A general framework for Noetherian well ordered polynomial reductions

Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly established. This paper presents a general definition of polynomial reduction structure, studies its features and highlights the aspects needed in order to grant and to efficiently test the main properties (noetherianity, confluence, ideal membership). The most significant aspect of this analysis is a negative reappraisal of the role of the notion of term order which is usually considered a central and crucial tool in the theory. In fact, as it was already established in the computer science context in relation with termination of algorithms, most of the properties can be obtained simply considering a well-founded ordering, while the classical requirement that it be preserved by multiplication is irrelevant. The last part of the paper shows how the polynomial basis concepts present in literature are interpreted in our language and their properties are consequences of the general results established in the first part of the paper.Comment: 36 pages. New title and substantial improvements to the presentation according to the comments of the reviewer

La queste del saint Gra(AL): A computational approach to local algebra

AbstractWe show how, by means of the Tangent Cone Algorithm, the basic functions related to the maximal ideal topology of a local ring can be effectively computed in the situations of geometrical significance, i.e.:(1)localizations of coordinate rings of a variety at the prime ideal defining a subvariety,(2)rings of algebraic formal power series rings.In particular we show how the method of “associated graded rings” can be turned into an effective tool to compute local algebraic invariants of varieties

Oracle-supported drawing of the Groebner {\em escalier}

The aim of this note is to discuss the following quite queer Problem: \noindent GIVEN \noindent i) the free non-commutative polynomial ring, {\Cal P} := {\Bbb F}\langle X_1,\ldots,X_n\rangle {\em (public)}, \noindent ii) a bilateral ideal ${\sf I}\subset {\Bbb F}\langle X_1,\ldots,X_n\rangle$ {\em (private)}, \noindent iii) a finite set $G := \{g_1,\ldots,g_l\}\subset{\sf I}$ of elements of the ideal ${\sf I}$ {\em (public)}, \noindent a noetherian semigroup term-ordering $\prec,$ {\rm (private)}, on the word semigroup {\Cal T} := , \noindent COMPUTE \noindent --a finite subset $H\subset\Gamma({\sf I})$ of the Gr\"obner basis $\Gamma({\sf I})$ of ${\sf I}$ w.r.t. $\prec$ s.t., for each $g_i\in G$ its {\em normal form} $NF(g_i,H)$ w.r.t. $H$ is zero, \noindent "by means of a finite number of queries to an oracle", which, \noindent given a term \tau\in{\Cal T} returns its {\em canonical form} \Can(\tau,{\sf I},\prec) w.r.t. the ideal ${\sf I}$ and the term-ordering $\prec$. \qed This queer problem has been suggested to us by Bulygin (2005) where a similar problem, but with stronger assumptions, is faced in order to set up a chosen-cyphertext attack against the cryptographic system proposed in Rai (2004)

Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis

BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London

Caffeine Ingestion Reverses the Circadian Rhythm Effects on Neuromuscular Performance in Highly Resistance-Trained Men

Purpose: To investigate whether caffeine ingestion counteracts the morning reduction in neuromuscular performance associated with the circadian rhythm pattern. Methods: Twelve highly resistance-trained men underwent a battery of neuromuscular tests under three different conditions; i) morning (10:00 a.m.) with caffeine ingestion (i.e., 3 mg kg 21; AMCAFF trial); ii) morning (10:00 a.m.) with placebo ingestion (AMPLAC trial); and iii) afternoon (18:00 p.m.) with placebo ingestion (PMPLAC trial). A randomized, doubleblind, crossover, placebo controlled experimental design was used, with all subjects serving as their own controls. The neuromuscular test battery consisted in the measurement of bar displacement velocity during free-weight full-squat (SQ) and bench press (BP) exercises against loads that elicit maximum strength (75 % 1RM load) and muscle power adaptations (1 m s 21 load). Isometric maximum voluntary contraction (MVCLEG) and isometric electrically evoked strength of the right knee (EVOK LEG) were measured to identify caffeine’s action mechanisms. Steroid hormone levels (serum testosterone, cortisol and growth hormone) were evaluated at the beginning of each trial (PRE). In addition, plasma norepinephrine (NE) and epinephrine were measured PRE and at the end of each trial following a standardized intense (85 % 1RM) 6 repetitions bout of SQ (POST). Results: In the PM PLAC trial, dynamic muscle strength and power output were significantly enhanced compared with AM PLA