Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach

By employing Hopf's functional method, we find the exact characteristic functional for a simple nonlinear dynamical system introduced by Orszag. Steady-state equal-time statistics thus obtained are compared to direct numerical simulation. The solution is both non-trivial and strongly non-Gaussian.Comment: 6 pages and 2 figure

Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the governing equation in terms of elliptic integrals. We show that the instances when the elliptic integrals degenerate to elementary functions were known to nineteenth century geometers. Finally, we characterize the associated normal congruences

The general classical solution of the superparticle

The theory of vectors and spinors in 9+1 dimensional spacetime is introduced in a completely octonionic formalism based on an octonionic representation of the Clifford algebra \Cl(9,1). The general solution of the classical equations of motion of the CBS superparticle is given to all orders of the Grassmann hierarchy. A spinor and a vector are combined into a $3 \times 3$ Grassmann, octonionic, Jordan matrix in order to construct a superspace variable to describe the superparticle. The combined Lorentz and supersymmetry transformations of the fermionic and bosonic variables are expressed in terms of Jordan products.Comment: 11 pages, REVTe

Differentiation Potential of Pancreatic Fibroblastoid Cells/Stellate Cells: Effects of Peroxisome Proliferator-Activated Receptor Gamma Ligands

Pancreatic stellate cells have been investigated mostly for their activation process, supposed to support the development of pancreatic disease. Few studies have been presented on reversal of the activation process in vitro. Thiazolidinediones (TZDs) have been used as antidiabetics and have now been reported to exert antifibrotic activity. We tested effects of natural and synthetic ligands of peroxisome proliferator-activated receptor gamma (PPARγ) on human pancreatic fibroblastoid cells (hPFCs) in search for specificity of action. Ciglitazone, as a prototype of TZDs, was shown to have reversible growth inhibitory effects on human pancreatic fibroblastoid cells/stellate cells. Cells treated with ciglitazone for three days showed enhanced lipid content and induction of proteins involved in lipid metabolism. Collagen synthesis was reduced in hPFC. Interaction of PPARγ with DNA binding sites upon ligand binding was shown by gel shift analysis. These findings point toward a potential for adipocyte differentiation in human pancreatic fibroblastoid cells

Relativistic ponderomotive force, uphill acceleration, and transition to chaos

Starting from a covariant cycle-averaged Lagrangian the relativistic oscillation center equation of motion of a point charge is deduced and analytical formulae for the ponderomotive force in a travelling wave of arbitrary strength are presented. It is further shown that the ponderomotive forces for transverse and longitudinal waves are different; in the latter, uphill acceleration can occur. In a standing wave there exists a threshold intensity above which, owing to transition to chaos, the secular motion can no longer be described by a regular ponderomotive force. PACS number(s): 52.20.Dq,05.45.+b,52.35.Mw,52.60.+hComment: 8 pages, RevTeX, 3 figures in PostScript, see also http://www.physik.th-darmstadt.de/tqe

A Transgenic Rat for Investigating the Anatomy and Function of Corticotrophin Releasing Factor Circuits.

Corticotrophin-releasing factor (CRF) is a 41 amino acid neuropeptide that coordinates adaptive responses to stress. CRF projections from neurons in the central nucleus of the amygdala (CeA) to the brainstem are of particular interest for their role in motivated behavior. To directly examine the anatomy and function of CRF neurons, we generated a BAC transgenic Crh-Cre rat in which bacterial Cre recombinase is expressed from the Crh promoter. Using Cre-dependent reporters, we found that Cre expressing neurons in these rats are immunoreactive for CRF and are clustered in the lateral CeA (CeL) and the oval nucleus of the BNST. We detected major projections from CeA CRF neurons to parabrachial nuclei and the locus coeruleus, dorsal and ventral BNST, and more minor projections to lateral portions of the substantia nigra, ventral tegmental area, and lateral hypothalamus. Optogenetic stimulation of CeA CRF neurons evoked GABA-ergic responses in 11% of non-CRF neurons in the medial CeA (CeM) and 44% of non-CRF neurons in the CeL. Chemogenetic stimulation of CeA CRF neurons induced Fos in a similar proportion of non-CRF CeM neurons but a smaller proportion of non-CRF CeL neurons. The CRF1 receptor antagonist R121919 reduced this Fos induction by two-thirds in these regions. These results indicate that CeL CRF neurons provide both local inhibitory GABA and excitatory CRF signals to other CeA neurons, and demonstrate the value of the Crh-Cre rat as a tool for studying circuit function and physiology of CRF neurons

Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et. al. for the analysis of classical simulated annealing using a classical-quantum correspondence.Comment: 6 pages, minor correction

Insecurity for compact surfaces of positive genus

A pair of points in a riemannian manifold $M$ is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is insecure. A manifold is secure if all pairs of points in $M$ are secure. A manifold is insecure if there exists an insecure point pair, and totally insecure if all point pairs are insecure. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. We prove this for surfaces of genus greater than zero. We also prove that a closed surface of genus greater than one with any riemannian metric and a closed surface of genus one with generic metric are totally insecure.Comment: 37 pages, 11 figure

Constraint and gauge shocks in one-dimensional numerical relativity

We study how different types of blow-ups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blow-ups can be expected. One criteria is related with the so-called geometric blow-up leading to gradient catastrophes, while the other is based upon the ODE-mechanism leading to blow-ups within finite time. We show how both mechanisms work in the case of a simple one-dimensional wave equation with a dynamic wave speed and sources, and later explore how those blow-ups can appear in one-dimensional numerical relativity. In the latter case we recover the well known ``gauge shocks'' associated with Bona-Masso type slicing conditions. However, a crucial result of this study has been the identification of a second family of blow-ups associated with the way in which the constraints have been used to construct a hyperbolic formulation. We call these blow-ups ``constraint shocks'' and show that they are formulation specific, and that choices can be made to eliminate them or at least make them less severe.Comment: 19 pages, 8 figures and 1 table, revised version including several amendments suggested by the refere