On the expressive power of read-once determinants

We introduce and study the notion of read-$k$ projections of the determinant: a polynomial $f \in \mathbb{F}[x_1, \ldots, x_n]$ is called a {\it read-$k$ projection of determinant} if $f=det(M)$, where entries of matrix $M$ are either field elements or variables such that each variable appears at most $k$ times in $M$. A monomial set $S$ is said to be expressible as read-$k$ projection of determinant if there is a read-$k$ projection of determinant $f$ such that the monomial set of $f$ is equal to $S$. We obtain basic results relating read-$k$ determinantal projections to the well-studied notion of determinantal complexity. We show that for sufficiently large $n$, the $n \times n$ permanent polynomial $Perm_n$ and the elementary symmetric polynomials of degree $d$ on $n$ variables $S_n^d$ for $2 \leq d \leq n-2$ are not expressible as read-once projection of determinant, whereas $mon(Perm_n)$ and $mon(S_n^d)$ are expressible as read-once projections of determinant. We also give examples of monomial sets which are not expressible as read-once projections of determinant

Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure

Review: Towards the agroecological management of ruminants, pigs and poultry through the development of sustainable breeding programmes. II. Breeding strategies

Agroecology uses ecological processes and local resources rather than chemical inputs to develop productive and resilient livestock and crop production systems. In this context, breeding innovations are necessary to obtain animals that are both productive and adapted to a broad range of local contexts and diversity of systems. Breeding strategies to promote agroecological systems are similar for different animal species. However, current practices differ regarding the breeding of ruminants, pigs and poultry. Ruminant breeding is still an open system where farmers continue to choose their own breeds and strategies. Conversely, pig and poultry breeding is more or less the exclusive domain of international breeding companies which supply farmers with hybrid animals. Innovations in breeding strategies must therefore be adapted to the different species. In developed countries, reorienting current breeding programmes seems to be more effective than developing programmes dedicated to agroecological systems that will struggle to be really effective because of the small size of the populations currently concerned by such systems. Particular attention needs to be paid to determining the respective usefulness of cross-breeding v. straight breeding strategies of well-adapted local breeds. While cross-breeding may offer some immediate benefits in terms of improving certain traits that enable the animals to adapt well to local environmental conditions, it may be difficult to sustain these benefits in the longer term and could also induce an important loss of genetic diversity if the initial pure-bred populations are no longer produced. As well as supporting the value of within-breed diversity, we must preserve between-breed diversity in order to maintain numerous options for adaptation to a variety of production environments and contexts. This may involve specific public policies to maintain and characterize local breeds (in terms of both phenotypes and genotypes), which could be used more effectively if they benefited from the scientific and technical resources currently available for more common breeds. Last but not least, public policies need to enable improved information concerning the genetic resources and breeding tools available for the agroecological management of livestock production systems, and facilitate its assimilation by farmers and farm technicians

Magnetic frustration in a stoichiometric spin-chain compound, Ca3_3CoIrO6_6

The temperature dependent ac and dc magnetization and heat capacity data of Ca$_3$CoIrO$_6$, a spin-chain compound crystallizing in a K$_4$CdCl$_6$-derived rhombohedral structure, show the features due to magnetic ordering of a frustrated-type below about 30 K, however without exhibiting the signatures of the so-called "partially disordered antiferromagnetic structure" encountered in the isostructural compounds, Ca$_3$Co$_2$O$_6$ and Ca$_3$CoRhO$_6$. This class of compounds thus provides a variety for probing the consequences of magnetic frustration due to topological reasons in stoichiometric spin-chain materials, presumably arising from subtle differences in the interchain and intrachain magnetic coupling strengths. This compound presents additional interesting situations in the sense that, ac susceptibility exhibits a large frequency dependence in the vicinity of 30 K uncharacteristic of conventional spin-glasses, with this frustrated magnetic state being robust to the application of external magnetic fields.Comment: Physical Review (Rapid Communications), in pres

Spin Gaps in High Temperature Superconductors

The phenomenology and theory of spin gap effects in high temperature superconductors is summarized. It is argued that the spin gap behavior can only be explained by a model of charge 0 spin 1/2 fermions which become paired into singlets and that there are both theoretical and experimental reasons for believing that the pairing is greatly enhanced in the bilayer structure of the $YBa_2Cu_3O_{6+x}$ system. This article will appear in the Proceedings of the Stanford Conference on Spectroscopies in Novel Superconductors. To obtain postscript files containing the figures send mail to [email protected]: 9 pages, revtex. To obtain figures contact [email protected]

Second-order shaped pulses for solid-state quantum computation

We present the constructon and detailed analysis of highly-optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order. This allows a semi-analytical analysis of the performance of the constructed shapes in sequences and composite pulses by computing the corresponding leading-order error operators. Higher orders can be analyzed with the numerical technique suggested by us previously. We illustrate the technique by analysing several composite pulses designed to protect against pulse amplitude errors, and on decoupling sequences for potentially long chains of qubits with on-site and nearest-neighbor couplings.Comment: 16 pages, 29 figure

Negotiations of minority ethnic rugby league players in the Cathar country of France

This article is based on new empirical, qualitative research with minority ethnic rugby league players in the southwest of France. Drawing on similar research on rugby league in the north and the south of England, the article examines how rugby league, traditionally viewed as a white, working-class male game (Collins, 2006; Denham, 2004; Spracklen, 1995, 2001) has had to re-imagine its symbolic boundaries as they are constituted globally and locally to accommodate the needs of players from minority ethnic backgrounds. In particular, the article examines the sense in which experiences of minority ethnic rugby league players in France compare with those of their counterparts in England (Spracklen, 2001, 2007), how rugby league is used in France to construct identity, and in what sense the norms associated with the imaginary community of rugby league are replicated or challenged by the involvement of minority ethnic rugby league players in France. Questions about what it means to be (provincial, national) French (Kumar, 2006) are posed, questions that relate to the role of sport in the construction of Frenchness, and in particular the role of rugby league (and union). © Copyright ISSA and SAGE Publications

Paediatric radiology seen from Africa. Part I: providing diagnostic imaging to a young population

Article approval pendingPaediatric radiology requires dedicated equipment, specific precautions related to ionising radiation, and specialist knowledge. Developing countries face difficulties in providing adequate imaging services for children. In many African countries, children represent an increasing proportion of the population, and additional challenges follow from extreme living conditions, poverty, lack of parental care, and exposure to tuberculosis, HIV, pneumonia, diarrhoea and violent trauma. Imaging plays a critical role in the treatment of these children, but is expensive and difficult to provide. The World Health Organisation initiatives, of which the World Health Imaging System for Radiography (WHIS-RAD) unit is one result, needs to expand into other areas such as the provision of maintenance servicing. New initiatives by groups such as Rotary and the World Health Imaging Alliance to install WHIS-RAD units in developing countries and provide digital solutions, need support. Paediatric radiologists are needed to offer their services for reporting, consultation and quality assurance for free by way of teleradiology. Societies for paediatric radiology are needed to focus on providing a volunteer teleradiology reporting group, information on child safety for basic imaging, guidelines for investigations specific to the disease spectrum, and solutions for optimising imaging in children