Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

simpcomp -- A GAP toolbox for simplicial complexes

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct new complexes from existing ones and an extensive library of triangulations of manifolds.Comment: 4 page

Topological Modes in Dual Lattice Models

Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four dimensions on a simplicial complex $K$. One finds that the dual theory, formulated on the dual block complex $\hat{K}$, contains topological modes which are in correspondence with the cohomology group $H^{2}(\hat{K},Z_{P})$, in addition to the usual dynamical link variables. This is a general phenomenon in all models with single plaquette based actions; the action of the dual theory becomes twisted with a field representing the above cohomology class. A similar observation is made about the dual version of the three dimensional Ising model. The importance of distinct topological sectors is confirmed numerically in the two dimensional Ising model where they are parameterized by $H^{1}(\hat{K},Z_{2})$.Comment: 10 pages, DIAS 94-3

Design Studies of an Electrostatic Storage Ring

Electrostatic storage rings combine a number of very interesting characteristics that make them an attractive tool in the low energy range. In contrast to magnetic rings, all of the fields in an electrostatic storage ring are completely mass independent. At the same particle energy and charge state, ions from light protons to heavy biomolecules can in principal be stored with identical field setups. A small ring for ions of energies up to 50 keV is planned to be built up at Goethe University in Frankfurt. Different designs have been calculated and the results are presented in this contribution. Furthermore, prototypes of the necessary optical elements have been manufactured and are described as well

Utility of plasma neurofilament light and total tau for clinical trials in Alzheimer's disease

INTRODUCTION: Several blood‐based biomarkers are associated with neuronal injury, but their utility in interventional clinical trials is unclear. This study retrospectively evaluated the utility of plasma neurofilament light (NfL) and total tau (t‐tau) in an 18‐month trial in mild Alzheimer's disease (AD). METHODS: Correlation and conditional independence analyses and Gaussian graphical models were used to investigate cross‐sectional and longitudinal relations between NfL, t‐tau, and clinical scales. RESULTS: NfL had a stronger association than t‐tau with clinical scales; t‐tau did not hold additional information to that given by NfL (P > 0.05 at all time points). NfL held independent information about shorter‐term (3‐ to 6‐month) progression beyond patient age and clinical scores. However, no meaningful gain in power was found when adjusting a longitudinal analysis of cognitive scores for baseline NfL. DISCUSSION: Plasma NfL is superior to t‐tau in mild AD. The ability of NfL to detect changes before clinical manifestations makes it a promising biomarker of drug response in trials of disease‐modifying drugs

Interatomic Coulombic Decay following Photoionization of the Helium Dimer: Observation of Vibrational Structure

Using synchrotron radiation we simultaneously ionize and excite one helium atom of a helium dimer (He_2) in a shakeup process. The populated states of the dimer ion (i.e. He^[*+](n = 2; 3)-He) are found to deexcite via interatomic coulombic decay. This leads to the emission of a second electron from the neutral site and a subsequent coulomb explosion. In this letter we present a measurement of the momenta of fragments that are created during this reaction. The electron energy distribution and the kinetic energy release of the two He^+ ions show pronounced oscillations which we attribute to the structure of the vibrational wave function of the dimer ion.Comment: 8 pages, 5 figure

Single photon double ionization of the helium dimer

We show that a single photon can ionize the two helium atoms of the helium dimer in a distance up to 10 {\deg}A. The energy sharing among the electrons, the angular distributions of the ions and electrons as well as comparison with electron impact data for helium atoms suggest a knock-off type double ionization process. The Coulomb explosion imaging of He_2 provides a direct view of the nuclear wave function of this by far most extended and most diffuse of all naturally existing molecules.Comment: 10 pages, 5 figure

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra