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Recently there were proposed some innovative convex optimization concepts,
namely, relative smoothness [1] and relative strong convexity [2,3]. These
approaches have significantly expanded the class of applicability of
gradient-type methods with optimal estimates of the convergence rate, which are
invariant regardless of the dimensionality of the problem. Later Yu. Nesterov
and H. Lu introduced some modifications of the Mirror Descent method for convex
minimization problems with the corresponding analogue of the Lipschitz
condition (so-called relative Lipschitz continuity). By introducing an
artificial inaccuracy to the optimization model, we propose adaptive methods
for minimizing a convex Lipschitz continuous function, as well as for the
corresponding class of variational inequalities. We also consider an adaptive
"universal" method, applicable to convex minimization problems both on the
class of relatively smooth and relatively Lipschitz continuous functionals with
optimal estimates of the convergence rate. The universality of the method makes
it possible to justify the applicability of the obtained theoretical results to
a wider class of convex optimization problems. We also present the results of
numerical experiments.
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Differential calculus on the quantum quaternionic group GL(1,H$_q$) is
introduced.
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We present the results of a multiwavelength campaign searching for young
objects in the intragroup medium of seven compact groups of galaxies: HCG 2, 7,
22, 23, 92, 100 and NGC 92. We used Fabry-Perot velocity fields and rotation
curves together with GALEX NUV and FUV images, optical R-band and HI maps to
evaluate the stage of interaction of each group. We conclude that groups (i)
HCG 7 and HCG 23 are in an early stage of interaction, (ii) HCG 2 and HCG 22
are mildly interacting, and (iii) HCG 92, HCG 100 and NGC 92 are in a late
stage of evolution. Evolved groups have a population of young objects in their
intragroup medium while no such population is found within the less evolved
groups. We also report the discovery of a tidal dwarf galaxy candidate in the
tail of NGC 92. These three groups, besides containing galaxies which have
peculiar velocity fields, also show extended HI tails. Our results indicate
that the advanced stage of evolution of a group together with the presence of
intragroup HI clouds may lead to star formation in the intragroup medium.
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In this paper, we analyze the temporal evolution of the age-dependent force
of infection and incidence of rubella, after the introduction of a very
specific vaccination programme in a previously nonvaccinated population where
rubella was in endemic steady state. We deduce an integral equation for the
age-dependent force of infection, which depends on a number of parameters that
can be estimated from the force of infection in steady state prior to the
vaccination program. We present the results of our simulations, which are
compared with observed data. We also examine the influence of contact patterns
among members of a community on the age-dependent intensity of transmission of
rubella and on the results of vaccination strategies. As an example of the
theory proposed, we calculate the effects of vaccination strategies for four
communities from Caieiras (Brazil), Huixquilucan (Mexico), Finland and the
United Kingdom. The results for each community differ considerably according to
the distinct intensity and pattern of transmission in the absence of
vaccination. We conclude that this simple vaccination program is not very
efficient (very slow) in the goal of eradicating the disease. This gives
support to a mixed strategy, proposed by Massad et al., accepted and
implemented by the government of the State of Sao Paulo, Brazil.
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Incompressible flows can be effective mixers by appropriately advecting a
passive tracer to produce small filamentation length scales. In addition,
diffusion is generally perceived as beneficial to mixing due to its ability to
homogenise a passive tracer. However we provided numerical evidence that, in
the case where advection and diffusion are both actively present, diffusion
produces nearly neutral or even negative effects by limiting the mixing
effectiveness of incompressible optimal flows. This limitation appears to be
due to the presence of a limiting length scale given by a generalised Batchelor
length. This length scale limitation in turn affects long-term mixing rates.
More specifically, we consider local-in-time flow optimisation under energy and
enstrophy flow constraints with the objective of maximising mixing rate
performance. We observe that, for enstrophy-bounded optimal flows, the strength
of diffusion has no impact on the long-term mixing rate performance. For
energy-constrained optimal flows, however an increase in the strength of
diffusion decreases the mixing rate. We provide analytical lower bounds on
mixing rates and length scales achievable under related constraints (point-wise
bounded speed and rate-of-strain) by extending the work of Z. Lin et al.
(Journal of Fluid Mech., 2011) and C.-C. Poon (Comm. in Partial Differential
Equations, 1996).
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I present a new formalism of the R-matrix theory where the formal parameters
for the resonance energies and widths are identical to the observed values. By
allowing the boundary condition parameters to vary from level to level, the
freedom required to adjust the formal parameters for the pole positions to the
observed values is obtained. The basis of the resulting theory becomes
nonorthogonal, and I describe the procedure to construct a consistent R-matrix
theory with such a nonorthogonal basis. And by adjusting the normalization of
the states that form the basis, the formal parameters for the reduced decay
widths also become the same as those observed, leaving no formal parameters
that are different from the observed ones. A demonstration of the developed
theory to the elastic 12C+p scattering data is presented.
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The presence of ferroelectricity in hexagonal (h-)InMnO3 has been highly
under debate. The results of our comprehensive experiments of low-temperature
(T) polarization, TEM and HAADF-STEM on well-controlled h-InMnO3 reveal that
the ground state is ferroelectric with P6_3cm symmetry, but a non-ferroelectric
P-3c1 state exists at high T, and can be quenched to room T. We also found that
the ferroelectric P6_3cm state of h-InMnO3 exhibits the domain configuration of
topological vortices, as has been observed in h-REMnO3 (RE=rare earths).
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Background: Selecting feature genes to predict phenotypes is one of the
typical tasks in analyzing genomics data. Though many general-purpose
algorithms were developed for prediction, dealing with highly correlated genes
in the prediction model is still not well addressed. High correlation among
genes introduces technical problems, such as multi-collinearity issues, leading
to unreliable prediction models. Furthermore, when a causal gene (whose
variants have an actual biological effect on a phenotype) is highly correlated
with other genes, most algorithms select the feature gene from the correlated
group in a purely data-driven manner. Since the correlation structure among
genes could change substantially when condition changes, the prediction model
based on not correctly selected feature genes is unreliable. Therefore, we aim
to keep the causal biological signal in the prediction process and build a more
robust prediction model.
Method: We propose a grouping algorithm, which treats highly correlated genes
as a group and uses their common pattern to represent the group's biological
signal in feature selection. Our novel grouping algorithm can be integrated
into existing prediction algorithms to enhance their prediction performance.
Our proposed grouping method has two advantages. First, using the gene group's
common patterns makes the prediction more robust and reliable under condition
change. Second, it reports whole correlated gene groups as discovered
biomarkers for prediction tasks, allowing researchers to conduct follow-up
studies to identify causal genes within the identified groups.
Result: Using real benchmark scRNA-seq datasets with simulated cell
phenotypes, we demonstrate our novel method significantly outperforms standard
models in both (1) prediction of cell phenotypes and (2) feature gene
selection.
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Given a smooth partial action $\alpha$ of a Lie groupoid $G$ on a smooth
manifold $M,$ we provide necessary and sufficient conditions for $\alpha$ to be
globalizable with smooth globalization. As an application, we provide results
on the differentiable structure of orbit and stabilizer spaces induced by
$\alpha,$ which leads to other criteria for its globalization in terms of its
orbit maps in the case that $\alpha$ is free and transitive. Further, under the
assumption that $\alpha$ is free and proper, we prove that there exists exactly
one differentiable structure on the quotient structure of the orbit equivalence
space $M/G$ such that the quotient map $\pi:M\to M/G$ is a submersion
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We propose a field-free switching mechanism that utilizes two spatially
orthogonal spin-orbit torque (SOT) currents. Initially applied simultaneously,
one of the currents is subsequently switched off. The superposition of these
two currents results in an in-plane magnetization, which is not orthogonal to
the remaining SOT current after the second one is deactivated. This
symmetry-breaking procedure leads to reproducible and rapid switching, with
field pulse durations as short as 0.25 nanoseconds.
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In (2+1)-dimensional hydrodynamic systems with broken parity, the shear and
bulk viscosity is joined by the Hall viscosity and curl viscosity. The dual
holographic model has been constructed by coupling a pseudo scalar to the
gravitational Chern-Simons term in (3+1)-dimensional bulk gravity. In this
paper, we investigate the non-relativistic fluid with Hall viscosity and curl
viscosity living on a finite radial cutoff surface in the bulk. Employing the
non-relativistic hydrodynamic expansion method, we obtain the incompressible
Navier-Stokes equations with Hall viscosity and curl viscosity. Unlike the
shear viscosity, the ratio of the Hall viscosity over entropy density is found
to be cutoff scale dependent, and it tends to zero when the cutoff surface
approaches to the horizon of the background spacetime.
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In this paper, we introduce an adaptive kernel method for solving the optimal
filtering problem. The computational framework that we adopt is the Bayesian
filter, in which we recursively generate an optimal estimate for the state of a
target stochastic dynamical system based on partial noisy observational data.
The mathematical model that we use to formulate the propagation of the state
dynamics is the Fokker-Planck equation, and we introduce an operator
decomposition method to efficiently solve the Fokker-Planck equation. An
adaptive kernel method is introduced to adaptively construct Gaussian kernels
to approximate the probability distribution of the target state. Bayesian
inference is applied to incorporate the observational data into the state model
simulation. Numerical experiments have been carried out to validate the
performance of our kernel method.
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We present results from our survey for planetary transits in the field of the
intermediate age (~2.5 Gyr), metal-rich ([Fe/H]~+0.07) open cluster NGC 6819.
We have obtained high-precision time-series photometry for over 38,000 stars in
this field and have developed an effective matched-filter algorithm to search
for photometric transits. This algorithm identified 8 candidate stars showing
multiple transit-like events, plus 3 stars with single eclipses. On closer
inspection, while most are shown to be low mass stellar binaries, some of these
events could be due to brown dwarf companions. The data for one of the
single-transit candidates indicates a minimum radius for the companion similar
to that of HD 209458b.
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Many-particle QED is applied to kinetic theory of radiative processes in
many- component plasmas with relativistic electrons and nonrelativistic heavy
particles. Within the framework of nonequilibrium Green's function technique,
transport and mass-shell equations for fluctuations of the electromagnetic
field are obtained. We show that the transverse field correlation functions can
be decomposed into sharply peaked (non-Lorentzian) parts that describe resonant
(propagating) photons and off-shell parts corresponding to virtual photons in
plasmas. Analogous decomposi- tions are found for the longitudinal field
correlation functions and the correlation functions of relativistic electrons.
As a novel result a kinetic equation for the reso- nant photons with a finite
spectral width is derived. The off-shell parts of the particle and field
correlation functions are shown to be essential to calculate the local ra-
diating power in relativistic plasmas and recover the results of vacuum QED.
The influence of plasma effects and collisional broadening of the relativistic
quasiparticle spectral function on radiative processes is discussed.
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A nonperturbative analytical description of the SU(2)_1 quantum critical
point in an explicitly dimerized two-leg spin-1/2 Heisenberg ladder is
presented. It is shown that this criticality essentially coincides with that
emerging in a weakly dimerized spin-1 chain with a small Haldane gap. The
approach is based on the mapping onto an SO(3)-symmetric model of three
strongly coupled quantum Ising chains. This mapping is used to establish the
correspondence between all physical fields of the spin ladder and those
characterizing the SU(2)_1 criticality at the infrared fixed point.
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(abridged) We have performed a set of phase-resolved X-ray observations of
the magnetic B star Beta Cep, for which theoretical models predict the presence
of a confined wind emitting X-rays from stationary shocks.
We obtained four observations spaced in rotational phase with XMM-Newton and
with Chandra. A detailed analysis of the data was performed to derive both
photometric and spectral parameters from the EPIC data, searching for
rotational modulation, and to derive the location of the X-ray plasma from the
line ratios in the He-like triplets of N, O and Ne from the RGS data. The LETG
data were used to constrain the presence of bulk motions in the plasma.
The strong rotational modulation predicted by the early, static magnetically
confined wind model for the X-ray emission is not observed in Beta Cep. The
small modulation present goes in the opposite direction, pointing to the
absence of any optically thick disk of neutral material, and showing a
modulation consistent with the later, dynamic models of magnetically confined
wind models in B stars. The lack of observed bulk motion points to the plasma
being confined by a magnetic field, but the low plasma temperature and lack of
any flaring show that the plasma is not heated by magnetic reconnection.
Therefore, the observations point to X-ray emission from shocks in a
magnetically confined wind, with no evidence of an optically thick, dense disk
at the magnetic equator
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The purpose of this note is to give a self contained description of Walls
finiteness obstruction.
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Pruning schemes have been widely used in practice to reduce the complexity of
trained models with a massive number of parameters. In fact, several practical
studies have shown that if a pruned model is fine-tuned with some
gradient-based updates it generalizes well to new samples. Although the above
pipeline, which we refer to as pruning + fine-tuning, has been extremely
successful in lowering the complexity of trained models, there is very little
known about the theory behind this success. In this paper, we address this
issue by investigating the pruning + fine-tuning framework on the
overparameterized matrix sensing problem with the ground truth $U_\star \in
\mathbb{R}^{d \times r}$ and the overparameterized model $U \in \mathbb{R}^{d
\times k}$ with $k \gg r$. We study the approximate local minima of the mean
square error, augmented with a smooth version of a group Lasso regularizer,
$\sum_{i=1}^k \| U e_i \|_2$. In particular, we provably show that pruning all
the columns below a certain explicit $\ell_2$-norm threshold results in a
solution $U_{\text{prune}}$ which has the minimum number of columns $r$, yet
close to the ground truth in training loss. Moreover, in the subsequent
fine-tuning phase, gradient descent initialized at $U_{\text{prune}}$ converges
at a linear rate to its limit. While our analysis provides insights into the
role of regularization in pruning, we also show that running gradient descent
in the absence of regularization results in models which {are not suitable for
greedy pruning}, i.e., many columns could have their $\ell_2$ norm comparable
to that of the maximum. To the best of our knowledge, our results provide the
first rigorous insights on why greedy pruning + fine-tuning leads to smaller
models which also generalize well.
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A process for the secure transmission of data is presented that has to a
certain degree the advantages of the one-time pad (OTP) cipher, that is,
simplicity, speed, and information-theoretically security, but overcomes its
fundamental weakness, the necessity of securely exchanging a key that is as
long as the message. For each transmission, a dedicated one-time pad is
generated for encrypting and decrypting the plaintext message. This one-time
pad is built from a randomly chosen set of basic keys taken from a public
library. Because the basic keys can be chosen and used multiple times, the
method is called multiple-time pad (MTP) cipher. The information on the choice
of basic keys is encoded in a short keyword that is transmitted by secure
means. The process is made secure against known-plaintext attack by additional
design elements. The process is particularly useful for high-speed transmission
of mass data and video or audio streaming.
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We discuss how SU$(1,1)$ coherent states from the discrete series allow for a
natural coarse graining operation. The physical application are quantum
theories based on a set of three extensive observables whose Poisson algebra is
isomorphic to su$(1,1)$. In particular, we show that a Perelomov coherent state
with representation label $N j_0$ and spinor label $z$ encodes the physics of
$N$ independent subsystems with labels $j_0, z$. This property is suggested by
existing results for the expectation values and variances of the observables.
We prove that it holds for all higher moments. Our results in particular apply
to a recent quantum cosmology model that has been derived using SU(1,1) group
theoretic quantisation techniques. For it, it follows that a certain notion of
fiducial cell independence holds exactly at the quantum level when using the
coherent states.
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A generalization of the differential geometry of forms and vector fields to
the case of quantum Lie algebras is given. In an abstract formulation that
incorporates many existing examples of differential geometry on quantum groups,
we combine an exterior derivative, inner derivations, Lie derivatives, forms
and functions all into one big algebra. In particular we find a generalized
Cartan identity that holds on the whole quantum universal enveloping algebra of
the left-invariant vector fields and implicit commutation relations for a
left-invariant basis of 1-forms.
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We give a characterization of forking in regular ordered Abelian groups. In
particular, we prove that the type of C over AB does not fork over A if and
only if the type over AB of each C-definable singleton does not fork over A in
these structures.
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We prove the existence and $C^{1,\alpha}$ regularity of solutions to nonlocal
fully nonlinear elliptic equations with gradient constraints. We do not assume
any regularity about the constraints; so the constraints need not be $C^1$ or
strictly convex. We also obtain $C^{0,1}$ boundary regularity for these
problems. Our approach is to show that these nonlocal equations with gradient
constraints are related to some nonlocal double obstacle problems. Then we
prove the regularity of the double obstacle problems. In this process, we also
employ the monotonicity property for the second derivative of obstacles, which
we have obtained in a previous work.
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Recent studies on domain-specific BERT models show that effectiveness on
downstream tasks can be improved when models are pretrained on in-domain data.
Often, the pretraining data used in these models are selected based on their
subject matter, e.g., biology or computer science. Given the range of
applications using social media text, and its unique language variety, we
pretrain two models on tweets and forum text respectively, and empirically
demonstrate the effectiveness of these two resources. In addition, we
investigate how similarity measures can be used to nominate in-domain
pretraining data. We publicly release our pretrained models at
https://bit.ly/35RpTf0.
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Answering questions about why characters perform certain actions is central
to understanding and reasoning about narratives. Despite recent progress in QA,
it is not clear if existing models have the ability to answer "why" questions
that may require commonsense knowledge external to the input narrative. In this
work, we introduce TellMeWhy, a new crowd-sourced dataset that consists of more
than 30k questions and free-form answers concerning why characters in short
narratives perform the actions described. For a third of this dataset, the
answers are not present within the narrative. Given the limitations of
automated evaluation for this task, we also present a systematized human
evaluation interface for this dataset. Our evaluation of state-of-the-art
models show that they are far below human performance on answering such
questions. They are especially worse on questions whose answers are external to
the narrative, thus providing a challenge for future QA and narrative
understanding research.
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Activity-related variations in the solar oscillation properties have been
known for 30 years. However, the relative importance of the different
contributions to the observed variations is not yet fully understood. Our goal
is to estimate the relative contribution from sunspots to the observed
activity-related variations in the frequencies of the acoustic modes. We use a
variational principle to relate the phase differences induced by sunspots on
the acoustic waves to the corresponding changes in the frequencies of the
global acoustic oscillations. From the sunspot properties (area and latitude as
a function of time), we are able to estimate the spot-induced frequency shifts.
These are then combined with a smooth frequency shift component, associated
with long-term solar-cycle variations, and the results compared with the
frequency shifts derived from the Global Oscillation Network Group (GONG) data.
The result of this comparison is consistent with a sunspot contribution to the
observed frequency shifts of roughly 30 per cent, with the remaining 70 per
cent resulting mostly from a global, non-stochastic variation, possibly related
to the changes in the overall magnetic field. Moreover, analysis of the
residuals obtained after the subtraction of the model frequency shifts from the
observations indicates the presence of a 1.5-yr periodicity in the data in
phase with the quasi-biennial variations reported in the literature.
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In this short note we review deterministic simulation of biochemical
pathways, i.e. networks of biochemical reactions obeying the law of mass
action. It is meant as a basis for the MATLAB code, written by the author,
which permits easy input and simulation of general biochemical networks. This
work was carried out for the European Project `CardioWorkBench'.
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We analyze the 1+1 dimensional Nambu-Jona-Lasinio model non-perturbatively.
We study non-trivial saddle points of the effective action in which the
composite fields $\sigx=<\bar\psi\psi>$ and $\pix=<\bar\psii\gam_5\psi>$ form
static space dependent configurations. These configurations may be viewed as
one dimensional chiral bags that trap the original fermions (``quarks'') into
stable extended entities (``hadrons''). We provide explicit expressions for the
profiles of some of these objects and calculate their masses. Our analysis of
these saddle points, and in particular, the proof that the $\sigx, \pix$
condensations must give rise to a reflectionless Dirac operator, appear to us
simpler and more direct than the calculations previously done by Shei, using
the inverse scattering method following Dashen, Hasslacher, and Neveu.
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The effective Hamiltonian describing the motion of an exciton in an external
non-homogeneous magnetic field is derived. The magnetic field plays the role of
an effective potential for the exciton motion, results into an increment of the
exciton mass and modifies the exciton kinetic energy operator. In contrast to
the homogeneous field case, the exciton in a non-homogeneous magnetic field can
also be trapped in the low field region and the field gradient increases the
exciton confinement. The trapping energy and wave function of the exciton in a
GaAs two-dimensional electron gas for specific circular magnetic field
configurations are calculated. The results show than excitons can be trapped by
non-homogeneous magnetic fields, and that the trapping energy is strongly
correlated with the shape and strength of the non-homogeneous magnetic field
profile.
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We study Wilson-'t Hooft loop operators in a class of N=2 superconformal
field theories recently introduced by Gaiotto. In the case that the gauge group
is a product of SU(2) groups, we classify all possible loop operators in terms
of their electric and magnetic charges subject to the Dirac quantization
condition. We then show that this precisely matches Dehn's classification of
homotopy classes of non-self-intersecting curves on an associated Riemann
surface--the same surface which characterizes the gauge theory. Our analysis
provides an explicit prediction for the action of S-duality on loop operators
in these theories which we check against the known duality transformation in
several examples.
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We describe a scalable database cluster for the spatial analysis and
annotation of high-throughput brain imaging data, initially for 3-d electron
microscopy image stacks, but for time-series and multi-channel data as well.
The system was designed primarily for workloads that build connectomes---neural
connectivity maps of the brain---using the parallel execution of computer
vision algorithms on high-performance compute clusters. These services and
open-science data sets are publicly available at http://openconnecto.me.
The system design inherits much from NoSQL scale-out and data-intensive
computing architectures. We distribute data to cluster nodes by partitioning a
spatial index. We direct I/O to different systems---reads to parallel disk
arrays and writes to solid-state storage---to avoid I/O interference and
maximize throughput. All programming interfaces are RESTful Web services, which
are simple and stateless, improving scalability and usability. We include a
performance evaluation of the production system, highlighting the effectiveness
of spatial data organization.
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In the machine learning era, sparsity continues to attract significant
interest due to the benefits it provides to learning models. Algorithms aiming
to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to
achieve sparsity. In this work, an alternative algorithm is proposed, which is
derived based on the assumption of a Cauchy distribution characterising the
coefficients in sparse domains. The Cauchy distribution is known to be able to
capture heavy-tails in the data, which are linked to sparse processes. We begin
by deriving the Cauchy proximal operator and subsequently propose an algorithm
for optimising a cost function which includes a Cauchy penalty term. We have
coined our contribution as Iterative Cauchy Thresholding (ICT). Results
indicate that sparser solutions can be achieved using ICT in conjunction with a
fixed over-complete discrete cosine transform dictionary under a sparse coding
methodology.
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A deep (98.2 ks) Chandra Cycle-1 observation has revealed a wealth of
discrete X-ray sources as well as diffuse emission in the nearby face-on spiral
galaxy M101. From this rich dataset we have created a catalog of the 110
sources from the S3 chip detected with a significance of >3 sigma,
corresponding to a flux of ~1.0E-16 ergs/cm/cm/s and a luminosity of 1.0E36
ergs/s for a distance to M101 of 7.2 Mpc. The sources display a distinct
correlation with the spiral arms and include a variety of X-ray binaries,
supersoft sources, supernova remnants, and other objects of which only ~27 are
likely to be background sources. There are only a few sources in the interarm
regions, and most of these have X-ray colors consistent with that of background
AGNs. The derived log N-log S relation for the sources in M101 (background
subtracted) has a slope of -0.80+/-0.05 over the range of 1.0E36 - 1.0E38
ergs/s. The nucleus is resolved into 2 nearly identical X-ray sources, each
with a 0.5-2.0 keV flux of 4.0E37 ergs/s. One of these sources coincides with
the optical nucleus, and the other coincides with a cluster of stars 110 pc to
the south.
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We show that the long-time limit of the two-point correlation function
obtained via the standard quantum regression theorem, a standard tool to
compute correlation functions in open quantum systems, does not respect the
Kubo-Martin-Schwinger equilibrium condition to the non-zero order of the
system-bath coupling. We then follow the recently developed Heisenberg operator
method for open quantum systems and by applying a ``{\it weak}" Markov
approximation, derive a new modified version of the quantum regression theorem
that not only respects the KMS condition but further predicts exact answers for
certain paradigmatic models in specific limits. We also show that in cases
where the modified quantum regression theorem does not match with exact
answers, it always performs better than the standard quantum regression
theorem.
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This is a survey on the analytic theory of linear wave equations on globally
hyperbolic Lorentzian manifolds. There is no claim of originality.
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Medical applications, such as Positron Emission Tomography (PET), and space
applications, such as Light Detection and Ranging (LIDAR), are in need of
highly specialized ASICs. Weeroc, in collaboration with different partners, is
highly involved in developing a new generation of front-end ASICs. In the
context of a joined LIDAR project among Weeroc, CNES, and Airbus, Weeroc is
working on the development of Liroc, an ASIC for space LIDAR application.
Weeroc is also working on advancing ASICs for medical applications with
Radioroc under development and intended to be used for PET applications. This
study experimentally evaluates the time resolution limits of these ASICs in
different configurations, with some of the most recent silicon photomultiplier
(SiPM) technologies available on the market, coupled to different scintillation
crystals. The best single-photon time resolution (SPTR) was achieved using FBK
NUV-HD SiPMs with an FWHM of 90 ps with Liroc and 73 ps with Radioroc.
Furthermore, the coincidence time resolution (CTR) of Radioroc was studied with
different crystal sizes. Using a large LYSO:Ce,Ca crystal of (3 x 3 x 20 mm3)
with Broadcom Near UltraViolet-Metal in Trench (NUV-MT) yields a CTR of 127 ps
(FWHM). The best CTR of Radioroc was determined to 83 ps (FWHM) with Broadcom
NUV-MT SiPMs coupled to LYSO:Ce,Ca (2 x 2 x 3 mm3) from Taiwan Applied Crystal
(TAC).
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Modern scientific research and applications very often encounter "fragmentary
data" which brings big challenges to imputation and prediction. By leveraging
the structure of response patterns, we propose a unified and flexible framework
based on Generative Adversarial Nets (GAN) to deal with fragmentary data
imputation and label prediction at the same time. Unlike most of the other
generative model based imputation methods that either have no theoretical
guarantee or only consider Missing Completed At Random (MCAR), the proposed
FragmGAN has theoretical guarantees for imputation with data Missing At Random
(MAR) while no hint mechanism is needed. FragmGAN trains a predictor with the
generator and discriminator simultaneously. This linkage mechanism shows
significant advantages for predictive performances in extensive experiments.
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We present new stellar kinematical profiles of four galaxy hosts of active
galactic nuclei, using the CO bandhead around 2.3 micron with the ISAAC/VLT
spectrograph. We find that the nuclear bars or discs, embedded in large-scale
primary bars, have all a decoupled kinematics, in the sense that the maximum of
the rotational velocity occurs in the nuclear region. In three cases (NGC 1097,
NGC 1808 and NGC 5728), the velocity dispersion displays a significant drop at
the nucleus, a rarely observed phenomenon. We also detect kinematical
asymmetries (m=1 mode) along the nuclear bar major-axis of NGC 1808 and NGC
5728, dynamical counterparts of corresponding asymmetries in the surface
brightness. We have derived simple dynamical models in an attempt to fit the
kinematics of each galaxy and reconstruct the full velocity field. For all four
targets, the fits are good, and confirm the presence of the decoupled nuclear
components. These models cannot however reproduce the observed central drop in
the dispersion. We suggest that this drop is due to a transient cold nuclear
disc, fuelled by gas inflow along the bar, that has recently formed new stars.
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We have observed significant progress in visual navigation for embodied
agents. A common assumption in studying visual navigation is that the
environments are static; this is a limiting assumption. Intelligent navigation
may involve interacting with the environment beyond just moving
forward/backward and turning left/right. Sometimes, the best way to navigate is
to push something out of the way. In this paper, we study the problem of
interactive navigation where agents learn to change the environment to navigate
more efficiently to their goals. To this end, we introduce the Neural
Interaction Engine (NIE) to explicitly predict the change in the environment
caused by the agent's actions. By modeling the changes while planning, we find
that agents exhibit significant improvements in their navigational
capabilities. More specifically, we consider two downstream tasks in the
physics-enabled, visually rich, AI2-THOR environment: (1) reaching a target
while the path to the target is blocked (2) moving an object to a target
location by pushing it. For both tasks, agents equipped with an NIE
significantly outperform agents without the understanding of the effect of the
actions indicating the benefits of our approach.
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In protoplanetary disks, the differential gravity-driven settling of dust
grains with respect to gas and with respect to grains of varying sizes
determines the observability of grains, and sets the conditions for grain
growth and eventually planet formation. In this work we explore the effect of
photophoresis on the settling of large dust grains in the inner regions of
actively accreting protoplanetary disks. Photophoretic forces on dust grains
result from the collision of gas molecules with differentially heated grains.
We undertake one dimensional dust settling calculations to determine the
equilibrium vertical distribution of dust grains in each column of the disk. In
the process we introduce a new treatment of the photophoresis force which is
consistent at all optical depths with the representation of the radiative
intensity field in a two-stream radiative transfer approximation. The
levitation of large dust grains creates a photophoretic dust trap several scale
heights above the mid-plane in the inner regions of the disk where the
dissipation of accretion energy is significant. We find that differential
settling of dust grains is radically altered in these regions of the disk, with
large dust grains trapped in a layer below the stellar irradiation surface in
where the dust to gas mass ratio can be enhanced by a factor of a hundred for
the relevant particles. The photophoretic trapping effect has a strong
dependence on particle size and porosity.
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We report the serendipitous detection of an X-ray source, AXJ1749+684, with
the ASCA Gas Imaging Spectrometer. AXJ1749+684 is identified with a
LINER/starburst-type spiral galaxy KUG 1750+683A at a redshift z = 0.05. It has
a hard X-ray spectrum, consistent with that of the X-ray background (XRB) in
the 1-10 keV band. Despite the optical classification, the X-ray luminosity
cannot be explained by starburst activity. Combined with spatial variations in
the optical emission line ratios, this suggests the presence of an obscured
Seyfert nucleus embedded within a starforming galaxy. Similar behaviour could
explain the ambiguous properties of the faint narrow-line X-ray galaxies
(NLXGs) emerging from deep X-ray surveys.
|
A previously developed field-theoretic model [R.D. Coalson et al., J. Chem.
Phys. 102, 4584 (1995)] that treats core collisions and Coulomb interactions on
the same footing is investigated in order to understand ion size effects on the
partition of neutral and charged particles at planar interfaces and the ionic
selectivity of slit nanopores. We introduce a variational scheme that can go
beyond the mean-field (MF) regime and couple in a consistent way pore modified
core interactions, steric effects, electrostatic solvation and image-charge
forces, and surface charge induced electrostatic potential. We show that in the
dilute limit, the MF and the variational theories agree well with MC simulation
results, in contrast to a recent RPA method. The partition of charged Yukawa
particles at a neutral dielectric interface (e.g air-water or protein-water
interface) is investigated. It is shown that as a result of the competition
between core collisions that push the ions towards the surface, and repulsive
solvation and image forces that exclude them from the interface, a
concentration peak of finite size ions sets in close to the dielectric
interface. We also characterize the role played by the ion size on the ionic
selectivity of neutral slit nanopores. We show that the complex interplay
between electrostatic forces, excluded volume effects induced by core
collisions and steric effects leads to an unexpected reversal in the ionic
selectivity of the pore with varying pore size: while large pores exhibits a
higher conductivity for large ions, narrow pores exclude large ions more
efficiently than small ones.
|
Information from the sky is important for rescue activity in large-scale
disaster or dangerous areas. Observation system using a balloon or an airplane
has been studied as an information gathering system from the sky. A balloon
observation system needs helium gas and relatively long time to be ready. An
airplane observation system can be prepared in a short time and its mobility is
good. However, a long time flight is difficult because of limited amount of
fuel.
This paper proposes a kite-based observation system that complements
activities of balloon and airplane observation systems by short preparation
time and long time flight. This research aims at construction of the autonomous
flight information gathering system using a tethered flying unit that consists
of the kite and the ground tether line control unit with a winding machine.
This paper reports development of the kite type tethered flying robot and an
autonomous flying control system inspired by how to fly a kite by a human.
|
An ultraproduct can be a helpful organizing principle in presenting solutions
of problems at many levels, as argued by Terence Tao. We apply it here to the
solution of a calculus problem: every infinite sequence has a monotone infinite
subsequence, and give other applications.
Keywords: ordered structures; monotone subsequence; ultrapower; saturation;
compactness
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Local quantum phase transitions driven by Kondo correlations have been
theoretically proposed in several magnetic nanosystems; however, clear
experimental signatures are scant. Modeling a nickelocene molecule on a Cu(100)
substrate as a two-orbital Anderson impurity with single-ion easy-plane
anisotropy coupled to two conduction bands, we find that recent scanning
tunneling spectra measured at different microscope tip heights reveal the
existence of a topological quantum phase transition from the usual local Fermi
liquid with high zero-bias conductance to a non-Landau Fermi liquid,
characterized by a non-trivial quantized Luttinger integral, with a small
conductance. The effects of intermediate valence, finite temperature, and
structural relaxation of the molecule position allow us to explain the
different observed behaviors.
|
A family of optimal control problems for a single and two coupled spinning
particles in the Euler-Lagrange formalism is discussed. A characteristic of
such problems is that the equations controlling the system are implicit and a
reduction procedure to deal with them must be carried on.
The reduction of the implicit control equations arising in these problems
will be discussed in the slightly more general setting of implicit equations
defined by invariant one-forms on Lie groups. As an instance, the first order
differential equations describing the extremal solutions of an optimal control
problem for a single spinning particle, obtained by using Pontryagin's Maximum
Principle (PMP), will be found and shown to be completely integrable.
Then, using again PMP, solutions for the problem of two coupled spinning
particles will be characterised as solutions of a system of coupled non-linear
matrix differential equations. The reduction of the implicit system will show
that the reduced space for them is the product of the space of states for the
independent systems, implying the absence of `entanglement' in this instance.
Finally it will be shown that, in the case of identical systems, the degree
three matrix polynomial differential equations determined by the optimal
feedback law, constitute a completely integrable Hamiltonian system and some of
its solutions are described explicitly.
|
We construct axisymmetric mass models for dwarf spheroidal (dSph) galaxies in
the Milky Way to obtain plausible limits on the non-spherical structure of
their dark halos. This is motivated by the fact that the observed luminous
parts of the dSphs are actually non-spherical and Cold Dark Matter (CDM) models
predict non-spherical virialized dark halos. Our models consider velocity
anisotropy of stars $\bar{v^2_R} / \bar{v^2_{\phi}}$, which can vary with the
adopted cylindrical coordinates under the assumption $\bar{v^2_z}=\bar{v^2_R}$
for simplicity, and also include an inclination of the system as a fitting
parameter to explain the observed line-of-sight velocity dispersion profile.
Applying these models to six of the bright dSphs in the Milky Way, we find that
the best-fitting cases for most of the dSphs yield oblate and flattened dark
halos, irrespective of assumed density profiles in their central parts. We also
find that the total mass of the dSphs enclosed within a spheroid with
major-axis length of 300 pc varies from $10^6M_{\odot}$ to $10^7M_{\odot}$,
contrary to the conclusion from spherical models. This suggests the importance
of considering shapes of dark halos in mass models of the dSphs. It is also
found that dark halos of the Galactic dSphs may be more flattened than N-body
predictions, thereby implying our yet incomplete understanding of baryonic
and/or non-baryonic dark matter physics in dwarf galaxy scales.
|
A linearized energy-balance model for global temperature is formulated,
featuring a scale-free long-range memory (LRM) response and stochastic forcing
representing the influence on the ocean heat reservoir from atmospheric weather
systems. The model is parametrized by an effective response strength, the
stochastic forcing strength, and the memory exponent. The instrumental global
surface temperature record and the deterministic component of the forcing are
used to estimate these parameters by means of the maximum-likelihood method.
The residual obtained by subtracting the deterministic solution from the
observed record is analyzed as a noise process and shown to be consistent with
a long-memory time-series model and inconsistent with a short-memory model. By
decomposing the forcing record in contributions from solar, volcanic, and
anthropogenic activity one can estimate the contribution of each to 20'th
century global warming. The LRM model is applied with a reconstruction of the
forcing for the last millennium to predict the large-scale features of northern
hemisphere temperature reconstructions, and the analysis of the residual also
clearly favors the LRM model on millennium time scale. The decomposition of the
forcing shows that volcanic aerosols give a considerably greater contribution
to the cooling during the Little Ice Age than the reduction in solar irradiance
associated with the Maunder minimum in solar activity. The LRM model implies a
transient climate response in agreement with IPCC AR4 projections, but the
stronger response on longer time scales suggests to replace the notion of
equilibrium climate sensitivity by a time-scale dependent sensitivity.
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Logo detection from images has many applications, particularly for brand
recognition and intellectual property protection. Most existing studies for
logo recognition and detection are based on small-scale datasets which are not
comprehensive enough when exploring emerging deep learning techniques. In this
paper, we introduce "LOGO-Net", a large-scale logo image database for logo
detection and brand recognition from real-world product images. To facilitate
research, LOGO-Net has two datasets: (i)"logos-18" consists of 18 logo classes,
10 brands, and 16,043 logo objects, and (ii) "logos-160" consists of 160 logo
classes, 100 brands, and 130,608 logo objects. We describe the ideas and
challenges for constructing such a large-scale database. Another key
contribution of this work is to apply emerging deep learning techniques for
logo detection and brand recognition tasks, and conduct extensive experiments
by exploring several state-of-the-art deep region-based convolutional networks
techniques for object detection tasks. The LOGO-net will be released at
http://logo-net.org/
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In 2013, Adams introduced the $n$-crossing number of a knot $K$, denoted by
$c_n(K)$. Inequalities between the $2$-, $3$-, $4$-, and $5$-crossing numbers
have been previously established. We prove $c_9(K)\leq c_3(K)-2$ for all knots
$K$ that are not the trivial, trefoil, or figure-eight knot. We show this
inequality is optimal and obtain previously unknown values of $c_9(K)$. We
generalize this inequality to prove that $c_{13}(K) < c_{5}(K)$ for a certain
set of classes of knots.
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The Euler buckling theorem states that the buckling critical strain is an
inverse square function of the length for a thin plate in the static
compression process. However, the suitability of this theorem in the dynamical
process is unclear, so we perform molecular dynamics simulations to examine the
applicability of the Euler buckling theorem in case of a fast compression of
the single-layer MoS2. We find that the Euler buckling theorem is not
applicable in such dynamical process, as the buckling critical strain becomes a
length-independent constant in the buckled system with many ripples. However,
the Euler buckling theorem can be resumed in this dynamical process after
restricting the theorem to an individual ripple in the buckled structure.
|
We have constructed a theory of dual canonical formalism to study the quantum
competing systems. In such a system, as the relationship between current and
voltage of each, we assumed the duality conditions. We considered competing
system of two types. One type of these system are composed of the sandwich
structure by SC(superconductor)/SI(superinsulator)/SC junction, and its dual
junction is consists of the sandwich structure by SI/SC/SI junction. Another
one type of these system is consists of the sandwich structure by
SC/FM(ferromagnet)/SC junction. and its dual junction is consists of the
sandwich structure by FM/SC/FM junction (spin Josephson junctions). We derived
the relationship between the phase and the number of particles in a dual system
of each other. As an application of the dual competitive systems, we introduced
the quantum spin transistor.
|
Let M be the cotangent bundle of S^2, with the standard symplectic structure.
By adapting an argument of Gromov we determine the weak homotopy type of the
group S of those symplectic automorphisms of M which are trivial at infinity.
It turns out that S is weakly homotopy equivalent to \Z. \pi_0(S) is generated
by the class of the standard "generalized Dehn twist". As a consequence, we
show that there are different connected components of S which lie in the same
connected component of the corresponding group of diffeomorphisms.
|
In this paper, we consider the spatially homogeneous Boltzmann equation
without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy
problem with finite moments of all order acquires the $C^\infty$ regularity in
the velocity variable for the positive time.
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Task parallelism is designed to simplify the task of parallel programming.
When executing a task parallel program on modern NUMA architectures, it can
fail to scale due to the phenomenon called work inflation, where the overall
processing time that multiple cores spend on doing useful work is higher
compared to the time required to do the same amount of work on one core, due to
effects experienced only during parallel executions such as additional cache
misses, remote memory accesses, and memory bandwidth issues. It's possible to
mitigate work inflation by co-locating the computation with the data, but this
is nontrivial to do with task parallel programs. First, by design, the
scheduling for task parallel programs is automated, giving the user little
control over where the computation is performed. Second, the platforms tend to
employ work stealing, which provides strong theoretical guarantees, but its
randomized protocol for load balancing does not discern between work items that
are far away versus ones that are closer. In this work, we propose NUMA-WS, a
NUMA-aware task parallel platform engineering based on the work-first
principle. By abiding by the work-first principle, we are able to obtain a
platform that is work efficient, provides the same theoretical guarantees as
the classic work stealing scheduler, and mitigates work inflation. Furthermore,
we implemented a prototype platform by modifying Intel's Cilk Plus runtime
system and empirically demonstrate that the resulting system is work efficient
and scalable.
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Let $G$ be a finite group acting linearly on $\mathbb{R}^n$. A celebrated
Theorem of Procesi and Schwarz gives an explicit description of the orbit space
$\mathbb{R}^n /\!/G$ as a basic closed semi-algebraic set. We give a new proof
of this statement and another description as a basic closed semi-algebraic set
using elementary tools from real algebraic geometry. Br\"ocker was able to show
that the number of inequalities needed to describe the orbit space generically
depends only on the group $G$. Here, we construct such inequalities explicitly
for abelian groups and in the case where only one inequality is needed.
Furthermore, we answer an open question raised by Br\"ocker concerning the
genericity of his result.
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Message passing graph neural networks (GNNs) are a popular learning
architectures for graph-structured data. However, one problem GNNs experience
is oversquashing, where a GNN has difficulty sending information between
distant nodes. Understanding and mitigating oversquashing has recently received
significant attention from the research community. In this paper, we continue
this line of work by analyzing oversquashing through the lens of the effective
resistance between nodes in the input graph. Effective resistance intuitively
captures the ``strength'' of connection between two nodes by paths in the
graph, and has a rich literature spanning many areas of graph theory. We
propose to use total effective resistance as a bound of the total amount of
oversquashing in a graph and provide theoretical justification for its use. We
further develop an algorithm to identify edges to be added to an input graph to
minimize the total effective resistance, thereby alleviating oversquashing. We
provide empirical evidence of the effectiveness of our total effective
resistance based rewiring strategies for improving the performance of GNNs.
|
We present HST photometry of a selected sample of 50 long-period,
low-extinction Milky Way Cepheids measured on the same WFC3 F555W, F814W, and
F160W-band photometric system as extragalactic Cepheids in SN Ia hosts. These
bright Cepheids were observed with the WFC3 spatial scanning mode in the
optical and near-infrared to mitigate saturation and reduce pixel-to-pixel
calibration errors to reach a mean photometric error of 5 millimags per
observation. We use the new Gaia DR2 parallaxes and HST photometry to
simultaneously constrain the cosmic distance scale and to measure the DR2
parallax zeropoint offset appropriate for Cepheids. We find a value for the
zeropoint offset of -46 +/- 13 muas or +/- 6 muas for a fixed distance scale,
higher than found from quasars, as expected, for these brighter and redder
sources. The precision of the distance scale from DR2 has been reduced by a
factor of 2.5 due to the need to independently determine the parallax offset.
The best fit distance scale is 1.006 +/- 0.033, relative to the scale from
Riess et al 2016 with H0=73.24 km/s/Mpc used to predict the parallaxes
photometrically, and is inconsistent with the scale needed to match the Planck
2016 CMB data combined with LCDM at the 2.9 sigma confidence level (99.6%). At
96.5% confidence we find that the formal DR2 errors may be underestimated as
indicated. We identify additional error associated with the use of augmented
Cepheid samples utilizing ground-based photometry and discuss their likely
origins. Including the DR2 parallaxes with all prior distance ladder data
raises the current tension between the late and early Universe route to the
Hubble constant to 3.8 sigma (99.99 %). With the final expected precision from
Gaia, the sample of 50 Cepheids with HST photometry will limit to 0.5% the
contribution of the first rung of the distance ladder to the uncertainty in the
Hubble constant.
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In this work we generalize the constant-roll condition for minimally coupled
canonical scalar field inflation. Particularly, we shall assume that the scalar
field satisfies the condition $\ddot{\phi}=\alpha (\phi) V'(\phi)$, and we
derive the field equations under this assumption. We call the framework
extended constant-roll framework. Accordingly we calculate the inflationary
indices and the corresponding observational indices of inflation. In order to
demonstrate the inflationary viability, we choose three potentials that are
problematic in the context of slow-roll dynamics, namely chaotic, linear
power-law and exponential inflation, and by choosing a simple power-law form
for the smooth function $\alpha (\phi)$, we show that in the extended
constant-roll framework, the models are compatible with the latest 2018 Planck
constraints on inflation. We also justify appropriately why we called this new
framework extended constant-roll framework, and we show that the condition
$\ddot{\phi}=\alpha (\phi) V'(\phi)$ is equivalent to the condition
$\ddot{\phi}=\beta (\phi) H \dot{\phi}$, with the latter condition being a
simple generalization of the constant-roll condition. Finally, we examine an
interesting physical situation, in which a general extended constant-roll
scalar field model is required to satisfy the cosmological tracker condition
used in quintessence models. In contrast to the slow-roll and ordinary
constant-roll cases, in which case the tracker condition is not compatible with
neither the slow-roll or the ordinary constant-roll conditions, the extended
constant-roll condition can be compatible with the tracker condition. This
feature leads to a new inflationary phenomenological framework, the essential
features of which we develop in brief.
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We study the transient photoluminescence (PL) of photoexcited metals by
solving the Boltzmann equation considering the effects of electron-electron
(e-e) and electron-phonon (e-ph) collisions, where the e-ph coupling function
is calculated from first-principles in order to account for the energy transfer
rate between electrons and phonons accurately. We apply the present scheme to
the transient PL of silver and demonstrate that the agreement between the
theory and experiment is good, where the effect of nonequilibrium electron
distribution is significant to fit the experimental data. The effects of the
nanoscale roughness at metal surfaces and the e-e umklapp scattering on
ultrafast electron dynamics are also discussed.
|
Defects play a key role in the electronic structure of graphene layers flat
or curved. Topological defects in which an hexagon is replaced by an n-sided
polygon generate long range interactions that make them different from
vacancies or other potential defects. In this work we review previous models
for topological defects in graphene. A formalism is proposed to study the
electronic and transport properties of graphene sheets with corrugations as the
one recently synthesized. The formalism is based on coupling the Dirac equation
that models the low energy electronic excitations of clean flat graphene
samples to a curved space. A cosmic string analogy allows to treat an arbitrary
number of topological defects located at arbitrary positions on the graphene
plane. The usual defects that will always be present in any graphene sample as
pentagon-heptagon pairs and Stone-Wales defects are studied as an example. The
local density of states around the defects acquires characteristic modulations
that could be observed in scanning tunnel and transmission electron microscopy.
|
Parametrizing beyond Standard Model physics by the SU(3) x SU(2)_L x U(1)_Y
dimension-six effective Lagrangian, we study the impact of anomalous Higgs
couplings in angular asymmetries of the crossing-symmetric processes H -->
Zl+l- and e+e- --> HZ. In the light of present bounds on d=6 couplings, we show
that some asymmetries can reveal BSM effects that would otherwise be hidden in
other observables. The d=6 HZgamma couplings as well as (to a lesser extent)
HZll contact interactions can generate asymmetries at the several percent
level, albeit having less significant effects on the di-lepton invariant mass
spectrum of the decay H --> Zl+l-. The higher di-lepton invariant mass probed
in e+e- --> HZ can lead to complementary anomalous coupling searches at e+e-
colliders.
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In this note we consider functions with Moebius-periodic rational
coefficients. These functions under some conditions take algebraic values and
can be recovered by theta functions and the Dedekind eta function. Special
cases are the elliptic singular moduli, the Rogers-Ramanujan continued
fraction, Eisenstein series and functions associated with Jacobi symbol
coefficients.
|
We analyze the emission plateaus in the X-ray afterglow lightcurves of
gamma-ray bursts (GRBs) and in the optical lightcurves of Type II superpernovae
(SNe IIP) in order to study whether they have similar late energy injection
behaviors. We show that correlations of bolometric energies (or luminosities)
between the prompt explosions and the plateaus for the two phenomena are
similar. The Type II SNe are in the low energy end of the GRBs. The bolometric
energies (or luminosities) in prompt phase E_{\rm expl} (or L_{\rm expl}) and
in plateau phase E_{\rm plateau} (or L_{\rm plateau}) share relations of E_{\rm
expl} \propto E_{\rm plateau}^{0.73\pm 0.14} and L_{\rm expl} \propto L_{\rm
plateau}^{\sim 0.70}. These results may indicate a similar late energy
injection behavior to reproduce the observed plateaus of the plateaus in the
two phenomena.
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We study the convergence time to equilibrium of the Metropolis dynamics for
the Generalized Random Energy Model with an arbitrary number of hierarchical
levels, a finite and reversible continuous-time Markov process, in terms of the
spectral gap of its transition probability matrix. This is done by deducing
bounds to the inverse of the gap using a Poincar\'e inequality and a path
technique. We also apply convex analysis tools to give the bounds in the most
general case of the model.
|
We consider the {\em Shaped Partition Problem} of partitioning $n$ given
vectors in real $k$-space into $p$ parts so as to maximize an arbitrary
objective function which is convex on the sum of vectors in each part, subject
to arbitrary constraints on the number of elements in each part. In addressing
this problem, we study the {\em Shaped Partition Polytope} defined as the
convex hull of solutions. The Shaped Partition Problem captures ${\cal N}{\cal
P}$-hard problems such as the Max-Cut problem and the Traveling Salesperson
problem, and the Shaped Partition Polytope may have exponentially many vertices
and facets, even when $k$ or $p$ are fixed. In contrast, we show that when both
$k$ and $p$ are fixed, the number of vertices is polynomial in $n$, and all
vertices can be enumerated and the optimization problem solved in strongly
polynomial time. Explicitly, we show that any Shaped Partition Polytope has
$O(n^{k{p\choose 2}})$ vertices which can be enumerated in $O(n^{k^2p^3})$
arithmetic operations, and that any Shaped Partition Problem is solvable in
$O(n^{kp^2})$ arithmetic operations.
|
Digital representations of the real world are being used in many
applications, such as augmented reality. 6G systems will not only support use
cases that rely on virtual worlds but also benefit from their rich contextual
information to improve performance and reduce communication overhead. This
paper focuses on the simulation of 6G systems that rely on a 3D representation
of the environment, as captured by cameras and other sensors. We present new
strategies for obtaining paired MIMO channels and multimodal data. We also
discuss trade-offs between speed and accuracy when generating channels via ray
tracing. We finally provide beam selection simulation results to assess the
proposed methodology.
|
On the basis of recently computed nonlinear convective pulsation models of
Galactic Cepheids, spanning wide ranges of input stellar parameters, we derive
theoretical mass-dependent Period-Wesenheit relations in the Gaia bands, namely
$G$, $G_{BP}$ and $G_{RP}$, that are found to be almost independent of the
assumed efficiency of super-adiabatic convection. The application to a selected
sub-sample of Gaia Data Release 2 Galactic Cepheids database allows us to
derive mass-dependent estimates of their individual distances. By imposing
their match with the astrometric values inferred from Gaia, we are able to
evaluate the individual mass of each pulsator. The inferred mass distribution
is peaked around 5.6$M_{\odot}$ and 5.4$M_{\odot}$ for the F and FO pulsators,
respectively. If the estimated Gaia parallax offset $<\Delta\varpi>$=0.046 mas
is applied to Gaia parallaxes before imposing their coincidence with the
theoretical ones, the inferred mass distribution is found to shift towards
lower masses, namely $\sim$5.2$M_{\odot}$ and 5.1$M_{\odot}$ for the F and FO
pulsators, respectively. The comparison with independent evaluations of the
stellar masses, for a subset of binary Cepheids in our sample, seems to support
the predictive capability of current theoretical scenario. By forcing the
coincidence of our mass determinations with these literature values we derive
an independent estimate of the mean offset to be applied to Gaia DR2
parallaxes, $<\Delta\varpi>$=0.053 $\pm$ 0.029 mas, slightly higher but in
agreement within the errors with Riess2018 value.
|
We analyze the temperature dependence of conductivity in thick granular
ferromagnetic compounds NiSiO2 and in thin weakly coupled films of Fe, Ni and
Py in vicinity of metal-insulator transition. Development of resistivity
minimum followed by a logarithmic variation of conductivity at lower
temperatures is attributed to granular structure of compounds and thin films
fabricated by conventional deposition techniques. Resistivity minimum is
identified as a transition between temperature dependent intra-granular
metallic conductance and thermally activated inter-granular tunneling.
|
Spatial information is essential in various fields. How to explicitly model
according to the spatial location of agents is also very important for the
multi-agent problem, especially when the number of agents is changing and the
scale is enormous. Inspired by the point cloud task in computer vision, we
propose a spatial information extraction structure for multi-agent
reinforcement learning in this paper. Agents can effectively share the
neighborhood and global information through a spatially encoder-decoder
structure. Our method follows the centralized training with decentralized
execution (CTDE) paradigm. In addition, our structure can be applied to various
existing mainstream reinforcement learning algorithms with minor modifications
and can deal with the problem with a variable number of agents. The experiments
in several multi-agent scenarios show that the existing methods can get
convincing results by adding our spatially explicit architecture.
|
We describe how the low-rank structure in an SDP can be exploited to reduce
the per-iteration cost of a convex primal-dual interior-point method down to
$O(n^{3})$ time and $O(n^{2})$ memory, even at very high accuracies. A
traditional difficulty is the dense Newton subproblem at each iteration, which
becomes progressively ill-conditioned as progress is made towards the solution.
Preconditioners have previously been proposed to improve conditioning, but
these can be expensive to set up, and become ineffective as the preconditioner
itself becomes increasingly ill-conditioned at high accuracies. Instead, we
present a \emph{well-conditioned reformulation} of the Newton subproblem that
is cheap to set up, and whose condition number is guaranteed to remain bounded
over all iterations of the interior-point method. In theory, applying an inner
iterative method to the reformulation reduces the per-iteration cost of the
outer interior-point method to $O(n^{3})$ time and $O(n^{2})$ memory. We also
present a \emph{well-conditioned preconditioner} that theoretically increases
the outer per-iteration cost to $O(n^{3}r^{3})$ time and $O(n^{2}r^{2})$
memory, where $r$ is an upper-bound on the solution rank, but in practice
greatly improves the convergence of the inner iterations.
|
Implications of inserting a conformal, monodromy line defect in three
dimensional O($N$) models are studied. We consider then the WF O($N$) model,
and study the two-point Green's function for bulk-local fields found from both
the bulk-defect expansion and Feynman diagrams. This yields the anomalous
dimensions for bulk- and defect-local primaries as well as one of the OPE
coefficients as $\epsilon$-expansions to the first loop order. As a check on
our results, we study the $(\phi^k)^2{\phi}^j$ operator both using the
bulk-defect expansion as well as the equations of motion.
|
In this article, we introduce a novel strategy for robotic exploration in
unknown environments using a semantic topometric map. As it will be presented,
the semantic topometric map is generated by segmenting the grid map of the
currently explored parts of the environment into regions, such as
intersections, pathways, dead-ends, and unexplored frontiers, which constitute
the structural semantics of an environment. The proposed exploration strategy
leverages metric information of the frontier, such as distance and angle to the
frontier, similar to existing frameworks, with the key difference being the
additional utilization of structural semantic information, such as properties
of the intersections leading to frontiers. The algorithm for generating
semantic topometric mapping utilized by the proposed method is lightweight,
resulting in the method's online execution being both rapid and computationally
efficient. Moreover, the proposed framework can be applied to both structured
and unstructured indoor and outdoor environments, which enhances the
versatility of the proposed exploration algorithm. We validate our exploration
strategy and demonstrate the utility of structural semantics in exploration in
two complex indoor environments by utilizing a Turtlebot3 as the robotic agent.
Compared to traditional frontier-based methods, our findings indicate that the
proposed approach leads to faster exploration and requires less computation
time.
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A new method to extract information from the pp data is proposed. The
approach is based on the use of the event structure variables: sphericity and
spherocity, to split the data into enhanced soft and hard processes samples
corresponding to events with large and low numbers of multi-parton
interactions, respectively. The present study was developed in the framework of
Pythia 8.180 for inelastic pp collisions at sqrt(s) =7 TeV. As an application
of the method, a study of the identified particle transverse momentum spectra
and their ratios; is presented for soft (isotropic) and hard (jetty-like)
events. The flow-like effect on these observables due to multi-parton
interactions and color reconnection is relevant for soft events suggesting that
partons inside the jet do not feel color reconnection and its flow-like
consequences.
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We examine the entanglement of general mixed states of a two qubit Heisenberg
XYZ chain in the presence of a magnetic field, and its detection by means of
different criteria. Both the exact separability conditions and the weaker
conditions implied by the disorder and the von Neumann entropic criteria are
analyzed. The ensuing limit temperatures for entanglement in thermal states of
different XYZ models are then examined and compared with the limit temperature
of the symmetry-breaking solution in a mean field type approximation. The
latter, though generally lower, can also be higher than the exact limit
temperature for entanglement in certain cases, indicating that
symmetry-breaking does not necessarily entail entanglement. The reentry of
entanglement for increasing temperatures is also discussed.
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A fuzzy multipreference semantics has been recently proposed for weighted
conditional knowledge bases, and used to develop a logical semantics for
Multilayer Perceptrons, by regarding a deep neural network (after training) as
a weighted conditional knowledge base. This semantics, in its different
variants, suggests some gradual argumentation semantics, which are related to
the family of the gradual semantics studied by Amgoud and Doder. The
relationships between weighted conditional knowledge bases and MLPs extend to
the proposed gradual semantics to capture the stationary states of MPs, in
agreement with previous results on the relationship between argumentation
frameworks and neural networks. The paper also suggests a simple way to extend
the proposed semantics to deal attacks/supports by a boolean combination of
arguments, based on the fuzzy semantics of weighted conditionals, as well as an
approach for defeasible reasoning over a weighted argumentation graph, building
on the proposed gradual semantics.
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We show analytically, numerically, and experimentally that a transversely
stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk
medium. The transverse instability of the soliton is completely eliminated if
it is made sufficiently incoherent along the transverse dimension. We derive a
criterion for the threshold of transverse instability that links the
nonlinearity to the largest transverse correlation distance for which the 1D
soliton is stable
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We study the zero-temperature equation of state (EOS) of solid 4He in the
hexagonal closed packet (hcp) phase over the 0-57 GPa pressure range by means
of the Diffusion Monte Carlo (DMC) method and the semi-empirical Aziz pair
potential HFD-B(HE). In the low pressure regime (P ~ 0-1 GPa) we assess
excellent agreement with experiments and we give an accurate description of the
atomic kinetic energy, Lindemann ratio and Debye temperature over a wide range
of molar volumes (22-6 cm^{3}/mol). However, on moving to higher pressures our
calculated P-V curve presents an increasingly steeper slope which ultimately
provides differences within ~40 % with respect to measurements. In order to
account for many-body interactions arising in the crystal with compression
which are not reproduced by our model, we perform additional electronic
density-functional theory (DFT) calculations for correcting the computed DMC
energies in a perturbative way. We explore both generalized gradient and local
density approximations (GGA and LDA, respectively) for the electronic
exchange-correlation potential. By proceeding in this manner, we show that
discrepancies with respect to high pressure data are reduced to 5-10 % with few
computational extra cost. Further comparison between our calculated EOSs and ab
initio curves deduced for the perfect crystal and corrected for the zero-point
motion of the atoms enforces the reliability of our approach.
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In this paper we prove the well-posedness and we study the asymptotic
behavior of nonoscillatory $L^p$-solutions for a third order nonlinear scalar
differential equation. The equation consists of two parts: a linear third order
with constant coefficients part and a nonlinear part represented by a
polynomial of fourth order in three variables with variable coefficients. The
results are obtained assuming three hypotheses: (i) the characteristic
polynomial associated with the linear part has simple and real roots, (ii) the
coefficients of the polynomial satisfy asymptotic integral smallness
conditions, and (iii) the polynomial coefficients are in $L^p([t_0,\infty[)$.
These results are applied to study a fourth order linear differential equation
of Poincar\'e type and a fourth order linear differential equation with
unbounded coefficients. Moreover, we give some examples where the classical
theorems can not be applied.
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We present a calculation of $H+j$ at NLO including the effect of a finite
top-mass. Where possible we include the complete dependence on $m_t$. This
includes the leading order amplitude, the infrared poles of the two-loop
amplitude and the real radiation amplitude. The remaining finite piece of the
virtual correction is considered in an asymptotic expansion in $m_t$, which is
accurate to $m_t^{-4}$. By successively including more $m_t$-exact pieces, the
dependence on the asymptotic series diminishes and we find convergent behavior
for $p_T^H>m_t$ for the first time. Our results justify rescaling by the
$m_t$-exact LO cross section to model top-mass effects in EFT results up to
$p_T$ of 250 to 300 GeV. We show that the error made by using the LO rescaling
becomes comparable to the NNLO scale uncertainty for such large energies. We
implement our results into the Monte Carlo code MCFM.
|
In this paper we investigate the long-time behavior of the subordination of
the constant speed traveling waves by a general class of kernels. We use the
Feller--Karamata Tauberian theorem in order to study the long-time behavior of
the upper and lower wave. As a result we obtain the long-time behavior for the
propagation of the front of the wave.
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We calculate the rate of two-photon absorption for frequency entangled
photons in a tapered optical fiber whose diameter is comparable to the
wavelength of the light. The confinement of the electric field in the
transverse direction increases the intensity associated with a single photon,
while the two-photon absorption rate is further enhanced by the fact that the
sum of the frequencies of the two photons is on resonance with the upper atomic
state, even though each photon has a relatively broad linewidth. As a result,
the photons are effectively confined in all three dimensions and the two-photon
absorption rate for frequency-entangled photons in a tapered fiber was found to
be comparable to that for unentangled photons in a microcavity with a small
mode volume.
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Spontaneous Rayleigh-Brillouin scattering experiments in air, N2 and O2 have
been performed for a wide range of temperatures and pressures at a wavelength
of 403 nm and at a 90 degrees scattering angle. Measurements of the
Rayleigh-Brillouin spectral scattering profile were conducted at high
signal-to-noise ratio for all three species, yielding high-quality spectra
unambiguously showing the small differences between scattering in air, and its
constituents N2 and O2. Comparison of the experimental spectra with
calculations using the Tenti S6 model, developed in 1970s based on linearized
kinetic equations for molecular gases, demonstrates that this model is valid to
high accuracy. After previous measurements performed at 366 nm, the Tenti S6
model is here verified for a second wavelength of 403 nm. Values for the bulk
viscosity for the gases are derived by optimizing the model to the
measurements. It is verified that the bulk viscosity parameters obtained from
previous experiments at 366 nm, are valid for wavelengths of 403 nm. Also for
air, which is treated as a single-component gas with effective gas transport
coefficients, the Tenti S6 treatment is validated for 403 nm as for the
previously used wavelength of 366 nm, yielding an accurate model description of
the scattering profiles for a range of temperatures and pressures, including
those of relevance for atmospheric studies. It is concluded that the Tenti S6
model, further verified in the present study, is applicable to LIDAR
applications for exploring the wind velocity and the temperature profile
distributions of the Earth's atmosphere. Based on the present findings,
predictions can be made on the spectral profiles for a typical LIDAR
backscatter geometry, which deviate by some 7 percent from purely Gaussian
profiles at realistic sub-atmospheric pressures occurring at 3-5 km altitude in
the Earth's atmosphere.
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We obtain solutions of the three dimensional Dirac equation for radial
power-law potentials at rest mass energy as an infinite series of square
integrable functions. These are written in terms of the confluent
hypergeometric function and chosen such that the matrix representation of the
Dirac operator is tridiagonal. The "wave equation" results in a three-term
recursion relation for the expansion coefficients of the spinor wavefunction
which is solved in terms of orthogonal polynomials. These are modified versions
of the Meixner-Pollaczek polynomials and of the continuous dual Hahn
polynomials. The choice depends on the values of the angular momentum and the
power of the potential.
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We review previously published and newly obtained crater size-frequency
distributions in the inner solar system. These data indicate that the Moon and
the terrestrial planets have been bombarded by two populations of objects.
Population 1, dominating at early times, had nearly the same size distribution
as the present-day asteroid belt, and produced the heavily cratered surfaces
with a complex, multi-sloped crater size-frequency distribution. Population 2,
dominating since about 3.8-3.7 Ga, has the same size distribution as near-Earth
objects (NEOs), had a much lower impact flux, and produced a crater size
distribution characterized by a differential -3 single-slope power law in the
crater diameter range 0.02 km to 100 km. Taken together with the results from a
large body of work on age-dating of lunar and meteorite samples and theoretical
work in solar system dynamics, a plausible interpretation of these data is as
follows. The NEO population is the source of Population 2 and it has been in
near-steady state over the past ~3.7-3.8 gigayears; these objects are derived
from the main asteroid belt by size-dependent non-gravitational effects that
favor the ejection of smaller asteroids. However, Population 1 were main belt
asteroids ejected from their source region in a size-independent manner,
possibly by means of gravitational resonance sweeping during giant planet orbit
migration; this caused the so-called Late Heavy Bombardment (LHB). The LHB
began some time before ~3.9 Ga, peaked and declined rapidly over the next ~100
to 300 megayears, and possibly more slowly from about 3.8-3.7 Ga to ~2 Ga. A
third crater population (Population S) consists of secondary impact craters
that can dominate the cratering record at small diameters.
|
This is a contribution to the ICM 2002. We explain the relation between the
(equivariant) Bloch-Kato conjecture for special values of L-functions and the
Main Conjecture of (non-abelian) Iwasawa theory. On the way we will discuss
briefly the case of Dirichlet characters in the abelian case. We will also
discuss how "twisting" in the non-abelian case would allow to reduce the
general conjecture to the case of number fields. This is one the main
motivations for a non-abelian Main Conjecture.
|
The integration of individual microgrids (MGs) into Microgrid Clusters (MGCs)
significantly improves the reliability and flexibility of energy supply,
through resource sharing and ensuring backup during outages. The dispatch of
MGCs is the key challenge to be tackled to ensure their secure and economic
operation. Currently, there is a lack of optimization method that can achieve a
trade-off among top-priority requirements of MGCs' dispatch, including fast
computation speed, optimality, multiple objectives, and risk mitigation against
uncertainty. In this paper, a novel Multi-Objective, Risk-Sensitive, and Online
Trust Region Policy Optimization (RS-TRPO) Algorithm is proposed to tackle this
problem. First, a dispatch paradigm for autonomous MGs in the MGC is proposed,
enabling them sequentially implement their self-dispatch to mitigate potential
conflicts. This dispatch paradigm is then formulated as a Markov Game model,
which is finally solved by the RS-TRPO algorithm. This online algorithm enables
MGs to spontaneously search for the Pareto Frontier considering multiple
objectives and risk mitigation. The outstanding computational performance of
this algorithm is demonstrated in comparison with mathematical programming
methods and heuristic algorithms in a modified IEEE 30-Bus Test System
integrated with four autonomous MGs.
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The CPT theorem originally proven by L\"uders and Pauli ensures the equality
of masses, lifetimes, magnetic moments and cross sections of any particle and
its antiparticle. We show that in a Lorentz invariant quantum field theory
described by its Lagrangian, CPT-violating interaction alone does not split the
masses of an elementary particle and its antiparticle but breaks only the
equality of lifetimes, magnetic moments and cross sections. However, CPT
violation in the mass term of a field in the Lagrangian, which can be
attributed to be due to the size of the particle described by a form factor,
breaks only the equality of masses. Also it is shown that the two separate
effects of CPT violation in the interaction terms or in the mass term do not
mix due to higher quantum corrections and remain distinguishable. Thus, we urge
the experimentalists to search for such observable effects concerning
differences in the masses, magnetic moments, lifetimes and cross sections
between the elementary or bound state particles and their antiparticles. In the
case of CPT violation only in the mass term, besides the difference in the
masses of elementary bound state particles and their antiparticles, there will
be also an extremely tiny difference in the lifetimes of bound states due to
the difference in their phase spaces. From the details of calculations, it
appears that the separate effects of the CPT violation described above are
quite general, neither depending on how the nonlocality is achieved, nor
depending on what this violation is due to: due to T violation, as considered
in the present work, which can be attributed to a cosmological direction of
time; to CP or to both T and CP violations. The latter two cases satisfy the
Sakharov's conditions for explaining the baryon asymmetry in the Universe.
|
Generative Artificial Intelligence (AI) has shown tremendous prospects in all
aspects of technology, including design. However, due to its heavy demand on
resources, it is usually trained on large computing infrastructure and often
made available as a cloud-based service. In this position paper, we consider
the potential, challenges, and promising approaches for generative AI for
design on the edge, i.e., in resource-constrained settings where memory,
compute, energy (battery) and network connectivity may be limited. Adapting
generative AI for such settings involves overcoming significant hurdles,
primarily in how to streamline complex models to function efficiently in
low-resource environments. This necessitates innovative approaches in model
compression, efficient algorithmic design, and perhaps even leveraging edge
computing. The objective is to harness the power of generative AI in creating
bespoke solutions for design problems, such as medical interventions, farm
equipment maintenance, and educational material design, tailored to the unique
constraints and needs of remote areas. These efforts could democratize access
to advanced technology and foster sustainable development, ensuring universal
accessibility and environmental consideration of AI-driven design benefits.
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The Equation of State (EOS) of dense strongly-interacting matter can be
probed by astrophysical observations of neutron stars (NS), such as X-ray
detections of pulsars or the measurement of the tidal deformability of NSs
during the inspiral stage of NS mergers. These observations constrain the EOS
at most up to the density of the maximum-mass configuration, $n_\textrm{TOV}$,
which is the highest density that can be explored by stable NSs for a given
EOS. However, under the right circumstances, binary neutron star (BNS) mergers
can create a postmerger remnant that explores densities above $n_\textrm{TOV}$.
In this work, we explore whether the EOS above $n_\textrm{TOV}$ can be measured
from gravitational-wave or electromagnetic observations of the postmerger
remnant. We perform a total of twenty-five numerical-relativity simulations of
BNS mergers for a range of EOSs and find no case in which different
descriptions of the matter above $n_{\rm TOV}$ have a detectable impact on
postmerger observables. Hence, we conclude that the EOS above $n_\textrm{TOV}$
can likely not be probed through BNS merger observations for the current and
next generation of detectors.
|
Numerical models are starting to be used for determining the future behaviour
of seismic faults and fault networks. Their final goal would be to forecast
future large earthquakes. In order to use them for this task, it is necessary
to synchronize each model with the current status of the actual fault or fault
network it simulates (just as, for example, meteorologists synchronize their
models with the atmosphere by incorporating current atmospheric data in them).
However, lithospheric dynamics is largely unobservable: important parameters
cannot (or can rarely) be measured in Nature. Earthquakes, though, provide
indirect but measurable clues of the stress and strain status in the
lithosphere, which should be helpful for the synchronization of the models. The
rupture area is one of the measurable parameters of earthquakes. Here we
explore how it can be used to at least synchronize fault models between
themselves and forecast synthetic earthquakes. Our purpose here is to forecast
synthetic earthquakes in a simple but stochastic (random) fault model. By
imposing the rupture area of the synthetic earthquakes of this model on other
models, the latter become partially synchronized with the first one. We use
these partially synchronized models to successfully forecast most of the
largest earthquakes generated by the first model. This forecasting strategy
outperforms others that only take into account the earthquake series. Our
results suggest that probably a good way to synchronize more detailed models
with real faults is to force them to reproduce the sequence of previous
earthquake ruptures on the faults. This hypothesis could be tested in the
future with more detailed models and actual seismic data.
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Residual motion of the arm cavity mirrors is expected to prove one of the
principal impediments to systematic lock acquisition in advanced
gravitational-wave interferometers. We present a technique which overcomes this
problem by employing auxiliary lasers at twice the fundamental measurement
frequency to pre-stabilise the arm cavities' lengths. Applying this approach,
we reduce the apparent length noise of a 1.3 m long, independently suspended
Fabry-Perot cavity to 30 pm rms and successfully transfer longitudinal control
of the system from the auxiliary laser to the measurement laser.
|
We consider mass concentration properties of Laplace eigenfunctions
$\varphi_\lambda$, that is, smooth functions satisfying the equation $-\Delta
\varphi_\lambda = \lambda \varphi_\lambda$, on a smooth closed Riemannian
manifold. Using a heat diffusion technique, we first discuss mass
concentration/localization properties of eigenfunctions around their nodal
sets. Second, we discuss the problem of avoided crossings and (non)existence of
nodal domains which continue to be thin over relatively long distances.
Further, using the above techniques, we discuss the decay of Laplace
eigenfunctions on Euclidean domains which have a central "thick" part and
"thin" elongated branches representing tunnels of sub-wavelength opening.
Finally, in an Appendix, we record some new observations regarding sub-level
sets of the eigenfunctions and interactions of different level sets.
|
Humans perceive and construct the world as an arrangement of simple
parametric models. In particular, we can often describe man-made environments
using volumetric primitives such as cuboids or cylinders. Inferring these
primitives is important for attaining high-level, abstract scene descriptions.
Previous approaches for primitive-based abstraction estimate shape parameters
directly and are only able to reproduce simple objects. In contrast, we propose
a robust estimator for primitive fitting, which meaningfully abstracts complex
real-world environments using cuboids. A RANSAC estimator guided by a neural
network fits these primitives to a depth map. We condition the network on
previously detected parts of the scene, parsing it one-by-one. To obtain
cuboids from single RGB images, we additionally optimise a depth estimation CNN
end-to-end. Naively minimising point-to-primitive distances leads to large or
spurious cuboids occluding parts of the scene. We thus propose an improved
occlusion-aware distance metric correctly handling opaque scenes. Furthermore,
we present a neural network based cuboid solver which provides more
parsimonious scene abstractions while also reducing inference time. The
proposed algorithm does not require labour-intensive labels, such as cuboid
annotations, for training. Results on the NYU Depth v2 dataset demonstrate that
the proposed algorithm successfully abstracts cluttered real-world 3D scene
layouts.
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We analyze the possible interaction-induced superconducting instabilities in
noncentrosymmetric systems based on symmetries of the normal state. It is
proven that pure electron-phonon coupling will always lead to a fully gapped
superconductor that does not break time-reversal symmetry and is topologically
trivial. We show that topologically nontrivial behavior can be induced by
magnetic doping without gapping out the resulting Kramers pair of Majorana edge
modes. In case of superconductivity arising from the particle-hole fluctuations
associated with a competing instability, the properties of the condensate
crucially depend on the time-reversal behavior of the order parameter of the
competing instability. When the order parameter preserves time-reversal
symmetry, we obtain exactly the same properties as in case of phonons. If it is
odd under time-reversal, the Cooper channel of the interaction will be fully
repulsive leading to sign changes of the gap and making spontaneous
time-reversal symmetry breaking possible. To discuss topological properties, we
focus on fully gapped time-reversal symmetric superconductors and derive
constraints on possible pairing states that yield necessary conditions for the
emergence of topologically nontrivial superconductivity. These conditions might
serve as a tool in the search for topological superconductors. We also discuss
implications for oxides heterostructures and single-layer FeSe.
|
The computational complexity of the partition, 0-1 subset sum, unbounded
subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple
variants were studied in numerous papers in the past where all the weights and
profits were assumed to be integers. We re-examine here the computational
complexity of all these problems in the setting where the weights and profits
are allowed to be any rational numbers. We show that all of these problems in
this setting become strongly NP-complete and, as a result, no pseudo-polynomial
algorithm can exist for solving them unless P=NP. Despite this result we show
that they all still admit a fully polynomial-time approximation scheme.
|
On the basis of the quantum q-oscillator algebra in the framework of quantum
groups and non-commutative q-differential calculus, we investigate a possible
q-deformation of the classical Poisson bracket in order to extend a generalized
q-deformed dynamics in the classical regime. In this framework, classical
q-deformed kinetic equations, Kramers and Fokker-Planck equations, are also
studied.
Pacs: 05.20.Dd, 45.20.-d, 02.20.Uw
Keywords: Kinetic theory, q-deformed classical mechanics, quantum groups,
quantum algebras
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We present a model for microwave photoconductivity in two-dimensional
electron systems (2DESs) in a magnetic field at the microwave frequencies lower
that the electron cyclotron frequency when the intra-Landau level (LL)
transitions dominate. Using this model, we explain the effect of decrease in
the 2DES dissipative conductivity (and resistivity) and smearing of its
Shubnikov -- de Haas oscillations by microwave radiation observed recently
\cite{1,2}. The model invokes the concept of suppression of elastic impurity
scattering of electrons by the microwave electric field. We calculated the
dependence of the 2DES conductivity associated with intra-LL transitions as a
function of the radiation and cyclotron frequencies and microwave power. The
obtained dependences are consistent with the results of recent experimental
observations \cite{1,2}.
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In this paper, we deal with a singular quasilinear critical elliptic equation
of Lichnerowicz type involving the p-Laplacian operator. With the help of the
subcritical approach from variational method, we obtain the non-existence,
existence, and multiplicity results under some given assumptions.
|
This paper presents a model of NAND flash SSD utilization and write
amplification when the ATA/ATAPI SSD Trim command is incorporated into
object-based storage under a variety of user workloads, including a uniform
random workload with objects of fixed size and a uniform random workload with
objects of varying sizes. We first summarize the existing models for write
amplification in SSDs for workloads with and without the Trim command, then
propose an alteration of the models that utilizes a framework of object-based
storage. The utilization of objects and pages in the SSD is derived, with the
analytic results compared to simulation. Finally, the effect of objects on
write amplification and its computation is discussed along with a potential
application to optimization of SSD usage through object storage metadata
servers that allocate object classes of distinct object size.
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Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.