Optimal data exchange algorithms on star graphs

AbstractStar graphs, as discussed in [1], are considered to be attractive alternatives for hypercubes. In this paper, we discuss optimal data exchange algorithms for star graphs of small dimension (n ≤ 6). In particular we study odd-distance and total exchange algorithms, using the tabular method introduced in [2]. The algorithms use no intermediate buffering of messages

Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow

The main result of the paper is Egorov's theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.Comment: 23 pages, no figures. Completely revised and improved version of dg-ga/970301

Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure

Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well--established method based on a power--series expansions weighted by a Gaussian factor with an adjustable parameter (the so--called Hill--determinant method)

Altered metabolic landscape in IDH‐mutant gliomas affects phospholipid, energy, and oxidative stress pathways

Heterozygous mutations in NADP‐dependent isocitrate dehydrogenases (IDH) define the large majority of diffuse gliomas and are associated with hypermethylation of DNA and chromatin. The metabolic dysregulations imposed by these mutations, whether dependent or not on the oncometabolite D‐2‐hydroxyglutarate (D2HG), are less well understood. Here, we applied mass spectrometry imaging on intracranial patient‐derived xenografts of IDH‐mutant versus IDH wild‐type glioma to profile the distribution of metabolites at high anatomical resolution in situ. This approach was complemented by in vivo tracing of labeled nutrients followed by liquid chromatography–mass spectrometry (LC‐MS) analysis. Selected metabolites were verified on clinical specimen. Our data identify remarkable differences in the phospholipid composition of gliomas harboring the IDH1 mutation. Moreover, we show that these tumors are characterized by reduced glucose turnover and a lower energy potential, correlating with their reduced aggressivity. Despite these differences, our data also show that D2HG overproduction does not result in a global aberration of the central carbon metabolism, indicating strong adaptive mechanisms at hand. Intriguingly, D2HG shows no quantitatively important glucose‐derived label in IDH‐mutant tumors, which suggests that the synthesis of this oncometabolite may rely on alternative carbon sources. Despite a reduction in NADPH, glutathione levels are maintained. We found that genes coding for key enzymes in de novo glutathione synthesis are highly expressed in IDH‐mutant gliomas and the expression of cystathionine‐β‐synthase (CBS) correlates with patient survival in the oligodendroglial subtype. This study provides a detailed and clinically relevant insight into the in vivo metabolism of IDH1‐mutant gliomas and points to novel metabolic vulnerabilities in these tumors

Effects of temperature on thick branes and the fermion (quasi-)localization

Following Campos's work [Phys. Rev. Lett. 88, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Following Campos's work [Phys. Rev. Lett. \textbf{88}, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Sitter (AdS) thick branes in five-dimensional (5D) warped spacetime, and on the fermion (quasi-)localization. First, in the case of flat brane, when the critical temperature reaches, the solution of the background scalar field and the warp factor is not unique. So the thickness of the flat thick brane is uncertain at the critical value of the temperature parameter, which is found to be lower than the one in flat 5D spacetime. The mass spectra of the fermion Kaluza-Klein (KK) modes are continuous, and there is a series of fermion resonances. The number and lifetime of the resonances are finite and increase with the temperature parameter, but the mass of the resonances decreases with the temperature parameter. Second, in the case of dS brane, we do not find such a critical value of the temperature parameter. The mass spectra of the fermion KK modes are also continuous, and there is a series of fermion resonances. The effects of temperature on resonance number, lifetime, and mass are the same with the case of flat brane. Last, in the case of AdS brane, {the critical value of the temperature parameter can less or greater than the one in the flat 5D spacetime.} The spectra of fermion KK modes are discrete, and the mass of fermion KK modes does not decrease monotonically with increasing temperature parameter.Comment: 24 pages, 15 figures, published versio