Flip Graphs of Degree-Bounded (Pseudo-)Triangulations

We study flip graphs of triangulations whose maximum vertex degree is bounded by a constant $k$. In particular, we consider triangulations of sets of $n$ points in convex position in the plane and prove that their flip graph is connected if and only if $k > 6$; the diameter of the flip graph is $O(n^2)$. We also show that, for general point sets, flip graphs of pointed pseudo-triangulations can be disconnected for $k \leq 9$, and flip graphs of triangulations can be disconnected for any $k$. Additionally, we consider a relaxed version of the original problem. We allow the violation of the degree bound $k$ by a small constant. Any two triangulations with maximum degree at most $k$ of a convex point set are connected in the flip graph by a path of length $O(n \log n)$, where every intermediate triangulation has maximum degree at most $k+4$.Comment: 13 pages, 12 figures, acknowledgments update

Semiclassical mechanics of a non-integrable spin cluster

We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states caused by classical periodic orbits: in the slowly varying part of the density of states we see signs of nontrivial topology changes happening to the energy surface as the energy is varied. Also, we can explain the hierarchy of quantum energy levels near the ferromagnetic and antiferromagnetic states with EKB quantization to explain large structures and tunneling to explain small structures.Comment: 9 pages. For related works see "http://www.msc.cornell.edu/~clh/clh.html

Stripes and holes in a two-dimensional model of spinless fermions and hardcore bosons

We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half-filling. The problem of a single stripe can be mapped to a spin-1/2 chain, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of two, three, and four stripes, finding that they repel, and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into particle-rich phase and hole-rich liquid, we evaluate the liquid's equation of state, finding the stripe-array is not stable for bosons but is possibly stable for fermions.Comment: 24 pages, 18 figure

Natural genetic variation in fluctuating asymmetry of wing shape in Drosophila melanogaster

Fluctuating asymmetry (FA), defined as random deviation from perfect symmetry, has been used to assay the inability of individuals to buffer their developmental processes from environmental perturbations (i.e., developmental instability). In this study, we aimed to characterize the natural genetic variation in FA of wing shape in Drosophila melanogaster, collected from across the Japanese archipelago. We quantified wing shapes at whole wing and partial wing component levels and evaluated their mean and FA. We also estimated the heritability of the mean and FA of these traits. We found significant natural genetic variation in all the mean wing traits and in FA of one of the partial wing components. Heritability estimates for mean wing shapes were significant in two and four out of five wing traits in males and females, respectively. On the contrary, heritability estimates for FA were low and not significant. This is a novel study of natural genetic variation in FA of wing shape. Our findings suggest that partial wing components behave as distinct units of selection for FA, and local adaptation of the mechanisms to stabilize developmental processes occur in nature

Requirements for Membrane Attack Complex Formation and Anaphylatoxins Binding to Collagen-Activated Platelets

The activation of complement during platelet activation is incompletely understood.We sought to explore the formation of C5b-9 and anaphylatoxins binding to collagen-activated platelets.C5b-9, anaphylatoxins C3a, C4a and C5a, and anaphylatoxin receptors C3aR1 and C5aR were measured by flow cytometry and/or confocal microscopy. Platelet microparticles were quantified by flow cytometry, and their C5b-9 content was determined by western blot analyses. In all experiments, sodium citrate was used for blood anticoagulation.C5b-9 rapidly formed on the platelet surface following activation with collagen, TRAP, ADP or A23187, but was surprisingly restricted to a subset of platelets (1 to 15%) independently of P-selectin or phosphatidylserine exposure. Following collagen activation, C5b-9-positive platelets in thrombi were found associated with collagen fibres. C5b-9 formation was obliterated by Mg(2+)-EGTA and significantly reduced by the thrombin inhibitor hirudin (-37%, p<0.05), but was unaffected by chondroitinase, compstatin, SCH79797 (PAR-1 inhibitor), or in the PRP of a MBL-deficient donor. Compstatin and Mg(2+)-EGTA, but not hirudin, SCH79797 or chondroitinase, inhibited the formation of collagen-induced microparticles (-71% and -44%, respectively, p<0.04). These microparticles contained greater amounts of C5b-9 compared with the other agonists. Platelet activation by collagen or convulxin resulted in the strong binding of anaphylatoxins and the exposure of receptors C3aR1 and C5aR (CD88) on their surface.C5b-9 formation on collagen-activated platelets is i) partially controlled by thrombin, ii) restricted to a subset of platelets, and iii) can occur without P-selectin expression or phosphatidylserine exposure. Activated platelets bind anaphylatoxins on their surface and express C3a and C5a receptors, which may contribute to the localization of inflammatory processes during thrombosis

Laboratory investigations of the interaction between benzene and bare silicate grain surfaces

Experimental results on the thermal desorption of benzene (C6H6) from amorphous silica (SiO2) are presented. The amorphous SiO2 substrate was imaged using atomic force microscopy (AFM), revealing a surface morphology reminiscent of that of interplanetary dust particles (IDPs). Temperature programmed desorption (TPD) experiments were conducted for a wide range of C6H6 exposures, yielding information on both C6H6-SiO2 interactions and the C6H6-C6H6 interactions present in the bulk C6H6 ice. The low coverage experiments reveal complicated desorption behaviour that results both from porosity and roughness in the SiO2 substrate, and repulsive interactions between C6H6 molecules. Kinetic parameters were obtained through a combination of direct analysis of the TPD traces and kinetic modelling, demonstrating the coverage dependence of both desorption energy and pre-exponential factor. Experiments were also performed whereby the pores were blocked by pre-exposure of the SiO2 to water vapour. C6H6 was observed to be adsorbed preferentially on the SiO2 film not covered by H2O at the temperature at which these experiments were performed. This observation means that intermolecular repulsion likely becomes important at smaller C6H6 exposures on grains with a H2O mantle. Kinetic modelling of C6H6 multilayer desorption yields kinetic parameters in good agreement with previous studies, with the SiO2 having little impact on the desorption beyond the first few layers.Comment: 23 pages, including 6 figures and 1 table ; Submitted to MNRA

Sexual Behaviors and HIV Status: A Population-Based Study Among Older Adults in Rural South Africa

Objective: To identify the unmet needs for HIV prevention among older adults in rural South Africa. Methods: We analyzed data from a population-based sample of 5059 men and women aged 40 years and older from the study Health and Aging in Africa: Longitudinal Studies of INDEPTH Communities (HAALSI), which was carried out in the Agincourt health and sociodemographic surveillance system in the Mpumalanga province of South Africa. We estimated the prevalence of HIV (laboratory-confirmed and self-reported) and key sexual behaviors by age and sex. We compared sexual behavior profiles across HIV status categories with and without age–sex standardization. Results: HIV prevalence was very high among HAALSI participants (23%, 95% confidence interval [CI]: 21 to 24), with no sex differences. Recent sexual activity was common (56%, 95% CI: 55 to 58) across all HIV status categories. Condom use was low among HIV-negative adults (15%, 95% CI: 14 to 17), higher among HIV-positive adults who were unaware of their HIV status (27%, 95% CI: 22 to 33), and dramatically higher among HIV-positive adults who were aware of their status (75%, 95% CI: 70 to 80). Casual sex and multiple partnerships were reported at moderate levels, with slightly higher estimates among HIV-positive compared to HIV-negative adults. Differences by HIV status remained after age–sex standardization. Conclusions: Older HIV-positive adults in an HIV hyperendemic community of rural South Africa report sexual behaviors consistent with high HIV transmission risk. Older HIV-negative adults report sexual behaviors consistent with high HIV acquisition risk. Prevention initiatives tailored to the particular prevention needs of older adults are urgently needed to reduce HIV risk in this and similar communities in sub-Saharan Africa.The HAALSI study was funded by the NIA of the NIH (P01 AG041710). HAALSI is nested within the Agincourt Health and Socio-Demographic Surveillance System, with funding from Wellcome Trust (058893/Z/99/A; 069683/Z/02/Z; 085477/Z/08/Z; 085477/B/08/Z), University of the Witwatersrand, and Medical Research Council, South Africa. T.W.B. received funding from the Wellcome Trust and NICHD of NIH (R01-HD084233) and NIAID of NIH (R01-AI124389 and R01-AI112339)

Characterization of the Endothelial Cell Cytoskeleton following HLA Class I Ligation

Vascular endothelial cells (ECs) are a target of antibody-mediated allograft rejection. In vitro, when the HLA class I molecules on the surface of ECs are ligated by anti-HLA class I antibodies, cell proliferation and survival pathways are activated and this is thought to contribute to the development of antibody-mediated rejection. Crosslinking of HLA class I molecules by anti-HLA antibodies also triggers reorganization of the cytoskeleton, which induces the formation of F-actin stress fibers. HLA class I induced stress fiber formation is not well understood.The present study examines the protein composition of the cytoskeleton fraction of ECs treated with HLA class I antibodies and compares it to other agonists known to induce alterations of the cytoskeleton in endothelial cells. Analysis by tandem mass spectrometry revealed unique cytoskeleton proteomes for each treatment group. Using annotation tools a candidate list was created that revealed 12 proteins, which were unique to the HLA class I stimulated group. Eleven of the candidate proteins were phosphoproteins and exploration of their predicted kinases provided clues as to how these proteins may contribute to the understanding of HLA class I induced antibody-mediated rejection. Three of the candidates, eukaryotic initiation factor 4A1 (eIF4A1), Tropomyosin alpha 4-chain (TPM4) and DDX3X, were further characterized by Western blot and found to be associated with the cytoskeleton. Confocal microscopy analysis showed that class I ligation stimulated increased eIF4A1 co-localization with F-actin and paxillin.Colocalization of eIF4A1 with F-actin and paxillin following HLA class I ligation suggests that this candidate protein could be a target for understanding the mechanism(s) of class I mediated antibody-mediated rejection. This proteomic approach for analyzing the cytoskeleton of ECs can be applied to other agonists and various cells types as a method for uncovering novel regulators of cytoskeleton changes