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

Analysis of weighted networks

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure

Early Host Tissue Response to Different Types of Vascular Prostheses Coated with Silver Acetate or Vaporized Metallic Silver

ObjectivesIn vascular surgery, the infection of prosthetic vascular grafts represents a serious life-threatening complication. Due to the increasing resistance of hospital micro-organisms to standard antibiotic therapies, maximum effort should be put in the primary prevention of such infections. For this purpose, grafts may be coated with different antibacterial silver formulations. In the present study the different effects of silver acetate-coating and vaporized metallic silver-coating on the vascularization and perigraft inflammation during the initial phase after implantation of Intergard Silver (IS) and Silver Graft (SG) were compared.MethodsSilver acetate-coated IS and vaporized metallic silver-coated SG were implanted into the dorsal skinfold chamber of C57BL/6 mice (n = 8 per group) to study angiogenesis and leukocyte inflammation at the implantation site by means of repetitive intravital fluorescence microscopy over a 14-day period. At the end of the in vivo experiments, apoptosis and cell proliferation in the newly developed granulation tissue surrounding the implants was analyzed by immunohistochemistry.ResultsIS exhibited an improved vascularization, resulting in a significantly higher functional capillary density when compared to SG. Moreover, the leukocyte inflammatory response to IS was less pronounced, as indicated by a reduced number of adherent leukocytes in perigraft venules. This was associated with a higher proliferative activity of the granulation tissue incorporating the IS when compared to SG. The numbers of apoptotic cells in the perigraft tissue were low and did not differ between the two groups.ConclusionSilver acetate-coated IS exhibits an improved vascularization and reduced perigraft inflammation during the first 14 days after implantation when compared to vaporized metallic silver-coated SG. This may contribute to reducing the risk of early perigraft seroma formation and subsequent infection

Synchronization Model for Stock Market Asymmetry

The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this, we introduce a market model consisting of randomly fluctuating stocks that occasionally synchronize their short term draw-downs. These synchronous events are parameterized by a ``fear factor'', that reflects the occurrence of dramatic external events which affect the financial market.Comment: 4 pages, 4 figure

Efficiency in Multi-objective Games

In a multi-objective game, each agent individually evaluates each overall action-profile on multiple objectives. I generalize the price of anarchy to multi-objective games and provide a polynomial-time algorithm to assess it. This work asserts that policies on tobacco promote a higher economic efficiency

Design of an Intelligent, Modular IGBT/SiC Inverter Platform up to 400 kW for Fast Realization of New Test-Bench Concepts

This paper presents an intelligent, modular two level, three phase inverter platform for up to 1200 V DC-link voltage and 400 kW continuous power at 10 kHz switching frequency. It features an integrated signal processing system and various sensors, which allow standalone as well as cross-linked operation. Customizable software of the signal processing system allows easy adaption to different applications such as Active-Front-End (AFE), DC/DC-converters, Dual-Active-Bridges or Drive Inverters. Focus of this paper is a design guideline for an inverter platform which fulfills requirements of various applications with regard to sensor setup, control, failure management and monitoring. Design goal of the platform is a fast setup of new testbench concepts for academic research and novel applications

Copyright and cultural work: an exploration

This article first discusses the contemporary debate on cultural “creativity” and the economy. Second, it considers the current state of UK copyright law and how it relates to cultural work. Third, based on empirical research on British dancers and musicians, an analysis of precarious cultural work is presented. A major focus is how those who follow their art by way of “portfolio” work handle their rights in ways that diverge significantly from the current simplistic assumptions of law and cultural policy. Our conclusions underline the distance between present top-down conceptions of what drives production in the cultural field and the actual practice of dancers and musicians

Microcirculatory alterations in ischemia–reperfusion injury and sepsis: effects of activated protein C and thrombin inhibition

Experimental studies in ischemia–reperfusion and sepsis indicate that activated protein C (APC) has direct anti-inflammatory effects at a cellular level. In vivo, however, the mechanisms of action have not been characterized thus far. Intravital multifluorescence microscopy represents an elegant way of studying the effect of APC on endotoxin-induced leukocyte–endothelial-cell interaction and nutritive capillary perfusion failure. These studies have clarified that APC effectively reduces leukocyte rolling and leukocyte firm adhesion in systemic endotoxemia. Protection from leukocytic inflammation is probably mediated by a modulation of adhesion molecule expression on the surface of leukocytes and endothelial cells. Of interest, the action of APC and antithrombin in endotoxin-induced leukocyte–endothelial-cell interaction differs in that APC inhibits both rolling and subsequent firm adhesion, whereas antithrombin exclusively reduces the firm adhesion step. The biological significance of this differential regulation of inflammation remains unclear, since both proteins are capable of reducing sepsis-induced capillary perfusion failure. To elucidate whether the action of APC and antithrombin is mediated by inhibition of thrombin, the specific thrombin inhibitor hirudin has been examined in a sepsis microcirculation model. Strikingly, hirudin was not capable of protecting from sepsis-induced microcirculatory dysfunction, but induced a further increase of leukocyte–endothelial-cell interactions and aggravated capillary perfusion failure when compared with nontreated controls. Thus, the action of APC on the microcirculatory level in systemic endotoxemia is unlikely to be caused by a thrombin inhibition-associated anticoagulatory action

Einstein's "Zur Elektrodynamik..." (1905) Revisited, with Some Consequences

Einstein, in his "Zur Elektrodynamik bewegter Korper", gave a physical (operational) meaning to "time" of a remote event in describing "motion" by introducing the concept of "synchronous stationary clocks located at different places". But with regard to "place" in describing motion, he assumed without analysis the concept of a system of co-ordinates. In the present paper, we propose a way of giving physical (operational) meaning to the concepts of "place" and "co-ordinate system", and show how the observer can define both the place and time of a remote event. Following Einstein, we consider another system "in uniform motion of translation relatively to the former". Without assuming "the properties of homogeneity which we attribute to space and time", we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, "one-way" and "two-way" velocities of light, symmetry, the "group property" of inertial reference frames, length contraction and time dilatation, and the "twin paradox". Finally, we point out a flaw in Einstein's argument in the "Electrodynamical Part" of his paper and show that the Lorentz force formula and Einstein's formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck's formula for mass suffices. (Except for the reference to Planck's formula, we restrict ourselves to Physics of 1905.)Comment: 55 pages, 4 figures, accepted for publication in "Foundations of Physics