The multilinear support problem for products of abelian varieties and tori

Let G be the product of an abelian variety and a torus defined over a number field K. The aim of this paper is detecting the dependence among some given rational points of G by studying their reductions modulo all primes of K. We show that if some simple conditions on the order of the reductions of the points are satisfied then there must be a dependency relation over the ring of K-endomorphisms of G. We generalize Larsen's result on the support problem to several points on products of abelian varieties and tori

The order of the reductions of an algebraic integer

Let K be a number field, and let a be a non-zero element of K. Fix some prime number l. We compute the density of the following set: the primes p of K such that the multiplicative order of the reduction of a modulo p is coprime to l (or, more generally, has some prescribed l-adic valuation). We evaluate the degree over K of extensions of the form K(\zeta_m, \sqrt[n]{a}) with n\leq m, which are obtained by adjoining a root of unity of order l^m and the l^n-th roots of a, as this is needed for computing the above density.Comment: revised and rewritten; new tables of examples checked with sage; the revisions include the referee's comment

The prime divisors of the number of points on abelian varieties

Let A,A' be elliptic curves or abelian varieties fully of type GSp defined over a number field K. This includes principally polarized abelian varieties with geometric endomorphism ring Z and dimension 2 or odd. We compare the number of points on the reductions of the two varieties. We prove that A and A' are K-isogenous if the following condition holds for a density-one set of primes p of K: the prime numbers dividing #A(k_p) also divide #A'(k_p). We generalize this statement to some extent for products of such varieties. This refines results of Hall and Perucca (2011) and of Ratazzi (2012).Comment: results generalized; to appear in Journal de Theorie des Nombres de Bordeau

A counterexample to the local-global principle of linear dependence for abelian varieties

Let A be an abelian variety defined over a number field k. Let P be a point in A(k) and let X be a subgroup of A(k). Gajda in 2002 asked whether it is true that the point P belongs to X if and only if the point (P mod p) belongs to (X mod p) for all but finitely many primes p of k. We answer negatively to Gajda's question.Comment: 3 page

The pharmacological treatment of epilepsy: recent advances and future perspectives

AbstractThe pharmacological armamentarium against epilepsy has expanded considerably over the last three decades, and currently includes over 30 different antiseizure medications. Despite this large armamentarium, about one third of people with epilepsy fail to achieve sustained seizure freedom with currently available medications. This sobering fact, however, is mitigated by evidence that clinical outcomes for many people with epilepsy have improved over the years. In particular, physicians now have unprecedented opportunities to tailor treatment choices to the characteristics of the individual, in order to maximize efficacy and tolerability. The present article discusses advances in the drug treatment of epilepsy in the last 5 years, focusing in particular on comparative effectiveness trials of second-generation drugs, the introduction of new pharmaceutical formulations for emergency use, and the results achieved with the newest medications. The article also includes a discussion of potential future developments, including those derived from advances in information technology, the development of novel precision treatments, the introduction of disease modifying agents, and the discovery of biomarkers to facilitate conduction of clinical trials as well as routine clinical management

Two variants of the support problem for products of abelian varieties and tori

Let G be the product of an abelian variety and a torus defined over a number field K. Let P and Q be K-rational points on G. Suppose that for all but finitely many primes p of K the order of (Q mod p) divides the order of (P mod p). Then there exist a K-endomorphism f of G and a non-zero integer c such that f(P)=cQ. Furthermore, we are able to prove the above result with weaker assumptions: instead of comparing the order of the points we only compare the radical of the order (radical support problem) or the l-adic valuation of the order for some fixed rational prime l (l-adic support problem).Comment: 13 pages; v2 results generalized; v3 incorporated referee comments, final version to appear in Journal of Number Theor

Applying logistic regression analysis to identify patient’s satisfaction predictors with general practitioner assistance: evidence from four Italian regions.

In the last years the interest for patient experience with health care services largely increased. Several surveys have been conducted in order to observe if health care systems answer to the overall patient needs. In 2000 World Health Organization challenged modern health care providers to ensure responsiveness to patients, i.e. to deliver also non-health assistance (respect for dignity, confidentiality, prompt attention, quality of amenities, access to social support networks, choice of provider, etc.). Poor evidence is available in Italy about connections between perceived quality and the capability of the healthcare system to respond to patients’ needs. This work aims at investigating patient experience with General Practitioner (GP) assistance and at measuring the impact of personal and organizational characteristics on overall satisfaction and on willingness to recommend. In 2009 a sample survey was conducted in four regions of Italy (Tuscany, Piedmont, Umbria, and Liguria). About 15.000 citizens answered to a large questionnaire related to Primary Care services, including a section dedicated to General Practitioner (GP) assistance. A logistic regression analysis was applied to analyze which are the predictors of overall satisfaction with GP, focusing mainly on variables related to patient’s expectations, continuity of care and organizational aspects (e.g. scheduled access, waiting time, health case history, etc.) and if there are differences across the four Italian Regions. Econometric analysis has been carried out through both ordered logistic regression and generalised ordered logit models. The inhabitants of the four Italian Regions refer a nice experience with GP assistance: more than 85% of them judged excellent or good the overall service. Generally, in some regions patient expectations affect more the willingness to recommend GP to friends or family members than the overall judgement on service. Besides, the findings provide convincing evidence that GP is a nodal point in the continuity of care process .: patient satisfaction, general practitioner, organizational aspects, continuity of care

Divided Timed and Continuous Timed Assessment Protocols and Academic Performance

Children from a low socioeconomic status (SES) are exposed to numerous stress factors that are negatively associated with sustained attention and academic performance. This association suggests that the timed component of lengthy assessments may be unfair for students from such backgrounds, as they may have an inability to sustain attention during lengthy tests. Research has also found academic disparities between gender. The purpose of this quasi-experimental study was to investigate the relationship between continuous and divided timed tests in terms of student test scores, with additional assessments incorporating gender. Two charter schools from a suburban Idaho school district were the sources of the convenience sample. Fifth grade students were tested in groups of approximately 30. The research questions for the study concerned the relationship between continuous and divided assessment protocols and Texas Assessment of Knowledge and Skills (TAKS) test scores for low- versus non-low-SES students and among gender. The hypothesis was that there would be a statistically significant difference in TAKS scores between continuous and divided assessments. An ANOVA was used to determine whether a statistical relationship existed between test scores and test protocol by gender. ANOVA results indicated no significant differences in math test scores between test protocols and among gender, suggesting that increased collaborative efforts between families and schools may mitigate factors associated with attentional and academic deficits among students from low-SES environments. The results of this study may be helpful for communities as they develop curricula that may close the academic gap among students of all SES backgrounds