Dynamical mass generation in quantum field theory : some methods with application to the Gross-Neveu model and Yang-Mills theory

We introduce some techniques to investigate dynamical mass generation. The Gross-Neveu model (GN) is used as a toy model, because the GN mass gap is exactly known, making it possible to check reliability of the various methods. Very accurate results are obtained. Also application to SU(N) Yang-Mills (YM) is discussed.Comment: 8 LaTeX2e pages, uses Kluwer class file crckbked.cls. Kluwer package included. To appear in: Proceedings of the NATO Advanced Research Workshop on "Confinement, Topology, and other Non-Perturbative Aspects of QCD", Stara Lesna, Slovakia, 21-27 jan 200

A 2k2k-Vertex Kernel for Maximum Internal Spanning Tree

We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a $3k$-vertex kernel. Here we propose a novel way to use the same reduction rule, resulting in an improved $2k$-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a deterministic algorithm for the problem running in time $4^k \cdot n^{O(1)}$

Finding detours is fixed-parameter tractable

We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k longer than a shortest (s,t)-path. Using insights into structural graph theory, we prove that Longest Detour is fixed-parameter tractable (FPT) on undirected graphs and actually even admits a single-exponential algorithm, that is, one of running time exp(O(k)) poly(n). This matches (up to the base of the exponential) the best algorithms for finding a path of length at least k. Furthermore, we study the related problem Exact Detour that asks whether a graph G contains an (s,t)-path that is exactly k longer than a shortest (s,t)-path. For this problem, we obtain a randomized algorithm with running time about 2.746^k, and a deterministic algorithm with running time about 6.745^k, showing that this problem is FPT as well. Our algorithms for Exact Detour apply to both undirected and directed graphs.Comment: Extended abstract appears at ICALP 201

Cross infection in a hospital ward and deposition of particles exhaled from a source patient

The cross infection in a hospital ward is studied. Deposition of particles exhaled from a source manikin is investigated in a full-scale hospital ward ventilated by downward directed ventilation. Deposition on vertical surfaces close to the source shows distribution of particles directed upwards in the room. Deposition at the four beds shows that particles smaller than 10 μm disperse evenly in the ward, indicating that particles smaller than this size are airborne. The influence of top and bottom extraction openings on dispersion of particles is investigated. Results show that vertical distribution in the room is not affected by the position of the return openings. Deposition of particles at the four beds gives some indication of a less wide spread of particles with the use of ceiling-mounted return openings, and thereby a better protection of patients compared with bottom return openings.postprint第五届居住建筑能源与环境国际研讨会 (EERB) & 第三届建筑环境与公共健康国际学术会议 (BEPH), 中国, 桂林, 2009年5月29至31日.The 5th International Workshop on Energy and Environment of Residential Buildings and the 3rd International Conference on Built Environment and Public Health (EERB-BEPH 2009), Guilin, China, 29-31 May 2009

Safety and immunogenicity of a new tuberculosis vaccine, MVA85A, in mycobacterium tuberculosis–infected individuals

Copyright © 2009 by the American Thoracic Society.Rationale: An effective new tuberculosis (TB) vaccine regimen must be safe in individuals with latent TB infection (LTBI) and is a priority for global health care. Objectives: To evaluate the safety and immunogenicity of a leading new TB vaccine, recombinant Modified Vaccinia Ankara expressing Antigen 85A (MVA85A) in individuals with LTBI. Methods: An open-label, phase I trial of MVA85A was performed in 12 subjects with LTBI recruited from TB contact clinics in Oxford and London or by poster advertisements in Oxford hospitals. Patients were assessed clinically and had blood samples drawn for immunological analysis over a 52-week period after vaccination with MVA85A. Thoracic computed tomography scans were performed at baseline and at 10 weeks after vaccination. Safety of MVA85A was assessed by clinical, radiological, and inflammatory markers. The immunogenicity of MVA85A was assessed by IFNγ and IL-2 ELISpot assays and FACS. Measurements and Main Results: MVA85A was safe in subjects with LTBI, with comparable adverse events to previous trials of MVA85A. There were no clinically significant changes in inflammatory markers or thoracic computed tomography scans after vaccination. MVA85A induced a strong antigen-specific IFN-γ and IL-2 response that was durable for 52 weeks. The magnitude of IFN-γ response was comparable to previous trials of MVA85A in bacillus Calmette-Guérin–vaccinated individuals. Antigen 85A–specific polyfunctional CD4+ T cells were detectable prior to vaccination with statistically significant increases in cell numbers after vaccination. Conclusions: MVA85A is safe and highly immunogenic in individuals with LTBI. These results will facilitate further trials in TB-endemic areas.Oxford Biomedical Research Centre, Wellcome Trust, and AFTBVAC

Spontaneous emission of radiation by metallic electrons in the presence of electromagnetic fields of surface plasmon oscillations

The spontaneous emission of radiation of metallic electrons embedded in a high-intensity enhanced surface plasmon field is considered analytically. The electrons are described by exact dressed quantum states which contain the interaction with the plasmon field non-perturbatively. Considerable deviations from the pertubative behaviour have been found in the intensity dependence of the emitted fundamental and the second harmonic signals, even at moderate incoming laser intensities. The theoretical predictions deduced from the formalism are in good qualitative agreement with the experimental results.Comment: 23 pages, 6 figure

Unit Interval Editing is Fixed-Parameter Tractable

Given a graph~$G$ and integers $k_1$, $k_2$, and~$k_3$, the unit interval editing problem asks whether $G$ can be transformed into a unit interval graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. We give an algorithm solving this problem in time $2^{O(k\log k)}\cdot (n+m)$, where $k := k_1 + k_2 + k_3$, and $n, m$ denote respectively the numbers of vertices and edges of $G$. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time $O(4^k \cdot (n + m))$. Another result is an $O(6^k \cdot (n + m))$-time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time $O(6^k \cdot n^6)$.Comment: An extended abstract of this paper has appeared in the proceedings of ICALP 2015. Update: The proof of Lemma 4.2 has been completely rewritten; an appendix is provided for a brief overview of related graph classe

Parameterized Edge Hamiltonicity

We study the parameterized complexity of the classical Edge Hamiltonian Path problem and give several fixed-parameter tractability results. First, we settle an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT parameterized by vertex cover, and that it also admits a cubic kernel. We then show fixed-parameter tractability even for a generalization of the problem to arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set. We also consider the problem parameterized by treewidth or clique-width. Surprisingly, we show that the problem is FPT for both of these standard parameters, in contrast to its vertex version, which is W-hard for clique-width. Our technique, which may be of independent interest, relies on a structural characterization of clique-width in terms of treewidth and complete bipartite subgraphs due to Gurski and Wanke

Pixel and Voxel Representations of Graphs

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are adjacent if they share an edge, two voxels if they share a face. We call a connected set of pixels or voxels a blob. Given a graph, we represent its vertices by disjoint blobs such that two blobs contain adjacent pixels or voxels if and only if the corresponding vertices are adjacent. We are interested in the size of a representation, which is the number of pixels or voxels it consists of. We first show that finding minimum-size representations is NP-complete. Then, we bound representation sizes needed for certain graph classes. In 2D, we show that, for $k$-outerplanar graphs with $n$ vertices, $\Theta(kn)$ pixels are always sufficient and sometimes necessary. In particular, outerplanar graphs can be represented with a linear number of pixels, whereas general planar graphs sometimes need a quadratic number. In 3D, $\Theta(n^2)$ voxels are always sufficient and sometimes necessary for any $n$-vertex graph. We improve this bound to $\Theta(n\cdot \tau)$ for graphs of treewidth $\tau$ and to $O((g+1)^2n\log^2n)$ for graphs of genus $g$. In particular, planar graphs admit representations with $O(n\log^2n)$ voxels

Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

A 3-path vertex cover in a graph is a vertex subset $C$ such that every path of three vertices contains at least one vertex from $C$. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at most $k$. In this paper, we give a kernel of $5k$ vertices and an $O^*(1.7485^k)$-time and polynomial-space algorithm for this problem, both new results improve previous known bounds.Comment: in TAMC 2016, LNCS 9796, 201