Min-Max Theorems for Packing and Covering Odd (u,v)(u,v)-trails

We investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail odd if the number of edges in the trail is odd. Let $\nu(u,v)$ denote the maximum number of edge-disjoint odd $(u,v)$-trails, and $\tau(u,v)$ denote the minimum size of an edge-set that intersects every odd $(u,v)$-trail. We prove that $\tau(u,v)\leq 2\nu(u,v)+1$. Our result is tight---there are examples showing that $\tau(u,v)=2\nu(u,v)+1$---and substantially improves upon the bound of $8$ obtained in [Churchley et al 2016] for $\tau(u,v)/\nu(u,v)$. Our proof also yields a polynomial-time algorithm for finding a cover and a collection of trails satisfying the above bounds. Our proof is simple and has two main ingredients. We show that (loosely speaking) the problem can be reduced to the problem of packing and covering odd $(uv,uv)$-trails losing a factor of 2 (either in the number of trails found, or the size of the cover). Complementing this, we show that the odd-$(uv,uv)$-trail packing and covering problems can be tackled by exploiting a powerful min-max result of [Chudnovsky et al 2006] for packing vertex-disjoint nonzero $A$-paths in group-labeled graphs

EFFECT OF INFARCT SIZE LIMITATION BY PROPRANOLOL ON VENTRICULAR ARRHYTHMIAS AFTER MYOCARDIAL INFARCTION

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75625/1/j.1749-6632.1982.tb55220.x.pd

On the trace identity in a model with broken symmetry

Considering the simple chiral fermion meson model when the chiral symmetry is explicitly broken, we show the validity of a trace identity -- to all orders of perturbation theory -- playing the role of a Callan-Symanzik equation and which allows us to identify directly the breaking of dilatations with the trace of the energy-momentum tensor. More precisely, by coupling the quantum field theory considered to a classical curved space background, represented by the non-propagating external vielbein field, we can express the conservation of the energy-momentum tensor through the Ward identity which characterizes the invariance of the theory under the diffeomorphisms. Our ``Callan-Symanzik equation'' then is the anomalous Ward identity for the trace of the energy-momentum tensor, the so-called ``trace identity''.Comment: 11 pages, Revtex file, final version to appear in Phys.Rev.

Regional versus global finite-state error repair

[Abstract] We focus on the domain of a regional least-cost strategy in order to illustrate the viability of non-global repair models over finitestate architectures. Our interest is justified by the difficulty, shared by all repair proposals, to determine how far to validate. A short validation may fail to gather sufficient information, and in a long one most of the effort can be wasted. The goal is to prove that our approach can provide, in practice, a performance and quality comparable to that attained by global criteria, with a significant saving in time and space. To the best of our knowledge, this is the first discussion of its kind.Ministerio de Educación y Ciencia; TIN2004-07246-C03-02Ministerio de Educación y Ciencia; HP2002-0081Xunta de Galcia; PGIDIT03SIN30501PRXunta de Galcia; PGIDIT02SIN01

Mechanics and dynamics of X-chromosome pairing at X inactivation

At the onset of X-chromosome inactivation, the vital process whereby female mammalian cells equalize X products with respect to males, the X chromosomes are colocalized along their Xic (X-inactivation center) regions. The mechanism inducing recognition and pairing of the X’s remains, though, elusive. Starting from recent discoveries on the molecular factors and on the DNA sequences (the so-called "pairing sites") involved, we dissect the mechanical basis of Xic colocalization by using a statistical physics model. We show that soluble DNA-specific binding molecules, such as those experimentally identified, can be indeed sufficient to induce the spontaneous colocalization of the homologous chromosomes but only when their concentration, or chemical affinity, rises above a threshold value as a consequence of a thermodynamic phase transition. We derive the likelihood of pairing and its probability distribution. Chromosome dynamics has two stages: an initial independent Brownian diffusion followed, after a characteristic time scale, by recognition and pairing. Finally, we investigate the effects of DNA deletion/insertions in the region of pairing sites and compare model predictions to available experimental data

Interpolating gauge fixing for Chern-Simons theory

Chern-Simons theory is analyzed with a gauge-fixing which allows to discuss the Landau gauge and the light-cone gauge at the same time.Comment: 11 pages, Report TUW-93-2

On the Lense-Thirring test with the Mars Global Surveyor in the gravitational field of Mars

I discuss some aspects of the recent test of frame-dragging performed by me by exploiting the Root-Mean-Square (RMS) orbit overlap differences of the out-of-plane component N of the orbit of the Mars Global Surveyor (MGS) spacecraft in the gravitational field of Mars. A linear fit of the full time series of the entire MGS data (4 February 1999-14 January 2005) yields a normalized slope 1.03 +/- 0.41 (with 95% confidence bounds). Other linear fits to different data sets confirm the agreement with general relativity. The huge systematic effects induced by the mismodeling in the martian gravitational field claimed by some authors are absent in the MGS out-of-plane record. The non-gravitational forces affect at the same level of the gravitomagnetic one the in-plane orbital components of MGS, not the out-of-plane one. Moreover, they experience high-frequency variations which does not matter in the present case in which secular effects are relevant.Comment: LaTex2e, 8 pages, no figures, no tables, 17 references. It refers to K. Krogh, Class. Quantum Grav., 24, 5709-5715, 2007 based on astro-ph/0701653. Final version to appear in CEJP (Central European Journal of Physics

Constraints from orbital motions around the Earth of the environmental fifth-force hypothesis for the OPERA superluminal neutrino phenomenology

It has been recently suggested by Dvali and Vikman that the superluminal neutrino phenomenology of the OPERA experiment may be due to an environmental feature of the Earth, naturally yielding a long-range fifth force of gravitational origin whose coupling with the neutrino is set by the scale M_*, in units of reduced Planck mass. Its characteristic length lambda should not be smaller than one Earth's radius R_e, while its upper bound is expected to be slightly smaller than the Earth-Moon distance (60 R_e). We analytically work out some orbital effects of a Yukawa-type fifth force for a test particle moving in the modified field of a central body. Our results are quite general since they are not restricted to any particular size of lambda; moreover, they are valid for an arbitrary orbital configuration of the particle, i.e. for any value of its eccentricity $e$. We find that the dimensionless strength coupling parameter alpha is constrained to |alpha| <= 1 10^-10-4 10^-9 for 1 R_e <= lambda <= 10 R_e by the laser data of the Earth's artificial satellite LAGEOS II, corresponding to M_* >= 4 10^9 -1.6 10^10. The Moon perigee allows to obtain |alpha| <= 3 10^-11 for the Earth-Moon pair in the range 15 R_e <= lambda = 3 10^10 - 4.5 10^10. Our results are neither necessarily limited to the superluminal OPERA scenario nor to the Dvali-Vikman model, in which it is M_* = 10^-6 at lambda = 1 R_e, in contrast with our bounds: they generally extend to any theoretical scenario implying a fifth-force of Yukawa-type.Comment: LaTex2e, 18 pages, 4 figures, 1 table, 81 reference

Supersymmetric Yang-Mills theories with local coupling: The supersymmetric gauge

Supersymmetric pure Yang-Mills theory is formulated with a local, i.e. space-time dependent, complex coupling in superspace. Super-Yang-Mills theories with local coupling have an anomaly, which has been first investigated in the Wess-Zumino gauge and there identified as an anomaly of supersymmetry. In a manifest supersymmetric formulation the anomaly appears in two other identities: The first one describes the non-renormalization of the topological term, the second relates the renormalization of the gauge coupling to the renormalization of the complex supercoupling. Only one of the two identities can be maintained in perturbation theory. We discuss the two versions and derive the respective beta function of the local supercoupling, which is non-holomorphic in the first version, but directly related to the coupling renormalization, and holomorphic in the second version, but has a non-trivial, i.e.anomalous, relation to the beta function of the gauge coupling.Comment: References correcte