2,346 research outputs found
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
Parametric Analysis of Donor Activation for Glycosylation Reactions
The chemical synthesis of complex oligosaccharides relies on efficient and highly reproducible glycosylation reactions. The outcome of a glycosylation is contingent upon several environmental factors, such as temperature, acidity, the presence of residual moisture, as well as the steric, electronic, and conformational aspects of the reactants. Each glycosylation proceeds rapidly and with a high yield within a rather narrow temperature range. For better control over glycosylations and to ensure fast and reliable reactions, a systematic analysis of 18 glycosyl donors revealed the effect of reagent concentration, water content, protecting groups, and structure of the glycosyl donors on the activation temperature. With these insights, we parametrize the first step of the glycosylation reaction to be executed reliably and efficiently
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
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