18,660 research outputs found
Combinatorial Alexander Duality -- a Short and Elementary Proof
Let X be a simplicial complex with the ground set V. Define its Alexander
dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The
combinatorial Alexander duality states that the i-th reduced homology group of
X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a
given commutative ring R). We give a self-contained proof.Comment: 7 pages, 2 figure; v3: the sign function was simplifie
Rehybridization of electronic structure in compressed two-dimensional quantum dot superlattices
Two-dimensional superlattices of organically passivated 2.6-nm silver quantum dots were prepared as Langmuir monolayers and transferred to highly oriented pyrolytic graphite substrates. The structural and electronic properties of the films were probed with variable temperature scanning tunneling microscopy. Particles passivated with decanethiol (interparticle separation distance of ∼1.1±0.2 nm) exhibited Coulomb blockade and staircase. For particles passivated with hexanethiol or pentanethiol (interparticle separation distance of ∼0.5±0.2 nm), the single-electron charging was quenched, and the redistribution of the density of states revealed that strong quantum mechanical exchange, i.e., wave-function hybridization, existed among the particles in these films
Ceramics for engines
The NASA Lewis Research Center's Ceramic Technology Program is focused on aerospace propulsion and power needs. Thus, emphasis is on high-temperature ceramics and their structural and environmental durability and reliability. The program is interdisciplinary in nature with major emphasis on materials and processing, but with significant efforts in design methodology and life prediction
Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies
The Ebola virus is spreading throughout West Africa and is causing thousands
of deaths. In order to quantify the effectiveness of different strategies for
controlling the spread, we develop a mathematical model in which the
propagation of the Ebola virus through Liberia is caused by travel between
counties. For the initial months in which the Ebola virus spreads, we find that
the arrival times of the disease into the counties predicted by our model are
compatible with World Health Organization data, but we also find that reducing
mobility is insufficient to contain the epidemic because it delays the arrival
of Ebola virus in each county by only a few weeks. We study the effect of a
strategy in which safe burials are increased and effective hospitalisation
instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii)
one in mid-August---which was the actual time that strong interventions began
in Liberia. We find that if scenario (i) had been pursued the lifetime of the
epidemic would have been three months shorter and the total number of infected
individuals 80\% less than in scenario (ii). Our projection under scenario (ii)
is that the spreading will stop by mid-spring 2015
Ceramics for engines
Structural ceramics were under nearly continuous development for various heat engine applications since the early 1970s. These efforts were sustained by the properties that ceramics offer in the areas of high-temperature strength, environmental resistance, and low density and the large benefits in system efficiency and performance that can result. The promise of ceramics was not realized because their brittle nature results in high sensitivity to microscopic flaws and catastrophic fracture behavior. This translated into low reliability for ceramic components and thus limited their application in engines. For structural ceramics to successfully make inroads into the terrestrial heat engine market requires further advances in low cost, net shape fabrication of high reliability components, and improvements in properties such as toughness, and strength. These advances will lead to very limited use of ceramics in noncritical applications in aerospace engines. For critical aerospace applications, an additional requirement is that the components display markedly improved toughness and noncatastrophic or graceful fracture. Thus the major emphasis is on fiber-reinforced ceramics
Magnetic structure and phase diagram in a spin-chain system: CaCoO
The low-temperature structure of the frustrated spin-chain compound
CaCoO is determined by the ground state of the 2D Ising model on
the triangular lattice. At high-temperatures it transforms to the honeycomb
magnetic structure. It is shown that the crossover between the two magnetic
structures at 12 K arises from the entropy accumulated in the disordered
chains. This interpretation is in an agreement with the experimental data.
General rules for for the phase diagram of frustrated Ising chain compounds are
formulated.Comment: 4 pages, 2 figure
Parking functions, labeled trees and DCJ sorting scenarios
In genome rearrangement theory, one of the elusive questions raised in recent
years is the enumeration of rearrangement scenarios between two genomes. This
problem is related to the uniform generation of rearrangement scenarios, and
the derivation of tests of statistical significance of the properties of these
scenarios. Here we give an exact formula for the number of double-cut-and-join
(DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective
bijections between the set of scenarios that sort a cycle and well studied
combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure
Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies
The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August—which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015.H.E.S. thanks the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. L.D.V. and L.A.B. wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio
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