The linear preservers of non-singularity in a large space of matrices

Let K be an arbitrary (commutative) field, and V be a linear subspace of M_n(K) such that codim V<n-1. Using a recent generalization of a theorem of Atkinson and Lloyd, we show that every linear embedding of V into M_n(K) which strongly preserves non-singularity must be M->PMQ or M->PM^TQ for some pair (P,Q) of non-singular matrices of M_n(K), unless n=3, codim V=1 and K is isomorphic to F_2. This generalizes a classical theorem of Dieudonn\'e with a similar strategy of proof. Weak linear preservers are also discussed, as well as the exceptional case of a hyperplane of M_3(F_2).Comment: 35 pages (v4: added some additional explanations

On the matrices of given rank in a large subspace

Let V be a linear subspace of M_{n,p}(K) with codimension lesser than n, where K is an arbitrary field and n >=p. In a recent work of the author, it was proven that V is always spanned by its rank p matrices unless n=p=2 and K is isomorphic to F_2. Here, we give a sufficient condition on codim V for V to be spanned by its rank r matrices for a given r between 1 and p-1. This involves a generalization of the Gerstenhaber theorem on linear subspaces of nilpotent matrices.Comment: 8 page

Domain-specific textual meta-modelling languages for model driven engineering

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-31491-9_20Proceedings of 8th European Conference, ECMFA 2012, Kgs. Lyngby, Denmark, July 2-5, 2012Domain-specific modelling languages are normally defined through general-purpose meta-modelling languages like the MOF. While this is satisfactory for many Model-Driven Engineering (MDE) projects, several researchers have identified the need for domain-specific meta-modelling (DSMM) languages providing customised meta-modelling primitives aimed at the definition of modelling languages in a specific domain, as well as the construction of meta-model families. In this paper, we discuss the potential of multi-level meta-modelling for the systematic engineering of DSMM architectures. For this purpose, we present: (i) several primitives and techniques to control the meta-modelling facilities offered to the users of the DSMM languages, (ii) a flexible approach to define textual concrete syntaxes for DSMM languages, (iii) extensions to model management languages enabling the practical use of DSMM in MDE, and (iv) an implementation of these ideas in the metaDepth tool.This work was funded by the Spanish Ministry of Economy and Competitivity (project “Go Lite” TIN2011-24139) and the R&D programme of the Madrid Region (project “e-Madrid” S2009/TIC-1650

Screening the genome to detect an association with hypertension

We report tree-based association analysis as applied to the two Framingham cohorts and to the first replication of the simulated data obtained from the Genetic Analysis Workshop 13. For this analysis, familial association is ignored. The two endpoints examined are hypertension status at initial visit and time-to-hypertension, using a censored data approach. Although linkage association has previously been reported with hypertension, we found no association using the tree-based methodology

Bump start needed: linking guidelines, policy and practice in promoting physical activity during and beyond pregnancy

First paragraph: There is compelling evidence that regular physical activity (PA) during pregnancy benefits both mother and baby.1 2 Notably, physical and psychological benefits are evident in the literature, such as marked reductions in the development of gestational diabetes and hypertensive disorders, alongside improvements in depressive symptoms and cardiorespiratory fitness.1 2 The evidence base has been reflected by recent policy initiatives, for example, in 2017 (relaunched in 2019), the UK‘s chief medical officers (CMOs) published PA guidelines for pregnant women, which made substantial strides in unifying and translating the evidence into recommendations.1 The CMO guidelines are aimed at supporting health professionals to provide consistent, evidence-based PA messages to women throughout pregnancy.1 Recently, the Chartered Institute for the Management of Sport and Physical Activity have updated their professional standards for working with antenatal and postnatal clients to align with these CMO guidelines.3 However, not all women have access to professionals with this level of expertise and training, potentially limiting the impact of the CMO guidelines

Effect of Interband Transitions on the c axis Penetration Depth of Layered Superconductors

The electromagnetic response of a system with two planes per unit cell involves, in addition to the usual intraband contribution, an added interband term. These transitions affect the temperature dependence and the magnitude of the zero temperature c-axis penetration depth. When the interplane hopping is sufficiently small, the interband transitions dominate the low temperature behaviour of the penetration depth which then does not reflect the linear temperature dependence of the intraband term and in comparison becomes quite flat even for a d-wave gap. It is in this regime that the pseudogap was found in our previous normal state calculations of the c-axis conductivity, and the effects are connected.Comment: 8 pages, 5 figure

Rate constants for the reaction of Cl atoms with O3 at temperatures from 298 to 184 K

Using the standard, low pressure, discharge-flow technique, with resonance fluorescence in the vacuum ultraviolet to observe Cl atoms, rate constants have been determined for the reaction of Cl atoms with O$_3$ at temperatures down to 184 K. The measured rate constants for 298-184 K fit the Arrhenius expression: k(T) = (3.6 $\pm$ 0.7) $\times$ 10$^{-11}$ exp(( - 310 $\pm$ 50 K) / T) cm$^3$ molecule$^{-1}$ s$^{-1}$. The results extend the data on this key atmospheric reaction to slightly lower temperatures. The data are in fairly good agreement with those currently in the literature but suggest that the rate constant approximately 15% lower than that given by currently recommended rate expressions at the lowest temperatures found in the stratosphere

Phase shifts as functions of the cross section

We show that an elastic scattering amplitute may be defined as an implicit function of the differential cross section. A practical method is given for a numerical investigation of this dependence, both in the elastic and in the inelastic regions. In particular, we consider the case of a polynomial amplitude, and we show that the Crichton ambiguity is not isolated

On the precision of chiral-dispersive calculations of ππ\pi\pi scattering

We calculate the combination $2a_0^{(0)}-5a_0^{(2)}$ (the Olsson sum rule) and the scattering lengths and effective ranges $a_1$, $a_2^{(I)}$ and $b_1$, $b_2^{(I)}$ dispersively (with the Froissart--Gribov representation) using, at low energy, the phase shifts for $\pi\pi$ scattering obtained by Colangelo, Gasser and Leutwyler (CGL) from the Roy equations and chiral perturbation theory, plus experiment and Regge behaviour at high energy, or directly, using the CGL parameters for $a$s and $b$s. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several (2 to 5) standard deviations, and is essentially independent of the details of the intermediate energy region ($0.82\leq E\leq 1.42$ GeV) and, in some cases, of the high energy behaviour assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.Comment: Version to appear in Phys. Rev. D. Graphs and sum rule added. Plain TeX fil

Defragmenting public space : a guide for policymakers

While social inequalities remain key features of numerous cities globally, many still manage to provide spaces for collective social life, including public streets, market spaces and parks. Yet many countries today, with growing and significant socio-economic disparities and a rising fear of crime and violence, now see a range of strategies by their wealthiest citizens to avoid public spaces. This avoidance has generated a more fragmented engagement with the city by particular social groups. These processes, including the avoidance of public spaces and normalisation of gated communities, are reshaping cities leaving fewer shared spaces for collective life as public spaces are privatised. This report comes from a dialogue between researchers with interests in the risks and challenges for the public life of cities and these new and growing patterns of segregation and social avoidance. The collaboration between scholars and institutions seeks to understand the increasingly defensive quality of many urban centres and to identify forms of policy, practice and urban interventions capable of ensuring public safety and participation by all citizens. The purpose of this report is to engage researchers and practitioners in the discussion about the risks and challenges associated with urban fragmentation strategies and the means by which safer, more inclusive and liveable public spaces might be achieved