Schrijver graphs and projective quadrangulations

In a recent paper [J. Combin. Theory Ser. B}, 113 (2015), pp. 1-17], the authors have extended the concept of quadrangulation of a surface to higher dimension, and showed that every quadrangulation of the $n$-dimensional projective space $P^n$ is at least $(n+2)$-chromatic, unless it is bipartite. They conjectured that for any integers $k\geq 1$ and $n\geq 2k+1$, the Schrijver graph $SG(n,k)$ contains a spanning subgraph which is a quadrangulation of $P^{n-2k}$. The purpose of this paper is to prove the conjecture

Rapidity Spectra Analysis in Terms of Non Extensive Statistic Approach

We provide description of rapidity spectra of particles produced in p-anti-p collisions using anomalous diffusion approach to account for their non-equilibrium character. In particular, we exhibit connection between multiproduction processes and anomalous diffusion described through the nonlinear Focker-Planck equation with nonlinearity given by the nonextensivity parameter q describing the underlying Tsallis q-statistics and demonstrate how it leads to the Feynman scaling violation in these collisions. The q parameter obtained this way turns out to be closely connected to parameter 1/k converting the original poissonian multiplicity distribution to its observed Negative Binomial form. The inelasticity of reaction has been also calculated and found to slightly decrease with the increasing energy of reaction. Keywords: inelasticity, rapidity spectra, nonextensivityComment: 4 pages, 4 figures, Presented at XII International Symposium on Very High Energy Cosmic Ray Interactions, CERN, Switzerland, 15-20 July 200

On Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions

Symbolic ultrametrics define edge-colored complete graphs K_n and yield a simple tree representation of K_n. We discuss, under which conditions this idea can be generalized to find a symbolic ultrametric that, in addition, distinguishes between edges and non-edges of arbitrary graphs G=(V,E) and thus, yielding a simple tree representation of G. We prove that such a symbolic ultrametric can only be defined for G if and only if G is a so-called cograph. A cograph is uniquely determined by a so-called cotree. As not all graphs are cographs, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of G. The latter problem is equivalent to find an optimal cograph edge k-decomposition {E_1,...,E_k} of E so that each subgraph (V,E_i) of G is a cograph. An upper bound for the integer k is derived and it is shown that determining whether a graph has a cograph 2-decomposition, resp., 2-partition is NP-complete

Initial experience with magnetic resonance imaging-safe pacemakers: A review

Due of its superior soft tissue imaging capabilities, magnetic resonance imaging (MRI) has become the imaging modality of choice in many clinical situations, as illustrated by the tremendous growth in the number of MRIs performed over the past 2 decades. In parallel, the number of patients who require pacemakers or implantable cardiac defibrillators is increasing as indications for these devices broaden and the population ages. Taken together, these phenomena present an important clinical issue, as MR scans are generally contraindicated—except in urgent situations—in patients who have implanted cardiovascular devices. Potentially deleterious interactions between the magnetic fields and radio frequency (RF) energy produced by MR equipment and implantable devices have been identified, including inhibition of pacing, asynchronous/high-rate pacing, lead tip heating, and loss of capture. New devices that incorporate technologies to improve MR safety in patients with pacemakers have recently received approval in Europe and are under evaluation in the United States. Initial data from these devices suggest that these devices are safe in the MRI environment

A Phase II Randomized, Double-Blind, Placebo-Controlled Safety and Efficacy Study of Lenalidomide in Lumbar Radicular Pain with a Long-Term Open-Label Extension Phase.

OBJECTIVE: This phase II study assessed lenalidomide efficacy and safety. DESIGN: Three-phase core study: 14-day prerandomization, 12-week treatment, and 52-week open-label extension. SETTING: Fourteen US centers from July 2005 to July 2007. SUBJECTS: Chronic lumbar radicular pain patients without history of nerve injury or deficit. METHODS: Subjects were randomized (1:1) to double-blind treatment with lenalidomide 10 mg or placebo once daily for 12 weeks, followed by a 52-week open-label extension. A 12-week, single-center, randomized-withdrawal (1:2, lenalidomide:placebo), exploratory study with open-label extension was undertaken in 12 subjects from the core extension who were naïve to neuropathic medications and with at least a two-point decrease from baseline average daily Pain Intensity-Numerical Rating Scale score. RESULTS: Of 180 subjects enrolled, 176 had at least one postbaseline measure; 132 completed the 12-week treatment phase. In the core study, no statistically significant difference in Pain Intensity-Numerical Rating Scale mean change (-0.02, P = 0.958) was observed at week 12 between lenalidomide and placebo; proportions achieving pain reduction at week 12 and other secondary measures were comparable between lenalidomide and placebo. In the exploratory study, week 12 mean changes in Pain Intensity-Numerical Rating Scale scores were -0.05 (lenalidomide: N = 3) and 2.11 (placebo: N = 8). Mean changes in Brief Pain Inventory-short form interference scores were -3.33 and 8.38, respectively; scores at six months were maintained or decreased in 10 of 12 subjects. CONCLUSIONS: While this study does not support lenalidomide use in an unselected lumbar radicular pain population, an immunomodulating agent may relieve pain in select subjects naïve to neuropathic pain medications.ClinicalTrials.gov identifier: NCT00120120

Testing the black disk limit in pppp collisions at very high energy

We use geometric scaling invariant quantities to measure the approach, or not, of the imaginary and real parts of the elastic scattering amplitude, to the black disk limit, in $pp$ collisions at very high energy.Comment: 11 pages, 4 figure

Prion protein interacts with bace1 and differentially regulates its activity towards wild type and swedish mutant amyloid precursor protein

In Alzheimer disease amyloid-β (Aβ) peptides derived from the amyloid precursor protein (APP) accumulate in the brain. Cleavage of APP by the β-secretase BACE1 is the rate-limiting step in the production of Aβ. We have reported previously that the cellular prion protein (PrP(C)) inhibited the action of BACE1 toward human wild type APP (APP(WT)) in cellular models and that the levels of endogenous murine Aβ were significantly increased in PrP(C)-null mouse brain. Here we investigated the molecular and cellular mechanisms underlying this observation. PrP(C) interacted directly with the prodomain of the immature Golgi-localized form of BACE1. This interaction decreased BACE1 at the cell surface and in endosomes where it preferentially cleaves APP(WT) but increased it in the Golgi where it preferentially cleaves APP with the Swedish mutation (APP(Swe)). In transgenic mice expressing human APP with the Swedish and Indiana familial mutations (APP(Swe,Ind)), PrP(C) deletion had no influence on APP proteolytic processing, Aβ plaque deposition, or levels of soluble Aβ or Aβ oligomers. In cells, although PrP(C) inhibited the action of BACE1 on APP(WT), it did not inhibit BACE1 activity toward APP(Swe). The differential subcellular location of the BACE1 cleavage of APP(Swe) relative to APP(WT) provides an explanation for the failure of PrP(C) deletion to affect Aβ accumulation in APP(Swe,Ind) mice. Thus, although PrP(C) exerts no control on cleavage of APP(Swe) by BACE1, it has a profound influence on the cleavage of APP(WT), suggesting that PrP(C) may be a key protective player against sporadic Alzheimer disease

The imprints of superstatistics in multiparticle production processes

We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the nonextensivity parameter q > 1. In nuclear collisions one additionally observes a q-dependence of the multiplicity fluctuations reflecting the finiteness of the hadronizing source. We present sum rules connecting parameters q obtained from an analysis of different observables, which allows us to combine different kinds of fluctuations seen in the data and analyze an ensemble in which the energy (E), temperature (T) and multiplicity (N) can all fluctuate. This results in a generalization of the so called Lindhard's thermodynamic uncertainty relation. Finally, based on the example of nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon collisions) we demonstrate that, for the standard Tsallis entropy with degree of nonextensivity q < 1, the corresponding standard Tsallis distribution is described by q' = 2 - q > 1.Comment: 12 pages, 3 figures. Based on invited talk given by Z.Wlodarczyk at SigmaPhi2011 conference, Larnaka, Cyprus, 11-15 July 2011. To be published in Cent. Eur. J. Phys. (2011

Measurement of the hadronic photon structure function F_{2}^{γ} at LEP2

The hadronic structure function of the photon F_{2}^{γ} (x, Q²) is measured as a function of Bjorken x and of the photon virtuality Q² using deep-inelastic scattering data taken by the OPAL detector at LEP at e⁺e⁻ centre-of-mass energies from 183 to 209 GeV. Previous OPAL measurements of the x dependence of F_{2}^{γ} are extended to an average Q² of 〈Q²〉=780 GeV² using data in the kinematic range 0.15<x<0.98. The Q² evolution of F_{2}^{γ} is studied for 12.1<〈Q²〉<780 GeV² using three ranges of x. As predicted by QCD, the data show positive scaling violations in F_{2}^{γ} with F_{2}^{γ} (Q²)/α = (0.08±0.02⁺⁰·⁰⁵_₀.₀₃) + (0.13±0.01⁺⁰·⁰¹_₀.₀₁) lnQ², where Q² is in GeV², for the central x region 0.10–0.60. Several parameterisations of F_{2}^{γ} are in qualitative agreement with the measurements whereas the quark-parton model prediction fails to describe the data