Viterbi Sequences and Polytopes

A Viterbi path of length n of a discrete Markov chain is a sequence of n+1 states that has the greatest probability of ocurring in the Markov chain. We divide the space of all Markov chains into Viterbi regions in which two Markov chains are in the same region if they have the same set of Viterbi paths. The Viterbi paths of regions of positive measure are called Viterbi sequences. Our main results are (1) each Viterbi sequence can be divided into a prefix, periodic interior, and suffix, and (2) as n increases to infinity (and the number of states remains fixed), the number of Viterbi regions remains bounded. The Viterbi regions correspond to the vertices of a Newton polytope of a polynomial whose terms are the probabilities of sequences of length n. We characterize Viterbi sequences and polytopes for two- and three-state Markov chains.Comment: 15 pages, 2 figures, to appear in Journal of Symbolic Computatio

Applications of Graphical Condensation for Enumerating Matchings and Tilings

A technique called graphical condensation is used to prove various combinatorial identities among numbers of (perfect) matchings of planar bipartite graphs and tilings of regions. Graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph, and then re-partitioning the united matching (actually a multigraph) into matchings of two other subgraphs, in one of two possible ways. This technique can be used to enumerate perfect matchings of a wide variety of bipartite planar graphs. Applications include domino tilings of Aztec diamonds and rectangles, diabolo tilings of fortresses, plane partitions, and transpose complement plane partitions.Comment: 25 pages; 21 figures Corrected typos; Updated references; Some text revised, but content essentially the sam

Mechanical and Combustion Performance of Multi-Walled Carbon Nanotubes as an Additive to Paraffin-Based Solid Fuels for Hybrid Rockets

Paraffin-based solid fuels for hybrid rocket motor applications are recognized as a fastburning alternative to other fuel binders such as HTPB, but efforts to further improve the burning rate and mechanical properties of paraffin are still necessary. One approach that is considered in this study is to use multi-walled carbon nanotubes (MWNT) as an additive to paraffin wax. Carbon nanotubes provide increased electrical and thermal conductivity to the solid-fuel grains to which they are added, which can improve the mass burning rate. Furthermore, the addition of ultra-fine aluminum particles to the paraffin/MWNT fuel grains can enhance regression rate of the solid fuel and the density impulse of the hybrid rocket. The multi-walled carbon nanotubes also present the possibility of greatly improving the mechanical properties (e.g., tensile strength) of the paraffin-based solid-fuel grains. For casting these solid-fuel grains, various percentages of MWNT and aluminum particles will be added to the paraffin wax. Previous work has been published about the dispersion and mixing of carbon nanotubes.1 Another manufacturing method has been used for mixing the MWNT with a phenolic resin for ablative applications, and the manufacturing and mixing processes are well-documented in the literature.2 The cost of MWNT is a small fraction of single-walled nanotubes. This is a scale-up advantage as future applications and projects will require low cost additives to maintain cost effectiveness. Testing of the solid-fuel grains will be conducted in several steps. Dog bone samples will be cast and prepared for tensile testing. The fuel samples will also be analyzed using thermogravimetric analysis and a high-resolution scanning electron microscope (SEM). The SEM will allow for examination of the solid fuel grain for uniformity and consistency. The paraffin-based fuel grains will also be tested using two hybrid rocket test motors located at the Pennsylvania State University s High Pressure Combustion Lab

High Current Density and Low Thermal Conductivity of Atomically Thin Semimetallic WTe2

Two-dimensional (2D) semimetals beyond graphene have been relatively unexplored in the atomically-thin limit. Here we introduce a facile growth mechanism for semimetallic WTe2 crystals, then fabricate few-layer test structures while carefully avoiding degradation from exposure to air. Low-field electrical measurements of 80 nm to 2 um long devices allow us to separate intrinsic and contact resistance, revealing metallic response in the thinnest encapsulated and stable WTe2 devices studied to date (3 to 20 layers thick). High-field electrical measurements and electro-thermal modeling demonstrate that ultra-thin WTe2 can carry remarkably high current density (approaching 50 MA/cm2, higher than most common interconnect metals) despite a very low thermal conductivity (of the order ~3 W/m/K). These results suggest several pathways for air-stable technological viability of this layered semimetal

Formulation, Casting, and Evaluation of Paraffin-Based Solid Fuels Containing Energetic and Novel Additives for Hybrid Rockets

This investigation studied the inclusion of various additives to paraffin wax for use in a hybrid rocket motor. Some of the paraffin-based fuels were doped with various percentages of LiAlH4 (up to 10%). Addition of LiAlH4 at 10% was found to increase regression rates between 7 - 10% over baseline paraffin through tests in a gaseous oxygen hybrid rocket motor. Mass burn rates for paraffin grains with 10% LiAlH4 were also higher than those of the baseline paraffin. RDX was also cast into a paraffin sample via a novel casting process which involved dissolving RDX into dimethylformamide (DMF) solvent and then drawing a vacuum on the mixture of paraffin and RDX/DMF in order to evaporate out the DMF. It was found that although all DMF was removed, the process was not conducive to generating small RDX particles. The slow boiling generated an inhomogeneous mixture of paraffin and RDX. It is likely that superheating the DMF to cause rapid boiling would likely reduce RDX particle sizes. In addition to paraffin/LiAlH4 grains, multi-walled carbon nanotubes (MWNT) were cast in paraffin for testing in a hybrid rocket motor, and assorted samples containing a range of MWNT percentages in paraffin were imaged using SEM. The fuel samples showed good distribution of MWNT in the paraffin matrix, but the MWNT were often agglomerated, indicating that a change to the sonication and mixing processes were required to achieve better uniformity and debundled MWNT. Fuel grains with MWNT fuel grains had slightly lower regression rate, likely due to the increased thermal conductivity to the fuel subsurface, reducing the burning surface temperature

Crystallographic and Functional Analysis of the ESCRT-I /HIV-1 Gag PTAP Interaction

SummaryBudding of HIV-1 requires the binding of the PTAP late domain of the Gag p6 protein to the UEV domain of the TSG101 subunit of ESCRT-I. The normal function of this motif in cells is in receptor downregulation. Here, we report the 1.4–1.6 Å structures of the human TSG101 UEV domain alone and with wild-type and mutant HIV-1 PTAP and Hrs PSAP nonapeptides. The hydroxyl of the Thr or Ser residue in the P(S/T)AP motif hydrogen bonds with the main chain of Asn69. Mutation of the Asn to Pro, blocking the main-chain amide, abrogates PTAP motif binding in vitro and blocks budding of HIV-1 from cells. N69P and other PTAP binding-deficient alleles of TSG101 did not rescue HIV-1 budding. However, the mutant alleles did rescue downregulation of endogenous EGF receptor. This demonstrates that the PSAP motif is not rate determining in EGF receptor downregulation under normal conditions

CMB polarimetry with BICEP: instrument characterization, calibration, and performance

BICEP is a ground-based millimeter-wave bolometric array designed to target the primordial gravity wave signature on the polarization of the cosmic microwave background (CMB) at degree angular scales. Currently in its third year of operation at the South Pole, BICEP is measuring the CMB polarization with unprecedented sensitivity at 100 and 150 GHz in the cleanest available 2% of the sky, as well as deriving independent constraints on the diffuse polarized foregrounds with select observations on and off the Galactic plane. Instrument calibrations are discussed in the context of rigorous control of systematic errors, and the performance during the first two years of the experiment is reviewed.Comment: 12 pages, 15 figures, updated version of a paper accepted for Millimeter and Submillimeter Detectors and Instrumentation for Astronomy IV, Proceedings of SPIE, 7020, 200

Absolute polarization angle calibration using polarized diffuse Galactic emission observed by BICEP

We present a method of cross-calibrating the polarization angle of a polarimeter using BICEP Galactic observations. \bicep\ was a ground based experiment using an array of 49 pairs of polarization sensitive bolometers observing from the geographic South Pole at 100 and 150 GHz. The BICEP polarimeter is calibrated to +/-0.01 in cross-polarization and less than +/-0.7 degrees in absolute polarization orientation. BICEP observed the temperature and polarization of the Galactic plane (R.A= 100 degrees ~ 270 degrees and Dec. = -67 degrees ~ -48 degrees). We show that the statistical error in the 100 GHz BICEP Galaxy map can constrain the polarization angle offset of WMAP Wband to 0.6 degrees +\- 1.4 degrees. The expected 1 sigma errors on the polarization angle cross-calibration for Planck or EPIC are 1.3 degrees and 0.3 degrees at 100 and 150 GHz, respectively. We also discuss the expected improvement of the BICEP Galactic field observations with forthcoming BICEP2 and Keck observations.Comment: 13 pages, 10 figures and 2 tables. To appear in Proceedings of SPIE Astronomical Telescopes and Instrumentation 201

The Atacama Cosmology Telescope: Extragalactic Sources at 148 GHz in the 2008 Survey

We report on extragalactic sources detected in a 455 square-degree map of the southern sky made with data at a frequency of 148 GHz from the Atacama Cosmology Telescope 2008 observing season. We provide a catalog of 157 sources with flux densities spanning two orders of magnitude: from 15 to 1500 mJy. Comparison to other catalogs shows that 98% of the ACT detections correspond to sources detected at lower radio frequencies. Three of the sources appear to be associated with the brightest cluster galaxies of low redshift X-ray selected galaxy clusters. Estimates of the radio to mm-wave spectral indices and differential counts of the sources further bolster the hypothesis that they are nearly all radio sources, and that their emission is not dominated by re-emission from warm dust. In a bright (>50 mJy) 148 GHz-selected sample with complete cross-identifications from the Australia Telescope 20 GHz survey, we observe an average steepening of the spectra between 5, 20, and 148 GHz with median spectral indices of $\alpha_{\rm 5-20} = -0.07 \pm 0.06$, $\alpha_{\rm 20-148} = -0.39 \pm0.04$, and $\alpha_{\rm 5-148} = -0.20 \pm 0.03$. When the measured spectral indices are taken into account, the 148 GHz differential source counts are consistent with previous measurements at 30 GHz in the context of a source count model dominated by radio sources. Extrapolating with an appropriately rescaled model for the radio source counts, the Poisson contribution to the spatial power spectrum from synchrotron-dominated sources with flux density less than 20 mJy is C^{\rm Sync} = (2.8 \pm 0.3) \times 10^{-6} \micro\kelvin^2.Comment: Accepted to Ap