Planar waveguide with "twisted" boundary conditions: discrete spectrum

We consider a planar waveguide with combined Dirichlet and Neumann conditions imposed in a "twisted" way. We study the discrete spectrum and describe it dependence on the configuration of the boundary conditions. In particular, we show that in certain cases the model can have discrete eigenvalues emerging from the threshold of the essential spectrum. We give a criterium for their existence and construct them as convergent holomorphic series

A rigorous analysis of high order electromagnetic invisibility cloaks

There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al. that are based in the transformation approach. They obtained their results using first order transformations. In recent papers Hendi et al. and Cai et al. considered invisibility cloaks with high order transformations. In this paper we study high order electromagnetic invisibility cloaks in transformation media obtained by high order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. We prove that for any incident plane wave, at any frequency, the scattered wave is identically zero. We also consider the scattering of finite energy wave packets. We prove that the scattering matrix is the identity, i.e., that for any incoming wave packet the outgoing wave packet is the same as the incoming one. This proves that the invisibility cloaks can not be detected in any scattering experiment with electromagnetic waves in high order transformation media, and in particular in the first order transformation media of Pendry et al. We also prove that the high order invisibility cloaks, as well as the first order ones, cloak passive and active devices. The cloaked objects completely decouple from the exterior. Actually, the cloaking outside is independent of what is inside the cloaked objects. The electromagnetic waves inside the cloaked objects can not leave the concealed regions and viceversa, the electromagnetic waves outside the cloaked objects can not go inside the concealed regions. As we prove our results for media that are obtained by transformation from general anisotropic materials, we prove that it is possible to cloak objects inside general crystals.Comment: The final version is now published in Journal of Physics A: Mathematical and Theoretical, vol 41 (2008) 065207 (21 pp). Included in IOP-Selec

Absence of bound states for waveguides in 2D periodic structures

We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a perturbation in form of a line defect. The defect is aligned along one of the coordinate axes, periodic in that direction (with the same periodicity as the background), and bounded in the other direction. This setting models a so-called "soft-wall" waveguide problem. We show that there are no bound states, i.e., the spectrum of the operator under study contains no point spectrum.Comment: This is an updated version of our paper (in slightly different form in Journal of Mathematical Physics). An anonymous reviewer kindly made us aware that ref. 10 is not applicable in our situation. An application of the theorem in ref. 10 would have proved the absence of singular continuous spectrum also. Our result on the absence of point spectrum is not affected by thi

On the spectrum of the periodic Dirac operator

The absolute continuity of the spectrum for the periodic Dirac operator $$\hat D=\sum_{j=1}^n(-i\frac {\partial}{\partial x_j}-A_j)\hat \alpha_j + \hat V^{(0)}+\hat V^{(1)}, x\in R^n, n\geq 3,$$ is proved given that either $A\in C(R^n;R^n)\cap H^q_{loc}(R^n;R^n)$, 2q > n-2, or the Fourier series of the vector potential $A:R^n\to R^n$ is absolutely convergent. Here, $\hat V^{(s)}=(\hat V^{(s)})^*$ are continuous matrix functions and \hat V^{(s)}\hat \alpha_j=(-1}^s\hat \alpha_j\hat V^{(s)} for all anticommuting Hermitian matrices $\hat \alpha_j$, $\hat \alpha_j^2=\hat I$, s=0,1.Comment: 17 page

Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and other areas. A Schnol type theorem is proven that allows one to detect that a point belongs to the spectrum when a generalized eigenfunction with an subexponential growth integral estimate is available. A theorem on spectral gap opening for ``decorated'' quantum graphs is established (its analog is known for the combinatorial case). It is also shown that if a periodic combinatorial or quantum graph has a point spectrum, it is generated by compactly supported eigenfunctions (``scars'').Comment: 4 eps figures, LATEX file, 21 pages Revised form: a cut-and-paste blooper fixe

Clinical biological and genetic heterogeneity of the inborn errors of pulmonary surfactant metabolism

Pulmonary surfactant is a multimolecular complex located at the air-water interface within the alveolus to which a range of physical (surface-active properties) and immune functions has been assigned. This complex consists of a surface-active lipid layer (consisting mainly of phospholipids), and of an aqueous subphase. From discrete surfactant sub-fractions one can isolate strongly hydrophobic surf acta nt proteins B (SP-B) and C (SP-C) as well as collectins SP-A and SP-D, which were shown to have specific structural, metabolic, or immune properties. Inborn or acquired abnormalities of the surfactant, qualitative or quantitative in nature, account for a number of human diseases. Beside hyaline membrane disease of the preterm neonate, a cluster of hereditary or acquired lung diseases has been characterized by periodic acid-Schiff-positive material filling the alveoli. From this heterogeneous nosologic group, at least two discrete entities presently emerge. The first is the SP-B deficiency, in which an essentially proteinaceous material is stored within the alveoli, and which represents an autosomal recessive Mendelian entity linked to the SFTPB gene (MIM 1786640). The disease usually generally entails neonatal respiratory distress with rapid fatal outcome, although partial or transient deficiencies have also been observed. The second is alveolar proteinosis, characterized by the storage of a mixed protein and lipid material, which constitutes a relatively heterogeneous clinical and biological syndrome, especially with regard to age at onset (from the neonate through to adulthood) as well as the severity of associated signs. Murine models, with a targeted mutation of the gene encoding granulocyte macrophage colony-stimulating factor (GM-CSF) (Csfgm) or the beta subunit of its receptor (II3rb1) support the hypothesis of an abnormality of surfactant turnover in which the alveolar macrophage is a key player. Apart from SP-B deficiency, in which a near-consensus diagnostic chart can be designed, the ascertainment of other abnormalities of surfactant metabolism is not straightforward. The disentanglement of this disease cluster is however essential to propose specific therapeutic procedures: repeated broncho-alveolar ravages, GM-CSF replacement, bone marrow grafting or lung transplantation

Negative DNA supercoiling induces genome-wide Cas9 off-target activity

CRISPR-Cas9 is a powerful gene-editing technology; however, off-target activity remains an important consideration for therapeutic applications. We have previously shown that force-stretching DNA induces off-target activity and hypothesized that distortions of the DNA topology in vivo, such as negative DNA supercoiling, could reduce Cas9 specificity. Using single-molecule optical-tweezers, we demonstrate that negative supercoiling λ-DNA induces sequence-specific Cas9 off-target binding at multiple sites, even at low forces. Using an adapted CIRCLE-seq approach, we detect over 10,000 negative-supercoiling-induced Cas9 off-target double-strand breaks genome-wide caused by increased mismatch tolerance. We further demonstrate in vivo that directed local DNA distortion increases off-target activity in cells and that induced off-target events can be detected during Cas9 genome editing. These data demonstrate that Cas9 off-target activity is regulated by DNA topology in vitro and in vivo, suggesting that cellular processes, such as transcription and replication, could induce off-target activity at previously overlooked sites

Schistosoma haematobium infection levels determine the effect of praziquantel treatment on anti-schistosome and anti-mite antibodies

Field studies show an association between schistosome infection and atopy, but the effects of anti-helminthic treatment on this association have not yet been investigated in human populations with different schistosome endemicity levels. This study aimed to compare the effects of anti-helminthic treatment on responses directed against the house dust mite Dermatophagoides pteronyssinus (Derp1) and Schistosoma haematobium in Zimbabwean populations living in high and low schistosome infection areas. Derp1- and schistosome-specific IgE and IgG4 antibodies were quantified by ELISA before and 6 weeks after anti-helminthic treatment. Following treatment, there were changes in the immune responses, which varied with place of residence. After allowing for the effects of sex, age and baseline infection intensity, there was no significant treatment effect on the change in anti-schistosome IgE and IgG4 in the high infection area. However, the anti-schistosome IgE/IgG4 ratio increased significantly, while anti-Derp1 IgE responses decreased as a result of treatment. In the low infection area, treatment resulted in a significant increase in anti-worm IgE levels, but there was no significant treatment effect on anti-schistosome or anti-Derp1 IgE/IgG4 ratios. Thus, the study shows that the level of schistosome endemicity affects the host responses to schistosome and mite antigens following anti-helminthic treatment

On absolute continuity of the spectrum of a periodic magnetic Schr\"odinger operator

We consider the Schr\"odinger operator in ${\mathbb R}^n$, $n\geq 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of the operator in question under some conditions which, in particular, are satisfied if $V\in L^{n/2}_{{\mathrm {loc}}}({\mathbb R}^n)$ and $A\in H^q_{{\mathrm {loc}}}({\mathbb R}^n;{\mathbb R}^n)$, $q>(n-1)/2$.Comment: 25 page