A Geometrical Method of Decoupling

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as for instance the method of Teng and Edwards. In a preceeding paper it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all thinkable cases. Hence a systematic derivation of a more general treatment seemed advisable. In a second paper the author suggested the use of real Dirac matrices as basic tools to coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. It is shown that this algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\vec E$, $\vec B$ and $\vec P$, that were introduced with the so-called "electromechanical equivalence". We present a structure-preserving block-diagonalization of symplectic or Hamiltonian matrices, respectively. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires ${\cal O}(n^2)$ iterations to converge to a given precision.Comment: 13 pages, 1 figur

Evidence for Vector-Meson Effects on π0 Photoproduction From Hydrogen

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Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space

We present in this paper a fully covariant quantization of the minimally-coupled massless field on de Sitter space. We thus obtain a formalism free of any infrared (e.g logarithmic) divergence. Our method is based on a rigorous group theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-G\"{a}rding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time. The minimally-coupled massless field is associated with a representation which is the lowest term of the discrete series of unitary representations of the de Sitter group. In spite of the presence of negative norm modes in the theory, no negative energy can be measured: expressions as \le n_{k_1}n_{k_2}...|T_{00}|n_{k_1}n_{k_2}...\re are always positive.Comment: 20 pages, appear in class. quantum gra

Separation of the Exchange-Correlation Potential into Exchange plus Correlation: an Optimized Effective Potential Approach

Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is useful since, for exchange, exact relations exist under uniform density scaling and spin scaling. In the past, accurate exchange-correlation potentials have been generated from essentially exact densities constructed using information from either quantum chemistry or quantum Monte Carlo calculations but they have not been correctly decomposed into their separate exchange and correlation components, except for two-electron systems. exchange and correlation components (except for two-electron systems). Using a recently proposed method, equivalent to the solution of an optimized effective potential problem with the corresponding orbitals replaced by the exact Kohn-Sham orbitals, we obtain the separation according to the density functional theory definition. We compare the results for the Ne and Be atoms with those obtained by the previously used approximate separation scheme

Protein kinase C-activating isophthalate derivatives mitigate Alzheimer's disease-related cellular alterations

Abnormal protein kinase C (PKC) function contributes to many pathophysiological processes relevant for Alzheimer's disease (AD), such as amyloid precursor protein (APP) processing. Phorbol esters and other PKC activators have been demonstrated to enhance the secretion of soluble APP alpha (sAPP alpha), reduce the levels of beta-amyloid (A beta), induce synaptogenesis, and promote neuroprotection. We have previously described isophthalate derivatives as a structurally simple family of PKC activators. Here, we characterised the effects of isophthalate derivatives HMI-1a3 and HMI-1b11 on neuronal viability, neuroinflammatory response, processing of APP and dendritic spine density and morphology in in vitro. HMI-1a3 increased the viability of embryonic primary cortical neurons and decreased the production of the pro-inflammatory mediator TNF alpha, but not that of nitric oxide, in mouse neuron-BV2 microglia co-cultures upon LPS- and IFN-gamma-induced neuroinflammation. Furthermore, both HMI-1a3 and HMI-1b11 increased the levels of sAPPa relative to total sAPP and the ratio of A beta 42/A beta 40 in human SH-Sv5v neuroblastoma cells. Finally, bryostatin-1, but not HMI-1a3, increased the number of mushroom spines in proportion to total spine density in mature mouse hippocampal neuron cultures. These results suggest that the PKC activator HMI-1a3 exerts neuroprotective functions in the in vitro models relevant for AD by reducing the production of TNF alpha and increasing the secretion of neuroprotective sAPPa.Peer reviewe

Measuring the Polarization of a Rapidly Precessing Deuteron Beam

This paper describes a time-marking system that enables a measurement of the in-plane (horizontal) polarization of a 0.97-GeV/c deuteron beam circulating in the Cooler Synchrotron (COSY) at the Forschungszentrum J\"ulich. The clock time of each polarimeter event is used to unfold the 120-kHz spin precession and assign events to bins according to the direction of the horizontal polarization. After accumulation for one or more seconds, the down-up scattering asymmetry can be calculated for each direction and matched to a sinusoidal function whose magnitude is proportional to the horizontal polarization. This requires prior knowledge of the spin tune or polarization precession rate. An initial estimate is refined by re-sorting the events as the spin tune is adjusted across a narrow range and searching for the maximum polarization magnitude. The result is biased toward polarization values that are too large, in part because of statistical fluctuations but also because sinusoidal fits to even random data will produce sizeable magnitudes when the phase is left free to vary. An analysis procedure is described that matches the time dependence of the horizontal polarization to templates based on emittance-driven polarization loss while correcting for the positive bias. This information will be used to study ways to extend the horizontal polarization lifetime by correcting spin tune spread using ring sextupole fields and thereby to support the feasibility of searching for an intrinsic electric dipole moment using polarized beams in a storage ring. This paper is a combined effort of the Storage Ring EDM Collaboration and the JEDI Collaboration.Comment: 28 pages, 15 figures, prepared for Physical Review ST - Accelerators and Beam

Optimized Effective Potential for Extended Hubbard Model

Antiferromagnetic and charge ordered Hartree-Fock solutions of the one-band Hubbard model with on-site and nearest-neighbor Coulomb repulsions are exactly mapped onto an auxiliary local Kohn-Sham (KS) problem within a density-functional theory. The mapping provides a new insight into the interpretation of the KS equations. (i) With an appropriate choice of the basic variable, there is a universal form of the KS potential, which is applicable both for the antiferromagnetic and the charge ordered solutions. (ii) The Kohn-Sham and Hartree-Fock eigenvalues are interconnected by a scaling transformation. (iii) The band-gap problem is attributed to the derivative discontinuity of the basic variable as the function of the electron number, rather than a finite discontinuity of the KS potential. (iv) It is argued that the conductivity gap and the energies of spin-wave excitations can be entirely defined by the parameters of the ground state and the KS eigenvalues.Comment: 21 page, 3 figure

Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation

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Stem cells are the most sensitive screening tool to identify toxicity of GATA4-targeted novel small-molecule compounds

Safety assessment of drug candidates in numerous in vitro and experimental animal models is expensive, time consuming and animal intensive. More thorough toxicity profiling already in the early drug discovery projects using human cell models, which more closely resemble the physiological cell types, would help to decrease drug development costs. In this study we aimed to compare different cardiac and stem cell models for in vitro toxicity testing and to elucidate structure-toxicity relationships of novel compounds targeting the cardiac transcription factor GATA4. By screening the effects of eight compounds at concentrations ranging from 10 nM up to 30 µM on the viability of eight different cell types, we identified significant cell type- and structure-dependent toxicity profiles. We further characterized two compounds in more detail using high-content analysis. The results highlight the importance of cell type selection for toxicity screening and indicate that stem cells represent the most sensitive screening model, which can detect toxicity that may otherwise remain unnoticed. Furthermore, our structure-toxicity analysis reveals a characteristic dihedral angle in the GATA4-targeted compounds that causes stem cell toxicity and thus helps to direct further drug development efforts towards non-toxic derivatives