Considering copositivity locally

Let $A$ be an element of the copositive cone $coposn$. A zero $vu$ of $A$ is a nonnegative vector whose elements sum up to one and such that $vu^TAvu = 0$. The support of $vu$ is the index set $Suppvu subset 1,dots,n$ corresponding to the nonzero entries of $vu$. A zero $vu$ of $A$ is called minimal if there does not exist another zero $vv$ of $A$ such that its support $Suppvv$ is a strict subset of $Suppvu$. Our main result is a characterization of the cone of feasible directions at $A$, i.e., the convex cone $VarKA$ of real symmetric $n times n$ matrices $B$ such that there exists $delta > 0$ satisfying $A + delta B in coposn$. This cone is described by a set of linear inequalities on the elements of $B$ constructed from the set of zeros of $A$ and their supports. This characterization furnishes descriptions of the minimal face of $A$ in $coposn$, and of the minimal exposed face of $A$ in $coposn$, by sets of linear equalities and inequalities constructed from the set of minimal zeros of $A$ and their supports. In particular, we can check whether $A$ lies on an extreme ray of $coposn$ by examining the solution set of a system of linear equations. In addition, we deduce a simple necessary and sufficient condition on the irreducibility of $A$ with respect to a copositive matrix $C$. Here $A$ is called irreducible with respect to $C$ if for all $delta > 0$ we have $A - delta C notin coposn$

High spatial resolution strain measurements at the surface of duplex stainless steels

International audienceThe determination of local strain fields at the surface of materials is of major importance for understanding their reactivity. In the present paper, lithography is used to fabricate grid points at the microscale and to map strain gradients within grains and between grains. This method was applied to duplex stainless steels which exhibit heterogeneous strain distributions under straining conditions. The influence of various parameters (the specimen microstructure, the density of slip bands, the number of systems activated and the grid geometry) on the strain value was discussed

Landscape equivalent of the shoving model

It is shown that the shoving model expression for the average relaxation time of viscous liquids follows largely from a classical "landscape" estimation of barrier heights from curvature at energy minima. The activation energy involves both instantaneous bulk and shear moduli, but the bulk modulus contributes less than 8% to the temperature dependence of the activation energy. This reflects the fact that the physics of the two models are closely related.Comment: 4 page

Microscopic Aspects of Stretched Exponential Relaxation (SER) in Homogeneous Molecular and Network Glasses and Polymers

Because the theory of SER is still a work in progress, the phenomenon itself can be said to be the oldest unsolved problem in science, as it started with Kohlrausch in 1847. Many electrical and optical phenomena exhibit SER with probe relaxation I(t) ~ exp[-(t/{\tau}){\beta}], with 0 < {\beta} < 1. Here {\tau} is a material-sensitive parameter, useful for discussing chemical trends. The "shape" parameter {\beta} is dimensionless and plays the role of a non-equilibrium scaling exponent; its value, especially in glasses, is both practically useful and theoretically significant. The mathematical complexity of SER is such that rigorous derivations of this peculiar function were not achieved until the 1970's. The focus of much of the 1970's pioneering work was spatial relaxation of electronic charge, but SER is a universal phenomenon, and today atomic and molecular relaxation of glasses and deeply supercooled liquids provide the most reliable data. As the data base grew, the need for a quantitative theory increased; this need was finally met by the diffusion-to-traps topological model, which yields a remarkably simple expression for the shape parameter {\beta}, given by d*/(d* + 2). At first sight this expression appears to be identical to d/(d + 2), where d is the actual spatial dimensionality, as originally derived. The original model, however, failed to explain much of the data base. Here the theme of earlier reviews, based on the observation that in the presence of short-range forces only d* = d = 3 is the actual spatial dimensionality, while for mixed short- and long-range forces, d* = fd = d/2, is applied to four new spectacular examples, where it turns out that SER is useful not only for purposes of quality control, but also for defining what is meant by a glass in novel contexts. (Please see full abstract in main text

HSF2BP negatively regulates homologous recombination in DNA interstrand crosslink repair

The tumor suppressor BRCA2 is essential for homologous recombination (HR), replication fork stability and DNA interstrand crosslink (ICL) repair in vertebrates. We show that ectopic production of HSF2BP, a BRCA2-interacting protein required for meiotic HR during mouse spermatogenesis, in non-germline human cells acutely sensitize them to ICL-inducing agents (mitomycin C and cisplatin) and PARP inhibitors, resulting in a phenotype characteristic of cells from Fanconi anemia (FA) patients. We biochemically recapitulate the suppression of ICL repair and establish that excess HSF2BP compromises HR by triggering the removal of BRCA2 from the ICL site and thereby preventing the loading of RAD51. This establishes ectopic expression of a wild-type meiotic protein in the absence of any other protein-coding mutations as a new mechanism that can lead to an FA-like cellular phenotype. Naturally occurring elevated production of HSF2BP in tumors may be a source of cancer-promoting genomic instability and also a targetable vulnerability

Heat-induced BRCA2 degradation in human tumours provides rationale for hyperthermia-PARP-inhibitor combination therapies

Purpose: Hyperthermia (40–44 °C) effectively sensitises tumours to radiotherapy by locally altering tumour biology. One of the effects of heat at the cellular level is inhibition of DNA repair by homologous recombination via degradation of the BRCA2-protein. This suggests that hyperthermia can expand the group of patients that benefit from PARP-inhibitors, a drug exploiting homologous recombination deficiency. Here, we explore whether the molecular mechanisms that cause heat-mediated degradation of BRCA2 are conserved in cell lines from various origins and, most importantly, whether, BRCA2 protein levels can be attenuated by heat in freshly biopted human tumours. Experimental design: Cells from four established cell lines and from freshly biopsied material of cervical (15), head- and neck (9) or bladder tumours (27) were heated to 42 °C for 60 min ex vivo. In vivo hyperthermia was studied by taking two biopsies of the same breast or cervical tumour: one before and one after treatment. BRCA2 protein levels were measured by immunoblotting. Results: We found decreased BRCA2-levels after hyperthermia in all established cell lines and in 91% of all tumours treated ex vivo. For tumours treated with hyperthermia in vivo, technical issues and intra-tumour heterogeneity prevented obtaining interpretable results. Conclusions: This study demonstrates that heat-mediated degradation of BRCA2 occurs in tumour material directly derived from patients. Although BRCA2-degradation may not be a practical biomarker for heat deposition in situ, it does suggest that application of hyperthermia could be an effective method to expand the patient group that could benefit from PARP-inhibitors

Global Search for New Physics with 2.0/fb at CDF

Data collected in Run II of the Fermilab Tevatron are searched for indications of new electroweak-scale physics. Rather than focusing on particular new physics scenarios, CDF data are analyzed for discrepancies with the standard model prediction. A model-independent approach (Vista) considers gross features of the data, and is sensitive to new large cross-section physics. Further sensitivity to new physics is provided by two additional algorithms: a Bump Hunter searches invariant mass distributions for "bumps" that could indicate resonant production of new particles; and the Sleuth procedure scans for data excesses at large summed transverse momentum. This combined global search for new physics in 2.0/fb of ppbar collisions at sqrt(s)=1.96 TeV reveals no indication of physics beyond the standard model.Comment: 8 pages, 7 figures. Final version which appeared in Physical Review D Rapid Communication