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We study estimation of (semi-)inner products between two nonparametric
probability distributions, given IID samples from each distribution. These
products include relatively well-studied classical $\mathcal{L}^2$ and Sobolev
inner products, as well as those induced by translation-invariant reproducing
kernels, for which we believe our results are the first. We first propose
estimators for these quantities, and the induced (semi)norms and
(pseudo)metrics. We then prove non-asymptotic upper bounds on their mean
squared error, in terms of weights both of the inner product and of the two
distributions, in the Fourier basis. Finally, we prove minimax lower bounds
that imply rate-optimality of the proposed estimators over Fourier ellipsoids.
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Let $\ell \geq 5$ be a prime and let $N$ be a square-free integer prime to
$\ell$. For each prime $p$ dividing $N$, let $a_p$ be either $1$ or $-1$. We
give sufficient criteria for the existence of a newform $f$ of weight 2 for
$\Gamma_0(N)$ such that the mod $\ell$ Galois representation attached to $f$ is
reducible and $U_p f = a_p f$ for primes $p$ dividing $N$. The main techniques
used are level raising methods based on an exact sequence due to Ribet.
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In this paper, we investigate Nash-regret minimization in congestion games, a
class of games with benign theoretical structure and broad real-world
applications. We first propose a centralized algorithm based on the optimism in
the face of uncertainty principle for congestion games with (semi-)bandit
feedback, and obtain finite-sample guarantees. Then we propose a decentralized
algorithm via a novel combination of the Frank-Wolfe method and G-optimal
design. By exploiting the structure of the congestion game, we show the sample
complexity of both algorithms depends only polynomially on the number of
players and the number of facilities, but not the size of the action set, which
can be exponentially large in terms of the number of facilities. We further
define a new problem class, Markov congestion games, which allows us to model
the non-stationarity in congestion games. We propose a centralized algorithm
for Markov congestion games, whose sample complexity again has only polynomial
dependence on all relevant problem parameters, but not the size of the action
set.
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The modified quasichemical model in the quadruplet approximation (MQMQA)
considers the first- and the second-nearest-neighbor coordination and
interactions, particularly useful in describing short-range ordering in complex
liquids such as molten salts, slag in metal processing, and electrolytic
solutions. The present work implements the MQMQA into the Python based
open-source software PyCalphad for thermodynamic calculations. This endeavor
facilitates the development of MQMQA-based thermodynamic database with
uncertainty quantification (UQ) using the open-source software ESPEI. A new
database structure based on Extensible Markup Language (XML) is proposed for
ESPEI evaluation of MQMQA model parameters. Using the KF-NiF2 system as an
example, we demonstrate the successful implementation of MQMQA in PyCalphad
through thermodynamic calculations of Gibbs energy, equilibrium quadruplet
fractions, and phase diagram, as well as database development with UQ using
ESPEI. The present implementation offers an open-source capability for
performing CALPHAD modeling for complex liquids with short-range ordering using
MQMQA.
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We investigate the energetics of droplets sourced by the thermal fluctuations
in a system undergoing a first-order transition. In particular, we confine our
studies to two dimensions with explicit calulations in the plane and on the
sphere. Using an isoperimetric inequality from the differential geometry
literature and a theorem on the inequality's saturation, we show how geometry
informs the critical droplet size and shape. This inequality establishes a
"mean field" result for nucleated droplets. We then study the effects of
fluctuations on the interfaces of droplets in two dimensions, treating the
droplet interface as a fluctuating line. We emphasize that care is needed in
deriving the line curvature energy from the Landau-Ginzburg energy functional
and in interpreting the scalings of the nucleation rate with the size of the
droplet. We end with a comparison of nucleation in the plane and on a sphere.
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This paper focuses on the probability that a portion of DNA closes on itself
through thermal fluctuations. We investigate the dependence of this probability
upon the size r of a protein bridge and/or the presence of a kink at half DNA
length. The DNA is modeled by the Worm-Like Chain model, and the probability of
loop formation is calculated in two ways: exact numerical evaluation of the
constrained path integral and the extension of the Shimada and Yamakawa saddle
point approximation. For example, we find that the looping free energy of a 100
base pairs DNA decreases from 24 kT to 13 kT when the loop is closed by a
protein of r = 10 nm length. It further decreases to 5 kT when the loop has a
kink of 120 degrees at half-length.
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We investigate the zero-temperature phase diagram of the fully frustrated
transverse field Ising model on the square lattice both in the classical limit
and in the presence of quantum fluctuations. At the classical level (the limit
of infinite spin $S$), we find that upon decreasing the transverse field
$\Gamma$ this model exhibits a phase transition from the fully polarized state
into an eight-fold degenerate translational symmetry breaking state. This phase
can be identified to correspond to plaquette order in the dimer language and
remains the lowest-energy state in the entire range of fields below the
critical one, $\Gamma_c$. The eight-fold degenerate solution which corresponds
to columnar order in the dimer language is a saddle point of the classical
energy. It is degenerate with the plaquette solution at $\Gamma=0$ and is only
slightly higher in energy in the whole interval $0<\Gamma<\Gamma_c$. The effect
of quantum fluctuations is investigated in the context of a large S expansion
both for the plaquette and columnar structures. For this purpose we employ an
approximate method allowing to estimate from above the fluctuation-induced
correction to the energy of a configuration which at the classical level is a
saddle point of the energy, \textit{not} a local minimum. Although the
convergence of the $1/S$ expansion in the $\Gamma/J\rightarrow 0$ limit remains
an open question, harmonic quantum fluctuations show a clear tendency to
overcome the energy difference between the two states and to change the
classical picture favoring the columnar order over the plaquette one in a wide
parameter range.
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For large matrix factorisation problems, we develop a distributed Markov
Chain Monte Carlo (MCMC) method based on stochastic gradient Langevin dynamics
(SGLD) that we call Parallel SGLD (PSGLD). PSGLD has very favourable scaling
properties with increasing data size and is comparable in terms of
computational requirements to optimisation methods based on stochastic gradient
descent. PSGLD achieves high performance by exploiting the conditional
independence structure of the MF models to sub-sample data in a systematic
manner as to allow parallelisation and distributed computation. We provide a
convergence proof of the algorithm and verify its superior performance on
various architectures such as Graphics Processing Units, shared memory
multi-core systems and multi-computer clusters.
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New spectroscopic observations of 36 HII regions in NGC 4258 obtained with
the Gemini telescope are combined with existing data from the literature to
measure the radial oxygen abundance gradient in this galaxy. The [OIII]4363
auroral line was detected in four of the outermost targets (17 to 22 kpc from
the galaxy center), allowing a determination of the electron temperature Te of
the ionized gas. From the use of different calibrations of the R23 abundance
indicator an oxygen abundance gradient of approximately -0.012 +/- 0.002
dex/kpc is derived. Such a shallow gradient, combined with the difference in
the distance moduli measured from the Cepheid Period-Luminosity relation by
Macri et al. between two distinct fields in NGC 4258, would yield an
unrealistically strong effect of metallicity on the Cepheid distances. This
strengthens the suggestion that systematic biases might affect the Cepheid
distance of the outer field. Evidence for a similar effect in the differential
study of M33 by Scowcroft et al. is presented. A revision of the transformation
between strong-line and Te-based abundances in Cepheid-host galaxies is
discussed. In the Te abundance scale, the oxygen abundance of the inner field
of NGC 4258 is found to be comparable with the LMC value.
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We propose a technique for sensitive magnetic point force detection using a
suspended carbon nanotube (CNT) mechanical resonator combined with a magnetic
field gradient generated by a ferromagnetic gate electrode. Numerical
calculations of the mechanical resonance frequency show that single Bohr
magneton changes in the magnetic state of an individual magnetic molecule
grafted to the CNT can translate to detectable frequency shifts, on the order
of a few kHz. The dependences of the resonator response to device parameters
such as length, tension, CNT diameter, and gate voltage are explored and
optimal operating conditions are identified. A signal-to-noise analysis shows
that in principle, magnetic switching at the level of a single Bohr magneton
can be read out in a single shot on timescales as short as 10 microseconds.
This force sensor should enable new studies of spin dynamics in isolated single
molecule magnets, free from the crystalline or ensemble settings typically
studied.
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The process of training an artificial neural network involves iteratively
adapting its parameters so as to minimize the error of the network's
prediction, when confronted with a learning task. This iterative change can be
naturally interpreted as a trajectory in network space -- a time series of
networks -- and thus the training algorithm (e.g. gradient descent optimization
of a suitable loss function) can be interpreted as a dynamical system in graph
space. In order to illustrate this interpretation, here we study the dynamical
properties of this process by analyzing through this lens the network
trajectories of a shallow neural network, and its evolution through learning a
simple classification task. We systematically consider different ranges of the
learning rate and explore both the dynamical and orbital stability of the
resulting network trajectories, finding hints of regular and chaotic behavior
depending on the learning rate regime. Our findings are put in contrast to
common wisdom on convergence properties of neural networks and dynamical
systems theory. This work also contributes to the cross-fertilization of ideas
between dynamical systems theory, network theory and machine learning
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A novel digital reconfigurable 2_bit metamaterial, equipped with a substrate
integrated feeding system, is designed for industrial quality control
applications within the terahertz frequency range. The proposed feeding
mechanism facilitates azimuthal beam steering, spanning from negative 90 degree
to positive 90 degree, thereby enabling the reconfiguration of beam patterns
within the digital metamaterial. Utilizing the phase distribution concept and
comprehensive analysis of coupling and the e_field effect on individual unit
cells, the metamaterial array spacing is meticulously designed. Operational at
0.7 THz, the system offers versatile reconfigurability, supporting single,
dual, and multibeam modes. Through meticulous optimization, the system
demonstrates an impressive negative 138 degree to positive 138 degree beam
steering capability. This dynamic beamforming ability, transitioning seamlessly
from a singular beam to multibeam configurations, requires minimal
software-hardware integration for scanning and inter_satellite links, thus
presenting significant potential for enhancing product quality within
industrial environments and satellite communication.
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Interferometric principles are widely used in precision physics experiments
and/or in advanced laboratory-based phase measurement systems. Phase resolution
of such systems is a few orders of magnitude higher compared to that of
standard mixer-based quadrature demodulators or lock-in technique. The first
attempt of applying interferometric signal processing to
transmitter-target-receiver based electromagnetic (EM) surveying in geophysical
prospecting is described. It is shown that it is possible to build an EM single
carrier surveying system that is, firstly, immune to amplitude variations of
both the primary and the secondary EM fields, and, secondly, can directly
measure phase variations between the primary and secondary EM fields. Its
inherent phase noise floor, if limited by the interferometer itself, can be as
low as tens of nanoradians/\surdHz or below -140 dBc/\surdHz level. A practical
example of an EM gradiometric surveying system based on an interferometric
principle and operating in the Extremely Low Frequency (ELF) range, is
presented. The system has been tested in regional outback Australia, in the
presence of a highly conducting overburden, in the search of a nickel sulphide
deposit.
Key words: EM gradiometer, interferometric methods, geophysical prospecting
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Tritium beta-decay is the most promising approach to measure the absolute
masses of active light neutrinos in the laboratory and in a model-independent
fashion. The development of Cyclotron Radiation Emission Spectroscopy
techniques and the use of atomic tritium has the potential to improve the
current limits by an order of magnitude in future experiments. In this paper,
we analyse the potential sensitivity of such future searches to keV-mass
sterile neutrinos and exotic interactions of either the active or sterile
neutrinos. We calculate the relevant decay distributions in both energy and
angle of the emitted electron with respect to a potential polarisation of the
tritium, including the interference with the Standard Model case as well as
incorporating relevant final state corrections for atomic tritium. We present
projected sensitivities on the active-sterile neutrino mixing and effective
coupling constants of exotic currents, demonstrating the potential to probe New
Physics in tritium experiments.
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In this paper, we first obtain the energy density by the approach of the new
agegraphic dark energy model, and then the $f(T,B)$ gravity model is studied as
an alternative to the dark energy in a viscous fluid by flat-FRW background, in
which $T$ and $B$ are torsion scalar and boundary term. The Friedmann equations
will obtain in the framework of modified teleparallel gravity by tetrad
components. We consider that the universe dominates with components such as
matter and dark energy by an interacting model. The Hubble parameter is
parameterized by the power-law for the scale factor, and then we fit the
corresponding Hubble parameter with observational data constraints. The
variation of the equation of state (EoS) for dark energy is plotted as a
function of the redshift parameter, and the accelerated expansion of the
universe is explored. In what follows, the stability of the model is also
studied on the base of the sound speed parameter. Finally, the generalized
second law of thermodynamics is investigated by entropies of inside and on the
boundary of the apparent horizon in thermodynamics equilibrium.
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Health disparity research often evaluates health outcomes across demographic
subgroups. Multilevel regression and poststratification (MRP) is a popular
approach for small subgroup estimation due to its ability to stabilize
estimates by fitting multilevel models and to adjust for selection bias by
poststratifying on auxiliary variables, which are population characteristics
predictive of the analytic outcome. However, the granularity and quality of the
estimates produced by MRP are limited by the availability of the auxiliary
variables' joint distribution; data analysts often only have access to the
marginal distributions. To overcome this limitation, we embed the estimation of
population cell counts needed for poststratification into the MRP workflow:
embedded MRP (EMRP). Under EMRP, we generate synthetic populations of the
auxiliary variables before implementing MRP. All sources of estimation
uncertainty are propagated with a fully Bayesian framework. Through simulation
studies, we compare different methods and demonstrate EMRP's improvements over
alternatives on the bias-variance tradeoff to yield valid subpopulation
inferences of interest. As an illustration, we apply EMRP to the Longitudinal
Survey of Wellbeing and estimate food insecurity prevalence among vulnerable
groups in New York City. We find that all EMRP estimators can correct for the
bias in classical MRP while maintaining lower standard errors and narrower
confidence intervals than directly imputing with the WFPBB and design-based
estimates. Performances from the EMRP estimators do not differ substantially
from each other, though we would generally recommend the WFPBB-MRP for its
consistently high coverage rates.
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We derive here Lagrangian fluctuation-dissipation relations for advected
scalars in wall-bounded flows. The relations equate the dissipation rate for
either passive or active scalars to the variance of scalar inputs from the
initial values, boundary values, and internal sources, as those are sampled
backward in time by stochastic Lagrangian trajectories. New probabilistic
concepts are required to represent scalar boundary conditions at the walls: the
boundary local-time density at points on the wall where scalar fluxes are
imposed and the boundary first hitting-time at points where scalar values are
imposed. These concepts are illustrated both by analytical results for the
problem of pure heat conduction and by numerical results from a database of
channel-flow flow turbulence, which also demonstrate the scalar mixing
properties of near-wall turbulence. As an application of the
fluctuation-dissipation relation, we examine for wall-bounded flows the
relation between anomalous scalar dissipation and Lagrangian spontaneous
stochasticity, i.e. the persistent non-determinism of Lagrangian particle
trajectories in the limit of vanishing viscosity and diffusivity. In the first
paper of this series, we showed that spontaneous stochasticity is the only
possible mechanism for anomalous dissipation of passive or active scalars, away
from walls. Here it is shown that this remains true when there are no scalar
fluxes through walls. Simple examples show, on the other hand, that a distinct
mechanism of non-vanishing scalar dissipation can be thin scalar boundary
layers near the walls. Nevertheless, we prove for general wall-bounded flows
that spontaneous stochasticity is another possible mechanism of anomalous
scalar dissipation.
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Biological agents, such as humans and animals, are capable of making
decisions out of a very large number of choices in a limited time. They can do
so because they use their prior knowledge to find a solution that is not
necessarily optimal but good enough for the given task. In this work, we study
the motion coordination of multiple drones under the above-mentioned paradigm,
Bounded Rationality (BR), to achieve cooperative motion planning tasks.
Specifically, we design a prior policy that provides useful goal-directed
navigation heuristics in familiar environments and is adaptive in unfamiliar
ones via Reinforcement Learning augmented with an environment-dependent
exploration noise. Integrating this prior policy in the game-theoretic bounded
rationality framework allows agents to quickly make decisions in a group
considering other agents' computational constraints. Our investigation assures
that agents with a well-informed prior policy increase the efficiency of the
collective decision-making capability of the group. We have conducted rigorous
experiments in simulation and in the real world to demonstrate that the ability
of informed agents to navigate to the goal safely can guide the group to
coordinate efficiently under the BR framework.
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While Transformers have had significant success in paragraph generation, they
treat sentences as linear sequences of tokens and often neglect their
hierarchical information. Prior work has shown that decomposing the levels of
granularity~(e.g., word, phrase, or sentence) for input tokens has produced
substantial improvements, suggesting the possibility of enhancing Transformers
via more fine-grained modeling of granularity. In this work, we propose a
continuous decomposition of granularity for neural paraphrase generation
(C-DNPG). In order to efficiently incorporate granularity into sentence
encoding, C-DNPG introduces a granularity-aware attention (GA-Attention)
mechanism which extends the multi-head self-attention with: 1) a granularity
head that automatically infers the hierarchical structure of a sentence by
neurally estimating the granularity level of each input token; and 2) two novel
attention masks, namely, granularity resonance and granularity scope, to
efficiently encode granularity into attention. Experiments on two benchmarks,
including Quora question pairs and Twitter URLs have shown that C-DNPG
outperforms baseline models by a remarkable margin and achieves
state-of-the-art results in terms of many metrics. Qualitative analysis reveals
that C-DNPG indeed captures fine-grained levels of granularity with
effectiveness.
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We propose instance segmentation as a useful tool for image analysis in
materials science. Instance segmentation is an advanced technique in computer
vision which generates individual segmentation masks for every object of
interest that is recognized in an image. Using an out-of-the-box implementation
of Mask R-CNN, instance segmentation is applied to images of metal powder
particles produced through gas atomization. Leveraging transfer learning allows
for the analysis to be conducted with a very small training set of labeled
images. As well as providing another method for measuring the particle size
distribution, we demonstrate the first direct measurements of the satellite
content in powder samples. After analyzing the results for the labeled data
dataset, the trained model was used to generate measurements for a much larger
set of unlabeled images. The resulting particle size measurements showed
reasonable agreement with laser scattering measurements. The satellite
measurements were self-consistent and showed good agreement with the expected
trends for different samples. Finally, we provide a small case study showing
how instance segmentation can be used to measure spheroidite content in the
UltraHigh Carbon Steel Database, demonstrating the flexibility of the
technique.
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The lack of large video databases obtained from real patients with
respiratory disorders makes the design and optimization of video-based
monitoring systems quite critical. The purpose of this study is the development
of suitable models and simulators of breathing behaviors and disorders, such as
respiratory pauses and apneas, in order to allow efficient design and test of
video-based monitoring systems. More precisely, a novel Continuous-Time Markov
Chain (CTMC) statistical model of breathing patterns is presented. The
Respiratory Rate (RR) pattern, estimated by measured vital signs of
hospital-monitored patients, is approximated as a CTMC, whose states and
parameters are selected through an appropriate statistical analysis. Then, two
simulators, software- and hardware-based, are proposed. After validation of the
CTMC model, the proposed simulators are tested with previously developed
video-based algorithms for the estimation of the RR and the detection of apnea
events. Examples of application to assess the performance of systems for
video-based RR estimation and apnea detection are presented. The results, in
terms of Kullback-Leibler divergence, show that realistic breathing patterns,
including specific respiratory disorders, can be accurately described by the
proposed model; moreover, the simulators are able to reproduce practical
breathing patterns for video analysis. The presented CTMC statistical model can
be strategic to describe realistic breathing patterns and devise simulators
useful to develop and test novel and effective video processing-based
monitoring systems.
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The puncture method for dealing with black holes in the numerical simulation
of vacuum spacetimes is remarkably successful when combined with the BSSN
formulation of the Einstein equations. We examine a generalized class of
formulations modeled along the lines of the Laguna-Shoemaker system, including
BSSN as a special case. The formulation is a two parameter generalization of
the choice of variables used in standard BSSN evolutions. Numerical stability
of the standard finite difference methods is proven for the formulation in the
linear regime around flat space, a special case of which is the numerical
stability of BSSN. Numerical evolutions are presented and compared with a
standard BSSN implementation. We find that a significant portion of the
parameter space leads to stable evolutions and that standard BSSN is located
near the edge of the stability region. Non-standard parameter choices typically
result in smoother behaviour of the evolution variables close to the puncture
and thus hold promise for improved accuracy in, e.g., long-term BH binary
inspirals, and for overcoming (numerical) stability problems still encountered
in some types of black-hole simulations, e.g., in $D \ge 6$ dimensions.
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A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> for
each choice of g(s) in G, s in S. In this paper we study invariable generation
of infinite groups, with emphasis on linear groups. Our main result shows that
a finitely generated linear group is invariably generated by some finite set of
elements if and only if it is virtually solvable. We also show that the
profinite completion of an arithmetic group having the congruence subgroup
property is invariably generated by a finite set of elements.
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We introduce a machine learning model to predict atomization energies of a
diverse set of organic molecules, based on nuclear charges and atomic positions
only. The problem of solving the molecular Schr\"odinger equation is mapped
onto a non-linear statistical regression problem of reduced complexity.
Regression models are trained on and compared to atomization energies computed
with hybrid density-functional theory. Cross-validation over more than seven
thousand small organic molecules yields a mean absolute error of ~10 kcal/mol.
Applicability is demonstrated for the prediction of molecular atomization
potential energy curves.
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We investigate the problem of counting 1/16 BPS operators in N=4
Super-Yang-Mills theory at weak coupling. We present the complete set of 1/16
BPS operators in the infinite N limit, which agrees with the counting of free
BPS multi-graviton states in the gravity dual AdS5xS5. Further, we conjecture
that all 1/16 BPS operators in N=4 SYM are of the multi-graviton form, and give
numerical evidences for this conjecture. We discuss the implication of our
conjecture and the seeming failure in reproducing the entropy of large 1/16 BPS
black holes in AdS5.
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We show how in a class of models Peccei--Quinn symmetry can be realized as an
automatic consequence of a gauged $U(1)$ family symmetry. These models provide
a solution to the strong CP problem either via a massless $u$--quark or via the
DFSZ invisible axion. The local family symmetry protects against potentially
large corrections to $\overline{\theta} $ induced by quantum gravitational
effects. In a supersymmetric extension, the `$\mu$--problem' is shown to have a
natural solution in the context of gravitationally induced operators. We also
present a plausible mechanism which can explain the inter--generational mass
hierarchy in such a context.
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Using the simple (symmetric) Hubbard dimer, we analyze some important
features of the $GW$ approximation. We show that the problem of the existence
of multiple quasiparticle solutions in the (perturbative) one-shot $GW$ method
and its partially self-consistent version is solved by full self-consistency.
We also analyze the neutral excitation spectrum using the Bethe-Salpeter
equation (BSE) formalism within the standard $GW$ approximation and find, in
particular, that i) some neutral excitation energies become complex when the
electron-electron interaction $U$ increases, which can be traced back to the
approximate nature of the $GW$ quasiparticle energies; ii) the BSE formalism
yields accurate correlation energies over a wide range of $U$ when the trace
(or plasmon) formula is employed; iii) the trace formula is sensitive to the
occurrence of complex excitation energies (especially singlet), while the
expression obtained from the adiabatic-connection fluctuation-dissipation
theorem (ACFDT) is more stable (yet less accurate); iv) the trace formula has
the correct behavior for weak (\ie, small $U$) interaction, unlike the ACFDT
expression.
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Magnetic fields, which are undoubtedly present in extragalactic jets and
responsible for the observed synchrotron radiation, can affect the morphology
and dynamics of the jets and their interaction with the ambient cluster medium.
We examine the jet propagation, morphology and magnetic field structure for a
wide range of density contrasts, using a globally consistent setup for both the
jet interaction and the magnetic field. The MHD code NIRVANA is used to evolve
the simulation, using the constrained-transport method. The density contrasts
are varied between \eta = 10^{-1} and 10^{-4} with constant sonic Mach number
6. The jets are supermagnetosonic and simulated bipolarly due to the low jet
densities and their strong backflows. The helical magnetic field is largely
confined to the jet, leaving the ambient medium nonmagnetic. We find magnetic
fields with plasma \beta \sim 10 already stabilize and widen the jet head.
Furthermore they are efficiently amplified by a shearing mechanism in the jet
head and are strong enough to damp Kelvin-Helmholtz instabilities of the
contact discontinuity. The cocoon magnetic fields are found to be stronger than
expected from simple flux conservation and capable to produce smoother lobes,
as found observationally. The bow shocks and jet lengths evolve self-similarly.
The radio cocoon aspect ratios are generally higher for heavier jets and grow
only slowly (roughly self-similar) while overpressured, but much faster when
they approach pressure balance with the ambient medium. In this regime,
self-similar models can no longer be applied. Bow shocks are found to be of low
excentricity for very light jets and have low Mach numbers. Cocoon turbulence
and a dissolving bow shock create and excite waves and ripples in the ambient
gas. Thermalization is found to be very efficient for low jet densities.
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We study the relaxation to equilibrium of two dimensional islands containing
up to 20000 atoms by Kinetic Monte Carlo simulations. We find that the commonly
assumed relaxation mechanism - curvature-driven relaxation via atom diffusion -
cannot explain the results obtained at low temperatures, where the island edges
consist in large facets. Specifically, our simulations show that the exponent
characterizing the dependence of the equilibration time on the island size is
different at high and low temperatures, in contradiction with the above cited
assumptions. Instead, we propose that - at low temperatures - the relaxation is
limited by the nucleation of new atomic rows on the large facets : this allows
us to explain both the activation energy and the island size dependence of the
equilibration time.
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We use Renormalization Group to prove local well posedness for a generalized
KPZ equation introduced by H. Spohn in the context of stochastic hydrodynamics.
The equation requires the addition of counter terms diverging with a cutoff
$\epsilon$ as $\epsilon^{-1}$ and $\log\epsilon^{-1}$.
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Cooperative multi-agent policy gradient (MAPG) algorithms have recently
attracted wide attention and are regarded as a general scheme for the
multi-agent system. Credit assignment plays an important role in MAPG and can
induce cooperation among multiple agents. However, most MAPG algorithms cannot
achieve good credit assignment because of the game-theoretic pathology known as
\textit{centralized-decentralized mismatch}. To address this issue, this paper
presents a novel method, \textit{\underline{M}ulti-\underline{A}gent
\underline{P}olarization \underline{P}olicy \underline{G}radient} (MAPPG).
MAPPG takes a simple but efficient polarization function to transform the
optimal consistency of joint and individual actions into easily realized
constraints, thus enabling efficient credit assignment in MAPG. Theoretically,
we prove that individual policies of MAPPG can converge to the global optimum.
Empirically, we evaluate MAPPG on the well-known matrix game and differential
game, and verify that MAPPG can converge to the global optimum for both
discrete and continuous action spaces. We also evaluate MAPPG on a set of
StarCraft II micromanagement tasks and demonstrate that MAPPG outperforms the
state-of-the-art MAPG algorithms.
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We consider self-loops and multiple edges in the configuration model as the
size of the graph tends to infinity. The interest in these random variables is
due to the fact that the configuration model, conditioned on being simple, is a
uniform random graph with prescribed degrees. Simplicity corresponds to the
absence of self-loops and multiple edges. We show that the number of self-loops
and multiple edges converges in distribution to two independent Poisson random
variables when the second moment of the empirical degree distribution
converges. We also provide an estimate on the total variation distance between
the number of self-loops and multiple edges and the Poisson limit of their sum.
This revisits previous works of Bollob\'as, of Janson, of Wormald and others.
The error estimates also imply sharp asymptotics for the number of simple
graphs with prescribed degrees. The error estimates follow from an application
of Stein's method for Poisson convergence, which is a novel method for this
problem. The asymptotic independence of self-loops and multiple edges follows
from a Poisson version of the Cram\'er-Wold device using thinning, which is of
independent interest. When the degree distribution has infinite second moment,
our general results break down. We can, however, prove a central limit theorem
for the number of self-loops, and for the multiple edges between vertices of
degrees much smaller than the square root of the size of the graph, or when we
truncate the degrees similarly. Our results and proofs easily extend to
directed and bipartite configuration models.
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Multimodal image alignment involves finding spatial correspondences between
volumes varying in appearance and structure. Automated alignment methods are
often based on local optimization that can be highly sensitive to their
initialization. We propose a global optimization method for rigid multimodal 3D
image alignment, based on a novel efficient algorithm for computing similarity
of normalized gradient fields (NGF) in the frequency domain. We validate the
method experimentally on a dataset comprised of 20 brain volumes acquired in
four modalities (T1w, Flair, CT, [18F] FDG PET), synthetically displaced with
known transformations. The proposed method exhibits excellent performance on
all six possible modality combinations, and outperforms all four reference
methods by a large margin. The method is fast; a 3.4Mvoxel global rigid
alignment requires approximately 40 seconds of computation, and the proposed
algorithm outperforms a direct algorithm for the same task by more than three
orders of magnitude. Open-source implementation is provided.
|
We consider a linear stochastic bandit problem where the dimension $K$ of the
unknown parameter $\theta$ is larger than the sampling budget $n$. In such
cases, it is in general impossible to derive sub-linear regret bounds since
usual linear bandit algorithms have a regret in $O(K\sqrt{n})$. In this paper
we assume that $\theta$ is $S-$sparse, i.e. has at most $S-$non-zero
components, and that the space of arms is the unit ball for the $||.||_2$ norm.
We combine ideas from Compressed Sensing and Bandit Theory and derive
algorithms with regret bounds in $O(S\sqrt{n})$.
|
The Golomb ruler problem is defined as follows: Given a positive integer n,
locate n marks on a ruler such that the distance between any two distinct pair
of marks are different from each other and the total length of the ruler is
minimized. The Golomb ruler problem has applications in information theory,
astronomy and communications, and it can be seen as a challenge for
combinatorial optimization algorithms. Although constructing high quality
rulers is well-studied, proving optimality is a far more challenging task. In
this paper, we provide a computational comparison of different optimization
paradigms, each using a different model (linear integer, constraint programming
and quadratic integer) to certify that a given Golomb ruler is optimal. We
propose several enhancements to improve the computational performance of each
method by exploring bound tightening, valid inequalities, cutting planes and
branching strategies. We conclude that a certain quadratic integer programming
model solved through a Benders decomposition and strengthened by two types of
valid inequalities performs the best in terms of solution time for small-sized
Golomb ruler problem instances. On the other hand, a constraint programming
model improved by range reduction and a particular branching strategy could
have more potential to solve larger size instances due to its promising
parallelization features.
|
We show that a new Regge trajectory with \alpha_{f_1} (0) \approx 1 and slope
\alpha_{f_1}'(0) \approx 0 explains the features of hadron-hadron scattering
and photoproduction of the rho and phi mesons at large energy and momentum
transfer. This trajectory with quantum numbers P = C = +1 and odd signature can
be considered as a natural partner of the Pomeron which has even signature. The
odd signature of the new exchange leads to contributions to the spin-dependent
cross sections, which do not vanish at large energy. The links between the
anomalous properties of this trajectory, the axial anomaly and the flavor
singlet axial vector f_1 (1285) meson are discussed.
|
For disordered elastic manifolds in the ground state (equilibrium) we obtain
the critical exponents for the roughness and the correction-to-scaling up to
3-loop order, i.e. third order in $\epsilon=4-d$, where $d$ is the internal
dimension $d$. We also give the full 2-point function up to order
$\epsilon^{2}$, i.e. at 2-loop order.
|
We study universal aspects of fluctuations in an ensemble of noninteracting
continuous quantum thermal machines in the steady state limit. Considering an
individual machine, such as a refrigerator, in which relative fluctuations (and
high order cumulants) of the cooling heat current to the absorbed heat current,
$\eta^{(n)}$, are upper-bounded, $\eta^{(n)}\leq \eta_C^n$ with $n\geq 2$ and
$\eta_C$ the Carnot efficiency, we prove that an {\it ensemble} of $N$ distinct
machines similarly satisfies this upper bound on the relative fluctuations of
the ensemble, $\eta_N^{(n)}\leq \eta_C^n$. For an ensemble of distinct quantum
{\it refrigerators} with components operating in the tight coupling limit we
further prove the existence of a {\it lower bound} on $\eta_N^{(n)}$ in
specific cases, exemplified on three-level quantum absorption refrigerators and
resonant-energy thermoelectric junctions. Beyond special cases, the existence
of a lower bound on $\eta_N^{(2)}$ for an ensemble of quantum refrigerators is
demonstrated by numerical simulations.
|
Recently, it has been shown that entropy can be used to sort Brownian
particles according to their size. In particular, a combination of a static and
a time-dependent force applied on differently sized particles which are
confined in an asymmetric periodic structure can be used to separate them
efficiently, by forcing them to move in opposite directions. In this paper, we
investigate the optimization of the performance of the 'entropic splitter'.
Specifically, the splitting mechanism and how it depends on the geometry of the
channel, and the frequency and strength of the periodic forcing is analyzed.
Using numerical simulations, we demonstrate that a very efficient and fast
separation with a practically 100% purity can be achieved by a proper
optimization of the control variables. The results of this work could be useful
for a more efficient separation of dispersed phases such as DNA fragments or
colloids dependent on their size.
|
We prove that the canonical twist $\zeta \colon K(\mathbb{Z},3) \rightarrow
BGL_1(MSpin^c)$ does not extend to a twist for unitary bordism by showing that
every continuous map $f \colon K(\mathbb{Z},3) \rightarrow BGL_1(MU)$ loops to
a null homotopic map.
|
Both neural networks and decision trees are popular machine learning methods
and are widely used to solve problems from diverse domains. These two
classifiers are commonly used base classifiers in an ensemble framework. In
this paper, we first present a new variant of oblique decision tree based on a
linear classifier, then construct an ensemble classifier based on the fusion of
a fast neural network, random vector functional link network and oblique
decision trees. Random Vector Functional Link Network has an elegant closed
form solution with extremely short training time. The neural network partitions
each training bag (obtained using bagging) at the root level into C subsets
where C is the number of classes in the dataset and subsequently, C oblique
decision trees are trained on such partitions. The proposed method provides a
rich insight into the data by grouping the confusing or hard to classify
samples for each class and thus, provides an opportunity to employ fine-grained
classification rule over the data. The performance of the ensemble classifier
is evaluated on several multi-class datasets where it demonstrates a superior
performance compared to other state-of- the-art classifiers.
|
The theory interest group in the International Virtual Observatory Alliance
(IVOA) has the goal of ensuring that theoretical data and services are taken
into account in the IVOA standards process. In this poster we present some of
the efforts carried out by this group to include evolutionary synthesis models
in the VO framework. In particular we present the VO tool PGos3, developed by
the INAOE (Mexico) and the Spanish Virtual Observatory which includes most of
public SSP models in the VO framework (e.g. VOSpec). We also describe the
problems related with the inclusion of synthesis models in the VO framework and
we try to encourage people to define the way in which synthesis models should
be described. This issue has implications not only for the inclusion of
synthesis models in the the VO framework but also for a proper usage of
synthesis models.
|
Knowing which factors are significant in credit rating assignment leads to
better decision-making. However, the focus of the literature thus far has been
mostly on structured data, and fewer studies have addressed unstructured or
multi-modal datasets. In this paper, we present an analysis of the most
effective architectures for the fusion of deep learning models for the
prediction of company credit rating classes, by using structured and
unstructured datasets of different types. In these models, we tested different
combinations of fusion strategies with different deep learning models,
including CNN, LSTM, GRU, and BERT. We studied data fusion strategies in terms
of level (including early and intermediate fusion) and techniques (including
concatenation and cross-attention). Our results show that a CNN-based
multi-modal model with two fusion strategies outperformed other multi-modal
techniques. In addition, by comparing simple architectures with more complex
ones, we found that more sophisticated deep learning models do not necessarily
produce the highest performance; however, if attention-based models are
producing the best results, cross-attention is necessary as a fusion strategy.
Finally, our comparison of rating agencies on short-, medium-, and long-term
performance shows that Moody's credit ratings outperform those of other
agencies like Standard & Poor's and Fitch Ratings.
|
In these lecture notes, we present a connection between the complex dynamics
of a family of rational functions $f_t: \mathbb{P}^1\to \mathbb{P}^1$,
parameterized by $t$ in a Riemann surface $X$, and the arithmetic dynamics of
$f_t$ on rational points $\mathbb{P}^1(k)$ where $k = \mathbb{C}(X)$ or
$\bar{\mathbb{Q}}(X)$. An explicit relation between stability and canonical
height is explained, with a proof that contains a piece of the Mordell-Weil
theorem for elliptic curves over function fields. Our main goal is to pose some
questions and conjectures about these families, guided by the principle of
"unlikely intersections" from arithmetic geometry, as in [Zannier 2012]. We
also include a proof that the hyperbolic postcritically-finite maps are Zariski
dense in the moduli space of rational maps of any given degree $d>1$. These
notes are based on four lectures at KAWA 2015, in Pisa, Italy, designed for an
audience specializing in complex analysis, expanding upon the main results of
[Baker-DeMarco 2013, DeMarco 2016, DeMarco-Wang-Ye 2016].
|
For analyzing anisotropic low relative-velocity correlation-functions and the
associated emission sources, we propose an expansion in terms of cartesian
spherical harmonics. The expansion coefficients represent angular moments of
the investigated functions. The respective coefficients for the correlation and
source are directly related to each other via one-dimensional integral
transforms. The shape features of the source may be partly read off from the
respective features of the correlation function and can be, otherwise, imaged.
|
We study an one{dimensional quasilinear system proposed by J. Tello and M.
Winkler [19] which models the population dynamics of two competing species
attracted by the same chemical. The kinetics terms of the interacting species
are chosen to be the Lotka{Volterra type. We prove the existence of global
bounded and classical solutions for all chemoattraction rates. Under
homogeneous Neumann boundary conditions, we establish the existence of
nonconstant steady states by local bifurcation theory. The stability of the
bifurcating solutions is also obtained when the diffusivity of both species is
large. Finally, we perform extensive numerical studies to demonstrate the
formation of stable positive steady states with various interesting spatial
structures.
|
Thanks to the excellent performances of ATLAS and CMS in triggering on muon
signals and reconstructing these particles down to low transverse momentum,
large samples of heavy-flavored hadrons have been collected in the 2011 LHC run
at sqrt(s) = 7 TeV. The analysis of these samples has enabled both experiments
to perform competitive measurements of heavy-flavor properties, such as
quarkonium polarization, lifetime and CP-violation measurements, hadron
spectroscopy and branching ratios of rare B decays.
|
StableDiffusion is a revolutionary text-to-image generator that is causing a
stir in the world of image generation and editing. Unlike traditional methods
that learn a diffusion model in pixel space, StableDiffusion learns a diffusion
model in the latent space via a VQGAN, ensuring both efficiency and quality. It
not only supports image generation tasks, but also enables image editing for
real images, such as image inpainting and local editing. However, we have
observed that the vanilla VQGAN used in StableDiffusion leads to significant
information loss, causing distortion artifacts even in non-edited image
regions. To this end, we propose a new asymmetric VQGAN with two simple
designs. Firstly, in addition to the input from the encoder, the decoder
contains a conditional branch that incorporates information from task-specific
priors, such as the unmasked image region in inpainting. Secondly, the decoder
is much heavier than the encoder, allowing for more detailed recovery while
only slightly increasing the total inference cost. The training cost of our
asymmetric VQGAN is cheap, and we only need to retrain a new asymmetric decoder
while keeping the vanilla VQGAN encoder and StableDiffusion unchanged. Our
asymmetric VQGAN can be widely used in StableDiffusion-based inpainting and
local editing methods. Extensive experiments demonstrate that it can
significantly improve the inpainting and editing performance, while maintaining
the original text-to-image capability. The code is available at
\url{https://github.com/buxiangzhiren/Asymmetric_VQGAN}.
|
We use a modified SampleRNN architecture to generate music in modern genres
such as black metal and math rock. Unlike MIDI and symbolic models, SampleRNN
generates raw audio in the time domain. This requirement becomes increasingly
important in modern music styles where timbre and space are used
compositionally. Long developmental compositions with rapid transitions between
sections are possible by increasing the depth of the network beyond the number
used for speech datasets. We are delighted by the unique characteristic
artifacts of neural synthesis.
|
The type IV pilus retraction motor is found in many important bacterial
pathogens. It is the strongest known linear motor protein and is required for
bacterial infectivity. We characterize the dynamics of type IV pilus retraction
in terms of a stochastic chemical reaction model. We find that a two state
model can describe the experimental force velocity relation and qualitative
dependence of ATP concentration. The results indicate that the dynamics is
limited by an ATP-dependent step at low load and a force-dependent step at high
load, and that at least one step is effectively irreversible in the measured
range of forces. The irreversible nature of the sub-step(s) lead to interesting
predictions for future experiments: We find different parameterizations with
mathematically identical force velocity relations but different fluctuations
(diffusion constant). We also find a longer elementary step compared to an
earlier analysis, which agrees better with known facts about the structure of
the pilus filament and energetic considerations. We conclude that more
experimental data is needed, and that further retraction experiments are likely
to resolve interesting details and give valuable insights into the PilT
machinery. In light of our findings, the fluctuations of the retraction
dynamics emerge as a key property to be studied in future experiments.
|
We present the results of a multiplicity survey of 212 T Tauri stars in the
Chamaeleon I and Taurus-Auriga star-forming regions, based on high-resolution
spectra from the Magellan Clay 6.5 m telescope. From these data, we achieved a
typical radial velocity precision of ~80 m/s with slower rotators yielding
better precision, in general. For 174 of these stars, we obtained multi-epoch
data with sufficient time baselines to identify binaries based on radial
velocity variations. We identified eight close binaries and four close triples,
of which three and two, respectively, are new discoveries. The spectroscopic
multiplicity fractions we find for Cha I (7%) and Tau-Aur (6%) are similar to
each other, and to the results of field star surveys in the same mass and
period regime. However, unlike the results from imaging surveys, the frequency
of systems with close companions in our sample is not seen to depend on primary
mass. Additionally, we do not find a strong correlation between accretion and
close multiplicity. This implies that close companions are not likely the main
source of the accretion shut down observed in weak-lined T Tauri stars. Our
results also suggest that sufficient radial velocity precision can be achieved
for at least a subset of slowly rotating young stars to search for hot Jupiter
planets.
|
The certification of quantum resources is a critical tool in the development
of quantum information processing. In particular, quantum state verification is
a fundamental building block for communication and computation applications,
determining whether the involved parties can trust the resources at hand or
whether the application should be aborted. Self-testing methods have been used
to tackle such verification tasks in a device-independent (DI) setting.
However, these approaches commonly consider the limit of large (asymptotic),
identically and independently distributed (IID) samples, which weakens the DI
claim and poses serious challenges to their experimental implementation. Here
we overcome these challenges by adopting a theoretical protocol enabling the
certification of quantum states in the few-copies and non-IID regime and by
leveraging a high-fidelity multipartite entangled photon source. This allows us
to show the efficient and device-independent certification of a single copy of
a four-qubit GHZ state that can readily be used for the robust and reliable
implementation of quantum information tasks.
|
We present the new code ALCAR developed to model multidimensional, multi
energy-group neutrino transport in the context of supernovae and neutron-star
mergers. The algorithm solves the evolution equations of the 0th- and 1st-order
angular moments of the specific intensity, supplemented by an algebraic
relation for the 2nd-moment tensor to close the system. The scheme takes into
account frame-dependent effects of order O(v/c) as well as the most important
types of neutrino interactions. The transport scheme is significantly more
efficient than a multidimensional solver of the Boltzmann equation, while it is
more accurate and consistent than the flux-limited diffusion method. The
finite-volume discretization of the essentially hyperbolic system of moment
equations employs methods well-known from hydrodynamics. For the time
integration of the potentially stiff moment equations we employ a scheme in
which only the local source terms are treated implicitly, while the advection
terms are kept explicit, thereby allowing for an efficient computational
parallelization of the algorithm. We investigate various problem setups in one
and two dimensions to verify the implementation and to test the quality of the
algebraic closure scheme. In our most detailed test, we compare a fully
dynamic, one-dimensional core-collapse simulation with two published
calculations performed with well-known Boltzmann-type neutrino-hydrodynamics
codes and we find very satisfactory agreement.
|
Axially symmetric stationary metrics governed by the Einstein-Euler equations
for slowly rotating perfect fluids have been constructed in an arbitrarily
large bounded domain containing the support of the mass density. However the
problem of global prolongation of the metric is still open. On the other hand
the so called matter-vacuum matching problem, particularly as the source
problem for the Kerr metric, has been discussed by several authors. This can be
regarded as the approach to the same open problem in the opposite direction. We
give a remark on this open problem.
|
We consider whether the asymptotic distributions for the log-likelihood ratio
test statistic are expected to be Gaussian or chi-squared. Two straightforward
examples provide insight on the difference.
|
We present a study of the radio continuum properties of two
luminous/ultraluminous infrared galaxy samples: the OH megamaser (OHM) sample
(74 objects) and the control sample (128 objects) without detected maser
emission. We carried out pilot observations for 140 objects with the radio
telescope RATAN-600 at 1.2, 2.3, 4.7, 8.2, 11.2, and 22.3 GHz in 2019-2021. The
OHM sample has two times more flat-spectrum sources (32 per cent) than the
control sample. Steep radio spectra prevail in both samples. The median
spectral index at 4.7 GHz $\alpha_{4.7}=-0.59$ for the OHM sample, and
$\alpha_{4.7}=-0.71$ for the non-OHM galaxies. We confirm a tight correlation
of the far-infrared (FIR) and radio luminosities for the OHM sample. We found
correlations between isotropic OH line luminosity $L_{OH}$ and the spectral
index $\alpha_{4.7}$ ($\rho$=0.26, p-val.=0.04) and between $L_{OH}$ and radio
luminosity $P_{1.4}$ ($\rho$=0.35, p-val.=0.005). Reviewing subsamples of
masers powered by active galactic nuclei (AGNs) and star formation revealed
insignificant differences for their FIR and radio properties. Nonetheless,
AGN-powered galaxies exhibit larger scatter in a range of parameters and their
standard deviations. The similarities in the radio and FIR properties in the
two samples are presumably caused by the presence of a significant amount of
AGN sources in both samples (47 and 30 per cent in the OHM and control samples)
and/or possibly by the presence of undetected OH emission sources in the
control sample.
|
In traditional ELM and its improved versions suffer from the problems of
outliers or noises due to overfitting and imbalance due to distribution. We
propose a novel hybrid adaptive fuzzy ELM(HA-FELM), which introduces a fuzzy
membership function to the traditional ELM method to deal with the above
problems. We define the fuzzy membership function not only basing on the
distance between each sample and the center of the class but also the density
among samples which based on the quantum harmonic oscillator model. The
proposed fuzzy membership function overcomes the shortcoming of the traditional
fuzzy membership function and could make itself adjusted according to the
specific distribution of different samples adaptively. Experiments show the
proposed HA-FELM can produce better performance than SVM, ELM, and RELM in text
classification.
|
We present an analysis of the effects of environment on the photometric
properties of galaxies in the core of the Shapley Supercluster at z=0.05, one
of the most massive structures in the local universe. The Shapley Optical
Survey (SOS) comprises archive WFI optical imaging of a 2.0 deg^2 region
containing the rich clusters A3556, A3558 and A3562 which demonstrate a highly
complex dynamical situation including ongoing cluster mergers. The B-R/R
colour-magnitude relation has an intrinsic dispersion of 0.045 mag and is
0.015\pm0.005 mag redder in the highest-density regions, indicative of the red
sequence galaxy population being 500 Myr older in the cluster cores than
towards the virial radius. The B-R colours of galaxies are dependent on their
environment, whereas their luminosities are independent of the local density,
except for the very brightest galaxies (M_R<-22). The global colours of faint
(>M*+2) galaxies change from the cluster cores where ~90% of galaxies lie along
the cluster red sequence to the virial radius, where the fraction has dropped
to just ~20%. This suggests that processes related to the supercluster
environment are responsible for transforming faint galaxies, rather than galaxy
merging, which should be infrequent in any of the regions studied here. The
largest concentrations of faint blue galaxies are found between the clusters,
coincident with regions containing high fractions of ~L* galaxies with radio
emission indicating starbursts. Their location suggests star-formation
triggered by cluster mergers, in particular the merger of A3562 and the poor
cluster SC1329-313, although they may also represent recent arrivals in the
supercluster core complex. (abstract truncated)
|
Let $G$ be the semidirect product $\Gamma \rtimes F_2$ where $\Gamma$ is
either the free group $F_n$, $n > 1$ or the fundamental group $S_g$ of a closed
surface of genus $g > 1$. We prove that $G$ is incoherent, solving two problems
posed by D. Wise. This implies an affirmative answer to a question of J.
Hillman on the fundamental group of a surface bundle over a surface. Although
many groups have been shown to be incoherent using virtual algebraic fibering,
we also show that not every free-by-free group virtually algebraically fibers.
|
We construct a spherically symmetric noncommutative space in three dimensions
by foliating the space with concentric fuzzy spheres. We show how to construct
a gauge theory in this space and in particular we derive the noncommutative
version of a Yang-Mills-Higgs theory. We find numerical monopole solutions of
the equations of motion.
|
Owing to the increasing popularity of lead-based hybrid perovskites for
photovoltaic (PV) applications, it is crucial to understand their defect
physics and its influence on their optoelectronic properties. In this work, we
simulate various point defects in pseudo-cubic structures of mixed
iodide-bromide and bromide-chloride methylammonium lead perovskites with the
general formula MAPbI_{3-y}Br_{y} or MAPbBr_{3-y}Cl_{y} (where y is between 0
and 3), and use first principles based density functional theory computations
to study their relative formation energies and charge transition levels. We
identify vacancy defects and Pb on MA anti-site defect as the lowest energy
native defects in each perovskite. We observe that while the low energy defects
in all MAPbI_{3-y}Br_{y} systems only create shallow transition levels, the Br
or Cl vacancy defects in the Cl-containing pervoskites have low energy and form
deep levels which become deeper for higher Cl content. Further, we study
extrinsic substitution by different elements at the Pb site in MAPbBr_{3},
MAPbCl_{3} and the 50-50 mixed halide perovskite, MAPbBr_{1.5}Cl_{1.5}, and
identify some transition metals that create lower energy defects than the
dominant intrinsic defects and also create mid-gap charge transition levels.
|
We compute multiprecision solutions of the Lane-Emden equation. This
differential equation arises when introducing the well-known polytropic model
into the equation of hydrostatic equilibrium for a nondistorted star. Since
such multiprecision computations are time-consuming, we apply to this problem
parallel programming techniques and thus the execution time of the computations
is drastically reduced.
|
We construct an open enumerative theory for the Landau-Ginzburg (LG) model
$(\mathbb{C}^2, \mu_r\times \mu_s, x^r+y^s)$. The invariants are defined as
integrals of multisections of a Witten bundle with descendents over a moduli
space that is a real orbifold with corners. In turn, a generating function for
these open invariants yields the mirror LG model and a versal deformation of it
with flat coordinates. After establishing an open topological recursion result,
we prove an LG/LG open mirror symmetry theorem in dimension two with all
descendents. The open invariants we define are not unique but depend on
boundary conditions that, when altered, exhibit wall-crossing phenomena for the
invariants. We describe an LG wall-crossing group classifying the wall-crossing
transformations that can occur.
|
We report the detection of type-B quasi-periodic oscillation (QPO) of the
black hole X-ray binary Swift J1728.9-3613 observed by NICER during the 2019
outburst. A type- B QPO was observed for the first two days and it disappeared
as flux increased, but again appeared at $\sim$ 7.70 Hz when flux was
dramatically decreased. The source was found in the soft-intermediate state
during these observations. We further studied the energy dependence of the QPO.
We found that QPO was observed only for a higher energy range implying that the
origin of QPO is possibly due to the corona emitting higher energy photons by
the inverse Compton process. The variation of spectral parameters can be
explained with the disk truncation model. The fractional rms found to be
monotonically increased with energy. The phase lag spectrum followed the
U-shaped curve. The rms and phase lag spectrum are modelled and explained with
the single-component comptonization model vkompthdk.
|
We present a family-non-universal extension of the Standard Model where the
the first two families feature both quark-lepton and electroweak-flavour
unification, via the $SU(4) \times Sp(4)_L \times Sp(4)_R$ gauge group, whereas
quark-lepton unification for the third family is realised \`a la Pati-Salam.
Via staggered symmetry breaking steps, this construction offers a natural
explanation for the observed hierarchical pattern of fermion masses and
mixings, while providing a natural suppression for flavour-changing processes
involving the first two generations. The last-but-one step in the
symmetry-breaking chain is a non-universal 4321 model, characterised by a
vector leptoquark naturally coupled mainly to the third generation. The
stability of the Higgs sector points to a 4321$\to$SM symmetry-breaking scale
around the TeV, with interesting phenomenological consequences in $B$ physics
and collider processes that differ from those of other known 4321 completions.
|
We report on a search for the flavor-changing neutral-current decay D0 \to
{\mu}+ {\mu}- in pp collisions at \surd s = 1.96 TeV using 360 pb-1 of
integrated luminosity collected by the CDF II detector at the Fermilab Tevatron
collider. A displaced vertex trigger selects long-lived D0 candidates in the
{\mu}+ {\mu}-, {\pi}+{\pi}-, and K-{\pi}+ decay modes. We use the
Cabibbo-favored D0 \to K-{\pi}+ channel to optimize the selection criteria in
an unbiased manner, and the kinematically similar D0 \to{\pi}+ {\pi}- channel
for normalization. We set an upper limit on the branching fraction (D0 -->
{\mu}+ {\mu}-) < 2.1 E-7 (3.0 E-7) at the 90% (95%) confidence level.
|
Vibrational dynamics in conventional molecules usually takes place on a
timescale of picoseconds or shorter. A striking exception are ultralong-range
Rydberg molecules, for which dynamics is dramatically slowed down as a
consequence of the huge bond length of up to several micrometers. Here, we
report on the direct observation of vibrational dynamics of a recently observed
Rydberg-atom-ion molecule. By applying a weak external electric field of a few
mV/cm, we are able to control the orientation of the photoassociated
ultralong-range Rydberg molecules and induce vibrational dynamics by quenching
the electric field. A high resolution ion microscope allows us to detect the
molecule's orientation and its temporal vibrational dynamics in real space. Our
study opens the door to the control of molecular dynamics in Rydberg molecules.
|
The rise in urbanization throughout the United States (US) in recent years
has required urban planners and transportation engineers to have greater
consideration for the transportation services available to residents of a
metropolitan region. This compels transportation authorities to provide better
and more reliable modes of public transit through improved technologies and
increased service quality. These improvements can be achieved by identifying
and understanding the factors that influence urban public transit demand.
Common factors that can influence urban public transit demand can be internal
and/or external factors. Internal factors include policy measures such as
transit fares, service headways, and travel times. External factors can include
geographic, socioeconomic, and highway facility characteristics. There is
inherent simultaneity between transit supply and demand, thus a two-stage least
squares (2SLS) regression modeling procedure should be conducted to forecast
urban transit supply and demand. As such, two multiple linear regression models
should be developed: one to predict transit supply and a second to predict
transit demand. It was found that service area density, total average cost per
trip, and the average number of vehicles operated in maximum service can be
used to forecast transit supply, expressed as vehicle revenue hours.
Furthermore, estimated vehicle revenue hours and total average fares per trip
can be used to forecast transit demand, expressed as unlinked passenger trips.
Additional data such as socioeconomic information of the surrounding areas for
each transit agency and travel time information of the various transit systems
would be useful to improve upon the models developed.
|
We investigate low-temperature electronic properties of the nondimeric
organic superconductor
$\beta^{\prime\prime}$-(BEDT-TTF)$_4$[(H$_3$O)Ga(C$_2$O$_4$)$_3$]PhNO$_2$. By
examining ultrasonic properties, charge disproportionation (CD) without
magnetic field dependence is detected below $T_{\rm CD}$$\sim$8~K just above
the superconducting critical temperature $T_{\rm c}$$\sim$6~K. From quantum
oscillations in high fields, we find variation in the Fermi surface and mass
enhancement induced by the CD. Heat capacity studies elucidate that the
superconducting gap function is fully gapped in the Fermi surface, but
anisotropic with fourfold symmetry. We point out that the pairing mechanism of
the superconductivity is possibly dominated by charge fluctuations.
|
In this paper, we study the physical significance of the thermodynamic
volumes of AdS black holes using the Noether charge formalism of Iyer and Wald.
After applying this formalism to study the extended thermodynamics of a few
examples, we discuss how the extended thermodynamics interacts with the recent
complexity = action proposal of Brown et al. (CA-duality). We, in particular,
discover that their proposal for the late time rate of change of complexity has
a nice decomposition in terms of thermodynamic quantities reminiscent of the
Smarr relation. This decomposition strongly suggests a geometric, and via
CA-duality holographic, interpretation for the thermodynamic volume of an AdS
black hole. We go on to discuss the role of thermodynamics in complexity =
action for a number of black hole solutions, and then point out the possibility
of an alternate proposal, which we dub "complexity = volume 2.0". In this
alternate proposal, the complexity would be thought of as the spacetime volume
of the Wheeler-DeWitt patch. Finally, we provide evidence that, in certain
cases, our proposal for complexity is consistent with the Lloyd bound whereas
CA-duality is not.
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The exploration of neural network quantum states has become widespread in the
search for ground states in complex quantum many-body systems. However,
achieving high precision remains challenging due to the intricate sign
structures and the exponential growth of the Hilbert space. In this work, we
propose a neural network state method that is confined to a significantly
smaller symmetric subspace, by the full space summation and Markov chain
Metropolis sampling approaches. Using symmetries and group theory, the proposed
method significantly reduces the number of parameters in neural network states
and achieves better accuracy and convergence properties. We validate our method
using the frustrated spin-$1/2$ $J_1$-$J_2$ antiferromagnetic Heisenberg chain
and compare its performance against NetKet, the standard library of neural
network states. The results indicate that our symmetrized neural network states
achieve a substantial improvement over the conventional neural network states
method, reducing energy errors by two orders of magnitude. We also compare
degenerate eigenstates with different quantum numbers, highlighting the
advantage of operating within a smaller variational space.
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Computer science would not be the same without personal computers. In the
West the so called PC revolution started in the late '70s and has its roots in
hobbyists and do-it-yourself clubs. In the following years the diffusion of
home and personal computers has made the discipline closer to many people. A
bit later, to a lesser extent, yet in a similar way, the revolution took place
also in East European countries. Today, the scenario of personal computing has
completely changed, however the computers of the '80s are still objects of
fascination for a number of retrocomputing fans who enjoy using, programming
and hacking the old 8-bits. The paper highlights the continuity between
yesterday's hobbyists and today's retrocomputing enthusiasts, particularly
focusing on East European PCs. Besides the preservation of old hardware and
software, the community is engaged in the development of emulators and cross
compilers. Such tools can be used for historical investigation, for example to
trace the origins of the BASIC interpreters loaded in the ROMs of East European
PCs.
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In this paper the theory of high-frequency acoustic signal detection by
Schottky diodes is presented. Physically, the detection was found to be due to
the quasi-static screening of the potential perturbation caused by the acoustic
strain by charge carriers. The total charge required for screening changes with
the value of strain at the edge of the semiconductor depletion region and
metal-semiconductor interface giving rise to displacement current. The
magnitude and frequency dependence of the electrical signals are analyzed for
both piezoelectric and deformation potential coupling mechanisms. The obtained
results are in good agreement with the recent experimental observations and
suggest feasibility of high-frequency (up to terahertz band) acoustic wave
detection provided that proper electrical measuring scheme is available.
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For a double solid $V\to P_3(C)$ branched over a surface $B\subset P_3(C)$
with only ordinary nodes as singularities, we give a set of generators of the
divisor class group $Pic(\tilde{V}})$ in terms of contact surfaces of $B$ with
only superisolated singularities in the nodes of $B$. As an application we give
a condition when the integral cohomology of $\tilde{V}$ has no 2-torsion. All
possible cases are listed if $B$ is a quartic surface. Furthermore we give a
new lower bound for the dimension of the code of $B$.
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Modeling the formation of the ice giants Uranus and Neptune is a long-lasting
problem in planetary science. Due to gas-drag, collisional damping, and
resonant shepherding, the planetary embryos repel the planetesimals away from
their reach and thus they stop growing (Levison et al. 2010). This problem
persists independently of whether the accretion took place at the current
locations of the ice giants or closer to the Sun. Instead of trying to push the
runaway/oligarchic growth of planetary embryos up to 10-15 Earth masses, we
envision the possibility that the planetesimal disk could generate a system of
planetary embryos of only 1-3 Earth masses. Then we investigate whether these
embryos could have collided with each other and grown enough to reach the
masses of current Uranus and Neptune. Our results point to two major problems.
First, there is typically a large difference in mass between the first and the
second most massive core formed and retained beyond Saturn. Second, in many
simulations the final planetary system has more than two objects beyond Saturn.
The growth of a major planet from a system of embryos requires strong damping
of eccentricities and inclinations from the disk of gas. But strong damping
also favors embryos and cores to find a stable resonant configuration, so that
systems with more than two surviving objects are found. In addition to these
problems, in order to have substantial mutual accretion among embryos, it is
necessary to assume that the surface density of the gas was several times
higher than that of the minimum-mass solar nebula. However this contrasts with
the common idea that Uranus and Neptune formed in a gas-starving disk, which is
suggested by the relatively small amount of hydrogen and helium contained in
the atmospheres of these planets. Only one of our simulations "by chance"
successfully reproduced the structure of the outer Solar System.
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Understanding and controlling the flow of heat is a major challenge in
nanoelectronics. When a junction is driven out of equilibrium by light or the
flow of electric charge, the vibrational and electronic degrees of freedom are,
in general, no longer described by a single temperature[1-6]. Moreover,
characterizing the steady-state vibrational and electronic distributions {\it
in situ} is extremely challenging. Here we show that surface-enhanced Raman
emission may be used to determine the effective temperatures for both the
vibrational modes and the flowing electrons in a biased metallic nanoscale
junction decorated with molecules[7]. Molecular vibrations show mode-specific
pumping by both optical excitation[8] and dc current[9], with effective
temperatures exceeding several hundred Kelvin. AntiStokes electronic Raman
emission\cite[10,11] indicates electronic effective temperature also increases
to as much as three times its no-current values at bias voltages of a few
hundred mV. While the precise effective temperatures are model-dependent, the
trends as a function of bias conditions are robust, and allow direct
comparisons with theories of nanoscale heating.
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We have used the IRAM 30-m telescope to map some targets with HCO$^+$ (1-0)
and H$^{13}$CO$^+$ (1-0) lines in order to search for gas infall evidence in
the clumps. In this paper, we report the mapping results for 13 targets. All of
these targets show HCO$^+$ emissions, while H$^{13}$CO$^+$ emissions are
observed in ten of them. The HCO$^+$ integrated intensity maps of ten targets
show clear clumpy structures, and nine targets show clumpy structures in the
H$^{13}$CO$^+$ maps. Using the RADEX radiative transfer code, we estimate the
column density of H$^{13}$CO$^+$, and determine the abundance ratio
[H$^{13}$CO$^+$]/[H$_2$] to be approximately 10$^{-12}$ to 10$^{-10}$. Based on
the asymmetry of the HCO$^+$ line profiles, we identify 11 targets show blue
profiles, while six clumps have global infall evidence. We use the RATRAN and
two-layer models to fit the HCO$^+$ line profiles of these infall sources, and
analyze their spatial distribution of the infall velocity. The average infall
velocities estimated by these two models are 0.24 -- 1.85 km s$^{-1}$ and 0.28
-- 1.45 km s$^{-1}$, respectively. The mass infall rate ranges from
approximately 10$^{-5}$ to 10$^{-2}$ M$_{\odot}$ yr$^{-1}$, which suggests that
intermediate- or high-mass stars may be forming in the target regions.
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We present the results of a 9.3 square degree infrared (ZYJHK) survey in the
Upper Scorpius association extracted from the UKIRT Infrared Deep Sky Survey
(UKIDSS) Galactic Cluster Survey Early Data Release. We have selected a total
of 112 candidates from the ($Z-J$,$Z$) colour-magnitude diagram over the
Z=12.5-20.5 magnitude range, corresponding to M = 0.25-0.01 Msun at an age of 5
Myr and a distance of 145 pc. Additional photometry in J and K filters revealed
most of them as reddened stars, leaving 32 possible members. Among them, 15
have proper motion consistent with higher mass members from Hipparcos and
optical spectra with strong Halpha in emission and weak gravity features. We
have also extracted two lower mass candidate members for which no optical
spectra are in hand. Three members exhibit strong Halpha equivalent widths (>20
Angstroms), suggesting that they could still undergo accretion whereas two
other dwarfs show signs of chromospheric activity. The likelihood of the
binarity of a couple of new stellar and substellar members is discussed as
well.
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We consider an inertial active Ornstein-Uhlenbeck particle self-propelling in
a saw-tooth ratchet potential. Using the Langevin simulation and matrix
continued fraction method, the particle transport, steady state diffusion, and
coherence in transport are investigated throughout the ratchet. Spatial
asymmetry is found to be the key criterion for the possibility of directed
transport in the ratchet. Interestingly, the simulated particle trajectories
and the corresponding position and velocity distribution functions reveal that
the system passes through an activity-induced transition in the transport from
the running phase to the locked phase with the self-propulsion/activity time of
the dynamics. This is further corroborated by the mean square displacement
(MSD) calculation. The MSD gets suppressed with increase in the persistence of
activity in the medium and finally approaches zero for very large value of self
propulsion time, reflecting a kind of trapping of the particle by the ratchet
for longer persistent of activity in the medium. The non-monotonic behaviour of
the particle current and Peclet number with self propulsion time confirms that
the particle transport and it's coherence can be enhanced or reduced by fine
tuning the persistent duration of activity. Moreover, for an intermediate range
of self-propulsion time in the dynamics as well as for an intermediate range of
mass of the particle, even though the particle current shows a pronounced
unusual maximum with mass, there is no enhancement in the Peclet number,
instead the Peclet number decreases with mass, confirming the degradation of
coherence in transport. Finally, from the analytical calculations, it is
observed that for a highly viscous medium, where the inertial influence is
negligibly small, the particle current approaches the current in the over
damped regime.
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Through stacking engineering of two-dimensional (2D) materials, a switchable
interface polarization can be generated through interlayer sliding, so called
sliding ferroelectricity, which is advantageous over the traditional
ferroelectricity due to ultra-thin thickness, high switching speed and low
fatigue. However, 2D materials with intrinsic sliding ferroelectricity are
still rare, with the exception of rhombohedral-stacked MoS2, which limits
sliding ferroelectricity for practical applications such as high-speed storage,
photovoltaic, and neuromorphic computing. Here, we reported the observation of
sliding ferroelectricity with multiple states in undoped rhombohedral-stacked
InSe ({\gamma}-InSe) via dual-frequency resonance tracking piezoresponse force
microscopy, scanning Kelvin probe microscopy and conductive atomic force
microscopy. The tunable bulk photovoltaic effect via the electric field is
achieved in the graphene/{\gamma}-InSe/graphene tunneling device with a
photovoltaic current density of ~15 mA/cm2, which is attributed to the multiple
sliding steps in {\gamma}-InSe according to our theoretical calculations. The
vdw tunneling device also features a high photo responsivity of ~255 A/W and a
fast response time for real-time imaging. Our work not only enriches
rhombohedral-stacked 2D materials for sliding ferroelectricity, but also sheds
light on their potential for tunable photovoltaics and imaging applications.
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As part of a long term monitoring campaign of Mrk 335, deep XMM-Newton
observations catch the narrow-line Seyfert 1 galaxy (NLS1) in a complex,
intermediate flux interval as the active galaxy is transiting from low- to
high-flux. Other works on these same data examined the general behaviour of the
NLS1 (Grupe et al.) and the conditions of its warm absorber (Longinotti et
al.). The analysis presented here demonstrates the X-ray continuum and timing
properties can be described in a self-consistent manner adopting a blurred
reflection model with no need to invoke partial covering. The rapid spectral
variability appears to be driven by changes in the shape of the primary emitter
that is illuminating the inner accretion disc around a rapidly spinning black
hole (a > 0.7). While light bending is certainly prominent, the rather constant
emissivity profile and break radius obtained in our spectral fitting suggest
that the blurring parameters are not changing as would be expected if the
primary source is varying its distance from the disc. Instead changes could be
intrinsic to the power law component. One possibility is that material in an
unresolved jet above the disc falls to combine with material at the base of the
jet producing the changes in the primary emitter (spectral slope and flux)
without changing its distance from the disc.
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R-parity violating supersymmetric models (RPV SUSY) are becoming increasingly
more appealing than its R-parity conserving counterpart in view of the hitherto
non-observation of SUSY signals at the LHC. In this talk, RPV scenarios where
neutrino masses are naturally generated are discussed, namely RPV through
bilinear terms (bRPV) and the "mu from nu" supersymmetric standard model. The
latter is characterised by a rich Higgs sector that easily accommodates a
125-GeV Higgs boson. The phenomenology of such models at the LHC is reviewed,
giving emphasis on final states with displaced objects, and relevant results
obtained by LHC experiments are presented. The implications for dark matter for
these theoretical proposals is also addressed.
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We consider generalized inversions and descents in finite Weyl groups. We
establish Coxeter-theoretic properties of indicator random variables of
positive roots such as the covariance of two such indicator random variables.
We then compute the variances of generalized inversions and descents in
classical types. We finally use the dependency graph method to prove central
limit theorems for general antichains in root posets and in particular for
generalized descents, and then for generalized inversions.
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Jets around low- and intermediate-mass young stellar objects (YSOs) contain a
fossil record of the recent accretion and outflow activity of their parent
star-forming systems. We aim to understand whether the accretion/ejection
process is similar across the entire stellar mass range of the parent YSOs. To
this end we have obtained VLT/X-shooter spectra of HH 1042 and HH 1043, two
newly discovered jets in the massive star-forming region RCW 36. HH 1042 is
associated with the intermediate-mass YSO 08576nr292. Over 90 emission lines
are detected in the spectra. High-velocity (up to 220 km/s) blue- and
redshifted emission from a bipolar flow is observed in typical shock tracers.
Low-velocity emission from the background cloud is detected in nebular tracers,
including lines from high ionization species. We applied combined optical and
infrared spectral diagnostic tools in order to derive the physical conditions
(density, temperature, and ionization) in the jets. The measured mass outflow
rates are Mjet ~ 10^-7 Msun/yr. We measure a high accretion rate for HH 1042
(Macc ~ 10^-6 Msun/yr) and Mjet/Macc ~ 0.1, comparable to low-mass sources and
consistent with models for magneto-centrifugal jet launching. The knotted
structure and velocity spread in both jets are interpreted as fossil signatures
of a variable outflow rate. The mean velocities in both lobes of the jets are
comparable, but the variations in Mjet and velocity in the two lobes are not
symmetric, suggesting that the launching mechanism on either side of the
accretion disk is not synchronized. For HH 1042, we have constructed an
interpretative physical model with a stochastic or periodic outflow rate and a
description of a ballistic flow as its constituents. The knotted structure and
velocity spread can be reproduced qualitatively with the model, indicating that
the outflow velocity varies on timescales on the order of 100 yr.
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The discipline of process mining has a solid track record of successful
applications to the healthcare domain. Within such research space, we conducted
a case study related to the Intensive Care Unit (ICU) ward of the Uniklinik
Aachen hospital in Germany. The aim of this work is twofold: developing a
normative model representing the clinical guidelines for the treatment of
COVID-19 patients, and analyzing the adherence of the observed behavior
(recorded in the information system of the hospital) to such guidelines. We
show that, through conformance checking techniques, it is possible to analyze
the care process for COVID-19 patients, highlighting the main deviations from
the clinical guidelines. The results provide physicians with useful indications
for improving the process and ensuring service quality and patient
satisfaction. We share the resulting model as an open-source BPMN file.
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We present a catalog of 182 galaxy clusters detected through the
Sunyaev-Zel'dovich effect by the Atacama Cosmology Telescope in a contiguous
987.5 deg$^{2}$ field. The clusters were detected as SZ decrements by applying
a matched filter to 148 GHz maps that combine the original ACT equatorial
survey with data from the first two observing seasons using the ACTPol
receiver. Optical/IR confirmation and redshift measurements come from a
combination of large public surveys and our own follow-up observations. Where
necessary, we measured photometric redshifts for clusters using a pipeline that
achieves accuracy $\Delta z/(1 + z)=0.015$ when tested on SDSS data. Under the
assumption that clusters can be described by the so-called Universal Pressure
Profile and its associated mass-scaling law, the full signal-to-noise > 4
sample spans the mass range $1.6 < M^{\rm UPP}_{\rm 500c}/10^{14}{\rm
M}_{\odot}<9.1$, with median $M^{\rm UPP}_{\rm 500c}=3.1 \times 10^{14}$
M$_{\odot}$. The sample covers the redshift range $0.1 < z < 1.4$ (median $z =
0.49$) and 28 clusters are new discoveries (median $z = 0.80$). We compare our
catalog with other overlapping cluster samples selected using the SZ,
optical,and X-ray wavelengths. We find the ratio of the UPP-based SZ mass to
richness-based weak-lensing mass is $\langle M^{\rm UPP}_{\rm 500c} \rangle /
\langle M^{\rm \lambda WL}_{\rm 500c} \rangle = 0.68 \pm 0.11$. After applying
this calibration, the mass distribution for clusters with $M_{\rm 500c} > 4
\times 10^{14}$ M$_{\odot}$ is consistent with the number of such clusters
found in the South Pole Telescope SZ survey.
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We prove that a smooth proper universally CH_0-trivial variety X over a field
k has universally trivial Brauer group. This fills a gap in the literature
concerning the p-torsion of the Brauer group when k has characteristic p.
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The discovery of the highly relativistic neutron star (NS) binary (in which
both NS's are pulsars) not only increases the estimated merging rate for the
two NS's by a large factor, but also adds the missing link in the double helium
star model of binary NS evolution. This model gives $\sim 20$ times more
gravitational merging of low-mass black-hole (LMBH), NS binaries than binary
NS's, whatever the rate for the latter is.
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Magnetotransport in chaotic quantum dots at low magnetic fields is
investigated by means of a tight binding Hamiltonian on L x L clusters of the
square lattice. Chaoticity is induced by introducing L bulk vacancies. The
dependence of weak localization on the Fermi energy, dot size and leads width
is investigated in detail and the results compared with those of previous
analyses, in particular with random matrix theory predictions. Our results
indicate that the dependence of the critical flux Phi_c on the square root of
the number of open modes, as predicted by random matrix theory, is obscured by
the strong energy dependence of the proportionality constant. Instead, the size
dependence of the critical flux predicted by Efetov and random matrix theory,
namely, Phi_c ~ sqrt{1/L}, is clearly illustrated by the present results. Our
numerical results do also show that the weak localization term significantly
decreases as the leads width W approaches L. However, calculations for W=L
indicate that the weak localization effect does not disappear as L increases.
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This paper describes a bounded generation result concerning the minimal
natural number $K$ such that for
$Q(C_2,2R):=\{A\varepsilon_{\phi}(2x)A^{-1}|x\in R,A\in{\rm Sp}_4(R),\phi\in
C_2\}$, one has $N_{C_2,2R}=\{X_1\cdots X_K|\forall 1\leq i\leq K:X_i\in
Q(C_2,2R)\}$ for rings of algebraic integers $R$ and the principal congruence
subgroup $N_{C_2,2R}$ in ${\rm Sp}_4(R).$ This gives an explicit version of an
abstract bounded generation result of a similar type as presented by Morris.
Furthermore, the result presented does not depend on several number-theoretic
quantities unlike Morris' result. Using this bounded generation result, we
further give explicit bounds for the strong boundedness of ${\rm Sp}_4(R)$ for
certain examples of rings $R,$ thereby giving explicit versions of results in
an earlier paper. We further give a classification of normally generating
subsets of ${\rm Sp}_4(R)$ for $R$ a ring of algebraic integers.
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We present the new parallel version (pCRASH2) of the cosmological radiative
transfer code CRASH2 for distributed memory supercomputing facilities. The code
is based on a static domain decomposition strategy inspired by geometric
dilution of photons in the optical thin case that ensures a favourable
performance speed-up with increasing number of computational cores. Linear
speed-up is ensured as long as the number of radiation sources is equal to the
number of computational cores or larger. The propagation of rays is segmented
and rays are only propagated through one sub-domain per time step to guarantee
an optimal balance between communication and computation. We have extensively
checked pCRASH2 with a standardised set of test cases to validate the
parallelisation scheme. The parallel version of CRASH2 can easily handle the
propagation of radiation from a large number of sources and is ready for the
extension of the ionisation network to species other than hydrogen and helium.
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I review recently completed (since Lattice 2013) and ongoing lattice
calculations in charm and bottom flavor physics. A comparison of the precision
of lattice and experiment is made using both current experimental results and
projected experimental precision in 2020. The combination of experiment and
theory reveals several tensions between nature and the Standard Model. These
tensions are reviewed in light of recent lattice results.
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We present a new, inexpensive, bench-top method for measuring groove period
over large areas with high mapping resolution and high measurement accuracy,
dubbed the grating mapper for accurate period (GMAP). The GMAP has the ability
to measure large groove period changes and non-parallel grooves, both of which
cannot be measured via optical interferometry. In this paper, we detail the
calibration and setup of the GMAP, and employ the instrument to measure three
distinct gratings. Two of these measured gratings have customized groove
patterns that prevent them from being measured via other traditional methods,
such as optical interferometry. Our implementation of this tool achieves a
spatial resolution of 0.1 mm$\times$0.1 mm and a period error of 1.7 nm for a 3
$\mu$m size groove period.
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Hyperparameter tuning is one of the most time-consuming workloads in deep
learning. State-of-the-art optimizers, such as AdaGrad, RMSProp and Adam,
reduce this labor by adaptively tuning an individual learning rate for each
variable. Recently researchers have shown renewed interest in simpler methods
like momentum SGD as they may yield better test metrics. Motivated by this
trend, we ask: can simple adaptive methods based on SGD perform as well or
better? We revisit the momentum SGD algorithm and show that hand-tuning a
single learning rate and momentum makes it competitive with Adam. We then
analyze its robustness to learning rate misspecification and objective
curvature variation. Based on these insights, we design YellowFin, an automatic
tuner for momentum and learning rate in SGD. YellowFin optionally uses a
negative-feedback loop to compensate for the momentum dynamics in asynchronous
settings on the fly. We empirically show that YellowFin can converge in fewer
iterations than Adam on ResNets and LSTMs for image recognition, language
modeling and constituency parsing, with a speedup of up to 3.28x in synchronous
and up to 2.69x in asynchronous settings.
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Two new forms of strongly coupled plasmas will be discussed. They have become
possible to create and observe in the laboratory only recently and exhibit a
wealth of intriguing complex behavior which can be studied, in many cases for
the first time, experimentally. Plasmas, gases of charged particles, are
universal in the sense that certain properties of complex behavior do only
depend on ratios of characteristic parameters of the plasma, not on the
parameters themselves. Therefore, it is of fundamental and far reaching
consequence, to be able to create and observe a strongly coupled plasma since
its behavior is paradigmatic for an entire class of plasmas.
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The gluon mass generation is a purely non-perturbative effect, and the
natural framework to study it in the continuum are the Schwinger-Dyson
equations (SDEs) of the theory. At the level of the SDEs the generation of such
a mass is associated with the existence of infrared finite solutions for the
gluon propagator. From the theoretical point of view, the dynamical gluon mass
generation has been traditionally plagued with seagull divergences. In this
work, we will review how such divergences can be eliminated completely by
virtue of a characteristic identity, valid in dimensional regularization. As a
pedagogical example, we will first discuss in the context of scalar QED how it
is possible to eliminate all seagull divergences, by triggering the
aforementioned special identity, which enforces the masslessness of the photon.
Then, we will discuss what happens in QCD and present an Ansatz for the three
gluon vertex, which completely eliminates all seagull divergences and at same
time allows for the possibility of a dynamical gluon mass generation.
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Symmetry in biological and physical systems is a product of self organization
driven by evolutionary processes, or mechanical systems under constraints.
Symmetry based feature extrac-tion or representation by neural networks may
unravel the most informative contents in large image databases. Despite
significant achievements of artificial intelligence in recognition and
classification of regular patterns, the problem of uncertainty remains a major
challenge in ambiguous data. In this study, we present an artificial neural
network that detects symmetry uncertainty states in human observers. To this
end, we exploit a neural network metric in the output of a biologically
inspired Self Organizing Map, the Quantization Error (SOM QE). Shape pairs with
perfect geometric mirror symmetry but a non-homogenous appearance, caused by
local variations in hue, saturation, or lightness within or across the shapes
in a given pair produce, as shown here, longer choice RT for yes responses
relative to symmetry. These data are consistently mirrored by the variations in
the SOM QE from unsupervised neural network analysis of the same stimulus
images. The neural network metric is thus capable of detecting and scaling
human symmetry uncertainty in response to patterns. Such capacity is tightly
linked to the metrics proven selectivity to local contrast and color variations
in large and highly complex image data.
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The symplectic group Sp(2g,Z) is a subgroup of the linear group SL(2g,Z) and
admits a faithful action on the sphere S^(2g-1), induced from its linear action
on Euclidean space R^(2g). Generalizing corresponding results for linear
groups, we show that, if m < 2g-1 and g > 2, any continuous action of Sp(2g,Z)
on a homology m-sphere, and in particular on S^m, is trivial.
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It is shown that the estimates obtained by Manfredo P. do Carmo and Detang
Zhou, in their paper "Eigenvalue estimate on complete noncompact Riemannian
manifolds and applications", for the first eigenvalue of the Laplace-Beltrami
operator on open manifolds, via an oscillation theorem, can be naturally
extended for the semi-elliptic singular operator operator, p-Laplace on
manifolds.
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The peristaltic motion of the stomach walls combines with the secretion of
enzymes to initiate the process that breaks down food. Computational modelling
of this phenomenon can help reveal the details that would be hard to capture
via in-vivo or in-vitro means. In this study, the digestion of a liquid meal
containing protein is simulated in a human-stomach model based on imaging data.
Pepsin, the gastric enzyme for protein hydrolysis, is secreted from the
proximal region of the stomach walls and allowed to react with the contents of
the stomach. The jet velocities, the emptying rate, and the extent of
hydrolysis are quantified for a control case, and also for three other cases of
reduced motility with varying peristaltic amplitudes. The findings quantify the
effect of motility on the rate of food breakdown and emptying, and correlate
the observations with the mixing in the stomach induced by the antral
contraction waves.
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Subsets and Splits