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

Efficacy of diadynamic currents as an adjunct to exercise to manage symptoms of knee osteoarthritis in adults: A randomized controlled clinical trial

Objective To investigate the effect of diadynamic currents administered prior to exercises on pain and disability in patients with osteoarthritis of the knee. Design A randomized-controlled trial. Setting Special Rehabilitation Services in Taboão da Serra. Participants Patients with bilateral knee osteoarthritis. Intervention Participants were randomly allocated to Group I (diadynamic currents and exercises; n = 30, 60 knees) or Group II (exercises alone; n = 30, 60 knees) and were treated three times a week for 8 weeks. Main outcome measures The primary outcome measures were change in knee pain evaluated by visual analog scale and disability Index Score (Lequesne). Secondary outcomes included change in mobility (Timed Up and Go test), range of motion (goniometer), muscle strength (dynamometer), a composite score for pain and disability (Western Ontario and McMaster Universities Osteoarthritis questionnaire), and a drug diary to measure consumption of rescue pain medication (paracetamol). All measurements were collected at baseline, 8 weeks, and 6 months from baseline (follow-up). Results There were 60 participants with a mean (SD) age of 63.40 (8.20) years. Between-group differences in the follow-up (8 weeks and 6 months) were observed for pain at rest, pain during activities of daily living and disability. There was improvement in Group I that was maintained for the three variables 6 months after treatment. Mean difference for pain at rest was −3.08 points (95% confidence interval −4.13; −2.02), p < 0.01 with an effect size of 1.4; mean difference for pain during activities of daily living was −2.40 points (95% confidence interval −3.34; −1.45), p < 0.01 with an effect size of 1.24; and mean difference for disability was −4.08 points (95% confidence interval −5.89; −2.26), p < 0.01 with an effect size of 1.04. Conclusion Patients with symptomatic knee osteoarthritis receiving 8 weeks of treatment with diadynamic currents as an adjunct to a program of exercises had significantly greater improvements in pain and disability than those receiving exercises alone. Beneficial effects were sustained for 6 months

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo

Interim 2017/18 influenza seasonal vaccine effectiveness: Combined results from five European studies

Between September 2017 and February 2018, influenza A(H1N1)pdm09, A(H3N2) and B viruses (mainly B/Yamagata, not included in 2017/18 trivalent vaccines) co-circulated in Europe. Interim results from five European studies indicate that, in all age groups, 2017/18 influenza vaccine effectiveness was 25 to 52% against any influenza, 55 to 68% against influenza A(H1N1)pdm09, -42 to 7% against influenza A(H3N2) and 36 to 54% against influenza B. 2017/18 influenza vaccine should be promoted where influenza still circulates

School Effects on the Wellbeing of Children and Adolescents

Well-being is a multidimensional construct, with psychological, physical and social components. As theoretical basis to help understand this concept and how it relates to school, we propose the Self-Determination Theory, which contends that self-determined motivation and personality integration, growth and well-being are dependent on a healthy balance of three innate psychological needs of autonomy, relatedness and competence. Thus, current indicators involve school effects on children’s well-being, in many diverse modalities which have been explored. Some are described in this chapter, mainly: the importance of peer relationships; the benefits of friendship; the effects of schools in conjunction with some forms of family influence; the school climate in terms of safety and physical ecology; the relevance of the teacher input; the school goal structure and the implementation of cooperative learning. All these parameters have an influence in promoting optimal functioning among children and increasing their well-being by meeting the above mentioned needs. The empirical support for the importance of schools indicates significant small effects, which often translate into important real-life effects as it is admitted at present. The conclusion is that schools do make a difference in children’s peer relationships and well-being

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology