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Critical fluctuations have been studied in the microwave conductivity of
Bi_2Sr_2CaCu_2O_(8+\delta), Bi_2Sr_2Ca_2Cu_3O_(10+delta), and
YBa_2Cu_3O_(7-delta) thin films above T_c. It is found that a consistent
analysis of the real and imaginary parts of the fluctuation conductivity can be
achieved only if an appropriate wavevector or energy cutoff in the fluctuation
spectrum is taken into account. In all of the three underdoped superconducting
films one observes strong fluctuations extending far above T_c. The coherence
length inferred from the imaginary part of the conductivity exhibits the static
critical exponent nu = 1 very close to T_c, and a crossover to the region with
nu = 2/3 at higher temperatures. In parallel, our analysis reveals the absence
of the normal conductivity near T_c, i.e. fully opened pseudogap. Following the
crossover to the region with nu = 2/3, the normal conductivity is gradually
recovered, i.e. the closing of the pseudogap is monitored.
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Query by Humming (QBH) is a system to provide a user with the song(s) which
the user hums to the system. Current QBH method requires the extraction of
onset and pitch information in order to track similarity with various versions
of different songs. However, we here focus on detecting precise onsets only and
use them to build a QBH system which is better than existing methods in terms
of speed and memory and empirically in terms of accuracy. We also provide
statistical analogy for onset detection functions and provide a measure of
error in our algorithm.
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In this paper we consider the $\mathcal{H}_2$-norm of networked systems with
multi-time scale consensus dynamics. We develop a general framework for such
systems that allows for edge weighting, independent agent-based time scales, as
well as measurement and process noise. From this general system description, we
highlight an interesting case where the influences of the weighting and scaling
can be separated in the design problem. We then consider the design of the time
scale parameters for minimizing the $\mathcal{H}_2$-norm for the purpose of
network resilience.
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We discuss two complementary problems: adiabatic loading of one-dimensional
bosons into an optical lattice and merging two one-dimensional Bose systems.
Both problems can be mapped to the sine-Gordon model. This mapping allows us to
find power-law scalings for the number of excitations with the ramping rate in
the regime where the conventional linear response approach fails. We show that
the exponent of this power law is sensitive to the interaction strength. In
particular, the response is larger, or less adiabatic, for strongly (weakly)
interacting bosons for the loading (merging) problem. Our results illustrate
that in general the nonlinear response to slow relevant perturbations can be a
powerful tool for characterizing properties of interacting systems.
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We study the number $N(n, A_n, X)$ of number fields of degree $n$ whose
Galois closure has Galois group $A_n$ and whose discriminant is bounded by $X$.
By a conjecture of Malle, we expect that $N(n, A_n, X) \sim C_n X^{1/2} (\log
X)^{b_n}$, for constants $b_n$ and $C_n$. For $5 < n < 84394$, the best known
upper bound is $N(n, A_n, X) \ll X^{\frac{n + 2}{4}}$; this bound follows from
Schmidt's Theorem, which implies there are $\ll X^{\frac{n + 2}{4}}$ number
fields of degree $n$. (For $n > 84393$, there are better bounds due to
Ellenberg and Venkatesh.) We show, using the important work of Pila on counting
integral points on curves, that $N(n, A_n, X) \ll X^{\frac{n^2 - 2}{4(n -
1)}+\epsilon}$, thereby improving the best previous exponent by approximately
1/4 for $5 < n < 84394$.
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Document-level machine translation manages to outperform sentence level
models by a small margin, but have failed to be widely adopted. We argue that
previous research did not make a clear use of the global context, and propose a
new document-level NMT framework that deliberately models the local context of
each sentence with the awareness of the global context of the document in both
source and target languages. We specifically design the model to be able to
deal with documents containing any number of sentences, including single
sentences. This unified approach allows our model to be trained elegantly on
standard datasets without needing to train on sentence and document level data
separately. Experimental results demonstrate that our model outperforms
Transformer baselines and previous document-level NMT models with substantial
margins of up to 2.1 BLEU on state-of-the-art baselines. We also provide
analyses which show the benefit of context far beyond the neighboring two or
three sentences, which previous studies have typically incorporated.
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In this paper, we study the maximum principle of mean field type control
problems when the volatility function depends on the state and its measure and
also the control, by using our recently developed method. Our method is to
embed the mean field type control problem into a Hilbert space to bypass the
evolution in the Wasserstein space. We here give a necessary condition and a
sufficient condition for these control problems in Hilbert spaces, and we also
derive a system of forward-backward stochastic differential equations.
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We present a detailed abundance analysis, including spectral syntheses, of a
very metal-poor ([Fe/H]= -2.7), peculiar main sequence star, HE0024-2523
detected during the course of the Keck Pilot Program. Radial velocities of this
star were obtained during four different observing runs over a time span of 1.1
years, and demonstrate that it is clearly a short period spectroscopic binary.
An orbital solution was obtained, and orbital parameters were determined with
high precision. The rotational velocity was also measured (vsin i=9.7$\pm$1.5
kms); rotation appears likely to be synchronous with the orbit. The abundance
analysis and spectral syntheses indicate that the object is a CH star
characterized by extreme s-process enrichment, likely due to mass accretion
from an evolved companion which has now probably become a white dwarf. The lead
(Pb) abundance of HE0024-2523 is very high, the same as that of the recently
discovered lead-rich metal-poor star CS 29526-110, [Pb/Fe]=+3.3. The abundance
ratio of the heavy-s to light-s elements, as characterized by Pb and Ba,
[Pb/Ba]=+1.9, is the highest yet found for any metal-poor star, and is about
0.7 dex higher than that of CS29526-110. On the basis of the measured isotopic
ratio of carbon (12C/13C about 6) we argue that the mass donor must have had an
original mass of at least 3 Msun. The unusually short period of this CH star
suggests that it underwent a past common-envelope phase with its evolved
companion. Our results are compared to the latest available models for AGB
yields and s-process nucleosynthesis. We also discuss the possible connection
between HE0024-2523 the lithium depletion of halo stars, and halo blue
straggler formation.
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The connection between the long GRBs and Type Ic Supernovae (SNe) has
revealed the interesting diversity: (i) GRB-SNe, (ii) Non-GRB Hypernovae (HNe),
(iii) X-Ray Flash (XRF)-SNe, and (iv) Non-SN GRBs (or dark HNe). We show that
nucleosynthetic properties found in the above diversity are connected to the
variation of the abundance patterns of extremely-metal-poor (EMP) stars, such
as the excess of C, Co, Zn relative to Fe. We explain such a connection in a
unified manner as nucleosynthesis of hyper-aspherical (jet-induced) explosions
Pop III core-collapse SNe. We show that (1) the explosions with large energy
deposition rate, $\dot{E}_{\rm dep}$, are observed as GRB-HNe and their yields
can explain the abundances of normal EMP stars, and (2) the explosions with
small $\dot{E}_{\rm dep}$ are observed as GRBs without bright SNe and can be
responsible for the formation of the C-rich EMP (CEMP) and the hyper metal-poor
(HMP) stars. We thus propose that GRB-HNe and the Non-SN GRBs (dark HNe) belong
to a continuous series of BH-forming stellar deaths with the relativistic jets
of different $\dot{E}_{\rm dep}$.
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The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold
r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of
weak normality for them is introduced. The partial differential equations for
the force field $\bold F(\bold r,\dot\bold r)$ of the dynamical systems with
weak and complete normality are derived.
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The class of generalized shearlet dilation groups has recently been developed
to allow the unified treatment of various shearlet groups and associated
shearlet transforms that had previously been studied on a case-by-case basis.
We consider several aspects of these groups: First, their systematic
construction from associative algebras, secondly, their suitability for the
characterization of wavefront sets, and finally, the question of constructing
embeddings into the symplectic group in a way that intertwines the
quasi-regular representation with the metaplectic one. For all questions, it is
possible to treat the full class of generalized shearlet groups in a
comprehensive and unified way, thus generalizing known results to an infinity
of new cases. Our presentation emphasizes the interplay between the algebraic
structure underlying the construction of the shearlet dilation groups, the
geometric properties of the dual action, and the analytic properties of the
associated shearlet transforms.
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Floer theory was originally devised to estimate the number of 1-periodic
orbits of Hamiltonian systems. In earlier works, we constructed Floer homology
for homoclinic orbits on two dimensional manifolds using combinatorial
techniques. In the present paper, we study theoretic aspects of computational
complexity of homoclinic Floer homology. More precisely, for finding the
homoclinic points and immersions that generate the homology and its boundary
operator, we establish sharp upper bounds in terms of iterations of the
underlying symplectomorphism. This prepares the ground for future numerical
works.
Although originally aimed at numerics, the above bounds provide also purely
algebraic applications, namely
1) Torsion-freeness of primary homoclinic Floer homology.
2) Morse type inequalities for primary homoclinic orbits.
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Analytical formulae are presented which provide quantitative estimates for
the suppression of the anticipated back-to-back particle--antiparticle
correlations in high energy nuclear collisions due to the finite duration of
the transition dynamics. They show that it is unlikely to observ the effect.
|
Understanding the driving forces behind the nucleation of different
polymorphs is of great importance for material sciences and the pharmaceutical
industry. This includes understanding the reaction coordinate that governs the
nucleation process as well as correctly calculating the relative free energies
of different polymorphs. Here we demonstrate, for the prototypical case of urea
nucleation from melt, how one can learn such a 1-dimensional reaction
coordinate as a function of pre-specified order parameters, and use it to
perform efficient biased all-atom molecular dynamics simulations. The reaction
coordinate is learnt as a function of generic thermodynamic and structural
order parameters using the "Spectral Gap Optimization of Order Parameters
(SGOOP)" approach [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. (2016)],
and is biased using well-tempered metadynamics simulations. The reaction
coordinate gives insight into the role played by different structural and
thermodynamics order parameters, and the biased simulations obtain accurate
relative free energies for different polymorphs. This includes accurate
prediction of the approximate pressure at which urea undergoes a phase
transition and one of the metastable polymorphs becomes the most stable
conformation. We believe the ideas demonstrated in thus work will facilitate
efficient sampling of nucleation in complex, generic systems.
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There is one, and only one way, consistent with fundamental physics, that the
efficiency of general digital computation can continue increasing indefinitely,
and that is to apply the principles of reversible computing. We need to begin
intensive development work on this technology soon if we want to maintain
advances in computing and the attendant economic growth.
NOTE: This paper is an extended author's preprint of the feature article
titled "Throwing Computing Into Reverse" (print) or "The Future of Computing
Depends on Making it Reversible" (online), published by IEEE Spectrum in
Aug.-Sep. 2017. This preprint is based on the original draft manuscript that
the author submitted to Spectrum, prior to IEEE edits and feedback from
external readers.
|
We investigate the properties of photometrically-selected compact groups
(CGs) in the Sloan Digital Sky Survey. In this paper, the fourth in a series,
we focus on understanding the characteristics of our observed CG sample with
particular attention paid to quantifying and removing contamination from
projected foreground or background galaxies. Based on a simple comparison of
pairwise redshift likelihoods, we find that approximately half of compact
groups in the parent sample contain one or more projected (interloping)
members; our final clean sample contains 4566 galaxies in 1086 compact groups.
We show that half of the remaining CGs are associated with rich groups (or
clusters), i.e. they are embedded sub-structure. The other half have spatial
distributions and number-density profiles consistent with the interpretation
that they are either independently distributed structures within the field
(i.e. they are isolated) or associated with relatively poor structures.
Comparisons of late-type and red-sequence fractions in radial annuli show that
galaxies around apparently isolated compact groups resemble the field
population by 300 to 500 kpc from the group centre. In contrast, the galaxy
population surrounding embedded compact groups appears to remain distinct from
the field out beyond 1 to 2 Mpc, consistent with results for rich groups. We
take this as additional evidence that the observed distinction between compact
groups, i.e. isolated vs. embedded, is a separation between different host
environments.
|
The L2,3 X-ray emission of Cu metal has been measured using monochromatic
synchrotron radiation. The self-absorption effect in the spectra is shown to be
very small in our experimental geometry. From the quantitative analysis of
spectra recorded at different excitation energies, the L3/L2 emission intensity
ratio and the partial Auger-width are extracted. High-energy satellite features
on the L3 emission line are separated by a subtraction procedure. The satellite
intensity is found to be slowly increasing for excitation energies between the
L3, L2 and L1 core-level thresholds due to shake-up and shake-off transitions.
As the excitation energy passes the L2 threshold, a step of rapidly increasing
satellite intensity of the L3 emission is found due to additional Coster-Kronig
processes.
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In this paper, we prove that the Cauchy problem for a generalized
Camassa-Holm equation with higher-order nonlinearity is ill-posed in the
critical Besov space $B^1_{\infty,1}(\R)$. It is shown in (J. Differ. Equ.,
327:127-144,2022) that the Camassa-Holm equation is ill-posed in
$B^1_{\infty,1}(\R)$, here we turn our attention to a higher-order nonlinear
generalization of Camassa-Holm equation proposed by Hakkaev and Kirchev (Commun
Partial Differ Equ 30:761-781,2005). With newly constructed initial data, we
get the norm inflation in the critical space $B^1_{\infty,1}(\R)$ which leads
to ill-posedness.
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In November 2019, the nearby single, isolated DQ-type white dwarf LAWD 37 (WD
1142-645) aligned closely with a distant background source and caused an
astrometric microlensing event. Leveraging astrometry from \Gaia{} and followup
data from the \textit{Hubble Space Telescope} we measure the astrometric
deflection of the background source and obtain a gravitational mass for
LAWD~37. The main challenge of this analysis is in extracting the lensing
signal of the faint background source whilst it is buried in the wings of
LAWD~37's point spread function. Removal of LAWD 37's point spread function
induces a significant amount of correlated noise which we find can mimic the
astrometric lensing signal. We find a deflection model including correlated
noise caused by the removal of LAWD~37's point spread function best explains
the data and yields a mass for LAWD 37 of $0.56\pm0.08 M_{\odot}$. This mass is
in agreement with the theoretical mass-radius relationship and cooling tracks
expected for CO core white dwarfs. Furthermore, the mass is consistent with no
or trace amounts of hydrogen that is expected for objects with helium-rich
atmospheres like LAWD 37. We conclude that further astrometric followup data on
the source is likely to improve the inference on LAWD 37's mass at the
$\approx3$ percent level and definitively rule out purely correlated noise
explanations of the data. This work provides the first semi-empirical test of
the white dwarf mass-radius relationship using a single, isolated white dwarf
and supports current model atmospheres of DQ white dwarfs and white dwarf
evolutionary theory.
|
Production of resonances is considered in the framework of the
single-freeze-out model of ultra-relativistic heavy ion collisions. The
formalism involves the virial expansion, where the probability to form a
resonance in a two-body channel is proportional to the derivative of the
phase-shift with respect to the invariant mass. The thermal model incorporates
longitudinal and transverse flow, as well as kinematic cuts of the STAR
experiment at RHIC. We find that the shape of the pi+ pi- spectral line
qualitatively reproduces the preliminary experimental data when the position of
the rho peak is lowered. This confirms the need to include the medium effects
in the description of the RHIC data. We also analyze the transverse-momentum
spectra of rho, K*(892), and f_0(980), and find that the slopes agree with the
observed values. Predictions are made for eta, eta', omega, phi, Lambda(1520),
and Sigma(1385).
|
This paper presents an approach for estimating the operational range for
mobile robot exploration on a single battery discharge. Deploying robots in the
wild usually requires uninterrupted energy sources to maintain the robot's
mobility throughout the entire mission. However, for most endeavors into the
unknown environments, recharging is usually not an option, due to the lack of
pre-installed recharging stations or other mission constraints. In these cases,
the ability to model the on-board energy consumption and estimate the
operational range is crucial to prevent running out of battery in the wild. To
this end, this work describes our recent findings that quantitatively break
down the robot's on-board energy consumption and predict the operational range
to guarantee safe mission completion on a single battery discharge cycle. Two
range estimators with different levels of generality and model fidelity are
presented, whose performances were validated on physical robot platforms in
both indoor and outdoor environments. Model performance metrics are also
presented as benchmarks.
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In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm
to recover block sparse signals $\x$ from measurements $\y=\A\x+\v$, where $\v$
is an $\ell_2$-bounded noise vector (i.e., $\|\v\|_2\leq \epsilon$ for some
constant $\epsilon$). We investigate some sufficient conditions based on the
block restricted isometry property (block-RIP) for exact (when $\v=\0$) and
stable (when $\v\neq\0$) recovery of block sparse signals $\x$. First, on the
one hand, we show that if $\A$ satisfies the block-RIP with
$\delta_{K+1}<1/\sqrt{K+1}$, then every block $K$-sparse signal $\x$ can be
exactly or stably recovered by BOMP in $K$ iterations. On the other hand, we
show that, for any $K\geq 1$ and $1/\sqrt{K+1}\leq \delta<1$, there exists a
matrix $\A$ satisfying the block-RIP with $\delta_{K+1}=\delta$ and a block
$K$-sparse signal $\x$ such that BOMP may fail to recover $\x$ in $K$
iterations. Then, we study some sufficient conditions for recovering block
$\alpha$-strongly-decaying $K$-sparse signals. We show that if $\A$ satisfies
the block-RIP with $\delta_{K+1}<\sqrt{2}/2$, then every
$\alpha$-strongly-decaying block $K$-sparse signal can be exactly or stably
recovered by BOMP in $K$ iterations under some conditions on $\alpha$. Our
newly found sufficient condition on the block-RIP of $\A$ is less restrictive
than that for $\ell_1$ minimization for this special class of sparse signals.
Furthermore, for any $K\geq 1$, $\alpha>1$ and $\sqrt{2}/2\leq \delta<1$, the
recovery of $\x$ may fail in $K$ iterations for a sensing matrix $\A$ which
satisfies the block-RIP with $\delta_{K+1}=\delta$. Finally, we study some
sufficient conditions for partial recovery of block sparse signals.
Specifically, if $\A$ satisfies the block-RIP with $\delta_{K+1}<\sqrt{2}/2$,
then BOMP is guaranteed to recover some blocks of $\x$ if these blocks satisfy
a sufficient condition.
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Let $R$ be a hypersurface in an equicharacteristic or unramified regular
local ring. For a pair of modules $(M,N)$ over $R$ we study applications of
rigidity of $\Tor^R(M,N)$, based on ideas by Huneke, Wiegand and Jorgensen. We
then focus on the hypersurfaces with isolated singularity and even dimension,
and show that modules over such rings behave very much like those over regular
local rings. Connections and applications to projective hypersurfaces such as
intersection dimension of subvarieties and cohomological criterion for
splitting of vector bundles are discussed.
|
We show that the modern quantum mechanics, and particularly the theory of
decoherence, allows formulating a sort of a physical metatheory of
consciousness. Particularly, the analysis of the necessary conditions for the
occurrence of decoherence, along with the hypothesis that consciousness bears
(more-or-less) well definable physical origin, leads to a wider physical
picture naturally involving consciousness. This can be considered as a sort of
a psycho-physical parallelism, but on very wide scales bearing some
cosmological relevance.
|
We present a modular Python library for computing many-body hydrodynamic and
phoretic interactions between spherical active particles in suspension, when
these are given by solutions of the Stokes and Laplace equations. Underpinning
the library is a grid-free methodology that combines dimensionality reduction,
spectral expansion, and Ritz-Galerkin discretization, thereby reducing the
computation to the solution of a linear system. The system can be solved
analytically as a series expansion or numerically at a cost quadratic in the
number of particles. Suspension-scale quantities like fluid flow, entropy
production, and rheological response are obtained at a small additional cost.
The library is agnostic to boundary conditions and includes, amongst others,
confinement by plane walls or liquid-liquid interfaces. The use of the library
is demonstrated with six fully coded examples simulating active phenomena of
current experimental interest.
|
The distribution functions of the codon usage probabilities, computed over
all the available GenBank data, for 40 eukaryotic biological species and 5
chloroplasts, do not follow a Zipf law, but are best fitted by the sum of a
constant, an exponential and a linear function in the rank of usage. For
mitochondriae the analysis is not conclusive. A quantum-mechanics-inspired
model is proposed to describe the observed behaviour. These functions are
characterized by parameters that strongly depend on the total GC content of the
coding regions of biological species. It is predicted that the codon usage is
the same in all exonic genes with the same GC content. The Shannon entropy for
codons, also strongly depending on the exonic GC content, is computed.
|
We show that the yielding transition in granular media displays second-order
critical-point scaling behavior. We carry out discrete element simulations in
the low inertial number limit for frictionless, purely repulsive spherical
grains undergoing simple shear at fixed nondimensional shear stress $\Sigma$ in
two and three spatial dimensions. To find a mechanically stable (MS) packing
that can support the applied $\Sigma$, isotropically prepared states with size
$L$ must undergo a total strain $\gamma_{\rm ms}(\Sigma,L)$. The number density
of MS packings ($\propto \gamma_{\rm ms}^{-1}$) vanishes for $\Sigma > \Sigma_c
\approx 0.11$ according to a critical scaling form with a length scale $\xi
\propto |\Sigma - \Sigma_c|^{-\nu}$, where $\nu \approx 1.7-1.8$. Above the
yield stress ($\Sigma>\Sigma_c$), no MS packings that can support $\Sigma$
exist in the large system limit, $L/\xi \gg 1$. MS packings generated via shear
possess anisotropic force and contact networks, suggesting that $\Sigma_c$ is
associated with an upper limit in the degree to which these networks can be
deformed away from those for isotropic packings.
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We present a new approach to integrating deep learning with knowledge-based
systems that we believe shows promise. Our approach seeks to emulate reasoning
structure, which can be inspected part-way through, rather than simply learning
reasoner answers, which is typical in many of the black-box systems currently
in use. We demonstrate that this idea is feasible by training a long short-term
memory (LSTM) artificial neural network to learn EL+ reasoning patterns with
two different data sets. We also show that this trained system is resistant to
noise by corrupting a percentage of the test data and comparing the reasoner's
and LSTM's predictions on corrupt data with correct answers.
|
Among existing privacy-preserving approaches, Differential Privacy (DP) is a
powerful tool that can provide privacy-preserving noisy query answers over
statistical databases and has been widely adopted in many practical fields. In
particular, as a privacy machine of DP, Randomized Aggregable
Privacy-Preserving Ordinal Response (RAPPOR) enables strong privacy, efficient,
and high-utility guarantees for each client string in data crowdsourcing.
However, as for Internet of Things(IoT), such as smart gird, data are often
processed in batches. Therefore, developing a new random response algorithm
that can support batch-processing tend to make it more efficient and suitable
for IoT applications than existing random response algorithms. In this paper,
we propose a new randomized response algorithm that can achieve
differential-privacy and utility guar-antees for consumer's behaviors, and
process a batch of data at each time. Firstly, by applying sparse coding in
this algorithm, a behavior signature dictionary is created from the aggregated
energy consumption data in fog. Then, we add noise into the behavior signature
dictionary by classical randomized response techniques and achieve the
differential privacy after data re-aggregation. Through the security analysis
with the principle of differential privacy and experimental results
verification, we find that our Algorithm can preserve consumer's privacy
with-out comprising utility.
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We introduce two properties, macroscopic mixing and transitive mixing, to
represent the macroscopic stability of time evolution of Gibbs measures. We
claim that these are fundamental properties of macroscopic systems that exhibit
relaxation to an equilibrium state. As an illustration, we show that a simple
mechanical system on a lattice possesses these two properties.
|
The quantum speed limit time of open system models is explored using the
Wasserstein-1-distance and the Wigner function. Use is made of the phase
covariant and a two-qubit model interacting with a squeezed thermal bath via
position-dependent coupling. The dependence of the coupling on the position of
the qubits allowed the study of the dynamics in the collective regime, which is
conducive to speeding up the evolution. The use of the Wigner function
naturally allows the study of the quantumness of the systems studied. An
interesting interplay is observed between non-Markovian behavior, quantumness,
and the quantum speed limit time. The presence of quantum correlations is seen
to speed up the evolution.
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We give here a new proof of a Tauberian Theorem of complex Laplace transform
using the Theory of measure and theory of function with bounded variations.
However we deduce the simple proof of Prime Number Theorem.
|
Cometary dust provides a unique window on dust growth mechanisms during the
onset of planet formation. Measurements by the Rosetta spacecraft show that the
dust in the coma of comet 67P/Churyumov-Gerasimenko has a granular structure at
size scales from sub-um up to several hundreds of um, indicating hierarchical
growth took place across these size scales. However, these dust particles may
have been modified during their collection by the spacecraft instruments. Here
we present the results of laboratory experiments that simulate the impact of
dust on the collection surfaces of COSIMA and MIDAS, instruments onboard the
Rosetta spacecraft. We map the size and structure of the footprints left by the
dust particles as a function of their initial size (up to several hundred um)
and velocity (up to 6 m/s). We find that in most collisions, only part of the
dust particle is left on the target; velocity is the main driver of the
appearance of these deposits. A boundary between sticking/bouncing and
fragmentation as an outcome of the particle-target collision is found at v ~ 2
m/s. For velocities below this value, particles either stick and leave a single
deposit on the target plate, or bounce, leaving a shallow footprint of
monomers. At velocities > 2 m/s and sizes > 80 um, particles fragment upon
collision, transferring up to 50 per cent of their mass in a rubble-pile-like
deposit on the target plate. The amount of mass transferred increases with the
impact velocity. The morphologies of the deposits are qualitatively similar to
those found by the COSIMA instrument.
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We search for new charmless decays of neutral $b$--hadrons to pairs of
charged hadrons with the upgraded Collider Detector at the Fermilab Tevatron.
Using a data sample corresponding to 1 fb$^{-1}$ of integrated luminosity, we
report the first observation of the \BsKpi decay, with a significance of
$8.2\sigma$, and measure $\BR(\BsKpi) = (5.0 \pm 0.7\stat \pm 0.8\syst)\times
10^{-6}$. We also report the first observation of charmless $b$--baryon decays
in the channels \Lbppi and \LbpK with significances of $6.0\sigma$ and
$11.5\sigma$ respectively, and we measure $\BR(\Lbppi) = (3.5 \pm 0.6\stat \pm
0.9\syst)\times 10^{-6}$ and $\BR(\LbpK) = (5.6 \pm 0.8\stat \pm
1.5\syst)\times 10^{-6}$. No evidence is found for the decays \BdKK and
\Bspipi, and we set an improved upper limit $\BR(\Bspipi) < 1.2\times 10^{-6}$
at the 90% confidence level. All quoted branching fractions are measured using
$\BR(\BdKpi)$ as a reference.
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In this paper we will define and investigate the imaginary powers
$\left(-\triangle_{k,1}\right)^{-i\sigma},\sigma\in\mathbb{R}$ of the
$(k,1)$-generalized harmonic oscillator
$-\triangle_{k,1}=-\left\|x\right\|\triangle_k+\left\|x\right\|$ and prove the
$L^p$-boundedness $(1<p<\infty)$ and weak $L^1$-boundedness of such operators.
It is a parallel result to the $L^p$-boundedness $(1<p<\infty)$ and weak
$L^1$-boundedness of the imaginary powers of the Dunkl harmonic oscillator
$-\triangle_k+\left\|x\right\|^2$. To prove this result, we develop the
Calder\'on--Zygmund theory adapted to the $(k,1)$-generalized setting by
constructing the metric space of homogeneous type corresponding to the
$(k,1)$-generalized setting, and show that
$\left(-\triangle_{k,1}\right)^{-i\sigma}$ are singular integral operators
satisfying the corresponding H\"ormander type condition.
|
Traffic scene recognition is an important and challenging issue in
Intelligent Transportation Systems (ITS). Recently, Convolutional Neural
Network (CNN) models have achieved great success in many applications,
including scene classification. The remarkable representational learning
capability of CNN remains to be further explored for solving real-world
problems. Vector of Locally Aggregated Descriptors (VLAD) encoding has also
proved to be a powerful method in catching global contextual information. In
this paper, we attempted to solve the traffic scene recognition problem by
combining the features representational capabilities of CNN with the VLAD
encoding scheme. More specifically, the CNN features of image patches generated
by a region proposal algorithm are encoded by applying VLAD, which subsequently
represent an image in a compact representation. To catch the spatial
information, spatial pyramids are exploited to encode CNN features. We
experimented with a dataset of 10 categories of traffic scenes, with
satisfactory categorization performances.
|
The Hydrogen Epoch of Reionization Array (HERA) is a radio interferometer
aiming to detect the power spectrum of 21 cm fluctuations from neutral hydrogen
from the Epoch of Reionization (EOR). Drawing on lessons from the Murchison
Widefield Array (MWA) and the Precision Array for Probing the Epoch of
Reionization (PAPER), HERA is a hexagonal array of large (14 m diameter) dishes
with suspended dipole feeds. Not only does the dish determine overall
sensitivity, it affects the observed frequency structure of foregrounds in the
interferometer. This is the first of a series of four papers characterizing the
frequency and angular response of the dish with simulations and measurements.
We focus in this paper on the angular response (i.e., power pattern), which
sets the relative weighting between sky regions of high and low delay, and
thus, apparent source frequency structure. We measure the angular response at
137 MHz using the ORBCOMM beam mapping system of Neben et al. We measure a
collecting area of 93 m^2 in the optimal dish/feed configuration, implying
HERA-320 should detect the EOR power spectrum at z~9 with a signal-to-noise
ratio of 12.7 using a foreground avoidance approach with a single season of
observations, and 74.3 using a foreground subtraction approach. Lastly we study
the impact of these beam measurements on the distribution of foregrounds in
Fourier space.
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An exotic crossed product is a way of associating a C*-algebra to each
C*-dynamical system that generalizes the well-known universal and reduced
crossed products. Exotic crossed products provide natural generalizations of,
and tools to study, exotic group C*-algebras as recently considered by
Brown-Guentner and others. They also form an essential part of a recent program
to reformulate the Baum-Connes conjecture with coefficients so as to mollify
the counterexamples caused by failures of exactness.
In this paper, we survey some constructions of exotic group algebras and
exotic crossed products. Summarising our earlier work, we single out a large
class of crossed products --- the correspondence functors --- that have many
properties known for the maximal and reduced crossed products: for example,
they extend to categories of equivariant correspondences, and have a compatible
descent morphism in KK-theory. Combined with known results on K-amenability and
the Baum-Connes conjecture, this allows us to compute the K-theory of many
exotic group algebras. It also gives new information about the reformulation of
the Baum-Connes Conjecture mentioned above. Finally, we present some new
results relating exotic crossed products for a group and its closed subgroups,
and discuss connections with the reformulated Baum-Connes conjecture.
|
The bilateralist approach to logical consequence maintains that judgments of
different qualities should be taken into account in determining
what-follows-from-what. We argue that such an approach may be actualized by a
two-dimensional notion of entailment induced by semantic structures that also
accommodate non-deterministic and partial interpretations, and propose a
proof-theoretical apparatus to reason over bilateralist judgments using
symmetrical two-dimensional analytical Hilbert-style calculi. We also provide a
proof-search algorithm for finite analytic calculi that runs in at most
exponential time, in general, and in polynomial time when only rules having at
most one formula in the succedent are present in the concerned calculus.
|
Ab initio molecular dynamic method within the framework of density functional
theory is applied to analyze the structural and electronic properties of
crystalline molecular hydrogen at temperature 100\,K. Pressure, pair
correlation function and band structure are calculated. The crossover of
molecular crystalline hydrogen from the state of a semiconductor to a
semimetallic and metallic state is observed upon compression in the pressure
range of 302-626\,GPa. At pressures below 361\,GPa, the molecular crystal with
the C2/c structure is a semiconductor with an indirect gap. In the pressure
range 361 - 527\,GPa, band structure of the monoclinic C2/c lattice has a
characteristic semimetalic profile with partially unoccupied valence band and
partially occupied conduction band. When compressed to pressures above
544\,GPa, the structure changes from monoclinic C2/c to orthorhombic Cmca,
accompanied by a sharp decrease (by more than two orders of magnitude) in the
value of the direct gap, which is an indication of the metallic conductivity of
the resulting structure. The metallic state is metastable and exists up to a
pressure of 626\,GPa.
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This paper deals with a hyperbolic Keller-Segel system of consumption type
with the logarithmic sensitivity \begin{equation*}
\partial_{t} \rho = - \chi\nabla \cdot \left (\rho \nabla \log c\right),\quad
\partial_{t} c = - \mu c\rho\quad (\chi,\,\mu>0) \end{equation*} in
$\mathbb{R}^d\; (d \ge1)$ for nonvanishing initial data. This system is closely
related to tumor angiogenesis, an important example of chemotaxis. We firstly
show the local existence of smooth solutions corresponding to nonvanishing
smooth initial data. Next, through Riemann invariants, we present some
sufficient conditions of this initial data for finite-time singularity
formation when $d=1$. We then prove that for any $d\ge1$, some nonvanishing
$C^\infty$-data can become singular in finite time. Moreover, we derive
detailed information about the behaviors of solutions when the singularity
occurs. In particular, this information tells that singularity formation from
some initial data is not because $c$ touches zero (which makes $\log c$
diverge) but due to the blowup of $C^1\times C^2$-norm of $(\rho,c)$. As a
corollary, we also construct initial data near any constant equilibrium state
which blows up in finite time for any $d\ge1$. Our results are the extension of
finite-time blow-up results in \cite{IJ21}, where initial data is required to
satisfy some vanishing conditions. Furthermore, we interpret our results in a
way that some kinds of damping or dissipation of $\rho$ are necessarily
required to ensure the global existence of smooth solutions even though initial
data are small perturbations around constant equilibrium states.
|
We investigate several classes of state-dependent quantum cloners for
three-level systems. These cloners optimally duplicate some of the four
maximally-conjugate bases with an equal fidelity, thereby extending the
phase-covariant qubit cloner to qutrits. Three distinct classes of qutrit
cloners can be distinguished, depending on two, three, or four
maximally-conjugate bases are cloned as well (the latter case simply
corresponds to the universal qutrit cloner). These results apply to symmetric
as well as asymmetric cloners, so that the balance between the fidelity of the
two clones can also be analyzed.
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With the compelling evidence for massive neutrinos from recent
neutrino-oscillation experiments, one of the most fundamental tasks of particle
physics over the next years will be the determination of the absolute mass
scale of neutrinos. The absolute value of neutrino-masses will have crucial
implications for cosmology, astrophysics and particle physics. We present the
case for a next generation tritium beta decay experiment to perform a high
precision direct measurement of the absolute mass of the electron neutrino with
sub-eV sensitivity. We discuss the experimental requirements and technical
challenges of the proposed Karlsruhe Tritium Neutrino experiment (KATRIN) and
outline its physics potential.
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Magnetic fluctuations induced by geometric frustration of local Ir-spins
disturb the formation of long range magnetic order in the family of pyrochlore
iridates, R$_{2}$Ir$_{2}$O$_{7}$ (R = lanthanide)$^{1}$. As a consequence,
Pr$_{2}$Ir$_{2}$O$_{7}$ lies at a tuning-free antiferromagnetic-to-paramagnetic
quantum critical point and exhibits a diverse array of complex phenomena
including Kondo effect, biquadratic band structure, metallic spin-liquid (MSL),
and anomalous Hall effect$^{2-5}$. Using spectroscopic imaging with the
scanning tunneling microscope, complemented with machine learning K-means
clustering analysis, density functional theory, and theoretical modeling, we
probe the local electronic states in single crystal of Pr$_{2}$Ir$_{2}$O$_{7}$
and discover an electronic phase separation. Nanoscale regions with a
well-defined Kondo resonance are interweaved with a non-magnetic metallic phase
with Kondo-destruction. Remarkably, the spatial nanoscale patterns display a
correlation-driven fractal geometry with power-law behavior extended over two
and a half decades, consistent with being in proximity to a critical point. Our
discovery reveals a new nanoscale tuning route, viz. using a spatial variation
of the electronic potential as a means of adjusting the balance between Kondo
entanglement and geometric frustration.
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We give a method for computing asymptotic formulas and approximations for the
volumes of spectrahedra, based on the maximum-entropy principle from
statistical physics. The method gives an approximate volume formula based on a
single convex optimization problem of minimizing $-\log \det P$ over the
spectrahedron. Spectrahedra can be described as affine slices of the convex
cone of positive semi-definite (PSD) matrices, and the method yields efficient
deterministic approximation algorithms and asymptotic formulas whenever the
number of affine constraints is sufficiently dominated by the dimension of the
PSD cone.
Our approach is inspired by the work of Barvinok and Hartigan who used an
analogous framework for approximately computing volumes of polytopes.
Spectrahedra, however, possess a remarkable feature not shared by polytopes, a
new fact that we also prove: central sections of the set of density matrices
(the quantum version of the simplex) all have asymptotically the same volume.
This allows for very general approximation algorithms, which apply to large
classes of naturally occurring spectrahedra.
We give two main applications of this method. First, we apply this method to
what we call the "multi-way Birkhoff spectrahedron" and obtain an explicit
asymptotic formula for its volume. This spectrahedron is the set of quantum
states with maximal entanglement (i.e., the quantum states having univariant
quantum marginals equal to the identity matrix) and is the quantum analog of
the multi-way Birkhoff polytope. Second, we apply this method to explicitly
compute the asymptotic volume of central sections of the set of density
matrices.
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We have calculated the magnetic properties of substituted 3d-impurities
(Cr-Ni) in a GaAs host by means of first principles electronic structure
calculations. We provide a novel model explaining the ferromagnetic long rang
order of III-V dilute magnetic semiconductors. The origin of the ferromagnetism
is shown to be due to delocalized spin-uncompensated As dangling bond
electrons. Besides the quantitative prediction of the magnetic moments, our
model provides an understanding of the halfmetallicity, and the raise of the
critical temperature with the impurity concentration.
|
Instrumenting and collecting annotated visual grasping datasets to train
modern machine learning algorithms can be extremely time-consuming and
expensive. An appealing alternative is to use off-the-shelf simulators to
render synthetic data for which ground-truth annotations are generated
automatically. Unfortunately, models trained purely on simulated data often
fail to generalize to the real world. We study how randomized simulated
environments and domain adaptation methods can be extended to train a grasping
system to grasp novel objects from raw monocular RGB images. We extensively
evaluate our approaches with a total of more than 25,000 physical test grasps,
studying a range of simulation conditions and domain adaptation methods,
including a novel extension of pixel-level domain adaptation that we term the
GraspGAN. We show that, by using synthetic data and domain adaptation, we are
able to reduce the number of real-world samples needed to achieve a given level
of performance by up to 50 times, using only randomly generated simulated
objects. We also show that by using only unlabeled real-world data and our
GraspGAN methodology, we obtain real-world grasping performance without any
real-world labels that is similar to that achieved with 939,777 labeled
real-world samples.
|
We consider the minimal supersymmetric grand unified model (MSGUT) based on
the group $\mathrm{SO}(10)$, and study conditions leading to possible domain
wall (DW) formation. It has been shown earlier that the supersymmetry
preserving vacuum expectation values (vev's) get mapped to distinct but
degenerate set of vev's under action of $D$ parity, leading to formation of
domain walls as topological pseudo-defects. The metastability of such walls can
make them relatively long lived and contradict standard cosmology. Thus we are
led to consider adding a nonrenormalisable Planck scale suppressed operator,
that breaks $\mathrm{SO}(10)$ symmetry but preserves Standard Model symmetry.
For a large range of right handed breaking scales $M_R$, this is shown to give
rise to the required pressure difference to remove the domain walls without
conflicting with consistent big bang nucleosynthesis (BBN) while avoiding
gravitino overproduction. However, if the walls persist till the onset of weak
(thermal) inflation, then a low $\sim 10 - 100$ TeV $M_R$ becomes problematic.
|
We prove that if d is an integer number bigger than 1 and f_1,...,f_d are
commuting circle diffeomorphisms respectively of class C^(1+\tau_k), where
\tau_1 + ... + \tau_k > 1, then these maps are simultaneously conjugate to
rotations provided that their rotation numbers are independent over the
rationals.
|
This theoretical review is intended to give non-theorists a flavor of the
ideas driving the current efforts to experimentally find supersymmetry. We
discuss the main reasons behind the expectation that supersymmetry may be "just
around the corner" and may be discovered in the near future. We use simple
quantum-mechanical examples to illustrate the concept---and the power---of
supersymmetry, the possible ways to break supersymmetry, and the dynamical
generation of small scales. We then describe how this theoretical machinery
helps shape our perception of what physics beyond the electroweak scale might
be.
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We study the following Schr\"odinger-Poisson system (P_\lambda)\{ll}
-\Delta u + (1+\mu g(x))u+\lambda \phi (x) u =|u|^{p-1}u, x\in \mathbb{R}^3,
|
Microwave conductivity experiments can directly measure the quasiparticle
scattering rate in the superconducting state. We show that this, combined with
knowledge of the Fermi surface geometry, allows one to distinguish between
closely related superconducting order parameters, e.g., d$_{x^2-y^2}$ and
d$_{xy}$ superconductivity. We benchmark this method on
YBa$_2$Cu$_3$O$_{7-\delta}$ and, unsurprisingly, confirm that this is a
d$_{x^2-y^2}$ superconductor. We then apply our method to
$\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, which we discover is a d$_{xy}$
superconductor.
|
We observe experimentally the harmonic oscillations of a macroscopic
many-body wavefunction of the bosonic condensate of exciton-polaritons confined
in an elliptical trap. The oscillations are caused by quantum beats between two
size-quantized states of the polariton condensate split in energy due to the
ellipticity of the trap. The eigen-functions of these states are $p$-shape
orbitals tilted with respect to the main and the short axes of the trap. The
beats between these states manifest themselves in a macroscopic periodical
redistribution of the polariton density in real space. The control of
frequency, amplitude and phase of the beats is achieved by sending non-resonant
laser pulses to specific spots inside the trap. We visualize the condensate
wave-function dynamics on a streak-camera and map them to the Bloch sphere
demonstrating the implementation of Hadamard and Pauli-Z operations. The decay
time of the observed oscillations is on a nanosecond scale. It exceeds the
individual exciton-polariton life-time by two orders of magnitude and the
coherence-time of the condensate by one order of magnitude.
|
We exhibit a canonical connection between maximal (0,1)-fillings of a moon
polyomino avoiding north-east chains of a given length and reduced pipe dreams
of a certain permutation. Following this approach we show that the simplicial
complex of such maximal fillings is a vertex-decomposable, and thus shellable,
sphere. In particular, this implies a positivity result for Schubert
polynomials. For Ferrers shapes, we moreover construct a bijection to maximal
fillings avoiding south-east chains of the same length which specializes to a
bijection between k-triangulations of the n-gon and k-fans of Dyck paths of
length 2(n-2k). Using this, we translate a conjectured cyclic sieving
phenomenon for k-triangulations with rotation to the language of k-flagged
tableaux with promotion.
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We follow the mathematical framework proposed by Bouchut and present in this
contribution a dual entropy approach for determining equilibrium states of a
lattice Boltzmann scheme. This method is expressed in terms of the dual of the
mathematical entropy relative to the underlying conservation law. It appears as
a good mathematical framework for establishing a "H-theorem" for the system of
equations with discrete velocities. The dual entropy approach is used with D1Q3
lattice Boltzmann schemes for the Burgers equation. It conducts to the
explicitation of three different equilibrium distributions of particles and
induces naturally a nonlinear stability condition. Satisfactory numerical
results for strong nonlinear shocks and rarefactions are presented. We prove
also that the dual entropy approach can be applied with a D1Q3 lattice
Boltzmann scheme for systems of linear and nonlinear acoustics and we present a
numerical result with strong nonlinear waves for nonlinear acoustics. We
establish also a negative result: with the present framework, the dual entropy
approach cannot be used for the shallow water equations.
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We present evidence that relativistic shocks propagating in unmagnetized
plasmas can self-consistently accelerate particles. We use long-term
two-dimensional particle-in-cell simulations to study the well-developed shock
structure in unmagnetized pair plasma. The particle spectrum downstream of such
a shock consists of two components: a relativistic Maxwellian, with
characteristic temperature set by the upstream kinetic energy of the flow, and
a high-energy tail, extending to energies >100 times that of the thermal peak.
This tail is best fitted as a power law in energy with index -2.4+-0.1,
modified by an exponential cutoff. The cutoff moves to higher energies with
time of the simulation, leaving a larger power law range. The number of
particles in the tail is ~1% of the downstream population, and they carry ~10%
of the kinetic energy in the downstream. Upon investigation of the trajectories
of particles in the tail, we find that the energy gains occur as particles
bounce between the upstream and downstream regions in the magnetic fields
generated by the Weibel instability. We compare this mechanism to the first
order Fermi acceleration, and set a lower limit on the efficiency of shock
acceleration process.
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We develop safe protocols for thermostatically controlled loads (TCLs) to
provide power pulses to the grid without a subsequent oscillatory response.
Such pulses can alleviate power fluctuations by intermittent resources and
maintain balance between generation and demand. Building on prior work, we
introduce timers to endpoint TCL control enabling better shaping of power
pulses.
|
Neumann boundary condition plays an important role in the initial proposal of
holographic dual of boundary conformal field theory, which has yield many
interesting results and passed several non-trivial tests. In this paper, we
show that Dirichlet boundary condition works as well as Neumann boundary
condition. For instance, it includes AdS solution and obeys the g-theorem.
Furthermore, it can produce the correct expression of one point function, the
boundary Weyl anomaly and the universal relations between them. We also study
the relative boundary condition for gauge fields, which is the counterpart of
Dirichlet boundary condition for gravitational fields. Interestingly, the
four-dimensional Reissner-Nordstrom black hole with magnetic charge is an exact
solution to relative boundary condition under some conditions. This holographic
model predicts that a constant magnetic field in the bulk can induce a constant
current on the boundary in three dimensions. We suggest to measure this
interesting boundary current in materials such as the graphene.
|
We present the first results from a 40 ks Guaranteed Time XMM-Newton pointing
in the Pleiades. We detect almost all early-mid dM members in the field and
several very low mass (VLM) stars - including the brown dwarf (BD) candidate
Roque 9 - and investigate the variation of X-ray activity levels, hardness
ratios and flare frequency with spectral type down to the BD regime.
|
In this paper we present a parameter estimation analysis of the polarization
and temperature power spectra from the second and third season of observations
with the QUaD experiment. QUaD has for the first time detected multiple
acoustic peaks in the E-mode polarization spectrum with high significance.
Although QUaD-only parameter constraints are not competitive with previous
results for the standard 6-parameter LCDM cosmology, they do allow meaningful
polarization-only parameter analyses for the first time. In a standard
6-parameter LCDM analysis we find the QUaD TT power spectrum to be in good
agreement with previous results. However, the QUaD polarization data shows some
tension with LCDM. The origin of this 1 to 2 sigma tension remains unclear, and
may point to new physics, residual systematics or simple random chance. We also
combine QUaD with the five-year WMAP data set and the SDSS Luminous Red
Galaxies 4th data release power spectrum, and extend our analysis to constrain
individual isocurvature mode fractions, constraining cold dark matter density,
alpha(cdmi)<0.11 (95 % CL), neutrino density, alpha(ndi)<0.26 (95 % CL), and
neutrino velocity, alpha(nvi)<0.23 (95 % CL), modes. Our analysis sets a
benchmark for future polarization experiments.
|
We study the properties of 2D fibre clusters and networks formed by
deposition processes. We first examine the growth and scaling properties of
single clusters. We then consider a network of such clusters, whose spatial
distribution obeys some effective pair distribution function. In particular, we
derive an expression for the two-point density autocorrelation function of the
network, which includes the internal structure of a cluster and the effective
cluster-cluster pair distribution function. This formula can be applied to
obtain information about nontrivial correlations in fibre networks.
|
We investigate the permutation modules associated to the set of
$k$-dimensional faces of the hyperoctahedron in dimension $n$, denoted $H^{n}.$
For any $k\leq n$ such a module can be defined over an arbitrary field $F$, it
is called a face module of $H^{n}$ over $F.$ We describe a spectral
decomposition of such face modules into submodules and show that these
submodules are irreducible under the hyperoctahedral group $B_{n}.$ The same
method can be used to describe the exact relationship between the face modules
in any two dimensions $0\leq t\leq k\leq n.$ Applications of this technique
include a rank formula for the rank of the incidence matrix of $t$-dimensional
versus $k$-dimensional faces of $H^{n}$ and a characterization of
$(t,k,\ell)$-designs on $H^{n}.$ We also prove an orbit theorem for subgroups
of the hyperoctahedral group on the set of faces of $H^{n}.$ The decomposition
method is elementary, mostly characteristic free and does not involve the
representation theory of automorphism groups. It is therefore quite general and
can be used to decompose permutation modules associated to other geometries.
|
We have obtained Spitzer Space Telescope Multiband Imaging Photometer for
Spitzer (MIPS) 24 {\mu}m and 70 {\mu}m observations of 215 nearby, Hipparcos B-
and A-type common proper motion single and binary systems in the nearest OB
association, Scorpius-Centaurus. Combining our MIPS observations with those of
other ScoCen stars in the literature, we estimate 24 {\mu}m B+A-type disk
fractions of 17/67 (25+6%), 36/131 (27+4%), and 23/95 (24+5%) for Upper
Scorpius (\sim11 Myr), Upper Centaurus Lupus (\sim15 Myr), and Lower Centaurus
Crux (\sim17 Myr), respectively, somewhat smaller disk fractions than
previously obtained for F- and G-type members. We confirm previous IRAS excess
detections and present new discoveries of 51 protoplanetary and debris disk
systems, with fractional infrared luminosities ranging from LIR/L\ast = 1e-6 to
1e-2 and grain temperatures ranging from Tgr = 40 - 300 K. In addition, we
confirm that the 24 {\mu}m and 70 {\mu}m excesses (or fractional infrared
luminosities) around B+A type stars are smaller than those measured toward F+G
type stars and hypothesize that the observed disk property dependence on
stellar mass may be the result of a higher stellar companion fraction around B-
and A-type stars at 10 - 200 AU and/or the presence of Jupiter-mass companions
in the disks around F- and G- type stars. Finally, we note that the majority of
the ScoCen 24 {\mu}m excess sources also possess 12 {\mu}m excess, indicating
that Earth-like planets may be forming via collisions in the terrestrial planet
zone at \sim10 - 100 Myr.
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The International Workshop on Locational Analysis and Related Problems will
take place during January 31-February 1, 2022 in Elche (Spain). It is organized
by the Spanish Location Network and the Location Group GELOCA from the Spanish
Society of Statistics and Operations Research (SEIO). The Spanish Location
Network is a group of more than 140 researchers from several Spanish
universities organized into 7 thematic groups. The Network has been funded by
the Spanish Government since 2003. This edition of the conference is organized
in collaboration with project PROMETEO/2021/063 funded by the Valencian
government.
One of the main activities of the Network is a yearly meeting aimed at
promoting the communication among its members and between them and other
researchers, and to contribute to the development of the location field and
related problems. The last meetings have taken place in Sevilla (January 23-24,
2020), C\'adiz (January 20-February 1, 2019), Segovia (September 27-29, 2017),
M\'alaga (September 14-16, 2016), Barcelona (November 25-28, 2015), Sevilla
(October 1-3, 2014), Torremolinos (M\'alaga, June 19-21, 2013), Granada (May
10-12, 2012), Las Palmas de Gran Canaria (February 2-5, 2011) and Sevilla
(February 1-3, 2010).
The topics of interest are location analysis and related problems. This
includes location models, networks, transportation, logistics, exact and
heuristic solution methods, and computational geometry, among others.
|
Minimal Flavor Violation offers an alternative symmetry rationale to R-parity
conservation for the suppression of proton decay in supersymmetric extensions
of the Standard Model. The naturalness of such theories is generically under
less tension from LHC searches than R-parity conserving models. The flavor
symmetry can also guarantee the stability of dark matter if it carries flavor
quantum numbers. We outline general features of supersymmetric flavored dark
matter (SFDM) models within the framework of MFV SUSY. A simple model of top
flavored dark matter is presented. If the dark matter is a thermal relic, then
nearly the entire parameter space of the model is testable by upcoming direct
detection and LHC searches.
|
Every regular map on a closed surface gives rise to generally six regular
maps, its "Petrie relatives", that are obtained through iteration of the
duality and Petrie operations (taking duals and Petrie-duals). It is shown that
the skeletal polyhedra in Euclidean 3-space which realize a Petrie relative of
the classical Gordan regular map and have full icosahedral symmetry, comprise
precisely four infinite families of polyhedra, as well as four individual
polyhedra.
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In this contribution, we review a general argument showing that de Sitter
critical points of extended supergravity are in tension with the magnetic weak
gravity conjecture if the gravitino mass is vanishing. Motivated by this
assumption, we review then the gravitino conjecture, which states that the
limit of vanishing gravitino mass is pathological for the effective field
theory description. Finally, we discuss more in general the fate of de Sitter
critical points (with massless gravitini) in supergravity and comment on
extensions of these works along various directions. Part of the material here
presented is unpublished.
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Solar-like oscillations are stochastically excited by turbulent convection at
the surface layers of the stars. We study the role of the surface metal
abundance on the efficiency of the stochastic driving in the case of the CoRoT
target HD 49933. We compute two 3D hydrodynamical simulations representative --
in effective temperature and gravity -- of the surface layers of the CoRoT
target HD 49933, a star that is rather metal poor and significantly hotter
compared to the Sun. One 3D simulation has a solar metal abundance and the
other has a surface iron-to-hydrogen, [Fe/H], abundance ten times smaller. For
each 3D simulation we match an associated global 1D model and we compute the
associated acoustic modes using a theoretical model of stochastic excitation
validated in the case of the Sun and Alpha Cen A. The rate at which energy is
supplied per unit time into the acoustic modes associated with the 3D
simulation with [Fe/H]=-1 are found about three times smaller than those
associated with the 3D simulation with [Fe/H]=0. As shown here, these
differences are related to the fact that low metallicity implies surface layers
with a higher mean density. In turn, a higher mean density favors smaller
convective velocities and hence less efficient driving of the acoustic modes.
Our result shows the importance of taking the surface metal abundance into
account in the modeling of the mode driving by turbulent convection. A
comparison with observational data is presented in a companion paper using
seismic data obtained for the CoRoT target HD 49933.
|
We consider Hilbert modular varieties in characteristic p with Iwahori level
at p and construct a geometric Jacquet-Langlands relation showing that the
irreducible components are isomorphic to products of projective bundles over
quaternionic Shimura varieties of level prime to p. We use this to establish a
relation between mod p Hilbert and quaternionic modular forms that reflects the
representation theory of GL_2 in characteristic p and generalizes a result of
Serre for classical modular forms. Finally we study the fibres of the
degeneracy map to level prime to p and prove a cohomological vanishing result
that is used to associate Galois representations to mod p Hilbert modular
forms.
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We consider a two-planet system, which migrates under the influence of
dissipative forces that mimic the effects of gas-driven (Type II) migration. It
has been shown that, in the planar case, migration leads to resonant capture
after an evolution that forces the system to follow families of periodic
orbits. Starting with planets that differ slightly from a coplanar
configuration, capture can, also, occur and, additionally, excitation of
planetary inclinations has been observed in some cases. We show that excitation
of inclinations occurs, when the planar families of periodic orbits, which are
followed during the initial stages of planetary migration, become vertically
unstable. At these points, {\em vertical critical orbits} may give rise to
generating stable families of $3D$ periodic orbits, which drive the evolution
of the migrating planets to non-coplanar motion. We have computed and present
here the vertical critical orbits of the $2/1$ and $3/1$ resonances, for
various values of the planetary mass ratio. Moreover, we determine the limiting
values of eccentricity for which the "inclination resonance" occurs.
|
We consider a configuration of strings and solitons in the type IIB
superstring theory on $M^5\times T^5$, which is composed of a set of
arbitrarily-wound D-fivebranes on $T^5$ and a set of arbitrarily-wound
D-strings on $S^1$ of the torus. For the configuration, it is shown that number
of microscopic states is bounded from above by the exponential of the
Hawking-Bekenstein entropy of the corresponding black hole and the temperature
of closed string radiation from the D-branes is bounded from below by the
Hawking temperature of the black hole. After discussing the necessary and
sufficient condition to saturate these bounds, we give some speculations about
black hole thermodynamics.
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We present here a systematic search for cyanopolyynes in the shock region
L1157-B1 and its associated protostar L1157-mm in the framework of the Large
Program "Astrochemical Surveys At IRAM" (ASAI), dedicated to chemical surveys
of solar-type star forming regions with the IRAM 30m telescope. Observations of
the millimeter windows between 72 and 272 GHz permitted the detection of
HC$_3$N and its $^{13}$C isotopologues, and HC$_5$N (for the first time in a
protostellar shock region). In the shock, analysis of the line profiles shows
that the emission arises from the outflow cavities associated with L1157-B1 and
L1157-B2. Molecular abundances and excitation conditions were obtained from
analysis of the Spectral Line Energy Distributions under the assumption of
Local Thermodynamical Equilibrium or using a radiative transfer code in the
Large Velocity Gradient approximation. Towards L1157mm, the HC$_3$N emission
arises from the cold envelope ($T_{rot}=10$ K) and a higher-excitation region
($T_{rot}$= $31$ K) of smaller extent around the protostar. We did not find any
evidence of $^{13}$C or D fractionation enrichment towards L1157-B1. We obtain
a relative abundance ratio HC$_3$N/HC$_5$N of 3.3 in the shocked gas. We find
an increase by a factor of 30 of the HC$_3$N abundance between the envelope of
L1157-mm and the shock region itself. Altogether, these results are consistent
with a scenario in which the bulk of HC$_3$N was produced by means of gas phase
reactions in the passage of the shock. This scenario is supported by the
predictions of a parametric shock code coupled with the chemical model
UCL_CHEM.
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AC-OPF (Alternative Current Optimal Power Flow)aims at minimizing the
operating costs of a power gridunder physical constraints on voltages and power
injections.Its mathematical formulation results in a nonconvex polynomial
optimizationproblem which is hard to solve in general,but that can be tackled
by a sequence of SDP(Semidefinite Programming) relaxationscorresponding to the
steps of the moment-SOS (Sums-Of-Squares) hierarchy.Unfortunately, the size of
these SDPs grows drastically in the hierarchy,so that even second-order
relaxationsexploiting the correlative sparsity pattern of AC-OPFare hardly
numerically tractable for largeinstances -- with thousands of power buses.Our
contribution lies in a new sparsityframework, termed minimal sparsity,
inspiredfrom the specific structure of power flowequations.Despite its
heuristic nature, numerical examples show that minimal sparsity allows the
computation ofhighly accurate second-order moment-SOS relaxationsof AC-OPF,
while requiring far less computing time and memory resources than the standard
correlative sparsity pattern. Thus, we manage to compute second-order
relaxations on test caseswith about 6000 power buses, which we believe to be
unprecedented.
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Training neural networks with first order optimisation methods is at the core
of the empirical success of deep learning. The scale of initialisation is a
crucial factor, as small initialisations are generally associated to a feature
learning regime, for which gradient descent is implicitly biased towards simple
solutions. This work provides a general and quantitative description of the
early alignment phase, originally introduced by Maennel et al. (2018) . For
small initialisation and one hidden ReLU layer networks, the early stage of the
training dynamics leads to an alignment of the neurons towards key directions.
This alignment induces a sparse representation of the network, which is
directly related to the implicit bias of gradient flow at convergence. This
sparsity inducing alignment however comes at the expense of difficulties in
minimising the training objective: we also provide a simple data example for
which overparameterised networks fail to converge towards global minima and
only converge to a spurious stationary point instead.
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The acquisition of late-time imaging is an important step in the analysis of
pre-explosion observations of the progenitors of supernovae. We present
late-time HST ACS WFC observations of the sites of five Type IIP SNe: 1999ev,
2003gd, 2004A, 2005cs and 2006my. Observations were conducted using the F435W,
F555W and F814W filters. We confirm the progenitor identifications for SNe
2003gd, 2004A and 2005cs, through their disappearance. We find that a source
previously excluded as being the progenitor of SN 2006my has now disappeared.
The late-time observations of the site of SN 1999ev cast significant doubt over
the nature of the source previously identified as the progenitor in
pre-explosion WFPC2 images. The use of image subtraction techniques yields
improved precision over photometry conducted on just the pre-explosion images
alone. In particular, we note the increased depth of detection limits derived
on pre-explosion frames in conjunction with late-time images. We use SED
fitting techniques to explore the effect of different reddening components
towards the progenitors. For SNe 2003gd and 2005cs, the pre-explosion
observations are sufficiently constraining that only limited amounts of dust
(either interstellar or circumstellar) are permitted. Assuming only a Galactic
reddening law, we determine the initial masses for the progenitors of SNe
2003gd, 2004A, 2005cs and 2006my of 8.4+/-2.0, 12.0+/-2.1, 9.5(+3.4,-2.2) and
9.8+/-1.7Msun, respectively.
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We propose a robust model predictive control (MPC) method for discrete-time
linear systems with polytopic model uncertainty and additive disturbances.
Optimizing over linear time-varying (LTV) state feedback controllers has been
successfully used for robust MPC when only additive disturbances are present.
However, it is challenging to design LTV state feedback controllers in the face
of model uncertainty whose effects are difficult to bound. To address this
issue, we propose a novel approach to over-approximate the effects of both
model uncertainty and additive disturbances by a filtered additive disturbance
signal. Using the System Level Synthesis framework, we jointly search for
robust LTV state feedback controllers and the bounds on the effects of
uncertainty online, which allows us to reduce the conservatism and minimize an
upper bound on the worst-case cost in robust MPC. We provide a comprehensive
numerical comparison of our method and representative robust MPC methods from
the literature. Numerical examples demonstrate that our proposed method can
significantly reduce the conservatism over a wide range of uncertainty
parameters with comparable computational effort as the baseline methods.
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Although synthetic training data has been shown to be beneficial for tasks
such as human pose estimation, its use for RGB human action recognition is
relatively unexplored. Our goal in this work is to answer the question whether
synthetic humans can improve the performance of human action recognition, with
a particular focus on generalization to unseen viewpoints. We make use of the
recent advances in monocular 3D human body reconstruction from real action
sequences to automatically render synthetic training videos for the action
labels. We make the following contributions: (i) we investigate the extent of
variations and augmentations that are beneficial to improving performance at
new viewpoints. We consider changes in body shape and clothing for individuals,
as well as more action relevant augmentations such as non-uniform frame
sampling, and interpolating between the motion of individuals performing the
same action; (ii) We introduce a new data generation methodology, SURREACT,
that allows training of spatio-temporal CNNs for action classification; (iii)
We substantially improve the state-of-the-art action recognition performance on
the NTU RGB+D and UESTC standard human action multi-view benchmarks; Finally,
(iv) we extend the augmentation approach to in-the-wild videos from a subset of
the Kinetics dataset to investigate the case when only one-shot training data
is available, and demonstrate improvements in this case as well.
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This paper presents an extension of Bhargava's theory of factorials
associated to any nonempty subset $S$ of $\mathbb{Z}$. Bhargava's factorials
$k!_S$ are invariants, constructed using the notion of $p$-orderings of $S$
where $p$ is a prime. This paper defines $b$-orderings of any nonempty subset
$S$ of $\mathbb{Z}$ for all integers $b\ge2$, as well as "extreme" cases $b=1$
and $b=0$. It defines generalized factorials $k !_{S,T}$ and generalized
binomial coefficients $\binom{k+\ell}{k}_{S,T}$ as nonnegative integers, for
all nonempty $S$ and allowing only $b$ in $T\subseteq\mathbb{N}$. It computes
$b$-ordering invariants when $S$ is $\mathbb{Z}$ and when $S$ is the set of all
primes.
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We study protecting a user's data (images in this work) against a learner's
unauthorized use in training neural networks. It is especially challenging when
the user's data is only a tiny percentage of the learner's complete training
set. We revisit the traditional watermarking under modern deep learning
settings to tackle the challenge. We show that when a user watermarks images
using a specialized linear color transformation, a neural network classifier
will be imprinted with the signature so that a third-party arbitrator can
verify the potentially unauthorized usage of the user data by inferring the
watermark signature from the neural network. We also discuss what watermarking
properties and signature spaces make the arbitrator's verification convincing.
To our best knowledge, this work is the first to protect an individual user's
data ownership from unauthorized use in training neural networks.
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Empirical mass formulae for the baryon octet and decuplet are presented.
These formulae are functions of one integer variable and charge state of the
baryons. With an exception of Lambda(1116), the formulae generate masses within
0.1% of the observed masses. The formulae also generate the same
electromagnetic mass splittings predicted by SU(6)model. Spin 1/2 octet
resonances and its relation to the octet mass formula is described.
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Alongside consistency, completeness of information is one of the key factors
influencing data quality. The objective of this paper is to define ways of
treating missing entries in pairwise comparisons (PC) method with respect to
inconsistency and sensitivity. Two important factors related to the
incompleteness of PC matrices have been identified, namely the number of
missing pairwise comparisons and their arrangements. Accordingly, four
incompleteness indices have been developed, simple to calculate, each of them
take into account both: the total number of missing data and their distribution
in the PC matrix. A numerical study of the properties of these indices has been
also conducted using a series of Montecarlo experiments. It demonstrated that
both incompleteness and inconsistency of data equally contribute to the
sensitivity of the PC matrix. Although incompleteness is only just one of the
factors influencing sensitivity, a relative simplicity of the proposed indices
may help decision makers to quickly estimate the impact of missing comparisons
on the quality of final result.
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We establish the Gr\"obner-Shirshov bases theory for differential Lie
$\Omega$-algebras. As an application, we give a linear basis of a free
differential Lie Rota-Baxter algebra on a set.
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We extend the effective field theory treatment of the thermodynamics of small
compactified black holes to the case of charged black holes. The relevant
thermodynamic quantities are computed to second order in the parameter
\lambda\sim(r_0/L)^(d-3). We discuss how the addition of charge to a caged
black hole may delay the phase transition to a black string. In the extremal
limit, we construct an exact black hole solution which serves as a check for
our perturbative results. Finite size effects are also included through higher
order operators in the worldline action. We calculate how the thermodynamic
quantities are modified in the presence of these operators, and show they enter
beyond order \lambda^2 as in the uncharged case. Finally, we use the exact
solution to constrain the Wilson coefficients of the finite size operators in
the extremal limit.
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Tailoring spectral properties of photon pairs is of great importance for
optical quantum information and measurement applications. High-resolution
spectral measurement is a key technique for engineering spectral properties of
photons, making them ideal for various quantum applications. Here we
demonstrate spectral measurements and optimization of frequency-entangled
photon pairs produced via spontaneous parametric downconversion (SPDC),
utilizing frequency-resolved sum-frequency generation (SFG), the reverse
process of SPDC. A joint phase-matching spectrum of a nonlinear crystal around
1580 nm is captured with a 40 pm resolution and a > 40 dB signal-to-noise
ratio, significantly improved compared to traditional frequency-resolved
coincidence measurements. Moreover, our scheme is applicable to collinear
degenerate sources whose characterization is difficult with previously
demonstrated stimulated difference frequency generation (DFG). We also
illustrate that the observed phase-matching function is useful for finding an
optimal pump spectrum to maximize the spectral indistinguishability of SPDC
photons. We expect that our precise spectral characterization technique will be
useful tool for characterizing and tailoring SPDC sources for a wide range of
optical quantum applications
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We exhibit examples of simple separable nuclear C*-algebras, along with
actions of the circle group and outer actions of the integers, which are not
equivariantly isomorphic to their opposite algebras. In fact, the fixed point
subalgebras are not isomorphic to their opposites. The C*-algebras we exhibit
are well behaved from the perspective of structure and classification of
nuclear C*-algebras: they are unital C*-algebras in the UCT class, with finite
nuclear dimension. One is an AH-algebra with unique tracial state and absorbs
the CAR algebra tensorially. The other is a Kirchberg algebra.
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We have characterized the one-dimensional (1D) to three-dimensional (3D)
crossover of a two-component spin-imbalanced Fermi gas of 6-lithium atoms in a
2D optical lattice by varying the lattice tunneling and the interactions. The
gas phase separates, and we detect the phase boundaries using in situ imaging
of the inhomogeneous density profiles. The locations of the phases are inverted
in 1D as compared to 3D, thus providing a clear signature of the crossover. By
scaling the tunneling rate with respect to the pair binding energy, we observe
a collapse of the data to a universal crossover point at a scaled tunneling
value of 0.025(7).
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We show that the three-dimensional layers-of-maxima problem can be solved in
$o(n\log n)$ time in the word RAM model. Our algorithm runs in $O(n(\log \log
n)^3)$ deterministic time or $O(n(\log\log n)^2)$ expected time and uses O(n)
space. We also describe an algorithm that uses optimal O(n) space and solves
the three-dimensional layers-of-maxima problem in $O(n\log n)$ time in the
pointer machine model.
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Contrastive Learning (CL) is a recent representation learning approach, which
encourages inter-class separability and intra-class compactness in learned
image representations. Since medical images often contain multiple semantic
classes in an image, using CL to learn representations of local features (as
opposed to global) is important. In this work, we present a novel
semi-supervised 2D medical segmentation solution that applies CL on image
patches, instead of full images. These patches are meaningfully constructed
using the semantic information of different classes obtained via pseudo
labeling. We also propose a novel consistency regularization (CR) scheme, which
works in synergy with CL. It addresses the problem of confirmation bias, and
encourages better clustering in the feature space. We evaluate our method on
four public medical segmentation datasets and a novel histopathology dataset
that we introduce. Our method obtains consistent improvements over
state-of-the-art semi-supervised segmentation approaches for all datasets.
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We bound the Castelnuovo-Mumford regularity and syzygies of the ideal of the
singular set of a plane curve, and more generally of the conductor scheme of
certain projectively Gorenstein varieties.
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We study how the supporting hyperplanes produced by the projection process
can complement the method of alternating projections and its variants for the
convex set intersection problem. For the problem of finding the closest point
in the intersection of closed convex sets, we propose an algorithm that, like
Dykstra's algorithm, converges strongly in a Hilbert space. Moreover, this
algorithm converges in finitely many iterations when the closed convex sets are
cones in $\mathbb{R}^{n}$ satisfying an alignment condition. Next, we propose
modifications of the alternating projection algorithm, and prove its
convergence. The algorithm converges superlinearly in $\mathbb{R}^{n}$ under
some nice conditions. Under a conical condition, the convergence can be finite.
Lastly, we discuss the case where the intersection of the sets is empty.
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Several applied problems are characterized by the need to numerically solve
equations with an operator function (matrix function). In particular, in the
last decade, mathematical models with a fractional power of an elliptic
operator and numerical methods for their study have been actively discussed.
Computational algorithms for such non-standard problems are based on
approximations by the operator function. The most widespread are the approaches
using various options for rational approximation. Also, we note the methods
that relate to approximation by exponential sums. In this paper, the
possibility of using approximation by exponential products is noted. The
solution of an equation with an operator function is based on the transition to
standard stationary or evolutionary problems. General approaches are
illustrated by a problem with a fractional power of the operator. The first
class of methods is based on the integral representation of the operator
function under rational approximation, approximation by exponential sums, and
approximation by exponential products. The second class of methods is
associated with solving an auxiliary Cauchy problem for some evolutionary
equation.
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While conventional reinforcement learning focuses on designing agents that
can perform one task, meta-learning aims, instead, to solve the problem of
designing agents that can generalize to different tasks (e.g., environments,
obstacles, and goals) that were not considered during the design or the
training of these agents. In this spirit, in this paper, we consider the
problem of training a provably safe Neural Network (NN) controller for
uncertain nonlinear dynamical systems that can generalize to new tasks that
were not present in the training data while preserving strong safety
guarantees. Our approach is to learn a set of NN controllers during the
training phase. When the task becomes available at runtime, our framework will
carefully select a subset of these NN controllers and compose them to form the
final NN controller. Critical to our approach is the ability to compute a
finite-state abstraction of the nonlinear dynamical system. This abstract model
captures the behavior of the closed-loop system under all possible NN weights,
and is used to train the NNs and compose them when the task becomes available.
We provide theoretical guarantees that govern the correctness of the resulting
NN. We evaluated our approach on the problem of controlling a wheeled robot in
cluttered environments that were not present in the training data.
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Let (g,K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold M
with non-positive Yamabe invariant (Y(M)). As noted by Fischer and Moncrief,
the reduced volume V(k)=(-k/3)^{3}Vol_{g(k)}(M) is monotonically decreasing in
the expanding direction and bounded below by V_{\inf}=(-1/6)Y(M))^{3/2}.
Inspired by this fact we define the ground state of the manifold M as "the
limit" of any sequence of CMC states {(g_{i},K_{i})} satisfying: i. k_{i}=-3,
ii. V_{i} --> V_{inf}, iii. Q_{0}((g_{i},K_{i}))< L where Q_{0} is the
Bel-Robinson energy and L is any arbitrary positive constant. We prove that (as
a geometric state) the ground state is equivalent to the Thurston
geometrization of M. Ground states classify naturally into three types. We
provide examples for each class, including a new ground state (the Double Cusp)
that we analyze in detail. Finally consider a long time and cosmologically
normalized flow (\g,\K)(s)=((-k/3)^{2}g,(-k/3))K) where s=-ln(-k) is in
[a,\infty). We prove that if E_{1}=E_{1}((\g,\K))< L (where E_{1}=Q_{0}+Q_{1},
is the sum of the zero and first order Bel-Robinson energies) the flow
(\g,\K)(s) persistently geometrizes the three-manifold M and the geometrization
is the ground state if V --> V_{inf}.
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This paper provides a technological evaluation of two Automatic Fingerprint
Identification Systems (AFIS) used in forensic applications. Both of them are
installed and working in Spanish police premises. The first one is a Printrak
AFIS 2000 system with a database of more than 450,000 fingerprints, while the
second one is a NEC AFIS 21 SAID NT-LEXS Release 2.4.4 with a database of more
than 15 million fingerprints. Our experiments reveal that although both systems
can manage inkless fingerprints, the latest one offers better experimental
results
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Structure pathology detection is an important security task in building
construction, which is performed by an operator by looking manually for damages
on the materials. This activity could be dangerous if the structure is hidden
or difficult to reach. On the other hand, embedded devices and wireless sensor
networks (WSN) are becoming popular and cheap, enabling the design of an
alternative pathology detection system to monitor structures based on these
technologies. This article introduces a ZigBee WSN system, intending to be
autonomous, easy to use and with low power consumption. Its functional parts
are fully discussed with diagrams, as well as the protocol used to collect
samples from sensor nodes. Finally, several tests focused on range and power
consumption of our prototype are shown, analysing whether the results obtained
were as expected or not.
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Coupled map lattices of non-hyperbolic local maps arise naturally in many
physical situations described by discretised reaction diffusion equations or
discretised scalar field theories. As a prototype for these types of lattice
dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order
which exhibit strongest possible chaotic behaviour for small coupling constants
a. We prove that the expectations of arbitrary observables scale with \sqrt{a}
in the low-coupling limit, contrasting the hyperbolic case which is known to
scale with a. Moreover we prove that there are log-periodic oscillations of
period \log N^2 modulating the \sqrt{a}-dependence of a given expectation
value. We develop a general 1st order perturbation theory to analytically
calculate the invariant 1-point density, show that the density exhibits
log-periodic oscillations in phase space, and obtain excellent agreement with
numerical results.
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A bipartite covering of a (multi)graph $G$ is a collection of bipartite
graphs, so that each edge of $G$ belongs to at least one of them. The capacity
of the covering is the sum of the numbers of vertices of these bipartite
graphs. In this note we establish a (modest) strengthening of old results of
Hansel and of Katona and Szemer\'edi, by showing that the capacity of any
bipartite covering of a graph on $n$ vertices in which the maximum size of an
independent set containing vertex number $i$ is $\alpha_i$, is at least $\sum_i
\log_2 (n/\alpha_i).$ We also obtain slightly improved bounds for a recent
result of Kim and Lee about the minimum possible capacity of a bipartite
covering of complete multigraphs.
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Evolution equations for leading twist operators in high orders of
perturbation theory can be restored from the spectrum of anomalous dimensions
and the calculation of the special conformal anomaly at one order less using
conformal symmetry of QCD at the Wilson-Fisher critical point at non-integer
$d=4-2\epsilon$ space-time dimensions. In this work we generalize this
technique to axial-vector operators. We calculate the corresponding three-loop
evolution kernels in Larin's scheme and derive explicit expressions for the
finite renormalization kernel that describes the difference to the vector case
to restore the conventional ${\overline{\mathrm{MS}}}$-scheme. The results are
directly applicable to deeply-virtual Compton scattering and the transition
form factor $\gamma^*\gamma\to\pi$.
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Efficient generation of spatially delocalised entangled states is at the
heart of quantum information science. Generally flying qubits are proposed for
long range entangling interactions, however here we introduce a bus-mediated
alternative for this task. Our scheme permits efficient and flexible generation
of deterministic two-qubit operator measurements and has links to the important
concepts of mode-entanglement and repeat-until-success protocols. Importantly,
unlike flying qubit protocols, our bus particle never contains information
about the individual quantum states of the particles, hence is
information-free.
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Two tetrad spaces reproducing spherically symmetric spacetime are applied to
the equations of motion of higher-order torsion theories. Assuming the
existence of conformal Killing vector, two isotropic solutions are derived. We
show that the first solution is not stable while the second one confirms a
stable behavior. We also discuss the construction of the stellar model and show
that one of our solution capable of such construction while the other cannot.
Finally, we discuss the generalized Tolman-Oppenheimer-Volkoff and show that
one of our models has a tendency to equilibrium.
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