On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

Fast Fourier Optimization: Sparsity Matters

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier transform} (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the "fast Fourier" version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is usually a good thing.Comment: 16 pages, 8 figure

On discretization in time in simulations of particulate flows

We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles immersed in the fluid or between a particle and the wall tends to zero. The idea consists in introducing a small threshold for the particle-wall distance below which the real trajectory of the particle is replaced by an approximated one where the distance is kept equal to the threshold value. The error of this approximation is estimated both theoretically and by numerical experiments. Our time marching scheme can be easily incorporated into a full simulation method where the velocity of the fluid is obtained by a numerical solution to Stokes or Navier-Stokes equations. We also provide a derivation of the asymptotic expansion for the lubrication force (used in our numerical experiments) acting on a disk immersed in a Newtonian fluid and approaching the wall. The method of this derivation is new and can be easily adapted to other cases

Model for initiation of quality factor degradation at high accelerating fields in superconducting radio-frequency cavities

A model for the onset of the reduction in SRF cavity quality factor, the so-called Q-drop, at high accelerating electric fields is presented. Breakdown of the surface barrier against magnetic flux penetration at the cavity equator is considered to be the critical event that determines the onset of Q-drop. The worst case of triangular grooves with low field of first flux penetration Hp, as analyzed previously by Buzdin and Daumens, [1998 Physica C 294: 257], was adapted. This approach incorporates both the geometry of the groove and local contamination via the Ginzburg-Landau parameter kappa, so the proposed model allows new comparisons of one effect in relation to the other. The model predicts equivalent reduction of Hp when either roughness or contamination were varied alone, so smooth but dirty surfaces limit cavity performance about as much as rough but clean surfaces do. When in combination, contamination exacerbates the negative effects of roughness and vice-versa. To test the model with actual data, coupons were prepared by buffered chemical polishing and electropolishing, and stylus profilometry was used to obtain distributions of angles. From these data, curves for surface resistance generated by simple flux flow as a function of magnetic field were generated by integrating over the distribution of angles for reasonable values of kappa. This showed that combined effects of roughness and contamination indeed reduce the Q-drop onset field by ~30%, and that that contamination contributes to Q-drop as much as roughness. The latter point may be overlooked by SRF cavity research, since access to the cavity interior by spectroscopy tools is very difficult, whereas optical images have become commonplace. The model was extended to fit cavity test data, which indicated that reduction of the superconducting gap by contaminants may also play a role in Q-drop.Comment: 15 pages with 7 figure

The energy gap of intermediate-valent SmB6 studied by point-contact spectroscopy

We have investigated the intermediate valence narrow-gap semiconductor SmB6 at low temperatures using both conventional spear-anvil type point contacts as well as mechanically controllable break junctions. The zero-bias conductance varied between less than 0.01 mikrosiemens and up to 1 mS. The position of the spectral anomalies, which are related to the different activation energies and band gaps of SmB6, did not depend on the the contact size. Two different regimes of charge transport could be distinguished: Contacts with large zero - bias conductance are in the diffusive Maxwell regime. They had spectra with only small non-linearities. Contacts with small zero - bias conductance are in the tunnelling regime. They had larger anomalies, but still indicating a finite 45 % residual quasiparticle density of states at the Fermi level at low temperatures of T = 0.1 K. The density of states derived from the tunelling spectra can be decomposed into two energy-dependent parts with Eg = 21 meV and Ed = 4.5 meV wide gaps, respectively.Comment: 9 pages incl. 13 figure

Valence and magnetic ordering in intermediate valence compounds : TmSe versus SmB6

The intermediate valent systems TmSe and SmB6 have been investigated up to 16 and 18 GPa by ac microcalorimetry with a pressure (p) tuning realized in situ at low temperature. For TmSe, the transition from an antiferromagnetic insulator for p<3 GPa to an antiferromagnetic metal at higher pressure has been confirmed. A drastic change in the p variation of the Neel temperature (Tn) is observed at 3 GPa. In the metallic phase (p>3 GPa), Tn is found to increase linearly with p. A similar linear p increase of Tn is observed for the quasitrivalent compound TmS which is at ambiant pressure equivalent to TmSe at p=7 GPa. In the case of SmB6 long range magnetism has been detected above p=8 GPa, i.e. at a pressure slightly higher than the pressure of the insulator to metal transition. However a homogeneous magnetic phase occurs only above 10 GPa. The magnetic and electronic properties are related to the renormalization of the 4f wavefunction either to the divalent or the trivalent configurations. As observed in SmS, long range magnetism in SmB6 occurs already far below the pressure where a trivalent Sm3+ state will be reached. It seems possible, to describe roughly the physical properties of the intermediate valence equilibrium by assuming formulas for the Kondo lattice temperature depending on the valence configuration. Comparison is also made with the appearance of long range magnetism in cerium and ytterbium heavy fermion compounds.Comment: 22 pages including figure

Platelet CD36 Signaling Through ERK5 Promotes Caspase-Dependent Procoagulant Activity and Fibrin Deposition In Vivo

Dyslipidemia is a risk factor for clinically significant thrombotic events. In this condition, scavenger receptor CD36 potentiates platelet reactivity through recognition of circulating oxidized lipids. CD36 promotes thrombosis by activating redox-sensitive signaling molecules, such as the MAPK extracellular signal-regulated kinase 5 (ERK5). However, the events downstream of platelet ERK5 are not clear. In this study, we report that oxidized low-density lipoprotein (oxLDL) promotes exposure of procoagulant phosphatidylserine (PSer) on platelet surfaces. Studies using pharmacologic inhibitors indicate that oxLDL-CD36 interaction–induced PSer exposure requires apoptotic caspases in addition to the downstream CD36-signaling molecules Src kinases, hydrogen peroxide, and ERK5. Caspases promote PSer exposure and, subsequently, recruitment of the prothrombinase complex, resulting in the generation of fibrin from the activation of thrombin. Caspase activity was observed when platelets were stimulated with oxLDL. This was prevented by inhibiting CD36 and ERK5. Furthermore, oxLDL potentiates convulxin/glycoprotein VI–mediated fibrin formation by platelets, which was prevented when CD36, ERK5, and caspases were inhibited. Using 2 in vivo arterial thrombosis models in apoE-null hyperlipidemic mice demonstrated enhanced arterial fibrin accumulation upon vessel injury. Importantly, absence of ERK5 in platelets or mice lacking CD36 displayed decreased fibrin accumulation in high-fat diet–fed conditions comparable to that seen in chow diet–fed animals. These findings suggest that platelet signaling through CD36 and ERK5 induces a procoagulant phenotype in the hyperlipidemic environment by enhancing caspase-mediated PSer exposure

Foot Injuries in Michigan, USA, Gray Wolves (\u3ci\u3eCanis lupus\u3c/i\u3e), 1992–2014

The range of gray wolves (Canis lupus) in the contiguous US is expanding. Research and monitoring to support population recovery and management often involves capture via foothold traps. A population-level epidemiologic assessment of the effect of trap injuries on wolf survival remains needed to inform management. We describe the baseline rate, type, and severity of foot injuries of wolves born 1992–2013 in Michigan’s Upper Peninsula, evaluate the reliability of field-scoring trap-related injuries, and the effect of injuries on wolf survival. We assessed foot injuries by physical and radiographic exam at postmortem and/or time of capture for 351 wolves using the International Organization for Standardization 10990-5 standard and the effects of injuries, sex, age, previous capture and body condition on survival using proportional hazards regression. We used ordinal regression to evaluate epidemiologic associations between sex, age, previous capture, body condition, cause of death and injury severity. Most wolves (53%) experienced no physically or radiographically discernable foot injuries over their lifetimes. Among those wolves that did experience injuries, 33% scored as mild. Foot injuries had little epidemiologically discernable effect on survival rates. Wolves with higher foot trauma scores did experience an increased risk of dying, but the magnitude of the increase was modest. Most limb injuries occurred below the carpus or tarsus, and scoring upper-limb injuries added little predictive information to population-level epidemiologic measures of survival and injury severity. There was little association between injury severity and cause of death. Based on necropsy exams, previous trap injuries likely contributed to death in only four wolves (1.1%). Our results suggest that injuries resulting from foothold traps are unlikely to be a limiting factor in recovery and ongoing survival of the Michigan gray wolf population

Spatio-temporal dynamics and plastic flow of vortices in superconductors with periodic arrays of pinning sites

We present simulations of flux-gradient-driven superconducting rigid vortices interacting with square and triangular arrays of columnar pinning sites in an increasing external magnetic field. These simulations allow us to quantitatively relate spatio-temporal microscopic information of the vortex lattice with typically measured macroscopic quantities, such as the magnetization $M(H)$. The flux lattice does not become completely commensurate with the pinning sites throughout the sample at the magnetization matching peaks, but forms a commensurate lattice in a region close to the edge of the sample. Matching fields related to unstable vortex configurations do not produce peaks in $M(H)$. We observe a variety of evolving complex flux profiles, including flat terraces or plateaus separated by winding current-carrying strings and, near the peaks in $M(H)$, plateaus only in certain regions, which move through the sample as the field increases

Vortex Plastic Motion in Twinned Superconductors

We present simulations, without electrodynamical assumptions, of $B(x,y,H(t)), M(H(t))$, and $J_c(H(t))$, in hard superconductors, for a variety of twin-boundary pinning potential parameters, and for a range of values of the density and strength of the pinning sites. We numerically solve the overdamped equations of motion of up to 10^4 flux-gradient-driven vortices which can be temporarily trapped at $\sim 10^6$ pinning centers. These simulations relate macroscopic measurements (e.g., M(H), ``flame'' shaped $B(x,y)$ profiles) with the underlying microscopic pinning landscape and the plastic dynamics of individual vortices