Improved bounds for reduction to depth 4 and depth 3

Koiran showed that if a $n$-variate polynomial of degree $d$ (with $d=n^{O(1)}$) is computed by a circuit of size $s$, then it is also computed by a homogeneous circuit of depth four and of size $2^{O(\sqrt{d}\log(d)\log(s))}$. Using this result, Gupta, Kamath, Kayal and Saptharishi gave a $\exp(O(\sqrt{d\log(d)\log(n)\log(s)}))$ upper bound for the size of the smallest depth three circuit computing a $n$-variate polynomial of degree $d=n^{O(1)}$ given by a circuit of size $s$. We improve here Koiran's bound. Indeed, we show that if we reduce an arithmetic circuit to depth four, then the size becomes $\exp(O(\sqrt{d\log(ds)\log(n)}))$. Mimicking Gupta, Kamath, Kayal and Saptharishi's proof, it also implies the same upper bound for depth three circuits. This new bound is not far from optimal in the sense that Gupta, Kamath, Kayal and Saptharishi also showed a $2^{\Omega(\sqrt{d})}$ lower bound for the size of homogeneous depth four circuits such that gates at the bottom have fan-in at most $\sqrt{d}$. Finally, we show that this last lower bound also holds if the fan-in is at least $\sqrt{d}$

Image-potential band-gap narrowing at a metal/semiconductor interface

GW approximation is used to systematically revisit the image-potential band-gap narrowing at metal/semiconductor interfaces proposed by Inkson in the 1970's. Here we have questioned how the narrowing as calculated from quasi-particle energy spectra for the jellium/Si interface depends on $r_s$ of the jellium. The gap narrowing is found to only weakly depend on $r_s$ (i.e., narrowing $\simeq 0.3$ eV even for a large $r_s = 6)$. Hence we can turn to smaller polarizability in the semiconductor side as an important factor in looking for larger narrowing.Comment: 6 pages, 7 figure

Diversity, genetic mapping, and signatures of domestication in the carrot (Daucus carota L.) genome, as revealed by Diversity Arrays Technology (DArT) markers

Carrot is one of the most economically important vegetables worldwide, but genetic and genomic resources supporting carrot breeding remain limited. We developed a Diversity Arrays Technology (DArT) platform for wild and cultivated carrot and used it to investigate genetic diversity and to develop a saturated genetic linkage map of carrot. We analyzed a set of 900 DArT markers in a collection of plant materials comprising 94 cultivated and 65 wild carrot accessions. The accessions were attributed to three separate groups: wild, Eastern cultivated and Western cultivated. Twenty-seven markers showing signatures for selection were identified. They showed a directional shift in frequency from the wild to the cultivated, likely reflecting diversifying selection imposed in the course of domestication. A genetic linkage map constructed using 188 F2 plants comprised 431 markers with an average distance of 1.1 cM, divided into nine linkage groups. Using previously anchored single nucleotide polymorphisms, the linkage groups were physically attributed to the nine carrot chromosomes. A cluster of markers mapping to chromosome 8 showed significant segregation distortion. Two of the 27 DArT markers with signatures for selection were segregating in the mapping population and were localized on chromosomes 2 and 6. Chromosome 2 was previously shown to carry the Vrn1 gene governing the biennial growth habit essential for cultivated carrot. The results reported here provide background for further research on the history of carrot domestication and identify genomic regions potentially important for modern carrot breeding

The Impatient May Use Limited Optimism to Minimize Regret

Discounted-sum games provide a formal model for the study of reinforcement learning, where the agent is enticed to get rewards early since later rewards are discounted. When the agent interacts with the environment, she may regret her actions, realizing that a previous choice was suboptimal given the behavior of the environment. The main contribution of this paper is a PSPACE algorithm for computing the minimum possible regret of a given game. To this end, several results of independent interest are shown. (1) We identify a class of regret-minimizing and admissible strategies that first assume that the environment is collaborating, then assume it is adversarial---the precise timing of the switch is key here. (2) Disregarding the computational cost of numerical analysis, we provide an NP algorithm that checks that the regret entailed by a given time-switching strategy exceeds a given value. (3) We show that determining whether a strategy minimizes regret is decidable in PSPACE

The Relationship of Metabolic Syndrome and Aerobic Exercise in Adult Male Fire Fighters

Previous studies have concluded that incidence of Metabolic Syndrome may be greater in male firefighters than in the US male population. A recent study reported that approximately 31% of firefighters were positive for Metabolic Syndrome; compared to 24% for the U.S. male population (NCEPIII). Participation in aerobic exercise may decrease the risk of Metabolic Syndrome as cardiac risk factors are improved. This study aims to determine the effect of aerobic exercise participation on the prevalence of metabolic syndrome in a sample of male firefighters. Purpose: To examine the effect of aerobic exercise participation on the prevalence of Metabolic Syndrome in a sample of adult male firefighters. Methods: As a part of an annual physical exam, 177 male firefighters (average age=36) participated in an evaluation of risk factors associated with Metabolic Syndrome as defined by NCEP III. Metabolic Syndrome is defined as having the presence of three or more of the following: Waist circumference \u3e 40”, HDL Cholesterol \u3c 40 mg/dl, Triglycerides \u3e 150 mg/dl, Blood Glucose \u3e 110 mg/dl and resting blood pressure \u3e 130/85 mm Hg. Aerobic exercise participation was determined by self reported activity from a standard health history questionnaire. Subjects were classified for aerobic exercise participation as: aerobic exercise participation of less than or equal to 1 day per week (LOW), 2 to 3 days per week (MOD), and aerobic exercise participation greater than or equal to 4 days per week (HIGH). Results: The subjects were divided into groups based on the level of weekly aerobic activity. All data were analyzed using a Chi Square test (p \u3c 0.05). Of the 177 firefighters tested 46.3% (82) reported LOW, 48% (85) reported MOD, and 5.6% (10) reported HIGH weekly aerobic activity. The prevalence of Metabolic Syndrome for LOW was 25.6% (21) while the prevalence of Metabolic Syndrome for MOD was 15.3% (13). No one in the HIGH group met the criteria for Metabolic Syndrome. Conclusion: Participation in aerobic exercise appears to affect the incidence of metabolic syndrome in adult male fire fighters

The development and validation of an urbanicity scale in a multi-country study

Background : Although urban residence is consistently identified as one of the primary correlates of non-communicable disease in low- and middle-income countries, it is not clear why or how urban settings predispose individuals and populations to non-communicable disease (NCD), or how this relationship could be modified to slow the spread of NCD. The urban–rural dichotomy used in most population health research lacks the nuance and specificity necessary to understand the complex relationship between urbanicity and NCD risk. Previous studies have developed and validated quantitative tools to measure urbanicity continuously along several dimensions but all have been isolated to a single country. The purposes of this study were 1) To assess the feasibility and validity of a multi-country urbanicity scale; 2) To report some of the considerations that arise in applying such a scale in different countries; and, 3) To assess how this scale compares with previously validated scales of urbanicity. Methods : Household and community-level data from the Young Lives longitudinal study of childhood poverty in 59 communities in Ethiopia, India and Peru collected in 2006/2007 were used. Household-level data include parents’ occupations and education level, household possessions and access to resources. Community-level data include population size, availability of health facilities and types of roads. Variables were selected for inclusion in the urbanicity scale based on inspection of the data and a review of literature on urbanicity and health. Seven domains were constructed within the scale: Population Size, Economic Activity, Built Environment, Communication, Education, Diversity and Health Services. Results : The scale ranged from 11 to 61 (mean 35) with significant between country differences in mean urbanicity; Ethiopia (30.7), India (33.2), Peru (39.4). Construct validity was supported by factor analysis and high corrected item-scale correlations suggest good internal consistency. High agreement was observed between this scale and a dichotomized version of the urbanicity scale (Kappa 0.76; Spearman’s rank-correlation coefficient 0.84 (p < 0.0001). Linear regression of socioeconomic indicators on the urbanicity scale supported construct validity in all three countries (p < 0.05). Conclusions : This study demonstrates and validates a robust multidimensional, multi-country urbanicity scale. It is an important step on the path to creating a tool to assess complex processes like urbanization. This scale provides the means to understand which elements of urbanization have the greatest impact on health

Pattern forming instability induced by light in pure and dye-doped nematic liquid crystals

We study theoretically the instabilities induced by a linearly polarized ordinary light wave incident at a small oblique angle on a thin layer of homeotropically oriented nematic liquid crystal with special emphasis on the dye-doped case. The spatially periodic Hopf bifurcation that occurs as the secondary instability after the stationary Freedericksz transition is analyzed.Comment: 8 pages, 7 figures, LaTeX, accepted to Phys. Rev.

Optimizing ExoMars rover remote sensing multispectral science : cross-rover comparison using laboratory and orbital data

PMG, RBS, CRC, and EJA thank the UK Space Agency for support (grant ST/T001747/1). SM acknowledges a UK Science and Technology Facilities Council (STFC) PhD studentship (grant ST/R504961/1).Multispectral imaging instruments have been core payload components of Mars lander and rover missions for several decades. In order to place into context the future performance of the ExoMars Rosalind Franklin rover, we have carried out a detailed analysis of the spectral performance of three visible and near-infrared (VNIR) multispectral instruments. We have determined the root mean square error (RMSE) between the expected multispectral sampling of the instruments and high-resolution spectral reflectance data, using both laboratory spectral libraries and Mars orbital hyperspectral data. ExoMars Panoramic Camera (PanCam) and Mars2020 Perseverance Mastcam-Z instruments have similar values of RMSE, and are consistently lower than for Mars Science Laboratory Mastcam, across both laboratory and orbital remote sensing data sets. The performance across mineral groups is similar across all instruments, with the lowest RMSE values for hematite, basalt, and basaltic soil. Minerals with broader, or absent, absorption features in these visible wavelengths, such as olivine, saponite, and vermiculite have overall larger RMSE values. Instrument RMSE as a function of filter wavelength and bandwidth suggests that spectral parameters that use shorter wavelengths are likely to perform better. Our simulations of the spectral performance of the PanCam instrument will allow the future use of targeted filter selection during ExoMars 2022 Rosalind Franklin operations on Mars.Publisher PDFPeer reviewe

Decision Problems for Nash Equilibria in Stochastic Games

We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we single out several decidable restrictions of the problem. First, restricting the search space to stationary, or pure stationary, equilibria results in problems that are typically contained in PSPACE and NP, respectively. Second, we show that the existence of an equilibrium with a binary payoff (i.e. an equilibrium where each player either wins or loses with probability 1) is decidable. We also establish that the existence of a Nash equilibrium with a certain binary payoff entails the existence of an equilibrium with the same payoff in pure, finite-state strategies.Comment: 22 pages, revised versio