Trakhtenbrot's Theorem in Coq, A Constructive Approach to Finite Model Theory

We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order signature of non-logical symbols. On the one hand, our development focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof proceeds by a many-one reduction chain starting from the Post correspondence problem. On the other hand, we establish the decidability of FSAT for monadic first-order logic, i.e. where the signature only contains at most unary function and relation symbols, as well as the enumerability of FSAT for arbitrary enumerable signatures. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs

The Home-Based Older People's Exercise (HOPE) trial: study protocol for a randomised controlled trial

<p>Abstract</p> <p>Background</p> <p>Frailty is common in older age, and is associated with important adverse health outcomes including increased risk of disability and admission to hospital or long-term care. Exercise interventions for frail older people have the potential to reduce the risk of these adverse outcomes by increasing muscle strength and improving mobility.</p> <p>Methods/Design</p> <p>The Home-Based Older People's Exercise (HOPE) trial is a two arm, assessor blind pilot randomised controlled trial (RCT) to assess the effectiveness of a 12 week exercise intervention (the HOPE programme) designed to improve the mobility and functional abilities of frail older people living at home, compared with usual care. The primary outcome is the timed-up-and-go test (TUGT), measured at baseline and 14 weeks post-randomisation. Secondary outcomes include the Barthel Index of activities of daily living (ADL), EuroQol Group 5-Dimension Self-Report Questionnaire (EQ-5D) quality of life measure and the geriatric depression scale (GDS), measured at baseline and 14 weeks post-randomisation. We will record baseline frailty using the Edmonton Frail Scale (EFS), record falls and document muscle/joint pain. We will test the feasibility of collection of data to identify therapy resources required for delivery of the intervention.</p> <p>Discussion</p> <p>The HOPE trial will explore and evaluate a home-based exercise intervention for frail older people. Although previous RCTs have used operationalised, non-validated methods of measuring frailty, the HOPE trial is, to our knowledge, the first RCT of an exercise intervention for frail older people that includes a validated method of frailty assessment at baseline.</p> <p>Trial registration</p> <p>ISRCTN: <a href="http://www.controlled-trials.com/ISRCTN57066881">ISRCTN57066881</a></p

Uniparental Genetic Heritage of Belarusians: Encounter of Rare Middle Eastern Matrilineages with a Central European Mitochondrial DNA Pool

Ethnic Belarusians make up more than 80% of the nine and half million people inhabiting the Republic of Belarus. Belarusians together with Ukrainians and Russians represent the East Slavic linguistic group, largest both in numbers and territory, inhabiting East Europe alongside Baltic-, Finno-Permic- and Turkic-speaking people. Till date, only a limited number of low resolution genetic studies have been performed on this population. Therefore, with the phylogeographic analysis of 565 Y-chromosomes and 267 mitochondrial DNAs from six well covered geographic sub-regions of Belarus we strove to complement the existing genetic profile of eastern Europeans. Our results reveal that around 80% of the paternal Belarusian gene pool is composed of R1a, I2a and N1c Y-chromosome haplogroups – a profile which is very similar to the two other eastern European populations – Ukrainians and Russians. The maternal Belarusian gene pool encompasses a full range of West Eurasian haplogroups and agrees well with the genetic structure of central-east European populations. Our data attest that latitudinal gradients characterize the variation of the uniparentally transmitted gene pools of modern Belarusians. In particular, the Y-chromosome reflects movements of people in central-east Europe, starting probably as early as the beginning of the Holocene. Furthermore, the matrilineal legacy of Belarusians retains two rare mitochondrial DNA haplogroups, N1a3 and N3, whose phylogeographies were explored in detail after de novo sequencing of 20 and 13 complete mitogenomes, respectively, from all over Eurasia. Our phylogeographic analyses reveal that two mitochondrial DNA lineages, N3 and N1a3, both of Middle Eastern origin, might mark distinct events of matrilineal gene flow to Europe: during the mid-Holocene period and around the Pleistocene-Holocene transition, respectively

An ultraviolet-optical flare from the tidal disruption of a helium-rich stellar core

The flare of radiation from the tidal disruption and accretion of a star can be used as a marker for supermassive black holes that otherwise lie dormant and undetected in the centres of distant galaxies. Previous candidate flares have had declining light curves in good agreement with expectations, but with poor constraints on the time of disruption and the type of star disrupted, because the rising emission was not observed. Recently, two `relativistic' candidate tidal disruption events were discovered, each of whose extreme X-ray luminosity and synchrotron radio emission were interpreted as the onset of emission from a relativistic jet. Here we report the discovery of a luminous ultraviolet-optical flare from the nuclear region of an inactive galaxy at a redshift of 0.1696. The observed continuum is cooler than expected for a simple accreting debris disk, but the well-sampled rise and decline of its light curve follows the predicted mass accretion rate, and can be modelled to determine the time of disruption to an accuracy of two days. The black hole has a mass of about 2 million solar masses, modulo a factor dependent on the mass and radius of the star disrupted. On the basis of the spectroscopic signature of ionized helium from the unbound debris, we determine that the disrupted star was a helium-rich stellar core.Comment: To appear in Nature on May 10, 201

Trakhtenbrot’s Theorem in Coq: A Constructive Approach to Finite Model Theory

International audienceWe study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order signature of non-logical symbols. On the one hand, our development focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof proceeds by a many-one reduction chain starting from the Post correspondence problem. On the other hand, we establish the decidability of FSAT for monadic first-order logic, i.e. where the signature only contains at most unary function and relation symbols, as well as the enumerability of FSAT for arbitrary enumerable signatures. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs

Mitochondrial echoes of first settlement and genetic continuity in El Salvador

Background: From Paleo-Indian times to recent historical episodes, the Mesoamerican isthmus played an important role in the distribution and patterns of variability all around the double American continent. However, the amount of genetic information currently available on Central American continental populations is very scarce. In order to shed light on the role of Mesoamerica in the peopling of the New World, the present study focuses on the analysis of the mtDNA variation in a population sample from El Salvador. Methodology/Principal Findings: We have carried out DNA sequencing of the entire control region of the mitochondrial DNA (mtDNA) genome in 90 individuals from El Salvador. We have also compiled more than 3,985 control region profiles from the public domain and the literature in order to carry out inter-population comparisons. The results reveal a predominant Native American component in this region: by far, the most prevalent mtDNA haplogroup in this country (at ~90%) is A2, in contrast with other North, Meso- and South American populations. Haplogroup A2 shows a star-like phylogeny and is very diverse with a substantial proportion of mtDNAs (45%; sequence range 16090–16365) still unobserved in other American populations. Two different Bayesian approaches used to estimate admixture proportions in El Salvador shows that the majority of the mtDNAs observed come from North America. A preliminary founder analysis indicates that the settlement of El Salvador occurred about 13,400±5,200 Y.B.P.. The founder age of A2 in El Salvador is close to the overall age of A2 in America, which suggests that the colonization of this region occurred within a few thousand years of the initial expansion into the Americas. Conclusions/Significance: As a whole, the results are compatible with the hypothesis that today's A2 variability in El Salvador represents to a large extent the indigenous component of the region. Concordant with this hypothesis is also the observation of a very limited contribution from European and African women (~5%). This implies that the Atlantic slave trade had a very small demographic impact in El Salvador in contrast to its transformation of the gene pool in neighbouring populations from the Caribbean facade

Cervical cytological changes in HIV-infected patients attending care and treatment clinic at Muhimbili National Hospital, Dar es Salaam, Tanzania

\ud Tanzania is among Sub-Saharan countries mostly affected by the HIV and AIDS pandemic, females being more vulnerable than males. HIV infected women appear to have a higher rate of persistent infection by high risk types of human papillomavirus (HPV) strongly associated with high-grade squamous intraepithelial lesions (HSIL) and invasive cervical carcinoma. Furthermore, although HIV infection and cervical cancer are major public health problems, the frequency and HIV/HPV association of cervical cancer and HSIL is not well documented in Tanzania, thus limiting the development of preventive and therapeutic strategies. A prospective unmatched, case-control study of HIV-seropositive, ≥ 18 years of age and consenting non-pregnant patients attending the care and treatment center (CTC) at Muhimbili National Hoospital (MNH) as cases was done between 2005 and 2006. HIV seronegative, non-pregnant and consenting women recruited from the Cervical Cancer Screening unit (CCSU) at ORCI were used as controls while those who did not consent to study participation and/or individuals under < 18 years were excluded. Pap smears were collected for routine cytodiagnosis and P53 immunohistochemistry (IHC). Cervical lesions were classified according to the Modified Bethesda System. A total of 170 participants from the two centers were recruited including 50 HIV-seronegative controls were from the CCSU. Ages ranged from 20-66 years (mean 40.5 years) for cases and 20-69 years (mean 41.6 years) for controls. The age group 36-45 years was the most affected by HIV (39.2%, n = 47). Cervicitis, squamous intraepithelial lesions (SIL) and carcinoma constituted 28.3% (n = 34), 38.3% (n = 46) and 5.8% (n = 7) respectively among cases, and 28% (n = 14), 34% (n = 17) and 2% (n = 1) for controls, although this was not statistically significant (P-value = 0.61). IHC showed that p53 was not detectable in HPV + Pap smears and cell blocks indicating possible degradation. The frequency of SIL and carcinoma appeared to be higher among HIV-infected women on HAART compared to seronegative controls and as expected increased with age. HIV seropositive patients appeared to present earlier with SIL compared to those HIV seronegative suggesting a role of HIV in altering the natural history of HPV infection and cervical lesions. The absence of p53 immunoreactivity in HPV + lesions is indicative of the ability of HPV E6 proteins to interact with the tumor suppressor gene and pave way for viral-induced oncogenesis in the studied Tanzanian women.\u

Participant Nonnaiveté and the reproducibility of cognitive psychology

Many argue that there is a reproducibility crisis in psychology. We investigated nine well-known effects from the cognitive psychology literature—three each from the domains of perception/action, memory, and language, respectively—and found that they are highly reproducible. Not only can they be reproduced in online environments, but they also can be reproduced with nonnaïve participants with no reduction of effect size. Apparently, some cognitive tasks are so constraining that they encapsulate behavior from external influences, such as testing situation and prior recent experience with the experiment to yield highly robust effects

The Procedural Index for Mortality Risk (PIMR): an index calculated using administrative data to quantify the independent influence of procedures on risk of hospital death

<p>Abstract</p> <p>Background</p> <p>Surgeries and other procedures can influence the risk of death in hospital. All published scales that predict post-operative death risk require clinical data and cannot be measured using administrative data alone. This study derived and internally validated an index that can be calculated using administrative data to quantify the independent risk of hospital death after a procedure.</p> <p>Methods</p> <p>For all patients admitted to a single academic centre between 2004 and 2009, we estimated the risk of all-cause death using the Kaiser Permanente Inpatient Risk Adjustment Methodology (KP-IRAM). We determined whether each patient underwent one of 503 commonly performed therapeutic procedures using Canadian Classification of Interventions codes and whether each procedure was emergent or elective. Multivariate logistic regression modeling was used to measure the association of each procedure-urgency combination with death in hospital independent of the KP-IRAM risk of death. The final model was modified into a scoring system to quantify the independent influence each procedure had on the risk of death in hospital.</p> <p>Results</p> <p>275 460 hospitalizations were included (137,730 derivation, 137,730 validation). In the derivation group, the median expected risk of death was 0.1% (IQR 0.01%-1.4%) with 4013 (2.9%) dying during the hospitalization. 56 distinct procedure-urgency combinations entered our final model resulting in a Procedural Index for Mortality Rating (PIMR) score values ranging from -7 to +11. In the validation group, the PIMR score significantly predicted the risk of death by itself (c-statistic 67.3%, 95% CI 66.6-68.0%) and when added to the KP-IRAM model (c-index improved significantly from 0.929 to 0.938).</p> <p>Conclusions</p> <p>We derived and internally validated an index that uses administrative data to quantify the independent association of a broad range of therapeutic procedures with risk of death in hospital. This scale will improve risk adjustment when administrative data are used for analyses.</p

Elevated Uptake of Plasma Macromolecules by Regions of Arterial Wall Predisposed to Plaque Instability in a Mouse Model

Atherosclerosis may be triggered by an elevated net transport of lipid-carrying macromolecules from plasma into the arterial wall. We hypothesised that whether lesions are of the thin-cap fibroatheroma (TCFA) type or are less fatty and more fibrous depends on the degree of elevation of transport, with greater uptake leading to the former. We further hypothesised that the degree of elevation can depend on haemodynamic wall shear stress characteristics and nitric oxide synthesis. Placing a tapered cuff around the carotid artery of apolipoprotein E -/- mice modifies patterns of shear stress and eNOS expression, and triggers lesion development at the upstream and downstream cuff margins; upstream but not downstream lesions resemble the TCFA. We measured wall uptake of a macromolecular tracer in the carotid artery of C57bl/6 mice after cuff placement. Uptake was elevated in the regions that develop lesions in hyperlipidaemic mice and was significantly more elevated where plaques of the TCFA type develop. Computational simulations and effects of reversing the cuff orientation indicated a role for solid as well as fluid mechanical stresses. Inhibiting NO synthesis abolished the difference in uptake between the upstream and downstream sites. The data support the hypothesis that excessively elevated wall uptake of plasma macromolecules initiates the development of the TCFA, suggest that such uptake can result from solid and fluid mechanical stresses, and are consistent with a role for NO synthesis. Modification of wall transport properties might form the basis of novel methods for reducing plaque rupture