Stability of Spatial Optical Solitons

We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type nonlinear models and their generalizations. In particular, we demonstrate that the soliton internal modes are responsible for the appearance of the soliton instability, and outline an analytical approach based on a multi-scale asymptotic technique that allows to analyze the soliton dynamics near the marginal stability point. We also discuss some results of the rigorous linear stability analysis of fundamental solitary waves and nonlinear impurity modes. Finally, we demonstrate that multi-hump vector solitary waves may become stable in some nonlinear models, and discuss the examples of stable (1+1)-dimensional composite solitons and (2+1)-dimensional dipole-mode solitons in a model of two incoherently interacting optical beams.Comment: 34 pages, 9 figures; to be published in: "Spatial Optical Solitons", Eds. W. Torruellas and S. Trillo (Springer, New York

The Rossiter-McLaughlin effect in Exoplanet Research

The Rossiter-McLaughlin effect occurs during a planet's transit. It provides the main means of measuring the sky-projected spin-orbit angle between a planet's orbital plane, and its host star's equatorial plane. Observing the Rossiter-McLaughlin effect is now a near routine procedure. It is an important element in the orbital characterisation of transiting exoplanets. Measurements of the spin-orbit angle have revealed a surprising diversity, far from the placid, Kantian and Laplacian ideals, whereby planets form, and remain, on orbital planes coincident with their star's equator. This chapter will review a short history of the Rossiter-McLaughlin effect, how it is modelled, and will summarise the current state of the field before describing other uses for a spectroscopic transit, and alternative methods of measuring the spin-orbit angle.Comment: Review to appear as a chapter in the "Handbook of Exoplanets", ed. H. Deeg & J.A. Belmont

Planet formation in Binaries

Spurred by the discovery of numerous exoplanets in multiple systems, binaries have become in recent years one of the main topics in planet formation research. Numerous studies have investigated to what extent the presence of a stellar companion can affect the planet formation process. Such studies have implications that can reach beyond the sole context of binaries, as they allow to test certain aspects of the planet formation scenario by submitting them to extreme environments. We review here the current understanding on this complex problem. We show in particular how each of the different stages of the planet-formation process is affected differently by binary perturbations. We focus especially on the intermediate stage of kilometre-sized planetesimal accretion, which has proven to be the most sensitive to binarity and for which the presence of some exoplanets observed in tight binaries is difficult to explain by in-situ formation following the "standard" planet-formation scenario. Some tentative solutions to this apparent paradox are presented. The last part of our review presents a thorough description of the problem of planet habitability, for which the binary environment creates a complex situation because of the presence of two irradation sources of varying distance.Comment: Review chapter to appear in "Planetary Exploration and Science: Recent Advances and Applications", eds. S. Jin, N. Haghighipour, W.-H. Ip, Springer (v2, numerous typos corrected

Interaction effects on common measures of sensitivity:Choice of measure, type I error, and power

Here we use simulation to assess previously unaddressed problems in the assessment of statistical interactions in detection and recognition tasks. The proportion of hits and false-alarms made by an observer on such tasks is affected by both their sensitivity and bias, and numerous measures have been developed to separate out these two factors. Each of these measures makes different assumptions regarding the underlying process and different predictions as to how false-alarm and hit rates should covary. Previous simulations have shown that choice of an inappropriate measure can lead to inflated type I error rates, or reduced power, for main effects, provided there are differences in response bias between the conditions being compared. Interaction effects pose a particular problem in this context. We show that spurious interaction effects in analysis of variance can be produced, or true interactions missed, even in the absence of variation in bias. Additional simulations show that variation in bias complicates patterns of type I error and power further. This under-appreciated fact has the potential to greatly distort the assessment of interactions in detection and recognition experiments. We discuss steps researchers can take to mitigate their chances of making an error

On Landau damping

Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation; new functional inequalities; a control of nonlinear echoes; sharp scattering estimates; and a Newton approximation scheme. Our results hold for any potential no more singular than Coulomb or Newton interaction; the limit cases are included with specific technical effort. As a side result, the stability of homogeneous equilibria of the nonlinear Vlasov equation is established under sharp assumptions. We point out the strong analogy with the KAM theory, and discuss physical implications.Comment: News: (1) the main result now covers Coulomb and Newton potentials, and (2) some classes of Gevrey data; (3) as a corollary this implies new results of stability of homogeneous nonmonotone equilibria for the gravitational Vlasov-Poisson equatio

Glycine Inhibitory Dysfunction Turns Touch into Pain through PKCgamma Interneurons

Dynamic mechanical allodynia is a widespread and intractable symptom of neuropathic pain for which there is a lack of effective therapy. During tactile allodynia, activation of the sensory fibers which normally detect touch elicits pain. Here we provide a new behavioral investigation into the dynamic component of tactile allodynia that developed in rats after segmental removal of glycine inhibition. Using in vivo electrophysiological recordings, we show that in this condition innocuous mechanical stimuli could activate superficial dorsal horn nociceptive specific neurons. These neurons do not normally respond to touch. We anatomically show that the activation was mediated through a local circuit involving neurons expressing the gamma isoform of protein kinase C (PKCγ). Selective inhibition of PKCγ as well as selective blockade of glutamate NMDA receptors in the superficial dorsal horn prevented both activation of the circuit and allodynia. Thus, our data demonstrates that a normally inactive circuit in the dorsal horn can be recruited to convert touch into pain. It also provides evidence that glycine inhibitory dysfunction gates tactile input to nociceptive specific neurons through PKCγ-dependent activation of a local, excitatory, NMDA receptor-dependent, circuit. As a consequence of these findings, we suggest that pharmacological inhibition of PKCγ might provide a new tool for alleviating allodynia in the clinical setting

Teacher Wellbeing: The Importance of Teacher–Student Relationships

Many studies have examined the importance of teacher-student relationships for the development of children. Much less is known, however, about how these relationships impact the professional and personal lives of teachers. This review considers the importance of teacher-student relationships for the wellbeing of teachers guided by the Transactional Model of Stress and Coping of Lazarus (1991). Based on theories on interpersonal relationships, it is postulated that teachers have a basic need for relatedness with the students in their class that originates from the close proximity between teacher and student. It is discussed that teachers internalize experiences with students in representational models of relationships that guide emotional responses in daily interactions with students, and changes teacher wellbeing in the long run. In addition, the notion of mental representations of relationships at different levels of generalization could offer a window to understand how individual teacher-student relationships may affect the professional and personal self-esteem of teachers. Lastly, it is argued that the influence of student misbehavior on teacher stress may be more fully understood from a relationship perspective. The review shows that few studies have directly tested these propositions and offers suggestions for future research

Diastolic dysfunction in diabetes and the metabolic syndrome: promising potential for diagnosis and prognosis

Cardiac disease in diabetes mellitus and in the metabolic syndrome consists of both vascular and myocardial abnormalities. The latter are characterised predominantly by diastolic dysfunction, which has been difficult to evaluate in spite of its prevalence. While traditional Doppler echocardiographic parameters enable only semiquantitative assessment of diastolic function and cannot reliably distinguish perturbations in loading conditions from altered diastolic functions, new technologies enable detailed quantification of global and regional diastolic function. The most readily available technique for the quantification of subclinical diastolic dysfunction is tissue Doppler imaging, which has been integrated into routine contemporary clinical practice, whereas cine magnetic resonance imaging (CMR) remains a promising complementary research tool for investigating the molecular mechanisms of the disease. Diastolic function is reported to vary linearly with age in normal persons, decreasing by 0.16 cm/s each year. Diastolic function in diabetes and the metabolic syndrome is determined by cardiovascular risk factors that alter myocardial stiffness and myocardial energy availability/bioenergetics. The latter is corroborated by the improvement in diastolic function with improvement in metabolic control of diabetes by specific medical therapy or lifestyle modification. Accordingly, diastolic dysfunction reflects the structural and metabolic milieu in the myocardium, and may allow targeted therapeutic interventions to modulate cardiac metabolism to prevent heart failure in insulin resistance and diabetes

A role for Piezo2 in EPAC1-dependent mechanical allodynia

N.E. and J.W. designed and supervised experiments. N.E. performed most of the in vivo and in vitro experiments. J.L. performed experiments to characterize hPiezo2. G.H and G.L. supervised by U.O., and J.T. and J.C. cloned hPiezo. L.B. performed the in vivo electrophysiology under the supervision of A.D. M.G. helped with the overexpression studies.M.M. performed surgery. Y.I. provided the Epac1 / mice. F.Z. provided the Epac constructs. N.E. and J.W. wrote manuscript with contributions of all authors. N.E., J.L. and L.B. contributed to data analysis and all authors contributed to the discussionsAberrant mechanosensation has an important role in different pain states. Here we show that Epac1 (cyclic AMP sensor) potentiation of Piezo2-mediated mechanotransduction contributes to mechanical allodynia. Dorsal root ganglia Epac1 mRNA levels increase during neuropathic pain, and nerve damage-induced allodynia is reduced in Epac1 / mice. The Epac-selective cAMP analogue 8-pCPT sensitizes mechanically evoked currents in sensory neurons. Human Piezo2 produces large mechanically gated currents that are enhanced by the activation of the cAMP-sensor Epac1 or cytosolic calcium but are unaffected by protein kinase C or protein kinase A and depend on the integrity of the cytoskeleton. In vivo, 8-pCPT induces long-lasting allodynia that is prevented by the knockdown of Epac1 and attenuated by mouse Piezo2 knockdown. Piezo2 knockdown also enhanced thresholds for light touch. Finally, 8-pCPT sensitizes responses to innocuous mechanical stimuli without changing the electrical excitability of sensory fibres. These data indicate that the Epac1–Piezo2 axis has a role in the development of mechanical allodynia during neuropathic pain.Netherlands Organization for Scientific Research (NWO)Jose Castillejo fellowship JC2010-0196Spanish GovernmentMedical Research Council UK (MRC)WCU at SNU R31-2008-000-10103-0EU IMI Europain grantBBSRC LOLA grantWellcome TrustVersus Arthritis 20200Biotechnology and Biological Sciences Research Council (BBSRC) BB/F000227/1Medical Research Council UK (MRC) G0901905 G9717869 G110034