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Let T be an involution of the finite dimensional complex reductive Lie
algebra g and g=k+p be the associated Cartan decomposition. Denote by K the
adjoint group of k.
The K-module p is the union of the subsets p^{(m)}={x | dim K.x =m}, indexed
by integers m, and the K-sheets of (g,T) are the irreducible components of the
p^{(m)}. The sheets can be, in turn, written as a union of so-called Jordan
K-classes.
We introduce conditions in order to describe the sheets and Jordan K-classes
in terms of Slodowy slices. When g is of classical type, the K-sheets are shown
to be smooth; if g=gl_N a complete description of sheets and Jordan K-classes
is then obtained.
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We show how the semiclassical Langevin method can be extended to calculations
of higher-than-second cumulants of noise. These cumulants are affected by
indirect correlations between the fluctuations, which may be considered as
"noise of noise." We formulate simple diagrammatic rules for calculating the
higher cumulants and apply them to mesoscopic diffusive contacts and chaotic
cavities. As one of the application of the method, we analyze the frequency
dependence of the third cumulant of current in these systems and show that it
contains additional peculiarities as compared to the second cumulant. The
effects of environmental feedback in measurements of the third cumulant are
also discussed in terms of this method.
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This paper proposes high-order accurate well-balanced (WB) energy stable (ES)
adaptive moving mesh finite difference schemes for the shallow water equations
(SWEs) with non-flat bottom topography. To enable the construction of the ES
schemes on moving meshes, a reformulation of the SWEs is introduced, with the
bottom topography as an additional conservative variable that evolves in time.
The corresponding energy inequality is derived based on a modified energy
function, then the reformulated SWEs and energy inequality are transformed into
curvilinear coordinates. A two-point energy conservative (EC) flux is
constructed, and high-order EC schemes based on such a flux are proved to be WB
that they preserve the lake at rest. Then high-order ES schemes are derived by
adding suitable dissipation terms to the EC schemes, which are newly designed
to maintain the WB and ES properties simultaneously. The adaptive moving mesh
strategy is performed by iteratively solving the Euler-Lagrangian equations of
a mesh adaptation functional. The fully-discrete schemes are obtained by using
the explicit strong-stability preserving third-order Runge-Kutta method.
Several numerical tests are conducted to validate the accuracy, WB and ES
properties, shock-capturing ability, and high efficiency of the schemes.
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Deep reinforcement learning (DRL) has revolutionized learning and actuation
in applications such as game playing and robotic control. The cost of data
collection, i.e., generating transitions from agent-environment interactions,
remains a major challenge for wider DRL adoption in complex real-world
problems. Following a cloud-native paradigm to train DRL agents on a GPU cloud
platform is a promising solution. In this paper, we present a scalable and
elastic library ElegantRL-podracer for cloud-native deep reinforcement
learning, which efficiently supports millions of GPU cores to carry out
massively parallel training at multiple levels. At a high-level,
ElegantRL-podracer employs a tournament-based ensemble scheme to orchestrate
the training process on hundreds or even thousands of GPUs, scheduling the
interactions between a leaderboard and a training pool with hundreds of pods.
At a low-level, each pod simulates agent-environment interactions in parallel
by fully utilizing nearly 7,000 GPU CUDA cores in a single GPU. Our
ElegantRL-podracer library features high scalability, elasticity and
accessibility by following the development principles of containerization,
microservices and MLOps. Using an NVIDIA DGX SuperPOD cloud, we conduct
extensive experiments on various tasks in locomotion and stock trading and show
that ElegantRL-podracer substantially outperforms RLlib. Our codes are
available on GitHub.
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In this study, we reveal noncontact frictional forces between surfaces in the
presence of peristaltic permittivity modulation. Our setup comprises a
conducting medium, an air gap, and a dielectric substrate on which we have a
space-time-modulated grating that emits electromagnetic radiation. The
radiation receives energy and momentum from the grating, which is eventually
absorbed by the conducting medium or propagates away from the grating on the
dielectric side, resulting in electromagnetic power loss and lateral forces at
the surfaces.
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ROSAT observations of the Vela pulsar and its surroundings revealed a
collimated X-ray feature almost 45' in length (Markwardt & Ogelman 1995),
interpreted as the signature ``cocoon'' of a one-sided jet from the Vela
pulsar. We report on a new ASCA observation of the Vela pulsar jet at its head,
the point where the jet is believed to interact with the supernova remnant. The
head is clearly detected, and its X-ray spectrum is remarkably similar to the
surrounding supernova remnant spectrum, extending to X-ray energies of at least
7 keV. A ROSAT+ASCA spectrum can be fit by two-component emission models but
not standard one-component models. The lower energy component is thermal and
has a temperature of 0.29+/-0.03 keV (1 sigma); the higher energy component can
be fit by either a thermal component of temperature ~4 keV or a power law with
photon index ~2.0. Compared to the ROSAT-only results, the mechanical
properties of the jet and its cocoon do not change much. If the observed
spectrum is that of a hot jet cocoon, then the speed of the jet is at least 800
km s^-1, depending on the angle of inclination. The mechanical power driving
the jet is >10^36 erg s^-1, and the mass flow rate at the head is > 10^-6 M_sun
yr^-1. We conclude that the jet must be entraining material all along its
length in order to generate such a large mass flow rate. We also explore the
possibility that the cocoon emission is synchrotron radiation instead of
thermal.
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Conical functions appear in a large number of applications in physics and
engineering. In this paper we describe an extension of our module CONICAL for
the computation of conical functions. Specifically, the module includes now a
routine for computing the function ${{\rm R}}^{m}_{-\frac{1}{2}+i\tau}(x)$, a
real-valued numerically satisfactory companion of the function ${\rm
P}^m_{-\tfrac12+i\tau}(x)$ for $x>1$. In this way, a natural basis for solving
Dirichlet problems bounded by conical domains is provided.
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The representation of the approximate posterior is a critical aspect of
effective variational autoencoders (VAEs). Poor choices for the approximate
posterior have a detrimental impact on the generative performance of VAEs due
to the mismatch with the true posterior. We extend the class of posterior
models that may be learned by using undirected graphical models. We develop an
efficient method to train undirected approximate posteriors by showing that the
gradient of the training objective with respect to the parameters of the
undirected posterior can be computed by backpropagation through Markov chain
Monte Carlo updates. We apply these gradient estimators for training discrete
VAEs with Boltzmann machines as approximate posteriors and demonstrate that
undirected models outperform previous results obtained using directed graphical
models. Our implementation is available at https://github.com/QuadrantAI/dvaess .
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Nowadays, it's a very significant way for researchers and other individuals
to achieve their interests because it provides short solutions to satisfy their
demands. Because there are so many pieces of information on the internet, news
recommendation systems allow us to filter content and deliver it to the user in
proportion to his desires and interests. RSs have three techniques:
content-based filtering, collaborative filtering, and hybrid filtering. We will
use the MIND dataset with our system, which was collected in 2019, the big
challenge in this dataset because there is a lot of ambiguity and complex text
processing. In this paper, will present our proposed recommendation system. The
core of our system we have used the GloVe algorithm for word embeddings and
representation. Besides, the Multi-head Attention Layer calculates the
attention of words, to generate a list of recommended news. Finally, we achieve
good results more than some other related works in AUC 71.211, MRR 35.72,
nDCG@5 38.05, and nDCG@10 44.45.
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We give a bound on the number of isolated, essential singularities of
determinantal quartic surfaces in 3-space. We also provide examples of
different configurations of real singularities on quartic surfaces with a
definite Hermitian determinantal representation, and conjecture an extension of
a theorem by Degtyarev and Itenberg.
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Forensic audio analysis for speaker verification offers unique challenges due
to location/scenario uncertainty and diversity mismatch between reference and
naturalistic field recordings. The lack of real naturalistic forensic audio
corpora with ground-truth speaker identity represents a major challenge in this
field. It is also difficult to directly employ small-scale domain-specific data
to train complex neural network architectures due to domain mismatch and loss
in performance. Alternatively, cross-domain speaker verification for multiple
acoustic environments is a challenging task which could advance research in
audio forensics. In this study, we introduce a CRSS-Forensics audio dataset
collected in multiple acoustic environments. We pre-train a CNN-based network
using the VoxCeleb data, followed by an approach which fine-tunes part of the
high-level network layers with clean speech from CRSS-Forensics. Based on this
fine-tuned model, we align domain-specific distributions in the embedding space
with the discrepancy loss and maximum mean discrepancy (MMD). This maintains
effective performance on the clean set, while simultaneously generalizes the
model to other acoustic domains. From the results, we demonstrate that diverse
acoustic environments affect the speaker verification performance, and that our
proposed approach of cross-domain adaptation can significantly improve the
results in this scenario.
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Stacking interactions in single stranded nucleic acids give rise to
configurations of an annealed rod-coil multiblock copolymer. Theoretical
analysis identifies the resulting signatures for long homopolynucleotides: A
non monotonous dependence of size on temperature, corresponding effects on
cyclization and a plateau in the extension force law. Explicit numerical
results for poly(dA) and poly(rU) are presented.
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The online optimization problem with non-convex loss functions over a closed
convex set, coupled with a set of inequality (possibly non-convex) constraints
is a challenging online learning problem. A proximal method of multipliers with
quadratic approximations (named as OPMM) is presented to solve this online
non-convex optimization with long term constraints.
Regrets of the violation of Karush-Kuhn-Tucker conditions of OPMM for solving
online non-convex optimization problems are analyzed. Under mild conditions, it
is shown that this algorithm exhibits ${\cO}(T^{-1/8})$ Lagrangian gradient
violation regret, ${\cO}(T^{-1/8})$ constraint violation regret and
${\cO}(T^{-1/4})$ complementarity residual regret if parameters in the
algorithm are properly chosen, where $T$ denotes the number of time periods.
For the case that the objective is a convex quadratic function, we demonstrate
that the regret of the objective reduction can be established even the feasible
set is non-convex. For the case when the constraint functions are convex, if
the solution of the subproblem in OPMM is obtained by solving its dual, OPMM is
proved to be an implementable projection method for solving the online
non-convex optimization problem.
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I will review the latest results for the presence of diffuse light in the
nearby universe and at intermediate redshift, and then discuss the latest
results from hydrodynamical cosmological simulations of cluster formation on
the expected properties of diffuse light in clusters. I shall present how
intracluster planetary nebulae (ICPNe) can be used as excellent tracers of the
diffuse stellar population in nearby clusters, and how their number density
profile and radial velocity distribution can provide an observational test for
models of cluster formation. The preliminary comparison of available ICPN
samples with predictions from cosmological simulations support late infall as
the most likely mechanism for the origin of diffuse stellar light in clusters.
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This work was inspired by the article of Parkhomenko, who drew attention to
the central role played in the work of Spindel, Sevrin, Troust and van Proyen,
by Manin triples. These authors have shown how to associate to a Manin triple
an $N=2$ superconformal field theory (the work of Kazama-Suzuki is a special
case of their results). In this paper, we construct a deformation of their
theory, with continuously varying central charge, analogous to the Fock
representations of the Virasoro algebra with stress-energy tensor
$-(\phi')^2/2+\alpha\phi''$.
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In Euclidean space of dimension 2 or 3, we study a minimum time problem
associated with a system of real-analytic vector fields satisfying
H\"ormander's bracket generating condition, where the target is a nonempty
closed set. We show that, in dimension 2, the minimum time function is locally
Lipschitz continuous while, in dimension 3, it is Lipschitz continuous in the
complement of a set of measure zero. In particular, in both cases, the minimum
time function is a.e. differentiable on the complement of the target. In
dimension 3, in general, there is no hope to have the same regularity result as
in dimension 2. Indeed, examples are known where the minimum time function
fails to be locally Lipschitz continuous.
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A long-term numerical integration of the classical Newtonian approximation to
the planetary orbital motions of the full Solar System (sun + 8 planets),
spanning 20 Gyr, was performed. The results showed no severe instability
arising over this time interval. Subsequently, utilizing a bifurcation method
described by Jacques Laskar, two numerical experiments were performed with the
goal of determining dynamically allowed evolutions for the Solar System in
which the planetary orbits become unstable. The experiments yielded one
evolution in which Mercury falls onto the Sun at ~1.261Gyr from now, and
another in which Mercury and Venus collide in ~862Myr. In the latter solution,
as a result of Mercury's unstable behavior, Mars was ejected from the Solar
System at ~822Myr. We have performed a number of numerical tests that confirm
these results, and indicate that they are not numerical artifacts. Using
synthetic secular perturbation theory, we find that Mercury is destabilized via
an entrance into a linear secular resonance with Jupiter in which their
corresponding eigenfrequencies experience extended periods of commensurability.
The effects of general relativity on the dynamical stability are discussed. An
application of the bifurcation method to the outer Solar System (Jupiter,
Saturn, Uranus, and Neptune) showed no sign of instability during the course of
24Gyr of integrations, in keeping with an expected Uranian dynamical lifetime
of 10^(18) years.
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In a recent paper Petrov and Pohoata developed a new algebraic method which
combines the Croot-Lev-Pach Lemma from additive combinatorics and Sylvester's
Law of Inertia for real quadratic forms. As an application, they gave a simple
proof of the Bannai-Bannai-Stanton bound on the size of $s$-distance sets
(subsets $\mbox{$\cal A$}\subseteq {\mathbb R}^n$ which determine at most $s$
different distances). In this paper we extend their work and prove upper bounds
for the size of $s$-distance sets in various real algebraic sets. This way we
obtain a novel and short proof for the bound of Delsarte-Goethals-Seidel on
spherical $s$-distance sets and a generalization of a bound by
Bannai-Kawasaki-Nitamizu-Sato on $s$-distance sets on unions of spheres. In our
arguments we use the method of Petrov and Pohoata together with some Gr\"obner
basis techniques.
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Most of the learning-based algorithms for bitrate adaptation are limited to
offline learning, which inevitably suffers from the simulation-to-reality gap.
Online learning can better adapt to dynamic real-time communication scenes but
still face the challenge of lengthy training convergence time. In this paper,
we propose a novel online grouped federated transfer learning framework named
Bamboo to accelerate training efficiency. The preliminary experiments validate
that our method remarkably improves online training efficiency by up to 302%
compared to other reinforcement learning algorithms in various network
conditions while ensuring the quality of experience (QoE) of real-time video
communication.
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Recent SPS data on the rapidity distribution of protons in p+S, p+Au and S+S
collisions at 200 AGeV and preliminary Pb+Pb collisions at 160 AGeV are
compared to HIJING and VENUS calculations as well as to predictions based on
the Multi-Chain Model (MCM). The preliminary Pb data suggest that a linear
dependence of the proton rapidity shift as a function of the nuclear thickness,
as first observed in p+A reactions, may apply up to Pb+Pb reactions. The
observed rapidity dependence of produced hyperons in both p+A and A+A reactions
however cannot be explained in terms of such models without introducing
additional non-linear effects.
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Polar codes are a class of channel capacity achieving codes that has been
selected for the next generation of wireless communication standards.
Successive-cancellation (SC) is the first proposed decoding algorithm,
suffering from mediocre error-correction performance at moderate code length.
In order to improve the error-correction performance of SC, two approaches are
available: (i) SC-List decoding which keeps a list of candidates by running a
number of SC decoders in parallel, thus increasing the implementation
complexity, and (ii) SC-Flip decoding that relies on a single SC module, and
keeps the computational complexity close to SC. In this work, we propose the
partitioned SC-Flip (PSCF) decoding algorithm, which outperforms SC-Flip in
terms of error-correction performance and average computational complexity,
leading to higher throughput and reduced energy consumption per codeword. We
also introduce a partitioning scheme that best suits our PSCF decoder.
Simulation results show that at equivalent frame error rate, PSCF has up to $5
\times$ less computational complexity than the SC-Flip decoder. At equivalent
average number of iterations, the error-correction performance of PSCF
outperforms SC-Flip by up to $0.15$ dB at frame error rate of $10^{-3}$.
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We study, within the fluctuation exchange approximation, the
spin-fluctuation-mediated superconductivity in Hubbard-type models possessing
electron and hole bands, and compare them with a model on a square lattice with
a large Fermi surface. In the square lattice model, superconductivity is more
enhanced for better nesting for a fixed band filling. By contrast, in the
models with electron and hole bands, superconductivity is optimized when the
Fermi surface nesting is degraded to some extent, where finite energy spin
fluctuation around the nesting vector develops. The difference lies in the
robustness of the nesting vector, namely, in models with electron and hole
bands, the wave vector at which the spin susceptibility is maximized is fixed
even when the nesting is degraded, whereas when the Fermi surface is large, the
nesting vector varies with the deformation of the Fermi surface. We also
discuss the possibility of realizing in actual materials the bilayer Hubbard
model, which is a simple model with electron and hole bands, and is expected to
have a very high T_c.
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The observed correlation between global low cloud amount and the flux of high
energy cosmic rays supports the idea that ionization plays a crucial role in
tropospheric cloud formation. We explore this idea quantitatively with a simple
model linking the concentration of cloud condensation nuclei to the varying
ionization rate due to cosmic rays. Among the predictions of the model is a
variation in global cloud optical thickness, or opacity, with cosmic-ray rate.
Using the International Satellite Cloud Climatology Project database
(1983-1999), we search for variations in the yearly mean visible cloud opacity
and visible cloud amount due to cosmic rays. After separating out temporal
variations in the data due to the Mt. Pinatubo eruption and El Nino/Southern
Oscillation, we identify systematic variations in opacity and cloud amount due
to cosmic rays. We find that the fractional amplitude of the opacity variations
due to cosmic rays increases with cloud altitude, becoming approximately zero
or negative (inverse correlation) for low clouds. Conversely, the fractional
changes in visible cloud amount due to cosmic rays are only
positively-correlated for low clouds and become negative or zero for the higher
clouds. The opacity trends suggest behavior contrary to the current predictions
of ion-mediated nucleation (IMN) models, but more accurate temporal modeling of
the ISCCP data is needed before definitive conclusions can be drawn.
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Screened modified gravity (SMG) is a kind of scalar-tensor theories with
screening mechanisms, which can generate screening effect to suppress the fifth
force in high density environments and pass the solar system tests. Meanwhile,
the potential of scalar field in the theories can drive the acceleration of the
late universe. In this paper, we calculate the parameterized post-Newtonian
(PPN) parameters $\gamma$ and $\beta$, the effective gravitational constant
$G_{\rm eff}$ and the effective cosmological constant $\Lambda$ for SMG with a
general potential $V$ and coupling function $A$. The dependence of these
parameters on the model parameters of SMG and/or the physical properties of the
source object are clearly presented. As an application of these results, we
focus on three specific theories of SMG (chameleon, symmetron and dilaton
models). Using the formulae to calculate their PPN parameters and cosmological
constant, we derive the constraints on the model parameters by combining the
observations on solar system and cosmological scales.
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Several properties of bound states in potential $ V(x)= g^2\exp (|x|)$ are
studied. Firstly, with the emphasis on the reliability of our
arbitrary-precision construction, wave functions are considered in the two
alternative (viz., asymptotically decreasing or regular) exact Bessel-function
forms which obey the asymptotic or matching conditions, respectively. The
merits of the resulting complementary transcendental secular equation
approaches are compared and their applicability is discussed.
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We analyze the neutrino conversions inside a supernova in the 3$\nu$ mixing
scheme, and their effects on the neutrino spectra observed at the earth. We
find that the observations of the energy spectra of neutrinos from a future
galactic supernova may enable us to identify the solar neutrino solution, to
determine the sign of $\Delta m^2_{32}$, and to probe the mixing matrix element
|U_{e3}|^2 to values as low as 10^{-4}-10^{-3}.
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The notion of Macaulayfication, which is analogous of the desingularization,
was introduced by Faltings in 1978 and he construct a Macaulayfication of
quasi-projective scheme whose non-Cohen-Macaulay locus is of dimension 0 or 1
by a characteristic free method. In this paper, we gave a Macaulayfication of a
quasi-projective scheme whose non-Cohen-Macaulay locus is of dimension 2. Of
course out method is independent of the characteristic.
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We have designed, constructed and put into operation a large area CCD camera
that covers a large fraction of the image plane of the 1 meter Schmidt
telescope at Llano del Hato in Venezuela. The camera consists of 16 CCD devices
arranged in a 4 x 4 mosaic covering 2.3 degrees x 3.5 degrees of sky. The CCDs
are 2048 x 2048 LORAL devices with 15 micron pixels. The camera is optimized
for drift scan photometry and objective prism spectroscopy. The design
considerations, construction features and performance parameters are described
in the following article.
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We present an overview of and preliminary results from an ongoing
comprehensive program that has a goal of determining the Hubble constant to a
systematic accuracy of 2%. As part of this program, we are currently obtaining
3.6 micron data using the Infrared Array Camera (IRAC) on Spitzer, and the
program is designed to include JWST in the future. We demonstrate that the
mid-infrared period-luminosity relation for Cepheids at 3.6 microns is the most
accurate means of measuring Cepheid distances to date. At 3.6 microns, it is
possible to minimize the known remaining systematic uncertainties in the
Cepheid extragalactic distance scale. We discuss the advantages of 3.6 micron
observations in minimizing systematic effects in the Cepheid calibration of the
Hubble constant including the absolute zero point, extinction corrections, and
the effects of metallicity on the colors and magnitudes of Cepheids. We are
undertaking three independent tests of the sensitivity of the mid-IR Cepheid
Leavitt Law to metallicity, which when combined will allow a robust constraint
on the effect. Finally, we are providing a new mid-IR Tully-Fisher relation for
spiral galaxies.
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In this work, we study the exact solution of Dirac equation in the
hyper-spherical coordinate under influence of separable q-Deformed quantum
potentials. The q-deformed hyperbolic Rosen-Morse potential is perturbed by
q-deformed non-central trigonometric Scarf potentials, where whole of them can
be solved by using Asymptotic Iteration Method (AIM). This work is limited to
spin symmetry case. The relativistic energy equation and orbital quantum number
equation lD-1 have been obtained using Asymptotic Iteration Method. The upper
radial wave function equations and angular wave function equations are also
obtained by using this method. The relativistic energy levels are numerically
calculated using Mat Lab, the increase of radial quantum number n causes the
increase of bound state relativistic energy level both in dimension D = 5 and D
= 3. The bound state relativistic energy level decreases with increasing of
both deformation parameter q and orbital quantum number nl.
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Giant cluster radio relics are thought to form at shock fronts in the course
of collisions between galaxy clusters. Via processes that are still poorly
understood, these shocks accelerate or re-accelerate cosmic-ray electrons and
might amplify magnetic fields. The best object to study this phenomenon is the
galaxy cluster CIZA J2242.8+5301 as it shows the most undisturbed relic. By
means of Giant Metrewave Radio Telescope (GMRT) and Westerbork Synthesis Radio
Telescope (WSRT) data at seven frequencies spanning from 153 MHz to 2272 MHz,
we study the synchrotron emission in this cluster. We aim at distinguishing
between theoretical injection and acceleration models proposed for the
formation of radio relics. We also study the head-tail radio sources to reveal
the interplay between the merger and the cluster galaxies. We produced spectral
index, curvature maps and radio colour-colour plots and compared our data with
predictions from models. We present one of the deepest 153 MHz maps of a
cluster ever produced, reaching a noise level of 1.5 mJy/beam. We derive
integrated spectra for four relics in the cluster, discovering extremely steep
spectrum diffuse emission concentrated in multiple patches. We find a possible
radio phoenix embedded in the relic to the south of the cluster. The spectral
index of the northern relic retains signs of steepening from the front towards
the back of the shock also at the radio frequencies below 600 MHz. The spectral
curvature in the same relic also increases in the downstream area. The data is
consistent with the Komissarov-Gubanov injection models, meaning that the
emission we observe is produced by a single burst of spectrally-aged
accelerated radio electrons.
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We use information from higher order moments to achieve identification of
non-Gaussian structural vector autoregressive moving average (SVARMA) models,
possibly non-fundamental or non-causal, through a frequency domain criterion
based on a new representation of the higher order spectral density arrays of
vector linear processes. This allows to identify the location of the roots of
the determinantal lag matrix polynomials based on higher order cumulants
dynamics and to identify the rotation of the model errors leading to the
structural shocks up to sign and permutation. We describe sufficient conditions
for global and local parameter identification that rely on simple rank
assumptions on the linear dynamics and on finite order serial and component
independence conditions for the structural innovations. We generalize previous
univariate analysis to develop asymptotically normal and efficient estimates
exploiting second and non-Gaussian higher order dynamics given a particular
structural shocks ordering without assumptions on causality or invertibility.
Bootstrap approximations to finite sample distributions and the properties of
numerical methods are explored with real and simulated data.
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We highlight the important role that canonical normalisation of kinetic terms
in flavour models based on family symmetries can play in determining the Yukawa
matrices. Even though the kinetic terms may be correctly canonically normalised
to begin with, they will inevitably be driven into a non-canonical form by a
similar operator expansion to that which determines the Yukawa operators.
Therefore in models based on family symmetry canonical re-normalisation is
mandatory before the physical Yukawa matrices can be extracted. In nearly all
examples in the literature this is not done. As an example we perform an
explicit calculation of such mixing associated with canonical normalisation of
the Kahler metric in a supersymmetric model based on SU(3) family symmetry,
where we show that such effects can significantly change the form of the Yukawa
matrix. In principle quark mixing could originate entirely from canonical
normalisation, with only diagonal Yukawa couplings before canonical
normalisation.
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Predictions state that graphene can spontaneously develop magnetism from the
Coulomb repulsion of its $\pi$-electrons, but its experimental verification has
been a challenge. Here, we report on the observation and manipulation of
individual magnetic moments localized in graphene nanostructures on a Au(111)
surface. Using scanning tunneling spectroscopy, we detected the presence of
single electron spins localized around certain zigzag sites of the carbon
backbone via the Kondo effect. Two near-by spins were found coupled into a
singlet ground state, and the strength of their exchange interaction was
measured via singlet-triplet inelastic tunnel electron excitations. Theoretical
simulations demonstrate that electron correlations result in spin-polarized
radical states with the experimentally observed spatial distributions. Hydrogen
atoms bound to these radical sites quench their magnetic moment, permitting us
to switch the spin of the nanostructure using the tip of the microscope.
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In this paper, we propose a phase attention residual network (PA-ResSeg) to
model multi-phase features for accurate liver tumor segmentation, in which a
phase attention (PA) is newly proposed to additionally exploit the images of
arterial (ART) phase to facilitate the segmentation of portal venous (PV)
phase. The PA block consists of an intra-phase attention (Intra-PA) module and
an inter-phase attention (Inter-PA) module to capture channel-wise
self-dependencies and cross-phase interdependencies, respectively. Thus it
enables the network to learn more representative multi-phase features by
refining the PV features according to the channel dependencies and
recalibrating the ART features based on the learned interdependencies between
phases. We propose a PA-based multi-scale fusion (MSF) architecture to embed
the PA blocks in the network at multiple levels along the encoding path to fuse
multi-scale features from multi-phase images. Moreover, a 3D boundary-enhanced
loss (BE-loss) is proposed for training to make the network more sensitive to
boundaries. To evaluate the performance of our proposed PA-ResSeg, we conducted
experiments on a multi-phase CT dataset of focal liver lesions (MPCT-FLLs).
Experimental results show the effectiveness of the proposed method by achieving
a dice per case (DPC) of 0.77.87, a dice global (DG) of 0.8682, a volumetric
overlap error (VOE) of 0.3328 and a relative volume difference (RVD) of 0.0443
on the MPCT-FLLs. Furthermore, to validate the effectiveness and robustness of
PA-ResSeg, we conducted extra experiments on another multi-phase liver tumor
dataset and obtained a DPC of 0.8290, a DG of 0.9132, a VOE of 0.2637 and a RVD
of 0.0163. The proposed method shows its robustness and generalization
capability in different datasets and different backbones.
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The tractor behavior of a zero-order Bessel acoustic beam acting on a fluid
sphere, and emanating from a finite circular aperture (as opposed to waves of
infinite extent) is demonstrated theoretically. Conditions for an attractive
force acting in opposite direction of the radiating waves, determined by the
choice of the beam's half-cone angle, the size of the radiator, and its
distance from a fluid sphere, are established and discussed. Numerical
predictions for the radiation force function, which is the radiation force per
unit energy density and cross-sectional surface, are provided using a
partial-wave expansion method stemming from the acoustic scattering. The
results suggest a simple and reliable analysis for the design of Bessel beam
acoustical tweezers and tractor beam devices.
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In statistical mechanics, the generally called Stirling approximation is
actually an approximation of Stirling's formula. In this article, it is shown
that the term that is dropped is in fact the one that takes fluctuations into
account. The use of the Stirling's exact formula forces us to reintroduce them
into the already proposed solutions of well-know puzzles such as the
extensivity paradox or the Gibbs' paradox of joining two volumes of identical
gas. This amendment clearly results in a gain in consistency and rigor of these
solutions.
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We propose a method to realize the Frenkel-Kontorova model using an array of
Rydberg dressed atoms. Our platform can be used to study this model with a
range of realistic interatomic potentials. In particular, we concentrate on two
types of interaction potentials: a springlike potential and a repulsive
long-range potential. We numerically calculate the phase diagram for such
systems and characterize the Aubry-like and commensurate-incommensurate phase
transitions. Experimental realizations of this system that are possible to
achieve using current technology are discussed.
|
There has been a tremendous progress in Domain Adaptation (DA) for visual
recognition tasks. Particularly, open-set DA has gained considerable attention
wherein the target domain contains additional unseen categories. Existing
open-set DA approaches demand access to a labeled source dataset along with
unlabeled target instances. However, this reliance on co-existing source and
target data is highly impractical in scenarios where data-sharing is restricted
due to its proprietary nature or privacy concerns. Addressing this, we
introduce a practical DA paradigm where a source-trained model is used to
facilitate adaptation in the absence of the source dataset in future. To this
end, we formalize knowledge inheritability as a novel concept and propose a
simple yet effective solution to realize inheritable models suitable for the
above practical paradigm. Further, we present an objective way to quantify
inheritability to enable the selection of the most suitable source model for a
given target domain, even in the absence of the source data. We provide
theoretical insights followed by a thorough empirical evaluation demonstrating
state-of-the-art open-set domain adaptation performance.
|
Regression discontinuity design (RDD) is a quasi-experimental approach used
to estimate the causal effects of an intervention assigned based on a cutoff
criterion. RDD exploits the idea that close to the cutoff units below and above
are similar; hence, they can be meaningfully compared. Consequently, the causal
effect can be estimated only locally at the cutoff point. This makes the cutoff
point an essential element of RDD. However, especially in medical applications,
the exact cutoff location may not always be disclosed to the researcher, and
even when it is, the actual location may deviate from the official one. As we
illustrate on the application of RDD to the HIV treatment eligibility data,
estimating the causal effect at an incorrect cutoff point leads to meaningless
results. Moreover, since the cutoff criterion often acts as a guideline rather
than as a strict rule, the location of the cutoff may be unclear from the data.
The method we present can be applied both as an estimation and validation tool
in RDD. We use a Bayesian approach to incorporate prior knowledge and
uncertainty about the cutoff location in the causal effect estimation. At the
same time, our Bayesian model LoTTA is fitted globally to the whole data,
whereas RDD is a local, boundary point estimation problem. In this work we
address a natural question that arises: how to make Bayesian inference more
local to render a meaningful and powerful estimate of the treatment effect?
|
The article is devoted to the investigation of operators on a non locally
compact group algebra. Their isomorphisms are also studied.
|
Interactions growing slower than a certain exponential of the square of a
scalar field, are well behaved when evolved under the functional
renormalization group linearised around the Gaussian fixed point. They satisfy
properties usually taken for granted, and reproduce standard perturbative
quantisation. However, ever more challenging effects appear the more
interactions grow faster than this. We show explicitly that firstly the flow no
longer splits uniquely into operators of definite scaling dimension; then
(linearised) flows to the infrared can end prematurely in a singularity; and
finally new interactions can spontaneously appear at any scale.
|
The equation $x^2 + 1 = 0\mod p$ has solutions whenever $p = 2$ or $4n + 1$.
A famous theorem of Fermat says that these primes are exactly the ones that can
be described as a sum of two squares. That the roots of the former equation are
equidistributed is a beautiful theorem of Duke, Friedlander and Iwaniec from
1995. We show that a subsequence of the roots of the equation remains
equidistributed even when one adds a restriction on the primes which has to do
with the angle in the plane formed by their corresponding representation as a
sum of squares.
Similar to Duke, Friedlander and Iwaniec, we reduce the problem to the study
of certain Poincare series, however, while their Poincare series were functions
on an arithmetic quotient of the upper half plane, our Poincare series are
functions on arithmetic quotients of $SL_2(\mathbb{R})$, as they have a
nontrivial dependence on their Iwasawa $\theta$-coordinate. Spectral analysis
on these higher dimensional varieties involves the nonspherical spectrum, which
posed a few new challenges. A couple of notable ones were that of obtaining
pointwise bounds for nonspherical Eisenstein series and utilizing a
non-spherical analogue of the Selberg inversion formula.
|
We studied double superconducting (SC) domes in LaFeAsO1-xHx by using 75As-
and 1H-nuclear magnetic resonance techniques, and unexpectedly discovered that
a new antiferromagnetic (AF) phase follows the double SC domes on further H
doping, forming a symmetric alignment of AF and SC phases in the electronic
phase diagram. We demonstrated that the new AF ordering originates from the
nesting between electron pockets, unlike the nesting between electron and hole
pockets as seen in the majority of undoped pnictides. The new AF ordering is
derived from the features common to high-Tc pnictides: however, it has not been
reported so far for other high-Tc pnictides because of their poor electron
doping capability.
|
Low-light image enhancement exhibits an ill-posed nature, as a given image
may have many enhanced versions, yet recent studies focus on building a
deterministic mapping from input to an enhanced version. In contrast, we
propose a lightweight one-path conditional generative adversarial network
(cGAN) to learn a one-to-many relation from low-light to normal-light image
space, given only sets of low- and normal-light training images without any
correspondence. By formulating this ill-posed problem as a modulation code
learning task, our network learns to generate a collection of enhanced images
from a given input conditioned on various reference images. Therefore our
inference model easily adapts to various user preferences, provided with a few
favorable photos from each user. Our model achieves competitive visual and
quantitative results on par with fully supervised methods on both noisy and
clean datasets, while being 6 to 10 times lighter than state-of-the-art
generative adversarial networks (GANs) approaches.
|
A theoretical estimate of the explicit time dependence of a drainage water of
shallow lakes is presented as an important contribution for understanding the
lake dynamics. This information can be obtained from a sum of functions,
largely used in fitting of experimental data. These functions were chosen
because their centre and weight yield a good description of the water basin
behaviour. The coefficients of these functions are here extracted using results
of measured and / or calculated data for the state variables describing the
shallow West Lake, Hangzou. This procedure can also be applied to other shallow
lakes, generating geological information about their drainage basin, which is
one of the most important parameters to describe their micrometeorological
behaviour. One concludes this work emphasizing the relevance of the explicit
time dependence of the drainage variables and the requirement of measured data
to validate this approach.
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Astrometry is one of the main science case which drives the requirements of
the next multiconjugate adaptive optics (MCAO) systems for future extremely
large telescopes. The small diffraction limited point-spread function (PSF) and
the high Signal-to-Noise Ratio (SNR) of these instruments, promise astrometric
precision at the level of micro-arcseconds. However, optical distortions have
to be as low as possible to achieve the high demanding astrometry requirements.
In addition to static distortions, the opto-mechanical instabilities cause
astrometric errors that can be major contributors to the astrometry error
budget. The present article describes the analysis, at design level, of the
effects of opto-mechanical instabilities when coupled with optical surface
irregularities due to the manufacturing process. We analyse the notable example
of the Multi-conjugate Adaptive Optics RelaY (MAORY) for the extremely large
telescope (ELT). Ray-tracing simulations combined with a Monte Carlo approach
are used to estimate the geometrical structure and magnitude of field
distortion resulting from the optical design. We consider the effects of
distortion on the MCAO correction showing that it is possible achieve the
micro-arcseconds astrometric precision once corresponding accuracy is obtained
by both optical design and manufacturing. We predict that for single-epoch
observations, an astrometric error below 50$\mu$as can be achieved for exposure
times up to 2 min, provided about 100 stars are available to remove fifth-order
distortions. Such performance could be reproducible for multi-epoch
observations despite the time-variable distortion induced by instrument
instabilities.
|
In Automatic Speech Recognition (ASR) systems, a recurring obstacle is the
generation of narrowly focused output distributions. This phenomenon emerges as
a side effect of Connectionist Temporal Classification (CTC), a robust sequence
learning tool that utilizes dynamic programming for sequence mapping. While
earlier efforts have tried to combine the CTC loss with an entropy maximization
regularization term to mitigate this issue, they employed a constant weighting
term on the regularization during the training, which we find may not be
optimal. In this work, we introduce Adaptive Maximum Entropy Regularization
(AdaMER), a technique that can modulate the impact of entropy regularization
throughout the training process. This approach not only refines ASR model
training but ensures that as training proceeds, predictions display the desired
model confidence.
|
We propose a new approach to automated theorem proving where an
AlphaZero-style agent is self-training to refine a generic high-level expert
strategy expressed as a nondeterministic program. An analogous teacher agent is
self-training to generate tasks of suitable relevance and difficulty for the
learner. This allows leveraging minimal amounts of domain knowledge to tackle
problems for which training data is unavailable or hard to synthesize. As a
specific illustration, we consider loop invariant synthesis for imperative
programs and use neural networks to refine both the teacher and solver
strategies.
|
We determine Davenport's constant for all groups of the form $\Z\_3\oplus
\Z\_3\oplus\Z\_{3d}$.
|
We provide new values for the model parameters of the covariant constituent
quark model (with built--in infrared confinement) in the meson sector by a fit
to the leptonic decay constants and a number of electromagnetic decays. We then
evaluate, in a parameter free way, the form factors of the $B(B_s)\to
P(V)$-transitions in the full kinematical region of momentum transfer. As an
application of our results we calculate the widths of the nonleptonic
$B_s$-decays into $D_s^- D_s^+,$ $D_s^{\ast\,-} D_s^{+}+D_s^- D_s^{\ast\,+}$
and $D_s^{\ast\,-} D_s^{\ast\,+}$. These modes give the largest contribution to
$\Delta\Gamma$ for the $B_s-\bar B_s$ system. We also treat the nonleptonic
decay $B_{s}\to\Jpsi\phi$. Although this mode is color suppressed this decay
has important implications for the search of possible CP-violating New Physics
effects in $B_s-\bar B_s$ mixing.
|
Speech emotion analysis is an important task which further enables several
application use cases. The non-verbal sounds within speech utterances also play
a pivotal role in emotion analysis in speech. Due to the widespread use of
smartphones, it becomes viable to analyze speech commands captured using
microphones for emotion understanding by utilizing on-device machine learning
models. The non-verbal information includes the environment background sounds
describing the type of surroundings, current situation and activities being
performed. In this work, we consider both verbal (speech commands) and
non-verbal sounds (background noises) within an utterance for emotion analysis
in real-life scenarios. We create an indigenous dataset for this task namely
"Indian EmoSpeech Command Dataset". It contains keywords with diverse emotions
and background sounds, presented to explore new challenges in audio analysis.
We exhaustively compare with various baseline models for emotion analysis on
speech commands on several performance metrics. We demonstrate that we achieve
a significant average gain of 3.3% in top-one score over a subset of speech
command dataset for keyword spotting.
|
In the absence of acceleration, the velocity formula gives "distance
travelled equals speed multiplied by time". For a broad class of Markov chains
such as circulant Markov chains or random walk on complete graphs, we prove a
probabilistic analogue of the velocity formula between entropy and hitting
time, where distance is the entropy of the Markov trajectories from state $i$
to state $j$ in the sense of [L. Ekroot and T. M. Cover. The entropy of Markov
trajectories. IEEE Trans. Inform. Theory 39(4): 1418-1421.], speed is the
classical entropy rate of the chain, and the time variable is the expected
hitting time between $i$ and $j$. This motivates us to define new entropic
counterparts of various hitting time parameters such as average hitting time or
commute time, and prove analogous velocity formulae and estimates between these
quantities.
|
More than 100 excited states of the Calcium-40 nucleus, with isospin 0, are
classified into rotational-vibrational bands of an intrinsic tetrahedral
structure. Almost all observed states below 8 MeV can be accommodated, as well
as many high-spin states above 8 MeV. The bands have some similarity to those
classifying states of Oxygen-16, but the A-mode vibrational frequency is lower
relative to the E-mode and F-mode frequencies than in Oxygen-16. Previously
identified rotational bands up to spin 16 and energy above 20 MeV are unified
here into a smaller number of tetrahedral bands.
|
Realizing direct-bandgap quantum dots working within the deep-ultraviolet
frequency is highly desired for electro-optical and biomedical applications
while remaining challenging. In this work, we combine the first-principles
many-body perturbation theory and effective Hamiltonian approximation to
propose the realization of arrays of deep-ultraviolet excitonic quantum dots in
twisted bilayer hexagonal boron nitride. The effective quantum confinement of
excitons can reach ~400 meV within small twisting angles, which is about four
times larger than those observed in twisted semiconducting transitional metal
dichalcogenides. Especially because of enhanced electron-hole attraction, those
excitons will accumulate via the so-call exciton funnel effect to the
direct-bandgap regime, giving the possibility to better luminescence
performance and manipulating coherent arrays of deep-ultraviolet quantum dots.
|
Here we show, combining a simulation and theoretical study, that
electrostatic correlations typical of multivalent ions can reverse the
selectivity of a biological nanochannel. Our results provide a physical
mechanism for a new, experimentally observed phenomenon, namely the inversion
of the selectivity of a bacterial porin (the E. Coli OmpF) in presence of
divalent and trivalent cations. Also, the differences and similarities between
the driving force for this phenomenon and other similar nano and micro-escale
electrokinetic effects (e.g. inversion of streaming current in silica
nanochannels) are explored.
|
The density density correlation function is computed for the Bogoliubov
pseudoparticles created in a Bose-Einstein condensate undergoing a black hole
flow. On the basis of the gravitational analogy, the method used relies only on
quantum field theory in curved spacetime techniques. A comparison with the
results obtained by ab initio full condensed matter calculations is given,
confirming the validity of the approximation used provided the profile of the
flow varies smoothly on scales compared to the condensate healing length.
|
This paper develops a Multiset Rewriting language with explicit time for the
specification and analysis of Time-Sensitive Distributed Systems (TSDS). Goals
are often specified using explicit time constraints. A good trace is an
infinite trace in which the goals are satisfied perpetually despite possible
interference from the environment. In our previous work (FORMATS 2016), we
discussed two desirable properties of TSDSes, realizability (there exists a
good trace) and survivability (where, in addition, all admissible traces are
good). Here we consider two additional properties, recoverability (all
compliant traces do not reach points-of-no-return) and reliability (the system
can always continue functioning using a good trace). Following (FORMATS 2016),
we focus on a class of systems called Progressing Timed Systems (PTS), where
intuitively only a finite number of actions can be carried out in a bounded
time period. We prove that for this class of systems the properties of
recoverability and reliability coincide and are PSPACE-complete. Moreover, if
we impose a bound on time (as in bounded model-checking), we show that for PTS
the reliability property is in the $\Pi_2^p$ class of the polynomial hierarchy,
a subclass of PSPACE. We also show that the bounded survivability is both
NP-hard and coNP-hard.
|
The obstructions for an arbitrary fusion algebra to be a fusion algebra of
some semisimple monoidal category are constructed. Those obstructions lie in
groups which are closely related to the Hochschild cohomology of fusion
algebras with coefficients in the K-theory of the ground (algebraically closed)
field.
|
We study mappings satisfying some estimate of distortion of modulus of
families of paths. Under some conditions on definition and mapped domains, we
have proved that these mappings are logarithmic H\"{o}lder continuous at
boundary points.
|
We investigate the dynamics of magnetization in the phase separated (PS)
state after introducing the quenched disorder at the Mn-site of a manganite
around half doping. The compound,
Pr$_{0.5}$Sr$_{0.5}$Mn$_{0.925}$Ga$_{0.075}$O$_{3}$, exhibits PS with the
coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) clusters where
the size of the FM clusters is substantially reduced due to the disorder
introduced by nonmagnetic Ga substitution. At low temperature, the system
develops a new magnetic anomaly, which is marked by a peak in the zero field
cooled magnetization. Detailed study of linear as well as nonlinear ac
susceptibilities coupled with dc magnetization indicates that this peak arises
due to the thermal blocking of nanometer size FM clusters demonstrating
superparamagnetic behavior. The system, however, exhibits slow magnetic
relaxation, aging effect, memory effect in both field cooled and zero field
cooled magnetization below the blocking temperature. These imply the presence
of collective behavior induced by the interaction between the clusters.
Moreover, the magnetic relaxation measured with positive and negative
temperature excursions exhibits asymmetric response suggesting that the
dynamics in this phase separated system is accounted by the hierarchical model
rather than the droplet model which are commonly used to describe the similar
collective dynamics in glassy system.
|
In this note we are going to consider a smooth projective surface equipped
with an involution and study the action of the involution at the level of Chow
group of zero cycles.
|
Szegedy developed a generic method for quantizing classical algorithms based
on random walks [Proceedings of FOCS, 2004, pp. 32-41]. A major contribution of
his work was the construction of a walk unitary for any reversible random walk.
Such unitary posses two crucial properties: its eigenvector with eigenphase $0$
is a quantum sample of the limiting distribution of the random walk and its
eigenphase gap is quadratically larger than the spectral gap of the random
walk. It was an open question if it is possible to generalize Szegedy's
quantization method for stochastic maps to quantum maps. We answer this in the
affirmative by presenting an explicit construction of a Szegedy walk unitary
for detailed balanced Lindbladians -- generators of quantum Markov semigroups
-- and detailed balanced quantum channels. We prove that our Szegedy walk
unitary has a purification of the fixed point of the Lindbladian as eigenvector
with eigenphase $0$ and that its eigenphase gap is quadratically larger than
the spectral gap of the Lindbladian. To construct the walk unitary we leverage
a canonical form for detailed balanced Lindbladians showing that they are
structurally related to Davies generators. We also explain how the quantization
method for Lindbladians can be applied to quantum channels. We give an
efficient quantum algorithm for quantizing Davies generators that describe many
important open-system dynamics, for instance, the relaxation of a quantum
system coupled to a bath. Our algorithm extends known techniques for simulating
quantum systems on a quantum computer.
|
Deep learning (DL) methods have been recently proposed for user equipment
(UE) localization in wireless communication networks, based on the channel
state information (CSI) between a UE and each base station (BS) in the uplink.
With the CSI from the available BSs, UE localization can be performed in
different ways. One the one hand, a single neural network (NN) can be trained
for the UE localization by considering the CSI from all the available BSs as
one overall fingerprint of the user's location. On the other hand, the CSI at
each BS can be used to obtain an estimate of the UE's position with a separate
NN at each BS, and then the position estimates of all BSs are combined to
obtain an overall estimate of the UE position. In this work, we show that UE
localization with the latter approach can achieve a higher positioning
accuracy. We propose to consider the uncertainty in the UE localization at each
BS, such that overall UE's position is determined by combining the position
estimates of the different BSs based on the uncertainty at each BS. With this
approach, a more reliable position estimate can be obtained in case of
variations in the channel.
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Learning from raw high dimensional data via interaction with a given
environment has been effectively achieved through the utilization of deep
neural networks. Yet the observed degradation in policy performance caused by
imperceptible worst-case policy dependent translations along high sensitivity
directions (i.e. adversarial perturbations) raises concerns on the robustness
of deep reinforcement learning policies. In our paper, we show that these high
sensitivity directions do not lie only along particular worst-case directions,
but rather are more abundant in the deep neural policy landscape and can be
found via more natural means in a black-box setting. Furthermore, we show that
vanilla training techniques intriguingly result in learning more robust
policies compared to the policies learnt via the state-of-the-art adversarial
training techniques. We believe our work lays out intriguing properties of the
deep reinforcement learning policy manifold and our results can help to build
robust and generalizable deep reinforcement learning policies.
|
Multitask Learning is a learning paradigm that deals with multiple different
tasks in parallel and transfers knowledge among them. XOF, a Learning
Classifier System using tree-based programs to encode building blocks
(meta-features), constructs and collects features with rich discriminative
information for classification tasks in an observed list. This paper seeks to
facilitate the automation of feature transferring in between tasks by utilising
the observed list. We hypothesise that the best discriminative features of a
classification task carry its characteristics. Therefore, the relatedness
between any two tasks can be estimated by comparing their most appropriate
patterns. We propose a multiple-XOF system, called mXOF, that can dynamically
adapt feature transfer among XOFs. This system utilises the observed list to
estimate the task relatedness. This method enables the automation of
transferring features. In terms of knowledge discovery, the resemblance
estimation provides insightful relations among multiple data. We experimented
mXOF on various scenarios, e.g. representative Hierarchical Boolean problems,
classification of distinct classes in the UCI Zoo dataset, and unrelated tasks,
to validate its abilities of automatic knowledge-transfer and estimating task
relatedness. Results show that mXOF can estimate the relatedness reasonably
between multiple tasks to aid the learning performance with the dynamic feature
transferring.
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We recall the generalization of the Feynman-Metropolis-Teller approximation
for a compressed atom using a relativistic Fermi-Thomas model. These results
within a Wigner-Seitz approximation lead to a new equation of state for white
dwarfs and to a new value of their critical mass, smaller than the one obtained
by Chandrasekhar. The possible observations of these effects in binary neutron
stars are outlined.
|
For each $n$, we construct a separable metric space $\mathbb{U}_n$ that is
universal in the coarse category of separable metric spaces with asymptotic
dimension ($\mathop{asdim}$) at most $n$ and universal in the uniform category
of separable metric spaces with uniform dimension ($\mathop{udim}$) at most
$n$. Thus, $\mathbb{U}_n$ serves as a universal space for dimension $n$ in both
the large-scale and infinitesimal topology. More precisely, we prove:
\[
\mathop{asdim} \mathbb{U}_n = \mathop{udim} \mathbb{U}_n = n
\] and such that for each separable metric space $X$,
a) if $\mathop{asdim} X \leq n$, then $X$ is coarsely equivalent to a subset
of $\mathbb{U}_n$;
b) if $\mathop{udim} X \leq n$, then $X$ is uniformly homeomorphic to a
subset of $\mathbb{U}_n$.
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In this paper we develop a quantitative Harris theorem with effective control
over the constants. A benefit of our methodology is the decoupling of the small
set and Lyapunov-Foster Drift conditions. Our methodology allows any small set
and any set in the Lyapunov-Foster condition as long as the second satisfies a
so-called ``quantitative petiteness" condition. The theorem relies on a novel
proof of a quantitative Kendall-type theorem which is inspired by the
techniques of Markov Chains on general state spaces. We give an application of
the technique to the Markov chain approximation of mixing processes.
|
Information on the existence and properties of diffuse interstellar bands
(DIBs) outside the optical domain is still limited. Additional infra-red (IR)
measurements and IR-optical correlative studies are needed to constrain DIB
carriers and locate various absorbers in 3D maps of the interstellar matter. We
extended our study of H-band DIBs in Apache Point Observatory Galactic
Evolution Experiment (APOGEE) Telluric Standard Star (TSS) spectra. We used the
strong 15273A band to select the most and least absorbed targets. We used
individual spectra of the former subsample to extract weaker DIBs, and we
searched the two stacked series for differences that could indicate additional
bands. High-resolution NARVAL and SOPHIE optical spectra for a subsample of 55
TSS targets were additionally recorded for NIR/optical correlative studies.
From the TSS spectra we extract a catalog of measurements of the poorly studied
15617, 15653, and 15673A DIBs in about 300 sightlines, we obtain a first
accurate determination of their rest wavelength and constrained their intrinsic
width and shape. In addition, we studied the relationship between these weak
bands and the strong 15273A DIB. We provide a first or second confirmation of
several other weak DIBs that have been proposed based on different instruments,
and we add new constraints on their widths and locations. We finally propose
two new DIB candidates. We compared the strength of the 15273A absorptions with
their optical counterparts 5780, 5797, 6196, 6283, and 6614A. Using the
5797-5780 ratio as a tracer of shielding against the radiation field, we showed
that the 15273A DIB carrier is significantly more abundant in unshielded
(sigma-type) clouds, and it responds even more strongly than the 5780A band
carrier to the local ionizing field.
|
Two types of room temperature detectors of terahertz laser radiation have
been developed which allow in an all-electric manner to determine the plane of
polarization of linearly polarized radiation and the ellipticity of
elliptically polarized radiation, respectively. The operation of the detectors
is based on photogalvanic effects in semiconductor quantum well structures of
low symmetry. The photogalvanic effects have sub-nanosecond time constants at
room temperature making a high time resolution of the polarization detectors
possible.
|
A versatile and portable magnetically shielded room with a field of (700 \pm
200) pT within a central volume of 1m x 1m x 1m and a field gradient less than
300 pT/m is described. This performance represents more than a hundred-fold
improvement of the state of the art for a two-layer magnetic shield and
provides an environment suitable for a next generation of precision experiments
in fundamental physics at low energies; in particular, searches for electric
dipole moments of fundamental systems and tests of Lorentz-invariance based on
spin-precession experiments. Studies of the residual fields and their sources
enable improved design of future ultra-low gradient environments and
experimental apparatus.
|
We analyze a task in which classical and quantum messages are simultaneously
communicated via a noisy quantum channel, assisted with a limited amount of
shared entanglement. We derive direct and converse bounds for the one-shot
capacity region, represented by the smooth conditional entropies and the error
tolerance. The proof is based on the randomized partial decoupling theorem,
which is a generalization of the decoupling theorem. The two bounds match in
the asymptotic limit of infinitely many uses of a memoryless channel and
coincide with the previous result obtained by Hsieh and Wilde. Direct and
converse bounds for various communication tasks are obtained as corollaries,
both for the one-shot and asymptotic scenarios.
|
As known, external fields can have a noticeable effect on a number of
processes such as recombination of radicals, processes occurring in biological
systems, some processes of adsorption, etc. However, there are no any mentions
in literature about the impact on chemical processes of non-magnetic and
non-charged bodies which do not have direct contact with the reagents. In the
current study we examine the effect on the hydration of YBa2Cu3O6.75 (YBCO) of
a closely placed non-magnetic and non-charged steel disk. For this purpose we
utilize a previously developed special method of material preparation that has
been published earlier. The resulting material we analyze by the iodometric
titration technique, X-ray diffraction, and X-ray photoelectron spectroscopy.
Conducting the experiment on a large number of the YBCO samples being hydrated
at different distances from the disk clearly indicates a significant inhibitory
effect of this factor. We find that there is a certain distance from the
surface of the metal body, at which the hydration process achieves maximum
sensitivity to the metal presence. At this stage of research, it is assumed
that the mediator, with the aid of which the influence on the hydration process
occurs, might be electromagnetic radiation emanating from the YBCO samples
during their hydration and reflected from the surface of metal.
|
In turbulent flows, local velocity differences often obey a cascade-like
hierarchical dynamics, in the sense that local velocity differences at a given
scale k are driven by deterministic and random forces from the next-higher
scale k-1. Here we consider such a hierarchically coupled model with periodic
boundary conditions, and show that it leads to an N-th order initial value
problem, where N is the number of cascade steps. We deal in detail with the
case N=7 and introduce a non-polynomial spline method that solves the problem
for arbitrary driving forces. Several examples of driving forces are
considered, and estimates of the numerical precision of our method are given.
We show how to optimize the numerical method to obtain a truncation error of
order O(h^5) rather than O(h^2), where h is the discretization step.
|
Rapid categorization paradigms have a long history in experimental
psychology: Characterized by short presentation times and speedy behavioral
responses, these tasks highlight the efficiency with which our visual system
processes natural object categories. Previous studies have shown that
feed-forward hierarchical models of the visual cortex provide a good fit to
human visual decisions. At the same time, recent work in computer vision has
demonstrated significant gains in object recognition accuracy with increasingly
deep hierarchical architectures. But it is unclear how well these models
account for human visual decisions and what they may reveal about the
underlying brain processes.
We have conducted a large-scale psychophysics study to assess the correlation
between computational models and human participants on a rapid animal vs.
non-animal categorization task. We considered visual representations of varying
complexity by analyzing the output of different stages of processing in three
state-of-the-art deep networks. We found that recognition accuracy increases
with higher stages of visual processing (higher level stages indeed
outperforming human participants on the same task) but that human decisions
agree best with predictions from intermediate stages.
Overall, these results suggest that human participants may rely on visual
features of intermediate complexity and that the complexity of visual
representations afforded by modern deep network models may exceed those used by
human participants during rapid categorization.
|
We show that the set of real polynomials in two variables that are sums of
three squares of rational functions is dense in the set of those that are
positive semidefinite. We also prove that the set of real surfaces in P^3 whose
function field has level 2 is dense in the set of those that have no real
points.
|
We study the adsorption geometry of
3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) on Ag(111) and Cu(111)
using X-ray standing waves. The element-specific analysis shows that the carbon
core of the molecule adsorbs in a planar configuration, whereas the oxygen
atoms experience a non-trivial and substrate dependent distortion. On copper
(silver) the carbon rings resides 2.66 A (2.86 A) above the substrate. In
contrast to the conformation on Ag(111), where the carboxylic oxygen atoms are
bent towards the surface, we find that on Cu(111) all oxygen atoms are above
the carbon plane at 2.73 A and 2.89 A, respectively.
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We present a new framework for multi-view geometry in computer vision. A
camera is a mapping between $\mathbb{P}^3$ and a line congruence. This model,
which ignores image planes and measurements, is a natural abstraction of
traditional pinhole cameras. It includes two-slit cameras, pushbroom cameras,
catadioptric cameras, and many more. We study the concurrent lines variety,
which consists of $n$-tuples of lines in $\mathbb{P}^3$ that intersect at a
point. Combining its equations with those of various congruences, we derive
constraints for corresponding images in multiple views. We also study
photographic cameras which use image measurements and are modeled as rational
maps from $\mathbb{P}^3$ to $\mathbb{P}^2$ or $\mathbb{P}^1\times
\mathbb{P}^1$.
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We prove a generalization of the Hochster-Roberts-Boutot-Kawamata Theorem
conjectured by Aschenbrenner and the author: let $R\to S$ be a pure
homomorphism of equicharacteristic zero Noetherian local rings. If $S$ is
regular, then $R$ is pseudo-rational, and if $R$ is moreover $\mathbb
Q$-Gorenstein, then it pseudo-log-terminal.
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The usual way to interpret language models (LMs) is to test their performance
on different benchmarks and subsequently infer their internal processes. In
this paper, we present an alternative approach, concentrating on the quality of
LM processing, with a focus on their language abilities. To this end, we
construct 'linguistic task spaces' -- representations of an LM's language
conceptualisation -- that shed light on the connections LMs draw between
language phenomena. Task spaces are based on the interactions of the learning
signals from different linguistic phenomena, which we assess via a method we
call 'similarity probing'. To disentangle the learning signals of linguistic
phenomena, we further introduce a method called 'fine-tuning via gradient
differentials' (FTGD). We apply our methods to language models of three
different scales and find that larger models generalise better to overarching
general concepts for linguistic tasks, making better use of their shared
structure. Further, the distributedness of linguistic processing increases with
pre-training through increased parameter sharing between related linguistic
tasks. The overall generalisation patterns are mostly stable throughout
training and not marked by incisive stages, potentially explaining the lack of
successful curriculum strategies for LMs.
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A spiral wave is a macroscopic dynamic of excitable media that plays an
important role in several distinct systems, including the Belousov-Zhabotinsky
reaction, seizures in the brain, and lethal arrhythmia in the heart. Because
spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise
quantification can be challenging. Here we present a hybrid geometric and
information-theoretic approach to quantifying spiral wave dynamics. We
demonstrate the effectiveness of our approach by applying it to numerical
simulations of a two-dimensional excitable medium with different numbers and
spatial patterns of spiral waves. We show that, by defining information flow
over the excitable medium, hidden coherent structures emerge that effectively
quantify the information transport underlying spiral wave dynamics. Most
importantly, we find that some coherent structures become more clearly defined
over a longer observation period. These findings validate our approach to
quantitatively characterize spiral wave dynamics by focusing on information
transport. Our approach is computationally efficient and is applicable to many
excitable media of interest in distinct physical, chemical and biological
systems. Our approach could ultimately contribute to an improved therapy of
clinical conditions such as seizures and cardiac arrhythmia by identifying
potential targets of interventional therapies.
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Crucial developments to the recently introduced signal-space approach for
multiplexing multiple data symbols using a single-radio switched antenna are
presented. First, we introduce a general framework for expressing the spatial
multiplexing relation of the transmit signals only from the antenna scattering
parameters and the modulating reactive loading. This not only avoids tedious
far-field calculations, but more importantly provides an efficient and
practical strategy for spatially multiplexing PSK signals of any modulation
order. The proposed approach allows ensuring a constant impedance matching at
the input of the driving antenna for all symbol combinations, and as
importantly uses only passive reconfigurable loads. This obviates the use of
reconfigurable matching networks and active loads, respectively, thereby
overcoming stringent limitations of previous single-feed MIMO techniques in
terms of complexity, efficiency, and power consumption. The proposed approach
is illustrated by the design of a realistic very compact antenna system
optimized for multiplexing QPSK signals. The results show that the proposed
approach can bring the MIMO benefits to the low-end user terminals at a reduced
RF complexity.
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Multi-layer graphene with rhombohedral stacking is a promising carbon phase
possibly displaying correlated states like magnetism or superconductivity due
to the occurrence of a flat surface band at the Fermi level. Recently, flakes
of thickness up to 17 layers were tentatively attributed ABC sequences although
the Raman fingerprint of rhombohedral multilayer graphene is currently unknown
and the 2D resonant Raman spectrum of Bernal graphite not understood. We
provide a first principles description of the 2D Raman peak in three and four
layers graphene (all stackings) as well as in Bernal, rhombohedral and an
alternation of Bernal and rhombohedral graphite. We give practical
prescriptions to identify long range sequences of ABC multi-layer graphene. Our
work is a prerequisite to experimental non-destructive identification and
synthesis of rhombohedral graphite.
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Furigana are pronunciation notes used in Japanese writing. Being able to
detect these can help improve optical character recognition (OCR) performance
or make more accurate digital copies of Japanese written media by correctly
displaying furigana. This project focuses on detecting furigana in Japanese
books and comics. While there has been research into the detection of Japanese
text in general, there are currently no proposed methods for detecting
furigana.
We construct a new dataset containing Japanese written media and annotations
of furigana. We propose an evaluation metric for such data which is similar to
the evaluation protocols used in object detection except that it allows groups
of objects to be labeled by one annotation. We propose a method for detection
of furigana that is based on mathematical morphology and connected component
analysis. We evaluate the detections of the dataset and compare different
methods for text extraction. We also evaluate different types of images such as
books and comics individually and discuss the challenges of each type of image.
The proposed method reaches an F1-score of 76\% on the dataset. The method
performs well on regular books, but less so on comics, and books of irregular
format. Finally, we show that the proposed method can improve the performance
of OCR by 5\% on the manga109 dataset.
Source code is available via
\texttt{\url{https://github.com/nikolajkb/FuriganaDetection}}
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Large-scale arrays of quantum-dot spin qubits in Si/SiGe quantum wells
require large or tunable energy splittings of the valley states associated with
degenerate conduction band minima. Existing proposals to deterministically
enhance the valley splitting rely on sharp interfaces or modifications in the
quantum well barriers that can be difficult to grow. Here, we propose and
demonstrate a new heterostructure, the "Wiggle Well," whose key feature is Ge
concentration oscillations inside the quantum well. Experimentally, we show
that placing Ge in the quantum well does not significantly impact our ability
to form and manipulate single-electron quantum dots. We further observe large
and widely tunable valley splittings, from 54 to 239 ueV. Tight-binding
calculations, and the tunability of the valley splitting, indicate that these
results can mainly be attributed to random concentration fluctuations that are
amplified by the presence of Ge alloy in the heterostructure, as opposed to a
deterministic enhancement due to the concentration oscillations. Quantitative
predictions for several other heterostructures point to the Wiggle Well as a
robust method for reliably enhancing the valley splitting in future qubit
devices.
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I. Raeburn and J. Taylor have constructed continuous-trace C*-algebras with a
prescribed Dixmier-Douady class, which also depend on the choice of an open
cover of the spectrum. We study the asymptotic behavior of these algebras with
respect to certain refinements of the cover and appropriate extension of
cocycles. This leads to the analysis of a limit groupoid G and a cocycle
\sigma, and the algebra C*(G, \sigma) may be regarded as a generalized direct
limit of the Raeburn-Taylor algebras. As a special case, all UHF C*-algebras
arise from this limit construction.
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Very faint X-ray binaries appear to be transient in many cases with peak
luminosities much fainter than that of usual soft X-ray transients, but their
nature still remains elusive. We investigate the possibility that this
transient behaviour is due to the same thermal/viscous instability which is
responsible for outbursts of bright soft X-ray transients, occurring in
ultracompact binaries for adequately low mass-transfer rates. More generally,
we investigate the observational consequences of this instability when it
occurs in ultracompact binaries. We use our code for modelling the
thermal-viscous instability of the accretion disc, assumed here to be hydrogen
poor. We also take into account the effects of disc X-ray irradiation, and
consider the impact of the mass-transfer rate on the outburst brightness. We
find that one can reproduce the observed properties of both the very faint and
the brighter short transients (peak luminosity, duration, recurrence times),
provided that the viscosity parameter in quiescence is slightly smaller
(typically a factor of between two and four) than in bright soft X-ray
transients and normal dwarf nova outbursts, the viscosity in outburst being
unchanged. This possibly reflects the impact of chemical composition on
non-ideal MHD effects affecting magnetically driven turbulence in poorly
ionized discs.
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Non-linear transport properties of single-layer metal-on-metal islands driven
with strong static and time-dependent forces are studied. We apply a
semi-empirical lattice model and use master equation and kinetic Monte Carlo
simulation methods to compute observables such as the velocity and the
diffusion coefficient. Two types of time-dependent driving are considered: a
pulsed rotated field and an alternating field with a zero net force
(electrophoretic ratchet). Small islands up to 12 atoms were studied in detail
with the master equation method and larger ones with simulations. Results are
presented mainly for a parametrization of Cu on Cu(001) surface, which has been
the main system of interest in several previous studies. The main results are
that the pulsed field can increase the current in both diagonal and axis
direction when compared to static field, and there exists a current inversion
in the electrophoretic ratchet. Both of these phenomena are a consequence of
the coupling of the internal dynamics of the island with its transport. In
addition to the previously discovered "magic size" effect for islands in
equilibrium, a strong odd-even effect was found for islands driven far out of
equilibrium. Master equation computations revealed non-monotonous behavior for
the leading relaxation constant and effective Arrhenius parameters. Using cycle
optimization methods, typical island transport mechanisms are identified for
small islands.
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We develop algorithms and computer programs which verify criteria of
properness of discrete group actions on semisimple homogeneous spaces. We apply
these algorithms to find new examples of non-virtually abelian discontinuous
group actions on homogeneous spaces which do not admit proper SL(2,R)-actions.
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Often in mathematics it is useful to summarize a multivariate phenomenon with
a single number and in fact, the determinant -- which is represented by det --
is one of the simplest cases. In fact, this number it is defined only for
square matrices and a lot of its properties are very well-known. For instance,
the determinant is a multiplicative function, i.e. det(AB)=detA detB, but it is
not, in general, an additive function. Another interesting function in the
matrix analysis is the characteristic polynomial -- in fact, given a matrix A,
this function is defined by $p_A(t)=det(tI-A)$ where I is the identity matrix
-- which elements are, up a sign, the elementary symmetric functions associated
to the eigenvalues of the matrix A. In the present paper new expressions
related with the determinant of sum of matrices and the elementary symmetric
functions are given. Moreover, the connection with the Mobius function and the
partial ordered sets (poset) is presented. Finally, a problem related with the
determinant of sum of matrices is solved.
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In this paper invariant subspace method has been employed for solving linear
and non-linear fractional partial differential equations involving Caputo
derivative. A variety of illustrative examples are solved to demonstrate the
effectiveness and applicability of the method.
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$B_s \to \rho(\omega) K^{\ast}$ are useful to determine the $B_s$
distribution amplitude, as well as constrain the CKM phase angle $\alpha$. We
study these decays within the Perturbative QCD (PQCD) picture. In this
approach, we calculate factorizable, non-factorizable, as well as annihilation
diagrams. We find the branching ratio for $B_s \to \rho^+ K^{*-}$ is big to
order $10^{-5}$, we also find there's large direct CP violation in $B_s(\bar
B_s) \to \rho^0(\omega) \bar K^{*0}(K^{*0})$. Our predictions are consistent
with those from other methods and current experiments.
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We address the problem of unambiguous discrimination among a given set of
quantum operations. The necessary and sufficient condition for them to be
unambiguously distinguishable is derived in the cases of single use and
multiple uses respectively. For the latter case we explicitly construct the
input states and corresponding measurements that accomplish the task. It is
found that the introduction of entanglement can improve the discrimination.
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While tunable filters are a recent development in night time astronomy, they
have long been used in other physical sciences, e.g. solar physics, remote
sensing and underwater communications. With their ability to tune precisely to
a given wavelength using a bandpass optimized for the experiment, tunable
filters are already producing some of the deepest narrowband images to date of
astrophysical sources. Furthermore, some classes of tunable filters can be used
in fast telescope beams and therefore allow for narrowband imaging over angular
fields of more than a degree over the sky.
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In a recent paper \cite{[Good1]} Good postulated new rules of quantization,
one of the major features of which is that the quantum evolution of the wave
function is always given by ordinary differential equations. In this paper we
analyse the proposal in some detail and discuss its viability and its
relationship with the standard quantum theory. As a byproduct, a simple
derivation of the `mass spectrum' for the Klein-Gordon field is presented, but
it is also shown that there is a complete additional spectrum of negative
`masses'. Finally, two major reasons are presented against the viability of
this alternative proposal: a) It does not lead to the correct energy spectrum
for the hydrogen atom. b) For field models, the standard quantum theory cannot
be recovered from this alternative description.
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Fairness in AI is a growing concern for high-stakes decision making. Engaging
stakeholders, especially lay users, in fair AI development is promising yet
overlooked. Recent efforts explore enabling lay users to provide AI
fairness-related feedback, but there is still a lack of understanding of how to
integrate users' feedback into an AI model and the impacts of doing so. To
bridge this gap, we collected feedback from 58 lay users on the fairness of a
XGBoost model trained on the Home Credit dataset, and conducted offline
experiments to investigate the effects of retraining models on accuracy, and
individual and group fairness. Our work contributes baseline results of
integrating user fairness feedback in XGBoost, and a dataset and code framework
to bootstrap research in engaging stakeholders in AI fairness. Our discussion
highlights the challenges of employing user feedback in AI fairness and points
the way to a future application area of interactive machine learning.
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A method of temporal factor prognosis of TE (tick-borne encephalitis)
infection has been developed. The high precision of the prognosis results for a
number of geographical regions of Primorsky Krai has been achieved. The method
can be applied not only to epidemiological research but also to others.
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This paper explores the combination of neural network quantization and
entropy coding for memory footprint minimization. Edge deployment of quantized
models is hampered by the harsh Pareto frontier of the accuracy-to-bitwidth
tradeoff, causing dramatic accuracy loss below a certain bitwidth. This
accuracy loss can be alleviated thanks to mixed precision quantization,
allowing for more flexible bitwidth allocation. However, standard mixed
precision benefits remain limited due to the 1-bit frontier, that forces each
parameter to be encoded on at least 1 bit of data. This paper introduces an
approach that combines mixed precision, zero-point quantization and entropy
coding to push the compression boundary of Resnets beyond the 1-bit frontier
with an accuracy drop below 1% on the ImageNet benchmark. From an
implementation standpoint, a compact decoder architecture features reduced
latency, thus allowing for inference-compatible decoding.
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Non-invertible symmetries have recently been understood to provide
interesting contraints on RG flows of QFTs. In this work, we show how
non-invertible symmetries can also be used to generate entirely new RG flows,
by means of so-called "non-invertible twisted compactification". We illustrate
the idea in the example of twisted compactifications of 4d $\mathcal{N}=4$
super-Yang-Mills (SYM) to three dimensions. After giving a catalogue of
non-invertible symmetries descending from Montonen-Olive duality
transformations of 4d $\mathcal{N}=4$ SYM, we show that twisted
compactification by non-invertible symmetries can be used to obtain 3d
$\mathcal{N}=6$ theories which appear otherwise unreachable if one restricts to
twists by invertible symmetries.
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