Optimal pebbling number of graphs with given minimum degree

Consider a distribution of pebbles on a connected graph $G$. A pebbling move removes two pebbles from a vertex and places one to an adjacent vertex. A vertex is reachable under a pebbling distribution if it has a pebble after the application of a sequence of pebbling moves. The optimal pebbling number $\pi^*(G)$ is the smallest number of pebbles which we can distribute in such a way that each vertex is reachable. It was known that the optimal pebbling number of any connected graph is at most $\frac{4n}{\delta+1}$, where $\delta$ is the minimum degree of the graph. We strengthen this bound by showing that equality cannot be attained and that the bound is sharp. If $\operatorname{diam}(G)\geq 3$ then we further improve the bound to $\pi^*(G)\leq\frac{3.75n}{\delta+1}$. On the other hand, we show that for arbitrary large diameter and any $\epsilon>0$ there are infinitely many graphs whose optimal pebbling number is bigger than $\left(\frac{8}{3}-\epsilon\right)\frac{n}{(\delta+1)}$

Regular dendritic patterns induced by non-local time-periodic forcing

The dynamic response of dendritic solidification to spatially homogeneous time-periodic forcing has been studied. Phase-field calculations performed in two dimensions (2D) and experiments on thin (quasi 2D) liquid crystal layers show that the frequency of dendritic side-branching can be tuned by oscillatory pressure or heating. The sensitivity of this phenomenon to the relevant parameters, the frequency and amplitude of the modulation, the initial undercooling and the anisotropies of the interfacial free energy and molecule attachment kinetics, has been explored. It has been demonstrated that besides the side-branching mode synchronous with external forcing as emerging from the linear Wentzel-Kramers-Brillouin analysis, modes that oscillate with higher harmonic frequencies are also present with perceptible amplitudes.Comment: 15 pages, 23 figures, Submitted to Phys. Rev.

Association of chronic obstructive pulmonary disease with morbidity and mortality in patients with peripheral artery disease: insights from the EUCLID trial

Background: Patients with chronic obstructive pulmonary disease (COPD) are at increased risk of developing lower extremity peripheral artery disease (PAD) and suffering PAD-related morbidity and mortality. However, the effect and burden of COPD on patients with PAD is less well defined. This post hoc analysis from EUCLID aimed to analyze the risk of major adverse cardiovascular events (MACE) and major adverse limb events (MALE) in patients with PAD and concomitant COPD compared with those without COPD, and to describe the adverse events specific to patients with COPD. Methods: EUCLID randomized 13,885 patients with symptomatic PAD to monotherapy with either ticagrelor or clopidogrel for the prevention of MACE. In this analysis, MACE, MALE, mortality, and adverse events were compared between groups with and without COPD using unadjusted and adjusted Cox proportional hazards model. Results: Of the 13,883 patients with COPD status available at baseline, 11% (n=1538) had COPD. Patients with COPD had a higher risk of MACE (6.02 vs 4.29 events/100 patient-years; p< 0.001) due to a significantly higher risk of myocardial infarction (MI) (3.55 vs 1.85 events/100 patient-years; p< 0.001) when compared with patients without COPD. These risks persisted after adjustment (MACE: adjusted hazard ratio (aHR) 1.30, 95% confidence interval [CI] 1.11– 1.52; p< 0.001; MI: aHR 1.45, 95% CI 1.18– 1.77; p< 0.001). However, patients with COPD did not have an increased risk of MALE or major bleeding. Patients with COPD were more frequently hospitalized for dyspnea and pneumonia (2.66 vs 0.9 events/100 patient-years; aHR 2.77, 95% CI 2.12– 3.63; p< 0.001) and more frequently discontinued study drug prematurely (19.36 vs 12.54 events/100 patient-years; p< 0.001; aHR 1.34, 95% CI 1.22– 1.47; p< 0.001). Conclusion: In patients with comorbid PAD and COPD, the risks of MACE, respiratory-related adverse events, and premature study drug discontinuation were higher when compared with patients without COPD. Registration: ClinicalTrials.gov: NCT01732822

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.Comment: 17 pages in revtex. changes: 1 reference adde

Is There Such a Thing as Psychological Pain? and Why It Matters

Medicine regards pain as a signal of physical injury to the body despite evidence contradicting the linkage and despite the exclusion of vast numbers of sufferers who experience psychological pain. By broadening our concept of pain and making it more inclusive, we would not only better accommodate the basic science of pain but also would recognize what is already appreciated by the layperson—that pain from diverse sources, physical and psychological, share an underlying felt structure

Communications Biophysics

Contains research objectives and reports on two research projects.National Institutes of Health (Grant 2 PO1 GM-14941-01)Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E)National Aeronautics and Space Administration (Grant NsG-496)National Institutes of Health (Grant 2 RO1 NB-05462-04)National Institutes of Health (Grant 1 TO1 GM-01555-01