A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation

We show that the minimal speed for the existence of monotonic fronts of the equation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m >1$ and $f>0$ in $(0,1)$ derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for arbitrary $f$. The case $m=1$ when $f'(0)=0$ is included as an extension of the results.Comment: Latex, postcript figure availabl

Relaxation under outflow dynamics with random sequential updating

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka . Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer rule.Comment: 9 figure

On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation

In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the hamiltonian system $u_{xx} + f(u) = 0$ and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure

Neutron, electron and X-ray scattering investigation of Cr1-xVx near Quantum Criticality

The weakness of electron-electron correlations in the itinerant antiferromagnet Cr doped with V has long been considered the reason that neither new collective electronic states or even non Fermi liquid behaviour are observed when antiferromagnetism in Cr$_{1-x}$V$_{x}$ is suppressed to zero temperature. We present the results of neutron and electron diffraction measurements of several lightly doped single crystals of Cr$_{1-x}$V$_{x}$ in which the archtypal spin density wave instability is progressively suppressed as the V content increases, freeing the nesting-prone Fermi surface for a new striped charge instability that occurs at x$_{c}$=0.037. This novel nesting driven instability relieves the entropy accumulation associated with the suppression of the spin density wave and avoids the formation of a quantum critical point by stabilising a new type of charge order at temperatures in excess of 400 K. Restructuring of the Fermi surface near quantum critical points is a feature found in materials as diverse as heavy fermions, high temperature copper oxide superconductors and now even elemental metals such as Cr.Comment: 6 pages, 6 figures. Accepted to Physical Review

Test of Special Relativity and Equivalence principle from K Physics

A violation of Local Lorentz Invariance (VLI) and hence the special theory of relativity or a violation of equivalence principle (VEP) in the Kaon system can, in principle, induce oscillations between $K^0$ and $\bar{K}^0$. We construct a general formulation in which simultaneous pairwise diagonalization of mass, momemtum, weak or gravitational eigenstates is not assumed. %and the maximum attainable %velocities of the velocity eigenstates are different. We discuss this problem in a general way and point out that, as expected, the VEP and VLI contributions are indistinguishable. We then insist on the fact that VEP or VLI can occur even when CPT is conserved. A possible CP violation of the superweak type induced by VEP or VLI is introduced and discussed. We show that the general VEP mechanism (or the VLI mechanism, but not both simultaneously), with or without conserved CPT, could be clearly tested experimentally through the energy dependence of the $K_L-K_S$ mass difference and of $\eta_{+-}$, $\eta_{00}$, $\delta$. Constraints imposed by present experiments are calculated.Comment: Latex, 15 pages, 1 figure, version to appear in Phys. Rev.

Practice patterns and outcomes of equivocal bone scans for patients with castration-resistant prostate cancer: Results from SEARCH.

ObjectiveTo review follow-up imaging after equivocal bone scans in men with castration resistant prostate cancer (CRPC) and examine the characteristics of equivocal bone scans that are associated with positive follow-up imaging.MethodsWe identified 639 men from five Veterans Affairs Hospitals with a technetium-99m bone scan after CRPC diagnosis, of whom 99 (15%) had equivocal scans. Men with equivocal scans were segregated into "high-risk" and "low-risk" subcategories based upon wording in the bone scan report. All follow-up imaging (bone scans, computed tomography [CT], magnetic resonance imaging [MRI], and X-rays) in the 3 months after the equivocal scan were reviewed. Variables were compared between patients with a positive vs. negative follow-up imaging after an equivocal bone scan.ResultsOf 99 men with an equivocal bone scan, 43 (43%) received at least one follow-up imaging test, including 32/82 (39%) with low-risk scans and 11/17 (65%) with high-risk scans (p = 0.052). Of follow-up tests, 67% were negative, 14% were equivocal, and 19% were positive. Among those who underwent follow-up imaging, 3/32 (9%) low-risk men had metastases vs. 5/11 (45%) high-risk men (p = 0.015).ConclusionWhile 19% of all men who received follow-up imaging had positive follow-up imaging, only 9% of those with a low-risk equivocal bone scan had metastases versus 45% of those with high-risk. These preliminary findings, if confirmed in larger studies, suggest follow-up imaging tests for low-risk equivocal scans can be delayed while high-risk equivocal scans should receive follow-up imaging

Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals

The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials.Comment: 4 page

Taxonomic corpus-based concept summary generation for document annotation.

Semantic annotation is an enabling technology which links documents to concepts that unambiguously describe their content. Annotation improves access to document contents for both humans and software agents. However, the annotation process is a challenging task as annotators often have to select from thousands of potentially relevant concepts from controlled vocabularies. The best approaches to assist in this task rely on reusing the annotations of an annotated corpus. In the absence of a pre-annotated corpus, alternative approaches suffer due to insufficient descriptive texts for concepts in most vocabularies. In this paper, we propose an unsupervised method for recommending document annotations based on generating node descriptors from an external corpus. We exploit knowledge of the taxonomic structure of a thesaurus to ensure that effective descriptors (concept summaries) are generated for concepts. Our evaluation on recommending annotations show that the content that we generate effectively represents the concepts. Also, our approach outperforms those which rely on information from a thesaurus alone and is comparable with supervised approaches