Balancing Bounded Treewidth Circuits

Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size $n^{O(1)}$ and treewidth $O(\log^i n)$ can be simulated by a circuit of width $O(\log^{i+1} n)$ and size $n^c$, where $c = O(1)$, if $i=0$, and $c=O(\log \log n)$ otherwise. For our main construction, we prove that multiplicatively disjoint arithmetic circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in arithmetic formulas of depth $O(k^2\log n)$. From this we derive the analogous statement for syntactically multilinear arithmetic circuits, which strengthens a theorem of Mahajan and Rao. As another application, we derive that constant width arithmetic circuits of size $n^{O(1)}$ can be balanced to depth $O(\log n)$, provided certain restrictions are made on the use of iterated multiplication. Also from our main construction, we derive that Boolean bounded fan-in circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in formulas of depth $O(k^2\log n)$. This strengthens in the non-uniform setting the known inclusion that $SC^0 \subseteq NC^1$. Finally, we apply our construction to show that {\sc reachability} for directed graphs of bounded treewidth is in $LogDCFL$

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

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

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

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Electronic structure of superconducting graphite intercalate compounds: The role of the interlayer state

Although not an intrinsic superconductor, it has been long--known that, when intercalated with certain dopants, graphite is capable of exhibiting superconductivity. Of the family of graphite--based materials which are known to superconduct, perhaps the most well--studied are the alkali metal--graphite intercalation compounds (GIC) and, of these, the most easily fabricated is the C${}_8$K system which exhibits a transition temperature $\bm{T_c\simeq 0.14}$K. By increasing the alkali metal concentration (through high pressure fabrication techniques), the transition temperature has been shown to increase to as much as $\bm 5$K in C${}_2$Na. Lately, in an important recent development, Weller \emph{et al.} have shown that, at ambient conditions, the intercalated compounds \cyb and \cca exhibit superconductivity with transition temperatures $\bm{T_c\simeq 6.5}$K and $\bm{11.5}$K respectively, in excess of that presently reported for other graphite--based compounds. We explore the architecture of the states near the Fermi level and identify characteristics of the electronic band structure generic to GICs. As expected, we find that charge transfer from the intercalant atoms to the graphene sheets results in the occupation of the $\bm\pi$--bands. Yet, remarkably, in all those -- and only those -- compounds that superconduct, we find that an interlayer state, which is well separated from the carbon sheets, also becomes occupied. We show that the energy of the interlayer band is controlled by a combination of its occupancy and the separation between the carbon layers.Comment: 4 Figures. Please see accompanying experimental manuscript "Superconductivity in the Intercalated Graphite Compounds C6Yb and C6Ca" by Weller et a

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

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.

Population assessment of future trajectories in coronary heart disease mortality.

Background: Coronary heart disease (CHD) mortality rates have been decreasing in Iceland since the 1980s, largely reflecting improvements in cardiovascular risk factors. The purpose of this study was to predict future CHD mortality in Iceland based on potential risk factor trends. Methods and findings: The previously validated IMPACT model was used to predict changes in CHD mortality between 2010 and 2040 among the projected population of Iceland aged 25–74. Calculations were based on combining: i) data on population numbers and projections (Statistics Iceland), ii) population risk factor levels and projections (Refine Reykjavik study), and iii) effectiveness of specific risk factor reductions (published meta-analyses). Projections for three contrasting scenarios were compared: 1) If the historical risk factor trends of past 30 years were to continue, the declining death rates of past decades would level off, reflecting population ageing. 2) If recent trends in risk factors (past 5 years) continue, this would result in a death rate increasing from 49 to 70 per 100,000. This would reflect a recent plateau in previously falling cholesterol levels and recent rapid increases in obesity and diabetes prevalence. 3) Assuming that in 2040 the entire population enjoys optimal risk factor levels observed in low risk cohorts, this would prevent almost all premature CHD deaths before 2040. Conclusions: The potential increase in CHD deaths with recent trends in risk factor levels is alarming both for Iceland and probably for comparable Western populations. However, our results show considerable room for reducing CHD mortality. Achieving the best case scenario could eradicate premature CHD deaths by 2040. Public health policy interventions based on these predictions may provide a cost effective means of reducing CHD mortality in the future