Sum of squares lower bounds for refuting any CSP

Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen literals. Provided the constraint density satisfies $\Delta \gg 1$, such an instance is unsatisfiable with high probability. The \emph{refutation} problem is to efficiently find a proof of unsatisfiability. We show that whenever the predicate $P$ supports a $t$-\emph{wise uniform} probability distribution on its satisfying assignments, the sum of squares (SOS) algorithm of degree $d = \Theta(\frac{n}{\Delta^{2/(t-1)} \log \Delta})$ (which runs in time $n^{O(d)}$) \emph{cannot} refute a random instance of $\mathrm{CSP}(P)$. In particular, the polynomial-time SOS algorithm requires $\widetilde{\Omega}(n^{(t+1)/2})$ constraints to refute random instances of CSP$(P)$ when $P$ supports a $t$-wise uniform distribution on its satisfying assignments. Together with recent work of Lee et al. [LRS15], our result also implies that \emph{any} polynomial-size semidefinite programming relaxation for refutation requires at least $\widetilde{\Omega}(n^{(t+1)/2})$ constraints. Our results (which also extend with no change to CSPs over larger alphabets) subsume all previously known lower bounds for semialgebraic refutation of random CSPs. For every constraint predicate~$P$, they give a three-way hardness tradeoff between the density of constraints, the SOS degree (hence running time), and the strength of the refutation. By recent algorithmic results of Allen et al. [AOW15] and Raghavendra et al. [RRS16], this full three-way tradeoff is \emph{tight}, up to lower-order factors.Comment: 39 pages, 1 figur

Effects of high summer temperatures on mortality in 50 Spanish cities.

BACKGROUND: Periods of high temperature have been widely found to be associated with excess mortality but with variable relationships in different cities. How these specifics depend on climatic and other characteristics of cities is not well understood. We assess summer temperature-mortality relationships using data from 50 provincial capitals in Spain, during the period 1990-2004. METHODS: Poisson time series regression analyses were applied to daily temperature and mortality data, adjusting for potential confounding seasonal factors. Associations of heat with mortality were summarised for each city as the risk increments at the 99th compared to the 90th percentiles of the whole-year temperature distributions, as predicted from spline curves. RESULTS: Risk increments averaged 14.6% between both centiles, or 3.3% per 1 Celsius degree. Although risk increments varied substantially between cities, the range of temperature from the 90th to 99th centile was the only characteristic independently significantly associated with them. The heat increment did not depend on other city climatic, socio-demographic and geographic determinants. CONCLUSIONS: Cities in Spain are partially adapted to high mean summer temperatures but not to high variation in summer temperatures

Estimation of value of travel-time savings using mixed logit models

In this paper, we discuss some of the issues that arise with the computation of the implied value of travel-time savings in the case of discrete choice models allowing for random taste heterogeneity. We specifically look at the case of models producing a non-zero probability of positive travel-time coefficients, and discuss the consistency of such estimates with theories of rational economic behaviour. We then describe how the presence of unobserved travel-experience attributes or conjoint activities can bias the estimation of the travel-time coefficient, and can lead to false conclusions with regards to the existence of negative valuations of travel-time savings. We note that while it is important not to interpret such estimates as travel-time coefficients per se, it is nevertheless similarly important to allow such effects to manifest themselves; as such, the use of distributions with fixed bounds is inappropriate. On the other hand, the use of unbounded distributions can lead to further problems, as their shape (especially in the case of symmetrical distributions) can falsely imply the presence of positive estimates. We note that a preferable solution is to use bounded distributions where the bounds are estimated from the data during model calibration. This allows for the effects of data impurities or model misspecifications to manifest themselves, while reducing the risk of bias as a result of the shape of the distribution. To conclude, a brief application is conducted to support the theoretical claims made in the paper

A multinational, multi-institutional study of assessment of programming skills of first-year CS students

In computer science, an expected outcome of a student's education is programming skill. This working group investigated the programming competency students have as they complete their first one or two courses in computer science. In order to explore options for assessing students, the working group developed a trial assessment of whether students can program. The underlying goal of this work was to initiate dialog in the Computer Science community on how to develop these types of assessments. Several universities participated in our trial assessment and the disappointing results suggest that many students do not know how to program at the conclusion of their introductory courses. For a combined sample of 216 students from four universities, the average score was 22.89 out of 110 points on the general evaluation criteria developed for this study. From this trial assessment we developed a framework of expectations for first-year courses and suggestions for further work to develop more comprehensive assessments

An amplitude code transmits information at a visual synapse

Most neurons transmit information digitally using spikes that trigger the release of synaptic vesicles with low probability. The first stages of vision and hearing are distinct in that they operate with analog signals, but it is unclear how these are recoded for synaptic transmission. By imaging the release of glutamate in live zebrafish, we demonstrate that ribbon synapses of retinal bipolar cells encode contrast through changes in both the frequency and amplitude of release events. Higher contrasts caused multiple vesicles to be released within an event, and such coding by amplitude often continued after the rate code had reached a maximum frequency. Glutamate packets equivalent to five vesicles transmitted four times as many bits of information per vesicle compared with those released individually. By discretizing analog signals into sequences of numbers up to about 11, ribbon synapses can increase the dynamic range, temporal precision and efficiency with which visual information is transmitted

Gradient estimates for a degenerate parabolic equation with gradient absorption and applications

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as time goes to infinity of the mass of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established

Interventions to improve immigrant health. A scoping review.

Background: Disparities in health between immigrants and their host populations have been described across countries and continents. Hence, interventions for improving health targeting general populations are not necessarily effective for immigrants. Aims: To conduct a systematic search of the literature evaluating health interventions for immigrants; to map the characteristics of identified studies including range of interventions, immigrant populations and their host countries, clinical areas targeted and reported evaluations, challenges and limitations of the interventions identified. Following the results, to develop recommendations for research in the field. Methods: A scoping review approach was chosen to provide an overview of the type, extent and quantity of research available. Studies were included if they empirically evaluated health interventions targeting immigrants and/or their descendants, included a control group, and were published in English (PubMed and Embase from 1990 to 2015). Results: Most of the 83 studies included were conducted in the USA, encompassed few immigrant groups and used a randomized controlled trial (RCT) or cluster RCT design. Most interventions addressed chronic and non-communicable diseases and attendance at cancer screening services, used individual targeted approaches, targeted adult women and recruited participants from health centres. Outcome measures were often subjective, with the exception of interventions for cardiovascular risk and diabetes. Generally, authors claimed that interventions were beneficial, despite a number of reported limitations. Conclusions: Recommendations for enhancing interventions to improve immigrant health are provided to help researchers, funders and health care commissioners when deciding upon the scope, nature and design of future research in this area

The Berlekamp-Massey Algorithm revisited

We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to explain it in a simpler way and to adapt it to lazy evaluation.Comment: in English and French version

The Candida albicans transcription factor Cas5 couples stress responses, drug resistance and cell cycle regulation

We thank Cowen lab members for helpful discussions. We also thank David Rogers (University of Tennessee) for sharing microarray analysis of the CAS5 homozygous mutant, and Li Ang (University of Macau) for assistance in optimizing the ChIP-Seq experiments. J.L.X. is supported by a Canadian Institutes of Health Research Doctoral award and M.D.L. is supported by a Sir Henry Wellcome Postdoctoral Fellowship (Wellcome Trust 096072). B.T.G. holds an Ontario Graduate Scholarship. C.B. and B.J.A. are supported by the Canadian Institutes of Health Research Foundation Grants (FDN-143264 and -143265). D.J.K. is supported by a National Institute of Allergy and Infectious Diseases grant (1R01AI098450) and J.D.L.C.D. is supported by the University of Rochester School of Dentistry and Medicine PREP program (R25 GM064133). A.S. is supported by the Creighton University and the Nebraska Department of Health and Human Services (LB506-2017-55). K.H.W. is supported by the Science and Technology Development Fund of Macau S.A.R. (FDCT; 085/2014/A2). L.E.C. is supported by the Canadian Institutes of Health Research Operating Grants (MOP-86452 and MOP-119520), the Natural Sciences and Engineering Council (NSERC) of Canada Discovery Grants (06261 and 462167), and an NSERC E.W.R. Steacie Memorial Fellowship (477598).Peer reviewedPublisher PD