A series of coverings of the regular n-gon

We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a regular n-gon for even n greater or equal to 8. These families give rise to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To appear in Geometriae Dedicata.

Direct calculation of the hard-sphere crystal/melt interfacial free energy

We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy, $\gamma$, for a system of hard spheres of diameter $\sigma$. The calculation is performed by thermodynamic integration along a reversible path defined by cleaving, using specially constructed movable hard-sphere walls, separate bulk crystal and fluid systems, which are then merged to form an interface. We find the interfacial free energy to be slightly anisotropic with $\gamma$ = 0.62$\pm 0.01$, 0.64$\pm 0.01$ and 0.58$\pm 0.01 k_BT/\sigma^2$ for the (100), (110) and (111) fcc crystal/fluid interfaces, respectively. These values are consistent with earlier density functional calculations and recent experiments measuring the crystal nucleation rates from colloidal fluids of polystyrene spheres that have been interpreted [Marr and Gast, Langmuir {\bf 10}, 1348 (1994)] to give an estimate of $\gamma$ for the hard-sphere system of $0.55 \pm 0.02 k_BT/\sigma^2$, slightly lower than the directly determined value reported here.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

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

A Search for Binary Active Galactic Nuclei: Double-Peaked [OIII] AGN in the Sloan Digital Sky Survey

We present AGN from the Sloan Digital Sky Survey (SDSS) having double-peaked profiles of [OIII] 5007,4959 and other narrow emission-lines, motivated by the prospect of finding candidate binary AGN. These objects were identified by means of a visual examination of 21,592 quasars at z < 0.7 in SDSS Data Release 7 (DR7). Of the spectra with adequate signal-to-noise, 148 spectra exhibit a double-peaked [OIII] profile. Of these, 86 are Type 1 AGN and 62 are Type 2 AGN. Only two give the appearance of possibly being optically resolved double AGN in the SDSS images, but many show close companions or signs of recent interaction. Radio-detected quasars are three times more likely to exhibit a double-peaked [OIII] profile than quasars with no detected radio flux, suggesting a role for jet interactions in producing the double-peaked profiles. Of the 66 broad line (Type 1) AGN that are undetected in the FIRST survey, 0.9% show double peaked [OIII] profiles. We discuss statistical tests of the nature of the double-peaked objects. Further study is needed to determine which of them are binary AGN rather than disturbed narrow line regions, and how many additional binaries may remain undetected because of insufficient line-of-sight velocity splitting. Previous studies indicate that 0.1% of SDSS quasars are spatially resolved binaries, with typical spacings of ~10 to 100 kpc. If a substantial fraction of the double-peaked objects are indeed binaries, then our results imply that binaries occur more frequently at smaller separations (< 10 kpc). This suggests that simultaneous fueling of both black holes is more common as the binary orbit decays through these spacings.Comment: 33 pages, 5 figures, LaTeX. Major revisions. Accepted for publication in ApJ

New Method for Phase transitions in diblock copolymers: The Lamellar case

A new mean-field type theory is proposed to study order-disorder transitions (ODT) in block copolymers. The theory applies to both the weak segregation (WS) and the strong segregation (SS) regimes. A new energy functional is proposed without appealing to the random phase approximation (RPA). We find new terms unaccounted for within RPA. We work out in detail transitions to the lamellar state and compare the method to other existing theories of ODT and numerical simulations. We find good agreements with recent experimental results and predict that the intermediate segregation regime may have more than one scaling behavior.Comment: 23 pages, 8 figure

The lower and upper bound problems for cubical polytopes

We construct a family of cubical polytypes which shows that the upper bound on the number of facets of a cubical polytope (given a fixed number of vertices) is higher than previously suspected. We also formulate a lower bound conjecture for cubical polytopes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41359/1/454_2005_Article_BF02189315.pd

Poliomyelitis in Intraspinally Inoculated Poliovirus Receptor Transgenic Mice

AbstractMice transgenic with the human poliovirus receptor gene develop clinical signs and neuropathology similar to those of human poliomyelitis when neurovirulent polioviruses are inoculated into the central nervous system (CNS). Factors contributing to disease severity and the frequencies of paralysis and mortality include the poliovirus strain, dose, and gender of the mouse inoculated. The more neurovirulent the virus, as defined by monkey challenge results, the higher the rate of paralysis, mortality, and severity of disease. Also, the time to disease onset is shorter for more neurovirulent viruses. Male mice are more susceptible to polioviruses than females. TGM-PRG-3 mice have a 10-fold higher transgene copy number and produce 3-fold more receptor RNA and protein levels in the CNS than TGM-PRG-1 mice. CNS inoculations with type III polioviruses differing in relative neurovirulence show that these mouse lines are similar in disease frequency and severity, demonstrating that differences in receptor gene dosage and concomitant receptor abundance do not affect susceptibility to infection. However, there is a difference in the rate of accumulation of clinical signs. The time to onset of disease is shorter for TGM-PRG-3 than TGM-PRG-1 mice. Thus, receptor dosage affects the rate of appearance of poliomyelitis in these mice

Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

Square-tiled cyclic covers

A cyclic cover of the complex projective line branched at four appropriate points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding Teichm\"uller curve, and compute the Lyapunov exponents of the determinant bundle over the Teichm\"uller curve with respect to the geodesic flow. This paper includes a new example (announced by G. Forni and C. Matheus in \cite{Forni:Matheus}) of a Teichm\"uller curve of a square-tiled cyclic cover in a stratum of Abelian differentials in genus four with a maximally degenerate Kontsevich--Zorich spectrum (the only known example found previously by Forni in genus three also corresponds to a square-tiled cyclic cover \cite{ForniSurvey}). We present several new examples of Teichm\"uller curves in strata of holomorphic and meromorphic quadratic differentials with maximally degenerate Kontsevich--Zorich spectrum. Presumably, these examples cover all possible Teichm\"uller curves with maximally degenerate spectrum. We prove that this is indeed the case within the class of square-tiled cyclic covers.Comment: 34 pages, 6 figures. Final version incorporating referees comments. In particular, a gap in the previous version was corrected. This file uses the journal's class file (jmd.cls), so that it is very similar to published versio