Towards the Formal Specification and Verification of Maple Programs

In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors in such programs w.r.t. their specifications by static analysis. This task is more complex for widely used computer algebra languages like Maple as these are fundamentally different from classical languages: they support non-standard types of objects such as symbols, unevaluated expressions and polynomials and require abstract computer algebraic concepts and objects such as rings and orderings etc. As a starting point we have defined and formalized a syntax, semantics, type system and specification language for MiniMaple

Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on Many-core Systems

We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algo- rithm targets not only the shared memory multicore computers, but also computers clusters or specialized hardware attached to a host computer, such as graphics processing units or many-core coprocessors. The scal- ability on the large number of cores is ensured by the lacks of synchro- nizations, locks and false-sharing during the main parallel step.Comment: 15 pages, 5 figure

A new approach to the method of source-sink potentials for molecular conduction

We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells. We make explicit the behaviour of the total current and individual MO and shell currents at molecular eigenvalues. A rich variety of behaviour is found. A SSP device has specific insulation or conduction at an eigenvalue of the molecular graph (a root of the characteristic polynomial) according to the multiplicities of that value in the spectra of four defined device polynomials. Conduction near eigenvalues is dominated by the transmission curves of nearby shells. A shell may be inert or active. An inert shell does not conduct at any energy, not even at its own eigenvalue. Conduction may occur at the eigenvalue of an inert shell, but is then carried entirely by other shells. If a shell is active, it carries all conduction at its own eigenvalue. For bipartite molecular graphs (alternant molecules), orbital conduction properties are governed by a pairing theorem. Inertness of shells for families such as chains and rings is predicted by selection rules based on node counting and degenerac

Unexpected effects of third-order cross-terms in heteronuclear spin systems under simultaneous radio-frequency irradiation and magic-angle spinning NMR

We recently noted [R. K. Harris, P. Hodgkinson, V. Zorin, J.-N. Dumez, B. Elena, L. Emsley, E. Salager, and R. Stein, Magn. Reson. Chem. 48, S103 (2010)10.1002/mrc.2636] anomalous shifts in apparent 1H chemical shifts in experiments using 1H homonuclear decoupling sequences to acquire high-resolution 1H NMR spectra for organic solids under magic-angle spinning (MAS). Analogous effects were also observed in numerical simulations of model 13C,1H spin systems under homonuclear decoupling and involving large 13C,1H dipolar couplings. While the heteronuclear coupling is generally assumed to be efficiently suppressed by sample spinning at the magic angle, we show that under conditions typically used in solid-state NMR, there is a significant third-order cross-term from this coupling under the conditions of simultaneous MAS and homonuclear decoupling for spins directly bonded to 1H. This term, which is of the order of 100 Hz under typical conditions, explains the anomalous behaviour observed on both 1H and 13C spins, including the fast dephasing observed in 13C{1H} heteronuclear spin-echo experiments under 1H homonuclear decoupling. Strategies for minimising the impact of this effect are also discussed

The Community Ecology of Herbivore Regulation in an Agroecosystem: Lessons from Complex Systems

AbstractWhether an ecological community is controlled from above or below remains a popular framework that continues generating interesting research questions and takes on especially important meaning in agroecosystems. We describe the regulation from above of three coffee herbivores, a leaf herbivore (the green coffee scale, Coccus viridis), a seed predator (the coffee berry borer, Hypothenemus hampei), and a plant pathogen (the coffee rust disease, caused by Hemelia vastatrix) by various natural enemies, emphasizing the remarkable complexity involved. We emphasize the intersection of this classical question of ecology with the burgeoning field of complex systems, including references to chaos, critical transitions, hysteresis, basin or boundary collision, and spatial self-organization, all aimed at the applied question of pest control in the coffee agroecosystem

Male responsibility and maternal morbidity: a cross-sectional study in two Nigerian states

<p>Abstract</p> <p>Background</p> <p>Nigeria continues to have high rates of maternal morbidity and mortality. This is partly associated with lack of adequate obstetric care, partly with high risks in pregnancy, including heavy work. We examined actionable risk factors and underlying determinants at community level in Bauchi and Cross River States of Nigeria, including several related to male responsibility in pregnancy.</p> <p>Method</p> <p>In 2009, field teams visited a stratified (urban/rural) last stage random sample of 180 enumeration areas drawn from the most recent censuses in each of Bauchi and Cross River states. A structured questionnaire administered in face-to-face interviews with women aged 15-49 years documented education, income, recent birth history, knowledge and attitudes related to safe birth, and deliveries in the last three years. Closed questions covered female genital mutilation, intimate partner violence (IPV) in the last year, IPV during the last pregnancy, work during the last pregnancy, and support during pregnancy. The outcome was complications in pregnancy and delivery (eclampsia, sepsis, bleeding) among survivors of childbirth in the last three years. We adjusted bivariate and multivariate analysis for clustering.</p> <p>Findings</p> <p>The most consistent and prominent of 28 candidate risk factors and underlying determinants for non-fatal maternal morbidity was intimate partner violence (IPV) during pregnancy (ORa 2.15, 95%CIca 1.43-3.24 in Bauchi and ORa 1.5, 95%CI 1.20-2.03 in Cross River). Other spouse-related factors in the multivariate model included not discussing pregnancy with the spouse and, independently, IPV in the last year. Shortage of food in the last week was a factor in both Bauchi (ORa 1.66, 95%CIca 1.22-2.26) and Cross River (ORa 1.32, 95%CIca 1.15-1.53). Female genital mutilation was a factor among less well to do Bauchi women (ORa 2.1, 95%CIca 1.39-3.17) and all Cross River women (ORa 1.23, 95%CIca 1.1-1.5).</p> <p>Interpretation</p> <p>Enhancing clinical protocols and skills can only benefit women in Nigeria and elsewhere. But the violence women experience throughout their lives – genital mutilation, domestic violence, and steep power gradients – is accentuated through pregnancy and childbirth, when women are most vulnerable. IPV especially in pregnancy, women's fear of husbands or partners and not discussing pregnancy are all within men's capacity to change.</p

POLY: A new polynomial data structure for Maple 17

We demonstrate how a new data structure for sparse distributed polynomials in the Maple kernel significantly accelerates several key Maple library routines. The POLY data structure and its associated kernel operations (degree, coeff, subs, has, diff, eval,...) are programmed for high scalability, allowing polynomials to have hundreds of millions of terms, and very low overhead, increasing parallel speedup in existing routines and improving the performance of high level Maple library routines