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arxiv_dataset-58001412.2022 | The taming of the Reverse Mathematics zoo
math.LO
Reverse Mathematics is a program in the foundations of mathematics. Its
results give rise to an elegant classification of theorems of ordinary
mathematics based on computability. In particular, the majority of these
theorems fall into only five categories of which the associated logical systems
are dubbed `the Big Five'. Recently, a lot of effort has been directed towards
finding \emph{exceptional} theorems, i.e.\ which fall outside the Big Five
categories. The so-called Reverse Mathematics zoo is a collection of such
exceptional theorems (and their relations). In this paper, we show that the
uniform versions of the zoo-theorems, i.e. where a functional computes the
objects stated to exist, all fall in the third Big Five category arithmetical
comprehension, inside Kohlenbach's higher-order Reverse Mathematics. In other
words, the zoo seems to disappear at the uniform level. Our classification
applies to all theorems whose objects exhibit little structure, a notion we
conjecture to be connected to Montalban's notion robustness. Surprisingly, our
methodology reveals a hitherto unknown `computational' aspect of Nonstandard
Analysis: We shall formulate an algorithm $\mathfrak{RS}$ which takes as input
the proof of a specific equivalence in Nelson's internal set theory, and
outputs the proof of the desired equivalence (not involving Nonstandard
Analysis) between the uniform zoo principle and arithmetical comprehension.
Moreover, the equivalences thus proved are even explicit, i.e. a term from the
language converts the functional from one uniform principle into the functional
from the other one and vice versa.
| arxiv topic:math.LO |
arxiv_dataset-58011412.2122 | Non-Verbal Communication Analysis in Victim-Offender Mediations
cs.HC cs.AI cs.CY
In this paper we present a non-invasive ambient intelligence framework for
the semi-automatic analysis of non-verbal communication applied to the
restorative justice field. In particular, we propose the use of computer vision
and social signal processing technologies in real scenarios of Victim-Offender
Mediations, applying feature extraction techniques to multi-modal
audio-RGB-depth data. We compute a set of behavioral indicators that define
communicative cues from the fields of psychology and observational methodology.
We test our methodology on data captured in real world Victim-Offender
Mediation sessions in Catalonia in collaboration with the regional government.
We define the ground truth based on expert opinions when annotating the
observed social responses. Using different state-of-the-art binary
classification approaches, our system achieves recognition accuracies of 86%
when predicting satisfaction, and 79% when predicting both agreement and
receptivity. Applying a regression strategy, we obtain a mean deviation for the
predictions between 0.5 and 0.7 in the range [1-5] for the computed social
signals.
| arxiv topic:cs.HC cs.AI cs.CY |
arxiv_dataset-58021412.2222 | A normal generating set for the Torelli group of a non-orientable closed
surface
math.GT
For a closed surface $S$, its Torelli group $\mathcal{I}(S)$ is the subgroup
of the mapping class group of $S$ consisting of elements acting trivially on
$H_1(S;\mathbb{Z})$. When $S$ is orientable, a generating set for
$\mathcal{I}(S)$ is known. In this paper, we give a normal generating set of
$\mathcal{I}(N_g)$ for $g\geq4$, where $N_g$ is a genus-$g$ non-orientable
closed surface.
| arxiv topic:math.GT |
arxiv_dataset-58031412.2322 | Partial restoration of chiral symmetry inside hadrons
hep-lat
By using the overlap-Dirac operator eigenmodes, we investigate spatial
distribution of the chiral condensate around static color sources for both
quark-antiquark and three quark systems. In the presence of color sources, a
characteristic flux-tube structure appears among them, suggesting a linear
confining potential. We show that the magnitude of the condensate is reduced
inside the color flux, which indicates the partial restoration of chiral
symmetry inside the "hadrons." Considering a periodic box containing a static
baryon source, which mimics the "nuclear matter," we estimate the chiral
symmetry restoration in the presence of finite baryon number density.
| arxiv topic:hep-lat |
arxiv_dataset-58041412.2422 | A stacked analysis of 115 pulsars observed by the Fermi LAT
astro-ph.HE
Due to the low gamma-ray fluxes from pulsars above 50 GeV and the small
collecting area of space-based telescopes, the gamma-ray emission discovered by
the Fermi-LAT in $\sim$150 pulsars is largely unexplored at these energies. In
this regime, the uncertainties on the spectral data points and/or the
constraints from upper-limits are not sufficient to provide robust tests of
competing emission models in individual pulsars. The discovery of
power-law-type emission from the Crab pulsar at energies exceeding 100 GeV
provides a compelling justification for exploration of other pulsars at these
energies. We applied the method of Aperture Photometry to measure pulsar
emission spectra from Fermi-LAT data and present a stacked analysis of 115
pulsars selected from the Second Fermi-LAT Catalog of Gamma-ray Pulsars. This
analysis, which uses an average of $\sim$4.2 years of data per pulsar,
aggregates low-level emission which cannot be resolved in individual objects
but can be detected in an ensemble. We find no significant stacked excess at
energies above 50 GeV. An upper limit of $\sim$30% of the Crab pulsar level is
found for the average flux from 115 pulsars in the 100-177 GeV energy range at
the 95% confidence level. Stacked searches exclusive to the young pulsar
sample, the millisecond pulsar sample, and several other promising sub-samples
also return no significant excesses above 50 GeV.
| arxiv topic:astro-ph.HE |
arxiv_dataset-58051412.2522 | The Potts and random-cluster models
math.CO math.PR
This is a short account of connections between the Tutte polynomial and the
Ising, Potts, and random-cluster models. The four principal elements are the
Ising model of 1925, the Tutte polynomial of 1947, the Potts model of 1952, and
the random-cluster model of 1972.
| arxiv topic:math.CO math.PR |
arxiv_dataset-58061412.2622 | Output stream of binding neuron with delayed feedback
q-bio.NC
A binding neuron (BN) whith delayed feedback is considered. The neuron is fed
externally with a Poisson stream of intensity $\lambda$. The neuron's output
spikes are fed into its input with time delay $\Delta$. The resulting output
stream of the BN is not Poissonian, and we look for its interspike intervals
(ISI) distribution. For BN with threshold 2 an exact mathematical expression as
function of $\lambda$, $\Delta$ and BN's internal memory, $\tau$ is derived for
the ISI distribution, and for higher thresholds it is found numerically. The
distributions found are characterized with discontinuities of jump type, and
include singularity of Dirac's $\delta$-function type. It is concluded that
delayed feedback presence can radically alter neuronal output firing
statistics.
| arxiv topic:q-bio.NC |
arxiv_dataset-58071412.2722 | Experimental measurement of the self-healing of the spatially
inhomogeneous states of polarization of radially and azimuthally polarized
vector Bessel beams
physics.optics
We experimentally measured the self-healing of the spatially inhomogeneous
states of polarization of radial and azimuthal polarized vector Bessel beams.
Radial and azimuthal polarized vector Bessel beams were generated via a digital
version of Durnin's method, using a spatial light modulator in concert with a
liquid crystal $q$-plate. As a proof of principle, their intensities and
spatially inhomogeneous states of polarization were measured using Stokes
polarimetry as they propagated through two disparate obstructions. It was
found, similar to their intensities, the spatially inhomogeneous states of
polarization of a radial and azimuthal polarized vector Bessel beams self-heal.
Similar to scalar Bessel beams, the self-healing of vector Bessel beams can be
understood via geometric optics, i.e., the interference of the unobstructed
conical rays in the shadow region of the obstruction. The self-healing of
vector Bessel beams may have applications in, for example, optical trapping.
| arxiv topic:physics.optics |
arxiv_dataset-58081412.2822 | The Algebraic Duality Resolution at $p=2$
math.AT
The goal of this paper is to develop some of the machinery necessary for
doing $K(2)$-local computations in the stable homotopy category using duality
resolutions at the prime $p=2$. The Morava stabilizer group $\mathbb{S}_2$
admits a norm whose kernel we denote by $\mathbb{S}_2^1$. The algebraic duality
resolution is a finite resolution of the trivial
$\mathbb{Z}_2[[\mathbb{S}_2^1]]$-module $\mathbb{Z}_2$ by modules induced from
representations of finite subgroups of $\mathbb{S}_2^1$. Its construction is
due to Goerss, Henn, Mahowald and Rezk. It is an analogue of their finite
resolution of the trivial $\mathbb{Z}_3[[\mathbb{G}_2^1]]$-module
$\mathbb{Z}_3$ at the prime $p=3$. The construction was never published and it
is the main result in this paper. In the process, we give a detailed
description of the structure of Morava stabilizer group $\mathbb{S}_2$ at the
prime $2$. We also describe the maps in the algebraic duality resolution with
the precision necessary for explicit computations.
| arxiv topic:math.AT |
arxiv_dataset-58091412.2922 | Two Lorentzian Lattices
math.AG
We prove a conjecture formulated by the first author, which in turn provides
a good deal of evidence for the monstrous proposal of Daniel Allcock.
| arxiv topic:math.AG |
arxiv_dataset-58101412.3022 | Fast Product-Matrix Regenerating Codes
cs.DC cs.IT cs.PF math.IT
Distributed storage systems support failures of individual devices by the use
of replication or erasure correcting codes. While erasure correcting codes
offer a better storage efficiency than replication for similar fault tolerance,
they incur higher CPU consumption, higher network consumption and higher disk
I/Os. To address these issues, codes specific to storage systems have been
designed. Their main feature is the ability to repair a single lost disk
efficiently. In this paper, we focus on one such class of codes that minimize
network consumption during repair, namely regenerating codes. We implement the
original Product-Matrix Regenerating codes as well as a new optimization we
propose and show that the resulting optimized codes allow achieving 790 MB/s
for encoding in typical settings. Reported speeds are significantly higher than
previous studies, highlighting that regenerating codes can be used with little
CPU penalty.
| arxiv topic:cs.DC cs.IT cs.PF math.IT |
arxiv_dataset-58111412.3122 | A 3D Kinematic Study of the Northern Ejecta "Jet" of the Crab Nebula
astro-ph.HE
We present [O III] 4959,5007 emission line spectra (FWHM = 40 km/s) of the
Crab Nebula's northern ejecta `jet'. These data, along with a recent [O III]
image of the Crab, are used to build 3-dimensional models of the jet and
adjacent remnant nebulosity to better understand the jet's properties and
possible formation. We find that the jet's radial velocities range from -190 to
+480 km/s with transverse velocities from 1600 to 2650 km/s from base to tip.
The jet appears virtually hollow in [O III] emission with the exception of some
material at the jet's base where the it connects with the remnant. Our 3D
reconstructions indicate that the jet is elliptical in shape and slightly
funnel-like rather than a straight cylindrical tube as previously thought. At
the base of the jet we find evidence for a significant opening or "channel" in
the Crab's main nebula shell. Our analysis of the jet's expansion properties
and location supports the theory that the jet may simply represent the highest
velocity component of the Crab's N-S bipolar expansion.
| arxiv topic:astro-ph.HE |
arxiv_dataset-58121412.3222 | Nonreciprocal transmission of neutrons through the noncoplanar magnetic
system
cond-mat.mes-hall cond-mat.other
We report on observation of the time reversal symmetry breaking in
unpolarized neutrons scattering experiment. Neutron transmittivity through the
system consisting of two magnetic mirrors placed in an external magnetic field
is measured. Time reversal symmetry holds for coplanar magnetic configuration,
meaning that transmitted intensity does not change when interchanging neutron
source and detector. Contrarily, for noncoplanar magnetic configuration the
time reversal symmetry breaks down. In this case the transmitted intensity
changes when interchanging the source and detector. The observed time reversal
symmetry breaking is the consequence of the one of the most fundamental
properties of quantum mechanics, namely the non-commutativity of spin algebra.
| arxiv topic:cond-mat.mes-hall cond-mat.other |
arxiv_dataset-58131412.3322 | Beyond the Q-process: various ways of conditioning the multitype
Galton-Watson process
math.PR
Conditioning a multitype Galton-Watson process to stay alive into the
indefinite future leads to what is known as its associated $Q$-process. We show
that the same holds true if the process is conditioned to reach a positive
threshold or a non-absorbing state. We also demonstrate that the stationary
measure of the $Q$-process, obtained by construction as two successive limits
(first by delaying the extinction in the original process and next by
considering the long-time behavior of the obtained $Q$-process), is as a matter
of fact a double limit. Finally, we prove that conditioning a multitype
branching process on having an infinite total progeny leads to a process
presenting the features of a $Q$-process. It does not however coincide with the
original associated $Q$-process, except in the critical regime.
| arxiv topic:math.PR |
arxiv_dataset-58141412.3422 | Large electropositive cations as surfactants for the growth of polar
epitaxial films
cond-mat.mtrl-sci
Using density functional theory (DFT) we demonstrate that the adsorption of
large cations such as potassium or cesium facilitates the epitaxial growth of
polar LaAlO$_3$ (LAO) on SrTiO$_3$ (STO). The low ionization potential of K
favors efficient electron transfer to the STO conduction band and results in a
2D electron gas which exactly compensates for the diverging potential with
increasing layer thickness. For large cations like K or Cs, DFT total energy
considerations show that they remain adsorbed on the LAO surface and do not
enter substitutionally into LAO. These results suggest a novel scheme for
growing clean LAO/STO interface systems, and polar systems in general, by
performing the growth process in the presence of large, low ionization
potential alkali metal ions.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-58151412.3522 | Spin-orbit couplings of quantum fields in Schwarzschild spacetime
gr-qc
In Schwarzschild spacetime, the gravitational spin-orbit couplings of the
massless Dirac field and the photon field can be studied in a unified way. In
contrary to the previous investigations presented mainly at the
quantum-mechanical level, our work is presented at the level of quantum field
theory without resorting to the Foldy-Wouthuysen transformation. If massless
Dirac particles and photons have the same momentums, their energy-level
splittings due to the gravitational spin-orbit couplings are the same. Massless
Dirac particles and photons coming from the Hawking radiations are partially
polarized as long as their original momentums are not parallel to the radial
direction of a Schwarzschild black hole.
| arxiv topic:gr-qc |
arxiv_dataset-58161412.3622 | Reconstruction of Eigenfunctions of q-ary n-dimensional Hypercube
math.CO
Under study are eigenfunctions of $q$-ary $n$-dimensional hypercube. Given
all values of an eigenfunction in the sphere we develop methods to reconstruct
the function in full or in part. First, we obtain that all values of the
function in the corresponding ball are uniquely determined under some
supplementary conditions. Secondly, if the radius is equal to the eigenvalue
number we obtain that all values of the eigenfunction are uniquiely determined
under some supplementary conditions.
| arxiv topic:math.CO |
arxiv_dataset-58171412.3722 | Note on off-shell relations in nonlinear sigma model
hep-th
In this note, we investigate relations between tree-level off-shell currents
in nonlinear sigma model. Under Cayley parametrization, all odd-point currents
vanish. We propose and prove a generalized $U(1)$ identity for even-point
currents. The off-shell $U(1)$ identity given in [1] is a special case of the
generalized identity studied in this note. The on-shell limit of this identity
is equivalent with the on-shell KK relation. Thus this relation provides the
full off-shell correspondence of tree-level KK relation in nonlinear sigma
model.
| arxiv topic:hep-th |
arxiv_dataset-58181412.3822 | Super-resolution discrete-Fourier-transform spectroscopy using precisely
periodic radiation beyond time window size limitation
physics.optics
Fourier transform spectroscopy (FTS) has been widely used in a variety of
fields in research, industry, and medicine due to its high signal-to-noise
ratio, simultaneous acquisition of signals in a broad spectrum, and versatility
for different radiation sources. Further improvement of the spectroscopic
performance will widen its scope of applications. Here, we demonstrate improved
spectral resolution by overcoming the time window limitation using discrete
Fourier transform spectroscopy (dFTS) with precisely periodic pulsed terahertz
(THz) radiation. Since infinitesimal resolution can be achieved at periodically
discrete frequencies when the time window size is exactly matched to the
repetition period T, a combination of THz-dFTS with a spectral interleaving
technique achieves a spectral resolution only limited by the spectral
interleaving interval. Linewidths narrower than 1/(50T) are fully resolved
allowing the attribution of rotational-transition absorption lines of
low-pressure molecular gases within a 1.25 MHz band. The proposed method
represents a powerful tool to improve spectrometer performance and accelerate
the practical use of various types of FTS.
| arxiv topic:physics.optics |
arxiv_dataset-58191412.3922 | Size sensitive packing number for Hamming cube and its consequences
cs.DM cs.CG cs.LG math.CO
We prove a size-sensitive version of Haussler's Packing
lemma~\cite{Haussler92spherepacking} for set-systems with bounded primal
shatter dimension, which have an additional {\em size-sensitive property}. This
answers a question asked by Ezra~\cite{Ezra-sizesendisc-soda-14}. We also
partially address another point raised by Ezra regarding overcounting of sets
in her chaining procedure. As a consequence of these improvements, we get an
improvement on the size-sensitive discrepancy bounds for set systems with the
above property. Improved bounds on the discrepancy for these special set
systems also imply an improvement in the sizes of {\em relative $(\varepsilon,
\delta)$-approximations} and $(\nu, \alpha)$-samples.
| arxiv topic:cs.DM cs.CG cs.LG math.CO |
arxiv_dataset-58201412.4022 | The Sums of a Double Hypergeometric Series and of the First m+1 Terms of
3F2(a,b,c;(a+b+1)/2,2c;1) when c = -m is a Negative Integer
math.CA
A summation formula is derived for the sum of the first m+1 terms of the
3F2(a,b,c;(a+b+1)/2,2c;1) series when c = -m is a negative integer. This
summation formula is used to derive a formula for the sum of a terminating
double hypergeometric series that arose in another project by one of us (C.D.)
| arxiv topic:math.CA |
arxiv_dataset-58211412.4122 | Supernova 1987A: neutrino-driven explosions in three dimensions and
light curves
astro-ph.SR
The well-studied type IIP SN 1987A, produced by the explosion of a blue
supergiant (BSG) star, is a touchstone for massive-star evolution, simulations
of neutrino-driven explosions, and modeling of light curves and spectra. In the
framework of the neutrino-driven mechanism, we study the dependence of
explosion properties on the structure of four different BSGs and compare the
corresponding light curves with observations of SN 1987A. We perform 3D
simulations with the PROMETHEUS code until about one day and map the results to
the 1D code CRAB for the light curve calculations. All of our 3D models with
explosion energies compatible with SN 1987A produce 56Ni in rough agreement
with the amount deduced from fitting the radioactively powered light-curve
tail. One of the progenitors yields maximum velocities of ~3000 km/s for the
bulk of ejected 56Ni, consistent with observations. In all of our models inward
mixing of hydrogen during the 3D evolution leads to minimum H-velocities below
100 km/s, in good agreement with spectral observations. The considered BSG
models, 3D explosion simulations, and light-curve calculations can thus explain
basic observational features of SN 1987A. However, all progenitors have too
large pre-SN radii to reproduce the narrow initial luminosity peak, and the
structure of their outer layers is not suitable to match the observed light
curve during the first 30-40 days. Only one stellar model has a structure of
the He core and the He/H composition interface that enables sufficient outward
mixing of 56Ni and inward mixing of hydrogen to produce a good match of the
dome-like shape of the observed light-curve maximum. But this model falls short
of the He-core mass of 6 Msun inferred from the absolute luminosity of the
pre-SN star. The lack of an adequate pre-SN model for SN 1987A is a pressing
challenge for the theory of massive-star evolution. (Abridged)
| arxiv topic:astro-ph.SR |
arxiv_dataset-58221412.4222 | A prediction interval for a function-valued forecast model
stat.ME math.ST stat.TH
Starting from the information contained in the shape of the load curves, we
have proposed a flexible nonparametric function-valued fore-cast model called
KWF (Kernel+Wavelet+Functional) well suited to handle nonstationary series. The
predictor can be seen as a weighted average of futures of past situations,
where the weights increase with the similarity between the past situations and
the actual one. In addi-tion, this strategy provides with a simultaneous
multiple horizon pre-diction. These weights induce a probability distribution
that can be used to produce bootstrap pseudo predictions. Prediction intervals
are constructed after obtaining the corresponding bootstrap pseudo pre-diction
residuals. We develop two propositions following directly the KWF strategy and
compare it to two alternative ways coming from proposals of econometricians.
They construct simultaneous prediction intervals using multiple comparison
corrections through the control of the family wise error (FWE) or the false
discovery rate. Alternatively, such prediction intervals can be constructed
bootstrapping joint prob-ability regions. In this work we propose to obtain
prediction intervals for the KWF model that are simultaneously valid for the H
predic-tion horizons that corresponds with the corresponding path forecast,
making a connection between functional time series and the econome-tricians'
framework.
| arxiv topic:stat.ME math.ST stat.TH |
arxiv_dataset-58231412.4322 | Priority based Bandwidth Adaptation for Multi-class Traffic in Wireless
Networks
cs.NI
The bandwidth adaptation is the technique that allows the flexibility in
bandwidth allocation for a call. Using the bandwidth adaptation technique, the
number of call admission in the system can be increased significantly. In this
paper we propose a priority based bandwidth adaptation scheme that can release
multi-level of bandwidth from the existing calls to accept call requests. The
amount of released bandwidth is based on the number of existing bandwidth
adaptive calls and the priority of requesting traffic call. This priority
scheme does not reduce the bandwidth utilization. Moreover, the proposed
bandwidth adaptation strategy provides significantly reduced call blocking
probability for the higher priority traffic calls. The performance analyses
show the improvement of the proposed scheme.
| arxiv topic:cs.NI |
arxiv_dataset-58241412.4422 | CCN Forwarding Strategies for Multihomed Mobile Terminals
cs.NI
Current IP-based networks are unable to fully exploit the capabilities of the
increasing number of multihomed mobile terminals. We argue that Content-Centric
Networking (CCN), a novel networking architecture based on named information
objects, can fill the gap. In this paper, we elicit requirements for CCN packet
forwarding on multihomed mobile terminals. We categorize CCN forwarding
strategies according to their ability to fulfill these requirements and provide
a real-world performance evaluation in the current CCNx prototype
implementation. Moreover, we describe the initial design of an advanced
multipath forwarding strategy.
| arxiv topic:cs.NI |
arxiv_dataset-58251412.4522 | Global weak solutions to the inviscid 3D Quasi-Geostrophic equation
math.AP
In this article, the authors prove the existence of global weak solutions to
the inviscid three-dimensional quasi-geostrophic equation. This equation models
the evolution of the temperature on the surface of the earth. It is widely used
in geophysics and meteorology.
| arxiv topic:math.AP |
arxiv_dataset-58261412.4622 | BSDEs with monotone generator driven by Brownian and Poisson noises in a
general filtration
math.PR
We analyze multidimensional BSDEs in a filtration that supports a Brownian
motion and a Poisson random measure. Under a monotonicity assumption on the
driver, the paper extends several results from the literature. We establish
existence and uniqueness of solutions in $L^p$ provided that the generator and
the terminal condition satisfy appropriate integrability conditions. The
analysis is first carried out under a deterministic time horizon, and then
generalized to random time horizons given by a stopping time with respect to
the underlying filtration. Moreover, we provide a comparison principle in
dimension one.
| arxiv topic:math.PR |
arxiv_dataset-58271412.4722 | Global bifurcation for fractional $p$-Laplacian and application
math.AP
We prove the existence of an unbounded branch of solutions to the non-linear
non-local equation $$ (-\Delta)^s_p u=\lambda |u|^{p-2}u + f(x,u,\lambda)
\quad\text{in}\quad \Omega,\quad u=0 \quad\text{in}\quad
\mathbb{R}^n\setminus\Omega, $$ bifurcating from the first eigenvalue. Here
$(-\Delta)^s_p$ denotes the fractional $p$-Laplacian and
$\Omega\subset\mathbb{R}^n$ is a bounded regular domain. The proof of the
bifurcation results relies in computing the Leray--Schauder degree by making an
homotopy respect to $s$ (the order of the fractional $p$-Laplacian) and then to
use results of local case (that is $s=1$) found in [17]. Finally, we give some
application to an existence result.
| arxiv topic:math.AP |
arxiv_dataset-58281412.4822 | Unusual ultralow frequency fluctuations in freestanding graphene
cond-mat.mes-hall
Intrinsic ripples in freestanding graphene have been exceedingly difficult to
study. Individual ripple geometry was recently imaged using scanning tunneling
microscopy, but these measurements are limited to static configurations.
Thermally-activated flexural phonon modes should generate dynamic changes in
curvature. Here we show how to track the vertical movement of a
one-square-angstrom region of freestanding graphene using scanning tunneling
microscopy, thereby allowing measurement of the out-of-plane time trajectory
and fluctuations over long time periods. We also present a model from
elasticity theory to explain the very-low-frequency oscillations. Unexpectedly,
we sometimes detect a sudden colossal jump, which we interpret as due to mirror
buckling. This innovative technique provides a much needed atomic-scale probe
for the time-dependent behavior of intrinsic ripples. The discovery of this
novel progenitor represents a fundamental advance in the use of scanning
tunneling microscopy, which together with the application of a thermal load
provides a low-frequency nano-resonator.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-58291412.4922 | Incomplete Dirac reduction of constrained Hamiltonian systems
nlin.CD
First-class constraints constitute a potential obstacle to the computation of
a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using
the pseudoinverse instead of the inverse of the matrix defined by the Poisson
brackets between the constraints, we show that a Dirac-Poisson bracket can be
constructed, even if it corresponds to an incomplete reduction of the original
Hamiltonian system. The uniqueness of Dirac brackets is discussed.
| arxiv topic:nlin.CD |
arxiv_dataset-58301412.5022 | The amplification method in the GL(3) Hecke algebra
math.NT
This article contains all of the technical ingredients required to implement
an effective, explicit and unconditional amplifier in the context of GL(3)
automorphic forms. In particular, several coset decomposition computations in
the GL(3) Hecke algebra are explicitly done.
| arxiv topic:math.NT |
arxiv_dataset-58311412.5122 | Fast computation of Tukey trimmed regions and median in dimension $p>2$
stat.CO
Given data in $\mathbb{R}^{p}$, a Tukey $\kappa$-trimmed region is the set of
all points that have at least Tukey depth $\kappa$ w.r.t. the data. As they are
visual, affine equivariant and robust, Tukey regions are useful tools in
nonparametric multivariate analysis. While these regions are easily defined and
interpreted, their practical use in applications has been impeded so far by the
lack of efficient computational procedures in dimension $p > 2$. We construct
two novel algorithms to compute a Tukey $\kappa$-trimmed region, a na\"{i}ve
one and a more sophisticated one that is much faster than known algorithms.
Further, a strict bound on the number of facets of a Tukey region is derived.
In a large simulation study the novel fast algorithm is compared with the
na\"{i}ve one, which is slower and by construction exact, yielding in every
case the same correct results. Finally, the approach is extended to an
algorithm that calculates the innermost Tukey region and its barycenter, the
Tukey median.
| arxiv topic:stat.CO |
arxiv_dataset-58321412.5222 | On the regularity of the interface of a thermodynamically consistent
two-phase Stefan problem with surface tension
math.AP
We study the regularity of the free boundary arising in a thermodynamically
consistent two-phase Stefan problem with surface tension by means of a family
of parameter-dependent diffeomorphisms, $L_p$-maximal regularity theory, and
the implicit function theorem.
| arxiv topic:math.AP |
arxiv_dataset-58331412.5322 | An Algebraical Model for Gray Level Images
cs.CV
In this paper we propose a new algebraical model for the gray level images.
It can be used for digital image processing. The model adresses to those images
which are generated in improper light conditions (very low or high level). The
vector space structure is able to illustrate some features into the image using
modified level of contrast and luminosity. Also, the defined structure could be
used in image enhancement. The general approach is presented with experimental
results to demonstrate image enhancement.
| arxiv topic:cs.CV |
arxiv_dataset-58341412.5422 | Method of Separating Tangents
math.GM
The well known Jensen inequality, holds true for every convex functions.
However, we found that it is possible to apply it to some problems related to
nonconvex functions for which Jensen's inequality holds true locally. Having
considered a set of such functions, we noted some general patterns. We show
that the key point, which provides Jensen's inequality holds true locally, is
that the plot of function should be situated at only one side from the local
base curve defined compatible with conditional variables. Moreover, we have
achieved even more general result. It turned out that the graph of the function
can be located on either sides of the local base curve, with the conditions.
This result allows one to prove easily difficult types of inequalities, and on
the other hand to broaden applications in physics, economy, and information
theory. On the basis of the conducted analysis of different sources it is
possible to claim, that our method is applicable to about three fourths of
studied inequalities related to Jensen's inequality.
| arxiv topic:math.GM |
arxiv_dataset-58351412.5522 | Condensation of dust in the ejecta of type II-P supernovae
astro-ph.SR
Aims: We study the production of dust in Type II-P supernova by coupling the
gas-phase chemistry to the dust nucleation and condensation phases. We consider
two supernova progenitor masses with homogeneous and clumpy ejecta to assess
the chemical type and quantity of dust that forms. Grain size distributions are
derived as a function of post-explosion time. Methods: The chemistry of the gas
phase and the simultaneous formation of dust clusters are described by a
chemical network. The formation of key species (CO, SiO) and dust clusters of
silicates, alumina, silica, metal carbides and sulphides, pure metals, and
amorphous carbon is considered. The master equations describing the chemistry
of the nucleation phase are coupled to a dust condensation formalism based on
Brownian coagulation. Results: Type II-P supernovae produce dust grains of
various chemical compositions and size distributions as a function of time. The
grain size distributions gain in complexity with time, are slewed towards large
grains, and differ from the usual MRN power-law distribution used for
interstellar dust. Gas density enhancements in the form of clumps strongly
affect the dust chemical composition and the grain size distributions.
Silicates and pure metallic grains are highly dependent on clumpiness.
Specifically, clumpy ejecta produce grains over 0.1 micron, and the final dust
mass reaches 0.14 Msun. Conversely, carbon and alumina dust masses are
controlled by the mass yields of alumina and carbon in the zones where the dust
is produced. Several dust components form in the ejecta and the total dust mass
gradually builds up over a time span of 3 to 5 years post-outburst. This
gradual growth provides a possible explanation for the discrepancy between the
small dust masses formed at early post-explosion times and the high dust masses
derived from recent observations of supernova remnants.
| arxiv topic:astro-ph.SR |
arxiv_dataset-58361412.5622 | Densities in large permutations and parameter testing
cs.DM math.CO
A classical theorem of Erdos, Lovasz and Spencer asserts that the densities
of connected subgraphs in large graphs are independent. We prove an analogue of
this theorem for permutations and we then apply the methods used in the proof
to give an example of a finitely approximable permutation parameter that is not
finitely forcible. The latter answers a question posed by two of the authors
and Moreira and Sampaio.
| arxiv topic:cs.DM math.CO |
arxiv_dataset-58371412.5722 | Hyperon Puzzle of Neutron Stars with Skyrme Force Models
nucl-th astro-ph.SR hep-ph
We consider the so called hyperon puzzle of neutron star (NS). We employ
Skyrme force models for the description of in-medium nucleon-nucleon,
nucleon-Lambda hyperon ($N\Lambda$), and Lambda-Lambda ($\Lambda\Lambda$)
interactions. A phenomenological finite-range force for the $\Lambda\Lambda$
interaction is considered as well. Equation of state (EoS) of NS matter is
obtained in the framework of density functional theory, and
Tolman-Oppenheimer-Volkoff equations are solved to obtain the mass-radius
relations of NSs. It has been generally known that the existence of hyperons in
the NS matter is not well supported by the recent discovery of large-mass NSs
($M \simeq 2 M_\odot$) since hyperons make the EoS softer than the one without
them. For the selected interaction models, $N\Lambda$ interactions reduce the
maximum mass of NS by about 30~\%, while $\Lambda\Lambda$ interactions can give
about 10~\% enhancement. Consequently, we find that some Skyrme force models
predict the maximum mass of NS consistent with the observation of $2 M_\odot$
NSs, and at the same time satisfy observationally constrained mass-radius
relations.
| arxiv topic:nucl-th astro-ph.SR hep-ph |
arxiv_dataset-58381412.5822 | Bounding the Number of Hyperedges in Friendship $r$-Hypergraphs
math.CO cs.DM
For $r \ge 2$, an $r$-uniform hypergraph is called a friendship
$r$-hypergraph if every set $R$ of $r$ vertices has a unique 'friend' - that
is, there exists a unique vertex $x \notin R$ with the property that for each
subset $A \subseteq R$ of size $r-1$, the set $A \cup \{x\}$ is a hyperedge.
We show that for $r \geq 3$, the number of hyperedges in a friendship
$r$-hypergraph is at least $\frac{r+1}{r} \binom{n-1}{r-1}$, and we
characterise those hypergraphs which achieve this bound. This generalises a
result given by Li and van Rees in the case when $r = 3$.
We also obtain a new upper bound on the number of hyperedges in a friendship
$r$-hypergraph, which improves on a known bound given by Li, van Rees, Seo and
Singhi when $r=3$.
| arxiv topic:math.CO cs.DM |
arxiv_dataset-58391412.5922 | Landau energy spectrum and quantum oscillator model for twisted
N-enlarged Newton-Hooke space-time
hep-th
We derive the energy levels for oscillator model defined on the twisted
N-enlarged Newton-Hooke space-time, i.e., we find time-dependent eigenvalues
and corresponding time-dependent eigenstates. We also demonstrate that for a
particular choice of deformation parameters of phase space the above spectrum
can be identified with the time-dependent Landau one.
| arxiv topic:hep-th |
arxiv_dataset-58401412.6022 | Ground states of nonlinear Schr\"odinger equations with sum of periodic
and inverse-square potentials
math.AP
We study the existence of solutions of the following nonlinear Schr\"odinger
equation \begin{equation*}
-\Delta u + \Big(V(x)-\frac{\mu}{|x|^2}\Big) u = f(x,u)
\hbox{ for } x\in\mathbb{R}^N\setminus\{0\}, \end{equation*} where
$V:\mathbb{R}^N\to\mathbb{R}$ and $f:\mathrm{R}^N\times\mathbb{R}\to\mathbb{R}$
are periodic in $x\in\mathbb{R}$. We assume that $0$ does not lie in the
spectrum of $-\Delta+V$ and $\mu<\frac{(N-2)^2}{4}$, $N\geq 3$. The superlinear
and subcritical term $f$ satisfies a weak monotonicity condition. For
sufficiently small $\mu\geq 0$ we find a ground state solution as a minimizer
of the energy functional on a natural constraint. If $\mu<0$ and $0$ lies below
the spectrum of $-\Delta+V$, then ground state solutions do not exist.
| arxiv topic:math.AP |
arxiv_dataset-58411412.6122 | Spread Unary Coding
cs.NE cs.IT math.IT
Unary coding is useful but it is redundant in its standard form. Unary coding
can also be seen as spatial coding where the value of the number is determined
by its place in an array. Motivated by biological finding that several neurons
in the vicinity represent the same number, we propose a variant of unary
numeration in its spatial form, where each number is represented by several 1s.
We call this spread unary coding where the number of 1s used is the spread of
the code. Spread unary coding is associated with saturation of the Hamming
distance between code words.
| arxiv topic:cs.NE cs.IT math.IT |
arxiv_dataset-58421412.6222 | Control of Electron Beam Using Strong Magnetic Field for Efficient Core
Heating in Fast Ignition
physics.plasm-ph
For enhancing the core heating efficiency in electron-driven fast ignition,
we proposed the fast electron beam guiding using externally applied
longitudinal magnetic fields. Based on the PIC simulations for the FIREX-class
experiments, we demonstrated the sufficient beam guiding performance in the
collisional dense plasma by kT-class external magnetic fields for the case with
moderate mirror ratio (~<10 ). Boring of the mirror field was found through the
formation of magnetic pipe structure due to the resistive effects, which
indicates a possibility of beam guiding in high mirror field for higher laser
intensity and/or longer pulse duration.
| arxiv topic:physics.plasm-ph |
arxiv_dataset-58431412.6322 | Indirect searches for sterile neutrinos at a high-luminosity Z-factory
hep-ph
A future high-luminosity $Z$-factory will offer the possibility to study rare
$Z$ decays, as those leading to lepton flavour violating final states.
Processes such as $Z \to \ell_1^\mp \ell_2^\pm$ are potentially complementary
to low-energy (high-intensity) observables of lepton flavour violation. In this
work we address the impact of new sterile fermions on lepton flavour violating
$Z$ decays, focusing on potential searches at FCC-ee (TLEP), and taking into
account experimental and observational constraints on the sterile states. We
consider a minimal extension of the Standard Model by one sterile fermion
state, and two well-motivated frameworks of neutrino mass generation, the
Inverse Seesaw embedded into the Standard Model, and the $\nu$MSM. Our study
shows that sterile neutrinos can give rise to contributions to BR($Z \to
\ell_1^\mp \ell_2^\pm$) within reach of the FCC-ee. We also discuss the
complementarity between a high-luminosity $Z$-factory and low-energy charged
lepton flavour violation facilities.
| arxiv topic:hep-ph |
arxiv_dataset-58441412.6422 | Comparison of the time-averaged power losses in the insulated-gate
bipolar transistors and the hybrid SIT-MOS thyristors
cond-mat.other
Two-dimensional numerical simulation of switching processes for equivalent
silicon insulated gate bipolar transistors of CSTBT-type and hybrid SITh-MOS
thyristors (HSMT) has been performed. It is shown that the energy of switching
losses during turning on and off periods in HSMT is greater than in totaly
equivalent CSTBT. Therefore, the time-averaged power Pav dissipated in HSMT is
smaller than in equivalent CSTBT only for rather long total current pulse
duration. However, lowering the lifetime of nonequilibrium charge carriers tnp
in the SITh can significantly reduce switching losses of the whole HSMT, while
maintaining its advantage for the static on state. Therefore, for each set of
CSTBT parameters it seams to be possible to select up such tnp in "almost
equivalent" HSMT that the averaged power dissipation in HSMT will be less, than
in equivalent CSTBT, for any set ranges of current pulse amplitude and
duration.
| arxiv topic:cond-mat.other |
arxiv_dataset-58451412.6522 | Area terms in entanglement entropy
hep-th
We discuss area terms in entanglement entropy and show that a recent formula
by Rosenhaus and Smolkin is equivalent to the term involving a correlator of
traces of the stress tensor in Adler-Zee formula for the renormalization of the
Newton constant. We elaborate on how to fix the ambiguities in these formulas:
Improving terms for the stress tensor of free fields, boundary terms in the
modular Hamiltonian, and contact terms in the Euclidean correlation functions.
We make computations for free fields and show how to apply these calculations
to understand some results for interacting theories which have been studied in
the literature. We also discuss an application to the F-theorem.
| arxiv topic:hep-th |
arxiv_dataset-58461412.6622 | Deep metric learning using Triplet network
cs.LG cs.CV stat.ML
Deep learning has proven itself as a successful set of models for learning
useful semantic representations of data. These, however, are mostly implicitly
learned as part of a classification task. In this paper we propose the triplet
network model, which aims to learn useful representations by distance
comparisons. A similar model was defined by Wang et al. (2014), tailor made for
learning a ranking for image information retrieval. Here we demonstrate using
various datasets that our model learns a better representation than that of its
immediate competitor, the Siamese network. We also discuss future possible
usage as a framework for unsupervised learning.
| arxiv topic:cs.LG cs.CV stat.ML |
arxiv_dataset-58471412.6722 | Cooperative Equilibrium: A solution predicting cooperative play
cs.GT
Nash equilibrium (NE) assumes that players always make a best response.
However, this is not always true; sometimes people cooperate even it is not a
best response to do so. For example, in the Prisoner's Dilemma, people often
cooperate. Are there rules underlying cooperative behavior? In an effort to
answer this question, we propose a new equilibrium concept: perfect cooperative
equilibrium (PCE), and two related variants: max-PCE and cooperative
equilibrium. PCE may help explain players' behavior in games where cooperation
is observed in practice. A player's payoff in a PCE is at least as high as in
any NE. However, a PCE does not always exist. We thus consider {\alpha}-PCE,
where {\alpha} takes into account the degree of cooperation; a PCE is a 0-PCE.
Every game has a Pareto-optimal max-PCE (M-PCE); that is, an {\alpha}-PCE for a
maximum {\alpha}. We show that M-PCE does well at predicting behavior in quite
a few games of interest. We also consider cooperative equilibrium (CE), another
generalization of PCE that takes punishment into account. Interestingly, all
Pareto-optimal M-PCE are CE. We prove that, in 2-player games, a PCE (if it
exists), a M-PCE, and a CE can all be found in polynomial time using bilinear
programming. This is a contrast to Nash equilibrium, which is PPAD complete
even in 2-player games [Chen, Deng, and Teng 2009]. We compare M-PCE to the
coco value [Kalai and Kalai 2009], another solution concept that tries to
capture cooperation, both axiomatically and in terms of an algebraic
characterization, and show that the two are closely related, despite their very
different definitions.
| arxiv topic:cs.GT |
arxiv_dataset-58481412.6822 | Spectra of Schreier graphs of Grigorchuk's group and Schroedinger
operators with aperiodic order
math.GR
We study spectral properties of the Laplacians on Schreier graphs arising
from Grigorchuk's group acting on the boundary of the infinite binary tree. We
establish a connection between the action of $G$ on its space of Schreier
graphs and a subshift associated to a non-primitive substitution and relate the
Laplacians on the Schreier graphs to discrete Schroedinger operators with
aperiodic order. We use this relation to prove that the spectrum of the
anisotropic Laplacians is a Cantor set of Lebesgue measure zero. We also use it
to show absence of eigenvalues both almost-surely and for certain specific
graphs. The methods developed here apply to a large class of examples.
| arxiv topic:math.GR |
arxiv_dataset-58491412.6922 | Growth kinetics and morphological stability of precipitates in 3-D: a
phase field study
cond-mat.mtrl-sci
We have studied the growth kinetics of isolated precipitates growing from a
supersaturated matrix in 3-dimensions (3-D) using phase field models; we assume
isotropic interfacial energy consider both constant and variable diffusivity.
We report and compare our numerical growth rates with the classic analytical
solutions of Zener and Frank (ZF). The numerical results deviate from the
analytical ones. These deviations can be understood in terms of the generalised
Gibbs-Thomson effect. Specifically, due to the higher capillary contribution in
3-D (curvature is twice for a sphere compared to a circle), the precipitate
growth kinetics deviates more from ZF in 3-D as compared to 2-D. In addition,
the kinetic parameter associated with the normal velocity of the
precipitate-matrix interface also modifies the deviation of the precipitate
composition from its equilibrium value and hence its growth kinetics. In phase
field models (such as the one used by us) which use a combination of Allen-Cahn
and Cahn-Hilliard type equations, we show how to choose the kinetic parameters
(namely, mobility and relaxation parameter) so that the kinetic coefficient (in
the generalised Gibbs-Thomson equation) is made effectively zero. We also show
that the kinetic parameter the precipitate-matrix interface might play a
crucial role in making the precipitate undergo morphological instabilities as
it grows (leading to "sea-weed"-like structures).
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-58501412.7022 | Audio Source Separation with Discriminative Scattering Networks
cs.SD cs.LG
In this report we describe an ongoing line of research for solving
single-channel source separation problems. Many monaural signal decomposition
techniques proposed in the literature operate on a feature space consisting of
a time-frequency representation of the input data. A challenge faced by these
approaches is to effectively exploit the temporal dependencies of the signals
at scales larger than the duration of a time-frame. In this work we propose to
tackle this problem by modeling the signals using a time-frequency
representation with multiple temporal resolutions. The proposed representation
consists of a pyramid of wavelet scattering operators, which generalizes
Constant Q Transforms (CQT) with extra layers of convolution and complex
modulus. We first show that learning standard models with this multi-resolution
setting improves source separation results over fixed-resolution methods. As
study case, we use Non-Negative Matrix Factorizations (NMF) that has been
widely considered in many audio application. Then, we investigate the inclusion
of the proposed multi-resolution setting into a discriminative training regime.
We discuss several alternatives using different deep neural network
architectures.
| arxiv topic:cs.SD cs.LG |
arxiv_dataset-58511412.7122 | Learning Deep Object Detectors from 3D Models
cs.CV cs.LG cs.NE
Crowdsourced 3D CAD models are becoming easily accessible online, and can
potentially generate an infinite number of training images for almost any
object category.We show that augmenting the training data of contemporary Deep
Convolutional Neural Net (DCNN) models with such synthetic data can be
effective, especially when real training data is limited or not well matched to
the target domain. Most freely available CAD models capture 3D shape but are
often missing other low level cues, such as realistic object texture, pose, or
background. In a detailed analysis, we use synthetic CAD-rendered images to
probe the ability of DCNN to learn without these cues, with surprising
findings. In particular, we show that when the DCNN is fine-tuned on the target
detection task, it exhibits a large degree of invariance to missing low-level
cues, but, when pretrained on generic ImageNet classification, it learns better
when the low-level cues are simulated. We show that our synthetic DCNN training
approach significantly outperforms previous methods on the PASCAL VOC2007
dataset when learning in the few-shot scenario and improves performance in a
domain shift scenario on the Office benchmark.
| arxiv topic:cs.CV cs.LG cs.NE |
arxiv_dataset-58521412.7222 | Unified Description of Quantum Mechanics on a Curved Space
hep-th math-ph math.MP
Starting with the first-order singular Lagrangian, the problem of the
quantization of a dynamical system constrained to a submanifold embedded in the
higher-dimensional Euclidean space is investigated within the framework of
operatorial quantization formalism. Through the projection operator method
(POM) with the constraint star-products, it is shown that both of the
constraint quantum system with the usual constraint and that with the
derivative-type constraint are naturally constructed from one Lagarangian. It
is proved that the system with the usual constraint is the sub-system of that
with the derivative-type one. Furthermore, the quantization of the dynamical
system subject to both of the usual constraint and the derivative-type one is
investigated by the POM, and the quantum corrections in the resultant
Hamiltonians are discussed.
| arxiv topic:hep-th math-ph math.MP |
arxiv_dataset-58531412.7322 | Incomplete measurement of work in a dissipative two level system
cond-mat.stat-mech quant-ph
We discuss work performed on a quantum two-level system coupled to multiple
thermal baths. To evaluate the work, a measurement of photon exchange between
the system and the baths is envisioned. In a realistic scenario, some photons
remain unrecorded as they are exchanged with baths that are not accessible to
the measurement, and thus only partial information on work and heat is
available. The incompleteness of the measurement leads to substantial
deviations from standard fluctuation relations. We propose a recovery of these
relations, based on including the mutual information given by the counting
efficiency of the partial measurement. We further present the experimental
status of a possible implementation of the proposed scheme, i.e. a calorimetric
measurement of work, currently with nearly single-photon sensitivity.
| arxiv topic:cond-mat.stat-mech quant-ph |
arxiv_dataset-58541412.7422 | Supercyclidic nets
math.DG
Supercyclides are surfaces with a characteristic conjugate parametrization
consisting of two families of conics. Patches of supercyclides can be adapted
to a Q-net (a discrete quadrilateral net with planar faces) such that
neighboring surface patches share tangent planes along common boundary curves.
We call the resulting patchworks 'supercyclidic nets' and show that every Q-net
in $\mathbb{R}P^3$ can be extended to a supercyclidic net. The construction is
governed by a multidimensionally consistent 3D system. One essential aspect of
the theory is the extension of a given Q-net in $\mathbb{R}P^N$ to a system of
circumscribed discrete torsal line systems. We present a description of the
latter in terms of projective reflections that generalizes the systems of
orthogonal reflections which govern the extension of circular nets to cyclidic
nets by means of Dupin cyclide patches.
| arxiv topic:math.DG |
arxiv_dataset-58551412.7522 | Learning Deep Temporal Representations for Brain Decoding
cs.LG cs.NE
Functional magnetic resonance imaging produces high dimensional data, with a
less then ideal number of labelled samples for brain decoding tasks (predicting
brain states). In this study, we propose a new deep temporal convolutional
neural network architecture with spatial pooling for brain decoding which aims
to reduce dimensionality of feature space along with improved classification
performance. Temporal representations (filters) for each layer of the
convolutional model are learned by leveraging unlabelled fMRI data in an
unsupervised fashion with regularized autoencoders. Learned temporal
representations in multiple levels capture the regularities in the temporal
domain and are observed to be a rich bank of activation patterns which also
exhibit similarities to the actual hemodynamic responses. Further, spatial
pooling layers in the convolutional architecture reduce the dimensionality
without losing excessive information. By employing the proposed temporal
convolutional architecture with spatial pooling, raw input fMRI data is mapped
to a non-linear, highly-expressive and low-dimensional feature space where the
final classification is conducted. In addition, we propose a simple heuristic
approach for hyper-parameter tuning when no validation data is available.
Proposed method is tested on a ten class recognition memory experiment with
nine subjects. The results support the efficiency and potential of the proposed
model, compared to the baseline multi-voxel pattern analysis techniques.
| arxiv topic:cs.LG cs.NE |
arxiv_dataset-58561412.7622 | Exciton diffusion, end quenching, and exciton-exciton annihilation in
individual air-suspended carbon nanotubes
cond-mat.mes-hall
Luminescence properties of carbon nanotubes are strongly affected by exciton
diffusion, which plays an important role in various nonradiative decay
processes. Here we perform photoluminescence microscopy on hundreds of
individual air-suspended carbon nanotubes to elucidate the interplay between
exciton diffusion, end quenching, and exciton-exciton annihilation processes. A
model derived from random-walk theory as well as Monte Carlo simulations are
utilized to analyze nanotube length dependence and excitation power dependence
of emission intensity. We have obtained the values of exciton diffusion length
and absorption cross section for different chiralities, and diameter-dependent
photoluminescence quantum yield have been observed. The simulations have also
revealed the nature of a one-dimensional coalescence process, and an analytical
expression for the power dependence of emission intensity is given.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-58571412.7722 | The Signed Weighted Resolution Set is Not a Complete Pseudoknot
Invariant
math.GT
When the signed weighted resolution set was defined as an invariant of
pseudoknots, it was unknown whether this invariant was complete. Using the
Gauss-diagrammatic invariants of pseudoknots introduced by Dorais et al, we
show that the signed were-set cannot distinguish all non-equivalent
pseudoknots. This goal is achieved through studying the effects of a flype-like
local move on a pseudodiagram.
| arxiv topic:math.GT |
arxiv_dataset-58581412.7822 | VLT/UVES spectroscopy of V4332 Sagittarii in 2005: The best view on a
decade-old stellar-merger remnant
astro-ph.SR
V4332 Sgr is a red transient (red nova) whose eruption was observed in 1994.
The remnant of the eruption shows a unique optical spectrum: strong emission
lines of atoms and molecules superimposed on an M-type stellar spectrum. The
stellar-like remnant is presumably embedded in a disc-like dusty envelope seen
almost face-on. The observed optical spectrum is assumed to result from
interactions of the central-star radiation with dust and gas in the disc and
outflows initiated in 1994. We reduced and measured a high-resolution (R = ~40
000) spectrum of V4332 Sgr obtained with VLT/UVES in April/May 2005. The
spectrum comes from the ESO archives and is the best quality spectrum of the
object ever obtained. We identified and measured over 200 emission features
belonging to 11 elements and 6 molecules. The continuous, stellar-like
component can be classified as ~M3. The interstellar reddening was estimated to
be 0.35 < E(B-V) < 0.75. From radial velocities of interstellar absorption
features in the NaI D lines, we estimated a lower limit of ~5.5 kpc to the
distance of V4332 Sgr. The spectrum of V4332 Sgr considerably evolved between
2005 and 2009. The object significantly faded in the optical, which resulted
from cooling of the main remnant by 300-350 K, corresponding to its
spectral-type change from M3 to M5-6. The object increased in luminosity by
~50%, however, implying a significant expansion of its dimensions. Most of the
emission features seen in 2005 significantly faded or even disappeared from the
spectrum of V4332 Sgr in 2009. These resulted from fading of the optical
central-star radiation and a decrease of the optical thickness of the
cirumstellar matter. V4332 Sgr bears several resemblances to V1309 Sco, which
erupted in 2008. This can indicate a similar nature of the eruptions of the two
objects. The outburst resulted from merger of a contact binary in V1309 Sco.
| arxiv topic:astro-ph.SR |
arxiv_dataset-58591412.7922 | Fast Partial Distance Estimation and Applications
cs.DC
We study approximate distributed solutions to the weighted {\it
all-pairs-shortest-paths} (APSP) problem in the CONGEST model. We obtain the
following results.
$1.$ A deterministic $(1+o(1))$-approximation to APSP in $\tilde{O}(n)$
rounds. This improves over the best previously known algorithm, by both
derandomizing it and by reducing the running time by a $\Theta(\log n)$ factor.
In many cases, routing schemes involve relabeling, i.e., assigning new names
to nodes and require that these names are used in distance and routing queries.
It is known that relabeling is necessary to achieve running times of $o(n/\log
n)$. In the relabeling model, we obtain the following results.
$2.$ A randomized $O(k)$-approximation to APSP, for any integer $k>1$,
running in $\tilde{O}(n^{1/2+1/k}+D)$ rounds, where $D$ is the hop diameter of
the network. This algorithm simplifies the best previously known result and
reduces its approximation ratio from $O(k\log k)$ to $O(k)$. Also, the new
algorithm uses uses labels of asymptotically optimal size, namely $O(\log n)$
bits.
$3.$ A randomized $O(k)$-approximation to APSP, for any integer $k>1$,
running in time $\tilde{O}((nD)^{1/2}\cdot n^{1/k}+D)$ and producing {\it
compact routing tables} of size $\tilde{O}(n^{1/k})$. The node lables consist
of $O(k\log n)$ bits. This improves on the approximation ratio of $\Theta(k^2)$
for tables of that size achieved by the best previously known algorithm, which
terminates faster, in $\tilde{O}(n^{1/2+1/k}+D)$ rounds.
| arxiv topic:cs.DC |
arxiv_dataset-58601412.8022 | A dynamical study of the chirally rotated Schr\"odinger functional in
QCD
hep-lat
The chirally rotated Schr\"odinger functional for Wilson-fermions allows for
finite-volume, mass-independent renormalization schemes compatible with
automatic O($a$) improvement. So far, in QCD, the set-up has only been studied
in the quenched approximation. Here we present first results for $N_{\rm f} =
2$ dynamical quark-flavours for several renormalization factors of
quark-bilinears. We discuss how these renormalization factors can be easily
obtained from simple ratios of two-point functions, and show how automatic
O($a$) improvement is at work. As a by-product of this investigation the
renormalization of the non-singlet axial current, $Z_A$, is determined very
precisely.
| arxiv topic:hep-lat |
arxiv_dataset-58611412.8122 | Short-time transport properties of bidisperse suspensions and porous
media: a Stokesian Dynamics study
cond-mat.soft
We present a comprehensive computational study of the short-time transport
properties of bidisperse neutral colloidal suspensions and the corresponding
porous media. Our study covers bidisperse particle size ratios up to $4$, and
total volume fractions up to and beyond the monodisperse hard-sphere close
packing limit. The many-body hydrodynamic interactions are computed using
conventional Stokesian Dynamics (SD) via a Monte-Carlo approach. We address
suspension properties including the short-time translational and rotational
self-diffusivities, the instantaneous sedimentation velocity, the
wavenumber-dependent partial hydrodynamic functions, and the high-frequency
shear and bulk viscosities; and porous media properties including the
permeability and the translational and rotational hindered diffusivities. We
carefully compare the SD computations with existing theoretical and numerical
results. For suspensions, we also explore the range of validity of various
approximation schemes, notably the Pairwise Additive (PA) approximations with
the Percus-Yevick structural input. We critically assess the strengths and
weaknesses of the SD algorithm for various transport properties. For very dense
systems, we discuss in detail the interplay between the hydrodynamic
interactions and the structures due to the presence of a second species of a
different size.
| arxiv topic:cond-mat.soft |
arxiv_dataset-58621412.8222 | Hole Detection and Shape-Free Representation and Double Landmarks Based
Geographic Routing in Wireless Sensor Networks
cs.NI
In wireless sensor networks, an important issue of Geographic Routing is
local minimum problem, which is caused by hole that blocks the greedy
forwarding process. To avoid the long detour path, recent research focuses on
detecting the hole in advance, then the nodes located on the boundary of the
hole advertise the hole information to the nodes near the hole.
| arxiv topic:cs.NI |
arxiv_dataset-58631412.8322 | Statistical Physics of 3D Hairy Black Holes
hep-th
We investigate the statistical behaviors of 3D hairy black holes in the
presence of a scalar field. The present study is made in terms of two relevant
parameters: rotation parameter a and B parameter related to the scalar field.
More precisely, we compute various statistical quantities including the
partition function for non-charged and charged black hole solutions. Using a
partition function calculation, we show that the probability is independent of
a and B parameters.
| arxiv topic:hep-th |
arxiv_dataset-58641412.8422 | De Sitter Space in Gauge/Gravity Duality
hep-th
We investigate gauge/gravity duality for gauge theories in de Sitter space.
More precisely, we study a five-dimensional consistent truncation of type IIB
supergravity, which encompasses a wide variety of gravity duals of strongly
coupled gauge theories, including the Maldacena-Nunez solution and its walking
deformations. We find several solutions of the 5d theory with dS_4 spacetime
and nontrivial profiles for (some of) the scalars along the fifth (radial)
direction. In the process, we prove that one of the equations of motion becomes
dependent on the others, for nontrivial warp factor. This dependence reduces
the number of field equations and, thus, turns out to be crucial for the
existence of solutions with (A)dS_4 spacetime. Finally, we comment on the
implications of our dS_4 solutions for building gravity duals of Glueball
Inflation.
| arxiv topic:hep-th |
arxiv_dataset-58651412.8522 | Deriving super-horizon curvature perturbations from the dynamics of
preheating
astro-ph.CO
We present a framework for calculating super-horizon curvature perturbation
from the dynamics of preheating, which gives a reasonable match to the lattice
results. Hubble patches with different initial background field values evolve
differently. From the bifurcation of their evolution trajectories we find
curvature perturbation using Lyapunov theorem and $\delta N$ formulation. In
this way we have established a connection between the finer dynamics of
preheating and the curvature perturbation produced in this era. From the
calculated analytical form of the curvature perturbation we have derived the
effective super-horizon curvature perturbation smoothed out on large scales of
CMB. The order of the amount of local form non-gaussianity generated in this
process has been calculated and problems regarding the precise determination of
it have been pointed out.
| arxiv topic:astro-ph.CO |
arxiv_dataset-58661412.8622 | Chemical analysis of ligand-free silicon nanocrystal surfaces by surface
enhanced Raman spectroscopy
cond-mat.mtrl-sci
Surface enhanced Raman spectroscopy (SERS) was used to probe the surface
chemistry of chlorine-terminated silicon nanocrystal (Si-NC) surfaces in an
air-free environment. SERS effect was observed from the thin films of Ag$_x$O
using 514 nm laser wavelength. When a monolayer of Si-NCs were spin-coated on
Ag$_x$O SERS substrates, a very clear signal of surface states, including
Si-Cl$_x$, and Si-H$_x$ were observed. Upon air-exposure, we observed the
temporal reduction of Si-Cl$_x$ peak intensity, and a development of
oxidation-related peak intensities, like Si-O$_x$ and Si-O-H$_x$. In addition,
first, second and third order transverse optical (TO) modes of Si-NCs were also
observed at 519, 1000 and 1600 cm$^{-1}$, respectively. As a comparison, Raman
analysis of a thick film (> 200 nm) of Si-NCs deposited on ordinary glass
substrates were performed. This analysis only demonstrated the first TO mode of
Si-NCs, and the all the other features originated from SERS enhancement did not
appear in the spectrum. These results conclude that, SERS is not only capable
of single-molecule detection, but also a powerful technique for monitoring the
surface chemistry of nanoparticles.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-58671412.8722 | On the number of connected components of complements to arrangements of
subtori
math.AT math.CO
We consider the arrangements of subtori in a flat d - dimensional torus T.
Let us consider an arrangement on n subtori of codimension one, let f be the
number of connected components of the complement in T to the union of subtori.
We found the set of all possible numbers f for given n and d and arbitrary
arrangements of subtori.
| arxiv topic:math.AT math.CO |
arxiv_dataset-58681501.00052 | Detailed Derivations of Small-Variance Asymptotics for some Hierarchical
Bayesian Nonparametric Models
stat.ML cs.LG
In this note we provide detailed derivations of two versions of
small-variance asymptotics for hierarchical Dirichlet process (HDP) mixture
models and the HDP hidden Markov model (HDP-HMM, a.k.a. the infinite HMM). We
include derivations for the probabilities of certain CRP and CRF partitions,
which are of more general interest.
| arxiv topic:stat.ML cs.LG |
arxiv_dataset-58691501.00152 | On a Robin problem with $p$-Laplacian and reaction bounded only from
above
math.AP
The existence of three smooth solutions, one negative, one positive, and one
nodal, to a homogeneous Robin problem with $p$-Laplacian and Carath\'eodory
reaction is established. No sub-critical growth condition is taken on. Proofs
exploit variational as well as truncation techniques. The case $p=2$ is
separately examined, obtaining a further nodal solution via Morse's theory.
| arxiv topic:math.AP |
arxiv_dataset-58701501.00252 | Torsional Alfven Waves in Solar Magnetic Flux Tubes of Axial Symmetry
astro-ph.SR
Aims: Propagation and energy transfer of torsional Alfv\'en waves in solar
magnetic flux tubes of axial symmetry is studied. Methods: An analytical model
of a solar magnetic flux tube of axial symmetry is developed by specifying a
magnetic flux and deriving general analytical formulae for the equilibrium mass
density and a gas pressure. The main advantage of this model is that it can be
easily adopted to any axisymmetric magnetic structure. The model is used to
simulate numerically the propagation of nonlinear Alfv\'en waves in such 2D
flux tubes of axial symmetry embedded in the solar atmosphere. The waves are
excited by a localized pulse in the azimuthal component of velocity and
launched at the top of the solar photosphere, and they propagate through the
solar chromosphere, transition region, and into the solar corona. Results: The
results of our numerical simulations reveal a complex scenario of twisted
magnetic field lines and flows associated with torsional Alfv\'en waves as well
as energy transfer to the magnetoacoustic waves that are triggered by the
Alfv\'en waves and are akin to the vertical jet flows. Alfv\'en waves
experience about 5 % amplitude reflection at the transition region. Magnetic
(velocity) field perturbations experience attenuation (growth) with height is
agreement with analytical findings. Kinetic energy of magnetoacoustic waves
consists of 25 % of the total energy of Alfv\'en waves. The energy transfer may
lead to localized mass transport in the form of vertical jets, as well as to
localized heating as slow magnetoacoustic waves are prone to dissipation in the
inner corona.
| arxiv topic:astro-ph.SR |
arxiv_dataset-58711501.00352 | The classification of ends of properly convex real projective orbifolds
II: Properly convex radial ends and totally geodesic ends
math.GT
Real projective structures on $n$-orbifolds are useful in understanding the
space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$
or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic
manifolds deform to manifolds with such structures not projectively equivalent
to the original ones. The purpose of this paper is to understand the structures
of properly convex ends of real projective $n$-dimensional orbifolds. In
particular, these have the radial or totally geodesic ends. For this, we will
study the natural conditions on eigenvalues of holonomy representations of ends
when these ends are manageably understandable. In this paper, we only study the
properly convex ends. The main techniques are the Vinberg duality and a
generalization of the work of Goldman, Labourie, and Margulis on flat
Lorentzian $3$-manifolds. Finally, we show that a noncompact strongly tame
properly convex real projective orbifold with generalized lens-type or
horospherical ends satisfying some topological conditions always has a strongly
irreducible holonomy group.
| arxiv topic:math.GT |
arxiv_dataset-58721501.00452 | Kinematics and Dynamics of kiloparsec-scale Jets in Radio Galaxies with
SKA
astro-ph.GA astro-ph.HE
We explore the use of SKA to deduce the physical parameters of
kiloparsec-scale jet flows in radio galaxies. Jets in Active Galactic Nuclei
are relativistic where they are first formed, but their speeds and compositions
change as they propagate. It has long been known that kiloparsec-scale jets in
radio galaxies can be divided into two flavours: strong (found in powerful
sources, narrow and terminating in compact hot-spots) and weak (found in
low-luminosity sources, geometrically flaring, unable to form hot-spots and
terminating in diffuse lobes or tails). We have developed methods to model AGN
jets as intrinsically symmetrical, relativistic flows by fitting to deep,
well-resolved radio images in Stokes I, Q and U. This has yielded a wealth of
information about the brightest few weak-flavour jets. Our first key objective
is to observe large samples of weak and transition jets at 0.1 - 0.5 arcsec
resolution with SKA1-MID. This would allow us to see how jet propagation
depends on power and environment and to quantify the energy and momentum input
into the IGM. We will require typical noise levels of 1 microJy/beam, and may
be able to exploit survey imaging in some cases. Our second, more challenging,
application is to determine the velocity fields in strong-flavour jets. Do they
have very fast spines with bulk Lorentz factors of 5 - 10? Is there evidence
for magnetic confinement by a toroidal field? What are their energy fluxes?
This is a major imaging challenge for SKA2: we need resolution better than 0.05
arcsec, ideally in the 1 - 10 GHz frequency range, with rms noise levels of
roughly 10 nJy/beam and extremely high dynamic range, imaging fidelity and
polarization purity.
| arxiv topic:astro-ph.GA astro-ph.HE |
arxiv_dataset-58731501.00552 | Resonance energy transport in an oscillator chain
nlin.PS nlin.CD
We investigate energy transfer and localization in a linear time-invariant
oscillator chain weakly coupled to a forced nonlinear actuator. Two types of
perturbation are studied: (1) harmonic forcing with a constant frequency is
applied to the actuator (the Duffing oscillator) with slowly changing
parameters; (2) harmonic forcing with a slowly increasing frequency is applied
to the nonlinear actuator with constant parameters. In both cases, stiffness of
linear oscillators as well as linear coupling remains constant, and the system
is initially engaged in resonance. The parameters of the systems and forcing
are chosen to guarantee autoresonance (AR) with gradually increasing energy in
the nonlinear actuator. As this paper demonstrates, forcing with constant
frequency generates oscillations with growing energy in the linear chain but in
the system excited by forcing with slowly time-dependent frequency energy
remains localized on the nonlinear actuator whilst the response of the linear
chain is bounded. This means that the systems that seem to be almost identical
exhibit different dynamical behavior caused by their different resonance
properties. Numerical examples a good agreement between exact (numerical)
solutions and their asymptotic approximations found by the multiple time scales
method.
| arxiv topic:nlin.PS nlin.CD |
arxiv_dataset-58741501.00652 | Gaussian optimizers and the additivity problem in quantum information
theory
math-ph math.MP quant-ph
We give a survey of the two remarkable analytical problems of quantum
information theory. The main part is a detailed report of the recent (partial)
solution of the quantum Gaussian optimizers problem which establishes an
optimal property of Glauber's coherent states -- a particular instance of pure
quantum Gaussian states. We elaborate on the notion of quantum Gaussian channel
as a noncommutative generalization of Gaussian kernel to show that the coherent
states, and under certain conditions only they, minimize a broad class of the
concave functionals of the output of a Gaussian channel. Thus, the output
states corresponding to the Gaussian input are "the least chaotic", majorizing
all the other outputs. The solution, however, is essentially restricted to the
gauge-invariant case where a distinguished complex structure plays a special
role. We also comment on the related famous additivity conjecture, which was
solved in principle in the negative some five years ago. This refers to the
additivity or multiplicativity (with respect to tensor products of channels) of
information quantities related to the classical capacity of quantum channel,
such as $(1\rightarrow p)$-norms or the minimal von Neumann or R\'enyi output
entropies. A remarkable corollary of the present solution of the quantum
Gaussian optimizers problem is that these additivity properties, while not
valid in general, do hold in the important and interesting class of the
gauge-covariant Gaussian channels.
| arxiv topic:math-ph math.MP quant-ph |
arxiv_dataset-58751501.00752 | A Deep-structured Conditional Random Field Model for Object Silhouette
Tracking
cs.CV cs.LG stat.ML
In this work, we introduce a deep-structured conditional random field
(DS-CRF) model for the purpose of state-based object silhouette tracking. The
proposed DS-CRF model consists of a series of state layers, where each state
layer spatially characterizes the object silhouette at a particular point in
time. The interactions between adjacent state layers are established by
inter-layer connectivity dynamically determined based on inter-frame optical
flow. By incorporate both spatial and temporal context in a dynamic fashion
within such a deep-structured probabilistic graphical model, the proposed
DS-CRF model allows us to develop a framework that can accurately and
efficiently track object silhouettes that can change greatly over time, as well
as under different situations such as occlusion and multiple targets within the
scene. Experiment results using video surveillance datasets containing
different scenarios such as occlusion and multiple targets showed that the
proposed DS-CRF approach provides strong object silhouette tracking performance
when compared to baseline methods such as mean-shift tracking, as well as
state-of-the-art methods such as context tracking and boosted particle
filtering.
| arxiv topic:cs.CV cs.LG stat.ML |
arxiv_dataset-58761501.00852 | Explicit ambient metrics and holonomy
math.DG
We present three large classes of examples of conformal structures for which
the equations for the Fefferman-Graham ambient metric to be Ricci-flat are
linear PDEs, which we solve explicitly. These explicit solutions enable us to
discuss the holonomy of the corresponding ambient metrics. Our examples include
conformal pp-waves and, more importantly, conformal structures that are defined
by generic rank 2 and 3 distributions in respective dimensions 5 and 6. The
corresponding explicit Fefferman-Graham ambient metrics provide a large class
of metrics with holonomy equal to the exceptional non-compact Lie group
$\mathbf{G}_2$ as well as ambient metrics with holonomy contained in
$\mathbf{Spin}(4,3)$.
| arxiv topic:math.DG |
arxiv_dataset-58771501.00952 | Heat Bath Algorithmic Cooling with Spins: Review and Prospects
quant-ph
Application of multiple rounds of Quantum Error Correction (QEC) is an
essential milestone towards the construction of scalable quantum information
processing devices. However, experimental realizations of it are still in their
infancy. The requirements for multiple round QEC are high control fidelity and
the ability to extract entropy from ancilla qubits. Nuclear Magnetic Resonance
(NMR) based quantum devices have demonstrated high control fidelity with up to
12 qubits. On the other hand, the major challenge in the NMR QEC experiment is
to efficiently supply ancilla qubits in highly pure states at the beginning of
each round of QEC. Purification of qubits in NMR, or in other ensemble based
quantum systems can be accomplished through Heat Bath Algorithmic Cooling
(HBAC). It is an efficient method for extracting entropy from qubits that
interact with a heat bath, allowing cooling below the bath temperature. For
practical HBAC, coupled electron-nuclear spin systems are more promising than
conventional NMR quantum processors, since electron spin polarization is about
$10^3$ times greater than that of a proton under the same experimental
conditions. We provide an overview on both theoretical and experimental aspects
of HBAC focusing on spin and magnetic resonance based systems, and discuss the
prospects of exploiting electron-nuclear coupled systems for the realization of
HBAC and multiple round QEC.
| arxiv topic:quant-ph |
arxiv_dataset-58781501.01052 | Multiple bubble dynamics and velocity selection in Laplacian growth
without surface tension
physics.flu-dyn nlin.PS nlin.SI
A new selection phenomenon in nonlinear interface dynamics is predicted. A
generic class of exact regular unsteady multi-bubble solutions in a Hele-Shaw
cell is presented. These solutions show that the case where the asymptotic
bubble velocity, $U$, is twice greater than the velocity, $V$, of the uniform
background flow, i.e., $U = 2V$, is the only attractor of the dynamics.
Contrary to common belief, the predicted velocity selection requires neither
surface tension nor other external regularization.
| arxiv topic:physics.flu-dyn nlin.PS nlin.SI |
arxiv_dataset-58791501.01152 | Linear decomposition attack on public key exchange protocols using
semidirect products of (semi)groups
cs.CR math.GR
We show that a linear decomposition attack based on the decomposition method
introduced by the author works by finding the exchanged secret keys in all main
protocols using semidirect products of (semi)grops proposed by Kahrobaei,
Shpilrain, Habeeb, Koupparis and Lam.
| arxiv topic:cs.CR math.GR |
arxiv_dataset-58801501.01252 | Optimisation using Natural Language Processing: Personalized Tour
Recommendation for Museums
cs.AI cs.CL
This paper proposes a new method to provide personalized tour recommendation
for museum visits. It combines an optimization of preference criteria of
visitors with an automatic extraction of artwork importance from museum
information based on Natural Language Processing using textual energy. This
project includes researchers from computer and social sciences. Some results
are obtained with numerical experiments. They show that our model clearly
improves the satisfaction of the visitor who follows the proposed tour. This
work foreshadows some interesting outcomes and applications about on-demand
personalized visit of museums in a very near future.
| arxiv topic:cs.AI cs.CL |
arxiv_dataset-58811501.01352 | Iso-Orthogonality and Type II Duadic Constacyclic Codes
cs.IT math.IT
Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic
codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic
codes, and study their properties and existence. We show that even-like duadic
constacyclic codes are isometrically orthogonal, and the duals of even-like
duadic constacyclic codes are odd-like duadic constacyclic codes. We exhibit
necessary and sufficient conditions for the existence of even-like duadic
constacyclic codes. A class of even-like duadic constacyclic codes which are
alternant MDS-codes is constructed.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-58821501.01452 | Genuine High-Order Einstein-Podolsky-Rosen Steering
quant-ph
Einstein-Podolsky-Rosen (EPR) steering demonstrates that two parties share
entanglement even if the measurement devices of one party are untrusted. Here,
going beyond this bipartite concept, we develop a novel formalism to explore a
large class of EPR steering from generic multipartite quantum systems of
arbitrarily high dimensionality and degrees of freedom, such as graph states
and hyperentangled systems. All of these quantum characteristics of genuine
high-order EPR steering can be efficiently certified with few measurement
settings in experiments. We faithfully demonstrate for the first time such
generality by experimentally showing genuine four-partite EPR steering and
applications to universal one-way quantum computing. Our formalism provides a
new insight into the intermediate type of genuine multipartite Bell
non-locality and potential applications to quantum of untrusted measurement
devices.
| arxiv topic:quant-ph |
arxiv_dataset-58831501.01552 | Finite size effects on liquid-solid phase coexistence and the estimation
of crystal nucleation barriers
cond-mat.stat-mech
A fluid in equilibrium in a finite volume $V$ with particle number $N$ at a
density $\rho = N/V$ exceeding the onset density $\rho_f $ of freezing may
exhibit phase coexistence between a crystalline nucleus and surrounding fluid.
Using a method suitable for the estimation of the chemical potential of dense
fluids we obtain the excess free energy due to the surface of the crystalline
nucleus. There is neither a need to precisely locate the interface nor to
compute the (anisotropic) interfacial tension. As a test case, a soft version
of the Asakura-Oosawa model for colloid polymer-mixtures is treated. While our
analysis is appropriate for crystal nuclei of arbitrary shape, we find the
nucleation barrier to be compatible with a spherical shape, and consistent with
classical nucleation theory.
| arxiv topic:cond-mat.stat-mech |
arxiv_dataset-58841501.01652 | A fast analysis-based discrete Hankel transform using asymptotic
expansions
math.NA
A fast and numerically stable algorithm is described for computing the
discrete Hankel transform of order $0$ as well as evaluating Schl\"{o}milch and
Fourier--Bessel expansions in $\mathcal{O}(N(\log N)^2/\log\!\log N)$
operations. The algorithm is based on an asymptotic expansion for Bessel
functions of large arguments, the fast Fourier transform, and the Neumann
addition formula. All the algorithmic parameters are selected from error bounds
to achieve a near-optimal computational cost for any accuracy goal. Numerical
results demonstrate the efficiency of the resulting algorithm.
| arxiv topic:math.NA |
arxiv_dataset-58851501.01752 | 3D periodic dielectric composite homogenization based on the Generalized
Source Method
physics.comp-ph
The article encloses a new Fourier space method for rigorous optical
simulation of 3D periodic dielectric structures. The method relies upon
rigorous solution of Maxwell's equations in complex composite structures by the
Generalized Source Method. Extremely fast GPU enabled calculations provide a
possibility for an efficient search of eigenmodes in 3D periodic complex
structures on the basis of rigorously obtained resonant electromagnetic
response. The method is applied to the homogenization problem demonstrating a
complete anisotropic dielectric tensor retrieval.
| arxiv topic:physics.comp-ph |
arxiv_dataset-58861501.01852 | Early Universe in the SU(3)_L X U(1)_X electroweak models
hep-ph
We present status of the 3-3-1 models and their implications to cosmological
evolution such as inflation, phase transitions and sphalerons. The models can
deal not only with the issues such as neutrino physics, dark matter, etc, but
they are also able to provide quite good agreement with the Standard Cosmology:
the inflation happens at the GUT scale, while phase transition has two
sequences corresponding two steps of symmetry breaking in the models, namely:
SU(3) --> SU(2) and SU(2) --> U(1). Some bounds on the model parameters are
obtained: in the RM331, the mass of the heavy neutral Higgs boson is fixed in
the range: 285.56 GeV <M_{h_2}< 1.746 TeV, and for the doubly charged scalar:
3.32 TeV <M_{h_{--}}< 5.61 TeV.
| arxiv topic:hep-ph |
arxiv_dataset-58871501.01952 | Complete All-Optical Quantum Control of Electron Spins in InAs/GaAs
Quantum Dot Molecule
cond-mat.mes-hall quant-ph
The spin states of electrons and holes confined in InAs quantum dot molecules
have recently come to fore as a promising system for the storage or
manipulation of quantum information. We describe here a feasible scheme for
complete quantum optical control of two electron spin qubits in two
vertically-stacked singly-charged InAs quantum dots coupled by coherent
electron tunneling. With an applied magnetic field transverse to the growth
direction, we construct a universal set of gates that corresponds to the
possible Raman transitions between the spin states. We detail the procedure to
decompose a given two-qubit unitary operation, so as to realize it with a
successive application of up to 8 of these gates. We give the pulse shapes for
the laser pulses used to implement this universal set of gates and demonstrate
the realization of the two-qubit quantum Fourier transform with fidelity of
0.881 and duration of 414 ps. Our proposal therefore offers an accessible path
to universal computation in quantum dot molecules and points to the advantages
of using pulse shaping incoherent manipulation of optically active quantum dots
to mitigate the negative effects of unintended dynamics and spontaneous
emission.
| arxiv topic:cond-mat.mes-hall quant-ph |
arxiv_dataset-58881501.02052 | General method of the relativistic Foldy-Wouthuysen transformation and
proof of validity of the Foldy-Wouthuysen Hamiltonian
math-ph hep-th math.MP quant-ph
A general method of the Foldy-Wouthuysen transformation is developed. This
method is applicable to relativistic particles with any spin in arbitrarily
strong external fields. It can be used when the de Broglie wavelength is much
smaller than the characteristic distance. Contrary to previously developed
relativistic methods, the present method satisfies the condition of the exact
Foldy-Wouthuysen transformation and is well substantiated. The derived
relativistic Foldy-Wouthuysen Hamiltonian is expanded in powers of the Planck
constant. In this expansion, terms proportional to the zero and first powers
are determined exactly in accordance with the above condition and terms
proportional to higher powers are not specified. The obtained result agrees
with the corresponding formula for the Foldy-Wouthuysen Hamiltonian previously
deduced by an iterative relativistic method and proves the validity of results
obtained with this formula.
| arxiv topic:math-ph hep-th math.MP quant-ph |
arxiv_dataset-58891501.02152 | A new div-curl result. Applications to the homogenization of elliptic
systems and to the weak continuity of the Jacobian
math.AP
In this paper a new div-curl result is established in an open set $\Omega$ of
$\mathbb{R}^N$, $N\geq 2$, for the product of two sequences of vector-valued
functions which are bounded respectively in $L^p(\Omega)^N$ and
$L^q(\Omega)^N$, with ${1/p}+{1/q}=1+{1/(N-1)}$, and whose respectively
divergence and curl are compact in suitable spaces. We also assume that the
product converges weakly in $W^{-1,1}(\Omega)$. The key ingredient of the proof
is a compactness result for bounded sequences in $W^{1,q}(\Omega)$, based on
the imbedding of $W^{1,q}(S\_{N-1})$ into $L^{p'}(S\_{N-1})$ ($S\_{N-1}$ the
unit sphere of $\mathbb{R}^N$) through a suitable selection of annuli on which
the gradients are not too high, in the spirit of De Giorgi and Manfredi. The
div-curl result is applied to the homogenization of equi-coercive systems whose
coefficients are equi-bounded in $L^\rho(\Omega)$ for some
$\rho\textgreater{}{N-1\over 2}$ if $N\textgreater{}2$, or in $L^1(\Omega)$ if
$N=2$. It also allows us to prove a weak continuity result for the Jacobian for
bounded sequences in $W^{1,N-1}(\Omega)$ satisfying an alternative assumption
to the $L^\infty$-strong estimate of Brezis and Nguyen. Two examples show the
sharpness of the results.
| arxiv topic:math.AP |
arxiv_dataset-58901501.02252 | Optimization Methods for Designing Sequences with Low Autocorrelation
Sidelobes
math.OC cs.IT math.IT stat.ME
Unimodular sequences with low autocorrelations are desired in many
applications, especially in the area of radar and code-division multiple access
(CDMA). In this paper, we propose a new algorithm to design unimodular
sequences with low integrated sidelobe level (ISL), which is a widely used
measure of the goodness of a sequence's correlation property. The algorithm
falls into the general framework of majorization-minimization (MM) algorithms
and thus shares the monotonic property of such algorithms. In addition, the
algorithm can be implemented via fast Fourier transform (FFT) operations and
thus is computationally efficient. Furthermore, after some modifications the
algorithm can be adapted to incorporate spectral constraints, which makes the
design more flexible. Numerical experiments show that the proposed algorithms
outperform existing algorithms in terms of both the quality of designed
sequences and the computational complexity.
| arxiv topic:math.OC cs.IT math.IT stat.ME |
arxiv_dataset-58911501.02352 | A `soft + hard' model for heavy-ion collisions
hep-ph
We describe the spectra of neutral pions stemming from AuAu collisions at
$\sqrt s$ = 200 AGeV in a `soft + hard' model. The model is based on the
assumptions that hadrons stemming from hard processes are described via
perturbative quantum chromodynamics improved parton model calculations, while
those stemming from the Quark-Gluon Plasma (we refer to as soft yields) can be
described in a super-statistical model induced by multiplicity fluctuations.
The obtained dependence of the parameters of the model on the event centrality
is compared to what is observed in PbPb collisions at $\sqrt s$ = 2.76 ATeV.
| arxiv topic:hep-ph |
arxiv_dataset-58921501.02452 | A construction of small (q-1)-regular graphs of girth 8
math.CO
In this note we construct a new infinite family of $(q-1)$-regular graphs of
girth $8$ and order $2q(q-1)^2$ for all prime powers $q\ge 16$, which are the
smallest known so far whenever $q-1$ is not a prime power or a prime power plus
one itself.
| arxiv topic:math.CO |
arxiv_dataset-58931501.02552 | $L_p$-discrepancy of the symmetrized van der Corput sequence
math.NT
It is well known that the $L_p$-discrepancy for $p \in [1,\infty]$ of the van
der Corput sequence is of exact order of magnitude $O((\log N)/N)$. This
however is for $p \in (1,\infty)$ not best possible with respect to the lower
bounds according to Roth and Proinov. For the case $p=2$ it is well known that
the symmetrization trick due to Davenport leads to the optimal
$L_2$-discrepancy rate $O(\sqrt{\log N}/N)$ for the symmetrized van der Corput
sequence. In this note we show that this result holds for all $p \in
(1,\infty)$. The proof is based on an estimate of the Haar coefficients of the
corresponding local discrepancy and on the use of the Littlewood-Paley
inequality.
| arxiv topic:math.NT |
arxiv_dataset-58941501.02652 | A Flexible Framework for Defining, Representing and Detecting Changes on
the Data Web
cs.DB
The dynamic nature of Web data gives rise to a multitude of problems related
to the identification, computation and management of the evolving versions and
the related changes. In this paper, we consider the problem of change
recognition in RDF datasets, i.e., the problem of identifying, and when
possible give semantics to, the changes that led from one version of an RDF
dataset to another. Despite our RDF focus, our approach is sufficiently general
to engulf different data models that can be encoded in RDF, such as relational
or multi-dimensional. In fact, we propose a flexible, extendible and
data-model-independent methodology of defining changes that can capture the
peculiarities and needs of different data models and applications, while being
formally robust due to the satisfaction of the properties of completeness and
unambiguity. Further, we propose an ontology of changes for storing the
detected changes that allows automated processing and analysis of changes,
cross-snapshot queries (spanning across different versions), as well as queries
involving both changes and data. To detect changes and populate said ontology,
we propose a customizable detection algorithm, which is applicable to different
data models and applications requiring the detection of custom, user-defined
changes. Finally, we provide a proof-of-concept application and evaluation of
our framework for different data models.
| arxiv topic:cs.DB |
arxiv_dataset-58951501.02752 | Reflection Symmetry in Higher Dimensional Black Hole Spacetimes
gr-qc hep-th math-ph math.MP
In 4 spacetime dimensions there is a well known proof that for any
asymptotically flat, stationary, and axisymmetric vacuum solution of Einstein's
equation there exists a "$t$-$\phi$" reflection isometry that reverses the
direction of the timelike Killing vector field and the direction of the axial
Killing vector field. However, this proof does not generalize to higher
spacetime dimensions. Here we consider asymptotically flat, stationary, and
axisymmetric (i.e., having one or more commuting rotational isometries) black
hole spacetimes in vacuum general relativity in $d \geq 4$ spacetime dimensions
such that the action of the isometry group is trivial. (Here "trivial" means
that if the "axes"---i.e., the points where the axial Killing fields are
linearly dependent---are removed, the action of the isometry group is that of a
trivial principal fiber bundle. This excludes actions like that found in the
Sorkin monopole.) We prove that there exists a "$t$-$\phi$" reflection isometry
that reverses the direction of the timelike Killing vector field and the
direction of each axial Killing vector field. The proof relies in an essential
way on the first law of black hole mechanics.
| arxiv topic:gr-qc hep-th math-ph math.MP |
arxiv_dataset-58961501.02852 | Generalized mutual informations of quantum critical chains
cond-mat.stat-mech cond-mat.str-el hep-th
We study the R\'enyi mutual information $\tilde{I}_n$ of the ground state of
different critical quantum chains. The R\'enyi mutual information definition
that we use is based on the well established concept of the R\'enyi divergence.
We calculate this quantity numerically for several distinct quantum chains
having either discrete $Z(Q)$ symmetries (Q-state Potts model with $Q=2,3,4$
and $Z(Q)$ parafermionic models with $Q=5,6,7,8$ and also Ashkin-Teller model
with different anisotropies) or the $U(1)$ continuous symmetries(Klein-Gordon
field theory, XXZ and spin-1 Fateev-Zamolodchikov quantum chains with different
anisotropies). For the spin chains these calculations were done by expressing
the ground-state wavefunctions in two special basis. Our results indicate some
general behavior for particular ranges of values of the parameter $n$ that
defines $\tilde{I}_n$. For a system, with total size $L$ and subsystem sizes
$\ell$ and $L-\ell$, the$\tilde{I}_n$ has a logarithmic leading behavior given
by $\frac{\tilde{c}_n}{4}\log(\frac{L}{\pi}\sin(\frac{\pi \ell}{L}))$ where the
coefficient $\tilde{c}_n$ is linearly dependent on the central charge $c$ of
the underlying conformal field theory (CFT) describing the system's critical
properties.
| arxiv topic:cond-mat.stat-mech cond-mat.str-el hep-th |
arxiv_dataset-58971501.02952 | Spectral resolution of the Neumann-Poincar\'{e} operator on intersecting
disks and analysis of plasmon resonance
math.AP
The purpose of this paper is to investigate the spectral nature of the
Neumann-Poincar\'e operator on the intersecting disks, which is a domain with
the Lipschitz boundary. The complete spectral resolution of the operator is
derived, which shows in particular that it admits only the absolutely
continuous spectrum, no singularly continuous spectrum and no pure point
spectrum. We then quantitatively analyze using the spectral resolution the
plasmon resonance at the absolutely continuous spectrum.
| arxiv topic:math.AP |
arxiv_dataset-58981501.03052 | Duflo involutions for 2-categories associated to tree quivers
math.RT math.CT
Motivated by the definition of Duflo involution for fiat $2$-categories, we
define certain analogues of Duflo involution for arbitrary finitary
$2$-categories and show that such Duflo involutions exist for two classes of
finitary $2$-categories associated with tree path algebras. Additionally, we
describe the quiver for the algebra underlying the principal $2$-representation
for these two classes of finitary $2$-categories.
| arxiv topic:math.RT math.CT |
arxiv_dataset-58991501.03152 | Early-type Eclipsing Binaries with Intermediate Orbital Periods
astro-ph.SR
We analyze 221 eclipsing binaries (EBs) in the Large Magellanic Cloud with
B-type main-sequence (MS) primaries ($M_1$ $\approx$ 4 - 14 M$_{\odot}$) and
orbital periods $P$ = 20 - 50 days that were photometrically monitored by the
Optical Gravitational Lensing Experiment. We utilize our three-stage automated
pipeline to (1) classify all 221 EBs, (2) fit physical models to the light
curves of 130 detached well-defined EBs from which unique parameters can be
determined, and (3) recover the intrinsic binary statistics by correcting for
selection effects. We uncover two statistically significant trends with age.
First, younger EBs tend to reside in dustier environments with larger
photometric extinctions, an empirical relation that can be implemented when
modeling stellar populations. Second, younger EBs generally have large
eccentricities. This demonstrates that massive binaries at moderate orbital
periods are born with a Maxwellian "thermal" orbital velocity distribution,
which indicates they formed via dynamical interactions. In addition, the
age-eccentricity anticorrelation provides a direct constraint for tidal
evolution in highly eccentric binaries containing hot MS stars with radiative
envelopes. The intrinsic fraction of B-type MS stars with stellar companions
$q$ = $M_2$/$M_1$ $>$ 0.2 and orbital periods $P$ = 20 - 50 days is (7 $\pm$
2)%. We find early-type binaries at $P$ = 20 - 50 days are weighted
significantly toward small mass ratios $q$ $\approx$ 0.2 - 0.3, which is
different than the results from previous observations of closer binaries with
$P$ $<$ 20 days. This indicates that early-type binaries at slightly wider
orbital separations have experienced substantially less coevolution and
competitive accretion during their formation in the circumbinary disk.
| arxiv topic:astro-ph.SR |
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