Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure

Homoclinic standing waves in focussing DNLS equations --Variational approach via constrained optimization

We study focussing discrete nonlinear Schr\"{o}dinger equations and present a new variational existence proof for homoclinic standing waves (bright solitons). Our approach relies on the constrained maximization of an energy functional and provides the existence of two one-parameter families of waves with unimodal and even profile function for a wide class of nonlinearities. Finally, we illustrate our results by numerical simulations.Comment: new version with revised introduction and improved condition (A3); 16 pages, several figure

On the ill-posedness result for the BBM equation

We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.Fundação para a Ciência e a Tecnologia (FCT

Co-periodic stability of periodic waves in some Hamiltonian PDEs

International audienceThe stability theory of periodic traveling waves is much less advanced than for solitary waves, which were first studied by Boussinesq and have received a lot of attention in the last decades. In particular, despite recent breakthroughs regarding periodic waves in reaction-diffusion equations and viscous systems of conservation laws [Johnson–Noble–Rodrigues–Zumbrun, Invent math (2014)], the stability of periodic traveling wave solutions to dispersive PDEs with respect to 'arbitrary' perturbations is still widely open in the absence of a dissipation mechanism. The focus is put here on co-periodic stability of periodic waves, that is, stability with respect to perturbations of the same period as the wave, for KdV-like systems of one-dimensional Hamiltonian PDEs. Fairly general nonlinearities are allowed in these systems, so as to include various models of mathematical physics, and this precludes complete integrability techniques. Stability criteria are derived and investigated first in a general abstract framework, and then applied to three basic examples that are very closely related, and ubiquitous in mathematical physics, namely, a quasilinear version of the generalized Korteweg–de Vries equation (qKdV), and the Euler–Korteweg system in both Eulerian coordinates (EKE) and in mass Lagrangian coordinates (EKL). Those criteria consist of a necessary condition for spectral stability , and of a sufficient condition for orbital stability. Both are expressed in terms of a single function, the abbreviated action integral along the orbits of waves in the phase plane, which is the counterpart of the solitary waves moment of instability introduced by Boussinesq. However, the resulting criteria are more complicated for periodic waves because they have more degrees of freedom than solitary waves, so that the action is a function of N + 2 variables for a system of N PDEs, while the moment of instability is a function of the wave speed only once the endstate of the 1 solitary wave is fixed. Regarding solitary waves, the celebrated Grillakis–Shatah– Strauss stability criteria amount to looking for the sign of the second derivative of the moment of instability with respect to the wave speed. For periodic waves, stability criteria involve all the second order, partial derivatives of the action. This had already been pointed out by various authors for some specific equations, in particular the generalized Korteweg–de Vries equation — which is special case of (qKdV) — but not from a general point of view, up to the authors' knowledge. The most striking results obtained here can be summarized as: an odd value for the difference between N and the negative signature of the Hessian of the action implies spectral instability, whereas a negative signature of the same Hessian being equal to N implies orbital stability. Furthermore, it is shown that, when applied to the Euler–Korteweg system, this approach yields several interesting connexions between (EKE), (EKL), and (qKdV). More precisely, (EKE) and (EKL) share the same abbreviated action integral, which is related to that of (qKdV) in a simple way. This basically proves simultaneous stability in both formulations (EKE) and (EKL) — as one may reasonably expect from the physical point view —, which is interesting to know when these models are used for different phenomena — e.g. shallow water waves or nonlinear optics. In addition, stability in (EKE) and (EKL) is found to be linked to stability in the scalar equation (qKdV). Since the relevant stability criteria are merely encoded by the negative signature of (N + 2) × (N + 2) matrices, they can at least be checked numerically. In practice, when N = 1 or 2, this can be done without even requiring an ODE solver. Various numerical experiments are presented, which clearly discriminate between stable cases and unstable cases for (qKdV), (EKE) and (EKL), thus confirming some known results for the generalized KdV equation and the Nonlinear Schrödinger equation, and pointing out some new results for more general (systems of) PDEs

Metastatic melanoma in an esophagus demonstrating Barrett esophagus with high grade dysplasia

BACKGROUND: Metastatic melanoma involving the esophagus is rare; the occurrence of metastatic melanoma in a background of Barrett esophagus is rarer still. We report a case of an 80 year-old male who presented to our institution for workup of Barrett esophagus with high-grade dysplasia and who proved to have metastatic melanoma occurring in the background of Barrett esophagus, the first report of this kind, to our knowledge, in the English literature. CASE PRESENTATION: An 80 year-old Caucasian male was diagnosed at an outside institution with Barrett’s esophagus with high grade dysplasia and presented to our institution for therapy. The patient underwent endoscopic mucosal resection using a band ligation technique of an area of nodularity within the Barrett esophagus. Microscopic examination demonstrated extensive Barrett esophagus with high-grade dysplasia as well as a second tumor which was morphologically different from the surrounding high-grade dysplasia and which was positive for S-100, HMB 45 and Melan-A on immunohistochemistry, consistent with melanoma. Further workup of the patient demonstrated multiple radiologic lesions consistent with metastases. Molecular studies demonstrated that the melanoma was positive for the 1799T>A (V600E) mutation in the BRAF gene. The overall features of the tumor were most consistent with metastatic melanoma occurring in a background of Barrett esophagus with high-grade dysplasia. CONCLUSION: This case demonstrates a unique intersection between a premalignant condition (Barrett esophagus with high grade dysplasia) and a separate malignancy (melanoma). This report also shows the utility of molecular testing to support the hypothesis of primary versus metastatic disease in melanoma

Percepção de estudantes de psicologia sobre a informática em sua formação profissional

Neste artigo analisa-se uma pesquisa de natureza qualitativa, cujo objetivo era explorar a percepção de 45 alunos de psicologia de diferentes universidades da cidade de Santiago do Chile, sobre a incorporação da informática como apoio para a aprendizagem em sua formação profissional. A informação foi coletada através de entrevistas semiestruturadas e analisou-se mediante o processo de codificação da Teoría Fundamentada. Os resultados mostram como categorias principais, o conhecimento da informática, a valoração da informática, e os fatores que obstaculizam o uso desta. Da codificação seletiva se desprende uma alta valoração da informática como ferramenta econômica e cômoda, mas também se observa uma alta reticência dos alunos diante de sua utilização no trabalho profissional tradicional do psicólogo. Encontraram-se fatores pessoais e institucionais nos que se baseia a valoração, a motivação e o nível de conhecimento dos estudantes diante do uso de ferramentas informáticas.This paper analyses a qualitative research aimed to exploring the perception of 45 psychology students from different universities in Santiago de Chile, about incorporating information systems to support learning in their professional training. Data were collected through semi structured interviews and their analysis was based on Grounded Theory's coding process. Results show that the major categories are computer knowledge, appreciation of computers and factors that hinder their use. From the selective coding a positive evaluation emerges of information systems as an economic and useful tool. However, there is also a high reluctance on the part of the students regarding the use of such tools in the psychologist' traditional professional work. Personal and organizational factors were found as bases for students' assessment, motivation and level of knowledge facing the use of these tools.En este artículo se analiza una investigación de naturaleza cualitativa, cuyo objetivo era explorar la percepción de 45 alumnos de psicología de diferentes universidades de la ciudad de Santiago de Chile, sobre la incorporación de la informática como apoyo para el aprendizaje en su formación profesional. La información se recolectó a través de entrevistas semiestructuradas y se analizó mediante el proceso de codificación de la Teoría Fundamentada. Los resultados muestran como categorías principales, el conocimiento de la informática, la valoración de la informática, y los factores que obstaculizan el uso de ésta. De la codificación selectiva se desprende una alta valoración de la informática como herramienta económica y cómoda, pero también se observa una alta reticencia de los alumnos frente a su utilización en el trabajo profesional tradicional del psicólogo. Se encontraron factores personales e institucionales en los cuales se fundamenta la valoración, la motivación y el nivel de conocimiento de los estudiantes frente al uso de herramientas informáticas

Sustainability disclosure and reputation: a comparative study

“This is a post-peer-review, pre-copyedit version of an article published in Corporate Reputation Review. The definitive publisher-authenticated version Corporate Reputation Review 14(2), pp.79-96 is available online at: http://www.palgrave-journals.com/crr/index.html”Drawing on legitimacy theory, we discuss that a company’s reputation is a determinant of sustainability disclosure. Specifically, we consider the concept of reputation into three dimensions for analysis: stakeholders’ commitment, financial performance and media exposure. This paper differs from previous social and environmental reporting studies in that it investigates both internal and external contextual factors that influence disclosure practice. We claim that companies with a good financial performance, that are adopting an active strategic position towards stakeholders and that are exposed to significant public pressure are more likely to use sustainability disclosure in order to communicate their legitimacy to operate to stakeholders. Moreover the paper analyses a wide range of corporate reports for their social and environmental content using an international sample that allows for a comparison of disclosure practices among Continental European, UK and USA companies. Our results show that stakeholder commitment and media exposure are positively associated with sustainability disclosure. Moreover, we find evidence that the drivers of disclosure vary by information type

Cause of Death and Predictors of All-Cause Mortality in Anticoagulated Patients With Nonvalvular Atrial Fibrillation : Data From ROCKET AF

M. Kaste on työryhmän ROCKET AF Steering Comm jäsen.Background-Atrial fibrillation is associated with higher mortality. Identification of causes of death and contemporary risk factors for all-cause mortality may guide interventions. Methods and Results-In the Rivaroxaban Once Daily Oral Direct Factor Xa Inhibition Compared with Vitamin K Antagonism for Prevention of Stroke and Embolism Trial in Atrial Fibrillation (ROCKET AF) study, patients with nonvalvular atrial fibrillation were randomized to rivaroxaban or dose-adjusted warfarin. Cox proportional hazards regression with backward elimination identified factors at randomization that were independently associated with all-cause mortality in the 14 171 participants in the intention-to-treat population. The median age was 73 years, and the mean CHADS(2) score was 3.5. Over 1.9 years of median follow-up, 1214 (8.6%) patients died. Kaplan-Meier mortality rates were 4.2% at 1 year and 8.9% at 2 years. The majority of classified deaths (1081) were cardiovascular (72%), whereas only 6% were nonhemorrhagic stroke or systemic embolism. No significant difference in all-cause mortality was observed between the rivaroxaban and warfarin arms (P=0.15). Heart failure (hazard ratio 1.51, 95% CI 1.33-1.70, P= 75 years (hazard ratio 1.69, 95% CI 1.51-1.90, P Conclusions-In a large population of patients anticoagulated for nonvalvular atrial fibrillation, approximate to 7 in 10 deaths were cardiovascular, whereasPeer reviewe

Transcription and Expression of Plasmodium falciparum Histidine-Rich Proteins in Different Stages and Strains: Implications for Rapid Diagnostic Tests

Background: Although rapid diagnostic tests (RDTs) for Plasmodium falciparum infection that target histidine rich protein 2 (PfHRP2) are generally sensitive, their performance has been reported to be variable. One possible explanation for variable test performance is differences in expression level of PfHRP in different parasite isolates. Methods: Total RNA and protein were extracted from synchronised cultures of 7 P. falciparum lines over 5 time points of the life cycle, and from synchronised ring stages of 10 falciparum lines. Using quantitative real-time polymerase chain reaction, Western blot analysis and ELISA we investigated variations in the transcription and protein levels of pfhrp2, pfhrp3 and PfHRP respectively in the different parasite lines, over the parasite intraerythrocytic life cycle. Results: Transcription of pfhrp2 and pfhrp3 in different parasite lines over the parasite life cycle was observed to vary relative to the control parasite K1. In some parasite lines very low transcription of these genes was observed. The peak transcription was observed in ring-stage parasites. Pfhrp2 transcription was observed to be consistently higher than pfhrp3 transcription within parasite lines. The intraerythrocytic lifecycle stage at which the peak level of protein was present varied across strains. Total protein levels were more constant relative to total mRNA transcription, however a maximum 24 fold difference in expression at ring-stage parasites relative to the K1 strain was observed. Conclusions: The levels of transcription of pfhrp2 and pfhrp3, and protein expression of PfHRP varied between different P. falciparum strains. This variation may impact on the detection sensitivity of PfHRP2-detecting RDTs

Sentinel network for monitoring in vitro susceptibility of Plasmodium falciparum to antimalarial drugs in Colombia: a proof of concept

Drug resistance is one of the principal obstacles blocking worldwide malaria control. In Colombia, malaria remains a major public health concern and drug-resistant parasites have been reported. In vitro drug susceptibility assays are a useful tool for monitoring the emergence and spread of drug-resistant Plasmodium falciparum. The present study was conducted as a proof of concept for an antimalarial drug resistance surveillance network based on in vitro susceptibility testing in Colombia. Sentinel laboratories were set up in three malaria endemic areas. The enzyme linked immunosorbent assay-histidine rich protein 2 and schizont maturation methods were used to assess the susceptibility of fresh P. falciparum isolates to six antimalarial drugs. This study demonstrates that an antimalarial drug resistance surveillance network based on in vitro methods is feasible in the field with the participation of a research institute, local health institutions and universities. It could also serve as a model for a regional surveillance network. Preliminary susceptibility results showed widespread chloroquine resistance, which was consistent with previous reports for the Pacific region. However, high susceptibility to dihydroartemisinin and lumefantrine compounds, currently used for treatment in the country, was also reported. The implementation process identified critical points and opportunities for the improvement of network sustainability strategies.PAHO [057-1-3144141]; COLCIENCIAS [ID 2229-405-20319]info:eu-repo/semantics/publishedVersio