Asymptotics of large bound states of localized structures

We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling

Stability of optically-active charged excitons in quasi-two dimensional systems

A negatively charged quasi-two dimensional exciton ($X^-$) is solved exactly numerically in the presence of a uniform perpendicular B-field. Various quasi-two dimensional geometries are studied. The charge distribution of the $X^-$ parallel to the B-field is found to be crucial in determining the stability of the optically-active $X^-$ and hence its photoluminescence (PL) signature. The theory provides a quantitative explanation of recent experimental results obtained for a GaAs quantum well. Effects are found which cannot be described within a lowest Landau level approximation. PACS: 78.20.Ls 78.66.-w 73.20.DxComment: Minor revisions, mainly removal of the term trion in favour of the term charged-exciton to comply with Physical Review B. To be published as a Rapid Communication in Physical Review

Challenges to smartphone applications for melanoma detection

This commentary addresses the emerging market for health-related smartphone applications. Specific to dermatology, there has been a significant increase not only in applications that promote skin cancer awareness and education but also in those meant for detection. With evidence showing that 365 dermatology-related applications were available in 2014--up from 230 in 2012--and that 1 in 5 patients under the age of 50 have used a smartphone to help diagnose a skin problem, there is clearly a large subset of patients participating in this growing trend. Therefore, we are obligated to take a closer look into this phenomenon. Studies have shown that applications are inferior to in-person consultations with one study showing that 3 out of 4 applications incorrectly classified 30% or more melanomas as low-risk lesions. Although the FDA gained regulatory oversight over mobile health applications in 2012 and recently released their statement in 2015, their reach only extends to cover a selected portion of these applications, leaving many unregulated as they continue to be marketed toward our patients. Dermatologists should be updated on our current situation in order to properly counsel patients on the risks and benefits of these applications and whether they are acceptable for use. © 2016 by the article author(s)

Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity

The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]

Hybrid Search: Effectively Combining Keywords and Semantic Searches

This paper describes hybrid search, a search method supporting both document and knowledge retrieval via the flexible combination of ontologybased search and keyword-based matching. Hybrid search smoothly copes with lack of semantic coverage of document content, which is one of the main limitations of current semantic search methods. In this paper we define hybrid search formally, discuss its compatibility with the current semantic trends and present a reference implementation: K-Search. We then show how the method outperforms both keyword-based search and pure semantic search in terms of precision and recall in a set of experiments performed on a collection of about 18.000 technical documents. Experiments carried out with professional users show that users understand the paradigm and consider it very powerful and reliable. K-Search has been ported to two applications released at Rolls-Royce plc for searching technical documentation about jet engines

Mobile radio propagation prediction using ray tracing methods

The basic problem is to solve the two-dimensional scalar Helmholtz equation for a point source (the antenna) situated in the vicinity of an array of scatterers (such as the houses and any other relevant objects in 1 square km of urban environment). The wavelength is a few centimeters and the houses a few metres across, so there are three disparate length scales in the problem. The question posed by BT concerned ray counting on the assumptions that: (i) rays were subject to a reflection coefficient of about 0.5 when bouncing off a house wall and (ii) that diffraction at corners reduced their energy by 90%. The quantity of particular interest was the number of rays that need to be accounted for at any particular point in order for those neglected to only contribute 10% of the field at that point; a secondary question concerned the use of rays to predict regions where the field was less than 1% of that in the region directly illuminated by the antenna. The progress made in answering these two questions is described in the next two sections and possibly useful representations of the solution of the Helmholtz equations in terms other than rays are given in the final section

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page

Report of the Terrestrial Bodies Science Working Group. Volume 6: The asteroids

Earth-based astronomical observations and laboratory analysis of meteorites provide the only scientific data available on asteroids. These data are summarized and subjects for future investigations are explored. The measurements required for potential missions are discussed and concepts for a multi-asteroid rendezvous mission in the mid-1980's are outlined