Polyhedral characteristics of balanced and unbalanced bipartite subgraph problems

We study the polyhedral properties of three problems of constructing an optimal complete bipartite subgraph (a biclique) in a bipartite graph. In the first problem we consider a balanced biclique with the same number of vertices in both parts and arbitrary edge weights. In the other two problems we are dealing with unbalanced subgraphs of maximum and minimum weight with nonnegative edges. All three problems are established to be NP-hard. We study the polytopes and the cone decompositions of these problems and their 1-skeletons. We describe the adjacency criterion in 1-skeleton of the polytope of the balanced complete bipartite subgraph problem. The clique number of 1-skeleton is estimated from below by a superpolynomial function. For both unbalanced biclique problems we establish the superpolynomial lower bounds on the clique numbers of the graphs of nonnegative cone decompositions. These values characterize the time complexity in a broad class of algorithms based on linear comparisons

On Graphs of the Cone Decompositions for the Min-Cut and Max-Cut Problems

We consider maximum and minimum cut problems with nonnegative weights of edges. We define the graphs of the cone decompositions and find a linear clique number for the min-cut problem and a superpolynomial clique number for the max-cut problem. These values characterize the time complexity in a broad class of algorithms based on linear comparisons

Полиэдральные характеристики задач о сбалансированном и несбалансированном двудольных подграфах

We study the polyhedral properties of three problems of constructing an optimal biclique in a bipartite graph. In the first problem we consider a balanced biclique with the same number of vertices in both parts and arbitrary edge weights. In the other two problems it is required to find maximum or minimum unbalanced bicliques with a fixed number of vertices and non-negative edges. All three problems are established to be NP-hard. We study the polytopes and the cone decompositions of these problems and their 1-skeletons. We describe the adjacency criterion in the 1-skeleton of the balanced biclique polytope. Clique number of 1-skeleton is estimated from below by a superpolynomial function. For both unbalanced biclique problems we establish the superpolynomial lower bounds on the clique numbers of the graphs of non-negative cone decompositions. These values characterize the time complexity in a broad class of algorithms based on linear comparisons.Исследуются полиэдральные характеристики трех задач о построении оптимальных полных двудольных подграфов двудольных графов. В первой задаче рассматриваются сбалансированные подграфы с одинаковым числом вершин в каждой доле и произвольными весами ребер. В двух других задачах речь идет о несбалансированных подграфах максимального и минимального веса с неотрицательными ребрами. Устанавливается, что все три задачи являются NP-трудными. В работе изучаются многогранники и конусные разбиения рассматриваемых задач, а также их графы. Для задачи о сбалансированном подграфе приводится условие смежности вершин в полиэдральном графе и графе соответствующего конусного разбиения. Плотность полиэдрального графа оценивается снизу сверхполиномиальной функцией. Для задач о несбалансированных подграфах строятся сверхполиномиальные нижние оценки плотности графов неотрицательных конусных разбиений. Полученные результаты характеризуют временную трудоемкость задач в широком классе алгоритмов, использующих линейные сравнения

Modelling effects of phytobiotic administration on coherent responses to Salmonella infection in laying hens

Practice of layer poultry farming and commercial egg production relies on the optimal use and improvement of the welfare and genetically determined functional abilities of laying hens, their efficient intake of feed and its components, adaptation to housing conditions and resistance to infectious diseases including salmonellosis. Previous studies were focussed on relationships of chicken performance and resistance with the expression profiles of individual genes involved in metabolic processes and immune system, or with genetic markers that can be closely associated with these processes in chickens. In this study, mathematical models of coherent changes in laying hens were developed for the expression of eight genes involved in immunity and metabolism, on the one hand, and biochemical and immunological blood parameters, on the other hand, in response to Salmonella infection and administration of a phytobiotic Intebio. The proposed modelling approach can be a further basis for an in-depth research of the relationship between the gene expression, functional state and welfare of poultry, impact of pathogenic microorganisms and use of immunomodulatory drugs

On the Prospects of Using Metallic Glasses for In-vessel Mirrors for Plasma Diagnostics in ITER

This chapter reviews main results obtained on mirror-like samples made of several grades of bulk metallic glasses (BMG). Experiments were carried out under simulated conditions typical for the operation of plasma facing in-vessel mirrors of optical plasma diagnostics in fusion reactor ITER. Bombardment with D0 and T0 atoms radiated from burning plasma was predicted to be the main reason for the degradation of optical properties of such mirrors. Therefore, to simulate the behavior of mirrors in ITER, mirror-like samples were subjected to bombardment by ions of deuterium plasma with fixed or wide energy distribution. The effects of ion bombardment on optical properties, development of roughness, uptake of deuterium, appearance of blisters, and manifestation of some chemical processes are presented and discussed

Nucleosome Chiral Transition under Positive Torsional Stress in Single Chromatin Fibers

Using magnetic tweezers to investigate the mechanical response of single chromatin fibers, we show that fibers submitted to large positive torsion transiently trap positive turns, at a rate of one turn per nucleosome. A comparison with the response of fibers of tetrasomes (the (H3-H4)2 tetramer bound with ~50 bp of DNA) obtained by depletion of H2A-H2B dimers, suggests that the trapping reflects a nucleosome chiral transition to a metastable form built on the previously documented righthanded tetrasome. In view of its low energy, <8 kT, we propose this transition is physiologically relevant and serves to break the docking of the dimers on the tetramer which in the absence of other factors exerts a strong block against elongation of transcription by the main RNA polymerase.Comment: 33 pages (double spacing), 7 figure

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration