Exact States in Waveguides With Periodically Modulated Nonlinearity

We introduce a one-dimensional model based on the nonlinear Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. Numerical stability analysis demonstrates that the periodic states become modulationally unstable for large periods, and regain stability in the limit of an infinite period, which corresponds to a bright soliton pinned to a localized nonlinearity-modulation pattern. Exact dark-bright soliton complex in a coupled system with a localized modulation structure is also briefly considered . The system can be realized in planar optical waveguides and cigar-shaped atomic Bose-Einstein condensates.Comment: EPL, in pres

Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities

We extend the investigation of the recently proposed Kerr/CFT correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theory whose Virasoro algebra arises as an asymptotic symmetry of the near-horizon geometry. In fact in dimension D there are [(D-1)/2] commuting Virasoro algebras. We consider a general canonical class of near-horizon geometries in arbitrary dimension D, and show that in any such metric, the [(D-1)/2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the Bekenstein-Hawking entropy of the associated extremal black hole. In the remainder of the paper we show for most of the known rotating black hole solutions of gauged supergravity, and for the ungauged supergravity solutions with four charges in D=4 and three charges in D=5, that their extremal near-horizon geometries indeed lie within the canonical form. This establishes that in all these examples, the microscopic entropies of the dual CFTs agree with the Bekenstein-Hawking entropies of the extremal rotating black holes.Comment: 32 pages, references added and minor typos fixe

Twisted and Nontwisted Bifurcations Induced by Diffusion

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex files. Hard copy of figures available on request from [email protected]

Electron tunneling time measured by photoluminescence excitation correlation spectroscopy

The tunneling time for electrons to escape from the lowest quasibound state in the quantum wells of GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostructures with barriers between 16 and 62 Å has been measured at 80 K using photoluminescence excitation correlation spectroscopy. The decay time for samples with barrier thicknesses from 16 Å (≈12 ps) to 34 Å(≈800 ps) depends exponentially on barrier thickness, in good agreement with calculations of electron tunneling time derived from the energy width of the resonance. Electron and heavy hole carrier densities are observed to decay at the same rate, indicating a coupling between the two decay processes

Aminopeptidases do not directly degrade tau protein

BACKGROUND: Tau hyperphosphorylation and aggregation to form intracellular neurofibrillar tangles is prevalent in a number of tauopathies. Thus there is current interest in the mechanisms involved in Tau clearance. It was recently reported that Tau can be degraded by an aminopeptidase known as the puromycin sensitive aminopeptidase (PSA). Until now PSA has been reported to only cleave peptides, with the largest reported substrates having 30-50 amino acids. We have studied this unique PSA cleavage reaction using a number of different PSA preparations. RESULTS: An N-terminally His tagged-PSA was expressed and purified from Sf9 insect cells. Although this PSA preparation cleaved Tau, product analysis with N and C terminal Tau antibodies coupled with mass spectrometry showed an endoproteolytic cleavage atypical for an aminopeptidase. Furthermore, the reaction was not blocked by the general aminopeptidase inhibitor bestatin or the specific PSA inhibitor puromycin. In order to test whether Tau hydrolysis might be caused by a protease contaminant the enzyme was expressed in E. coli as glutathione S-transferase and maltose binding protein fusion proteins or in Sf9 cells as a C-terminally His-tagged protein. After purification to near homogeneity none of these other recombinant forms of PSA cleaved Tau. Further, Tau-cleaving activity and aminopeptidase activities derived from the Sf9 cell expression system were separable by molecular sieve chromatography. When tested in a cellular context we again failed to see a PSA dependent cleavage of Tau. A commercial preparation of a related aminopeptidase, aminopeptidase N, also exhibited Tau cleaving activity, but this activity could also be separated from aminopeptidase activity. CONCLUSION: It is concluded that PSA does not directly cleave Tau

A KINEMATIC ANALYSIS OF TRUNK ABILITY IN WHEELCHAIR FENCING: A PILOT STUDY

The purpose of this study was to explore the trunk ability differences between category A and B participants in wheelchair fencing. The result showed that category B participants might perform similar performance as category A participants in maximum lunge velocity, maximum lunge angle and maximum fast return velocity. This result may provide information to International Wheelchair Fencing Committee (IWFC) for the need of research on Wheelchair Fencing Classification (WFC) to clarify the differences between these two categories of participants

A KINEMATIC ANALYSIS OF TRUNK ABILITY IN WHEELCHAIR FENCING: A PILOT STUDY

The purpose of this study was to explore the trunk ability differences between category A and B participants in wheelchair fencing. The result showed that category B participants might perform similar performance as category A participants in maximum lunge velocity, maximum lunge angle and maximum fast return velocity. This result may provide information to International Wheelchair Fencing Committee (IWFC) for the need of research on Wheelchair Fencing Classification (WFC) to clarify the differences between these two categories of participants

Aminopeptidases do not directly degrade tau protein

BACKGROUND: Tau hyperphosphorylation and aggregation to form intracellular neurofibrillar tangles is prevalent in a number of tauopathies. Thus there is current interest in the mechanisms involved in Tau clearance. It was recently reported that Tau can be degraded by an aminopeptidase known as the puromycin sensitive aminopeptidase (PSA). Until now PSA has been reported to only cleave peptides, with the largest reported substrates having 30-50 amino acids. We have studied this unique PSA cleavage reaction using a number of different PSA preparations. RESULTS: An N-terminally His tagged-PSA was expressed and purified from Sf9 insect cells. Although this PSA preparation cleaved Tau, product analysis with N and C terminal Tau antibodies coupled with mass spectrometry showed an endoproteolytic cleavage atypical for an aminopeptidase. Furthermore, the reaction was not blocked by the general aminopeptidase inhibitor bestatin or the specific PSA inhibitor puromycin. In order to test whether Tau hydrolysis might be caused by a protease contaminant the enzyme was expressed in E. coli as glutathione S-transferase and maltose binding protein fusion proteins or in Sf9 cells as a C-terminally His-tagged protein. After purification to near homogeneity none of these other recombinant forms of PSA cleaved Tau. Further, Tau-cleaving activity and aminopeptidase activities derived from the Sf9 cell expression system were separable by molecular sieve chromatography. When tested in a cellular context we again failed to see a PSA dependent cleavage of Tau. A commercial preparation of a related aminopeptidase, aminopeptidase N, also exhibited Tau cleaving activity, but this activity could also be separated from aminopeptidase activity. CONCLUSION: It is concluded that PSA does not directly cleave Tau

Symmetries of supergravity black holes

We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric, and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the "physical" metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity, but also consider some other solutions.Comment: 36 pages; v2: minor changes; v3: slightly shorte