Breaking the PPSZ Barrier for Unique 3-SAT

The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane (FOCS 1998) is the fastest known algorithm for (Promise) Unique k-SAT. We give an improved algorithm with exponentially faster bounds for Unique 3-SAT. For uniquely satisfiable 3-CNF formulas, we do the following case distinction: We call a clause critical if exactly one literal is satisfied by the unique satisfying assignment. If a formula has many critical clauses, we observe that PPSZ by itself is already faster. If there are only few clauses allover, we use an algorithm by Wahlstr\"om (ESA 2005) that is faster than PPSZ in this case. Otherwise we have a formula with few critical and many non-critical clauses. Non-critical clauses have at least two literals satisfied; we show how to exploit this to improve PPSZ.Comment: 13 pages; major revision with simplified algorithm but slightly worse constant

SOME SPECIAL EFFICIENCY FACTORS IN GYMNASTICS

Hungarian University of Physical Education, Budapest, Hungary A gymnast's high-level performance consists of several factors. The neuromuscular and cardio-respiratory systems are burdened to extreme. Proprioreceptors, visual receptor and their reliable mobilization have an important role fro111 the beginning of the exercise to its end. Restoring and maintaining equilibrium in different elements of gymnastics have dominant significance in certain phases. Posturography interests coaches of gymnastics being a type of sports requiring high accuracy equilibrium. The aim of our present study is to examine equilibrium in model-situations: in traditional and sharpened Romberg position. The examination included the situation with closed feet, too. The circle of subjects in the experiment is the Hungarian national male team of gymnastics: 10 persons. (Age 18-24.) Measurements were carried out with a force platform hype Adam/, whose output signals were used to determine continuously the centre of mass ofthe subject. Excerpts of results After exercise, traditional Romberg test with closed feet: R-s: 11, 11, 9, - 9, 8 - 19, 10 - 9,8,7 nun. Sharpened Romberg test: R-s: 20, 14, 13 - 18, 19, 13 - 15, 10 - 18, 16 mm. 'Mean values: for R1 = 10,l nun and for R2 = 15,6 nun /Closed eyes

Assessment of Daylight in Relation to the Agitation Levels of People with Dementia

This research aims to develop the design guidelines for designing daylight levels that may positively impact on reducing agitation behaviour in people with dementia based on principles of behavioural and psychological symptoms. The research methodology was based on the literature review, fieldwork and building performance simulation (BPS). Quantitative and qualitative approach was conducted by assessing indoor daylight quality and agitation levels. In addition, evaluation of daylight parameters (i.e. daylight factor and relation to the agitation level) was also carried out during the observation. The results suggest that agitation level is indeed higher in the top floor of the nursing house, mostly in the most occupied areas such as: communal area and dining room. According to the carers, the main reason to such phenomenon might be due to the sundown syndrome that usually happens after tea time. Moreover, the daylight strategies were carried out to increase the effectiveness of daylight illuminance levels for indoor environment

Multilevel Estimation of Normalization Constants Using the Ensemble Kalman-Bucy Filter

In this article we consider the application of multilevel Monte Carlo, for the estimation of normalizing constants. In particular we will make use of the filtering algorithm, the ensemble Kalman-Bucy filter (EnKBF), which is an N-particle representation of the Kalma-Bucy filter (KBF). The EnKBF is of interest as it coincides with the optimal filter in the continuous-linear setting, i.e. the KBF. This motivates our particular setup in the linear setting. The resulting methodology we will use is the multilevel ensemble Kalman-Bucy filter (MLEnKBF). We provide an analysis based on deriving Lq-bounds for the normalizing constants using both the single-level, and the multilevel algorithms. Our results will be highlighted through numerical results, where we firstly demonstrate the error-to-cost rates of the MLEnKBF comparing it to the EnKBF on a linear Gaussian model. Our analysis will be specific to one variant of the MLEnKBF, whereas the numerics will be tested on different variants. We also exploit this methodology for parameter estimation, where we test this on the models arising in atmospheric sciences, such as the stochastic Lorenz 63 and 96 model.Comment: 33 pages, 21 figure

Translated Poisson approximation to equilibrium distributions of Markov population processes

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in Kolmogorov distance, is of the smallest order that is compatible with their having integer support. Here, an approximation in the much stronger total variation norm is established, without any loss in the asymptotic order of accuracy; the approximating distribution is a translated Poisson distribution having the same variance and (almost) the same mean. Our arguments are based on the Stein-Chen method and Dynkin's formula.Comment: 18 page