Generalized Satisfiability Problems via Operator Assignments

Schaefer introduced a framework for generalized satisfiability problems on the Boolean domain and characterized the computational complexity of such problems. We investigate an algebraization of Schaefer's framework in which the Fourier transform is used to represent constraints by multilinear polynomials in a unique way. The polynomial representation of constraints gives rise to a relaxation of the notion of satisfiability in which the values to variables are linear operators on some Hilbert space. For the case of constraints given by a system of linear equations over the two-element field, this relaxation has received considerable attention in the foundations of quantum mechanics, where such constructions as the Mermin-Peres magic square show that there are systems that have no solutions in the Boolean domain, but have solutions via operator assignments on some finite-dimensional Hilbert space. We obtain a complete characterization of the classes of Boolean relations for which there is a gap between satisfiability in the Boolean domain and the relaxation of satisfiability via operator assignments. To establish our main result, we adapt the notion of primitive-positive definability (pp-definability) to our setting, a notion that has been used extensively in the study of constraint satisfaction problems. Here, we show that pp-definability gives rise to gadget reductions that preserve satisfiability gaps. We also present several additional applications of this method. In particular and perhaps surprisingly, we show that the relaxed notion of pp-definability in which the quantified variables are allowed to range over operator assignments gives no additional expressive power in defining Boolean relations

Synthesized grain size distribution in the interstellar medium

We examine a synthetic way of constructing the grain size distribution in the interstellar medium (ISM). First we formulate a synthetic grain size distribution composed of three grain size distributions processed with the following mechanisms that govern the grain size distribution in the Milky Way: (i) grain growth by accretion and coagulation in dense clouds, (ii) supernova shock destruction by sputtering in diffuse ISM, and (iii) shattering driven by turbulence in diffuse ISM. Then, we examine if the observational grain size distribution in the Milky Way (called MRN) is successfully synthesized or not. We find that the three components actually synthesize the MRN grain size distribution in the sense that the deficiency of small grains by (i) and (ii) is compensated by the production of small grains by (iii). The fraction of each {contribution} to the total grain processing of (i), (ii), and (iii) (i.e., the relative importance of the three {contributions} to all grain processing mechanisms) is 30-50%, 20-40%, and 10-40%, respectively. We also show that the Milky Way extinction curve is reproduced with the synthetic grain size distributions.Comment: 10 pages, 6 figures, accepted for publication in Earth, Planets, and Spac

Impact of Scotland’s comprehensive, smoke-free legislation on stroke

<p>Background: Previous studies have reported a reduction in acute coronary events following smoke-free legislation. Evidence is lacking on whether stroke is also reduced. The aim was to determine whether the incidence of stroke, overalland by sub-type, fell following introduction of smoke-free legislation across Scotland on 26 March 2006.</p> <p>Methods and Findings: A negative binomial regression model was used to determine whether the introduction of smokefree legislation resulted in a step and/or slope change in stroke incidence. The model was adjusted for age-group, sex, socioeconomic deprivation quintile, urban/rural residence and month. Interaction tests were also performed. Routine hospital administrative data and death certificates were used to identify all hospital admissions and pre-hospital deaths due to stroke (ICD10 codes I61, I63 and I64) in Scotland between 2000 and 2010 inclusive. Prior to the legislation, rates of all stroke, intracerebral haemorrhage and unspecified stroke were decreasing, whilst cerebral infarction was increasing at 0.97% per annum. Following the legislation, there was a dramatic fall in cerebral infarctions that persisted for around 20 months. No visible effect was observed for other types of stroke. The model confirmed an 8.90% (95% CI 4.85, 12.77, p,0.001) stepwise reduction in cerebral infarction at the time the legislation was implemented, after adjustment for potential cofounders.</p> <p>Conclusions: Following introduction of national, comprehensive smoke-free legislation there was a selective reduction in cerebral infarction that was not apparent in other types of stroke.</p&gt

Estimation and inference under economic restrictions

Estimation of economic relationships often requires imposition of constraints such as positivity or monotonicity on each observation. Methods to impose such constraints, however, vary depending upon the estimation technique employed. We describe a general methodology to impose (observation-specific) constraints for the class of linear regression estimators using a method known as constraint weighted bootstrapping. While this method has received attention in the nonparametric regression literature, we show how it can be applied for both parametric and nonparametric estimators. A benefit of this method is that imposing numerous constraints simultaneously can be performed seamlessly. We apply this method to Norwegian dairy farm data to estimate both unconstrained and constrained parametric and nonparametric models

Osteoid osteoma of the femur in a 7-month-old infant treated with radiofrequency ablation

Osteoid osteoma occurs most commonly in children, adolescents, and young adults between the ages of 5 and 30 years. In the preschool age group, it is quite uncommon, accounting for only 3–8% of all osteoid osteoma cases. We report a case of osteoid osteoma in a 7-month-old infant, who presented with decreased use of the right lower extremity due to pain. Magnetic resonance imaging (MRI) showed an atypical appearance. A biopsy of the lesion, with histopathological examination, confirmed the diagnosis of osteoid osteoma. Radiofrequency ablation (RFA) of the nidus under computed tomography (CT) guidance was performed. The patient developed a recurrence after 3 months, which was treated with a second RFA. On subsequent follow-up, the infant did not show signs of pain after 1 month. In summary, this case report shows that osteoid osteoma can present in early infancy and can be successfully treated with RFA at this age, however, recurrence after the procedure can occur and close follow-up is recommended

Parental Monitoring During Early Adolescence Deters Adolescent Sexual Initiation: Discrete-Time Survival Mixture Analysis

We used discrete-time survival mixture modeling to examine 5,305 adolescents from the 1997 National Longitudinal Survey of Youth regarding the impact of parental monitoring during early adolescence (ages 14–16) on initiation of sexual intercourse and problem behavior engagement (ages 14–23). Four distinctive parental-monitoring groups were identified and labeled as “High,” “Increasing,” “Decreasing,” and “Low”. About 68% of adolescents received a high level of parental monitoring from ages 14 to 16 (High), 6 and 9% respectively exhibited an accelerated (Increasing) and a decelerated trajectory (Decreasing), and 17% had consistently low parental monitoring (Low). Relative to participants in the Low group, adolescents in the High group delayed sexual initiation by 1.5 years. Males, relative to females, were more likely to have had a low trajectory of parental monitoring, and were more likely to initiate sexual intercourse before age 14. In contrast to White Adolescents, Hispanics and Blacks were less likely to receive High parental monitoring, and had a higher rate of early sexual initiation before age 14. The study demonstrates the temporal relationship of parental monitoring with adolescent sexual initiation from a longitudinal perspective. An increase of parental monitoring across ages is accompanied with a decrease of sexual risk. The continual high level of parental monitoring from ages 14 to 16 also mitigated the risk of engagement in substance use and delinquent behaviors from ages 14 to 23

Malaria parasites regulate the duration of the intra-erythrocytic cycle via serpentine receptor 10 and coordinate development with host daily rhythms

Malaria parasites complete their intra-erythrocytic developmental cycle (IDC) in multiples of 24 h suggesting a circadian basis, but the mechanism controlling this periodicity is unknown. Combining in vivo and in vitro approaches utilizing rodent and human malaria parasites, we reveal that: (i) 57% of Plasmodium chabaudi genes exhibit daily rhythms in transcription; (ii) 58% of these genes lose transcriptional rhythmicity when the IDC is out-of-synchrony with host rhythms; (iii) 6% of Plasmodium falciparum genes show 24 h rhythms in expression under free-running conditions; (iv) Serpentine receptor 10 (SR10) has a 24 h transcriptional rhythm and disrupting it in rodent malaria parasites shortens the IDC by 2-3 h; (v) Multiple processes including DNA replication, and the ubiquitin and proteasome pathways, are affected by loss of coordination with host rhythms and by disruption of SR10. Our results reveal malaria parasites are at least partly responsible for scheduling the IDC and coordinating their development with host daily rhythms

Glassy State Lead Tellurite Nanobelts: Synthesis and Properties

The lead tellurite nanobelts have been first synthesized in the composite molten salts (KNO3/LiNO3) method, which is cost-effective, one-step, easy to control, and performed at low-temperature and in ambient atmosphere. Scanning electron microscopy, X-ray diffraction, transmission electron microscopy, X-ray photoelectron spectrum, energy dispersive X-ray spectroscopy and FT-IR spectrum are used to characterize the structure, morphology, and composition of the samples. The results show that the as-synthesized products are amorphous and glassy nanobelts with widths of 200–300 nm and lengths up to tens of microns and the atomic ratio of Pb:Te:O is close to 1:1.5:4. Thermo-gravimetric analysis (TGA) and differential scanning calorimetry (DSC) and investigations of the corresponding structure and morphology change confirm that the nanobelts have low glass transition temperature and thermal stability. Optical diffuse reflectance spectrum indicates that the lead tellurite nanobelts have two optical gaps at ca. 3.72 eV and 4.12 eV. Photoluminescence (PL) spectrum and fluorescence imaging of the products exhibit a blue emission (round 480 nm)