The absolute position of a resonance peak

It is common practice in scattering theory to correlate between the position of a resonance peak in the cross section and the real part of a complex energy of a pole of the scattering amplitude. In this work we show that the resonance peak position appears at the absolute value of the pole's complex energy rather than its real part. We further demonstrate that a local theory of resonances can still be used even in cases previously thought impossible

Fano Resonances in Stubbed Quantum Waveguides with Impurities

We consider T--shaped, two--dimensional quantum waveguides containing attractive or repulsive impurities with a smooth, realistic shape, and study how the resonance behavior of the total conductance depends upon the strength of the defect potential and the geometry of the device. The resonance parameters are determined locating the relevant S-matrix poles in the Riemann energy surface. The total scattering operator is obtained from the S-matrices of the various constituent segments of the device through the *-product composition rule. This allows for a numerically stable evaluation of the scattering matrix and of the resonance parameters.Comment: 23 pages, 6 figure

Familial amyloid precursor protein mutants cause caspase-6-dependent but amyloid β-peptide-independent neuronal degeneration in primary human neuron cultures.

Although familial Alzheimer disease (AD)-associated autosomal dominant mutants have been extensively studied, little is known about the underlying molecular mechanisms of neurodegeneration induced by these mutants in AD. Wild-type, Swedish or London amyloid precursor protein (APP) transfection in primary human neurons induced neuritic beading, in which several co-expressed proteins, such as enhanced green fluorescent protein, red fluorescent protein (RFP)-tau and RFP-ubiquitin, accumulated. APP-induced neuritic beading was dependent on caspase-6 (Casp6), because it was inhibited with 5 μM z-VEID-fmk or with dominant-negative Casp6. Neuritic beading was independent from APP-mediated amyloid β-peptide (Aβ) production, because the APPM596V (APPMV) mutant, which cannot generate Aβ, still induced Casp6-dependent neuritic beading. However, the beaded neurons underwent Casp6- and Aβ-dependent cell death. These results indicate that overexpression of wild-type or mutant APP causes Casp6-dependent but Aβ-independent neuritic degeneration in human neurons. Because Casp6 is activated early in AD and is involved in axonal degeneration, these results suggest that the inhibition of Casp6 may represent an efficient early intervention against familial forms of AD. Furthermore, these results indicate that removing Aβ without inhibiting Casp6 may have little effect in preventing the progressive dementia associated with sporadic or familial AD

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

A Whole Cell Assay to Measure Caspase-6 Activity by Detecting Cleavage of Lamin A/C

Caspase-6 is a cysteinyl protease implicated in neurodegenerative conditions including Alzheimer's and Huntington's disease making it an attractive target for therapeutic intervention. A greater understanding of the role of caspase-6 in disease has been hampered by a lack of suitable cellular assays capable of specifically detecting caspase-6 activity in an intact cell environment. This is mainly due to the use of commercially available peptide substrates and inhibitors which lack the required specificity to facilitate development of this type of assay. We report here a 384-well whole-cell chemiluminescent ELISA assay that monitors the proteolytic degradation of endogenously expressed lamin A/C during the early stages of caspase-dependent apoptosis. The specificity of lamin A/C proteolysis by caspase-6 was demonstrated against recombinant caspase family members and further confirmed in genetic deletion studies. In the assay, plasma membrane integrity remained intact as assessed by release of lactate dehydrogenase from the intracellular environment and the exclusion of cell impermeable peptide inhibitors, despite the induction of an apoptotic state. The method described here is a robust tool to support drug discovery efforts targeting caspase-6 and is the first reported to specifically monitor endogenous caspase-6 activity in a cellular context

PT-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators

Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations

Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures

Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.Comment: review article (invited), 14 pages, 7 figures, 105 reference