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

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

Leukaemogenic effects of Ptpn11 activating mutations in the stem cell microenvironment

Germline activating mutations of the protein tyrosine phosphatase SHP2 (encoded by PTPN11), a positive regulator of the RAS signalling pathway, are found in 50% of patients with Noonan syndrome. These patients have an increased risk of developing leukaemia, especially juvenile myelomonocytic leukaemia (JMML), a childhood myeloproliferative neoplasm (MPN). Previous studies have demonstrated that mutations in Ptpn11 induce a JMML-like MPN through cell-autonomous mechanisms that are dependent on Shp2 catalytic activity. However, the effect of these mutations in the bone marrow microenvironment remains unclear. Here we report that Ptpn11 activating mutations in the mouse bone marrow microenvironment promote the development and progression of MPN through profound detrimental effects on haematopoietic stem cells (HSCs). Ptpn11 mutations in mesenchymal stem/progenitor cells and osteoprogenitors, but not in differentiated osteoblasts or endothelial cells, cause excessive production of the CC chemokine CCL3 (also known as MIP-1α), which recruits monocytes to the area in which HSCs also reside. Consequently, HSCs are hyperactivated by interleukin-1β and possibly other proinflammatory cytokines produced by monocytes, leading to exacerbated MPN and to donor-cell-derived MPN following stem cell transplantation. Remarkably, administration of CCL3 receptor antagonists effectively reverses MPN development induced by the Ptpn11-mutated bone marrow microenvironment. This study reveals the critical contribution of Ptpn11 mutations in the bone marrow microenvironment to leukaemogenesis and identifies CCL3 as a potential therapeutic target for controlling leukaemic progression in Noonan syndrome and for improving stem cell transplantation therapy in Noonan-syndrome-associated leukaemias

Characterisation of stellar activity of M dwarfs. I. Long-timescale variability in a large sample and detection of new cycles

M dwarfs are active stars that exhibit variability in chromospheric emission and photometry at short and long timescales, including long cycles that are related to dynamo processes. This activity also impacts the search for exoplanets because it affects the radial velocities. We analysed a large sample of 177 M dwarfs observed with HARPS (2003-2020) in order to characterise the long-term variability of these stars. We compared the variability obtained in three chromospheric activity indices (Ca II H & K, the Na D doublet, and Halpha) and with ASAS photometry. We focused on the detailed analysis of the chromospheric emission based on linear, quadratic, and sinusoidal models. We used various tools to estimate the significance of the variability and to quantify the improvement brought by the models. In addition, we analysed complementary photometric time series for the most variable stars to be able to provide a broader view of the long-term variability in M dwarfs. We find that most stars are significantly variable, even the quietest stars. Most stars in our sample (75%) exhibit a long-term variability, which manifests itself mostly through linear or quadratic variability, although the true behaviour may be more complex. We found significant variability with estimated timescales for 24 stars, and estimated the lower limit for a possible cycle period for an additional 9 stars that were not previously published. We found evidence of complex variability because more than one long-term timescale may be present for at least 12 stars, together with significant differences between the behaviour of the three activity indices. This complexity may also be the source of the discrepancies observed between previous publications. We conclude that long-term variability is present for all spectral types and activity level in M dwarfs, without a significant trend with spectral type or mean activity level.Comment: article accepted in Astronomy and Astrophysics, February 2023, 31 page

A new approach to local hardness

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness - in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results.Comment: 30 pages (including 6 figures, 1 table

Bubbles and denaturation in DNA

The local opening of DNA is an intriguing phenomenon from a statistical physics point of view, but is also essential for its biological function. For instance, the transcription and replication of our genetic code can not take place without the unwinding of the DNA double helix. Although these biological processes are driven by proteins, there might well be a relation between these biological openings and the spontaneous bubble formation due to thermal fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois model, have fairly accurately reproduced some experimental denaturation curves and the sharp phase transition in the thermodynamic limit. It is, hence, tempting to see whether these models could be used to predict the biological activity of DNA. In a previous study, we introduced a method that allows to obtain very accurate results on this subject, which showed that some previous claims in this direction, based on molecular dynamics studies, were premature. This could either imply that the present PBD should be improved or that biological activity can only be predicted in a more complex frame work that involves interactions with proteins and super helical stresses. In this article, we give detailed description of the statistical method introduced before. Moreover, for several DNA sequences, we give a thorough analysis of the bubble-statistics as function of position and bubble size and the so-called $l$-denaturation curves that can be measured experimentally. These show that some important experimental observations are missing in the present model. We discuss how the present model could be improved.Comment: 15 pages, 5 figures, published as Eur. Phys. J. E 20 : 421-434 AUG 200

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]

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