2,602 research outputs found
I Do Know Your Tongue : The Shakespeare Editions of William Rolfe and H. H. Furness as American Cultural Signifiers
Simpler, faster and shorter labels for distances in graphs
We consider how to assign labels to any undirected graph with n nodes such
that, given the labels of two nodes and no other information regarding the
graph, it is possible to determine the distance between the two nodes. The
challenge in such a distance labeling scheme is primarily to minimize the
maximum label lenght and secondarily to minimize the time needed to answer
distance queries (decoding). Previous schemes have offered different trade-offs
between label lengths and query time. This paper presents a simple algorithm
with shorter labels and shorter query time than any previous solution, thereby
improving the state-of-the-art with respect to both label length and query time
in one single algorithm. Our solution addresses several open problems
concerning label length and decoding time and is the first improvement of label
length for more than three decades.
More specifically, we present a distance labeling scheme with label size (log
3)/2 + o(n) (logarithms are in base 2) and O(1) decoding time. This outperforms
all existing results with respect to both size and decoding time, including
Winkler's (Combinatorica 1983) decade-old result, which uses labels of size
(log 3)n and O(n/log n) decoding time, and Gavoille et al. (SODA'01), which
uses labels of size 11n + o(n) and O(loglog n) decoding time. In addition, our
algorithm is simpler than the previous ones. In the case of integral edge
weights of size at most W, we present almost matching upper and lower bounds
for label sizes. For r-additive approximation schemes, where distances can be
off by an additive constant r, we give both upper and lower bounds. In
particular, we present an upper bound for 1-additive approximation schemes
which, in the unweighted case, has the same size (ignoring second order terms)
as an adjacency scheme: n/2. We also give results for bipartite graphs and for
exact and 1-additive distance oracles
Bubbles in graphene - a computational study
Strain-induced deformations in graphene are predicted to give rise to large
pseudomagnetic fields. We examine theoretically the case of gas-inflated
bubbles to determine whether signatures of such fields are present in the local
density of states. Sharp-edged bubbles are found to induce Friedel-type
oscillations which can envelope pseudo-Landau level features in certain regions
of the bubble. However, bubbles which minimise interference effects are also
unsuitable for pseudo-Landau level formation due to more spatially varying
field profiles.Comment: Submitted to Edison1
Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
We present a numerically efficient technique to evaluate the Green's function
for extended two dimensional systems without relying on periodic boundary
conditions. Different regions of interest, or `patches', are connected using
self energy terms which encode the information of the extended parts of the
system. The calculation scheme uses a combination of analytic expressions for
the Green's function of infinite pristine systems and an adaptive recursive
Green's function technique for the patches. The method allows for an efficient
calculation of both local electronic and transport properties, as well as the
inclusion of multiple probes in arbitrary geometries embedded in extended
samples. We apply the Patched Green's function method to evaluate the local
densities of states and transmission properties of graphene systems with two
kinds of deviations from the pristine structure: bubbles and perforations with
characteristic dimensions of the order of 10-25 nm, i.e. including hundreds of
thousands of atoms. The strain field induced by a bubble is treated beyond an
effective Dirac model, and we demonstrate the existence of both Friedel-type
oscillations arising from the edges of the bubble, as well as pseudo-Landau
levels related to the pseudomagnetic field induced by the nonuniform strain.
Secondly, we compute the transport properties of a large perforation with
atomic positions extracted from a TEM image, and show that current vortices may
form near the zigzag segments of the perforation
Dissipation in monotonic and non-monotonic relaxation to equilibrium
Using molecular dynamics simulations, we study field free relaxation from a non-uniform initial density, monitored using both density distributions and the dissipation function. When this density gradient is applied to colour labelled particles, the density distribution decays to a sine curve of fundamental wavelength, which then decays conformally towards a uniform distribution. For conformal relaxation, the dissipation function is found to decay towards equilibrium monotonically, consistent with the predictions of the relaxation theorem. When the system is initiated with a more dramatic density gradient, applied to all particles, non-conformal relaxation is seen in both the dissipation function and the Fourier components of the density distribution. At times, the system appears to be moving away from a uniform density distribution. In both cases, the dissipation function satisfies the modified second law inequality, and the dissipation theorem is demonstrated
Next-Generation Sequencing in Equine Genomics
Next-generation sequencing of both DNA and RNA represents a second revolution in equine genetics following publication of the equine genome sequence. Technological advancements have resulted in a wide selection of next-generation sequencing platforms capable of completing small targeted experiments or resequencing complete genomes. DNA and RNA sequencing have applications in clinical and research environments. Standards for the validation and sharing of next-generation sequencing data are critical for the widespread application of the technology and applications discussed herein. As researchers and clinicians develop a better understanding of how genetic variation and phenotypic variation are linked, next-generation sequencing could help pave the way to personalized and precision management of horses
The instantaneous fluctuation theorem
We give a derivation of a new instantaneous fluctuation relation for an arbitrary phase function which is odd under time reversal. The form of this new relation is not obvious, and involves observing the system along its transient phase space trajectory both before and after the point in time at which the fluctuations are being compared. We demonstrate this relation computationally for a number of phase functions in a shear flow system and show that this non-locality in time is an essential component of the instantaneous fluctuation theorem
CARTAM : the Cartesian Access Method for Data Structures with n-Dimensional Keys
The Cartesian Access Method (CARTAM) is a data
structure and its attendant access program designed to
provide rapid retrievals from a data file based upon
multi-dimensional keys: for example, using earth surface points
defined by latitude and longitude, retrieve all points
within x nautical miles. This thesis describes that data
structure and program in detail and provides the actual
routines as implemented on the International Business
Machine (IBM) System/370 series of computers. The search
technique is analogous to the binary search for a linear
sorted file and seems to run in O(log(N)) time. An
indication of the performance is the extraction, in less
than 25 milliseconds CPU time on an IBM 370, Model 3033, of
all points within a 10,000-foot circle from a geographic
data base containing approximately 100,000 basic records
Dual-probe spectroscopic fingerprints of defects in graphene
Recent advances in experimental techniques emphasize the usefulness of
multiple scanning probe techniques when analyzing nanoscale samples. Here, we
analyze theoretically dual-probe setups with probe separations in the nanometer
range, i.e., in a regime where quantum coherence effects can be observed at low
temperatures. In a dual-probe setup the electrons are injected at one probe and
collected at the other. The measured conductance reflects the local transport
properties on the nanoscale, thereby yielding information complementary to that
obtained with a standard one-probe setup (the local density-of-states). In this
work we develop a real space Green's function method to compute the
conductance. This requires an extension of the standard calculation schemes,
which typically address a finite sample between the probes. In contrast, the
developed method makes no assumption on the sample size (e.g., an extended
graphene sheet). Applying this method, we study the transport anisotropies in
pristine graphene sheets, and analyze the spectroscopic fingerprints arising
from quantum interference around single-site defects, such as vacancies and
adatoms. Furthermore, we demonstrate that the dual-probe setup is a useful tool
for characterizing the electronic transport properties of extended defects or
designed nanostructures. In particular, we show that nanoscale perforations, or
antidots, in a graphene sheet display Fano-type resonances with a strong
dependence on the edge geometry of the perforation
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