 95% confidence level on simplified models of chargino-neutralino pair production for masses up to 345 GeV

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Ricci curvature of finite Markov chains via convexity of the entropy

We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry--Emery and Otto--Villani. Furthermore we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.Comment: 39 pages, to appear in Arch. Ration. Mech. Ana

A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes

A Lagrangian numerical scheme for solving nonlinear degenerate Fokker{Planck equations in space dimensions d>2 is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies and given external potentials, e.g. the porous medium equation and the fast diffusion equation. The key ingredient in our approach is the gradient ow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretisation, the fully discrete solution inherits energy estimates from the original gradient ow, and these lead to weak compactness of the trajectories in the continuous limit. Consistency is analyzed in the planar situation, d = 2. A variety of numerical experiments for the porous medium equation indicates that the scheme is well-adapted to track the growth of the solution's support

Low NKp30, NKp46 and NKG2D expression and reduced cytotoxic activity on NK cells in cervical cancer and precursor lesions

<p>Abstract</p> <p>Background</p> <p>Persistent high risk HPV infection can lead to cervical cancer, the second most common malignant tumor in women worldwide. NK cells play a crucial role against tumors and virus-infected cells through a fine balance between activating and inhibitory receptors. Expression of triggering receptors NKp30, NKp44, NKp46 and NKG2D on NK cells correlates with cytolytic activity against tumor cells, but these receptors have not been studied in cervical cancer and precursor lesions. The aim of the present work was to study NKp30, NKp46, NKG2D, NKp80 and 2B4 expression in NK cells from patients with cervical cancer and precursor lesions, in the context of HPV infection.</p> <p>Methods</p> <p>NKp30, NKp46, NKG2D, NKp80 and 2B4 expression was analyzed by flow cytometry on NK cells from 59 patients with cervical cancer and squamous intraepithelial lesions. NK cell cytotoxicity was evaluated in a 4 hour CFSE/7-AAD flow cytometry assay. HPV types were identified by PCR assays.</p> <p>Results</p> <p>We report here for the first time that NK cell-activating receptors NKp30 and NKp46 are significantly down-regulated in cervical cancer and high grade squamous intraepithelial lesion (HGSIL) patients. NCRs down-regulation correlated with low cytolytic activity, HPV-16 infection and clinical stage. NKG2D was also down-regulated in cervical cancer patients.</p> <p>Conclusion</p> <p>Our results suggest that NKp30, NKp46 and NKG2D down-regulation represent an evasion mechanism associated to low NK cell activity, HPV-16 infection and cervical cancer progression.</p

Augmented serum level of major histocompatibility complex class I-related chain A (MICA) protein and reduced NKG2D expression on NK and T cells in patients with cervical cancer and precursor lesions

<p>Abstract</p> <p>Background</p> <p>Cervical cancer is the second most common cancer in women worldwide. NK and cytotoxic T cells play an important role in the elimination of virus-infected and tumor cells through NKG2D activating receptors, which can promote the lysis of target cells by binding to the major histocompatibility complex class I-related chain A (MICA) proteins. Increased serum levels of MICA have been found in patients with epithelial tumors. The aim of this study was to compare the levels of soluble MICA (sMICA) and NKG2D-expressing NK and T cells in blood samples from patients with cervical cancer or precursor lesions with those from healthy donors.</p> <p>Methods</p> <p>Peripheral blood with or without heparin was collected to obtain mononuclear cells or sera, respectively. Serum sMICA levels were measured by ELISA and NKG2D-expressing immune cells were analyzed by flow cytometry. Also, a correlation analysis was performed to associate sMICA levels with either NKG2D expression or with the stage of the lesion.</p> <p>Results</p> <p>Significant amounts of sMICA were detected in sera from nearly all patients. We found a decrease in the number of NKG2D-expressing NK and T cells in both cervical cancer and lesion groups when compared to healthy donors. Pearson analysis showed a negative correlation between sMICA and NKG2D-expressing T cells; however, we did not find a significant correlation when the analysis was applied to sMICA and NKG2D expression on NK cells.</p> <p>Conclusion</p> <p>Our results show for the first time that high sMICA levels are found in sera from patients with both cervical cancer and precursor lesions when compared with healthy donors. We also observed a diminution in the number of NKG2D-expressing NK and T cells in the patient samples; however, a significant negative correlation between sMICA and NKG2D expression was only seen in T cells.</p