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

Evidence for different accretion regimes in GRO J1008-57

We present a comprehensive spectral analysis of the BeXRB GRO J1008-57 over a luminosity range of three orders of magnitude using NuSTAR, Suzaku and RXTE data. We find significant evolution of the spectral parameters with luminosity. In particular the photon index hardens with increasing luminosity at intermediate luminosities between $10^{36}$ $-$ $10^{37}$ erg s$^{-1}$. This evolution is stable and repeatedly observed over different outbursts. However, at the extreme ends of the observed luminosity range, we find that the correlation breaks down, with a significance level of at least $3.7\sigma$. We conclude that these changes indicate transitions to different accretion regimes, which are characterized by different deceleration processes, such as Coulomb or radiation breaking. We compare our observed luminosity levels of these transitions to theoretical predications and discuss the variation of those theoretical luminosity values with fundamental neutron star parameters. Finally, we present detailed spectroscopy of the unique "triple peaked" outburst in 2014/15 which does not fit in the general parameter evolution with luminosity. The pulse profile on the other hand is consistent with what is expected at this luminosity level, arguing against a change in accretion geometry. In summary, GRO J1008-57 is an ideal target to study different accretion regimes due to the well constrained evolution of its broad-band spectral continuum over several orders of magnitude in luminosity.Comment: 13 pages, 7 figures, 3 tables. Accepted for publication in A&

Mixing Effects in the Crystallization of Supercooled Quantum Binary Liquids

By means of Raman spectroscopy of liquid microjets we have investigated the crystallization process of supercooled quantum liquid mixtures composed of parahydrogen (pH$_2$) diluted with small amounts of up to 5\% of either neon or orthodeuterium (oD$_2$), and of oD$_2$ diluted with either Ne or pH$_2$. We show that the introduction of Ne impurities affects the crystallization kinetics in both the pH$_2$-Ne and oD$_2$-Ne mixtures in terms of a significant reduction of the crystal growth rate, similarly to what found in our previous work on supercooled pH$_2$-oD$_2$ liquid mixtures [M. K\"uhnel et {\it al.}, Phys. Rev. B \textbf{89}, 180506(R) (2014)]. Our experimental results, in combination with path-integral simulations of the supercooled liquid mixtures, suggest in particular a correlation between the measured growth rates and the ratio of the effective particle sizes originating from quantum delocalization effects. We further show that the crystalline structure of the mixture is also affected to a large extent by the presence of the Ne impurities, which likely initiate the freezing process through the formation of Ne crystallites.Comment: 19 pages, 7 figures, submitted to J. Chem. Phy

Observation of crystallization slowdown in supercooled para-hydrogen and ortho-deuterium quantum liquid mixtures

We report a quantitative experimental study of the crystallization kinetics of supercooled quantum liquid mixtures of para-hydrogen (pH$_2$) and ortho-deuterium (oD$_2$) by high spatial resolution Raman spectroscopy of liquid microjets. We show that in a wide range of compositions the crystallization rate of the isotopic mixtures is significantly reduced with respect to that of the pure substances. To clarify this behavior we have performed path-integral simulations of the non-equilibrium pH$_2$-oD$_2$ liquid mixtures, revealing that differences in quantum delocalization between the two isotopic species translate into different effective particle sizes. Our results provide first experimental evidence for crystallization slowdown of quantum origin, offering a benchmark for theoretical studies of quantum behavior in supercooled liquids.Comment: 6 pages, 3 figure

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

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

Experiments on microjets of undercooled liquid hydrogen

28th International Symposium on Rarefied Gas Dynamics 2012 (2012). AIP Conf. Proc.; 9 pags. ; 7 figs. ; 1 tab. ; PACS: 67.63.Cd, 33.20.Fb, 64.60.My, 64.70.dg, 47.60.KzNovel experiments on liquid microjets (filaments) of hydrogen and deuterium, carried out at the Laboratory of Molecular Fluid Dynamics of the IEM, are reported. These filaments, less than 10 microns in diameter, are an ideal medium to produce highly undercooled liquid samples and to investigate the homogeneous solidification process, free from wall effects. The filaments exit from cryogenic capillary nozzles into a vacuum chamber, to cool down very fast by surface evaporation. Finite size radius leads to a temperature gradient across the filament, determined by thermal conductivity, and, possibly, to a velocity gradient as well. The filaments are monitored by laser shadowgraphy, and analyzed by means of high performance Raman spectroscopy. Real-time measurements in the rotational and vibrational spectral regions reveal the structure and temperature along the filaments, allowing to track the crystal growth process. The high spatial resolution of Raman spectroscopy allows observing in situ the structural changes of the liquid microjets, with a time resolution of ∼ 10 ns. The filaments of pure para-H2 can be cooled down to 9 K (65% of its melting point at 13.8 K), while staying liquid, before eventually solidifying into a metastable polymorph. Crystallization kinetics revealed a growth rate of 33 cm/s, much higher than expected for a thermally activated process. The time and spatial control attained in these experiments offers new opportunities for investigating the processes of nonequilibrium phase transformations in undercooled fluids, as well as the propagation of liquid jets into a rarefied gas media. © 2012 American Institute of PhysicsThis work has been supported by the the Spanish Ministerio de Ciencia e Innovacion, through grants FIS2007-61430, FIS2010-22064-C02-01, and HD2008-0068, by the Helmholtz Gemeinschaft, through grant VH-NG-331, and by the German academic exchange service (DAAD) under reference Nr. 50025171.Peer reviewe

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations