Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions

For the hard-core lattice gas model defined on independent sets weighted by an activity $\lambda$, we study the critical activity $\lambda_c(\mathbb{Z}^2)$ for the uniqueness/non-uniqueness threshold on the 2-dimensional integer lattice $\mathbb{Z}^2$. The conjectured value of the critical activity is approximately $3.796$. Until recently, the best lower bound followed from algorithmic results of Weitz (2006). Weitz presented an FPTAS for approximating the partition function for graphs of constant maximum degree $\Delta$ when $\lambda<\lambda_c(\mathbb{T}_\Delta)$ where $\mathbb{T}_\Delta$ is the infinite, regular tree of degree $\Delta$. His result established a certain decay of correlations property called strong spatial mixing (SSM) on $\mathbb{Z}^2$ by proving that SSM holds on its self-avoiding walk tree $T_{\mathrm{saw}}^\sigma(\mathbb{Z}^2)$ where $\sigma=(\sigma_v)_{v\in \mathbb{Z}^2}$ and $\sigma_v$ is an ordering on the neighbors of vertex $v$. As a consequence he obtained that $\lambda_c(\mathbb{Z}^2)\geq\lambda_c( \mathbb{T}_4) = 1.675$. Restrepo et al. (2011) improved Weitz's approach for the particular case of $\mathbb{Z}^2$ and obtained that $\lambda_c(\mathbb{Z}^2)>2.388$. In this paper, we establish an upper bound for this approach, by showing that, for all $\sigma$, SSM does not hold on $T_{\mathrm{saw}}^\sigma(\mathbb{Z}^2)$ when $\lambda>3.4$. We also present a refinement of the approach of Restrepo et al. which improves the lower bound to $\lambda_c(\mathbb{Z}^2)>2.48$.Comment: 19 pages, 1 figure. Polished proofs and examples compared to earlier versio

On centralizer algebras for spin representations

We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q = 1 the relations boil down to Lie algebra relations

Whole genome sequencing and the application of a SNP panel reveal primary evolutionary lineages and genomic variation in the lion (Panthera leo)

Background Previous phylogeographic studies of the lion (Panthera leo) have improved our insight into the distribution of genetic variation, as well as a revised taxonomy which now recognizes a northern (Panthera leo leo) and a southern (Panthera leo melanochaita) subspecies. However, existing whole range phylogeographic studies on lions either consist of very limited numbers of samples, or are focused on mitochondrial DNA and/or a limited set of microsatellites. The geographic extent of genetic lineages and their phylogenetic relationships remain uncertain, clouded by massive sampling gaps, sex-biased dispersal and incomplete lineage sorting. Results In this study we present results of low depth whole genome sequencing and subsequent variant calling in ten lions sampled throughout the geographic range, resulting in the discovery of >150,000 Single Nucleotide Polymorphisms (SNPs). Phylogenetic analyses revealed the same basal split between northern and southern populations, as well as four population clusters on a more local scale. Further, we designed a SNP panel, including 125 autosomal and 14 mitochondrial SNPs, which was tested on >200 lions from across their range. Results allow us to assign individuals to one of these four major clades (West & Central Africa, India, East Africa, or Southern Africa) and delineate these clades in more detail. Conclusions The results presented here, particularly the validated SNP panel, have important applications, not only for studying populations on a local geographic scale, but also for tracing samples of unknown origin for forensic purposes, and for guiding conservation management of ex situ populations. Thus, these genomic resources not only contribute to our understanding of the evolutionary history of the lion, but may also play a crucial role in conservation efforts aimed at protecting the species in its full diversity.Environmental Biolog

Study of the Cabibbo-suppressed decay modes D0-->Pi-pi+ and D0-->K-K+

Using data from the FOCUS (E831) experiment at Fermilab, we present a new measurement for the branching ratios of the Cabibbo-suppressed decay modes D0-->Pi-Pi+ and D0-->K-K+. We measured: Gamma(D0-->K-K+)/Gamma(D0-->Pi-Pi+) = 2.81 +/- 0.10(stat) +/- 0.06(syst), Gamma(D0-->K-K+)/Gamma(D0-->K-Pi+) = 0.0993 +/- 0.0014(stat) +/- 0.0014(syst), and Gamma(D0-->Pi-Pi+)/Gamma(D0-->K-Pi+) = 0.0353 +/- 0.0012 (stat) +/- 0.0006(syst). These values have been combined with other experimental data to extract the ratios of isospin amplitudes and the phase shifts for the D-->KK and D-->PiPi decay channels.Comment: 12 pages, 1 Figure, accepted for publication in Phys.Lett.

Study of the decay mode D^0 -> K-K-K+pi+

Using data from the FOCUS (E831) experiment at Fermilab, we present a new measurement of the branching ratio for the Cabibbo-favored decay mode $D^0 \to K^-K^-K^+\pi^+$. From a sample of $143 \pm 19$ fully reconstructed $D^0 \to K^-K^-K^+\pi^+$ events, we measure $\Gamma(D^0 \to K^-K^-K^+\pi^+)/\Gamma(D^0 \to K^-\pi^-\pi^+\pi^+) = 0.00257 \pm 0.00034(stat.) \pm 0.00024(syst.)$. A coherent amplitude analysis has been performed to determine the resonant substructure of this decay mode. This analysis reveals a dominant contribution from $\phi$ and $\bar K^{*0}(890)$ states.Comment: 15 pages, 4 figures, to be submitted to Physics Letters

Bounds and phase diagram of efficiency at maximum power for tight-coupling molecular motors

The efficiency at maximum power (EMP) for tight-coupling molecular motors is investigated within the framework of irreversible thermodynamics. It is found that the EMP depends merely on the constitutive relation between the thermodynamic current and force. The motors are classified into four generic types (linear, superlinear, sublinear, and mixed types) according to the characteristics of the constitutive relation, and then the corresponding ranges of the EMP for these four types of molecular motors are obtained. The exact bounds of the EMP are derived and expressed as the explicit functions of the free energy released by the fuel in each motor step. A phase diagram is constructed which clearly shows how the region where the parameters (the load distribution factor and the free energy released by the fuel in each motor step) are located can determine whether the value of the EMP is larger or smaller than 1/2. This phase diagram reveals that motors using ATP as fuel under physiological conditions can work at maximum power with higher efficiency ($>1/2$) for a small load distribution factor ($<0.1$).Comment: 5 pages, 4 figure

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe