Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation

We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any δ[much less-than]1,K [much greater-than] 1, s > 1, we construct smooth initial data u 0 with ||u0||Hs , so that the corresponding time evolution u satisfies u(T)Hs[greater than]K at some time T. This growth occurs despite the Hamiltonian’s bound on ||u(t)||H1 and despite the conservation of the quantity ||u(t)||L2. The proof contains two arguments which may be of interest beyond the particular result described above. The first is a construction of the solution’s frequency support that simplifies the system of ODE’s describing each Fourier mode’s evolution. The second is a construction of solutions to these simpler systems of ODE’s which begin near one invariant manifold and ricochet from arbitrarily small neighborhoods of an arbitrarily large number of other invariant manifolds. The techniques used here are related to but are distinct from those traditionally used to prove Arnold Diffusion in perturbations of Hamiltonian systems

Interoception and mental health: a roadmap

Interoception refers to the process by which the nervous system senses, interprets, and integrates signals originating from within the body, providing a moment-by moment mapping of the body’s internal landscape across conscious and unconscious levels. Interoceptive signaling has been considered a component process of reflexes, urges, feelings, drives, adaptive responses, and cognitive and emotional experiences, highlighting its contributions to the maintenance of homeostatic functioning, body regulation, and survival. Dysfunction of interoception is increasingly recognized as an important component of different mental health conditions, including anxiety disorders, mood disorders, eating disorders, addictive disorders, and somatic symptom disorders. However, a number of conceptual and methodological challenges have made it difficult for interoceptive constructs to be broadly applied in mental health research and treatment settings. In November 2016, the Laureate Institute for Brain Research organized the first Interoception Summit, a gathering of interoception experts from around the world, with the goal of accelerating progress in understanding the role of interoception in mental health. The discussions at the meeting were organized around four themes: interoceptive assessment, interoceptive integration, interoceptive psychopathology, and the generation of a roadmap that could serve as a guide for future endeavors. This review article presents an overview of the emerging consensus generated by the meeting

Back Complaints in the Elders (BACE); design of cohort studies in primary care: an international consortium

Background: Although back complaints are common among older people, limited information is available in the literature about the clinical course of back pain in older people and the identification of older persons at risk for the transition from acute back complaints to chronic back pain. The aim of this study is to assess the course of back complaints and identify prognostic factors for the transition from acute back complaints to chronic back complaints in older people who visit a primary health care physician. Methods/design. The design is a prospective cohort study with one-year follow-up. There will be no interference with usual care. Patients older than 55 years who consult a primary health care physician with a new episode of back complaints will be included in this study. Data will be collected using a questionnaire, physical examination and X-ray at baseline, and follow-up questionnaires afte

Minimal information for studies of extracellular vesicles 2018 (MISEV2018):a position statement of the International Society for Extracellular Vesicles and update of the MISEV2014 guidelines

The last decade has seen a sharp increase in the number of scientific publications describing physiological and pathological functions of extracellular vesicles (EVs), a collective term covering various subtypes of cell-released, membranous structures, called exosomes, microvesicles, microparticles, ectosomes, oncosomes, apoptotic bodies, and many other names. However, specific issues arise when working with these entities, whose size and amount often make them difficult to obtain as relatively pure preparations, and to characterize properly. The International Society for Extracellular Vesicles (ISEV) proposed Minimal Information for Studies of Extracellular Vesicles (“MISEV”) guidelines for the field in 2014. We now update these “MISEV2014” guidelines based on evolution of the collective knowledge in the last four years. An important point to consider is that ascribing a specific function to EVs in general, or to subtypes of EVs, requires reporting of specific information beyond mere description of function in a crude, potentially contaminated, and heterogeneous preparation. For example, claims that exosomes are endowed with exquisite and specific activities remain difficult to support experimentally, given our still limited knowledge of their specific molecular machineries of biogenesis and release, as compared with other biophysically similar EVs. The MISEV2018 guidelines include tables and outlines of suggested protocols and steps to follow to document specific EV-associated functional activities. Finally, a checklist is provided with summaries of key points

Minimal information for studies of extracellular vesicles (MISEV2023): From basic to advanced approaches

Extracellular vesicles (EVs), through their complex cargo, can reflect the state of their cell of origin and change the functions and phenotypes of other cells. These features indicate strong biomarker and therapeutic potential and have generated broad interest, as evidenced by the steady year-on-year increase in the numbers of scientific publications about EVs. Important advances have been made in EV metrology and in understanding and applying EV biology. However, hurdles remain to realising the potential of EVs in domains ranging from basic biology to clinical applications due to challenges in EV nomenclature, separation from non-vesicular extracellular particles, characterisation and functional studies. To address the challenges and opportunities in this rapidly evolving field, the International Society for Extracellular Vesicles (ISEV) updates its 'Minimal Information for Studies of Extracellular Vesicles', which was first published in 2014 and then in 2018 as MISEV2014 and MISEV2018, respectively. The goal of the current document, MISEV2023, is to provide researchers with an updated snapshot of available approaches and their advantages and limitations for production, separation and characterisation of EVs from multiple sources, including cell culture, body fluids and solid tissues. In addition to presenting the latest state of the art in basic principles of EV research, this document also covers advanced techniques and approaches that are currently expanding the boundaries of the field. MISEV2023 also includes new sections on EV release and uptake and a brief discussion of in vivo approaches to study EVs. Compiling feedback from ISEV expert task forces and more than 1000 researchers, this document conveys the current state of EV research to facilitate robust scientific discoveries and move the field forward even more rapidly