2,808 research outputs found
The number of graphs and a random graph with a given degree sequence
We consider the set of all graphs on n labeled vertices with prescribed degrees D = ( d 1 ,…, d n ). For a wide class of tame degree sequences D we obtain a computationally efficient asymptotic formula approximating the number of graphs within a relative error which approaches 0 as n grows. As a corollary, we prove that the structure of a random graph with a given tame degree sequence D is well described by a certain maximum entropy matrix computed from D . We also establish an asymptotic formula for the number of bipartite graphs with prescribed degrees of vertices, or, equivalently, for the number of 0‐1 matrices with prescribed row and column sums. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97179/1/20409_ftp.pd
Strain-aware assembly of genomes from mixed samples using flow variation graphs
The goal of strain-aware genome assembly is to reconstruct all individual haplotypes from a mixed sample at the strain level and to provide abundance estimates for the strains
Linguistic DNA: Investigating Conceptual Change in Early Modern English Discourse
This article describes the background and premises of the AHRC-funded project, ‘The Linguistic DNA of Modern Western Thought’. We offer an empirical, encyclopaedic approach to historical semantics regarding ‘conceptual history’, i.e. the history of concepts that shape thought, culture and society in a particular period. We relate the project to traditional work in conceptual and semantic history and define our object of study as the discursive concept, a category of meaning encoded linguistically as a cluster of expressions that co-occur in discourse. We describe our principal data source, EEBO-TCP, and introduce our key research interests, namely, the contexts of conceptual change, the semantic structure of lexical fields and the nature of lexicalisation pressure. We outline our computational processes, which build upon the theoretical definition of discursive concepts, to discover the linguistically encoded forms underpinning the discursive concepts we seek to identify in EEBO-TCP. Finally, we share preliminary results via a worked example, exploring the discursive contexts in which paradigmatic terms of key cultural concepts emerge. We consider the extent to which particular genres, discourses and users in the early modern period make paradigms, and examine the extent to which these contexts determine the characteristics of key concepts
Counter-propagating entangled photons from a waveguide with periodic nonlinearity
The conditions required for spontaneous parametric down-conversion in a
waveguide with periodic nonlinearity in the presence of an unguided pump field
are established. Control of the periodic nonlinearity and the physical
properties of the waveguide permits the quasi-phase matching equations that
describe counter-propagating guided signal and idler beams to be satisfied. We
compare the tuning curves and spectral properties of such counter-propagating
beams to those for co-propagating beams under typical experimental conditions.
We find that the counter-propagating beams exhibit narrow bandwidth permitting
the generation of quantum states that possess discrete-frequency entanglement.
Such states may be useful for experiments in quantum optics and technologies
that benefit from frequency entanglement.Comment: submitted to Phys. Rev.
Bethe Ansatz Equations for General Orbifolds of N=4 SYM
We consider the Bethe Ansatz Equations for orbifolds of N =4 SYM w.r.t. an
arbitrary discrete group. Techniques used for the Abelian orbifolds can be
extended to the generic non-Abelian case with minor modifications. We show how
to make a transition between the different notations in the quiver gauge
theory.Comment: LaTeX, 66 pages, 9 eps figures, minor corrections, references adde
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
Mechanically induced current and quantum evaporation from Luttinger liquids
We investigate transport through a tunnelling junction between an
uncorrelated metallic lead and a Luttinger liquid when the latter is subjected
to a time dependent perturbation. The tunnelling current as well as the
electron energy distribution function are found to be strongly affected by the
perturbation due to generation of harmonics in the density oscillations. Using
a semiconducting lead instead of a metallic one results in electrons being
injected into the lead even without applied voltage. Some applications to
carbon nanotubes are discussed.Comment: 7 pages, 2 figures (eps files
The Dynamics of Small Instanton Phase Transitions
The small instanton transition of a five-brane colliding with one end of the
S1/Z2 interval in heterotic M-theory is discussed, with emphasis on the
transition moduli, their potential function and the associated non-perturbative
superpotential. Using numerical methods, the equations of motion of these
moduli coupled to an expanding Friedmann-Robertson-Walker spacetime are solved
including non-perturbative interactions. It is shown that the five-brane
collides with the end of the interval at a small instanton. However, the moduli
then continue to evolve to an isolated minimum of the potential, where they are
trapped by gravitational damping. The torsion free sheaf at the small instanton
is ``smoothed out'' into a vector bundle at the isolated minimum, thus
dynamically completing the small instanton phase transition. Radiative damping
at the origin of moduli space is discussed and shown to be insufficient to trap
the moduli at the small instanton point.Comment: LaTeX, 23 pages, 7 figures; minor corrections, references adde
Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses
A huge number of independent true ground-state configurations is calculated
for two-, three- and four-dimensional +- J spin-glass models. Using the genetic
cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are
treated. A ``ballistic-search'' algorithm is applied which allows even for
large system sizes to identify clusters of ground states which are connected by
chains of zero-energy flips of spins. The number of clusters n_C diverges with
N going to infinity. For all dimensions considered here, an exponential
increase of n_C appears to be more likely than a growth with a power of N. The
number of different ground states is found to grow clearly exponentially with
N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B
(3d) respectively s_0=0.027(5)k_B (4d) is obtained.Comment: large extensions, now 12 pages, 9 figures, 27 reference
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