Reducible Correlations in Dicke States

We apply a simple observation to show that the generalized Dicke states can be determined from their reduced subsystems. In this framework, it is sufficient to calculate the expression for only the diagonal elements of the reudced density matrices in terms of the state coefficients. We prove that the correlation in generalized Dicke states $|GD_N^{(\ell)}>$ can be reduced to $2\ell$-partite level. Application to the Quantum Marginal Problem is also discussed.Comment: 12 pages, single column; accepted in J. Phys. A as FT

The ball in play demands of international rugby union

Objectives: Rugby union is a high intensity intermittent sport, typically analysed via set time periods or rolling average methods. This study reports the demands of international rugby union via global positioning system (GPS) metrics expressed as mean ball in play (BiP), maximum BiP (max BiP), and whole match outputs. Design: Single cohort cross sectional study involving 22 international players, categorised as forwards and backs. Methods: A total of 88 GPS files from eight international test matches were collected during 2016. An Opta sportscode timeline was integrated into the GPS software to split the data into BiP periods. Metres per min (m.min-1), high metabolic load per min (HML), accelerations per min (Acc), high speed running per min (HSR), and collisions per min (Coll) were expressed relative to BiP periods and over the whole match (>60min). Results: Whole match metrics were significantly lower than all BiP metrics (p < 0.001). Mean and max BiP HML, (p < 0.01) and HSR (p < 0.05) were significantly higher for backs versus forwards, whereas Coll were significantly higher for forwards (p < 0.001). In plays lasting 61s or greater, max BiP m.min-1 were higher for backs. Max BiP m.min-1, HML, HSR and Coll were all time dependant (p < 0.05) showing that both movement metrics and collision demands differ as length of play continues. Conclusions: This study uses a novel method of accurately assessing the BiP demands of rugby union. It also reports typical and maximal demands of international rugby union that can be used by practitioners and scientists to target training of worst-case scenario's equivalent to international intensity. Backs covered greater distances at higher speeds and demonstrated higher HML, in general play as well as 'worst case scenarios'; conversely forwards perform a higher number of collisions

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

Observatorio permanente de la imagen exterior de España en la prensa internacional (OPIEX), 4to trimestre de 2007

Finalizamos la serie de documentos de trabajo del Observatorio Permanente de la Imagen Exterior de España en la Prensa Internacional (OPIEX) correspondiente al año 2007, con el análisis de este último trimestre. Como recordatorio para quienes se incorporan ahora a esta serie de informes, repetimos aquí las preguntas que guían nuestra investigación. Con las limitaciones que más adelante se señalan, el OPIEX trata de establecer qué países son los que más se interesan por lo que ocurre en nuestro país y cuáles son los temas que más atención despiertan. Se quiere indagar de este modo sobre las imágenes de España y de los españoles que se difunden en los medios internacionales. La metodología utilizada es la de documentos anteriores. Utilizamos los boletines de prensa internacional editados por el servicio de prensa de La Moncloa entre el 1 de octubre y el 28 de diciembre de 2007, a los que se puede acceder a través de su página web, como la fuente principal de datos para la investigación

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

On the minimum rank of not necessarily symmetric matrices : a preliminary study

The minimum rank of a directed graph G is defined to be the smallest possible rank over all real matrices whose ijth entry is nonzero whenever (i, j) is an arc in G and is zero otherwise. The symmetric minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i _= j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity is equal to the difference between the order of the graph and minimum rank in either case. Definitions of various graph parameters used to bound symmetric maximum nullity, including path cover number and zero forcing number, are extended to digraphs, and additional parameters related to minimum rank are introduced. It is shown that for directed trees, maximum nullity, path cover number, and zero forcing number are equal, providing a method to compute minimum rank for directed trees. It is shown that the minimum rank problem for any given digraph or zero-nonzero pattern may be converted into a symmetric minimum rank problem

The Enhanced Principal Rank Characteristic Sequence for Hermitian Matrices

The enhanced principal rank characteristic sequence (epr-sequence) of an n x n matrix is a sequence l(1) l(2) . . .l(n), where each l(k) is A, S, or N according as all, some, or none of its principal minors of order k are nonzero. There has been substantial work on epr-sequences of symmetric matrices (especially real symmetric matrices) and real skew-symmetric matrices, and incidental remarks have been made about results extending (or not extending) to (complex) Hermitian matrices. A systematic study of epr-sequences of Hermitian matrices is undertaken; the differences with the case of symmetric matrices are quite striking. Various results are established regarding the attainability by Hermitian matrices of epr-sequences that contain two Ns with a gap in between. Hermitian adjacency matrices of mixed graphs that begin with N A N are characterized. All attainable epr-sequences of Hermitian matrices of orders 2, 3, 4, and 5, are listed with justifications