Normal edge-colorings of cubic graphs

A normal $k$-edge-coloring of a cubic graph is an edge-coloring with $k$ colors having the additional property that when looking at the set of colors assigned to any edge $e$ and the four edges adjacent it, we have either exactly five distinct colors or exactly three distinct colors. We denote by $\chi'_{N}(G)$ the smallest $k$, for which $G$ admits a normal $k$-edge-coloring. Normal $k$-edge-colorings were introduced by Jaeger in order to study his well-known Petersen Coloring Conjecture. More precisely, it is known that proving $\chi'_{N}(G)\leq 5$ for every bridgeless cubic graph is equivalent to proving Petersen Coloring Conjecture and then, among others, Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture. Considering the larger class of all simple cubic graphs (not necessarily bridgeless), some interesting questions naturally arise. For instance, there exist simple cubic graphs, not bridgeless, with $\chi'_{N}(G)=7$. On the other hand, the known best general upper bound for $\chi'_{N}(G)$ was $9$. Here, we improve it by proving that $\chi'_{N}(G)\leq7$ for any simple cubic graph $G$, which is best possible. We obtain this result by proving the existence of specific no-where zero $\mathbb{Z}_2^2$-flows in $4$-edge-connected graphs.Comment: 17 pages, 6 figure

Risk, rationality, and resilience

Improving our ability to cope with large risks is one of the key challenges for humankind in this century. This article outlines a research program in this perspective. Starting with a concrete example of a relatively small disaster, it questions simplistic ideas of rationality. It then proposes a fresh look at the concepts of probability and utility in the context of socio-ecological systems. This leads first to an emphasis on the problem of equilibrium selection, and then to a distinction between three kinds of resilience that matter both for theory and practice of risk management. They can be investigated by paying attention to the transitions into and out of actual disasters

A study in the mathematical theory of the conduction of heat

This work represents a study in the application of the Laplace Trans format! on method to the Theory of Conduction of Heat; with a few exceptions indicated in footnotes, the derivation by this method of all the results is new. In Chapters II, VI, VIII, and X which contain collections of results, some of these are classical and given for completeness, and some are new* Almost all the results of Chapters I, III, IV, VII, and IX are believed to be new# None of this work has been submitted for any degree, and it is entirely my own with the exception of Chapters I and X, which have been written for publication in collaboration with Professor Carslaw. These are included here since they form an essential part of the whole scheme; the problems considered were solved independently and published jointly. The parts of this thesis which the referee may deem suitable will be published as soon as possible. Chapters I, VII, and X, and portion of Chapter I1/ have already been published, and Chapter III, and portions of Chapters VIII and IX are in the press# It is my pleasure to adknowledge my great indebtedness to Professor Carslaw who not only aroused my interest in the subject, but in the course of a frequent correspondence extending over several years has been most generous with advice and criticism# I am also indebted to Miss M. E. Clarke for her assistance with the computations of Chapter V and for the preparation of the typescript

Agents, Bayes, and Climatic Risks - a modular modelling approach

International audienceWhen insurance firms, energy companies, governments, NGOs, and other agents strive to manage climatic risks, it is by no way clear what the aggregate outcome should and will be. As a framework for investigating this subject, we present the LAGOM model family. It is based on modules depicting learning social agents. For managing climate risks, our agents use second order probabilities and update them by means of a Bayesian mechanism while differing in priors and risk aversion. The interactions between these modules and the aggregate outcomes of their actions are implemented using further modules. The software system is implemented as a series of parallel processes using the CIAMn approach. It is possible to couple modules irrespective of the language they are written in, the operating system under which they are run, and the physical location of the machine

Nurses\u27 Alumnae Association Bulletin, April 1955

Alumnae Notes Annual Giving Committee Reports Digest of Alumnae Meetings Graduation Awards - 1954 Legal Aspects of Nursing Marriages Necrology New Arrivals Physical Advances at Jefferson President\u27s Message School of Nursing Report The Challenge of Neurosurgical Nursin

Condensation of Hard Spheres Under Gravity

Starting from Enskog equation of hard spheres of mass m and diameter D under the gravity g, we first derive the exact equation of motion for the equilibrium density profile at a temperature T and examine its solutions via the gradient expansion. The solutions exist only when \beta\mu \le \mu_o \approx 21.756 in 2 dimensions and \mu_o\approx 15.299 in 3 dimensions, where \mu is the dimensionless initial layer thickness and \beta=mgD/T. When this inequality breaks down, a fraction of particles condense from the bottom up to the Fermi surface.Comment: 9 pages, one figur

WSC-07: Evolving the Web Services Challenge

Service-oriented architecture (SOA) is an evolving architectural paradigm where businesses can expose their capabilities as modular, network-accessible software services. By decomposing capabilities into modular services, organizations can share their offerings at multiple levels of granularity while also creating unique access points for their peer organizations. The true impact of SOA will be realized when 3rd party organizations can obtain a variety of services, on-demand, and create higher-order composite business processes. The Web Services Challenge (WSC) is a forum where academic and industry researchers can share experiences of developing tools that automate the integration of web services. In the third year (i.e. WSC-07) of the Web Services Challenge, software platforms will address several new composition challenges. Requests and results will be transmitted within SOAP messages. In addition, semantic representations will be both represented in the eXtensible Markup Language (XML) and in the Web Ontology Language (OWL). Finally, composite processes will have both sequential and concurrent branches