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

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

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]

PI3K p110δ uniquely promotes gain-of-function Shp2-induced GM-CSF hypersensitivity in a model of JMML

Although hyperactivation of the Ras-Erk signaling pathway is known to underlie the pathogenesis of juvenile myelomonocytic leukemia (JMML), a fatal childhood disease, the PI3K-Akt signaling pathway is also dysregulated in this disease. Using genetic models, we demonstrate that inactivation of phosphatidylinositol-3-kinase (PI3K) catalytic subunit p110δ, but not PI3K p110α, corrects gain-of-function (GOF) Shp2-induced granulocyte macrophage-colony-stimulating factor (GM-CSF) hypersensitivity, Akt and Erk hyperactivation, and skewed hematopoietic progenitor distribution. Likewise, potent p110δ-specific inhibitors curtail the proliferation of GOF Shp2-expressing hematopoietic cells and cooperate with mitogen-activated or extracellular signal-regulated protein kinase kinase (MEK) inhibition to reduce proliferation further and maximally block Erk and Akt activation. Furthermore, the PI3K p110δ-specific inhibitor, idelalisib, also demonstrates activity against primary leukemia cells from individuals with JMML. These findings suggest that selective inhibition of the PI3K catalytic subunit p110δ could provide an innovative approach for treatment of JMML, with the potential for limiting toxicity resulting from the hematopoietic-restricted expression of p110δ

Superconducting Order Parameter Symmetry in Multi-layer Cuprates

We discuss the allowed order parameter symmetries in multi-layer cuprates and their physical consequences using highly non-specific forms of the inter- and intra-plane interactions. Within this framework, the bi-layer case is discussed in detail with particular attention paid to the role of small orthorhombic distortions as would derive from the chains in YBCO or superlattice effects in BSCCO. In the orthorhombic bi-layer case the (s,-s) state is of special interest, since for a wide range of parameters this state exhibits pi phase shifts in corner Josephson junction experiments. In addition, its transition temperature is found to be insensitive to non-magnetic inter-plane disorder, as would be present at the rare earth site in YBCO, for example. Of particular interest, also, are the role of van Hove singularities which are seen to stabilize states with d_{x^2 - y^2}-like symmetry, (as well as nodeless s-states) and to elongate the gap functions along the four van Hove points, thereby leading to a substantial region of gaplessness. We find that d_{x^2 - y^2}-like states are general solutions for repulsive interactions; they possess the fewest number of nodes and therefore the highest transition temperatures. In this way, they should not be specifically associated with a spin fluctuation driven pairing mechanism.Comment: REVTeX documentstyle, 34 pages, 10 figures include