An upper bound for the minimum rank of a graph

For a graph G of order n, the minimum rank of G is defined to be the smallest possible rank over all real symmetric n×n matrices A whose (i,j)th entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We prove an upper bound for minimum rank in terms of minimum degree of a vertex is valid for many graphs, including all bipartite graphs, and conjecture this bound is true over for all graphs, and prove a related bound for all zero-nonzero patterns of (not necessarily symmetric) matrices. Most of the results are valid for matrices over any infinite field, but need not be true for matrices over finite fields

Estimation Of Fluid Loading On Offshore Structures

This paper is a working guide to methods and associated data for estimating loading on offshore structures due to waves and currents. Its primary concern is with existing practice in which the formula known as Morison' s equation is extensively used but some attention is given to diffraction theory methods now quite widely adopted for large monolithic types of structure and a section on the influence of marine roughness on loading is included. Regarding Morison's equation, a comprehensive review of published data on the relevant coefficients is presented, stressing the considerable uncertainties which still exist in some areas but offering advice on the best values to be used in the light of current knowledge, systematically documented by references to the corresponding data sources. Other important questions discussed include selection of appropriate wave theories and associated particle kinematics, the effects on fluid loading of proximity and inclination of structural members and the special problems of estimating impact or 'slamming' forces. The section on diffraction theory analysis discusses the interpretation of the results for both fixed and moving bodies and problems of practical application. It also reviews published information on both analytical and numerical solutions including comments on reliability and experimental validation and tabular summaries of the capabilities of an extensive range of methods and computer programs already available. In discussing marine roughness recent published data indicating the substantial effects which it can have on drag coefficients in both waves and currents are reviewed and advice is given on how these should be estimated. A general conclusion of the paper is that although data on fluid loading available in the literature is very plentiful there are still many serious uncertainties and gaps in knowledge. It is therefore important that research should continue with emphasis on the need for more reliable data from large scale structures in the real environment

A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. The \emph{strong metric dimension}, $sdim(G)$, of a graph $G$ is the minimum among cardinalities of all strong resolving sets: $W \subseteq V(G)$ is a \emph{strong resolving set} of $G$ if for any $u, v \in V(G)$, there exists an $x \in W$ such that either $u$ lies on an $x-v$ geodesic or $v$ lies on an $x-u$ geodesic. In this paper, we prove that $Z(G) \le sdim(G)+3r(G)$ for a connected graph $G$, where $r(G)$ is the cycle rank of $G$. Further, we prove the sharp bound $Z(G) \leq sdim(G)$ when $G$ is a tree or a unicyclic graph, and we characterize trees $T$ attaining $Z(T)=sdim(T)$. It is easy to see that $sdim(T+e)-sdim(T)$ can be arbitrarily large for a tree $T$; we prove that $sdim(T+e) \ge sdim(T)-2$ and show that the bound is sharp.Comment: 8 pages, 5 figure

Algebraic inversion of the Dirac equation for the vector potential in the non-abelian case

We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell-Dirac equations, we set up the formalism for non-abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series.Comment: 21pp, uses iopar

Identifying outbreaks of sexually transmitted infection: who cares?

BACKGROUND: Current routine surveillance schemes for sexually transmitted infections (STIs) in the United Kingdom (UK) are not designed for outbreak identification. Recognising STI outbreaks, therefore, depends almost entirely on the alertness of health professionals. The objective of this study was to explore health professionals' knowledge of, and attitudes towards, identification and investigation of STI outbreaks in Wales. METHODS: We conducted a cross-sectional survey in Wales in June 2005, and sent a questionnaire to consultants of genitourinary medicine (GUM, n = 11), a consultant microbiologist from each laboratory (n = 14), all consultants in communicable disease control (n = 5), and to epidemiologists of the National Public Health Service (n = 4). RESULTS: 26 (76%) of 34 survey recipients responded. Of these, 17 (65%) ranked the investigation of STI outbreaks as important or very important, and 19 (73%) perceived participation in the investigation of an STI outbreak as part of their responsibility. Only six (25%) respondents had actively searched their computer system or patient records for a possible STI outbreak in the previous twelve months, and 15 (63%) had never looked for an outbreak. Of seven GUM physicians who said they had identified at least one STI outbreak, three had never informed public health authorities. CONCLUSION: Prompt identification and coordinated investigation of outbreaks, usually through a multidisciplinary outbreak control team, is central to the control of many infectious diseases. This does not appear to be the case for STIs, which we believe represents a lost opportunity to reduce transmission. Besides improved surveillance methods, a change in culture towards STI outbreaks is needed among health professionals in Wales

Some pioneers of European human genetics

Some of the pioneers of human genetics across Europe are described, based on a series of 100 recorded interviews made by the author. These interviews, and the memories of earlier workers in the field recalled by interviewees, provide a vivid picture, albeit incomplete, of the early years of human and medical genetics. From small beginnings in the immediate post-World War 2 years, human genetics grew rapidly across many European countries, a powerful factor being the development of human cytogenetics, stimulated by concerns over the risks of radiation exposure. Medical applications soon followed, with the recognition of human chromosome abnormalities, the need for genetic counselling, the possibility of prenatal diagnosis and later, the applications of human molecular genetics. The evolution of the field has been strongly influenced by the characters and interests of the relatively small number of founding workers in different European countries, as well as by wider social, medical and scientific factors in the individual countries

Hydro-ionothermal synthesis of lanthanide-organic frameworks with 1,4-phenylenebis(methylene)diphosphonate

A synthetic approach combining hydrothermal and ionothermal (eutectic mixture of choline chloride and malonic acid) procedures is proposed that allowed the isolation of the first lanthanide-organic frameworks with residues of 1,4-phenylenebis(methylene)- diphosphonic acid (H4pmd), [Ln(Hpmd)(H2O)] (where Ln3+ ) Ce3+ and Pr3+), exhibiting an unprecedented trinodal topology with 3- and 8-connected nodes. The structural details were unveiled from single-crystal X-ray diffraction and the materials were characterized using standard techniques.FCT - POCI-PPCDT/QUI/58377/2004FEDER - POCIGrant - SFRH/BPD/9309/200

Better than nothing? Patient-delivered partner therapy and partner notification for chlamydia: the views of Australian general practitioners

<p>Abstract</p> <p>Background</p> <p>Genital chlamydia is the most commonly notified sexually transmissible infection (STI) in Australia and worldwide and can have serious reproductive health outcomes. Partner notification, testing and treatment are important facets of chlamydia control. Traditional methods of partner notification are not reaching enough partners to effectively control transmission of chlamydia. Patient-delivered partner therapy (PDPT) has been shown to improve the treatment of sexual partners. In Australia, General Practitioners (GPs) are responsible for the bulk of chlamydia testing, diagnosis, treatment and follow up. This study aimed to determine the views and practices of Australian general practitioners (GPs) in relation to partner notification and PDPT for chlamydia and explored GPs' perceptions of their patients' barriers to notifying partners of a chlamydia diagnosis.</p> <p>Methods</p> <p>In-depth, semi-structured telephone interviews were conducted with 40 general practitioners (GPs) from rural, regional and urban Australia from November 2006 to March 2007. Topics covered: GPs' current practice and views about partner notification, perceived barriers and useful supports, previous use of and views regarding PDPT.</p> <p>Transcripts were imported into NVivo7 and subjected to thematic analysis. Data saturation was reached after 32 interviews had been completed.</p> <p>Results</p> <p>Perceived barriers to patients telling partners (patient referral) included: stigma; age and cultural background; casual or long-term relationship, ongoing relationship or not. Barriers to GPs undertaking partner notification (provider referral) included: lack of time and staff; lack of contact details; uncertainty about the legality of contacting partners and whether this constitutes breach of patient confidentiality; and feeling both personally uncomfortable and inadequately trained to contact someone who is not their patient. GPs were divided on the use of PDPT - many felt concerned that it is not best clinical practice but many also felt that it is better than nothing.</p> <p>GPs identified the following factors which they considered would facilitate partner notification: clear clinical guidelines; a legal framework around partner notification; a formal chlamydia screening program; financial incentives; education and practical support for health professionals, and raising awareness of chlamydia in the community, in particular amongst young people.</p> <p>Conclusions</p> <p>GPs reported some partners do not seek medical treatment even after they are notified of being a sexual contact of a patient with chlamydia. More routine use of PDPT may help address this issue however GPs in this study had negative attitudes to the use of PDPT. Appropriate guidelines and legislation may make the use of PDPT more acceptable to Australian GPs.</p