The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average

We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a tropical analogue of the shadow-vertex simplex algorithm, which solves mean payoff games via linear feasibility problems over the tropical semiring $(\mathbb{R} \cup \{-\infty\}, \max, +)$. The key ingredient in our approach is that the shadow-vertex pivoting rule can be transferred to tropical polyhedra, and that its computation reduces to optimal assignment problems through Pl\"ucker relations.Comment: 17 pages, 7 figures, appears in 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part

On the Rational Type 0f Moment Angle Complexes

In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1)) which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the literature in the proof of Theorem 1.3. There is some text overlap with arXiv:1410.645

Generation of small-scale structures in the developed turbulence

The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolmogorov law $r^{2/3}$.Comment: 18 page

Second Stage String Fragmentation Model

A string model, advocated by Bowler, provides a physical and intuitive picture of heavy quark fragmentation. When supplemented by an ad hoc factor of (1-z), to suppress fragmentation near z=1, it supplies an excellent fit to the data. We extend Bowler's model by accounting for the further decay of the massive mesonic states produced by the initial string breaking. We find that each subsequent string break and cascade decay beyond the first, introduces a factor of (1-z). Furthermore we find that including a finite mass for the quarks, which pop out of the vacuum and split the string, forces the first string breaking to produce massive states requiring further decay. This sequence terminates at the second stage of fragmentation where only relatively "light" heavy meson systems are formed. Thus we naturally account for the phenomenologically required factor of (1-z). We also predict that the ratio of (primary) fragments-vector/(vector plus scalar) should be .61. Our second stage string fragmentation model provides an appealing picture of heavy quark fragmentation.Comment: 15 page

Semiclassical Decay of Excited String States on Leading Regge Trajectories

We study the decay of hadrons based on a semiclassical string model. By including quark mass effects we find that the width to mass ratio \G/m is an increasing function of $m$, which increases most rapidly for massive quarks. This is consistent with the available data. The decay probability of hadrons on the leading Regge trajectories is computed taking the effect of the string rotation into account. The resulting decay probability is no longer uniform along the length of the string but varies in a manner that is in qualitative agreement with the available data. We argue in favour of possible experiments that would test our predictions more accurately and help open a window to the nonperturbative aspects of QCD.Comment: 15 PAGES, UR-1326, ER-40685-776, SU-4240-55

Thermodynamic aspects of materials' hardness: prediction of novel superhard high-pressure phases

In the present work we have proposed the method that allows one to easily estimate hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent radii. It has been shown that hardness and bulk moduli of compounds strongly correlate with their thermodynamic and structural properties. The proposed method may be used for a large number of compounds with various types of chemical bonding and structures; moreover, the temperature dependence of hardness may be calculated, that has been performed for diamond and cubic boron nitride. The correctness of this approach has been shown for the recently synthesized superhard diamond-like BC5. It has been predicted that the hypothetical forms of B2O3, diamond-like boron, BCx and COx, which could be synthesized at high pressures and temperatures, should have extreme hardness

Three-way symbolic tree-maps and ultrametrics

Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis and have been used in areas such as psychology and phylogenetics, where three-way data tables can arise. Special examples of such dissimilarities are three-way tree-metrics and ultrametrics, which arise from leaf-labelled trees with edges labelled by positive real numbers. Here we consider three-way maps which arise from leaf-labelled trees where instead the interior vertices are labelled by an arbitrary set of values. For unrooted trees, we call such maps three-way symbolic tree-maps; for rooted trees, we call them three-way symbolic ultrametrics since they can be considered as a generalization of the (two-way) symbolic ultrametrics of Bocker and Dress. We show that, as with two- and three-way tree-metrics and ultrametrics, three-way symbolic tree-maps and ultrametrics can be characterized via certain k-point conditions. In the unrooted case, our characterization is mathematically equivalent to one presented by Gurvich for a certain class of edge-labelled hypergraphs. We also show that it can be decided whether or not an arbitrary three-way symbolic map is a tree-map or a symbolic ultrametric using a triplet-based approach that relies on the so-called BUILD algorithm for deciding when a set of 3-leaved trees or triplets can be displayed by a single tree. We envisage that our results will be useful in developing new approaches and algorithms for understanding 3-way data, especially within the area of phylogenetics

Genetic markers of Munc13 protein family member, BAIAP3, are gender-specifically associated with anxiety and benzodiazepine abuse in mouse and man

Anxiety disorders and substance abuse, including benzodiazepine use disorder, frequently occur together. Unfortunately, treatment of anxiety disorders still includes benzodiazepines, and patients with an existing comorbid benzodiazepine use disorder or a genetic susceptibility for benzodiazepine use disorder may be at risk of adverse treatment outcomes. The identification of genetic predictors for anxiety disorders, and especially for benzodiazepine use disorder, could aid the selection of the best treatment option and improve clinical outcomes. The brain-specific angiogenesis inhibitor I–associated protein 3 (Baiap3) is a member of the mammalian uncoordinated 13 (Munc13) protein family of synaptic regulators of neurotransmitter exocytosis, with a striking expression pattern in amygdalae, hypothalamus and periaqueductal gray. Deletion of Baiap3 in mice leads to enhanced seizure propensity and increased anxiety, with the latter being more pronounced in female than in male animals. We hypothesized that genetic variation in human BAIAP3 may also be associated with anxiety. By using a phenotype-based genetic association study, we identified two human BAIAP3 single-nucleotide polymorphism risk genotypes (AA for rs2235632, TT for rs1132358) that show a significant association with anxiety in women and, surprisingly, with benzodiazepine abuse in men. Returning to mice, we found that male, but not female, Baiap3 knockout (KO) mice develop tolerance to diazepam more quickly than control animals. Analysis of cultured Baiap3 KO hypothalamus slices revealed an increase in basal network activity and an altered response to diazepam withdrawal. Thus, Baiap3/BAIAP3 is gender specifically associated with anxiety and benzodiazepine use disorder, and the analysis of Baiap3/BAIAP3-related functions may help elucidate mechanisms underlying the development of both disorders

A Relationship Between Stellar Metallicity Gradients and Galaxy Age in Dwarf Galaxies

We explore the origin of stellar metallicity gradients in simulated and observed dwarf galaxies. We use FIRE-2 cosmological baryonic zoom-in simulations of 26 isolated galaxies as well as existing observational data for 10 Local Group dwarf galaxies. Our simulated galaxies have stellar masses between $10^{5.5}$ and 10^{8.6} \msun. Whilst gas-phase metallicty gradients are generally weak in our simulated galaxies, we find that stellar metallicity gradients are common, with central regions tending to be more metal-rich than the outer parts. The strength of the gradient is correlated with galaxy-wide median stellar age, such that galaxies with younger stellar populations have flatter gradients. Stellar metallicty gradients are set by two competing processes: (1) the steady "puffing" of old, metal-poor stars by feedback-driven potential fluctuations, and (2) the accretion of extended, metal-rich gas at late times, which fuels late-time metal-rich star formation. If recent star formation dominates, then extended, metal-rich star formation washes out pre-existing gradients from the "puffing" process. We use published results from ten Local Group dwarf galaxies to show that a similar relationship between age and stellar metallicity-gradient strength exists among real dwarfs. This suggests that observed stellar metallicity gradients may be driven largely by the baryon/feedback cycle rather than by external environmental effects.Comment: 14 pages, 13 figures, submitted to MNRA