A variational approach to dislocation problems for periodic Schr\"odinger operators

As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential $V = V(x,y)$ on $\R^2$ with period lattice $\Z^2$ by setting $W_t(x,y) = V(x+t,y)$ for $x < 0$ and $W_t(x,y) = V(x,y)$ for $x \ge 0$, for $t \in [0,1]$. For Lipschitz-continuous $V$ it is shown that the Schr\"odinger operators $H_t = -\Delta + W_t$ have spectrum (surface states) in the spectral gaps of $H_0$, for suitable $t \in (0,1)$. We also discuss the density of these surface states as compared to the density of the bulk. Our approach is variational and it is first applied to the well-known dislocation problem [E. Korotyaev, Commun. Math. Phys. 213 (2000), 471-489], [E. Korotyaev, Asymptotic Anal. 45 (2005), 73-97] on the real line. We then proceed to the dislocation problem for an infinite strip and for the plane. In an appendix, we discuss regularity properties of the eigenvalue branches in the one-dimensional dislocation problem for suitable classes of potentials.Comment: 19 pages, 3 figure

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators

In this paper, we consider one dimensional adiabatic quasi-periodic Schr\"{o}dinger operators in the regime of strong resonant tunneling. We show the emergence of a level repulsion phenomenon which is seen to be very naturally related to the local spectral type of the operator: the more singular the spectrum, the weaker the repulsion

Transport properties of \nu=1 quantum Hall bilayers. Phenomenological description

We propose a phenomenological model that describes counterflow and drag experiments with quantum Hall bilayers in a \nu_T=1 state. We consider the system consisting of statistically distributed areas with local total filling factors \nu_{T1}>1 and \nu_{T2}<1. The excess or deficit of electrons in a given area results in an appearance of vortex excitations. The vortices in quantum Hall bilayers are charged. They are responsible for a decay of the exciton supercurrent, and, at the same time, contribute to the conductivity directly. The experimental temperature dependence of the counterflow and drive resistivities is described under accounting viscous forces applied to vortices that are the exponentially increase functions of the inverse temperature. The presence of defect areas where the interlayer phase coherence is destroyed completely can result in an essential negative longitudinal drag resistivity as well as in a counterflow Hall resistivity

Tracking cardiovascular comorbidity in models of chronic inflammatory disease

Immune-mediated inflammatory diseases (IMIDs) are commonly associated with complex coexisting conditions, and cardiovascular comorbidities are a common cause of mortality in systemic inflammation. Experimental models of disease provide an opportunity to dissect inflammatory mechanisms that promote damage to vascular tissues affected by comorbidity. Here, we describe methods to recover the thoracic aorta from mice during experimental inflammatory arthritis and assess vascular constriction responses by isometric tension myography. To complement the assessment of functional changes in the vasculature during inflammatory arthritis, we also outline a method to characterize vascular inflammation by immunohistochemistry

Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

Canagliflozin impairs T cell effector function via metabolic suppression in autoimmunity

Augmented T cell function leading to host damage in autoimmunity is supported by metabolic dysregulation, making targeting immunometabolism an attractive therapeutic avenue. Canagliflozin, a type 2 diabetes drug, is a sodium glucose co-transporter 2 (SGLT2) inhibitor with known off-target effects on glutamate dehydrogenase and complex I. However, the effects of SGLT2 inhibitors on human T cell function have not been extensively explored. Here, we show that canagliflozin-treated T cells are compromised in their ability to activate, proliferate, and initiate effector functions. Canagliflozin inhibits T cell receptor signaling, impacting on ERK and mTORC1 activity, concomitantly associated with reduced c-Myc. Compromised c-Myc levels were encapsulated by a failure to engage translational machinery resulting in impaired metabolic protein and solute carrier production among others. Importantly, canagliflozin-treated T cells derived from patients with autoimmune disorders impaired their effector function. Taken together, our work highlights a potential therapeutic avenue for repurposing canagliflozin as an intervention for T cell-mediated autoimmunity

Gene Flow in Genetically Modified Wheat

Understanding gene flow in genetically modified (GM) crops is critical to answering questions regarding risk-assessment and the coexistence of GM and non-GM crops. In two field experiments, we tested whether rates of cross-pollination differed between GM and non-GM lines of the predominantly self-pollinating wheat Triticum aestivum. In the first experiment, outcrossing was studied within the field by planting “phytometers” of one line into stands of another line. In the second experiment, outcrossing was studied over distances of 0.5–2.5 m from a central patch of pollen donors to adjacent patches of pollen recipients. Cross-pollination and outcrossing was detected when offspring of a pollen recipient without a particular transgene contained this transgene in heterozygous condition. The GM lines had been produced from the varieties Bobwhite or Frisal and contained Pm3b or chitinase/glucanase transgenes, respectively, in homozygous condition. These transgenes increase plant resistance against pathogenic fungi. Although the overall outcrossing rate in the first experiment was only 3.4%, Bobwhite GM lines containing the Pm3b transgene were six times more likely than non-GM control lines to produce outcrossed offspring. There was additional variation in outcrossing rate among the four GM-lines, presumably due to the different transgene insertion events. Among the pollen donors, the Frisal GM line expressing a chitinase transgene caused more outcrossing than the GM line expressing both a chitinase and a glucanase transgene. In the second experiment, outcrossing after cross-pollination declined from 0.7–0.03% over the test distances of 0.5–2.5 m. Our results suggest that pollen-mediated gene flow between GM and non-GM wheat might only be a concern if it occurs within fields, e.g. due to seed contamination. Methodologically our study demonstrates that outcrossing rates between transgenic and other lines within crops can be assessed using a phytometer approach and that gene-flow distances can be efficiently estimated with population-level PCR analyses