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

Large-Scale Suppression from Stochastic Inflation

We show non-perturbatively that the power spectrum of a self-interacting scalar field in de Sitter space-time is strongly suppressed on large scales. The cut-off scale depends on the strength of the self-coupling, the number of e-folds of quasi-de Sitter evolution, and its expansion rate. As a consequence, the two-point correlation function of field fluctuations is free from infra-red divergencies.Comment: 4 pages, 1 figure; v2 minor changes to match published PRL versio

Stochastic Inflation and Replica Field Theory

We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on the shape of the filter that separates long from short wavelength modes. While for filters with infinite support the phenomenon of dimensional reductions is found on large super-horizon scales, filters with compact support return a scale-invariant power spectrum in the infra-red. Features of the power spectrum, induced by the filter, decay within a few e-foldings. Thus the late-time power spectrum is independent of the filter details.Comment: 15 pages, 14 figure

Production of bio resin from palm oil

Nowadays, the demand for fossil fuels is quite high. But, the extensive use of fossil fuels is causing the gradual decrease of fossil fuels. Therefore, a way to get rid of widespread of using fossil fuels is by developing a new renewable source that can benefit our environment. Resin is one of the important polymeric in the chemical industry. Resins such as alkyd resins are widely used in coatings and paint industry. There are many researches about producing a resin from renewable sources such as vegetable oils. The naturally used vegetable oils in producing resin are soyabean, rapeseed, coconut, castor or linseed oils. Other than that, there are many potential vegetable oils such as karawila, nahar, rubber or safflower oil. Scientist and engineers are dedicated to find another alternative to replace using fossil fuels as the main components in resin making. This study was inspired to do a research by using palm oil as the main components in making renewable resin or bio resin. In this study, waste cooking oil was used as the main component in making bio resin. The synthesis of resin begins with alcoholysis of waste cooking oil with glycerol followed by esterification process. Then, the monoglyceride was reacted with anhydride to obtain bio resin. The resulting product which is bio resin was characterized for physiochemical properties, thermogravimetric analysis (TGA), the infrared spectrum using Fourier Transform Infrared Spectroscopy (FTIR), melting point using Differential Scanning Calorimeter (DSC). The result was compared with previous literature about producing resin from renewable material such as karawila seed oil. The expected resin is feasible in replacing synthetic resin. Thus, improvements and more research need to be made as to market the resin

The neuroscience of face processing and identification in eyewitnesses and offenders

Werner N-S, Kühnel S, Markowitsch HJ. The neuroscience of face processing and identification in eyewitnesses and offenders. Frontiers in Behavioral Neuroscience. 2013;7: 189.Humans are experts in face perception. We are better able to distinguish between the differences of faces and their components than between any other kind of objects. Several studies investigating the underlying neural networks provided evidence for deviated face processing in criminal individuals, although results are often confounded by accompanying mental or addiction disorders. On the other hand, face processing in non-criminal healthy persons can be of high juridical interest in cases of witnessing a felony and afterward identifying a culprit. Memory and therefore recognition of a person can be affected by many parameters and thus become distorted. But also face processing itself is modulated by different factors like facial characteristics, degree of familiarity, and emotional relation. These factors make the comparison of different cases, as well as the transfer of laboratory results to real live settings very challenging. Several neuroimaging studies have been published in recent years and some progress was made connecting certain brain activation patterns with the correct recognition of an individual. However, there is still a long way to go before brain imaging can make a reliable contribution to court procedures

Combinatorial 3-manifolds with transitive cyclic symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 201

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

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

Simulation of cyclotron resonant scattering features: The effect of bulk velocity

X-ray binary systems consisting of a mass donating optical star and a highly magnetized neutron star, under the right circumstances, show quantum mechanical absorption features in the observed spectra called cyclotron resonant scattering features (CRSFs). We have developed a simulation to model CRSFs using Monte Carlo methods. We calculate Green's tables which can be used to imprint CRSFs to arbitrary X-ray continua. Our simulation keeps track of scattering parameters of individual photons, extends the number of variable parameters of previous works, and allows for more flexible geometries. Here we focus on the influence of bulk velocity of the accreted matter on the CRSF line shapes and positions