The Harish-Chandra isomorphism for reductive symmetric superpairs

We consider symmetric pairs of Lie superalgebras which are strongly reductive and of even type, and introduce a graded Harish-Chandra homomorphism. We prove that its image is a certain explicit filtered subalgebra of the Weyl invariants on a Cartan subspace whose associated graded is the image of Chevalley's restriction map on symmetric invariants. This generalises results of Harish-Chandra and V. Kac, M. Gorelik.Comment: 43 pages; v2: substantially improved versio

Opto-SICM framework combines optogenetics with scanning ion conductance microscopy for probing cell-to-cell contacts

We present a novel framework, Opto-SICM, for studies of cellular interactions in live cells with high spatiotemporal resolution. The approach combines scanning ion conductance microscopy, SICM, and cell-type-specific optogenetic interrogation. Light-excitable cardiac fibroblasts (FB) and myofibroblasts (myoFB) were plated together with non-modified cardiomyocytes (CM) and then paced with periodic illumination. Opto-SICM reveals the extent of FB/myoFB-CM cell-cell contacts and the dynamic changes over time not visible by optical microscopy. FB-CM pairs have lower gap junctional expression of connexin-43 and higher contact dynamism compared to myoFB-CM pairs. The responsiveness of CM to pacing via FB/myoFB depends on the dynamics of the contact but not on the area. The non-responding pairs have higher net cell-cell movement at the contact. These findings are relevant to cardiac disease states, where adverse remodeling leads to abnormal electrical excitation of CM. The Opto-SICM framework can be deployed to offer new insights on cellular and subcellular interactions in various cell types, in real-time

Far-infrared induced current in a ballistic channel -- potential barrier structure

We consider electron transport in a ballistic multi-mode channel structure in the presence of a transversely polarized far-infrared (FIR) field. The channel structure consists of a long resonance region connected to an adiabatic widening with a potential barrier at the end. At frequencies that match the mode energy separation in the resonance region we find distinct peaks in the photocurrent, caused by Rabi oscillations in the mode population. For an experimental situation in which the width of the channel is tunable via gates, we propose a method for reconstructing the spectrum of propagating modes, without having to use a tunable FIR source. With this method the change in the spectrum as the gate voltage is varied can be monitored.Comment: Submitted to Phys. Rev.

Homological algebra for osp(1/2n)

We discuss several topics of homological algebra for the Lie superalgebra osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical results although the cohomology is not given by the kernel of the Kostant quabla operator. Based on this cohomology we can derive strong Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules. Then we state the Bott-Borel-Weil theorem which follows immediately from the Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally we calculate the projective dimension of irreducible and Verma modules in the category O

Spearhead Nanometric Field-Effect Transistor Sensors for Single-Cell Analysis.

Nanometric field-effect-transistor (FET) sensors are made on the tip of spear-shaped dual carbon nanoelectrodes derived from carbon deposition inside double-barrel nanopipettes. The easy fabrication route allows deposition of semiconductors or conducting polymers to comprise the transistor channel. A channel from electrodeposited poly pyrrole (PPy) exhibits high sensitivity toward pH changes. This property is exploited by immobilizing hexokinase on PPy nano-FETs to give rise to a selective ATP biosensor. Extracellular pH and ATP gradients are key biochemical constituents in the microenvironment of living cells; we monitor their real-time changes in relation to cancer cells and cardiomyocytes. The highly localized detection is possible because of the high aspect ratio and the spear-like design of the nano-FET probes. The accurately positioned nano-FET sensors can detect concentration gradients in three-dimensional space, identify biochemical properties of a single living cell, and after cell membrane penetration perform intracellular measurements

Electromechanical instability in suspended carbon nanotubes

We have theoretically investigated electromechanical properties of freely suspended carbon nanotubes when a current is injected into the tubes using a scanning tunneling microscope. We show that a shuttle-like electromechanical instability can occur if the bias voltage exceeds a dissipation-dependent threshold value. An instability results in large amplitude vibrations of the carbon nanotube bending mode, which modify the current-voltage characteristics of the system

Shuttle Mechanism for Charge Transfer in Coulomb Blockade Nanostructures

Room-temperature Coulomb blockade of charge transport through composite nanostructures containing organic inter-links has recently been observed. A pronounced charging effect in combination with the softness of the molecular links implies that charge transfer gives rise to a significant deformation of these structures. For a simple model system containing one nanoscale metallic cluster connected by molecular links to two bulk metallic electrodes we show that self-excitation of periodic cluster oscillations in conjunction with sequential processes of cluster charging and decharging appears for a sufficiently large bias voltage. This new `electron shuttle' mechanism of discrete charge transfer gives rise to a current through the nanostructure, which is proportional to the cluster vibration frequency.Comment: 4 pages, 4 figure

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.Comment: Latex, 75 pages. Minor corrections. Final version, to appear in the Japanese Journal of Mathematic

Nanoscale Study of Calcium Handling Remodeling in Right Ventricular Cardiomyocytes Following Pulmonary Hypertension

Pulmonary hypertension is a complex disorder characterized by pulmonary vascular remodeling and right ventricular hypertrophy, leading to right heart failure. The mechanisms underlying this process are not well understood. We hypothesize that the structural remodeling occurring in the cardiomyocytes of the right ventricle affects the cytosolic Ca2+ handling leading to arrhythmias. After 12 days of monocrotaline-induced pulmonary hypertension in rats, epicardial mapping showed electrical remodeling in both ventricles. In myocytes isolated from the hypertensive rats, a combination of high-speed camera and confocal line-scan documented a prolongation of Ca2+ transients along with a higher local Ca2+-release activity. These Ca2+ transients were less synchronous than in controls, likely due to disorganized transverse-axial tubular system. In fact, following pulmonary hypertension, hypertrophied right ventricular myocytes showed significantly reduced number of transverse tubules and increased number of axial tubules; however, Stimulation Emission Depletion microscopy demonstrated that the colocalization of L-type Ca2+ channels and RyR2 (ryanodine receptor 2) remained unchanged. Finally, Stimulation Emission Depletion microscopy and super-resolution scanning patch-clamp analysis uncovered a decrease in the density of active L-type Ca2+ channels in right ventricular myocytes with an elevated open probability of the T-tubule anchored channels. This may represent a general mechanism of how nanoscale structural changes at the early stage of pulmonary hypertension impact on the development of the end stage failing phenotype in the right ventricle

Subharmonic Shapiro steps and assisted tunneling in superconducting point contacts

We analyze the current in a superconducting point contact of arbitrary transmission in the presence of a microwave radiation. The interplay between the ac Josephson current and the microwave signal gives rise to Shapiro steps at voltages V = (m/n) \hbar \omega_r/2e, where n,m are integer numbers and \omega_r is the radiation frequency. The subharmonic steps (n different from 1) are a consequence of the ocurrence of multiple Andreev reflections (MAR) and provide an unambiguous signature of the peculiar ac Josephson effect at high transmission. Moreover, the dc current exhibits a rich subgap structure due to photon-assisted MARs.Comment: Revtex, 4 pages, 4 figure