41 research outputs found
Bounding the radii of balls meeting every connected component of semi-algebraic sets
We prove explicit bounds on the radius of a ball centered at the origin which
is guaranteed to contain all bounded connected components of a semi-algebraic
set S \subset \mathbbm{R}^k defined by a quantifier-free formula involving
polynomials in \mathbbm{Z}[X_1, ..., X_k] having degrees at most , and
whose coefficients have bitsizes at most . Our bound is an explicit
function of and , and does not contain any undetermined
constants. We also prove a similar bound on the radius of a ball guaranteed to
intersect every connected component of (including the unbounded
components). While asymptotic bounds of the form on these
quantities were known before, some applications require bounds which are
explicit and which hold for all values of and . The bounds
proved in this paper are of this nature.Comment: 11 page
An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions
We prove an asymptotically tight bound (asymptotic with respect to the number
of polynomials for fixed degrees and number of variables) on the number of
semi-algebraically connected components of the realizations of all realizable
sign conditions of a family of real polynomials. More precisely, we prove that
the number of semi-algebraically connected components of the realizations of
all realizable sign conditions of a family of polynomials in
whose degrees are at most is bounded by This improves the best upper bound known
previously which was The new
bound matches asymptotically the lower bound obtained for families of
polynomials each of which is a product of generic polynomials of degree one.Comment: 19 pages. Bibliography has been updated and a few more references
have been added. This is the final version of this paper which will appear in
Combinatoric
Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets
In this paper we describe a singly exponential algorithm for computing the
first Betti number of a given semi-algebraic set. Singly exponential algorithms
for computing the zero-th Betti number, and the Euler-Poincar\'e
characteristic, were known before. No singly exponential algorithm was known
for computing any of the individual Betti numbers other than the zero-th one.
We also give algorithms for obtaining semi-algebraic descriptions of the
semi-algebraically connected components of any given real algebraic or
semi-algebraic set in single-exponential time improving on previous results
A bound on the minimum of a real positive polynomial over the standard simplex
We consider the problem of bounding away from 0 the minimum value m taken by
a polynomial P of Z[X_1,...,X_k] over the standard simplex, assuming that m>0.
Recent algorithmic developments in real algebraic geometry enable us to obtain
a positive lower bound on m in terms of the dimension k, the degree d and the
bitsize of the coefficients of P. The bound is explicit, and obtained without
any extra assumption on P, in contrast with previous results reported in the
literature
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
Surgical site infection after gastrointestinal surgery in high-income, middle-income, and low-income countries: a prospective, international, multicentre cohort study
Background: Surgical site infection (SSI) is one of the most common infections associated with health care, but its importance as a global health priority is not fully understood. We quantified the burden of SSI after gastrointestinal surgery in countries in all parts of the world.
Methods: This international, prospective, multicentre cohort study included consecutive patients undergoing elective or emergency gastrointestinal resection within 2-week time periods at any health-care facility in any country. Countries with participating centres were stratified into high-income, middle-income, and low-income groups according to the UN's Human Development Index (HDI). Data variables from the GlobalSurg 1 study and other studies that have been found to affect the likelihood of SSI were entered into risk adjustment models. The primary outcome measure was the 30-day SSI incidence (defined by US Centers for Disease Control and Prevention criteria for superficial and deep incisional SSI). Relationships with explanatory variables were examined using Bayesian multilevel logistic regression models. This trial is registered with ClinicalTrials.gov, number NCT02662231.
Findings: Between Jan 4, 2016, and July 31, 2016, 13 265 records were submitted for analysis. 12 539 patients from 343 hospitals in 66 countries were included. 7339 (58·5%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31·2%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10·2%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12·3%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9·4%] of 7339 patients), middle (549 [14·0%] of 3918 patients), and low (298 [23·2%] of 1282) HDI (p < 0·001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17·8%] of 574 patients in high-HDI countries; 74 [31·4%] of 236 patients in middle-HDI countries; 72 [39·8%] of 181 patients in low-HDI countries). Following risk factor adjustment, patients in low-HDI countries were at greatest risk of SSI (adjusted odds ratio 1·60, 95% credible interval 1·05–2·37; p=0·030). 132 (21·6%) of 610 patients with an SSI and a microbiology culture result had an infection that was resistant to the prophylactic antibiotic used. Resistant infections were detected in 49 (16·6%) of 295 patients in high-HDI countries, in 37 (19·8%) of 187 patients in middle-HDI countries, and in 46 (35·9%) of 128 patients in low-HDI countries (p < 0·001).
Interpretation: Countries with a low HDI carry a disproportionately greater burden of SSI than countries with a middle or high HDI and might have higher rates of antibiotic resistance. In view of WHO recommendations on SSI prevention that highlight the absence of high-quality interventional research, urgent, pragmatic, randomised trials based in LMICs are needed to assess measures aiming to reduce this preventable complication
Quantative Fundamental Theorem of Algebra
sing subresultants, we modify a recent real-algebraic proof due to Eisermann of the Fundamental Theorem of Algebra ([FTA]) to obtain the following quantitative information: in order to prove the [FTA] for polynomials of degree d, the Intermediate Value Theorem ([IVT]) is requested to hold for real polynomials of degree at most d^2. We also explain that the classical proof due to Laplace requires [IVT] for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs. See arXiv:1803.04358v3Non UBCUnreviewedAuthor affiliation: Universite de Rennes 1Facult