Effectively Open Real Functions

A function f is continuous iff the PRE-image f^{-1}[V] of any open set V is open again. Dual to this topological property, f is called OPEN iff the IMAGE f[U] of any open set U is open again. Several classical Open Mapping Theorems in Analysis provide a variety of sufficient conditions for openness. By the Main Theorem of Recursive Analysis, computable real functions are necessarily continuous. In fact they admit a well-known characterization in terms of the mapping V+->f^{-1}[V] being EFFECTIVE: Given a list of open rational balls exhausting V, a Turing Machine can generate a corresponding list for f^{-1}[V]. Analogously, EFFECTIVE OPENNESS requires the mapping U+->f[U] on open real subsets to be effective. By effectivizing classical Open Mapping Theorems as well as from application of Tarski's Quantifier Elimination, the present work reveals several rich classes of functions to be effectively open.Comment: added section on semi-algebraic functions; to appear in Proc. http://cca-net.de/cca200

On the asymptotic and practical complexity of solving bivariate systems over the reals

This paper is concerned with exact real solving of well-constrained, bivariate polynomial systems. The main problem is to isolate all common real roots in rational rectangles, and to determine their intersection multiplicities. We present three algorithms and analyze their asymptotic bit complexity, obtaining a bound of \sOB(N^{14}) for the purely projection-based method, and \sOB(N^{12}) for two subresultant-based methods: this notation ignores polylogarithmic factors, where $N$ bounds the degree and the bitsize of the polynomials. The previous record bound was \sOB(N^{14}). Our main tool is signed subresultant sequences. We exploit recent advances on the complexity of univariate root isolation, and extend them to sign evaluation of bivariate polynomials over two algebraic numbers, and real root counting for polynomials over an extension field. Our algorithms apply to the problem of simultaneous inequalities; they also compute the topology of real plane algebraic curves in \sOB(N^{12}), whereas the previous bound was \sOB(N^{14}). All algorithms have been implemented in MAPLE, in conjunction with numeric filtering. We compare them against FGB/RS, system solvers from SYNAPS, and MAPLE libraries INSULATE and TOP, which compute curve topology. Our software is among the most robust, and its runtimes are comparable, or within a small constant factor, with respect to the C/C++ libraries. Key words: real solving, polynomial systems, complexity, MAPLE softwareComment: 17 pages, 4 algorithms, 1 table, and 1 figure with 2 sub-figure

Upper-Room Ultraviolet Light and Negative Air Ionization to Prevent Tuberculosis Transmission

Background Institutional tuberculosis (TB) transmission is an important public health problem highlighted by the HIV/AIDS pandemic and the emergence of multidrug- and extensively drug-resistant TB. Effective TB infection control measures are urgently needed. We evaluated the efficacy of upper-room ultraviolet (UV) lights and negative air ionization for preventing airborne TB transmission using a guinea pig air-sampling model to measure the TB infectiousness of ward air. Methods and Findings For 535 consecutive days, exhaust air from an HIV-TB ward in Lima, Perú, was passed through three guinea pig air-sampling enclosures each housing approximately 150 guinea pigs, using a 2-d cycle. On UV-off days, ward air passed in parallel through a control animal enclosure and a similar enclosure containing negative ionizers. On UV-on days, UV lights and mixing fans were turned on in the ward, and a third animal enclosure alone received ward air. TB infection in guinea pigs was defined by monthly tuberculin skin tests. All guinea pigs underwent autopsy to test for TB disease, defined by characteristic autopsy changes or by the culture of Mycobacterium tuberculosis from organs. 35% (106/304) of guinea pigs in the control group developed TB infection, and this was reduced to 14% (43/303) by ionizers, and to 9.5% (29/307) by UV lights (both p < 0.0001 compared with the control group). TB disease was confirmed in 8.6% (26/304) of control group animals, and this was reduced to 4.3% (13/303) by ionizers, and to 3.6% (11/307) by UV lights (both p < 0.03 compared with the control group). Time-to-event analysis demonstrated that TB infection was prevented by ionizers (log-rank 27; p < 0.0001) and by UV lights (log-rank 46; p < 0.0001). Time-to-event analysis also demonstrated that TB disease was prevented by ionizers (log-rank 3.7; p = 0.055) and by UV lights (log-rank 5.4; p = 0.02). An alternative analysis using an airborne infection model demonstrated that ionizers prevented 60% of TB infection and 51% of TB disease, and that UV lights prevented 70% of TB infection and 54% of TB disease. In all analysis strategies, UV lights tended to be more protective than ionizers. Conclusions Upper-room UV lights and negative air ionization each prevented most airborne TB transmission detectable by guinea pig air sampling. Provided there is adequate mixing of room air, upper-room UV light is an effective, low-cost intervention for use in TB infection control in high-risk clinical settings

Evaluating strategies for control of tuberculosis in prisons and prevention of spillover into communities: An observational and modeling study from Brazil

Background It has been hypothesized that prisons serve as amplifiers of general tuberculosis (TB) epidemics, but there is a paucity of data on this phenomenon and the potential population-level effects of prison-focused interventions. This study (1) quantifies the TB risk for prisoners as they traverse incarceration and release, (2) mathematically models the impact of prison-based interventions on TB burden in the general population, and (3) generalizes this model to a wide range of epidemiological contexts. Methods and findings We obtained individual-level incarceration data for all inmates (n = 42,925) and all reported TB cases (n = 5,643) in the Brazilian state of Mato Grosso do Sul from 2007 through 2013. We matched individuals between prisoner and TB databases and estimated the incidence of TB from the time of incarceration and the time of prison release using Cox proportional hazards models. We identified 130 new TB cases diagnosed during incarceration and 170 among individuals released from prison. During imprisonment, TB rates increased from 111 cases per 100,000 person-years at entry to a maximum of 1,303 per 100,000 person-years at 5.2 years. At release, TB incidence was 229 per 100,000 person-years, which declined to 42 per 100,000 person-years (the average TB incidence in Brazil) after 7 years. We used these data to populate a compartmental model of TB transmission and incarceration to evaluate the effects of various prison-based interventions on the incidence of TB among prisoners and the general population. Annual mass TB screening within Brazilian prisons would reduce TB incidence in prisons by 47.4% (95% Bayesian credible interval [BCI], 44.4%–52.5%) and in the general population by 19.4% (95% BCI 17.9%–24.2%). A generalized model demonstrates that prison-based interventions would have maximum effectiveness in reducing community incidence in populations with a high concentration of TB in prisons and greater degrees of mixing between ex-prisoners and community members. Study limitations include our focus on a single Brazilian state and our retrospective use of administrative databases. Conclusions Our findings suggest that the prison environment, more so than the prison population itself, drives TB incidence, and targeted interventions within prisons could have a substantial effect on the broader TB epidemic

Effectiveness of virtual reality in the treatment of hand function in children with cerebral palsy: A systematic review.

STUDY DESIGN: Systematic review. INTRODUCTION: Children with cerebral palsy (CP) may have limited use of their hands for functional activities and for fine motor skills. Virtual reality (VR) is a relatively new and innovative approach to facilitate hand function in children with CP. PURPOSE OF THE STUDY: The primary purpose of this study was to determine the effectiveness of VR as an intervention to improve hand function in children with CP compared to either conventional physiotherapy or other therapeutic interventions. The secondary purpose was to classify the outcomes evaluated according to the International Classification of Functioning, Disability and Health (ICF) dimensions. METHODS: A International prospective register of systematic reviews (PROSPERO)-registered literature search was carried out in August 2015 in MEDLINE, CINAHL, ERIC, HealthSTAR, AMED, BNI, Embase, PsycINFO, PEDro, Cochrane Central Register, DARE, OTSeeker, REHABDATA, HaPI, CIRRIE, and Scopus. PRISMA guidelines were followed. Only randomized controlled trials (RCTs) were included, and their methodological qualities were examined using the Cochrane collaboration's risk of bias (RoB) tool. A narrative synthesis was performed. RESULTS: The 6 RCTs published on this topic provide conflicting results. Four studies reported improved hand function (2 low RoB, 1 high RoB, and 1 unclear RoB), whereas 2 studies reported no improvement. All of the RCTs reported the activity element of ICF, but no study explicitly described the effect of VR intervention based on the ICF model. CONCLUSION: The role of VR ti imrpove hand fucntion in children with CP is unclear due to limited evidence; use as an adjunct has some support

Phase-specific and lifetime costs of cancer care in Ontario, Canada

BACKGROUND: Cancer is a major public health issue and represents a significant economic burden to health care systems worldwide. The objective of this analysis was to estimate phase-specific, 5-year and lifetime net costs for the 21 most prevalent cancer sites, and remaining tumour sites combined, in Ontario, Canada. METHODS: We selected all adult patients diagnosed with a primary cancer between 1997 and 2007, with valid ICD-O site and histology codes, and who survived 30 days or more after diagnosis, from the Ontario Cancer Registry (N = 394,092). Patients were linked to treatment data from Cancer Care Ontario and administrative health care databases at the Institute for Clinical and Evaluative Sciences. Net costs (i.e., cost difference between patients and matched non-cancer control subjects) were estimated by phase of care and sex, and used to estimate 5-year and lifetime costs. RESULTS: Mean net costs of care (2009 CAD) were highest in the initial (6 months post-diagnosis) and terminal (12 months pre-death) phases, and lowest in the (3 months) pre-diagnosis and continuing phases of care. Phase-specific net costs were generally lowest for melanoma and highest for brain cancer. Mean 5-year net costs varied from less than $25,000 for melanoma, thyroid and testicular cancers to more than$60,000 for multiple myeloma and leukemia. Lifetime costs ranged from less than $55,000 for lung and liver cancers to over$110,000 for leukemia, multiple myeloma, lymphoma and breast cancer. CONCLUSIONS: Costs of cancer care are substantial and vary by cancer site, phase of care and time horizon analyzed. These cost estimates are valuable to decision makers to understand the economic burden of cancer care and may be useful inputs to researchers undertaking cancer-related economic evaluations

Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear

An effect of a mean velocity shear on a turbulence and on the effective force which is determined by the gradient of Reynolds stresses is studied. Generation of a mean vorticity in a homogeneous incompressible turbulent flow with an imposed mean velocity shear due to an excitation of a large-scale instability is found. The instability is caused by a combined effect of the large-scale shear motions (''skew-induced" deflection of equilibrium mean vorticity) and ''Reynolds stress-induced" generation of perturbations of mean vorticity. Spatial characteristics, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This instability and the dynamics of the mean vorticity are associated with the Prandtl's turbulent secondary flows. This instability is similar to the mean-field magnetic dynamo instability. Astrophysical applications of the obtained results are discussed.Comment: 8 pages, 3 figures, REVTEX4, submitted to Phys. Rev.

Lipid Composition of the Human Eye: Are Red Blood Cells a Good Mirror of Retinal and Optic Nerve Fatty Acids?

International audienceBACKGROUND: The assessment of blood lipids is very frequent in clinical research as it is assumed to reflect the lipid composition of peripheral tissues. Even well accepted such relationships have never been clearly established. This is particularly true in ophthalmology where the use of blood lipids has become very common following recent data linking lipid intake to ocular health and disease. In the present study, we wanted to determine in humans whether a lipidomic approach based on red blood cells could reveal associations between circulating and tissue lipid profiles. To check if the analytical sensitivity may be of importance in such analyses, we have used a double approach for lipidomics. METHODOLOGY AND PRINCIPAL FINDINGS: Red blood cells, retinas and optic nerves were collected from 9 human donors. The lipidomic analyses on tissues consisted in gas chromatography and liquid chromatography coupled to an electrospray ionization source-mass spectrometer (LC-ESI-MS). Gas chromatography did not reveal any relevant association between circulating and ocular fatty acids except for arachidonic acid whose circulating amounts were positively associated with its levels in the retina and in the optic nerve. In contrast, several significant associations emerged from LC-ESI-MS analyses. Particularly, lipid entities in red blood cells were positively or negatively associated with representative pools of retinal docosahexaenoic acid (DHA), retinal very-long chain polyunsaturated fatty acids (VLC-PUFA) or optic nerve plasmalogens. CONCLUSIONS AND SIGNIFICANCE: LC-ESI-MS is more appropriate than gas chromatography for lipidomics on red blood cells, and further extrapolation to ocular lipids. The several individual lipid species we have identified are good candidates to represent circulating biomarkers of ocular lipids. However, further investigation is needed before considering them as indexes of disease risk and before using them in clinical studies on optic nerve neuropathies or retinal diseases displaying photoreceptors degeneration