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

Aquilegia, Vol. 29 No. 5, November-December 2005: Newsletter of the Colorado Native Plant Society

https://epublications.regis.edu/aquilegia/1114/thumbnail.jp

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

Etude des propriétés magnéto-optiques des couches minces à base de ferrite de cobalt obtenues par voie sol-gel

Ce travail est consacré à l'étude des propriétés magnéto-optiques (rotation Faraday) de couches minces à base de ferrite de cobalt obtenues par voie sol-gel. La contribution de la méthode sol-gel utilisée est très importante et cela permet d’obtenir des couches minces ayant une bonne qualité optique. Cette démarche nécessite juste l’utilisation de liquides magnétiques ou ferro fluides, de précurseurs de silice (pas cher) et d’un substrat de verre. Le but est d’obtenir des couches minces et étudier leurs propriétés magnéto-optiques. Les courbes obtenues à la longueur d’onde de 820 nm présentent des cycles d’hystérésis avec des rotations rémanentes de 40, 60 et 81°/cm. Ces résultats présentent une excellente rotation Faraday de 212, 318 et 340°/cm à la longueur d’onde de 820 nm. Ceci montre la forte potentialité de la matrice sol-gel dopée.Mots-clés: nanoparticules magnétiques, ferrite de cobalt, sol-gel, couches minces, rotation Faraday. Study of themagneto-optical properties of thin films cobalt ferrite obtainedby the sol-gel This work is devoted to the study of magneto-optical (Faraday rotation) of thin cobalt ferrite layers obtained by sol-gel. The contribution of the sol-gel method is very important and it allows obtaining thin film shaving a good optical quality. This requires only the use of magnetic fluids or ferro fluids, silica precursors (cheap) and a glass substrate. The goal is to obtain thin layers and study their magneto-optical properties. The curves obtained for the wave length of 820 nm have hysteresis loops with retentive rotations of 40, 60 and 81°/ cm. These results show excellentFaradayrotation 212, 318 and 340°/cm ata wave length of 820 nm. This shows the high potential of the doped sol-gel matrix.Keywords: agnetic nanoparticles, cobalt ferrite, sol-gel, thin films, Faraday rotation

Exploring the characteristics and most bothersome symptoms in MECP2 duplication syndrome to pave the path toward developing parent-oriented outcome measures

BACKGROUND: MECP2 Duplication Syndrome (MDS), resulting from the duplication of Xq28 region, including MECP2, is a rare disorder with a nascent understanding in clinical features and severity. Studies using antisense oligonucleotides revealed a broad phenotypic rescue in transgenic mice. With human clinical trials on the horizon, there is a need to develop clinical outcome measures for MDS. METHODS: We surveyed caregivers of MDS individuals to explore the frequency and severity of MDS clinical features, and identify the most meaningful symptoms/domains that need to be included in the outcome measure scales. RESULTS: A total of 101 responses were eligible for the survey. The top six most meaningful symptoms to caregivers in descending order included epilepsy, gross motor, fine motor, communication, infection, and constipation problems. Epilepsy was present in 58.4% of the subjects and 75% were drug‐resistant, Furthermore, ~12% required intensive care unit (ICU) admission. Infections were present in 55% of the subjects, and one‐fourth of them required ICU admission. Constipation was present in ~85% of the subjects and one‐third required enemas/suppositories. CONCLUSION: Our study is one of the largest cohorts conducted on MDS individuals characterizing the frequency and severity of MDS symptoms. Additionally, these study results will contribute to establishing a foundation to develop parent‐reported outcomes in MDS

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

New investigations around CYP11A1 and its possible involvement in an androstenone QTL characterised in Large White pigs

<p>Abstract</p> <p>Background</p> <p>Previously, in boars with extreme androstenone levels, differential expression of the <it>CYP11A1 </it>gene in the testes has been characterised. <it>CYP11A1 </it>is located in a region where a QTL influencing boar fat androstenone levels has been detected in a Large White pig population. Clarifying the role of CYP11A1 in boar taint is important because it catalyses the initial step of androstenone synthesis and also of steroid synthesis.</p> <p>Results</p> <p>A genome-wide association study located <it>CYP11A1 </it>at approximately 1300 kb upstream from SNP H3GA0021967, defining the centre of the region containing the QTL for androstenone variation. In this study, we partially sequenced the <it>CYP11A1 </it>gene and identified several new single nucleotide polymorphisms (SNP) within it. Characterisation of one animal, heterozygous for <it>CYP11A1 </it>testicular expression but homozygous for a haplotype of a large region containing <it>CYP11A1</it>, revealed that variation of <it>CYP11A1 </it>expression is probably regulated by a mutation located downstream from the SNP H3GA0021967. We analysed <it>CYP11A1 </it>expression in LW families according to haplotypes of the QTL region's centre. Effects of haplotypes on <it>CYP11A1 </it>expression and on androstenone accumulation were not concordant.</p> <p>Conclusion</p> <p>This study shows that testicular expression of <it>CYP11A1 </it>is not solely responsible for the QTL influencing boar fat androstenone levels. As a conclusion, we propose to refute the hypothesis that a single mutation located near the centre of the QTL region could control androstenone accumulation in fat by regulating the <it>CYP11A1 </it>expression.</p