4,538 research outputs found
Constructive Relationships Between Algebraic Thickness and Normality
We study the relationship between two measures of Boolean functions;
\emph{algebraic thickness} and \emph{normality}. For a function , the
algebraic thickness is a variant of the \emph{sparsity}, the number of nonzero
coefficients in the unique GF(2) polynomial representing , and the normality
is the largest dimension of an affine subspace on which is constant. We
show that for , any function with algebraic thickness
is constant on some affine subspace of dimension
. Furthermore, we give an algorithm
for finding such a subspace. We show that this is at most a factor of
from the best guaranteed, and when restricted to the
technique used, is at most a factor of from the best
guaranteed. We also show that a concrete function, majority, has algebraic
thickness .Comment: Final version published in FCT'201
Parameterized Edge Hamiltonicity
We study the parameterized complexity of the classical Edge Hamiltonian Path
problem and give several fixed-parameter tractability results. First, we settle
an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT
parameterized by vertex cover, and that it also admits a cubic kernel. We then
show fixed-parameter tractability even for a generalization of the problem to
arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set.
We also consider the problem parameterized by treewidth or clique-width.
Surprisingly, we show that the problem is FPT for both of these standard
parameters, in contrast to its vertex version, which is W-hard for
clique-width. Our technique, which may be of independent interest, relies on a
structural characterization of clique-width in terms of treewidth and complete
bipartite subgraphs due to Gurski and Wanke
Flow diagram of the metal-insulator transition in two dimensions
The discovery of the metal-insulator transition (MIT) in two-dimensional (2D)
electron systems challenged the veracity of one of the most influential
conjectures in the physics of disordered electrons, which states that `in two
dimensions, there is no true metallic behaviour'; no matter how weak the
disorder, electrons would be trapped and unable to conduct a current. However,
that theory did not account for interactions between the electrons. Here we
investigate the interplay between the electron-electron interactions and
disorder near the MIT using simultaneous measurements of electrical resistivity
and magnetoconductance. We show that both the resistance and interaction
amplitude exhibit a fan-like spread as the MIT is crossed. From these data we
construct a resistance-interaction flow diagram of the MIT that clearly reveals
a quantum critical point, as predicted by the two-parameter scaling theory
(Punnoose and Finkel'stein, Science 310, 289 (2005)). The metallic side of this
diagram is accurately described by the renormalization group theory without any
fitting parameters. In particular, the metallic temperature dependence of the
resistance sets in when the interaction amplitude reaches gamma_2 = 0.45 - a
value in remarkable agreement with the one predicted by the theory.Comment: as publishe
Stellar Coronal and Wind Models: Impact on Exoplanets
Surface magnetism is believed to be the main driver of coronal heating and
stellar wind acceleration. Coronae are believed to be formed by plasma confined
in closed magnetic coronal loops of the stars, with winds mainly originating in
open magnetic field line regions. In this Chapter, we review some basic
properties of stellar coronae and winds and present some existing models. In
the last part of this Chapter, we discuss the effects of coronal winds on
exoplanets.Comment: Chapter published in the "Handbook of Exoplanets", Editors in Chief:
Juan Antonio Belmonte and Hans Deeg, Section Editor: Nuccio Lanza. Springer
Reference Work
Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Order One and Two
Coupled discrete models abound in several areas of physics. Here we provide
an extensive set of exact quasiperiodic solutions of a number of coupled
discrete models in terms of Lame polynomials of order one and two. Some of the
models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik
model, (iii) coupled saturated discrete nonlinear Schrodinger equation, (iv)
coupled phi4 model, and (v) coupled phi6 model. Furthermore, we show that most
of these coupled models in fact also possess an even broader class of exact
solutions.Comment: 31 pages, to appear in Pramana (Journal of Physics) 201
Interleaved Parton Showers and Tuning Prospects
General-purpose Monte Carlo event generators have become important tools in
particle physics, allowing the simulation of exclusive hadronic final states.
In this article we examine the Pythia 8 generator, in particular focusing on
its parton-shower algorithms. Some relevant new additions to the code are
introduced, that should allow for a better description of data. We also
implement and compare with 2 to 3 real-emission QCD matrix elements, to check
how well the shower algorithm fills the phase space away from the soft and
collinear regions. A tuning of the generator to Tevatron data is performed for
two PDF sets and the impact of first new LHC data is examined
Aharonov-Bohm interference in topological insulator nanoribbons
Topological insulators represent novel phases of quantum matter with an
insulating bulk gap and gapless edges or surface states. The two-dimensional
topological insulator phase was predicted in HgTe quantum wells and confirmed
by transport measurements. Recently, Bi2Se3 and related materials have been
proposed as three-dimensional topological insulators with a single Dirac cone
on the surface and verified by angle-resolved photoemission spectroscopy
experiments. Here, we show unambiguous transport evidence of topological
surface states through periodic quantum interference effects in layered
single-crystalline Bi2Se3 nanoribbons. Pronounced Aharonov-Bohm oscillations in
the magnetoresistance clearly demonstrate the coverage of two-dimensional
electrons on the entire surface, as expected from the topological nature of the
surface states. The dominance of the primary h/e oscillation and its
temperature dependence demonstrate the robustness of these electronic states.
Our results suggest that topological insulator nanoribbons afford novel
promising materials for future spintronic devices at room temperature.Comment: 5 pages, 4 figures, RevTex forma
Semiparametric Multivariate Accelerated Failure Time Model with Generalized Estimating Equations
The semiparametric accelerated failure time model is not as widely used as
the Cox relative risk model mainly due to computational difficulties. Recent
developments in least squares estimation and induced smoothing estimating
equations provide promising tools to make the accelerate failure time models
more attractive in practice. For semiparametric multivariate accelerated
failure time models, we propose a generalized estimating equation approach to
account for the multivariate dependence through working correlation structures.
The marginal error distributions can be either identical as in sequential event
settings or different as in parallel event settings. Some regression
coefficients can be shared across margins as needed. The initial estimator is a
rank-based estimator with Gehan's weight, but obtained from an induced
smoothing approach with computation ease. The resulting estimator is consistent
and asymptotically normal, with a variance estimated through a multiplier
resampling method. In a simulation study, our estimator was up to three times
as efficient as the initial estimator, especially with stronger multivariate
dependence and heavier censoring percentage. Two real examples demonstrate the
utility of the proposed method
Mesozoic fossils (>145 Mya) suggest the antiquity of the subgenera of Daphnia and their coevolution with chaoborid predators
<p>Abstract</p> <p>Background</p> <p>The timescale of the origins of <it>Daphnia </it>O. F. Mueller (Crustacea: Cladocera) remains controversial. The origin of the two main subgenera has been associated with the breakup of the supercontinent Pangaea. This vicariance hypothesis is supported by reciprocal monophyly, present day associations with the former Gondwanaland and Laurasia regions, and mitochondrial DNA divergence estimates. However, previous multilocus nuclear DNA sequence divergence estimates at < 10 Million years are inconsistent with the breakup of Pangaea. We examined new and existing cladoceran fossils from a Mesozoic Mongolian site, in hopes of gaining insights into the timescale of the evolution of <it>Daphnia</it>.</p> <p>Results</p> <p>We describe new fossils of ephippia from the Khotont site in Mongolia associated with the Jurassic-Cretaceous boundary (about 145 MYA) that are morphologically similar to several modern genera of the family Daphniidae, including the two major subgenera of <it>Daphnia</it>, i.e., <it>Daphnia </it>s. str. and <it>Ctenodaphnia</it>. The daphniid fossils co-occurred with fossils of the predaceous phantom midge (Chaoboridae).</p> <p>Conclusions</p> <p>Our findings indicate that the main subgenera of <it>Daphnia </it>are likely much older than previously known from fossils (at least 100 MY older) or from nuclear DNA estimates of divergence. The results showing co-occurrence of the main subgenera far from the presumed Laurasia/Gondwanaland dispersal barrier shortly after formation suggests that vicariance from the breakup of Pangaea is an unlikely explanation for the origin of the main subgenera. The fossil impressions also reveal that the coevolution of a dipteran predator (Chaoboridae) with the subgenus <it>Daphnia </it>is much older than previously known -- since the Mesozoic.</p
Rare coding SNP in DZIP1 gene associated with late-onset sporadic Parkinson's disease
We present the first application of the hypothesis-rich mathematical theory
to genome-wide association data. The Hamza et al. late-onset sporadic
Parkinson's disease genome-wide association study dataset was analyzed. We
found a rare, coding, non-synonymous SNP variant in the gene DZIP1 that confers
increased susceptibility to Parkinson's disease. The association of DZIP1 with
Parkinson's disease is consistent with a Parkinson's disease stem-cell ageing
theory.Comment: 14 page
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