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2007-12-01
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On Myopic Sensing for Multi-Channel Opportunistic Access: Structure, Optimality, and Performance
|
We consider a multi-channel opportunistic communication system where the
states of these channels evolve as independent and statistically identical
Markov chains (the Gilbert-Elliot channel model). A user chooses one channel to
sense and access in each slot and collects a reward determined by the state of
the chosen channel. The problem is to design a sensing policy for channel
selection to maximize the average reward, which can be formulated as a
multi-arm restless bandit process. In this paper, we study the structure,
optimality, and performance of the myopic sensing policy. We show that the
myopic sensing policy has a simple robust structure that reduces channel
selection to a round-robin procedure and obviates the need for knowing the
channel transition probabilities. The optimality of this simple policy is
established for the two-channel case and conjectured for the general case based
on numerical results. The performance of the myopic sensing policy is analyzed,
which, based on the optimality of myopic sensing, characterizes the maximum
throughput of a multi-channel opportunistic communication system and its
scaling behavior with respect to the number of channels. These results apply to
cognitive radio networks, opportunistic transmission in fading environments,
and resource-constrained jamming and anti-jamming.
|
0712.0035v3
|
2007-12-12
|
Two-connected graphs with prescribed three-connected components
|
We adapt the classical 3-decomposition of any 2-connected graph to the case
of simple graphs (no loops or multiple edges). By analogy with the
block-cutpoint tree of a connected graph, we deduce from this decomposition a
bicolored tree tc(g) associated with any 2-connected graph g, whose white
vertices are the 3-components of g (3-connected components or polygons) and
whose black vertices are bonds linking together these 3-components, arising
from separating pairs of vertices of g. Two fundamental relationships on graphs
and networks follow from this construction. The first one is a dissymmetry
theorem which leads to the expression of the class B=B(F) of 2-connected
graphs, all of whose 3-connected components belong to a given class F of
3-connected graphs, in terms of various rootings of B. The second one is a
functional equation which characterizes the corresponding class R=R(F) of
two-pole networks all of whose 3-connected components are in F. All the
rootings of B are then expressed in terms of F and R. There follow
corresponding identities for all the associated series, in particular the edge
index series. Numerous enumerative consequences are discussed.
|
0712.1869v2
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2008-03-13
|
Optimal spatial transportation networks where link-costs are sublinear in link-capacity
|
Consider designing a transportation network on $n$ vertices in the plane,
with traffic demand uniform over all source-destination pairs. Suppose the cost
of a link of length $\ell$ and capacity $c$ scales as $\ell c^\beta$ for fixed
$0<\beta<1$. Under appropriate standardization, the cost of the minimum cost
Gilbert network grows essentially as $n^{\alpha(\beta)}$, where $\alpha(\beta)
= 1 - \frac{\beta}{2}$ on $0 < \beta \leq {1/2}$ and $\alpha(\beta) = {1/2} +
\frac{\beta}{2}$ on ${1/2} \leq \beta < 1$. This quantity is an upper bound in
the worst case (of vertex positions), and a lower bound under mild regularity
assumptions. Essentially the same bounds hold if we constrain the network to be
efficient in the sense that average route-length is only $1 + o(1)$ times
average straight line length. The transition at $\beta = {1/2}$ corresponds to
the dominant cost contribution changing from short links to long links. The
upper bounds arise in the following type of hierarchical networks, which are
therefore optimal in an order of magnitude sense. On the large scale, use a
sparse Poisson line process to provide long-range links. On the medium scale,
use hierachical routing on the square lattice. On the small scale, link
vertices directly to medium-grid points. We discuss one of many possible
variant models, in which links also have a designed maximum speed $s$ and the
cost becomes $\ell c^\beta s^\gamma$.
|
0803.2037v1
|
2008-03-24
|
Was the Andromeda Stream Produced by a Disk Galaxy?
|
The halo region of M31 exhibits a startling level of stellar inhomogeneities,
the most prominent of which is the "giant southern stream". Our previous
analysis indicates that this stream, as well as several other observed
features, are products of the tidal disruption of a single satellite galaxy
with stellar mass ~10^9 solar masses less than 1 Gyr ago. Here we show that the
specific observed morphology of the stream and halo debris favors a cold,
rotating, disk-like progenitor over a dynamically hot, non-rotating one. These
observed characteristics include the asymmetric distribution of stars along the
stream cross-section and its metal-rich core/metal-poor sheath structure. We
find that a disk-like progenitor can also give rise to arc-like features on the
minor axis at certain orbital phases that resemble the recently discovered
minor-axis "streams", even reproducing the lower observed metallicity of these
streams. Though interpreted by the discoverers as new, independent tidal
streams, our analysis suggests that these minor-axis streams may alternatively
arise from the progenitor of the giant southern stream. Overall, our study
points the way to a more complete reconstruction of the stream progenitor and
its merger with M31, based on the emerging picture that most of the major
inhomogeneities observed in the M31 halo share a common origin with the giant
stream.
|
0803.3476v2
|
2008-04-23
|
Geometric dynamics of Vlasov kinetic theory and its moments
|
The Vlasov equation of kinetic theory is introduced and the Hamiltonian
structure of its moments is presented. Then we focus on the geodesic evolution
of the Vlasov moments. As a first step, these moment equations generalize the
Camassa-Holm equation to its multi-component version. Subsequently, adding
electrostatic forces to the geodesic moment equations relates them to the
Benney equations and to the equations for beam dynamics in particle
accelerators. Next, we develop a kinetic theory for self assembly in
nano-particles. Darcy's law is introduced as a general principle for
aggregation dynamics in friction dominated systems (at different scales). Then,
a kinetic equation is introduced for the dissipative motion of isotropic
nano-particles. The zeroth-moment dynamics of this equation recovers the
classical Darcy's law at the macroscopic level. A kinetic-theory description
for oriented nano-particles is also presented. At the macroscopic level, the
zeroth moments of this kinetic equation recover the magnetization dynamics of
the Landau-Lifshitz-Gilbert equation. The moment equations exhibit the
spontaneous emergence of singular solutions (clumpons) that finally merge in
one singularity. This behaviour represents aggregation and alignment of
oriented nano-particles. Finally, the Smoluchowski description is derived from
the dissipative Vlasov equation for anisotropic interactions. Various levels of
approximate Smoluchowski descriptions are proposed as special cases of the
general treatment. As a result, the macroscopic momentum emerges as an
additional dynamical variable that in general cannot be neglected.
|
0804.3676v1
|
2008-05-05
|
On Expanded Cyclic Codes
|
The paper has a threefold purpose. The first purpose is to present an
explicit description of expanded cyclic codes defined in $\GF(q^m)$. The
proposed explicit construction of expanded generator matrix and expanded parity
check matrix maintains the symbol-wise algebraic structure and thus keeps many
important original characteristics. The second purpose of this paper is to
identify a class of constant-weight cyclic codes. Specifically, we show that a
well-known class of $q$-ary BCH codes excluding the all-zero codeword are
constant-weight cyclic codes. Moreover, we show this class of codes achieve the
Plotkin bound. The last purpose of the paper is to characterize expanded cyclic
codes utilizing the proposed expanded generator matrix and parity check matrix.
We characterize the properties of component codewords of a codeword and
particularly identify the precise conditions under which a codeword can be
represented by a subbasis. Our developments reveal an alternative while more
general view on the subspace subcodes of Reed-Solomon codes. With the new
insights, we present an improved lower bound on the minimum distance of an
expanded cyclic code by exploiting the generalized concatenated structure. We
also show that the fixed-rate binary expanded Reed-Solomon codes are
asymptotically "bad", in the sense that the ratio of minimum distance over code
length diminishes with code length going to infinity. It overturns the
prevalent conjecture that they are "good" codes and deviates from the ensemble
of generalized Reed-Solomon codes which asymptotically achieves the
Gilbert-Varshamov bound.
|
0805.0615v2
|
2008-05-14
|
Path Diversity over Packet Switched Networks: Performance Analysis and Rate Allocation
|
Path diversity works by setting up multiple parallel connections between the
end points using the topological path redundancy of the network. In this paper,
\textit{Forward Error Correction} (FEC) is applied across multiple independent
paths to enhance the end-to-end reliability. Network paths are modeled as
erasure Gilbert-Elliot channels. It is known that over any erasure channel,
\textit{Maximum Distance Separable} (MDS) codes achieve the minimum probability
of irrecoverable loss among all block codes of the same size. Based on the
adopted model for the error behavior, we prove that the probability of
irrecoverable loss for MDS codes decays exponentially for an asymptotically
large number of paths. Then, optimal rate allocation problem is solved for the
asymptotic case where the number of paths is large. Moreover, it is shown that
in such asymptotically optimal rate allocation, each path is assigned a
positive rate \textit{iff} its quality is above a certain threshold. The
quality of a path is defined as the percentage of the time it spends in the bad
state. Finally, using dynamic programming, a heuristic suboptimal algorithm
with polynomial runtime is proposed for rate allocation over a finite number of
paths. This algorithm converges to the asymptotically optimal rate allocation
when the number of paths is large. The simulation results show that the
proposed algorithm approximates the optimal rate allocation (found by
exhaustive search) very closely for practical number of paths, and provides
significant performance improvement compared to the alternative schemes of rate
allocation.
|
0805.2185v1
|
2008-06-25
|
HAT-P-9b: A Low Density Planet Transiting a Moderately Faint F star
|
We report the discovery of a planet transiting a moderately faint (V=12.3
mag) late F star, with an orbital period of 3.92289 +/- 0.00004 days. From the
transit light curve and radial velocity measurements we determine that the
radius of the planet is R_p = 1.40 +/- 0.06 R_Jup and that the mass is M_p =
0.78 +/- 0.09 M_Jup. The density of the new planet, rho = 0.35 +/- 0.06 g
cm^{-3}, fits to the low-density tail of the currently known transiting
planets. We find that the center of transit is at T_c = 2454417.9077 +/- 0.0003
(HJD), and the total transit duration is 0.143 +/- 0.004 days. The host star
has M_s = 1.28 +/- 0.13 M_Sun and R_s = 1.32 +/- 0.07 R_Sun.
|
0806.4008v2
|
2008-07-07
|
Micropropagation of three genotypes of Indian mustard [{Brassica juncea} (L.) Czern.] using seedling-derived transverse thin cell layer (tTCL) explants
|
Micropropagation of three genotypes of Indian mustard [\textit{Brassica
juncea} (L.) Czern.] using 7-days old seedling-derived transverse thin cell
layer (tTCL) explants was accomplished.
The genotype, explant source and addition of silver nitrate to the medium
significantly influenced shoot bud induction. MS medium with 26.6 $\mu$M of
6-Benzylaminopurin (BAP) and 3.22 $\mu$M of 1-naphtaleneacetic acid (NAA) was
identical (in the case of cotyledon tTCLs whatever the organ) and superior for
the induction of buds (in the cases of petiole tTCL explants of genotypes 1 and
2 and hypocotyl tTCL explants of genotypes 1 and 3) than 53.3 $\mu$M of BAP and
3.22 $\mu$M of NAA. However, 53.3 $\mu$M of BAP was superior for the induction
of buds than 26.6 $\mu$M in the presence of the same concentration of NAA for
petiole tTCL explants of genotype 3 and hypocotyl tTCL explants of genotype 2.
The addition of silver nitrate significantly enhanced the rate of shoot
induction in all genotypes. Cotyledon-derived tTCL explants exhibited the
highest shoot bud induction potential and was followed by petiole- and
hypocotyl-derived ones. Addition of 10 $\mu$M of silver nitrate to BAP and NAA
supplemented medium induced higher frequency shoot bud induction (up to 100 %)
with the highest means of 4.45 shoots per cotyledon-derived tTCL explants
obtained with the genotype 2. Shoot regenerated were rooted on MS basal medium
without PGRs which induced 99 % of roots per shoot. The plantlets established
in greenhouse conditions with 99 % survival, flowered normally and set seeds.
|
0807.1061v1
|
2008-07-18
|
On Probability Distributions for Trees: Representations, Inference and Learning
|
We study probability distributions over free algebras of trees. Probability
distributions can be seen as particular (formal power) tree series [Berstel et
al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely
studied class of tree series is the class of rational (or recognizable) tree
series which can be defined either in an algebraic way or by means of
multiplicity tree automata. We argue that the algebraic representation is very
convenient to model probability distributions over a free algebra of trees.
First, as in the string case, the algebraic representation allows to design
learning algorithms for the whole class of probability distributions defined by
rational tree series. Note that learning algorithms for rational tree series
correspond to learning algorithms for weighted tree automata where both the
structure and the weights are learned. Second, the algebraic representation can
be easily extended to deal with unranked trees (like XML trees where a symbol
may have an unbounded number of children). Both properties are particularly
relevant for applications: nondeterministic automata are required for the
inference problem to be relevant (recall that Hidden Markov Models are
equivalent to nondeterministic string automata); nowadays applications for Web
Information Extraction, Web Services and document processing consider unranked
trees.
|
0807.2983v1
|
2008-11-02
|
Stretch-Twist torus dynamo in compact Riemannian manifolds
|
Earlier Arnold, Zeldovich, Ruzmaikin and Sokoloff [\textbf{JETP (1982)}] have
computed the eigenvalue of a uniform stretching torus transformation which
result on the first Riemann metric solution of the dynamo action problem.
Recently some other attempts to obtain Riemann metrics representing dynamo
action through conformal maps have been undertaken [{\textbf{Phys. Plasmas 14
(2007)}]. Earlier, Gilbert [\textbf{Proc. Roy. Soc. London A(2003)}] has
investigated a more realistic dynamo map solution than the one presented by
Arnold et al by producing a shearing of the Arnold's cat map, by eigenvalue
problem of a dynamo operator. In this paper, the eigenvalue of the Riemann
twisted torus dynamo flow metric is obtained as the ratio between the poloidal
and toroidal components of the flow. This result is obtained from the Euler
equation. In the twisted torus, the eigenvalue of the Riemann metric is
${m}_{\pm}=\frac{1\pm{\sqrt{5}}}{2}$, which is quite close to the value
obtained by Arnold. In the case the viscosity Reynolds number $Re\to{\infty}$,
the torus flow is unstable as one approaches the torus axis. In Arnold's dynamo
metric the eigenvalues are ${\chi}_{\pm}=\frac{3\pm{\sqrt{5}}}{2}$ which are
very close to the above value. Eigenvalues determine the growth rates of the
velocity ratio between poloidal and toroidal components of the flow. The curved
flow in torus follow previous work by Chen et al [\textbf{Phys Fluids (2006)}].
The ${\alpha}$-effect dynamo is shown to be a second-order effect in the torus
curvature and velocity flow. Loop dynamo flows and maps are also discussed.
|
0811.0142v1
|
2008-11-21
|
Geodesic dynamo chaotic flows and non-Anosov maps in twisted magnetic flux tubes
|
Recently Tang and Boozer [{\textbf{Phys. Plasmas (2000)}}], have investigated
the anisotropies in magnetic field dynamo evolution, from local Lyapunov
exponents, giving rise to a metric tensor, in the Alfven twist in magnetic flux
tubes (MFTs). Thiffeault and Boozer [\textbf{Chaos}(2001)] have investigated
the how the vanishing of Riemann curvature constrained the Lyapunov exponential
stretching of chaotic flows. In this paper, Tang-Boozer-Thiffeault differential
geometric framework is used to investigate effects of twisted magnetic flux
tube filled with helical chaotic flows on the Riemann curvature tensor. When
Frenet torsion is positive, the Riemann curvature is unstable, while the
negative torsion induces an stability when time $t\to{\infty}$. This enhances
the dynamo action inside the MFTs. The Riemann metric, depends on the radial
random flows along the poloidal and toroidal directions. The Anosov flows has
been applied by Arnold, Zeldovich, Ruzmaikin and Sokoloff [\textbf{JETP
(1982)}] to build a uniformly stretched dynamo flow solution, based on Arnold's
Cat Map. It is easy to show that when the random radial flow vanishes, the
magnetic field vanishes, since the exponential Lyapunov stretches vanishes.
This is an example of the application of the Vishik's anti-fast dynamo theorem
in the magnetic flux tubes. Geodesic flows of both Arnold and twisted MFT
dynamos are investigated. It is shown that a constant random radial flow can be
obtained from the geodesic equation. Throughout the paper one assumes, the
reasonable plasma astrophysical hypothesis of the weak torsion. Pseudo-Anosov
dynamo flows and maps have also been addressed by Gilbert [\textbf{Proc Roy Soc
A London (1993)}
|
0811.3630v1
|
2008-12-03
|
Gravitino Dark Matter and the Cosmic Lithium Abundances
|
Supersymmetric extensions of the standard model of particle physics assuming
the gravitino to be the lightest supersymmetric particle (LSP), and with the
next-to-LSP decaying to the gravitino during Big Bang nucleosynthesis, are
analyzed. Particular emphasis is laid on their potential to solve the "Li7
problem", an apparent factor 2-4 overproduction of Li7 in standard Big Bang
nucleosynthesis (BBN), their production of cosmologically important amounts of
Li6, as well as the resulting gravitino dark matter densities in these models.
The study includes several improvements compared to prior studies. Heavy
gravitinos in the constrained minimal supersymmetric standard model (CMMSM) are
reanalyzed, whereas light gravitinos in gauge-mediated supersymmetry breaking
scenarios (GMSB) are studied for the first time. It is confirmed that decays of
NLSP staus to heavy gravitinos, while producing all the dark matter, may at the
same time resolve the Li7 problem. For NLSP decay times ~ 1000 sec, such
scenarios also lead to cosmologically important Li6 (and possibly Be9)
abundances. However, as such scenarios require heavy > 1 TeV staus they are
likely not testable at the LHC. It is found that decays of NLSP staus to light
gravitinos may lead to significant Li6 (and Be9) abundances, whereas NLSP
neutralinos decaying into light gravitinos may solve the Li7 problem. Though
both scenarios are testable at the LHC they may not lead to the production of
the bulk of the dark matter. A section of the paper outlines particle
properties required to significantly reduce the Li7 abundance, and/or enhance
the Li6 (and possibly Be9) abundances, by the decay of an arbitrary relic
particle.
|
0812.0788v2
|
2009-01-26
|
A Bayesian framework for estimating vaccine efficacy per infectious contact
|
In vaccine studies for infectious diseases such as human immunodeficiency
virus (HIV), the frequency and type of contacts between study participants and
infectious sources are among the most informative risk factors, but are often
not adequately adjusted for in standard analyses. Such adjustment can improve
the assessment of vaccine efficacy as well as the assessment of risk factors.
It can be attained by modeling transmission per contact with infectious
sources. However, information about contacts that rely on self-reporting by
study participants are subject to nontrivial measurement error in many studies.
We develop a Bayesian hierarchical model fitted using Markov chain Monte Carlo
(MCMC) sampling to estimate the vaccine efficacy controlled for exposure to
infection, while adjusting for measurement error in contact-related factors.
Our method is used to re-analyze two recent HIV vaccine studies, and the
results are compared with the published primary analyses that used standard
methods. The proposed method could also be used for other vaccines where
contact information is collected, such as human papilloma virus vaccines.
|
0901.4025v1
|
2009-01-28
|
Theoretical characterization of a model of aragonite crystal orientation in red abalone nacre
|
Nacre, commonly known as mother-of-pearl, is a remarkable biomineral that in
red abalone consists of layers of 400-nm thick aragonite crystalline tablets
confined by organic matrix sheets, with the $(001)$ crystal axes of the
aragonite tablets oriented to within $\pm$ 12 degrees from the normal to the
layer planes. Recent experiments demonstrate that this orientational order
develops over a distance of tens of layers from the prismatic boundary at which
nacre formation begins.
Our previous simulations of a model in which the order develops because of
differential tablet growth rates (oriented tablets growing faster than
misoriented ones) yield patterns of tablets that agree qualitatively and
quantitatively with the experimental measurements. This paper presents an
analytical treatment of this model, focusing on how the dynamical development
and eventual degree of order depend on model parameters. Dynamical equations
for the probability distributions governing tablet orientations are introduced
whose form can be determined from symmetry considerations and for which
substantial analytic progress can be made. Numerical simulations are performed
to relate the parameters used in the analytic theory to those in the
microscopic growth model. The analytic theory demonstrates that the dynamical
mechanism is able to achieve a much higher degree of order than naive estimates
would indicate.
|
0901.4482v1
|
2009-02-07
|
Partially-erupting prominences: a comparison between observations and model-predicted observables
|
AIM: To investigate several partially-erupting prominences to study their
relationship with other CME-associated phenomena and to compare these
observations with observables predicted by a model of partially-expelled flux
ropes (Gibson & Fan, 2006a, b).
METHODS: We have studied 6 selected events with partially-erupting
prominences using multi wavelength observations recorded by the
Extreme-ultraviolet Imaging Telescope (EIT), Transition Region and Coronal
Explorer (TRACE), Mauna Loa Solar Observatory (MLSO), Big Bear Solar
Observatory (BBSO) and soft X-ray telescope (SXT). The observational features
associated with partially-erupting prominences were then compared with the
predicted observables from the model.
RESULTS: The partially-expelled-flux-rope (PEFR) model of Gibson & Fan
(2006a, b) can explain the partial eruption of these prominences, and in
addition predicts a variety of other CME-related observables that provide
evidence for internal reconnection during eruption. We find that all of the
partially-erupting prominences studied in this paper exhibit indirect evidence
for internal reconnection. Moreover, all cases showed evidence of at least one
observable unique to the PEFR model, e.g., dimmings external to the source
region, and/or a soft X-ray cusp overlying a reformed sigmoid.
CONCLUSIONS: The PEFR model provides a plausible mechanism to explain the
observed evolution of partially-erupting-prominence-associated CMEs in our
study.
|
0902.1228v1
|
2009-03-03
|
Proportional hazards models with continuous marks
|
For time-to-event data with finitely many competing risks, the proportional
hazards model has been a popular tool for relating the cause-specific outcomes
to covariates [Prentice et al. Biometrics 34 (1978) 541--554]. This article
studies an extension of this approach to allow a continuum of competing risks,
in which the cause of failure is replaced by a continuous mark only observed at
the failure time. We develop inference for the proportional hazards model in
which the regression parameters depend nonparametrically on the mark and the
baseline hazard depends nonparametrically on both time and mark. This work is
motivated by the need to assess HIV vaccine efficacy, while taking into account
the genetic divergence of infecting HIV viruses in trial participants from the
HIV strain that is contained in the vaccine, and adjusting for covariate
effects. Mark-specific vaccine efficacy is expressed in terms of one of the
regression functions in the mark-specific proportional hazards model. The new
approach is evaluated in simulations and applied to the first HIV vaccine
efficacy trial.
|
0903.0487v1
|
2009-03-06
|
Five More Massive Binaries in the Cygnus OB2 Association
|
We present the orbital solutions for four OB spectroscopic binaries, MT145,
GSC 03161-00815, 2MASS J20294666+4105083, and Schulte 73, and the partial
orbital solution to the B spectroscopic binary, MT372, as part of an ongoing
study to determine the distribution of orbital parameters for massive binaries
in the Cygnus OB2 Association. MT145 is a new, single-lined, moderately
eccentric (e=0.291+/-0.009) spectroscopic binary with period of 25.140+/-0.008
days. GSC 03161-00815 is a slightly eccentric (e=0.10+/-0.01), eclipsing,
interacting and double-lined spectroscopic binary with a period of
4.674+/-0.004 days. 2MASS J20294666+4105083 is a moderately eccentric
(e=0.273+/-0.002) double-lined spectroscopic binary with a period of
2.884+/-0.001 days. Schulte 73 is a slightly eccentric (e=0.169+/-0.009),
double-lined spectroscopic binary with a period of 17.28+/-0.03 days and the
first "twin" in our survey with a mass ratio of q=0.99+/-0.02. MT372 is a
single-lined, eclipsing system with a period of 2.228 days and low eccentricity
(e~0). Of the now 18 known OB binaries in Cyg OB2, 14 have periods and mass
ratios. Emerging evidence also shows that the distribution of log(P) is flat
and consistent with Oepik's Law.
|
0903.1265v1
|
2009-03-16
|
The Transit Light Curve Project. XII. Six Transits of the Exoplanet XO-2b
|
We present photometry of six transits of the exoplanet XO-2b. By combining
the light-curve analysis with theoretical isochrones to determine the stellar
properties, we find the planetary radius to be 0.996 +0.031/-0.018 rjup and the
planetary mass to be 0.565 +/- 0.054 mjup. These results are consistent with
those reported previously, and are also consistent with theoretical models for
gas giant planets. The mid-transit times are accurate to within 1 min and are
consistent with a constant period. However, the period we derive differs by 2.5
sigma from the previously published period. More data are needed to tell
whether the period is actually variable (as it would be in the presence of an
additional body) or if the timing errors have been underestimated.
|
0903.2687v1
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2009-03-19
|
Approximation of Bounds on Mixed Level Orthogonal Arrays
|
Mixed level orthogonal arrays are basic structures in experimental design. We
develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for
mixed level orthogonal arrays. The computational complexity of the terms
involved in these bounds can grow fast as the parameters of the arrays increase
and this justifies the construction of these algorithms. The first is a
recursive algorithm that computes the bounds exactly, the second is based on an
asymptotic analysis and the third is a simulation algorithm. They are all based
on the representation of the combinatorial expressions that appear in the
bounds as expectations involving a symmetric random walk. The Markov property
of the underlying random walk gives the recursive formula to compute the
expectations. A large deviation (LD) analysis of the expectations provide the
asymptotic algorithm. The asymptotically optimal importance sampling (IS) of
the same expectation provides the simulation algorithm. Both the LD analysis
and the construction of the IS algorithm uses a representation of these
problems as a sequence of stochastic optimal control problems converging to a
limit calculus of variations problem. The construction of the IS algorithm uses
a recently discovered method of using subsolutions to the Hamilton Jacobi
Bellman equation associated with the limit problem.
|
0903.3438v2
|
2009-04-16
|
Good Concatenated Code Ensembles for the Binary Erasure Channel
|
In this work, we give good concatenated code ensembles for the binary erasure
channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code
ensembles formed by the serial concatenation of a repetition code with multiple
accumulators, and the hybrid concatenated code (HCC) ensembles recently
introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics,
Lausanne, Switzerland) consisting of an outer multiple parallel concatenated
code serially concatenated with an inner accumulator. We introduce stopping
sets for iterative constituent code oriented decoding using maximum a
posteriori erasure correction in the constituent codes. We then analyze the
asymptotic stopping set distribution for RMA and HCC ensembles and show that
their stopping distance hmin, defined as the size of the smallest nonempty
stopping set, asymptotically grows linearly with the block length. Thus, these
code ensembles are good for the BEC. It is shown that for RMA code ensembles,
contrary to the asymptotic minimum distance dmin, whose growth rate coefficient
increases with the number of accumulate codes, the hmin growth rate coefficient
diminishes with the number of accumulators. We also consider random puncturing
of RMA code ensembles and show that for sufficiently high code rates, the
asymptotic hmin does not grow linearly with the block length, contrary to the
asymptotic dmin, whose growth rate coefficient approaches the Gilbert-Varshamov
bound as the rate increases. Finally, we give iterative decoding thresholds for
the different code ensembles to compare the convergence properties.
|
0904.2482v1
|
2009-10-10
|
Multi-channel Opportunistic Access: A Case of Restless Bandits with Multiple Plays
|
This paper considers the following stochastic control problem that arises in
opportunistic spectrum access: a system consists of n channels (Gilbert-Elliot
channels)where the state (good or bad) of each channel evolves as independent
and identically distributed Markov processes. A user can select exactly k
channels to sense and access (based on the sensing result) in each time slot. A
reward is obtained whenever the user senses and accesses a good channel. The
objective is to design a channel selection policy that maximizes the expected
discounted total reward accrued over a finite or infinite horizon. In our
previous work we established the optimality of a greedy policy for the special
case of k = 1 (i.e., single channel access) under the condition that the
channel state transitions are positively correlated over time. In this paper we
show under the same condition the greedy policy is optimal for the general case
of k >= 1; the methodology introduced here is thus more general. This problem
may be viewed as a special case of the restless bandit problem, with multiple
plays. We discuss connections between the current problem and existing
literature on this class of problems.
|
0910.1954v1
|
2010-03-12
|
Anosov branches of dynamo spectra in one dimensional plasmas
|
Recently Guenther et al the globally diagonalized ${\alpha}^{2}$ dynamo
operator spectrum [J Phys A 2007) in mean field media, and its Krein space
related perturbation theory [J Phys A 2006). Earlier, an example of fast
dynamos in stretch shear and fold Anosov maps have been given by Gilbert [PRSA
[1993)). In this paper, analytical solutions representing general turbulent
dynamo filaments are obtained in resistive plasmas. When turbulent diffusivity
is present and kinetic helicity vanishes, a fast dynamo mode is obtained, and
the Anosov eigenvalue obtained. The magnetic field lays down on a Frenet 2
plane along the filaments embedded in a 3D flow. Curvature effects on fast
dynamo are also investigate. In case of weak curvature filaments the one
dimensional manifolds in plasmas present a fast dynamo action. A parallel
result has been obtained by Chicone et al [Comm Math Phys), in the case fast
dynamo spectrum in two dimensional compact Riemannian manifolds of negative
constant curvature, called Anosov spaces. While problems of embedding may
appear in their case here no embedding problems appear since the one
dimensional curved plasmas are embedded in three dimensional Euclidean spaces.
In the examples considered here, equipartion between normal and binormal
components of the magnetic field components is considered. In the opposite
case, non Anosov oscillatory, purely imaginary, branches of the spectrum are
found in dynamo manifold. Negative constant curvature non-compact
$\textbf{H}^{2}$ manifold, has also been used in one-component electron 2D
plasma by Fantoni and Tellez (Stat. Phys, (2008))
|
1003.2482v1
|
2010-04-05
|
A Prograde, Low-Inclination Orbit for the Very Hot Jupiter WASP-3b
|
We present new spectroscopic and photometric observations of the transiting
exoplanetary system WASP-3. Spectra obtained during two separate transits
exhibit the Rossiter-McLaughlin (RM) effect and allow us to estimate the
sky-projected angle between the planetary orbital axis and the stellar rotation
axis, lambda = 3.3^{+2.5}_{-4.4} degrees. This alignment between the axes
suggests that WASP-3b has a low orbital inclination relative to the equatorial
plane of its parent star. During our first night of spectroscopic measurements,
we observed an unexpected redshift briefly exceeding the expected sum of the
orbital and RM velocities by 140 m/s. This anomaly could represent the
occultation of material erupting from the stellar photosphere, although it is
more likely to be an artifact caused by moonlight scattered into the
spectrograph.
|
1004.0692v2
|
2010-06-09
|
NLTT 41135: a field M-dwarf + brown dwarf eclipsing binary in a triple system, discovered by the MEarth observatory
|
We report the discovery of an eclipsing companion to NLTT 41135, a nearby M5
dwarf that was already known to have a wider, slightly more massive common
proper motion companion, NLTT 41136, at 2.4 arcsec separation. Analysis of
combined-light and radial velocity curves of the system indicates that NLTT
41135B is a 31-34 +/- 3 MJup brown dwarf (where the range depends on the
unknown metallicity of the host star) on a circular orbit. The visual M-dwarf
pair appears to be physically bound, so the system forms a hierarchical triple,
with masses approximately in the ratio 8:6:1. The eclipses are grazing,
preventing an unambiguous measurement of the secondary radius, but follow-up
observations of the secondary eclipse (e.g. with the James Webb Space
Telescope) could permit measurements of the surface brightness ratio between
the two objects, and thus place constraints on models of brown dwarfs.
|
1006.1793v1
|
2010-09-28
|
Connectivity in Sub-Poisson Networks
|
We consider a class of point processes (pp), which we call {\em sub-Poisson};
these are pp that can be directionally-convexly ($dcx$) dominated by some
Poisson pp. The $dcx$ order has already been shown useful in comparing various
point process characteristics, including Ripley's and correlation functions as
well as shot-noise fields generated by pp, indicating in particular that
smaller in the $dcx$ order processes exhibit more regularity (less clustering,
less voids) in the repartition of their points. Using these results, in this
paper we study the impact of the $dcx$ ordering of pp on the properties of two
continuum percolation models, which have been proposed in the literature to
address macroscopic connectivity properties of large wireless networks. As the
first main result of this paper, we extend the classical result on the
existence of phase transition in the percolation of the Gilbert's graph (called
also the Boolean model), generated by a homogeneous Poisson pp, to the class of
homogeneous sub-Poisson pp. We also extend a recent result of the same nature
for the SINR graph, to sub-Poisson pp. Finally, as examples we show that the
so-called perturbed lattices are sub-Poisson. More generally, perturbed
lattices provide some spectrum of models that ranges from periodic grids,
usually considered in cellular network context, to Poisson ad-hoc networks, and
to various more clustered pp including some doubly stochastic Poisson ones.
|
1009.5696v1
|
2010-10-23
|
Closure method for spatially averaged dynamics of particle chains
|
We study the closure problem for continuum balance equations that model
mesoscale dynamics of large ODE systems. The underlying microscale model
consists of classical Newton equations of particle dynamics. As a mesoscale
model we use the balance equations for spatial averages obtained earlier by a
number of authors: Murdoch and Bedeaux, Hardy, Noll and others. The momentum
balance equation contains a flux (stress), which is given by an exact function
of particle positions and velocities. We propose a method for approximating
this function by a sequence of operators applied to average density and
momentum. The resulting approximate mesoscopic models are systems in closed
form. The closed from property allows one to work directly with the mesoscale
equaitons without the need to calculate underlying particle trajectories, which
is useful for modeling and simulation of large particle systems. The proposed
closure method utilizes the theory of ill-posed problems, in particular
iterative regularization methods for solving first order linear integral
equations. The closed from approximations are obtained in two steps. First, we
use Landweber regularization to (approximately) reconstruct the interpolants of
relevant microscale quantitites from the average density and momentum. Second,
these reconstructions are substituted into the exact formulas for stress. The
developed general theory is then applied to non-linear oscillator chains. We
conduct a detailed study of the simplest zero-order approximation, and show
numerically that it works well as long as fluctuations of velocity are nearly
constant.
|
1010.4832v1
|
2010-10-26
|
Dualities and Identities for Entanglement-Assisted Quantum Codes
|
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is
the code resulting from exchanging the original code's information qubits with
its ebits. To introduce this notion, we show how entanglement-assisted (EA)
repetition codes and accumulator codes are dual to each other, much like their
classical counterparts, and we give an explicit, general quantum shift-register
circuit that encodes both classes of codes.We later show that our constructions
are optimal, and this result completes our understanding of these dual classes
of codes. We also establish the Gilbert-Varshamov bound and the Plotkin bound
for EAQEC codes, and we use these to examine the existence of some EAQEC codes.
Finally, we provide upper bounds on the block error probability when
transmitting maximal-entanglement EAQEC codes over the depolarizing channel,
and we derive variations of the hashing bound for EAQEC codes, which is a lower
bound on the maximum rate at which reliable communication over Pauli channels
is possible with the use of pre-shared entanglement.
|
1010.5506v4
|
2010-11-12
|
Magnetization Dynamics, Bennett Clocking and Associated Energy Dissipation in Multiferroic Logic
|
It has been recently shown that multiferroic logic - where logic bits are
encoded in the magnetization orientation of a nanoscale magnetostrictive layer
elastically coupled to a piezoelectric layer - can be Bennett clocked with
small electrostatic potentials of few tens of mV applied to the piezoelectric
layer. The potential generates stress in the magnetostrictive layer and rotates
its magnetization by a large angle to carry out Bennett clocking. This method
of clocking is far more energy-efficient than using spin transfer torque. In
order to assess if such a clocking scheme can be also reasonably fast, we have
studied the magnetization dynamics of a multiferroic logic array with nearest
neighbor dipole coupling using the Landau-Lifshitz-Gilbert (LLG) equation. We
find that switching delays of ~ 3 ns (clock rates of 0.33 GHz) can be achieved
with proper design provided we clock non-adiabatically and dissipate ~48,000 kT
(at room temperature) of energy per clock cycle per bit flip in the clocking
circuit. This dissipation far exceeds the energy barrier separating the two
logic states, which we assumed to be 32 kT to yield a bit error probability of
. Had we used spin transfer torque to switch with the same ~ 3 ns delay, the
energy dissipation would have been much larger (~ $6 \times 106$ kT). This
shows that spin transfer torque, widely used in magnetic random access memory,
is an inefficient way to switch a magnet, and multiferroic logic clocked with
voltage-induced stress is a superior nanomagnetic logic scheme.
|
1011.2914v2
|
2010-12-30
|
One-dimensional Gromov minimal filling
|
The present paper opens a new branch in the theory of variational problems
with branching extremals, the investigation of one-dimensional minimal fillings
of finite pseudo-metric spaces. On the one hand, this problem is a
one-dimensional version of a generalization of Gromov's minimal fillings
problem to the case of stratified manifolds (the filling in our case is a
weighted graph). On the other hand, this problem is interesting in itself and
also can be considered as a generalization of another classical problem,
namely, the Steiner problem on the construction of a shortest network joining a
given set of terminals. Besides the statement of the problem, we discuss
several properties of the minimal fillings, describe minimal fillings of
additive spaces, and state several conjectures. We also include some
announcements concerning the very recent results obtained in our group,
including a formula calculating the weight of the minimal filling for an
arbitrary finite pseudo-metric space and the concept of pseudo-additive space
which generalizes the classical concept of additive space. We hope that the
theory of one-dimensional minimal fillings refreshes the interest in the
Steiner problem and gives an opportunity to solve several long standing
problems, such as the calculation of the Steiner ratio, in particular the
verification of the Gilbert--Pollack conjecture on the Steiner ratio of the
Euclidean plane.
|
1101.0106v2
|
2011-02-02
|
Kepler Input Catalog: Photometric Calibration and Stellar Classification
|
We describe the photometric calibration and stellar classification methods
used to produce the Kepler Input Catalog (KIC). The KIC is a catalog containing
photometric and physical data for sources in the Kepler Mission field of view;
it is used by the mission to select optimal targets. We derived atmospheric
extinction corrections from hourly observations of secondary standard fields
within the Kepler field of view. Repeatability of absolute photometry for stars
brighter than magnitude 15 is typically 2%. We estimated stellar parameters
Teff, log(g), log (Z), E_{B-V} using Bayesian posterior probability
maximization to match observed colors to Castelli stellar atmosphere models. We
applied Bayesian priors describing the distribution of solar-neighborhood stars
in the color-magnitude diagram (CMD), in log (Z)$, and in height above the
galactic plane. Comparisons with samples of stars classified by other means
indicate that in most regions of the CMD, our classifications are reliable
within about +/- 200 K and +/- 0.4 dex in log (g). It is difficult to assess
the reliability of our log(Z) estimates, but there is reason to suspect that it
is poor, particularly at extreme Teff. Of great importance for the Kepler
Mission, for Teff <= 5400 K, the distinction between main-sequence stars and
giants has proved to be reliable with better than 98% confidence. The KIC is
available through the MAST data archive.
|
1102.0342v2
|
2011-05-10
|
Interstellar Solid Hydrogen
|
We consider the possibility that solid molecular hydrogen is present in
interstellar space. If so cosmic-rays and energetic photons cause ionisation in
the solid leading to the formation of H6+. This ion is not produced by
gas-phase reactions and its radiative transitions therefore provide a signature
of solid H2 in the astrophysical context. The vibrational transitions of H6+
are yet to be observed in the laboratory, but we have characterised them in a
quantum-theoretical treatment of the molecule; our calculations include
anharmonic corrections, which are large. Here we report on those calculations
and compare our results with astronomical data. In addition to the H6+
isotopomer, we focus on the deuterated species (HD)3+ which is expected to
dominate at low ionisation rates as a result of isotopic condensation
reactions. We can reliably predict the frequencies of the fundamental bands for
five modes of vibration. For (HD)3+ all of these are found to lie close to some
of the strongest of the pervasive mid-infrared astronomical emission bands,
making it difficult to exclude hydrogen precipitates on observational grounds.
By the same token these results suggest that (HD)3+ could be the carrier of the
observed bands. We consider this possibility within the broader picture of ISM
photo-processes and we conclude that solid hydrogen may indeed be abundant in
astrophysical environments.
|
1105.1861v1
|
2011-05-12
|
The History of Star Formation in Galaxy Disks in the Local Volume as Measured by the ACS Nearby Galaxy Survey Treasury
|
We present a measurement of the age distribution of stars residing in spiral
disks and dwarf galaxies. We derive a complete star formation history of the
~140 Mpc^3 covered by the volume-limited sample of galaxies in the Advanced
Camera for Surveys (ACS) Nearby Galaxy Survey Treasury (ANGST). The total star
formation rate density history is dominated by the large spirals in the volume,
although the sample consists mainly of dwarf galaxies. Our measurement shows a
factor of ~3 drop at z~2, in approximate agreement with results from other
measurement techniques. While our results show that the overall star formation
rate density has decreased since z~1, the measured rates during this epoch are
higher than those obtained from other measurement techniques. This enhanced
recent star formation rate appears to be largely due to an increase in the
fraction of star formation contained in low-mass disks at recent times.
Finally, our results indicate that despite the differences at recent times, the
epoch of formation of ~50% of the stellar mass in dwarf galaxies was similar to
that of ~50% of the stellar mass in large spiral galaxies (z>~2), despite the
observed galaxy-to-galaxy diversity among the dwarfs.
|
1105.2571v1
|
2011-06-30
|
Revisiting No-Scale Supergravity Inspired Scenarios: Updated Theoretical and Phenomenological Constraints
|
We consider no-scale inspired supergravity scenarios, where the gravitino
mass and related soft supersymmetry-breaking parameters are determined
dynamically by radiative corrections to an essentially flat tree-level
potential in the supersymmetry breaking hidden sector. We examine the
theoretical and phenomenological viability of such a mechanism, when including
up-to-date calculations of the low energy sparticle spectrum and taking into
account the latest LHC results and other experimental constraints. We
(re)emphasize the role of the scale-dependent vacuum energy contribution to the
effective potential, in obtaining realistic no-scale electroweak minima,
examining carefully the impact of boundary conditions and of variants of the
minimization procedure. We also discuss and implement the B_0 (soft breaking
Higgs mixing parameter) input boundary condition at high scale, therefore
fixing tan beta(B_0) at low scales. For general high scale boundary conditions
with non-vanishing B_0, m_0..., our analysis provides theoretical correlations
among the supersymmetric, soft and vacuum energy parameters and related
phenomenological consequences at the LHC. For instance, a zero vacuum energy at
the GUT scale would lead to a decoupled supersymmetric spectrum, together with
a light standard model-like Higgs boson at the electroweak scale. Given the
experimental exclusion limits, a substantial class of the boundary conditions,
and in particular the strict no-scale with m_0=A_0=B_0=0, are only compatible
with a stau being the lightest MSSM particle. Then an enlarged allowed
parameter space emerges when assuming a gravitino LSP to account for the
observed dark matter relic density.
|
1106.6325v2
|
2012-02-21
|
Making Evildoers Pay: Resource-Competitive Broadcast in Sensor Networks
|
Consider a time-slotted, single-hop, wireless sensor network (WSN) consisting
of n correct devices and and t=f*n Byzantine devices where f>=0 is any
constant; that is, the Byzantine devices may outnumber the correct ones. There
exists a trusted sender Alice who wishes to deliver a message m over a single
channel to the correct devices. There also exists a malicious user Carol who
controls the t Byzantine devices and uses them to disrupt the communication
channel. For a constant k>=2, the correct and Byzantine devices each possess a
meager energy budget of O(n^{1/k}), Alice and Carol each possess a limited
budget of \tilde{O}(n^{1/k}), and sending or listening in a slot incurs unit
cost. This general setup captures the inherent challenges of guaranteeing
communication despite scarce resources and attacks on the network. Given this
Alice versus Carol scenario, we ask: Is communication of m feasible and, if so,
at what cost?
We develop a protocol which, for an arbitrarily small constant \epsilon>0,
ensures that at least (1-\epsilon)n correct devices receive m with high
probability. Furthermore, if Carol's devices expend T energy jamming the
channel, then Alice and the correct devices each spend only
\tilde{O}(T^{1/(k+1)}). In other words, delaying the transmission of m forces a
jammer to rapidly deplete its energy supply and, consequently, cease attacks on
the network.
|
1202.4576v4
|
2012-03-28
|
Bispectrum of the Sunyaev-Zel'dovich Effect
|
We perform a detailed study of the bispectrum of the Sunyaev-Zel'dovich
effect. Using an analytical model for the pressure profiles of the intracluster
medium, we demonstrate the SZ bispectrum to be a sensitive probe of the
amplitude of the matter power spectrum parameter sigma_8. We find that the
bispectrum amplitude scales as B_SZ ~ sigma_8^{11-12}, compared to that of the
power spectrum, which scales as A_tSZ ~ sigma_8^{7-9}. We show that the SZ
bispectrum is principally sourced by massive clusters at redshifts around
z~0.4, which have been well-studied observationally. This is in contrast to the
SZ power spectrum, which receives a significant contribution from less-well
understood low-mass and high-redshift groups and clusters. Therefore, the
amplitude of the bispectrum at l~3000 is less sensitive to astrophysical
uncertainties than the SZ power spectrum. We show that current high resolution
CMB experiments should be able to detect the SZ bispectrum amplitude with high
significance, in part due to the low contamination from extra-galactic
foregrounds. A combination of the SZ bispectrum and the power spectrum can
sharpen the measurements of thermal and kinetic SZ components and help
distinguish cosmological and astrophysical information from high-resolution CMB
maps.
|
1203.6368v3
|
2012-05-01
|
A quasi-analytical model for energy-delay-reliability tradeoff studies during write operations in perpendicular STT-RAM cell
|
One of the biggest challenges the current STT-RAM industry faces is
maintaining a high thermal stability while trying to switch within a given
voltage pulse and energy cost. In this paper, we present a physics based
analytical model that uses a modified Simmons' tunneling expression to capture
the spin dependent tunneling in a magnetic tunnel junction(MTJ). Coupled with
an analytical derivation of the critical switching current based on the
Landau-Lifshitz-Gilbert equation, and the write error rate derived from a
solution to the Fokker-Planck equation, this model provides us a quick estimate
of the energydelay- reliability tradeoffs in perpendicular STTRAMs due to
thermal fluctuations. In other words, the model provides a simple way to
calculate the energy consumed during a write operation that ensures a certain
error rate and delay time, while being numerically far less intensive than a
full-fledged stochastic calculation. We calculate the worst case energy
consumption during anti-parallel (AP) to parallel (P) and P to AP switchings
and quantify how increasing the anisotropy field HK and lowering the saturation
magnetization MS, can significantly reduce the energy consumption. A case study
on how manufacturing variations of the MTJ cell can affect the energy
consumption and delay is also reported.
|
1205.0183v1
|
2012-05-16
|
Transients in porous media: asymptotic time-domain Green functions and limits of current frequency-domain models
|
Time domain responses of porous media have been studied by some authors, but
generally the possible descriptions have been given in the frequency domain.
The aim of this paper, limited to materials with rigid skeleton considered as
equivalent fluids, is to compare the descriptions by Johnson-Allard ($JA$%) as
well as by Pride-Lafarge ($PL$) with i) some analytical, approximate formulas,
based upon asymptotic high frequency expansion ; ii) the exact formula by
Zwikker and Kosten for the case of cylindrical pores. The paper starts with a
short summary of the statement of the different general full frequency models
($JA$ and $PL).$ The Green function in the time domain is shown to exhibit
interesting properties of materials. In particular the maximum response depends
on one dimensionless parameter only, which is denoted $\xi $ and is the ratio
of the travelled distance to the product of the \textquotedblleft
frozen\textquotedblright\ sound speed and a characteristic viscous relaxation
time. The distance $\xi $ is related to a time domain Stokes number. The
numerical computation of the Green function is done by FFT, with some
precautions, because of the importance of the higher frequencies on the
response shape. The $PL$ description is shown to be the best full frequency
general model, but some discrepancies with the exact model appear at short
times or short distances. When the distance $\xi $ increases from zero, the
asymptotic expansion shows that the maximum of the Green function decreases
first as $1/\xi ^{2}$, then exponentially.
|
1205.3775v2
|
2012-05-20
|
Externally-driven transformations of vortex textures in flat submicrometer magnets
|
Two effects of oscillatory transformations of vortex textures in flat
nanomagnets due to the application of an external field or a spin-polarized
electric current are analytically described with relevance to soft-magnetic
structures of submicrometer sizes (whose thickness is significantly bigger than
the magnetostatic exchange length). These are changes of a domain wall (DW)
structure in a long magnetic stripe (oscillations between a transverse DW, a
vortex DW, and an antivortex DW) and periodic vortex-core reversals in a
circular magnetic dot which are accompanied by oscillatory displacements of the
vortex from the dot center. In nanostructures of smaller thicknesses
(comparable to the exchange length), where nonlocal magnetostatic effects are
very strong because of fast spatial variation of the magnetization, similar
phenomena have been widely studied previously. Here, the dynamics is
investigated within a local approach including magnetostatic field via boundary
conditions on solutions to the Landau-Lifshitz-Gilbert equation only. Both the
DWs in stripes and vortex states of the dot are treated as fragments of a
cross-tie DW. Despite similarity of the cyclic transformations of the ordering
to the dynamics of more strongly confined nanomagnets, details of motion
(trajectories) of the vortices and antivortices (Bloch lines) of the textures
under study are different, which is related to prohibition of rapid jumps of
the polarization of Bloch lines. In addition to the magnetization rotation
about the direction of magnetic field or current polarization, the evolution of
textures is shown to relate to oscillatory changes of the direction of a
cross-tie DW with respect to any arbitrary axis in the magnet plane accompanied
by oscillations of the DW width.
|
1205.5008v1
|
2012-06-11
|
Multi-Gigabit Wireless data transfer at 60 GHz
|
In this paper we describe the status of the first prototype of the 60 GHz
wireless Multi-gigabit data transfer topology currently under development at
University of Heidelberg using IBM 130 nm SiGe HBT BiCMOS technology. The 60
GHz band is very suitable for high data rate and short distance applications as
for example needed in the HEP experments. The wireless transceiver consist of a
transmitter and a receiver. The transmitter includes an On-Off Keying (OOK)
modulator, an Local Oscillator (LO), a Power Amplifier (PA) and a BandPass
Filter (BPF). The receiver part is composed of a BandPass- Filter (BPF), a Low
Noise Amplifier (LNA), a double balanced down-convert Gilbert mixer, a Local
Oscillator (LO), then a BPF to remove the mixer introduced noise, an
Intermediate Amplifier (IF), an On-Off Keying demodulator and a limiting
amplifier. The first prototype would be able to handle a data-rate of about 3.5
Gbps over a link distance of 1 m. The first simulations of the LNA show that a
Noise Figure (NF) of 5 dB, a power gain of 21 dB at 60 GHz with a 3 dB
bandwidth of more than 20 GHz with a power consumption 11 mW are achieved.
Simulations of the PA show an output referred compression point P1dB of 19.7 dB
at 60 GHz.
|
1206.2287v1
|
2012-06-14
|
On the Interpretation of the Foundations of Quantum Mechanics
|
This study discusses the quantum behavior of a particle, which is controlled
by fluctuations in the physical space-time (ST) variables, rather than provides
a novel interpretation of quantum theory. The fluctuations, i.e.,
inhomogeneities in a homogeneous phase ST, are prescribed by their probability.
They determine the reciprocal space and correlate with the correlation entropy
different from zero. Alongside with the minimum entropy, action, and the
presence of the Winn-Ehrenfest adiabatic invariant (AI), the fluctuations
require the Gilbert information (probabilistic) space linking the physical and
the reciprocal ST. Physical quantities in the information space are represented
by linear Hermitian operators, which is due to the entropy production in the
presence of an AI. Evolution of a quantum system is described by the wave
functions having the meaning of information concerning all virtually possible
states of a quantum particle. The wave functions are the solutions to the
Schrodinger equation and represent a navigation 'roadmap' for the particle to
follow. A quantum system is in fact a classical Hamiltonian system in the space
of coefficients of the wave function decomposition with respect to the operator
eigenfunctions. It is the linearity and the Hermitian nature of the operators
which determine the trajectory and the superposition principle in case of the
wave behavior of fluctuations. The uncertainty principle, reflects correlation
of the fluctuations and, hence, their nonlocality. This study discusses the
wave function phase, the Berry phase and its relationship to quantization,
discriminability of states and macroscopic quantum effects caused by
localization of the particle, followed by a possible entropy change during its
transition into a new thermodynamic state.
|
1206.2998v1
|
2012-08-08
|
RMR-Efficient Randomized Abortable Mutual Exclusion
|
Recent research on mutual exclusion for shared-memory systems has focused on
"local spin" algorithms. Performance is measured using the "remote memory
references" (RMRs) metric. As common in recent literature, we consider a
standard asynchronous shared memory model with N processes, which allows atomic
read, write and compare-and-swap (short: CAS) operations.
In such a model, the asymptotically tight upper and lower bound on the number
of RMRs per passage through the Critical Section is Theta(log N) for the
optimal deterministic algorithms (see Yang and Anderson,1995, and Attiya,
Hendler and Woelfel, 2008). Recently, several randomized algorithms have been
devised that break the Omega(log N) barrier and need only o(log N) RMRs per
passage in expectation (see Hendler and Woelfel, 2010, Hendler and Woelfel,
2011, and Bender and Gilbert, 2011). In this paper we present the first
randomized "abortable" mutual exclusion algorithm that achieves a
sub-logarithmic expected RMR complexity. More precisely, against a weak
adversary (which can make scheduling decisions based on the entire past
history, but not the latest coin-flips of each process) every process needs an
expected number of O(log N/ log log N) RMRs to enter end exit the critical
section. If a process receives an abort-signal, it can abort an attempt to
enter the critical section within a finite number of its own steps and by
incurring O(log N/ log log N) RMRs.
|
1208.1723v1
|
2012-08-16
|
QIRAL: A High Level Language for Lattice QCD Code Generation
|
Quantum chromodynamics (QCD) is the theory of subnuclear physics, aiming at
mod- eling the strong nuclear force, which is responsible for the interactions
of nuclear particles. Lattice QCD (LQCD) is the corresponding discrete
formulation, widely used for simula- tions. The computational demand for the
LQCD is tremendous. It has played a role in the history of supercomputers, and
has also helped defining their future. Designing efficient LQCD codes that
scale well on large (probably hybrid) supercomputers requires to express many
levels of parallelism, and then to explore different algorithmic solutions.
While al- gorithmic exploration is the key for efficient parallel codes, the
process is hampered by the necessary coding effort. We present in this paper a
domain-specific language, QIRAL, for a high level expression of parallel
algorithms in LQCD. Parallelism is expressed through the mathematical struc-
ture of the sparse matrices defining the problem. We show that from these
expressions and from algorithmic and preconditioning formulations, a parallel
code can be automatically generated. This separates algorithms and mathematical
formulations for LQCD (that be- long to the field of physics) from the
effective orchestration of parallelism, mainly related to compilation and
optimization for parallel architectures.
|
1208.4035v1
|
2012-08-22
|
Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
|
We study the single particle entanglement spectrum in 2D topological
insulators which possess $n$-fold rotation symmetry. By defining a series of
special choices of subsystems on which the entanglement is calculated, or real
space cuts, we find that the number of protected in-gap states for each type of
these real space cuts is a quantum number indexing (if any) non-trivial
topology in these insulators. We explicitly show the number of protected in-gap
states is determined by a $Z^n$-index, $(z_1,...,z_n)$, where $z_m$ is the
number of occupied states that transform according to $m$-th one-dimensional
representation of the $C_n$ point group. We find that the entanglement spectrum
contains in-gap states pinned in an interval of entanglement eigenvalues
$[1/n,1-1/n]$. We determine the number of such in-gap states for an exhaustive
variety of cuts, in terms of the $Z_m$ quantum numbers. Furthermore, we show
that in a homogeneous system, the $Z^n$ index can be determined through an
evaluation of the eigenvalues of point group symmetry operators at all
high-symmetry points in the Brillouin zone. When disordered $n$-fold
rotationally symmetric systems are considered, we find that the number of
protected in-gap states is identical to that in the clean limit as long as the
disorder preserves the underlying point group symmetry and does not close the
bulk insulating gap.
|
1208.4603v1
|
2012-09-25
|
Multiscale modeling in micromagnetics: existence of solutions and numerical integration
|
Various applications ranging from spintronic devices, giant magnetoresistance
sensors, and magnetic storage devices, include magnetic parts on very different
length scales. Since the consideration of the Landau-Lifshitz-Gilbert equation
(LLG) constrains the maximum element size to the exchange length within the
media, it is numerically not attractive to simulate macroscopic parts with this
approach. On the other hand, the magnetostatic Maxwell equations do not
constrain the element size, but cannot describe the short-range exchange
interaction accurately. A combination of both methods allows to describe
magnetic domains within the micromagnetic regime by use of LLG and also
considers the macroscopic parts by a non-linear material law using the Maxwell
equations. In our work, we prove that under certain assumptions on the
non-linear material law, this multiscale version of LLG admits weak solutions.
Our proof is constructive in the sense that we provide a linear-implicit
numerical integrator for the multiscale model such that the numerically
computable finite element solutions admit weak $H^1$-convergence (at least for
a subsequence) towards a weak solution.
|
1209.5548v2
|
2012-10-05
|
Rapid Size-Controlled Synthesis of Dextran-Coated, 64Cu-Doped Iron Oxide Nanoparticles
|
Research into developing dual modality probes enabled for magnetic resonance
imaging (MRI) and positron emission tomography (PET) has been on the rise
recently due to the potential to combine the high resolution of MRI and the
high sensitivity of PET. Current synthesis techniques for developing multimodal
probes is largely hindered in part by prolonged reaction times during
radioisotope incorporation - leading to a weakening of the radioactivity. Along
with a time-efficient synthesis, the resulting products must fit within a
critical size range (between 20-100nm) to increase blood retention time. In
this work, we describe a novel, rapid, microwave-based synthesis technique to
grow dextran-coated iron oxide nanoparticles doped with copper (DIO/Cu).
Traditional methods for coprecipitation of dextran-coated iron oxide
nanoparticles require refluxing for 2 hours and result in approximately 50 nm
diameter particles. We demonstrate that microwave synthesis can produce 50 nm
nanoparticles with 5 minutes of heating. We discuss the various parameters used
in the microwave synthesis protocol to vary the size distribution of DIO/Cu,
and demonstrate the successful incorporation of 64Cu into these particles with
the aim of future use for dual-mode MR/PET imaging.
|
1210.1823v1
|
2012-10-05
|
Rapid Microwave-Assisted Synthesis of Dextran-Coated Iron Oxide Nanoparticles for Magnetic Resonance Imaging
|
Currently, magnetic iron oxide nanoparticles are the only nano-sized magnetic
resonance imaging (MRI) contrast agents approved for clinical use, yet
commercial manufacturing of these agents has been limited or discontinued.
Though there is still widespread demand for these particles both for clinical
use and research, they are difficult to obtain commercially, and complicated
syntheses make in-house preparation infeasible for most biological research
labs or clinics. To make commercial production viable and increase
accessibility of these products, it is crucial to develop simple, rapid, and
reproducible preparations of biocompatible iron oxide nanoparticles. Here, we
report a rapid, straightforward microwave-assisted synthesis of
superparamagnetic dextran-coated iron oxide nanoparticles. The nanoparticles
were produced in two hydrodynamic sizes with differing core morphologies by
varying the synthetic method as either a two-step or single step process. A
striking benefit of these methods is the ability to obtain swift and consistent
results without the necessity for air, pH, or temperature sensitive techniques;
therefore, reaction times and complex manufacturing processes are greatly
reduced as compared to conventional synthetic methods. This is a great benefit
for cost-effective translation to commercial production. The nanoparticles are
found to be superparamagnetic and exhibit properties consistent for use in MRI.
In addition, the dextran coating imparts the water-solubility and
biocompatibility necessary for in vivo utilization.
|
1210.1827v1
|
2012-10-16
|
Dark Matter Substructure Detection Using Spatially Resolved Spectroscopy of Lensed Dusty Galaxies
|
We investigate how strong lensing of dusty, star-forming galaxies by
foreground galaxies can be used as a probe of dark matter halo substructure. We
find that spatially resolved spectroscopy of lensed sources allows dramatic
improvements to measurements of lens parameters. In particular we find that
modeling of the full, three-dimensional (angular position and radial velocity)
data can significantly facilitate substructure detection, increasing the
sensitivity of observables to lower mass subhalos. We carry out simulations of
lensed dusty sources observed by early ALMA (Cycle 1) and use a Fisher matrix
analysis to study the parameter degeneracies and mass detection limits of this
method. We find that, even with conservative assumptions, it is possible to
detect galactic dark matter subhalos of ~ 10^8 M_{\odot} with high significance
in most lensed DSFGs. Specifically, we find that in typical DSFG lenses, there
is a ~ 55 % probability of detecting a substructure with M>10^8 M_{\odot} with
more than 5 sigma detection significance in each lens, if the abundance of
substructure is consistent with previous lensing results. The full ALMA array,
with its significantly enhanced sensitivity and resolution, should improve
these estimates considerably. Given the sample of ~100 lenses provided by
surveys like the South Pole Telescope, our understanding of dark matter
substructure in typical galaxy halos is poised to improve dramatically over the
next few years.
|
1210.4562v1
|
2012-10-22
|
Shared Information -- New Insights and Problems in Decomposing Information in Complex Systems
|
How can the information that a set ${X_{1},...,X_{n}}$ of random variables
contains about another random variable $S$ be decomposed? To what extent do
different subgroups provide the same, i.e. shared or redundant, information,
carry unique information or interact for the emergence of synergistic
information?
Recently Williams and Beer proposed such a decomposition based on natural
properties for shared information. While these properties fix the structure of
the decomposition, they do not uniquely specify the values of the different
terms. Therefore, we investigate additional properties such as strong symmetry
and left monotonicity. We find that strong symmetry is incompatible with the
properties proposed by Williams and Beer. Although left monotonicity is a very
natural property for an information measure it is not fulfilled by any of the
proposed measures.
We also study a geometric framework for information decompositions and ask
whether it is possible to represent shared information by a family of posterior
distributions.
Finally, we draw connections to the notions of shared knowledge and common
knowledge in game theory. While many people believe that independent variables
cannot share information, we show that in game theory independent agents can
have shared knowledge, but not common knowledge. We conclude that intuition and
heuristic arguments do not suffice when arguing about information.
|
1210.5902v1
|
2012-10-23
|
Lensing Noise in mm-wave Galaxy Cluster Surveys
|
We study the effects of gravitational lensing by galaxy clusters of the
background of dusty star-forming galaxies (DSFGs) and the Cosmic Microwave
Background (CMB), and examine the implications for Sunyaev-Zel'dovich-based
(SZ) galaxy cluster surveys. At the locations of galaxy clusters, gravitational
lensing modifies the probability distribution of the background flux of the
DSFGs as well as the CMB. We find that, in the case of a single-frequency 150
GHz survey, lensing of DSFGs leads to both a slight increase (~10%) in detected
cluster number counts (due to a ~ 50% increase in the variance of the DSFG
background, and hence an increased Eddington bias), as well as to a rare
(occurring in ~2% of clusters) "filling-in" of SZ cluster signals by bright
strongly lensed background sources. Lensing of the CMB leads to a ~55%
reduction in CMB power at the location of massive galaxy clusters in a
spatially-matched single-frequency filter, leading to a net decrease in
detected cluster number counts. We find that the increase in DSFG power and
decrease in CMB power due to lensing at cluster locations largely cancel, such
that the net effect on cluster number counts for current SZ surveys is
sub-dominant to Poisson errors.
|
1210.6354v1
|
2012-10-29
|
Spin-Transfer Torque Magnetization Reversal in Uniaxial Nanomagnets with Thermal Noise
|
We consider the general Landau-Lifshitz-Gilbert (LLG) dynamical theory
underlying the magnetization switching rates of a thin film uniaxial magnet
subject to spin-torque effects and thermal fluctuations (thermal noise). After
discussing the various dynamical regimes governing the switching phenomena, we
present analytical results for the mean switching time behavior. Our approach,
based on explicitly solving the first passage time problem, allows for a
straightforward analysis of the thermally assisted, low spin-torque, switching
asymptotics of thin film magnets. To verify our theory, we have developed an
efficient GPU-based micromagnetic code to simulate the stochastic LLG dynamics
out to millisecond timescales. We explore the effects of geometrical tilts
between the spin-current and uniaxial anisotropy axes on the thermally assisted
dynamics. We find that even in the absence of axial symmetry, the switching
times can be functionally described in a form virtually identical to the
collinear case. We further verify that asymptotic behavior is reached fairly
slowly, thus quantifying the role of thermal noise in the crossover regime
linking deterministic to thermally assisted magnetization reversal.
|
1210.7675v3
|
2012-12-06
|
Splittings and automorphisms of relatively hyperbolic groups
|
We study automorphisms of a relatively hyperbolic group G. When G is
one-ended, we describe Out(G) using a preferred JSJ tree over subgroups that
are virtually cyclic or parabolic. In particular, when G is toral relatively
hyperbolic, Out(G) is virtually built out of mapping class groups and subgroups
of GL_n(Z) fixing certain basis elements. When more general parabolic groups
are allowed, these subgroups of GL_n(Z) have to be replaced by McCool groups:
automorphisms of parabolic groups acting trivially (i.e. by conjugation) on
certain subgroups. Given a malnormal quasiconvex subgroup P of a hyperbolic
group G, we view G as hyperbolic relative to P and we apply the previous
analysis to describe the group Out(P to G) of automorphisms of P that extend to
G: it is virtually a McCool group. If Out(P to G) is infinite, then P is a
vertex group in a splitting of G. If P is torsion-free, then Out(P to G) is of
type VF, in particular finitely presented. We also determine when Out(G) is
infinite, for G relatively hyperbolic. The interesting case is when G is
infinitely-ended and has torsion. When G is hyperbolic, we show that Out(G) is
infinite if and only if G splits over a maximal virtually cyclic subgroup with
infinite center. In general we show that infiniteness of Out(G) comes from the
existence of a splitting with infinitely many twists, or having a vertex group
that is maximal parabolic with infinitely many automorphisms acting trivially
on incident edge groups.
|
1212.1434v3
|
2013-01-23
|
Localization, metabelian groups, and the isomorphism problem
|
If G and H are finitely generated, residually nilpotent metabelian groups, H
is termed para-G if there is a homomorphism of G into H which induces an
isomorphism between the corresponding terms of their lower central quotient
groups. We prove that this is an equivalence relation. It is a much coarser
relation than isomorphism, our ultimate concern. It turns out that many of the
groups in a given equivalence class share various properties including finite
presentability. There are examples, such as the lamplighter group, where an
equivalence class consists of a single isomorphism class and others where this
is not the case. We give several examples where we solve the Isomorphism
Problem. We prove also that the sequence of torsion-free ranks of the lower
central quotients of a finitely generated metabelian group is computable. In a
future paper we plan on proving that there is an algorithm to compute the
numerator and denominator of the rational Poincar\'e series of a finitely
generated metabelian group and will carry out this computation in a number of
examples, which may shed a tiny bit of light on the Isomorphism Problem. Our
proofs use localization, class field theory and some constructive commutative
algebra.
|
1301.5533v2
|
2013-01-26
|
Crystal nucleation and near-epitaxial growth in nacre
|
Nacre is a layered, iridescent lining found inside many mollusk shells, with
a unique brick-and-mortar periodic structure at the sub-micron scale, and
remarkable resistance to fracture. Despite extensive studies, it remains
unclear how nacre forms. Here we present 20-nm, 2{\deg}-resolution
Polarization-dependent Imaging Contrast (PIC) images of shells from 15 mollusk
shell species, mapping nacre tablets and their orientation patterns, showing
where new crystal orientations appear and how they propagate across organic
sheets as nacre grows. In all shells we found stacks of co-oriented aragonite
(CaCO3) tablets arranged into vertical columns or staggered diagonally. Only
near the nacre-prismatic boundary are disordered crystals nucleated, as
spherulitic aragonite. Overgrowing nacre tablet crystals are most frequently
co-oriented with the underlying spherulitic aragonite or with another tablet,
connected by mineral bridges. Therefore aragonite crystal growth in nacre is
epitaxial or near-epitaxial, with abrupt or gradual changes in orientation,
with c-axes within 20{\deg}. Based on these data, we propose that there is one
mineral bridge per tablet, and that "bridge-tilting" is a possible mechanism to
introduce small, gradual or abrupt changes in the orientation of crystals
within a stack of tablets as nacre grows.
|
1301.6273v2
|
2013-02-03
|
A generalization of variable elimination for separable inverse problems beyond least squares
|
In linear inverse problems, we have data derived from a noisy linear
transformation of some unknown parameters, and we wish to estimate these
unknowns from the data. Separable inverse problems are a powerful
generalization in which the transformation itself depends on additional unknown
parameters and we wish to determine both sets of parameters simultaneously.
When separable problems are solved by optimization, convergence can often be
accelerated by elimination of the linear variables, a strategy which appears
most prominently in the variable projection methods due to Golub, Pereyra, and
Kaufman. Existing variable elimination methods require an explicit formula for
the optimal value of the linear variables, so they cannot be used in problems
with Poisson likelihoods, bound constraints, or other important departures from
least squares.
To address this limitation, we propose a generalization of variable
elimination in which standard optimization methods are modified to behave as
though a variable has been eliminated. We verify that this approach is a proper
generalization by using it to re-derive several existing variable elimination
techniques. We then extend the approach to bound-constrained and Poissonian
problems, showing in the process that many of the best features of variable
elimination methods can be duplicated in our framework. Tests on difficult
exponential sum fitting and blind deconvolution problems indicate that the
proposed approach can have significant speed and robustness advantages over
standard methods.
|
1302.0441v2
|
2013-04-05
|
City versus wetland: Predicting urban growth in the Vecht area with a cellular automaton model
|
There are many studies dealing with the protection or restoration of wetlands
and the sustainable economic growth of cities as separate subjects. This study
investigates the conflict between the two in an area where city growth is
threatening a protected wetland area. We develop a stochastic cellular
automaton model for urban growth and apply it to the Vecht area surrounding the
city of Hilversum in the Netherlands, using topographic maps covering the past
150 years. We investigate the dependence of the urban growth pattern on the
values associated with the protected wetland and other types of landscape
surrounding the city. The conflict between city growth and wetland protection
is projected to occur before 2035, assuming full protection of the wetland. Our
results also show that a milder protection policy, allowing some of the wetland
to be sacrificed, could be beneficial for maintaining other valuable
landscapes. This insight would be difficult to achieve by other analytical
means. We conclude that even slight changes in usage priorities of landscapes
can significantly affect the landscape distribution in near future. Our results
also point to the importance of a protection policy to take the value of
surrounding landscapes and the dynamic nature of urban areas into account.
|
1304.1609v1
|
2013-04-22
|
Topological Insulators with Commensurate Antiferromagnetism
|
We study the topological features of non-interacting insulators subject to an
antiferromangetic (AFM) Zeeman field, or AFM insulators, the period of which is
commensurate with the lattice period. These insulators can be classified by the
presence/absence of an emergent anti-unitary symmetry: the combined operation
of time-reversal and a lattice translation by vector $\mathbf{D}$. For AFM
insulators that preserve this combined symmetry, regardless of any details in
lattice structure or magnetic structure, we show that (i) there is a new type
of Kramers' degeneracy protected by the combined symmetry; (ii) a new $Z_2$
index may be defined for 3D AFM insulators, but not for those in lower
dimensions and (iii) in 3D AFM insulators with a non-trivial $Z_2$ index, there
are odd number of gapless surface modes if and only if the surface termination
also preserves the combined symmetry, but the dispersion of surface states
becomes highly anisotropic if the AFM propagation vector becomes small compared
with the reciprocal lattice vectors. We numerically demonstrate the theory by
calculating the spectral weight of the surface states of a 3D TI in the
presence of AFM fields with different propagation vectors, which may be
observed by ARPES in Bi$_2$Se$_3$ or Bi$_2$Te$_3$ with induced
antiferromagnetism.
|
1304.6081v3
|
2013-05-17
|
Spectral gap for stochastic energy exchange model with nonuniformly positive rate function
|
We give a lower bound on the spectral gap for a class of stochastic energy
exchange models. In 2011, Grigo et al. introduced the model and showed that,
for a class of stochastic energy exchange models with a uniformly positive rate
function, the spectral gap of an $N$-component system is bounded from below by
a function of order $N^{-2}$. In this paper, we consider the case where the
rate function is not uniformly positive. For this case, the spectral gap
depends not only on $N$ but also on the averaged energy $\mathcal{E}$, which is
the conserved quantity under the dynamics. Under some assumption, we obtain a
lower bound of the spectral gap which is of order $C(\mathcal{E})N^{-2}$ where
$C(\mathcal{E})$ is a positive constant depending on $\mathcal {E}$. As a
corollary of the result, a lower bound of the spectral gap for the mesoscopic
energy exchange process of billiard lattice studied by Gaspard and Gilbert [J.
Stat. Mech. Theory Exp. 2008 (2008) p11021, J. Stat. Mech. Theory Exp. 2009
(2009) p08020] and the stick process studied by Feng et al. [Stochastic
Process. Appl. 66 (1997) 147-182] are obtained.
|
1305.4066v3
|
2013-08-18
|
Layered Constructions for Low-Delay Streaming Codes
|
We propose a new class of error correction codes for low-delay streaming
communication. We consider an online setup where a source packet arrives at the
encoder every $M$ channel uses, and needs to be decoded with a maximum delay of
$T$ packets. We consider a sliding-window erasure channel --- $\cC(N,B,W)$ ---
which introduces either up to $N$ erasures in arbitrary positions, or $B$
erasures in a single burst, in any window of length $W$. When $M=1$, the case
where source-arrival and channel-transmission rates are equal, we propose a
class of codes --- MiDAS codes --- that achieve a near optimal rate. Our
construction is based on a {\em layered} approach. We first construct an
optimal code for the $\cC(N=1,B,W)$ channel, and then concatenate an additional
layer of parity-check symbols to deal with $N>1$. When $M > 1$, the case where
source-arrival and channel-transmission rates are unequal, we characterize the
capacity when $N=1$ and $W \ge M(T+1),$ and for $N>1$, we propose a
construction based on a layered approach. Numerical simulations over
Gilbert-Elliott and Fritchman channel models indicate significant gains in the
residual loss probability over baseline schemes. We also discuss the connection
between the error correction properties of the MiDAS codes and their underlying
column distance and column span.
|
1308.3827v1
|
2013-08-31
|
Delay Minimization for Instantly Decodable Network Coding in Persistent Channels with Feedback Intermittence
|
In this paper, we consider the problem of minimizing the multicast decoding
delay of generalized instantly decodable network coding (G-IDNC) over
persistent forward and feedback erasure channels with feedback intermittence.
In such an environment, the sender does not always receive acknowledgement from
the receivers after each transmission. Moreover, both the forward and feedback
channels are subject to persistent erasures, which can be modelled by a two
state (good and bad states) Markov chain known as Gilbert-Elliott channel
(GEC). Due to such feedback imperfections, the sender is unable to determine
subsequent instantly decodable packets combination for all receivers. Given
this harsh channel and feedback model, we first derive expressions for the
probability distributions of decoding delay increments and then employ these
expressions in formulating the minimum decoding problem in such environment as
a maximum weight clique problem in the G-IDNC graph. We also show that the
problem formulations in simpler channel and feedback models are special cases
of our generalized formulation. Since this problem is NP-hard, we design a
greedy algorithm to solve it and compare it to blind approaches proposed in
literature. Through extensive simulations, our adaptive algorithm is shown to
outperform the blind approaches in all situations and to achieve significant
improvement in the decoding delay, especially when the channel is highly
persistent
|
1309.0145v2
|
2013-09-06
|
Energy release from impacting prominence material following the 2011 June 7 eruption
|
Solar filaments exhibit a range of eruptive-like dynamic activity, ranging
from the full or partial eruption of the filament mass and surrounding magnetic
structure as a coronal mass ejection (CME), to a fully confined or 'failed'
eruption. On 2011 June 7, a dramatic partial eruption of a filament was
observed by multiple instruments on SDO and STEREO. One of the interesting
aspects of this event is the response of the solar atmosphere as non-escaping
material falls inward under the influence of gravity. The impact sites show
clear evidence of brightening in the observed EUV wavelengths due to energy
release. Two plausible physical mechanisms explaining the brightening are
considered: heating of the plasma due to the kinetic energy of impacting
material compressing the plasma, or reconnection between the magnetic field of
low-lying loops and the field carried by the impacting material. By analyzing
the emission of the brightenings in several SDO/AIA wavelengths, and comparing
the kinetic energy of the impacting material (7.6 x 10^26 - 5.8 x 10^27 ergs)
to the radiative energy (1.9 x 10^25 - 2.5 x 10^26 ergs) we find the dominant
mechanism of energy release involved in the observed brightening is plasma
compression.
|
1309.1769v1
|
2013-09-26
|
Constraints on a second planet in the WASP-3 system
|
There have been previous hints that the transiting planet WASP-3 b is
accompanied by a second planet in a nearby orbit, based on small deviations
from strict periodicity of the observed transits. Here we present 17 precise
radial velocity measurements and 32 transit light curves that were acquired
between 2009 and 2011. These data were used to refine the parameters of the
host star and transiting planet. This has resulted in reduced uncertainties for
the radii and masses of the star and planet. The radial-velocity data and the
transit times show no evidence for an additional planet in the system.
Therefore, we have determined the upper limit on the mass of any hypothetical
second planet, as a function of its orbital period.
|
1309.6733v1
|
2013-09-28
|
Synthetic Multiferroic Interconnects for Magnetic Logic Circuits
|
In this work, we consider the possibility of using synthetic multiferroics
comprising piezoelectric and magnetostrictive materials as an interconnect for
nano magnetic logic circuits. The proposed interconnect resembles a parallel
plate capacitor filled with a piezoelectric, where one of the plates is made of
a magnetoelastic material. The operation of the interconnect is based on the
effect of stress-mediated anisotropy modulation, where an electric field
applied across the piezoelectric material produces stress, which, in turn,
affects the anisotropy field in the magnetostrictive material. We present the
results of numerical modeling illustrating signal propagation through the
interconnect. The model combines electric and magnetic parts, where the
electric part describes the distribution of an electric field through the
piezoelectric and the magnetic part describes the change of magnetization in
the magnetoelastic layer. The model is based on the Landau-Lifshitz-Gilbert
equation with the electric field dependent anisotropy term included. The
utilization of the electro-magnetic coupling makes it possible to amplify
magnetic signal during its propagation via energy conversion from the electric
to magnetic domains. Potentially, synthetic multiferroic interconnects can be
implemented in a variety of spin-based devices ensuring reliable and low-energy
consuming data transmission. According to the estimates, the group velocity of
magnetic signals may be up to 100 km/s with energy dissipation less than aJ per
bit per 100nm. The fundamental limits and practical shortcoming of the proposed
approach are also discussed.
|
1309.7399v1
|
2013-10-01
|
Ionized Plasma and Neutral Gas Coupling in the Sun's Chromosphere and Earth's Ionosphere/Thermosphere
|
We review our understanding of ionized plasma and neutral gas coupling in the
weakly ionized, stratified, electromagnetically-permeated regions of the Sun's
chromosphere and Earth's ionosphere/thermosphere. Using representative models
for each environment we derive fundamental descriptions of the coupling of the
constituent parts to each other and to the electric and magnetic fields, and we
examine the variation in magnetization of the ionized component. Using these
descriptions we compare related phenomena in the two environments, and discuss
electric currents, energy transfer and dissipation. We present a coupled
theoretical and numerical study of plasma instabilities in the two environments
that serves as an example of how the chromospheric and ionospheric communities
can further collaborate. We also suggest future collaborative studies that will
help improve our understanding of these two different atmospheres which share
many similarities, but have large disparities in key quantities.
|
1310.0405v4
|
2013-11-13
|
Excitation of radial collective modes in a quantum dot: Beyond linear response
|
We compare the response of five different models of two interacting electrons
in a quantum dot to an external short lived radial excitation that is strong
enough to excite the system well beyond the linear response regime. The models
considered describe the Coulomb interaction between the electrons in different
ways ranging from mean-field approaches to configuration interaction (CI)
models, where the two-electron Hamiltonian is diagonalized in a large truncated
Fock space. The radially symmetric excitation is selected in order to severely
put to test the different approaches to describe the interaction and
correlations of an electron system in a nonequilibrium state. As can be
expected for the case of only two electrons none of the mean-field models can
in full details reproduce the results obtained by the CI model. Nonetheless,
some linear and nonlinear characteristics are reproduced reasonably well. All
the models show activation of an increasing number of collective modes as the
strength of the excitation is increased. By varying slightly the confinement
potential of the dot we observe how sensitive the properties of the excitation
spectrum are to the Coulomb interaction and its correlation effects. In order
to approach closer the question of nonlinearity we solve one of the mean-field
models directly in a nonlinear fashion without resorting to iterations.
|
1311.3252v2
|
2013-11-20
|
Neutron-induced dpa, transmutations, gas production, and helium embrittlement of fusion materials
|
In a fusion reactor materials will be subjected to significant fluxes of
high-energy neutrons. As well as causing radiation damage, the neutrons also
initiate nuclear reactions leading to changes in the chemical composition of
materials (transmutation). Many of these reactions produce gases, particularly
helium, which cause additional swelling and embrittlement of materials. This
paper investigates, using a combination of neutron-transport and inventory
calculations, the variation in displacements per atom (dpa) and helium
production levels as a function of position within the high flux regions of a
recent conceptual model for the "next-step" fusion device DEMO. Subsequently,
the gas production rates are used to provide revised estimates, based on new
density-functional-theory results, for the critical component lifetimes
associated with the helium-induced grain-boundary embrittlement of materials.
The revised estimates give more optimistic projections for the lifetimes of
materials in a fusion power plant compared to a previous study, while at the
same time indicating that helium embrittlement remains one of the most
significant factors controlling the structural integrity of fusion power plant
components.
|
1311.5079v1
|
2013-12-19
|
The availability of research data declines rapidly with article age
|
Policies ensuring that research data are available on public archives are
increasingly being implemented at the government [1], funding agency [2-4], and
journal [5,6] level. These policies are predicated on the idea that authors are
poor stewards of their data, particularly over the long term [7], and indeed
many studies have found that authors are often unable or unwilling to share
their data [8-11]. However, there are no systematic estimates of how the
availability of research data changes with time since publication. We therefore
requested datasets from a relatively homogenous set of 516 articles published
between 2 and 22 years ago, and found that availability of the data was
strongly affected by article age. For papers where the authors gave the status
of their data, the odds of a dataset being extant fell by 17% per year. In
addition, the odds that we could find a working email address for the first,
last or corresponding author fell by 7% per year. Our results reinforce the
notion that, in the long term, research data cannot be reliably preserved by
individual researchers, and further demonstrate the urgent need for policies
mandating data sharing via public archives.
|
1312.5670v1
|
2014-01-13
|
On List-decodability of Random Rank Metric Codes
|
In the present paper, we consider list decoding for both random rank metric
codes and random linear rank metric codes. Firstly, we show that, for arbitrary
$0<R<1$ and $\epsilon>0$ ($\epsilon$ and $R$ are independent), if
$0<\frac{n}{m}\leq \epsilon$, then with high probability a random rank metric
code in $F_{q}^{m\times n}$ of rate $R$ can be list-decoded up to a fraction
$(1-R-\epsilon)$ of rank errors with constant list size $L$ satisfying $L\leq
O(1/\epsilon)$. Moreover, if $\frac{n}{m}\geq\Theta_R(\epsilon)$, any rank
metric code in $F_{q}^{m\times n}$ with rate $R$ and decoding radius
$\rho=1-R-\epsilon$ can not be list decoded in ${\rm poly}(n)$ time. Secondly,
we show that if $\frac{n}{m}$ tends to a constant $b\leq 1$, then every
$F_q$-linear rank metric code in $F_{q}^{m\times n}$ with rate $R$ and list
decoding radius $\rho$ satisfies the Gilbert-Varsharmov bound, i.e., $R\leq
(1-\rho)(1-b\rho)$. Furthermore, for arbitrary $\epsilon>0$ and any $0<\rho<1$,
with high probability a random $F_q$-linear rank metric codes with rate
$R=(1-\rho)(1-b\rho)-\epsilon$ can be list decoded up to a fraction $\rho$ of
rank errors with constant list size $L$ satisfying $L\leq O(\exp(1/\epsilon))$.
|
1401.2693v2
|
2014-01-30
|
Quantitative Decoding of Interactions in Tunable Nanomagnet Arrays Using First Order Reversal Curves
|
To develop a full understanding of interactions in nanomagnet arrays is a
persistent challenge, critically impacting their technological acceptance. This
paper reports the experimental, numerical and analytical investigation of
interactions in arrays of Co nanoellipses using the first-order reversal curve
(FORC) technique. A mean-field analysis has revealed the physical mechanisms
giving rise to all of the observed features: a shift of the non-interacting
FORC-ridge at the low-H$_c$ end off the local coercivity H$_c$ axis; a stretch
of the FORC-ridge at the high-H$_c$ end without shifting it off the H$_c$ axis;
and a formation of a tilted edge connected to the ridge at the low-H$_c$ end.
Changing from flat to Gaussian coercivity distribution produces a negative
feature, bends the ridge, and broadens the edge. Finally, nearest neighbor
interactions segment the FORC-ridge. These results demonstrate that the FORC
approach provides a comprehensive framework to qualitatively and quantitatively
decode interactions in nanomagnet arrays.
|
1401.7749v1
|
2014-02-07
|
For-all Sparse Recovery in Near-Optimal Time
|
An approximate sparse recovery system in $\ell_1$ norm consists of parameters
$k$, $\epsilon$, $N$, an $m$-by-$N$ measurement $\Phi$, and a recovery
algorithm, $\mathcal{R}$. Given a vector, $\mathbf{x}$, the system approximates
$x$ by $\widehat{\mathbf{x}} = \mathcal{R}(\Phi\mathbf{x})$, which must satisfy
$\|\widehat{\mathbf{x}}-\mathbf{x}\|_1 \leq
(1+\epsilon)\|\mathbf{x}-\mathbf{x}_k\|_1$. We consider the 'for all' model, in
which a single matrix $\Phi$, possibly 'constructed' non-explicitly using the
probabilistic method, is used for all signals $\mathbf{x}$. The best existing
sublinear algorithm by Porat and Strauss (SODA'12) uses $O(\epsilon^{-3}
k\log(N/k))$ measurements and runs in time $O(k^{1-\alpha}N^\alpha)$ for any
constant $\alpha > 0$.
In this paper, we improve the number of measurements to $O(\epsilon^{-2} k
\log(N/k))$, matching the best existing upper bound (attained by super-linear
algorithms), and the runtime to $O(k^{1+\beta}\textrm{poly}(\log
N,1/\epsilon))$, with a modest restriction that $\epsilon \leq (\log k/\log
N)^{\gamma}$, for any constants $\beta,\gamma > 0$. When $k\leq \log^c N$ for
some $c>0$, the runtime is reduced to $O(k\textrm{poly}(N,1/\epsilon))$. With
no restrictions on $\epsilon$, we have an approximation recovery system with $m
= O(k/\epsilon \log(N/k)((\log N/\log k)^\gamma + 1/\epsilon))$ measurements.
|
1402.1726v2
|
2014-03-11
|
Measuring the power spectrum of dark matter substructure using strong gravitational lensing
|
In recent years, it has become possible to detect individual dark matter
subhalos near images of strongly lensed extended background galaxies.
Typically, only the most massive subhalos in the strong lensing region may be
detected this way. In this work, we show that strong lenses may also be used to
constrain the much more numerous population of lower mass subhalos that are too
small to be detected individually. In particular, we show that the power
spectrum of projected density fluctuations in galaxy halos can be measured
using strong gravitational lensing. We develop the mathematical framework of
power spectrum estimation, and test our method on mock observations. We use our
results to determine the types of observations required to measure the
substructure power spectrum with high significance. We predict that deep
observations ($\sim10$ hours on a single target) with current facilities can
measure this power spectrum at the $3\sigma$ level, with no apparent degeneracy
with unknown clumpiness in the background source structure or fluctuations from
detector noise. Upcoming ALMA measurements of strong lenses are capable of
placing strong constraints on the abundance of dark matter subhalos and the
underlying particle nature of dark matter.
|
1403.2720v3
|
2014-03-14
|
Cosmological Spectral Deconvolution
|
One of the main goals of modern observational cosmology is to map the large
scale structure of the Universe. A potentially powerful approach for doing this
would be to exploit three-dimensional spectral maps, i.e. the specific
intensity of extragalactic light as a function of wavelength and direction on
the sky, to measure spatial variations in the total extragalactic light
emission and use these as a tracer of the clustering of matter. A main
challenge is that the observed intensity as a function of wavelength is a
convolution of the source luminosity density with the rest-frame spectral
energy distribution. In this paper, we introduce the method of spectral
deconvolution as a way to invert this convolution and extract the clustering
information. We show how one can use observations of the mean and angular
fluctuations of extragalactic light as a function of wavelength, assuming
statistical isotropy, to reconstruct jointly the rest-frame spectral energy
distribution of the sources and the source spatial density fluctuations. This
method is more general than the well known line mapping technique as it does
not rely on spectral lines in the emitted spectra. After introducing the
general formalism, we discuss its implementation and limitations. This formal
paper sets the stage for future more practical studies.
|
1403.3727v1
|
2014-03-27
|
On the Performance of Short Block Codes over Finite-State Channels in the Rare-Transition Regime
|
As the mobile application landscape expands, wireless networks are tasked
with supporting different connection profiles, including real-time traffic and
delay-sensitive communications. Among many ensuing engineering challenges is
the need to better understand the fundamental limits of forward error
correction in non-asymptotic regimes. This article characterizes the
performance of random block codes over finite-state channels and evaluates
their queueing performance under maximum-likelihood decoding. In particular,
classical results from information theory are revisited in the context of
channels with rare transitions, and bounds on the probabilities of decoding
failure are derived for random codes. This creates an analysis framework where
channel dependencies within and across codewords are preserved. Such results
are subsequently integrated into a queueing problem formulation. For instance,
it is shown that, for random coding on the Gilbert-Elliott channel, the
performance analysis based on upper bounds on error probability provides very
good estimates of system performance and optimum code parameters. Overall, this
study offers new insights about the impact of channel correlation on the
performance of delay-aware, point-to-point communication links. It also
provides novel guidelines on how to select code rates and block lengths for
real-time traffic over wireless communication infrastructures.
|
1403.7232v1
|
2014-04-08
|
Cost-oblivious storage reallocation
|
Databases need to allocate and free blocks of storage on disk. Freed blocks
introduce holes where no data is stored. Allocation systems attempt to reuse
such deallocated regions in order to minimize the footprint on disk. If
previously allocated blocks cannot be moved, the problem is called the memory
allocation problem, which is known to have a logarithmic overhead in the
footprint.
This paper defines the storage reallocation problem, where previously
allocated blocks can be moved, or reallocated, but at some cost. The algorithms
presented here are cost oblivious, in that they work for a broad and reasonable
class of cost functions, even when they do not know what the cost function is.
The objective is to minimize the storage footprint, that is, the largest
memory address containing an allocated object, while simultaneously minimizing
the reallocation costs. This paper gives asymptotically optimal algorithms for
storage reallocation, in which the storage footprint is at most (1+epsilon)
times optimal, and the reallocation cost is at most (1/epsilon) times the
original allocation cost, which is also optimal. The algorithms are cost
oblivious as long as the allocation/reallocation cost function is subadditive.
|
1404.2019v3
|
2014-04-14
|
Magneto-photonic phenomena at terahertz frequencies
|
Magneto-terahertz phenomena are the main focus of the thesis. This work
started as supporting research for the science of an X-ray laser (SwissFEL).
X-ray lasers have recently drawn great attention as an unprecedented tool for
scientific research on the ultrafast scale..... To answer this fundamental
question, we performed original numerical simulations using a coupled Landau-
Lifshitz-Gilbert Maxwell model. ... Those requirements were the motivations for
the experiments performed in the second part of the thesis. To shape the
terahertz pulses, .... Regarding the field intensities, we followed two
approaches. The first deals with field enhancement in nanoslits arrays. We
designed a subwavelength structure characterized by simultaneous high field
enhancement and high transmission at terahertz frequencies to suit nonlinear
sources. The second approach depended on up-scaling the generation from
laser-induced plasma by increasing the pump wavelengths. Numerical calculations
have also brought to our attention the importance of linear magnetoterahertz
effects. In particular, the simulations showed that the ultrafast dynamics
could lead to significant rotation of the polarization plane of the triggering
terahertz pulse. Motivated by this finding, we focused in the last part of the
thesis on the linear effects. We performed three original studies coming out
with first demonstrations of broadband non-reciprocal terahertz phase
retarders, terahertz magnetic modulators, and the non-reciprocal terahertz
isolators. In the first two experiments, we extended the unique properties of
the magnetic liquids (Ferrofluids) to the terahertz regime. In the latter
experiment, we used a permanent magnet (Ferrite) to experimentally show
complete isolation (unidirectional transmission) of the terahertz waves.
|
1404.3764v1
|
2014-05-13
|
The Star Formation Histories of Local Group Dwarf Galaxies II. Searching For Signatures of Reionization
|
We search for signatures of reionization in the star formation histories
(SFHs) of 38 Local Group dwarf galaxies (10$^4$ $<$ M$_{\star}$ $<$ 10$^9$
M$_{\odot}$). The SFHs are derived from color-magnitude diagrams using archival
Hubble Space Telescope/Wide Field Planetary Camera 2 imaging. Only five
quenched galaxies (And V, And VI, And XIII, Leo IV, Hercules) are consistent
with forming the bulk of their stars before reionization, when full
uncertainties are considered. Observations of 13 of the predicted `true
fossils' identified by Bovill & Ricotti show that only two (Hercules and Leo
IV) indicate star formation quenched by reionization. However, both are within
the virial radius of the Milky Way and evidence of tidal disturbance
complicates this interpretation. We argue that the late-time gas capture
scenario posited by Ricotti for the low mass, gas-rich, and star-forming fossil
candidate Leo T is observationally indistinguishable from simple gas retention.
Given the ambiguity between environmental effects and reionization, the best
reionization fossil candidates are quenched low mass field galaxies (e.g., KKR
25).
|
1405.3281v1
|
2014-05-26
|
Constraints for the Progenitor Masses of 17 Historic Core-Collapse Supernovae
|
Using resolved stellar photometry measured from archival HST imaging, we
generate color-magnitude diagrams of the stars within 50 pc of the locations of
historic core-collapse supernovae that took place in galaxies within 8 Mpc. We
fit these color-magnitude distributions with stellar evolution models to
determine the best-fit age distribution of the young population. We then
translate these age distributions into probability distributions for the
progenitor mass of each SNe. The measurements are anchored by the main-sequence
stars surrounding the event, making them less sensitive to assumptions about
binarity, post-main-sequence evolution, or circumstellar dust. We demonstrate
that, in cases where the literature contains masses that have been measured
from direct imaging, our measurements are consistent with (but less precise
than) these measurements. Using this technique, we constrain the progenitor
masses of 17 historic SNe, 11 of which have no previous estimates from direct
imaging. Our measurements still allow the possibility that all SNe progenitor
masses are <20 M_sun. However, the large uncertainties for the highest-mass
progenitors also allow the possibility of no upper-mass cutoff.
|
1405.6626v1
|
2014-06-09
|
Calibrating CHIME, A New Radio Interferometer to Probe Dark Energy
|
The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a transit
interferometer currently being built at the Dominion Radio Astrophysical
Observatory (DRAO) in Penticton, BC, Canada. We will use CHIME to map neutral
hydrogen in the frequency range 400 -- 800\,MHz over half of the sky, producing
a measurement of baryon acoustic oscillations (BAO) at redshifts between 0.8 --
2.5 to probe dark energy. We have deployed a pathfinder version of CHIME that
will yield constraints on the BAO power spectrum and provide a test-bed for our
calibration scheme. I will discuss the CHIME calibration requirements and
describe instrumentation we are developing to meet these requirements.
|
1406.2267v1
|
2014-07-10
|
Beating the Heat! Automated Characterization of Piezoelectric Tubes for Starbugs
|
The Australian Astronomical Observatory has extensively prototyped a new
robotic positioner to allow simultaneous positioning of optical fibers at the
focal plane called 'Starbugs'. The Starbug devices each consist of two
concentric piezoelectric tubes that 'walk' the optical fiber over the focal
plane to accuracy of several microns. Ongoing research has led to the
development of several Starbug prototypes, but lack of performance data has
hampered further progress in the design of the Starbug positioners and the
support equipment required to power and control them. Furthermore, Starbugs
have been selected for the TAIPAN instrument, a prototype for MANIFEST on the
GMT. A need now arises to measure and characterize 100's of piezoelectric tubes
before full scale production of Starbugs for TAIPAN. The manual measurements of
these piezoelectric tubes are a time consuming process taking several hours.
Therefore, a versatile automated system is needed to measure and characterize
these tubes in the laboratory before production of Starbugs. We have solved
this problem with the design of an automated LabVIEW application that
significantly reduces test times to several minutes. We present the various
design aspects of the automation system and provide analyses of example
piezoelectric tubes for Starbugs.
|
1407.2681v1
|
2014-07-16
|
TriAnd and its Siblings: Satellites of Satellites in the Milky Way Halo
|
We explore the Triangulum-Andromeda (TriAnd) overdensity in the SPLASH
(Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo) and SEGUE
(the Sloan Extension for Galactic Understanding and Exploration) spectroscopic
surveys. Milky Way main sequence turn-off stars in the SPLASH survey reveal
that the TriAnd overdensity and the recently discovered PAndAS stream (Martin
et al. 2014) share a common heliocentric distance (D ~ 20 kpc), position on the
sky, and line-of-sight velocity (V_GSR ~ 50 km/s). Similarly, A-type, giant,
and main sequence turn-off stars selected from the SEGUE survey in the vicinity
of the Segue 2 satellite show that TriAnd is prevalent in these fields, with a
velocity and distance similar to Segue 2. The coincidence of the PAndAS stream
and Segue 2 satellite in positional and velocity space to TriAnd suggests that
these substructures are all associated, and may be a fossil record of
group-infall onto the Milky Way halo. In this scenario, the Segue 2 satellite
and PAndAS stream are "satellites of satellites", and the large, metal-rich
TriAnd overdensity is the remains of the group central.
|
1407.4458v2
|
2014-07-17
|
The Green's Function for the Hückel (Tight Binding) Model
|
Applications of the H\"uckel (tight binding) model are ubiquitous in quantum
chemistry and solid state physics. The matrix representation of this model is
isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which
is also the Laplacian matrix plus twice the identity. In this paper, we
analytically calculate the determinant and, when it exists, the inverse of this
matrix in connection with the Green's function, $\mathbf{G}$, of the $N\times
N$ H\"uckel matrix. A corollary is a closed form expression for a Harmonic sum
(Eq. 12). We then extend the results to $d-$dimensional lattices, whose linear
size is $N$. The existence of the inverse becomes a question of number theory.
We prove a new theorem in number theory pertaining to vanishing sums of cosines
and use it to prove that the inverse exists if and only if $N+1$ and $d$ are
odd and $d$ is smaller than the smallest divisor of $N+1$. We corroborate our
results by demonstrating the entry patterns of the Green's function and discuss
applications related to transport and conductivity.
|
1407.4780v4
|
2014-07-29
|
Formation of magnetic skyrmions with tunable properties in PdFe bilayer deposited on Ir(111)
|
We perform an extensive study of the spin-configurations in a PdFe bilayer on
Ir(111) in terms of ab initio and spin-model calculations. We use the
spin-cluster expansion technique to obtain spin model parameters, and solve the
Landau-Lifshitz-Gilbert equations at zero temperature. In particular, we focus
on effects of layer relaxations and the evolution of the magnetic ground state
in external magnetic field. In the absence of magnetic field, we find a
spin-spiral ground state, while applying external magnetic field skyrmions are
generated in the system. Based on energy calculations of frozen spin
configurations with varying magnetic field we obtain excellent agreement for
the phase boundaries with available experiments. We find that the wave length
of spin-spirals and the diameter of skyrmions decrease with increasing inward
Fe layer relaxation which is correlated with the increasing ratio of the
nearest-neighbor Dzyaloshinskii-Moriya interaction and the isotropic exchange
coupling, $D/J$. Our results also indicate that the applied field needed to
stabilize the skyrmion lattice increases when the diameter of individual
skyrmions decreases. Based on our observations, we suggest that the formation
of the skyrmion lattice can be tuned by small structural modification of the
thin film.
|
1407.7718v2
|
2014-08-14
|
Developing Structural, High-heat flux and Plasma Facing Materials for a near-term DEMO Fusion Power Plant: the EU Assessment
|
The findings of the EU 'Materials Assessment Group' (MAG), within the 2012 EU
Fusion Roadmap exercise, are discussed. MAG analysed the technological
readiness of structural, plasma facing and high heat flux materials for a DEMO
concept to be constructed in the early 2030s, proposing a coherent strategy for
R&D up to a DEMO construction decision. Technical consequences for the
materials required and the development, testing and modelling programmes, are
analysed using: a systems engineering approach, considering reactor operational
cycles, efficient maintenance and inspection requirements, and interaction with
functional materials/coolants; and a project-based risk analysis, with R&D to
mitigate risks from material shortcomings including development of specific
risk mitigation materials.
|
1408.3546v1
|
2014-08-26
|
Weedy adaptation in Setaria spp.: IX. Effects of salinity, temperature, light and seed dormancy on Setaria faberi seed germination
|
Life in salty habitats is a function of tolerance to those chemicals at all
critical phases of a plant's life history. The ability to withstand salt as an
established plant may require different mechanisms and plant traits than those
needed to germinate in salty soils. Seeds establishing themselves in high salt
content may respond differently depending on the light conditions and seed
germinability at the time of salty water imbibition. S. faberi seed (and S.
viridis and S. pumila) plants were discovered thriving along the seacoasts of
Southern Japan. These plants possess the ability to after-ripen, germinate,
emerge and establish themselves, grow and reproduce in the salty soils and
salt-laden atmospheres present in these windy habitats. The objectives of this
paper are to determine the effect of salt (NaCl) in water imbibed by S. faberi
seed during after-ripening and germination, as well temperature and light.
Observations made also provide insights on the possible relationship between
salt and drought tolerance. Seed germination of all phenotypes inhibited by two
percent or more of NaCl. The effects of lesser amounts of NaCl on each of the
three phenotypes was highly dependent on the specific temperature and light
conditions. The three test phenotypes provided a good range to detect responses
to salinity, allowing the observation of both stimulatory and inhibitory
responses.
|
1408.6187v1
|
2014-09-02
|
Accessing Different Spin-Disordered States using First Order Reversal Curves
|
Combined first order reversal curve (FORC) analyses of the magnetization
(M-FORC) and magnetoresistance (MR-FORC) have been employed to provide a
comprehensive study of the M-MR correlation in two canonical systems: a
NiFe/Cu/FePt pseudo spin-valve (PSV) and a [Co/Cu]8 multilayer. In the PSV, due
to the large difference in switching fields and minimal interactions between
the NiFe and FePt layers, the M and MR show a simple one-to-one relationship
during reversal. In the [Co/Cu]8 multilayer, the correlation between the
magnetization reversal and MR evolution is more complex. This is primarily due
to the similar switching fields of, and interactions between, the constituent
Co layers. The FORC protocol accesses states with much higher spin disorders
and larger MR than those found along the conventional major loop field-cycle.
Unlike the M-FORC measurements, which only probe changes in the macroscopic
magnetization, the MR-FORCs are more sensitive to the microscopic domain
configurations, as those are most important in determining the resultant MR
effect size. This approach is generally applicable to spintronic systems to
realize the maximum spin-disorder and the largest MR.
|
1409.0825v1
|
2014-10-20
|
Momentum space imaging of Cooper pairing in a half-Dirac-gas topological superconductor (a helical 2D topological superconductor)
|
Superconductivity in Dirac electrons has recently been proposed as a new
platform between novel concepts in high-energy and condensed matter physics. It
has been proposed that supersymmetry and exotic quasiparticles, both of which
remain elusive in particle physics, may be realized as emergent particles in
superconducting Dirac electron systems. Using artificially fabricated
topological insulator-superconductor heterostructures, we present direct
spectroscopic evidence for the existence of Cooper pairing in a half Dirac gas
2D topological superconductor. Our studies reveal that superconductivity in a
helical Dirac gas is distinctly different from that of in an ordinary
two-dimensional superconductor while considering the spin degrees of freedom of
electrons. We further show that the pairing of Dirac electrons can be
suppressed by time-reversal symmetry breaking impurities removing the
distinction. Our demonstration and momentum-space imaging of Cooper pairing in
a half Dirac gas and its magnetic behavior taken together serve as a critically
important 2D topological superconductor platform for future testing of novel
fundamental physics predictions such as emergent supersymmetry and quantum
criticality in topological systems.
|
1410.5405v1
|
2014-12-23
|
Dynamical symmetries of Markov processes with multiplicative white noise
|
We analyse various properties of stochastic Markov processes with
multiplicative white noise. We take a single-variable problem as a simple
example, and we later extend the analysis to the Landau-Lifshitz-Gilbert
equation for the stochastic dynamics of a magnetic moment. In particular, we
focus on the non-equilibrium transfer of angular momentum to the magnetization
from a spin-polarised current of electrons, a technique which is widely used in
the context of spintronics to manipulate magnetic moments. We unveil two hidden
dynamical symmetries of the generating functionals of these Markovian
multiplicative white-noise processes. One symmetry only holds in equilibrium
and we use it to prove generic relations such as the fluctuation-dissipation
theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to
prove fluctuation theorems. The other symmetry yields strong dynamical
relations between correlation and response functions which can notably simplify
the numerical analysis of these problems. Our construction allows us to clarify
some misconceptions on multiplicative white-noise stochastic processes that can
be found in the literature. In particular, we show that a first-order
differential equation with multiplicative white noise can be transformed into
an additive-noise equation, but that the latter keeps a non-trivial memory of
the discretisation prescription used to define the former.
|
1412.7564v2
|
2015-01-09
|
Random Triangle Theory with Geometry and Applications
|
What is the probability that a random triangle is acute? We explore this old
question from a modern viewpoint, taking into account linear algebra, shape
theory, numerical analysis, random matrix theory, the Hopf fibration, and much
much more. One of the best distributions of random triangles takes all six
vertex coordinates as independent standard Gaussians. Six can be reduced to
four by translation of the center to $(0,0)$ or reformulation as a 2x2 matrix
problem.
In this note, we develop shape theory in its historical context for a wide
audience. We hope to encourage other to look again (and differently) at
triangles.
We provide a new constructive proof, using the geometry of parallelians, of a
central result of shape theory: Triangle shapes naturally fall on a hemisphere.
We give several proofs of the key random result: that triangles are uniformly
distributed when the normal distribution is transferred to the hemisphere. A
new proof connects to the distribution of random condition numbers.
Generalizing to higher dimensions, we obtain the "square root ellipticity
statistic" of random matrix theory.
Another proof connects the Hopf map to the SVD of 2 by 2 matrices. A new
theorem describes three similar triangles hidden in the hemisphere. Many
triangle properties are reformulated as matrix theorems, providing insight to
both. This paper argues for a shift of viewpoint to the modern approaches of
random matrix theory. As one example, we propose that the smallest singular
value is an effective test for uniformity. New software is developed and
applications are proposed.
|
1501.03053v1
|
2015-02-03
|
The use of covariates and random effects in evaluating predictive biomarkers under a potential outcome framework
|
Predictive or treatment selection biomarkers are usually evaluated in a
subgroup or regression analysis with focus on the treatment-by-marker
interaction. Under a potential outcome framework (Huang, Gilbert and Janes
[Biometrics 68 (2012) 687-696]), a predictive biomarker is considered a
predictor for a desirable treatment benefit (defined by comparing potential
outcomes for different treatments) and evaluated using familiar concepts in
prediction and classification. However, the desired treatment benefit is
unobservable because each patient can receive only one treatment in a typical
study. Huang et al. overcome this problem by assuming monotonicity of potential
outcomes, with one treatment dominating the other in all patients. Motivated by
an HIV example that appears to violate the monotonicity assumption, we propose
a different approach based on covariates and random effects for evaluating
predictive biomarkers under the potential outcome framework. Under the proposed
approach, the parameters of interest can be identified by assuming conditional
independence of potential outcomes given observed covariates, and a sensitivity
analysis can be performed by incorporating an unobserved random effect that
accounts for any residual dependence. Application of this approach to the
motivating example shows that baseline viral load and CD4 cell count are both
useful as predictive biomarkers for choosing antiretroviral drugs for
treatment-naive patients.
|
1502.00757v1
|
2015-02-03
|
The Blackhole-Dark Matter Halo Connection
|
We explore the connection between the central supermassive blackholes (SMBH)
in galaxies and the dark matter halo through the relation between the masses of
the SMBHs and the maximum circular velocities of the host galaxies, as well as
the relationship between stellar velocity dispersion of the spheroidal
component and the circular velocity. Our assumption here is that the circular
velocity is a proxy for the mass of the dark matter halo. We rely on a
heterogeneous sample containing galaxies of all types. The only requirement is
that the galaxy has a direct measurement of the mass of its SMBH and a direct
measurement of its circular velocity and its velocity dispersion. Previous
studies have analyzed the connection between the SMBH and dark matter halo
through the relationship between the circular velocity and the bulge velocity
dispersion, with the assumption that the bulge velocity dispersion stands in
for the mass of the SMBH, via the well{}-established SMBH mass{}-bulge velocity
dispersion relation. Using intermediate relations may be misleading when one is
studying them to decipher the active ingredients of galaxy formation and
evolution. We believe that our approach will provide a more direct probe of the
SMBH and the dark matter halo connection. We find that the correlation between
the mass of supermassive blackholes and the circular velocities of the host
galaxies is extremely weak, leading us to state the dark matter halo may not
play a major role in regulating the blackhole growth in the present Universe.
|
1502.00775v1
|
2015-03-01
|
Computing in continuous space with self-assembling polygonal tiles
|
In this paper we investigate the computational power of the polygonal tile
assembly model (polygonal TAM) at temperature 1, i.e. in non-cooperative
systems. The polygonal TAM is an extension of Winfree's abstract tile assembly
model (aTAM) which not only allows for square tiles (as in the aTAM) but also
allows for tile shapes that are polygons. Although a number of self-assembly
results have shown computational universality at temperature 1, these are the
first results to do so by fundamentally relying on tile placements in
continuous, rather than discrete, space. With the square tiles of the aTAM, it
is conjectured that the class of temperature 1 systems is not computationally
universal. Here we show that the class of systems whose tiles are composed of a
regular polygon P with n > 6 sides is computationally universal. On the other
hand, we show that the class of systems whose tiles consist of a regular
polygon P with n <= 6 cannot compute using any known techniques. In addition,
we show a number of classes of systems whose tiles consist of a non-regular
polygon with n >= 3 sides are computationally universal.
|
1503.00327v2
|
2015-03-05
|
Nonparametric Bounds and Sensitivity Analysis of Treatment Effects
|
This paper considers conducting inference about the effect of a treatment (or
exposure) on an outcome of interest. In the ideal setting where treatment is
assigned randomly, under certain assumptions the treatment effect is
identifiable from the observable data and inference is straightforward.
However, in other settings such as observational studies or randomized trials
with noncompliance, the treatment effect is no longer identifiable without
relying on untestable assumptions. Nonetheless, the observable data often do
provide some information about the effect of treatment, that is, the parameter
of interest is partially identifiable. Two approaches are often employed in
this setting: (i) bounds are derived for the treatment effect under minimal
assumptions, or (ii) additional untestable assumptions are invoked that render
the treatment effect identifiable and then sensitivity analysis is conducted to
assess how inference about the treatment effect changes as the untestable
assumptions are varied. Approaches (i) and (ii) are considered in various
settings, including assessing principal strata effects, direct and indirect
effects and effects of time-varying exposures. Methods for drawing formal
inference about partially identified parameters are also discussed.
|
1503.01598v1
|
2015-03-16
|
Dynamics of Current and Field Driven Domain Wall Motion under the Influence of Transverse Magnetic Field
|
The dynamics of transverse Neel domain wall in a ferromagnetic nanostrip in
the presence of driving field, current and transverse magnetic field is
investigated by the Landau-Lifshitz-Gilbert(LLG) equation with the adiabatic
and non-adiabatic spin-transfer torques both analytically and numerically. The
analytical expressions for the velocity, width, excitation angle and
displacement for the domain wall are obtained by using small angle
approximation along with Walkers trial function. The results show that the
initial velocity of the domain wall can be controlled by the adiabatic
spin-transfer torque and the saturated velocity can be controlled by the
non-adiabatic spin-transfer torque and driving field. The large increase in the
saturated velocity of the domain wall driven by current and field due to the
transverse magnetic field is identified through the presence of driving field.
There is no impact in the saturated velocity of the domain wall driven by
current from the transverse magnetic field. For the domain wall driven by the
current in the presence of the transverse magnetic field, the saturated
velocity remains constant. The transverse magnetic field along with current and
driving field is more advantageous that the transverse magnetic field along
with current for increasing the saturated velocity of the domain wall. The
numerical results showed that the saturated velocity is increased by the
transverse magnetic field with the irrespective of the directions of the
driving field and current further it is higher and lower when the directions of
driving field and current are antiparallel and parallel respectively. The
obtained analytical solutions are closely coincided with the computed numerical
results.
|
1503.04560v2
|
2015-03-17
|
Single Hit Energy-resolved Laue Diffraction
|
In-situ white light Laue diffraction has been successfully used to
interrogate the structure of single crystal materials undergoing rapid
(nanosecond) dynamic compression up to megabar pressures. However, information
on strain state accessible via this technique is limited, reducing its
applicability for a range of applications. We present an extension to the
existing Laue diffraction platform in which we record the photon energy of a
subset of diffraction peaks. This allows for a measurement of the longitudinal
and transverse strains in-situ during compression. Consequently, we demonstrate
measurement of volumetric compression of the unit cell, in addition to the
limited aspect ratio information accessible in conventional white light Laue.
We present preliminary results for silicon, where only an elastic strain is
observed. VISAR measurements show the presence of a two wave structure and
measurements show that material downstream of the second wave does not
contribute to the observed diffraction peaks, supporting the idea that this
material may be highly disordered, or has undergone large scale rotation.
|
1503.05131v2
|
2015-03-24
|
No variations in transit times for Qatar-1 b
|
The transiting hot Jupiter planet Qatar-1 b was presented to exhibit
variations in transit times that could be of perturbative nature. A hot Jupiter
with a planetary companion on a nearby orbit would constitute an unprecedented
planetary configuration, important for theories of formation and evolution of
planetary systems. We performed a photometric follow-up campaign to confirm or
refute transit timing variations. We extend the baseline of transit
observations by acquiring 18 new transit light curves acquired with 0.6-2.0 m
telescopes. These photometric time series, together with data available in the
literature, were analyzed in a homogenous way to derive reliable transit
parameters and their uncertainties. We show that the dataset of transit times
is consistent with a linear ephemeris leaving no hint for any periodic
variations with a range of 1 min. We find no compelling evidence for the
existence of a close-in planetary companion to Qatar-1 b. This finding is in
line with a paradigm that hot Jupiters are not components of compact
multi-planetary systems. Based on dynamical simulations, we place tighter
constraints on a mass of any fictitious nearby planet in the system.
Furthermore, new transit light curves allowed us to redetermine system
parameters with the precision better than that reported in previous studies.
Our values generally agree with previous determinations.
|
1503.07191v1
|
2015-03-25
|
Rigorous numerical study of strong microwave photon-magnon coupling in all-dielectric magnetic multilayers
|
We demonstrate theoretically a strong local enhancement of the intensity of
the in-plane microwave magnetic field in multilayered structures made from a
magneto-insulating yttrium iron garnet (YIG) layer sandwiched between two
non-magnetic layers with a high dielectric constant matching that of YIG. The
enhancement is predicted for the excitation regime when the microwave magnetic
field is induced inside the multilayer by the transducer of a stripline
Broadband Ferromagnetic Resonance (BFMR) setup. By means of a rigorous
numerical solution of the Landau-Lifshitz-Gilbert equation consistently with
the Maxwell's equations, we investigate the magnetisation dynamics in the
multilayer. We reveal a strong photon-magnon coupling, which manifests itself
as anti-crossing of the ferromagnetic resonance (FMR) magnon mode supported by
the YIG layer and the electromagnetic resonance mode supported by the whole
multilayered structure. The frequency of the magnon mode depends on the
external static magnetic field, which in our case is applied tangentially to
the multilayer in the direction perpendicular to the microwave magnetic field
induced by the stripline of the BFMR setup. The frequency of the
electromagnetic mode is independent of the static magnetic field. Consequently,
the predicted photon-magnon coupling is sensitive to the applied magnetic field
and thus can be used in magnetically tuneable metamaterials based on
simultaneously negative permittivity and permeability achievable thanks to the
YIG layer. We also suggest that the predicted photon-magnon coupling may find
applications in microwave quantum information systems.
|
1503.07282v1
|
2015-04-22
|
Thermally Driven Ratchet Motion of Skyrmion Microcrystal and Topological Magnon Hall Effect
|
Spontaneously emergent chirality is an issue of fundamental importance across
the natural sciences. It has been argued that a unidirectional (chiral)
rotation of a mechanical ratchet is forbidden in thermal equilibrium, but
becomes possible in systems out of equilibrium. Here we report our finding that
a topologically nontrivial spin texture known as a skyrmion - a particle-like
object in which spins point in all directions to wrap a sphere - constitutes
such a ratchet. By means of Lorentz transmission electron microscopy we show
that micron-sized crystals of skyrmions in thin films of Cu2OSeO3 and MnSi
display a unidirectional rotation motion. Our numerical simulations based on a
stochastic Landau-Lifshitz-Gilbert equation suggest that this rotation is
driven solely by thermal fluctuations in the presence of a temperature
gradient, whereas in thermal equilibrium it is forbidden by the Bohr-van
Leeuwen theorem. We show that the rotational flow of magnons driven by the
effective magnetic field of skyrmions gives rise to the skyrmion rotation,
therefore suggesting that magnons can be used to control the motion of these
spin textures.
|
1504.05860v1
|
2015-05-05
|
Evaluating the Potential of a Dual Randomized Kaczmarz Solver for Laplacian Linear Systems
|
A new method for solving Laplacian linear systems proposed by Kelner et al.
involves the random sampling and update of fundamental cycles in a graph.
Kelner et al. proved asymptotic bounds on the complexity of this method but did
not report experimental results. We seek to both evaluate the performance of
this approach and to explore improvements to it in practice. We compare the
performance of this method to other Laplacian solvers on a variety of real
world graphs. We consider different ways to improve the performance of this
method by exploring different ways of choosing the set of cycles and the
sequence of updates, with the goal of providing more flexibility and potential
parallelism. We propose a parallel model of the Kelner et al. method, for
evaluating potential parallelism in terms of the span of edges updated at each
iteration. We provide experimental results comparing the potential parallelism
of the fundamental cycle basis and our extended cycle set. Our preliminary
experiments show that choosing a non-fundamental set of cycles can save
significant work compared to a fundamental cycle basis.
|
1505.00875v3
|
2015-06-18
|
Area-Delay-Energy Tradeoffs of Strain-Mediated Multiferroic Devices
|
Multiferroic devices hold profound promise for ultra-low energy computing in
beyond Moore's law era. The magnetization of a magnetostrictive
shape-anisotropic single-domain nanomagnet strain-coupled with a piezoelectric
layer in a multiferroic composite structure can be switched between its two
stable states (separated by an energy barrier) with a tiny amount of voltage
via converse magnetoelectric effect. With appropriate choice of materials, the
magnetization can be switched with a few tens of millivolts of voltages in
sub-nanosecond switching delay while spending a miniscule amount of energy of
~1 attojoule at room-temperature. Here, we analyze the area-delay-energy
trade-offs of these multiferroic devices by solving stochastic
Landau-Lifshitz-Gilbert equation in the presence of room-temperature thermal
fluctuations. We particularly put attention on scaling down the lateral area of
the magnetostrictive nanomagnet that can increase the device density on a chip.
We show that the vertical thickness of the nanomagnet can be increased while
scaling down the lateral area and keeping the assumption of single-domain limit
valid. This has important consequence since it helps to some extent preventing
the deterioration of the induced stress-anisotropy energy in the
magnetostrictive nanomagnet, which is proportional to the nanomagnet's volume.
The results show that if we scale down the lateral area, the switching delay
increases while energy dissipation decreases. Avenues available to decrease the
switching delay while still reducing the energy dissipation are discussed.
|
1506.07859v1
|
2015-07-30
|
Confirmation of the Planetary Microlensing Signal and Star and Planet Mass Determinations for Event OGLE-2005-BLG-169
|
We present Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3)
observations of the source and lens stars for planetary microlensing event
OGLE-2005-BLG-169, which confirm the relative proper motion prediction due to
the planetary light curve signal observed for this event. This (and the
companion Keck result) provide the first confirmation of a planetary
microlensing signal, for which the deviation was only 2%. The follow-up
observations determine the flux of the planetary host star in multiple
passbands and remove light curve model ambiguity caused by sparse sampling of
part of the light curve. This leads to a precise determination of the
properties of the OGLE-2005-BLG-169Lb planetary system. Combining the
constraints from the microlensing light curve with the photometry and
astrometry of the HST/WFC3 data, we find star and planet masses of M_* = 0.69+-
0.02 M_solar and m_p = 14.1 +- 0.9 M_earth. The planetary microlens system is
located toward the Galactic bulge at a distance of D_L = 4.1 +- 0.4 kpc, and
the projected star-planet separation is a_perp = 3.5 +- 0.3 AU, corresponding
to a semi-major axis of a = 4.0 (+2.2 -0.6) AU.
|
1507.08661v1
|
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