Enhanced binding revisited for a spinless particle in non-relativistic QED

We consider a spinless particle coupled to a quantized Bose field and show that such a system has a ground state for two classes of short-range potentials which are alone too weak to have a zero-energy resonance

Spectra of soft ring graphs

We discuss of a ring-shaped soft quantum wire modeled by $\delta$ interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the dependence of eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is investigated also in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.Comment: LaTeX 2e, 17 pages, with 10 ps figure

Magnetic transport in a straight parabolic channel

We study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under influence of a potential perturbation $W$. If $W$ is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any finite number of open gaps provided the confining potential is sufficiently strong. However, if $W$ depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if $W$ is small and satisfies a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists

Cantor and band spectra for periodic quantum graphs with magnetic fields

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band structure for a rational flux. The Dirichlet eigenvalues can be isolated or embedded, subject to the choice of parameters. Conditions for both possibilities are given. We show that generically there are infinitely many gaps in the spectrum, and the Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte

Localization via fractional moments for models on Z\mathbb{Z} with single-site potentials of finite support

One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new variant of these results for one-dimensional alloy-type potentials with finitely supported sign-changing single-site potentials using the fractional moment method.Comment: LaTeX-file, 26 pages with 2 LaTeX figure

Increasing condom use in heterosexual men: development of a theory-based interactive digital intervention

Increasing condom use to prevent sexually transmitted infections is a key public health goal. Interventions are more likely to be effective if they are theory- and evidence-based. The Behaviour Change Wheel (BCW) provides a framework for intervention development. To provide an example of how the BCW was used to develop an intervention to increase condom use in heterosexual men (the MenSS website), the steps of the BCW intervention development process were followed, incorporating evidence from the research literature and views of experts and the target population. Capability (e.g. knowledge) and motivation (e.g. beliefs about pleasure) were identified as important targets of the intervention. We devised ways to address each intervention target, including selecting interactive features and behaviour change techniques. The BCW provides a useful framework for integrating sources of evidence to inform intervention content and deciding which influences on behaviour to target

Control and stabilization of waves on 1-d networks

We present some recent results on control and stabilization of waves on 1-d networks.The fine time-evolution of solutions of wave equations on networks and, consequently, their control theoretical properties, depend in a subtle manner on the topology of the network under consideration and also on the number theoretical properties of the lengths of the strings entering in it. Therefore, the overall picture is quite complex.In this paper we summarize some of the existing results on the problem of controllability that, by classical duality arguments in control theory, can be reduced to that of observability of the adjoint uncontrolled system. The problem of observability refers to that of recovering the total energy of solutions by means of measurements made on some internal or external nodes of the network. They lead, by duality, to controllability results guaranteeing that L 2-controls located on those nodes may drive sufficiently smooth solutions to equilibrium at a final time. Most of our results in this context, obtained in collaboration with R. Dáger, refer to the problem of controlling the network from one single external node. It is, to some extent, the most complex situation since, obviously, increasing the number of controllers enhances the controllability properties of the system. Our methods of proof combine sidewise energy estimates (that in the particular case under consideration can be derived by simply applying the classical d'Alembert's formula), Fourier series representations, non-harmonic Fourier analysis, and number theoretical tools.These control results belong to the class of the so-called open-loop control systems.We then discuss the problem of closed-loop control or stabilization by feedback. We present a recent result, obtained in collaboration with J. Valein, showing that the observability results previously derived, regardless of the method of proof employed, can also be recast a posteriori in the context of stabilization, so to derive explicit decay rates (as) for the energy of smooth solutions. The decay rate depends in a very sensitive manner on the topology of the network and the number theoretical properties of the lengths of the strings entering in it.In the end of the article we also present some challenging open problems

Silencing of PINK1 Expression Affects Mitochondrial DNA and Oxidative Phosphorylation in DOPAMINERGIC Cells

Background: Mitochondrial dysfunction has been implicated in the pathogenesis of Parkinson's disease (PD). Impairment of the mitochondrial electron transport chain (ETC) and an increased frequency in deletions of mitochondrial DNA (mtDNA), which encodes some of the subunits of the ETC, have been reported in the substantia nigra of PD brains. The identification of mutations in the PINK1 gene, which cause an autosomal recessive form of PD, has supported mitochondrial involvement in PD. The PINK1 protein is a serine/threonine kinase localized in mitochondria and the cytosol. Its precise function is unknown, but it is involved in neuroprotection against a variety of stress signalling pathways.Methodology/Principal Findings: In this report we have investigated the effect of silencing PINK1 expression in human dopaminergic SH-SY5Y cells by siRNA on mtDNA synthesis and ETC function. Loss of PINK1 expression resulted in a decrease in mtDNA levels and mtDNA synthesis. We also report a concomitant loss of mitochondrial membrane potential and decreased mitochondrial ATP synthesis, with the activity of complex IV of the ETC most affected. This mitochondrial dysfunction resulted in increased markers of oxidative stress under basal conditions and increased cell death following treatment with the free radical generator paraquat.Conclusions: This report highlights a novel function of PINK1 in mitochondrial biogenesis and a role in maintaining mitochondrial ETC activity. Dysfunction of both has been implicated in sporadic forms of PD suggesting that these may be key pathways in the development of the disease