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We present the discovery of five quasars at z~6 selected from 260 deg^2 of
the Sloan Digital Sky Survey (SDSS) southern survey, a deep imaging survey
obtained by repeatedly scanning a stripe along the Celestial Equator. The five
quasars with 20<z_{AB}<21 are 1-2 magnitudes fainter than the luminous z~6
quasars discovered in the SDSS main survey. One of them was independently
discovered by the UKIRT Infrared Deep Sky Survey. These quasars, combined with
another z~6 quasar known in this region, make a complete flux- limited quasar
sample at z_{AB}<21. The sample spans the redshift range 5.85<z<6.12 and the
luminosity range -26.5<M_{1450}<-25.4 (H_0=70 km s^{-1} Mpc^{-1},
Omega_{m}=0.3, and Omega_{Lambda}=0.7). We use the 1/V_{a} method to determine
that the comoving quasar spatial density at <z>=6.0 and <M_{1450}>=-25.8 is
(5.0+/-2.1) x 10^{-9} Mpc^{-3} mag^{-1}. We model the bright-end quasar
luminosity function (QLF) at z~6 as a power law Phi(L_{1450}) \propto
L_{1450}^{beta}. The slope beta calculated from a combination of our sample and
the luminous SDSS quasar sample is -3.1+/-0.4, significantly steeper than the
slope of the QLF at z~4. Based on the derived QLF, we find that the quasar/AGN
population cannot provide enough photons to ionize the intergalactic medium
(IGM) at z~6 unless the IGM is very homogeneous and the luminosity (L*_{1450})
at which the QLF power law breaks is very low.
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Four classic criteria used to the classification of complex flows are
discussed here. These criteria are useful to identify regions of the flow
related to shear, elongation or rigid-body motion. These usual criteria, namely
$Q$, $\Delta$, $\lambda_{2}$ and $\lambda_{cr}/\lambda_{ci}$, use the fluid's
rate-of-rotation tensor, which is known to vary with respect to a reference
frame. The advantages of using objective (invariant with respect to a general
transformation on the reference frame) criteria are discussed in the present
work. In this connection, we construct versions of classic criteria replacing
standard vorticity, a non-objective quantity, by effective vorticity, a rate of
rotation tensor with respect to the angular velocity of the eigenvectors of the
strain rate tensor. The classic criteria and their corresponding objective
versions are applied to classify two complex flows: the transient ABC flow and
the flow through the abrupt 4:1 contraction. It is shown that the objective
versions of the criteria provide richer information on the kinematics of the
flow
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We propose to use a quantum ratchet to transport quantum information in a
chain of atoms trapped in an optical superlattice. The quantum ratchet is
created by a continuous modulation of the optical superlattice which is
periodic in time and in space. Though there is zero average force acting on the
atoms, we show that indeed the ratchet effect permits atoms on even and odd
sites to move along opposite directions. By loading the optical lattice with
two-level bosonic atoms, this scheme permits to perfectly transport a qubit or
entangled state imprinted in one or more atoms to any desired position in the
lattice. From the quantum computation point of view, the transport is achieved
by a smooth concatenation of perfect swap gates. We analyze setups with
noninteracting and interacting particles and in the latter case we use the
tools of optimal control to design optimal modulations. We also discuss the
feasibility of this method in current experiments.
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Motivated by the dynamics in the deep interiors of many stars, we study the
interaction between overshooting convection and the large-scale poloidal fields
residing in radiative zones. We have run a suite of 3D Boussinesq numerical
calculations in a spherical shell that consists of a convection zone with an
underlying stable region that initially compactly contains a dipole field. By
varying the strength of the convective driving, we find that, in the less
turbulent regime, convection acts as turbulent diffusion that removes the field
faster than solely molecular diffusion would do. However, in the more turbulent
regime, turbulent pumping becomes more efficient and partially counteracts
turbulent diffusion, leading to a local accumulation of the field below the
overshoot region. These simulations suggest that dipole fields might be
confined in underlying stable regions by highly turbulent convective motions at
stellar parameters. The confinement is of large-scale field in an average sense
and we show that it is reasonably modeled by mean-field ideas. Our findings are
particularly interesting for certain models of the Sun, which require a
large-scale, poloidal magnetic field to be confined in the solar radiative zone
in order to explain simultaneously the uniform rotation of the latter and the
thinness of the solar tachocline.
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For Banach spaces $X,Y,$ we consider a distance problem in the space of
bounded linear operators $\mathcal{L}(X,Y).$ Motivated by a recent paper
\cite{RAO21}, we obtain sufficient conditions so that for a compact operator
$T\in\mathcal{L}(X,Y)$ and a closed subspace $Z\subset Y,$ the following
equation holds, which relates global approximation with local approximation:
\[d(T,\mathcal{L}(X,Z))=\sup\{d(Tx,Z):x\in X,\|x\|=1\}.\]
In some cases, we show that the supremum is attained at an extreme point of
the corresponding unit ball. Furthermore, we obtain some situations when the
following equivalence holds:
$$T\perp_B \mathcal{L}(X,Z)\Leftrightarrow T^{**}x_0^{**}\perp_B
Z^{\perp\perp}\Leftrightarrow
T^{**}\perp_B\mathcal{L}(X^{**},Z^{\perp\perp}),$$ for some $x_0^{**}\in
X^{**}$ satisfying $\|T^{**}x_0^{**}\|=\|T^{**}\|\|x_0^{**}\|,$ where $Z^\perp$
is the annihilator of $Z.$ One such situation is when $Z$ is an $L^1-$predual
space and an $M-$ideal in $Y$ and $T$ is a multi-smooth operator of finite
order. Another such situation is when $X$ is an abstract $L_1-$space and $T$ is
a multi-smooth operator of finite order. Finally, as a consequence of the
results, we obtain a sufficient condition for proximinality of a subspace $Z$
in $Y.$
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Angular momentum transport in protostellar discs can take place either
radially, through turbulence induced by the magnetorotational instability
(MRI), or vertically, through the torque exerted by a large-scale magnetic
field that threads the disc. Using semi-analytic and numerical results, we
construct a model of steady-state discs that includes vertical transport by a
centrifugally driven wind as well as MRI-induced turbulence. We present
approximate criteria for the occurrence of either one of these mechanisms in an
ambipolar diffusion-dominated disc. We derive ``strong field'' solutions in
which the angular momentum transport is purely vertical and ``weak field''
solutions that are the stratified-disc analogues of the previously studied MRI
channel modes; the latter are transformed into accretion solutions with
predominantly radial angular-momentum transport when we implement a
turbulent-stress prescription based on published results of numerical
simulations. We also analyze ``intermediate field strength'' solutions in which
both modes of transport operate at the same radial location; we conclude,
however, that significant spatial overlap of these two mechanisms is unlikely
to occur in practice. To further advance this study, we have developed a
general scheme that incorporates also the Hall and Ohm conductivity regimes in
discs with a realistic ionization structure.
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Convolutional neural networks (CNNs) are typically over-parameterized,
bringing considerable computational overhead and memory footprint in inference.
Pruning a proportion of unimportant filters is an efficient way to mitigate the
inference cost. For this purpose, identifying unimportant convolutional filters
is the key to effective filter pruning. Previous work prunes filters according
to either their weight norms or the corresponding batch-norm scaling factors,
while neglecting the sequential dependency between adjacent layers. In this
paper, we further develop the norm-based importance estimation by taking the
dependency between the adjacent layers into consideration. Besides, we propose
a novel mechanism to dynamically control the sparsity-inducing regularization
so as to achieve the desired sparsity. In this way, we can identify unimportant
filters and search for the optimal network architecture within certain resource
budgets in a more principled manner. Comprehensive experimental results
demonstrate the proposed method performs favorably against the existing strong
baseline on the CIFAR, SVHN, and ImageNet datasets. The training sources will
be publicly available after the review process.
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This paper gives a construction, using heat kernels, of differential forms on
the moduli space of metrised ribbon graphs, or equivalently on the moduli space
of Riemann surfaces with boundary. The construction depends on a manifold with
a bundle of Frobenius algebras, satisfying various conditions. These forms
satisfy gluing conditions which mean they form an open topological conformal
field theory, i.e. a kind of open string theory.
If the integral of these forms converged, it would yield the purely quantum
part of the partition function of a Chern-Simons type gauge theory. Yang-Mills
theory on a four manifold arises as one of these Chern-Simons type gauge
theories.
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The application of data-intensive automatic speech recognition (ASR)
technologies to dysarthric and elderly adult speech is confronted by their
mismatch against healthy and nonaged voices, data scarcity and large
speaker-level variability. To this end, this paper proposes two novel
data-efficient methods to learn homogeneous dysarthric and elderly
speaker-level features for rapid, on-the-fly test-time adaptation of DNN/TDNN
and Conformer ASR models. These include: 1) speaker-level variance-regularized
spectral basis embedding (VR-SBE) features that exploit a special
regularization term to enforce homogeneity of speaker features in adaptation;
and 2) feature-based learning hidden unit contributions (f-LHUC) transforms
that are conditioned on VR-SBE features. Experiments are conducted on four
tasks across two languages: the English UASpeech and TORGO dysarthric speech
datasets, the English DementiaBank Pitt and Cantonese JCCOCC MoCA elderly
speech corpora. The proposed on-the-fly speaker adaptation techniques
consistently outperform baseline iVector and xVector adaptation by
statistically significant word or character error rate reductions up to 5.32%
absolute (18.57% relative) and batch-mode LHUC speaker adaptation by 2.24%
absolute (9.20% relative), while operating with real-time factors speeding up
to 33.6 times against xVectors during adaptation. The efficacy of the proposed
adaptation techniques is demonstrated in a comparison against current ASR
technologies including SSL pre-trained systems on UASpeech, where our best
system produces a state-of-the-art WER of 23.33%. Analyses show VR-SBE features
and f-LHUC transforms are insensitive to speaker-level data quantity in
testtime adaptation. T-SNE visualization reveals they have stronger
speaker-level homogeneity than baseline iVectors, xVectors and batch-mode LHUC
transforms.
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The conditions to induce appreciable CP-and T-odd effects in neutrino
oscillations are discussed. The propagation in matter leads to fake CP-and
CPT-odd asymmetries, besides a Bohm-Aharonov type modification of the
interference pattern. We study the separation of fake and genuine CP violation
by means of energy and distance dependence.
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We obtain some general restrictions on the continuous endomorphisms of a
profinite group G under the assumption that G has only finitely many open
subgroups of each index (an assumption which automatically holds, for instance,
if G is finitely generated). In particular, given such a group G and a
continuous endomorphism phi we obtain a semidirect decomposition of G into a
'contracting' normal subgroup and a complement on which phi induces an
automorphism; both the normal subgroup and the complement are closed. If G is
isomorphic to a proper open subgroup of itself, we show that G has an infinite
abelian normal pro-p subgroup.
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We present a versatile electric trap for the exploration of a wide range of
quantum phenomena in the interaction between polar molecules. The trap combines
tunable fields, homogeneous over most of the trap volume, with steep gradient
fields at the trap boundary. An initial sample of up to 10^8 CH3F molecules is
trapped for as long as 60 seconds, with a 1/e storage time of 12 seconds.
Adiabatic cooling down to 120 mK is achieved by slowly expanding the trap
volume. The trap combines all ingredients for opto-electrical cooling, which,
together with the extraordinarily long storage times, brings field-controlled
quantum-mechanical collision and reaction experiments within reach.
|
Over the past half-decade, many methods have been considered for neural
architecture search (NAS). Bayesian optimization (BO), which has long had
success in hyperparameter optimization, has recently emerged as a very
promising strategy for NAS when it is coupled with a neural predictor. Recent
work has proposed different instantiations of this framework, for example,
using Bayesian neural networks or graph convolutional networks as the
predictive model within BO. However, the analyses in these papers often focus
on the full-fledged NAS algorithm, so it is difficult to tell which individual
components of the framework lead to the best performance.
In this work, we give a thorough analysis of the "BO + neural predictor"
framework by identifying five main components: the architecture encoding,
neural predictor, uncertainty calibration method, acquisition function, and
acquisition optimization strategy. We test several different methods for each
component and also develop a novel path-based encoding scheme for neural
architectures, which we show theoretically and empirically scales better than
other encodings. Using all of our analyses, we develop a final algorithm called
BANANAS, which achieves state-of-the-art performance on NAS search spaces. We
adhere to the NAS research checklist (Lindauer and Hutter 2019) to facilitate
best practices, and our code is available at
https://github.com/naszilla/naszilla.
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In the case of cyclic quiver we prove that the deformed Harish-Chandra map
whose existence was conjectured by Etingof and Ginzburg is well defined. As an
application we prove Kirillov-type formula for the cyclotomic Bessel function.
|
We study the Voronoi Diagram of Rotating Rays, a Voronoi structure where the
input sites are rays and the distance function between a point and a site/ray,
is the counterclockwise angular distance. This novel Voronoi diagram is
motivated by illumination or coverage problems, where a domain must be covered
by floodlights/wedges of uniform angle, and the goal is to find the minimum
angle necessary to cover the domain. We study the diagram in the plane, and we
present structural properties, combinatorial complexity bounds, and a
construction algorithm. If the rays are induced by a convex polygon, we show
how to construct the Voronoi diagram within this polygon in linear time. Using
this information, we can find in optimal linear time the Brocard angle, the
minimum angle required to illuminate a convex polygon with floodlights of
uniform angle.
|
Improvements in main memory storage density are primarily driven by process
technology scaling, which negatively impacts reliability by exacerbating
various circuit-level error mechanisms. To compensate for growing error rates,
both memory manufacturers and consumers use error-mitigation mechanisms that
improve manufacturing yield and allow system designers to meet reliability
targets. Developing effective error mitigations requires understanding the
errors' characteristics (e.g., worst-case behavior, statistical properties).
Unfortunately, we observe that proprietary on-die Error-Correcting Codes (ECC)
used in modern memory chips introduce new challenges to efficient error
mitigation by obfuscating CPU-visible error characteristics in an
unpredictable, ECC-dependent manner.
This dissertation builds a detailed understanding of how on-die ECC
obfuscates the statistical properties of main memory error mechanisms using a
combination of real-chip experiments and statistical analyses. We
experimentally study memory errors, examine how on-die ECC obfuscates their
statistical characteristics, and develop new testing techniques to overcome the
obfuscation. Our results show that the obfuscated error characteristics can be
recovered using new memory testing techniques that exploit the interaction
between on-die ECC and the statistical characteristics of memory error
mechanisms to expose physical cell behavior. We conclude by discussing the
critical need for transparency in DRAM reliability characteristics in order to
enable DRAM consumers to better understand and adapt commodity DRAM chips to
their system-specific needs. We hope and believe that the analysis, techniques,
and results we present in this dissertation will enable the community to better
understand and tackle current and future reliability challenges as well as
adapt commodity memory to new advantageous applications.
|
The sensing and positioning capabilities foreseen in 6G have great potential
for technology advancements in various domains, such as future smart cities and
industrial use cases. Channel charting has emerged as a promising technology in
recent years for radio frequency-based sensing and localization. However, the
accuracy of these techniques is yet far behind the numbers envisioned in 6G. To
reduce this gap, in this paper, we propose a novel channel charting technique
capitalizing on the time of arrival measurements from surrounding Transmission
Reception Points (TRPs) along with their locations and leveraging sensor fusion
in channel charting by incorporating laser scanner data during the training
phase of our algorithm. The proposed algorithm remains self-supervised during
training and test phases, requiring no geometrical models or user position
ground truth. Simulation results validate the achievement of a sub-meter level
localization accuracy using our algorithm 90% of the time, outperforming the
state-of-the-art channel charting techniques and the traditional
triangulation-based approaches.
|
The BL Lac PKS 1413+135 was observed by the Large Survey Project "MeerKAT
Absorption Line Survey" (MALS) in the L-band, at 1139 MHz and 1293-1379 MHz,
targeting the HI and OH lines in absorption at z = 0.24671. The radio continuum
is thought to come from a background object at redshift lower than 0.5, as
suggested by the absence of gravitational images. The HI absorption line is
detected at high signal-to-noise, with a narrow central component, and a red
wing, confirming previous results. The OH 1720 MHz line is clearly detected in
(maser) emission, peaking at a velocity shifted by -10 to -15 km/s with respect
to the HI peak. The 1612 MHz line is lost due to radio interferences. The OH
1667 MHz main line is tentatively detected in absorption, but not the 1665 MHz
one. Over 30 years, a high variability is observed in optical depths, due to
the rapid changes of the line of sight, caused by the superluminal motions of
the radio knots. The HI line has varied by 20 per cent in depth, while the
OH-1720 MHz depth has varied by a factor 4. The position of the central
velocity and the widths also varied. The absorbing galaxy is an early-type
spiral (maybe S0) seen edge-on, with a prominent dust lane, covering the whole
disk. Given the measured mass concentration, and the radio continuum size at
centimeter wavelengths (100 mas corresponding to 400 pc at z = 0.25), the width
of absorption lines from the nuclear regions are expected up to 250 km/S. The
narrowness of the observed lines (< 15 km/s) suggest that the absorption comes
from an outer gas ring, as frequently observed in S0 galaxies. The millimetric
lines are even narrower (< 1 km/s), which corresponds to the continuum size
restricted to the core. The core source is covered by individual 1 pc molecular
clouds, of column density a few 10^22 cm-2, which is compatible with the gas
screen detected in X-rays.
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To reduce the size of recommendation models, there have been many studies on
compressing recommendation models using knowledge distillation. In this paper,
we decompose recommendation models into three layers, i.e., the input layer,
the intermediate layer, and the output layer, and address deficiencies layer by
layer. First, previous methods focus only on two layers, neglecting the input
layer. Second, in the intermediate layer, existing methods ignore the
inconsistency of user preferences induced by the projectors. Third, in the
output layer, existing methods use only hard labels rather than soft labels
from the teacher. To address these deficiencies, we propose
\textbf{M}ulti-layer \textbf{K}nowledge \textbf{D}istillation (MKD), which
consists of three components: 1) Distillation with Neighbor-based Knowledge
(NKD) utilizes the teacher's knowledge about entities with similar
characteristics in the input layer to enable the student to learn robust
representations. 2) Distillation with Consistent Preference (CPD) reduces the
inconsistency of user preferences caused by projectors in the intermediate
layer by two regularization terms. 3) Distillation with Soft Labels (SLD)
constructs soft labels in the output layer by considering the predictions of
both the teacher and the student. Our extensive experiments show that MKD even
outperforms the teacher with one-tenth of the model size.
|
Optical precision experiments are a powerful tool to explore hidden sectors
of a variety of standard-model extensions with potentially tiny couplings to
photons. An important example is given by extensions involving an extra light
U(1) gauge degree of freedom, so-called paraphotons, with gauge-kinetic mixing
with the normal photon. These models naturally give rise to minicharged
particles which can be searched for with optical experiments. In this paper, we
study the effects of paraphotons in such experiments. We describe in detail the
role of a magnetic field for photon-paraphoton oscillations in models with
low-mass minicharged particles. In particular, we find that the upcoming
light-shining-through-walls experiments are sensitive to paraphotons and can
distinguish them from axion-like particles.
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The notion of Total Interference Degree (TID) is traditionally used to
estimate the intensity of prevalent interference in a
Multi-RadioMulti-ChannelWirelessMesh Network (MRMC WMN). Numerous Channel
Assignment (CA) approaches, linkscheduling algorithms and routing schemes have
been proposed for WMNs which rely entirely on the concept of TID estimates.
They focus on minimizing TID to create a minimal interference scenario for the
network. In our prior works [1] and [2], we have questioned the efficacy of TID
estimate and then proposed two reliable interference estimation metrics viz.,
Channel Distribution Across Links Cost (CDALcost) and Cumulative X-Link-Set
Weight (CXLSwt). In this work, we assess the ability of these interference
estimation metrics to replace TID as the interferenceminimizing factor in a CA
scheme implemented on a grid MRMC WMN. We carry out a comprehensive evaluation
on ns-3 and then conclude from the results that the performance of the network
increases by 10-15% when the CA scheme uses CXLSwt as the underlying
Interference Mitigation Function (IMF) when compared with CA using TID as IMF.
We also confirm that CDALcost is not a better IMF than TID and CXLSwt.
|
Pulsar data analysis pipelines have historically been comprised of bespoke
software systems, supporting the off-line analysis of data. However modern data
acquisition systems are making off-line analyses impractical. They often output
multiple simultaneous high volume data streams, significantly increasing data
capture rates. This leads to the accumulation of large data volumes, which are
prohibitively expensive to retain. To maintain processing capabilities when
off-line analysis becomes infeasible due to cost, requires a shift to on-line
data processing. This paper makes four contributions facilitating this shift
with respect to the search for radio pulsars: i) it characterises for the
modern era, the key components of a pulsar search science (not signal
processing) pipeline, ii) it examines the feasibility of implementing on-line
pulsar search via existing tools, iii) problems preventing an easy transition
to on-line search are identified and explained, and finally iv) it provides the
design for a new prototype pipeline capable of overcoming such problems.
Realised using Commercial off-the-shelf (COTS) software components, the
deployable system is open source, simple, scalable, and cheap to produce. It
has the potential to achieve pulsar search design requirements for the Square
Kilometre Array (SKA), illustrated via testing under simulated SKA loads.
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We study the intrinsic structure of parametric minimal discs in metric spaces
admitting a quadratic isoperimetric inequality. We associate to each minimal
disc a compact, geodesic metric space whose geometric, topological, and
analytic properties are controlled by the isoperimetric inequality. Its
geometry can be used to control the shapes of all curves and therefore the
geometry and topology of the original metric space. The class of spaces arising
in this way as intrinsic minimal discs is a natural generalization of the class
of Ahlfors regular discs, well-studied in analysis on metric spaces.
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Observations of young star-forming regions suggest that star clusters are
born completely mass segregated. These initial conditions are, however,
gradually lost as the star cluster evolves dynamically. For star clusters with
single stars only and a canonical initial mass function, it has been suggested
that traces of these initial conditions vanish at a time $\tau_\mathrm{v}$
between 3 and $3.5\,t_\mathrm{rh}$ (initial half-mass relaxation times). Since
a significant fraction of stars are observed in binary systems and it is widely
accepted that most stars are born in binary systems, we aim to investigate what
role a primordial binary population (even up to $100\,\%$ binaries) plays in
the loss of primordial mass segregation of young star clusters. We used
numerical $N$-body models similar in size to the Orion Nebula Cluster (ONC) --
a representative of young open clusters -- integrated over several relaxation
times to draw conclusions on the evolution of its mass segregation. We also
compared our models to the observed ONC. We found that $\tau_\mathrm{v}$
depends on the binary star fraction and the distribution of initial binary
parameters that include a semi-major axis, eccentricity, and mass ratio. For
instance, in the models with $50\,\%$ binaries, we find $\tau_\mathrm{v} = (2.7
\pm 0.8)\,t_\mathrm{rh}$, while for $100\,\%$ binary fraction, we find a lower
value $\tau_\mathrm{v} = (2.1 \pm 0.6)\,t_\mathrm{rh}$. We also conclude that
the initially completely mass segregated clusters, even with binaries, are more
compatible with the present-day ONC than the non-segregated ones.
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Lattice simulations can play an important role in the study of dynamical
electroweak symmetry breaking by providing quantitative results on the
nonperturbative dynamics of candidate theories. For this programme to succeed,
it is crucial to identify the questions that are relevant for phenomenology,
and develop the tools that will provide robust answers to these questions. The
existence of a conformal window for nonsupersymmetric gauge theories, and its
characterization, is one of the phenomenologically important problems that can
be studied on the lattice. We summarize the recent results from studies of IR
fixed points by numerical simulations, discuss their current limitations, and
analyze the future perspectives.
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In this paper, we introduce a bilevel optimization framework for addressing
inverse mean-field games, alongside an exploration of numerical methods
tailored for this bilevel problem. The primary benefit of our bilevel
formulation lies in maintaining the convexity of the objective function and the
linearity of constraints in the forward problem. Our paper focuses on inverse
mean-field games characterized by unknown obstacles and metrics. We show
numerical stability for these two types of inverse problems. More importantly,
we, for the first time, establish the identifiability of the inverse mean-field
game with unknown obstacles via the solution of the resultant bilevel problem.
The bilevel approach enables us to employ an alternating gradient-based
optimization algorithm with a provable convergence guarantee. To validate the
effectiveness of our methods in solving the inverse problems, we have designed
comprehensive numerical experiments, providing empirical evidence of its
efficacy.
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Alfven waves created by sub-photospheric motions or by magnetic reconnection
in the low solar atmosphere seem good candidates for coronal heating. However,
the corona is also likely to be heated more directly by magnetic reconnection,
with dissipation taking place in current sheets. Distinguishing observationally
between these two heating mechanisms is an extremely difficult task. We perform
1.5-dimensional MHD simulations of a coronal loop subject to each type of
heating and derive observational quantities that may allow these to be
differentiated.
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The class of Cressie-Read empirical likelihoods are constructed with weights
derived at a minimum distance from the empirical distribution in the
Cressie-Read family of divergences indexed by $\gamma$ under the constraint of
an unbiased set of $M$-estimating equations. At first order, they provide valid
posterior probability statements for any given prior, but the bias in coverage
of the resulting empirical quantile is inversely proportional to the asymptotic
efficiency of the corresponding $M$-estimator. The Cressie-Read empirical
likelihoods based on the maximum likelihood estimating equations bring about
quantiles covering with $O(n^{-1})$ accuracy at the underlying posterior
distribution. The choice of $\gamma$ has an impact on the variance in small
samples of the posterior quantile function. Examples are given for the $M$-type
estimating equations of location and for the quasi-likelihood functions in the
generalized linear models.
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We propose a modified density estimation problem that is highly effective for
detecting anomalies in tabular data. Our approach assumes that the density
function is relatively stable (with lower variance) around normal samples. We
have verified this hypothesis empirically using a wide range of real-world
data. Then, we present a variance-stabilized density estimation problem for
maximizing the likelihood of the observed samples while minimizing the variance
of the density around normal samples. To obtain a reliable anomaly detector, we
introduce a spectral ensemble of autoregressive models for learning the
variance-stabilized distribution. We have conducted an extensive benchmark with
52 datasets, demonstrating that our method leads to state-of-the-art results
while alleviating the need for data-specific hyperparameter tuning. Finally, we
have used an ablation study to demonstrate the importance of each of the
proposed components, followed by a stability analysis evaluating the robustness
of our model.
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Due to the powerful computing capability of quantum computers, cryptographic
researchers have applied quantum algorithms to cryptanalysis and obtained many
interesting results in recent years. In this paper, we study related-key attack
in the quantum setting, and proposed a specific related-key attack which can
recover the key of block ciphers efficiently, as long as the attacked block
ciphers satisfy certain conditions. The attack algorithm employs
Bernstein-Vazirani algorithm as a subroutine and requires the attacker to query
the encryption oracle with quantum superpositions. Afterwards, we rigorously
demonstrate the validity of the attack and analyze its complexity. Our work
shows that related-key attack is quite powerful when combined with quantum
algorithms, and provides some guidance for the design of block ciphers that are
secure against quantum adversaries.
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In this paper we provide a (negative) solution to a problem posed by
Stanis{\l}aw Krajewski. Consider a recursively enumerable theory U and a finite
expansion of the signature of U that contains at least one predicate symbol of
arity $\ge$ 2. We show that, for any finite extension $\alpha$ of U in the
expanded language that is conservative over U, there is a conservative
extension $\beta$ of U in the expanded language, such that $\alpha\vdash\beta$
and $\beta\nvdash\alpha$. The result is preserved when we consider either
extensions or model-conservative extensions of U in stead of conservative
extensions. Moreover, the result is preserved when we replace $\vdash$ as
ordering on the finitely axiomatized extensions in the expanded language by a
special kind of interpretability, to wit interpretability that identically
translates the symbols of the U-language.
We show that the result fails when we consider an expansion with only unary
predicate symbols for conservative extensions of U ordered by interpretability
that preserves the symbols of U.
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We employ a continuous dynamical decoupling scheme to suppress the
decoherence induced by elastic collisions of cold atoms. Using a continuous
echo pulse we achieve a thirty-fold increase in the coherence time of Rb87
atoms trapped in a dipole trap. Coherence times of more than 100ms are
demonstrated for an ensemble with an optical depth of 120.
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We compute quantum corrections to the Raychaudhuri equation, by replacing
classical geodesics with quantal (Bohmian) trajectories, and show that they
prevent focusing of geodesics, and the formation of conjugate points. We
discuss implications for the Hawking-Penrose singularity theorems, and for
curvature singularities.
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Boundary value problems for nonlocal fractional elliptic equations with
parameter in Banach spaces are studied. Uniform $L_p$-separability properties
and sharp resolvent estimates are obtained for elliptic equations in terms of
fractional derivatives. Particularly, it is proven that the fractional
ellipitic operator generated by these equations is sectorial and also is a
generator of an analytic semigroup. Moreover, maximal regularity properties of
nonlocal fractional abstract parabolic equation are established. As an
application, the nonlocal anisotropic fractional differential equations and the
system of nonlocal fractional differential equations are studied.
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In this paper we show that BF topological superconductors (insulators) exibit
phase transitions between different topologically ordered phases characterized
by different ground state degeneracy on manifold with non-trivial topology.
These phase transitions are induced by the condensation (or lack of) of
topological defects. We concentrate on the (2+1)-dimensional case where the BF
model reduce to a mixed Chern-Simons term and we show that the superconducting
phase has a ground state degeneracy $k$ and not $k^2$. When the symmetry is
$U(1) \times U(1)$, namely when both gauge fields are compact, this model is
not equivalent to the sum of two Chern-Simons term with opposite chirality,
even if naively diagonalizable. This is due to the fact that U(1) symmetry
requires an ultraviolet regularization that make the diagonalization
impossible. This can be clearly seen using a lattice regularization, where the
gauge fields become angular variables. Moreover we will show that the phase in
which both gauge fields are compact is not allowed dynamically.
|
The magnetic and iron vacancy orders in superconducting (Tl,Rb)2Fe4Se5
single-crystals are investigated by using a high-pressure neutron diffraction
technique. Similar to the temperature effect, the block antiferromagnetic order
gradually decreases upon increasing pressure while the Fe vacancy
superstructural order remains intact before its precipitous disappearance at
the critical pressure Pc = 8.3 GPa. Combined with previously determined Pc for
superconductivity, our phase diagram under pressure reveals the concurrence of
the block AFM order, the iron vacancy order and superconductivity for the 245
superconductor. A synthesis of current experimental data in a coherent physical
picture is attempted.
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We consider ${\cal N}=(n,0)$ supersymmetric AdS$_3$ vacua of type II
supergravity realising the superconformal algebra $\mathfrak{osp}(n|2)$ for
$n>4$. For the cases $n=6$ and $n=5$, one can realise these algebras on
backgrounds that decompose as foliations of AdS$_3\times \mathbb{CP}^3$ (
squashed $\mathbb{CP}^3$ for $n=5$) over an interval. We classify such
solutions with bi-spinor techniques and find the local form of each of them:
They only exist in (massive) IIA and are defined locally in terms of an order 3
polynomial $h$ similar to the AdS$_7$ vacua of (massive) IIA. Many distinct
local solutions exist for different tunings of $h$ that give rise to bounded
(or semi infinite) intervals bounded by physical behaviour. We show that it is
possible to glue these local solutions together by placing D8 branes on the
interior of the interval without breaking supersymmetry, which expands the
possibilities for global solutions immensely. We illustrate this point with
some simple examples. Finally we also show that AdS$_3$ vacua for $n=7,8$ only
exist in $d=11$ supergravity and are all locally AdS$_4\times$S$^7$.
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This paper proposes the creation of different interfaces in the mobile
operating system for different age groups. The different age groups identified
are kids, elderly people and all others. The motive behind creating different
interfaces is to make the smartphones of today's world usable to all age
groups.
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In this paper we propose the first better than second order accurate method
in space and time for the numerical solution of the resistive relativistic
magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space
dimensions. The nonlinear system under consideration is purely hyperbolic and
contains a source term, the one for the evolution of the electric field, that
becomes stiff for low values of the resistivity. For the spatial discretization
we propose to use high order $\PNM$ schemes as introduced in \cite{Dumbser2008}
for hyperbolic conservation laws and a high order accurate unsplit time
discretization is achieved using the element-local space-time discontinuous
Galerkin approach proposed in \cite{DumbserEnauxToro} for one-dimensional
balance laws with stiff source terms. The divergence free character of the
magnetic field is accounted for through the divergence cleaning procedure of
Dedner et al. \cite{Dedneretal}. To validate our high order method we first
solve some numerical test cases for which exact analytical reference solutions
are known and we also show numerical convergence studies in the stiff limit of
the RRMHD equations using $\PNM$ schemes from third to fifth order of accuracy
in space and time. We also present some applications with shock waves such as a
classical shock tube problem with different values for the conductivity as well
as a relativistic MHD rotor problem and the relativistic equivalent of the
Orszag-Tang vortex problem. We have verified that the proposed method can
handle equally well the resistive regime and the stiff limit of ideal
relativistic MHD. For these reasons it provides a powerful tool for
relativistic astrophysical simulations involving the appearance of magnetic
reconnection.
|
In this article I attempt to collect some ideas,opinions and formulae which
may be useful in solving the problem of gauge/ string / space-time
correspondence This includes the validity of D-brane representation, counting
of gauge-invariant words, relations between the null states and the Yang-Mills
equations and the discussion of the strong coupling limit of the string sigma
model. The article is based on the talk given at the "Odyssey 2001" conference.
|
Let $C,A$ be countable abelian groups. In this paper we determine the
complexity of classifying extensions $C$ by $A$, in the cases when $C$ is
torsion-free and $A$ is a $p$-group, a torsion group with bounded primary
components, or a free $R$-module for some subring $R\subseteq \mathbb{Q}$.
Precisely, for such $C$ and $A$ we describe in terms of $C$ and $A$ the
potential complexity class in the sense of Borel complexity theory of the
equivalence relation $\mathcal{R}_{\mathbf{Ext}\left( C,A\right) }$ of
isomorphism of extensions of $C$ by $A$. This complements a previous result by
the same author, settling the case when $C$ is torsion and $A$ is arbitrary. We
establish the main result within the framework of Borel-definable homological
algebra, recently introduced in collaboration with Bergfalk and
Panagiotopoulos. As a consequence of our main results, we will obtain that if
$C$ is torsion-free and $A$ is either a free $R$-module or a torsion group with
bounded components, then an extension of $C$ by $A$ splits if and only if it
splits on all finite-rank subgroups of $C$. This is a purely algebraic
statements obtained with methods from Borel-definable homological algebra.
|
Global dimensions for fusion categories defined by a pair (G,k), where G is a
Lie group and k a positive integer, are expressed in terms of Lie quantum
superfactorial functions. The global dimension is defined as the square sum of
quantum dimensions of simple objects, for the category of integrable modules
over an affine Lie algebra at some level. The same quantities can also be
defined from the theory of quantum groups at roots of unity or from conformal
field theory WZW models. Similar results are also presented for those
associated module-categories that can be obtained via conformal embeddings
(they are "quantum subgroups" of a particular kind). As a side result, we
express the classical (or quantum) Weyl denominator of simple Lie groups in
terms of products of classical (or quantum) factorials calculated for the
exponents of the group. Some calculations use the correspondence existing
between periodic quivers for simply-laced Lie groups and fusion rules for
module-categories (alias nimreps) of type SU(2).
|
This work concerns random dynamics of hyperbolic entire and meromorphic
functions of finite order and whose derivative satisfies some growth condition
at infinity. This class contains most of the classical families of
transcendental functions and goes much beyond. Based on uniform versions of
Nevanlinna's value distribution theory we first build a thermodynamical
formalism which, in particular, produces unique geometric and fiberwise
invariant Gibbs states. Moreover, spectral gap property for the associated
transfer operator along with exponential decay of correlations and a central
limit theorem are shown. This part relies on our construction of new positive
invariant cones that are adapted to the setting of unbounded phase spaces. This
setting rules out the use of Hilbert's metric along with the usual contraction
principle. However these cones allow us to apply a contraction argument
stemming from Bowen's initial approach.
|
We establish several new bounds for the number of conjugacy classes of a
finite group, all of which involve the maximal number c of conjugacy classes of
a normal subgroup fixed by some element of a suitable subset of the group. To
apply these formulas effectively, the parameter c, which in general is hard to
control, is studied in some important situations. These results are then used
to provide a new, shorter proof of the most difficult case of the well-known
k(GV)-problem, which occurs for p=5 and V induced from the natural module of a
5-complement of GL(2,5). We also show how, for large p, the new results reduce
the k(GV)-problem to the primitive case, thereby improving previous work on
this. Furthermore, we discuss how they can be used in tackling the imprimitive
case of the as of yet unsolved noncoprime k(GV)-problem.
|
This paper studies the transmission of Gaussian sources through additive
white Gaussian noise (AWGN) channels in bandwidth expansion regime, i.e., the
channel bandwidth is greater than the source bandwidth. To mitigate the error
propagation phenomenon of conventional digital transmission schemes, we propose
in this paper a new capacity-approaching joint source channel coding (JSCC)
scheme based on partially block Markov superposition transmission (BMST) of
nested lattice codes. In the proposed scheme, first, the Gaussian source
sequence is discretized by a lattice-based quantizer, resulting in a sequence
of lattice points. Second, these lattice points are encoded by a short
systematic group code. Third, the coded sequence is partitioned into blocks of
equal length and then transmitted in the BMST manner. Main characteristics of
the proposed JSCC scheme include: 1) Entropy coding is not used explicitly. 2)
Only parity-check sequence is superimposed, hence, termed partially BMST
(PBMST). This is different from the original BMST. To show the superior
performance of the proposed scheme, we present extensive simulation results
which show that the proposed scheme performs within 1.0 dB of the Shannon
limits. Hence, the proposed scheme provides an attractive candidate for
transmission of Gaussian sources.
|
When subjected to electro-mechanical loading, ferroelectrics see their
polarization evolve through the nucleation and evolution of domains. Existing
mesoscale phase-field models for ferroelectrics are typically based on a
gradient-descent law for the evolution of the order parameter. While this
implicitly assumes that domain walls evolve with linear kinetics, experiments
instead indicate that domain wall kinetics is nonlinear. This, in turn, is an
important feature for the modeling of rate-dependent effects in polarization
switching. We propose a new multiple-phase-field model for ferroelectrics,
which permits domain wall motion with nonlinear kinetics, with applications in
other solid-solid phase transformation problems. By means of analytical
traveling wave solutions, we characterize the interfacial properties (energy
and width) and the interface kinetics of straight domain walls, as furnished by
the general kinetics model, and compare them to those of the classical
Allen--Cahn model. We show that the proposed model propagates domain walls with
arbitrarily chosen nonlinear kinetic relations, which can be tuned to differ
for the different types of domain walls in accordance with experimental
evidence.
|
Fetal neuroinflammation and prenatal stress (PS) may contribute to lifelong
neurological disabilities. Astrocytes and microglia, among the brain's
non-neuronal glia cell populations, play a pivotal role in neurodevelopment,
predisposition to and initiation of disease throughout lifespan. One of the
most common neurodevelopmental disorders manifesting between 1-4 years of age
is autism spectrum disorder (ASD). A pathological glial-neuronal interplay is
thought to increase the risk for clinical manifestation of ASD in at-risk
children, but the mechanisms remain poorly understood and integrative,
multi-scale models are needed. We propose a model that integrates the data
across the scales of physiological organization, from genome to phenotype, and
provides a foundation to explain the disparate findings on the genomic level.
We hypothesize that via gene-environment interactions, fetal neuroinflammation
and PS may reprogram glial immunometabolic phenotypes that impact
neurodevelopment and neurobehavior. Drawing on genomic data from the recently
published series of ovine and rodent glial transcriptome analyses with fetuses
exposed to neuroinflammation or PS, we conduct an analysis on the Simons
Foundation Autism Research Initiative (SFARI) Gene database. We confirm 21 gene
hits. Using unsupervised statistical network analysis, we then identify six
clusters of probable protein-protein interactions mapping onto the
immunometabolic and stress response networks and epigenetic memory. These
findings support our hypothesis. We discuss the implications for ASD etiology,
early detection, and novel therapeutic approaches. We conclude with delineation
of the next steps to verify our model on the individual gene level in an
assumption-free manner.
|
We have measured magnetic trap lifetimes of ultra-cold Rb87 atoms at
distances of 5-1000 microns from surfaces of conducting metals with varying
resistivity. Good agreement is found with a theoretical model for losses
arising from near-field magnetic thermal noise, confirming the complications
associated with holding trapped atoms close to conducting surfaces. A
dielectric surface (silicon) was found in contrast to be so benign that we are
able to evaporatively cool atoms to a Bose-Einstein condensate by using the
surface to selectively adsorb higher energy atoms.
|
Prostate cancer is a highly prevalent cancer and ranks as the second leading
cause of cancer-related deaths in men globally. Recently, the utilization of
multi-modality transrectal ultrasound (TRUS) has gained significant traction as
a valuable technique for guiding prostate biopsies. In this study, we propose a
novel learning framework for clinically significant prostate cancer (csPCa)
classification using multi-modality TRUS. The proposed framework employs two
separate 3D ResNet-50 to extract distinctive features from B-mode and shear
wave elastography (SWE). Additionally, an attention module is incorporated to
effectively refine B-mode features and aggregate the extracted features from
both modalities. Furthermore, we utilize few shot segmentation task to enhance
the capacity of classification encoder. Due to the limited availability of
csPCa masks, a prototype correction module is employed to extract
representative prototypes of csPCa. The performance of the framework is
assessed on a large-scale dataset consisting of 512 TRUS videos with
biopsy-proved prostate cancer. The results demonstrate the strong capability in
accurately identifying csPCa, achieving an area under the curve (AUC) of 0.86.
Moreover, the framework generates visual class activation mapping (CAM), which
can serve as valuable assistance for localizing csPCa. These CAM images may
offer valuable guidance during TRUS-guided targeted biopsies, enhancing the
efficacy of the biopsy procedure.The code is available at
https://github.com/2313595986/SmileCode.
|
In this article, we separate the vector and axialvector components of the
tensor diquark operators explicitly, construct the axialvector-axialvector type
and vector-vector type scalar tetraquark currents and scalar-tensor type tensor
tetraquark current to study the scalar, vector and axialvector tetraquark
states with the QCD sum rules in a consistent way. The present calculations do
not favor assigning the $Z_c(4100)$ to be a scalar or vector tetraquark state.
If the $Z_c(4100)$ is a scalar tetraquark state without mixing effects, it
should have a mass about $3.9\,\rm{GeV}$ or $4.0\,\rm{GeV}$ rather than
$4.1\,\rm{GeV}$; on the other hand, if the $Z_c(4100)$ is a vector tetraquark
state, it should have a mass about $4.2\,\rm{GeV}$ rather than $4.1\,\rm{GeV}$.
However, if we introduce mixing, a mixing scalar tetraquark state can have a
mass about $4.1\,\rm{GeV}$. As a byproduct, we obtain an axialvector tetraquark
candidate for the $Z_c(4020)$.
|
The formation of nanostructures during metalorganic vapor-phase epitaxy on
patterned (001)/(111)B GaAs substrates is reviewed. The focus of this review is
on the seminal experiments that revealed the key kinetic processes during
nanostructure formation and the theory and modelling that explained the
phenomenology in successively greater detail. Experiments have demonstrated
that V-groove quantum wires and pyramidal quantum dots result from
self-limiting concentration profiles that develop at the bottom of V-grooves
and inverted pyramids, respectively. In the 1950s, long before the practical
importance of patterned substrates became evident, the mechanisms of
capillarity during the equilibration of non-planar surfaces were identified and
characterized. This was followed, from the late 1980s by the identification of
growth rate anisotropies (i.e. differential growth rates of crystallographic
facets) and precursor decomposition anisotropies, with parallel developments in
the fabrication of V-groove quantum wires and pyramidal quantum dots. The
modelling of these growth processes began at the scale of facets and culminated
in systems of coupled reaction-diffusion equations, one for each
crystallographic facet that defines the pattern, which takes account of the
decomposition and surface diffusion kinetics of the group-III precursors and
the subsequent surface diffusion and incorporation of the group-III atoms
released by these precursors. Solutions of the equations with optimized
parameters produced concentration profiles that provided a quantitative
interpretation of the time-, temperature-, and alloy-concentration dependence
of the self-ordering process seen in experiments.
|
The study of topology in solids is undergoing a renaissance following renewed
interest in the properties of ferroic domain walls as well as recent
discoveries regarding topological insulators and skyrmionic lattices. Each of
these systems possess a property that is `protected' in a symmetry sense, and
is defined rigorously using a branch of mathematics known as topology. In this
article we review the formal definition of topological defects as they are
classified in terms of homotopy theory, and discuss the precise
symmetry-breaking conditions that lead to their formation. We distinguish
topological defects from geometric defects, which arise from the details of the
stacking or structure of the material but are not protected by symmetry. We
provide simple material examples of both topological and geometric defect
types, and discuss the implications of the classification on the resulting
material properties.
|
Security of a continuous-variable quantum key distribution protocol based on
noisy coherent states and channel is analyzed. Assuming the noise of coherent
states is induced by Fred, a neutral party relative to others, we prove that
the prepare and measurement scheme and entanglement-based scheme are
equivalent. Then, we show that this protocol is secure against Gaussian
collective attacks even if the channel is lossy and noisy, and further, a lower
bound to the secure key rate is derived.
|
We discuss a sample of over 3000 candidate RR Lyrae stars selected by various
methods using Sloan Digital Sky Survey data for about 1000 deg^2 of sky. These
stars probe the halo structure out to ~100 kpc from the Galactic center. Their
spatial and radial velocity distributions are very inhomogeneous, with the most
prominent features tracing the Sgr dwarf tidal stream. Outside the Sgr dwarf
tidal stream, the spatial distribution in the 5-60 kpc range of Galactocentric
radius R is well described by an R^{-3} power law.
|
We show that if an open arc J of the boundary of a Jordan domain $\Omega$ is
rectifiable, then the derivative $\Phi$' of the Riemann map $\Phi: D\rightarrow
\Omega$ from the open unit disk D onto $\Omega$ behaves as an $H^1$ function
when we approach the arc $\Phi^{-1}(J^{\prime})$,where $J^{\prime}$ is any
compact subarc of $J$. "
|
We present Hubble Space Telescope imaging of 14 gas-rich, low surface
brightness galaxies in the field at distances of 25-36 Mpc, with mean effective
radii and $g$-band central surface brightnesses of 1.9 kpc and 24.2 mag
arcsec$^{-2}$. Nine meet the standard criteria to be considered ultra-diffuse
galaxies (UDGs). An inspection of point-like sources brighter than the turnover
magnitude of the globular cluster luminosity function and within twice the
half-light radii of each galaxy reveals that, unlike those in denser
environments, gas-rich, field UDGs host very few old globular clusters (GCs).
Most of the targets (nine) have zero candidate GCs, with the remainder having
one or two candidates each. These findings are broadly consistent with
expectations for normal dwarf galaxies of similar stellar mass. This rules out
gas-rich, field UDGs as potential progenitors of the GC-rich UDGs that are
typically found in galaxy clusters. However, some in galaxy groups may be
directly accreted from the field. In line with other recent results, this
strongly suggests that there must be at least two distinct formation pathways
for UDGs, and that this sub-population is simply an extreme low surface
brightness extension of the underlying dwarf galaxy population. The root cause
of their diffuse stellar distributions remains unclear, but the formation
mechanism appears to only impact the distribution of stars (and potentially
dark matter), without strongly impacting the distribution of neutral gas, the
overall stellar mass, or the number of GCs.
|
Tongue cancer is a common oral cavity malignancy that originates in the mouth
and throat. Much effort has been invested in improving its diagnosis,
treatment, and management. Surgical removal, chemotherapy, and radiation
therapy remain the major treatment for tongue cancer. The survival of patients
determines the treatment effect. Previous studies have identified certain
survival and risk factors based on descriptive statistics, ignoring the
complex, nonlinear relationship among clinical and demographic variables. In
this study, we utilize five cutting-edge machine learning models and clinical
data to predict the survival of tongue cancer patients after treatment.
Five-fold cross-validation, bootstrap analysis, and permutation feature
importance are applied to estimate and interpret model performance. The
prognostic factors identified by our method are consistent with previous
clinical studies. Our method is accurate, interpretable, and thus useable as
additional evidence in tongue cancer treatment and management.
|
In this paper, we consider testing the martingale difference hypothesis for
high-dimensional time series. Our test is built on the sum of squares of the
element-wise max-norm of the proposed matrix-valued nonlinear dependence
measure at different lags. To conduct the inference, we approximate the null
distribution of our test statistic by Gaussian approximation and provide a
simulation-based approach to generate critical values. The asymptotic behavior
of the test statistic under the alternative is also studied. Our approach is
nonparametric as the null hypothesis only assumes the time series concerned is
martingale difference without specifying any parametric forms of its
conditional moments. As an advantage of Gaussian approximation, our test is
robust to the cross-series dependence of unknown magnitude. To the best of our
knowledge, this is the first valid test for the martingale difference
hypothesis that not only allows for large dimension but also captures nonlinear
serial dependence. The practical usefulness of our test is illustrated via
simulation and a real data analysis. The test is implemented in a user-friendly
R-function.
|
We report the discovery of HAT-P-17b,c, a multi-planet system with an inner
transiting planet in a short-period, eccentric orbit and an outer planet in a
4.8 yr, nearly circular orbit. The inner planet, HAT-P-17b, transits the bright
V = 10.54 early K dwarf star GSC 2717-00417, with an orbital period P =
10.338523 +/- 0.000009 d, orbital eccentricity e = 0.346 +/- 0.007, transit
epoch T_c = 2454801.16945 +/- 0.00020, and transit duration 0.1691 +/- 0.0009
d. HAT-P-17b has a mass of 0.530 +/- 0.018 M_J and radius of 1.010 +/- 0.029
R_J yielding a mean density of 0.64 +/- 0.05 g cm^-3. This planet has a
relatively low equilibrium temperature in the range 780-927 K, making it an
attractive target for follow-up spectroscopic studies. The outer planet,
HAT-P-17c, has a significantly longer orbital period P_2 = 1797^+58_-89 d and a
minimum mass m_2 sin i_2 = 1.4^+1.1_-0.4 M_J. The orbital inclination of
HAT-P-17c is unknown as transits have not been observed and may not be present.
The host star has a mass of 0.86 +/- 0.04 M_Sun, radius of 0.84 +/- 0.02,
effective temperature 5246 +/- 80 K, and metallicity [Fe/H] = 0.00 +/- 0.08.
HAT-P-17 is the second multi-planet system detected from ground-based transit
surveys.
|
Future microwave sky surveys will have the sensitivity to detect the
kinematic Sunyaev-Zeldovich signal from moving galaxy clusters, thus providing
a direct measurement of their line-of-sight peculiar velocity. We show that
cluster peculiar velocity statistics applied to foreseeable surveys will put
significant constraints on fundamental cosmological parameters. We consider
three statistical quantities that can be constructed from a cluster peculiar
velocity catalog: the probability density function, the mean pairwise streaming
velocity, and the pairwise velocity dispersion. These quantities are applied to
an envisioned data set which measures line-of-sight cluster velocities with
normal errors of 100 km/s for all clusters with masses larger than $10^{14}$
solar masses over a sky area of up to 5000 square degrees. A simple Fisher
matrix analysis of this survey shows that the normalization of the matter power
spectrum and the dark energy equation of state can be constrained to better
than 10 percent, and the Hubble constant and the primordial power spectrum
index can be constrained to a few percent, independent of any other
cosmological observations. We also find that the current constraint on the
power spectrum normalization can be improved by more than a factor of two using
data from a 400 square degree survey and WMAP third-year priors. We also show
how the constraints on cosmological parameters changes if cluster velocities
are measured with normal errors of 300 km/s.
|
We develop a Bayesian hierarchical semiparametric model for phenomena related
to time series of counts. The main feature of the model is its capability to
learn a latent pattern of heterogeneity in the distribution of the process
innovation rates, which are softly clustered through time with the help of a
Dirichlet process placed at the top of the model hierarchy. The probabilistic
forecasting capabilities of the model are put to test in the analysis of crime
data in Pittsburgh, with favorable results.
|
We demonstrate quantum entanglement of two trapped atomic ion qubits using a
sequence of ultrafast laser pulses. Unlike previous demonstrations of
entanglement mediated by the Coulomb interaction, this scheme does not require
confinement to the Lamb-Dicke regime and can be less sensitive to ambient noise
due to its speed. To elucidate the physics of an ultrafast phase gate, we
generate a high entanglement rate using just 10 pulses, each of $\sim20$ ps
duration, and demonstrate an entangled Bell-state with $(76\pm1)$% fidelity.
These results pave the way for entanglement operations within a large
collection of qubits by exciting only local modes of motion.
|
In mixed-initiative co-creation tasks, wherein a human and a machine jointly
create items, it is important to provide multiple relevant suggestions to the
designer. Quality-diversity algorithms are commonly used for this purpose, as
they can provide diverse suggestions that represent salient areas of the
solution space, showcasing designs with high fitness and wide variety. Because
generated suggestions drive the search process, it is important that they
provide inspiration, but also stay aligned with the designer's intentions.
Additionally, often many interactions with the system are required before the
designer is content with a solution. In this work, we tackle these challenges
with an interactive constrained MAP-Elites system that leverages emitters to
learn the preferences of the designer and then use them in automated steps. By
learning preferences, the generated designs remain aligned with the designer's
intent, and by applying automatic steps, we generate more solutions per user
interaction, giving a larger number of choices to the designer and thereby
speeding up the search. We propose a general framework for preference-learning
emitters (PLEs) and apply it to a procedural content generation task in the
video game Space Engineers. We built an interactive application for our
algorithm and performed a user study with players.
|
Cells perform directed motion in response to external stimuli that they
detect by sensing the environment with their membrane protrusions. In
particular, several biochemical and biophysical cues give rise to tactic
migration in the direction of their specific targets. This defines a multi-cue
environment in which cells have to sort and combine different, and potentially
competitive, stimuli. We propose a non-local kinetic model for cell migration
in presence of two external factors both influencing cell polarization: contact
guidance and chemotaxis. We propose two different sensing strategies and we
analyze the two resulting models by recovering the appropriate macroscopic
limit in different regimes, in order to see how the size of the cell, with
respect to the variation of both external fields, influences the overall
behavior. Moreover, we integrate numerically the kinetic transport equation in
a two-dimensional setting in order to investigate qualitatively various
scenarios.
|
The design of gate drivers is an important topic in power converter
topologies that can help reduce switching losses and increase power density.
Gate driving techniques that offer zero-voltage switching and/or zero current
switching have recently been successfully proposed for different modular
multilevel converters such as the cascaded H bridge. Previous papers on other
multilevel converters such as the multi-active bridge, however, do not
sufficiently assess the topics of gate driver design for this topology. This
work presents a novel isolated gate driver architecture tailored to the
multi-active bridge topology. Zero voltage switching is then achieved using two
multi-winding transformers. The advantages of the proposed topology are not
only a reduction of switching losses but also reduced component count.
The topology is evaluated on a prototype using experimental results.
It was shown using simulation and experiments that the proposed topology has
a high efficiency while providing compact power packaging.
Especially for converters with many levels, the proposed topology is
therefore advantageous compared to existing solutions.
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In this paper we give an algorithm for solving a main case of the conjugacy
problem in the braid groups. We also prove that half-twists satisfy a special
root property which allows us to reduce the solution for the conjugacy problem
in half-twists into the free group. Using this algorithm one is able to check
conjugacy of a given braid to one of E. Artin's generators in any power, and
compute its root. Moreover, the braid element which conjugates a given
half-twist to one of E. Artin's generators in any power can be restored. The
result is applicable to calculations of braid monodromy of branch curves and
verification of Hurwitz equivalence of braid monodromy factorizations, which
are essential in order to determine braid monodromy type of algebraic surfaces
and symplectic 4-manifolds.
|
The paper has been withdrawn by the author, due to a fatal error. A horse
stumbles that has four legs.
|
In the presence of P,T-violating interactions, the exchange of axion-like
particles between electrons and nucleons in atoms and molecules induces
electric dipole moments (EDMs) of atoms and molecules. We perform calculations
of such axion-exchange-induced atomic EDMs using the relativistic
Hartree-Fock-Dirac method including electron core polarisation (RPA)
corrections. We present analytical estimates to explain the dependence of these
induced atomic EDMs on the axion mass and atomic parameters. From the
experimental bounds on the EDMs of atoms and molecules, including $^{133}$Cs,
$^{205}$Tl, $^{129}$Xe, $^{199}$Hg, $^{171}$Yb$^{19}$F, $^{180}$Hf$^{19}$F$^+$
and $^{232}$Th$^{16}$O, we constrain the P,T-violating scalar-pseudoscalar
nucleon-electron and electron-electron interactions mediated by a generic
axion-like particle of arbitrary mass. Our limits improve on existing
laboratory bounds from other experiments by many orders of magnitude for $m_a
\gtrsim 10^{-2}~\textrm{eV}$. We also place constraints on CP violation in
certain types of relaxion models.
|
We prove an asymptotic formula for the Fourier transform of the arithmetic
surface measure associated to the Waring--Goldbach problem and provide several
applications, including bounds for discrete spherical maximal functions along
the primes and distribution results such as ergodic theorems.
|
Deep neural networks currently deliver promising results for microscopy image
cell segmentation, but they require large-scale labelled databases, which is a
costly and time-consuming process. In this work, we relax the labelling
requirement by combining self-supervised with semi-supervised learning. We
propose the prediction of edge-based maps for self-supervising the training of
the unlabelled images, which is combined with the supervised training of a
small number of labelled images for learning the segmentation task. In our
experiments, we evaluate on a few-shot microscopy image cell segmentation
benchmark and show that only a small number of annotated images, e.g. 10% of
the original training set, is enough for our approach to reach similar
performance as with the fully annotated databases on 1- to 10-shots. Our code
and trained models is made publicly available
|
It ia well-known that surface plasmon wave propagates along a straight line,
but this common sense was broken by the artificial curved light - plasmon Airy
beam. In this paper we introduce a new class of curved surface plasmon wave -
the photonic hook plasmon. It propagates along wavelength scaled curved
trajectory with radius less than surface plasmon polariton wavelength, and can
exist despite the strong energy dissipation at the metal surface.
|
In this paper we extend a previous investigation by us regarding an iterative
construction of irreducible polynomials over finite fields of odd
characteristic. In particular, we show how it is possible to iteratively
construct irreducible polynomials by means of two families of transforms, which
we call the $Q_k$ and $\hat{Q}_k$-transforms, related to certain degree two
isogenies over elliptic curves, which split the multiplication-by-$2$ map.
|
Industrial computing devices, in particular cyber-physical, real-time and
safety-critical systems, focus on reacting to external events and the need to
cooperate with other devices to create a functional system. They are often
implemented with languages that focus on a simple, local description of how a
component reacts to external input data and stimuli. Despite the trend in
modern software architectures to structure systems into largely independent
components, the remaining interdependencies still create rich behavioural
dynamics even for small systems. Standard and industrial programming approaches
do usually not model or extensively describe the global properties of an entire
system. Although a large number of approaches to solve this dilemma have been
suggested, it remains a hard and error-prone task to implement systems with
complex interdependencies correctly.
We introduce multiple coupled finite state machines (McFSMs), a novel
mechanism that allows us to model and manage such interdependencies. It is
based on a consistent, well-structured and simple global description. A sound
theoretical foundation is provided, and associated tools allow us to generate
efficient low-level code in various programming languages using model-driven
techniques. We also present a domain specific language to express McFSMs and
their connections to other systems, to model their dynamic behaviour, and to
investigate their efficiency and correctness at compile-time.
|
The real numbers, it is taught at universities, correspond to our idea of a
continuum, although the hyperreal numbers are located ``in between'' the real
numbers. The number $x + dx$, where $dx$ should be an infinitesimal number and
$x$ real, is infinitesimally close to $x$ but ``infinitely'' far away from all
other real numbers. Analogously: If $f'(x_0)$ and $f(x_0)$ are given for a
differentiable function $f:\mathbb{R}\rightarrow\mathbb{R}$ at
$x_0\in\mathbb{R}$, we can not determine $f(x)$ at {\em any} point $x\in
\mathbb{R}$ different from $x_0$. These points seem to be ``infinitely'' far
away. That is one conceptual problem of solving differential equations in
numerical mathematics. In this article, we will present a numerical algorithm
to solve very simple initial value problems. However, the change of paradigm
is, that we will not ``leave'' the point $x_0$. Solving ordinary differential
equations is like searching for ``recipes'' $f$. Instead of trying to find
these recipes for values $x\in\mathbb{R}$, we will learn them from special
relations in the ``monad'' of $x_0$.
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We consider the challenging problem of tracking multiple objects using a
distributed network of sensors. In the practical setting of nodes with limited
field of views (FoVs), computing power and communication resources, we develop
a novel distributed multi-object tracking algorithm. To accomplish this, we
first formalise the concept of label consistency, determine a sufficient
condition to achieve it and develop a novel \textit{label consensus approach}
that reduces label inconsistency caused by objects' movements from one node's
limited FoV to another. Second, we develop a distributed multi-object fusion
algorithm that fuses local multi-object state estimates instead of local
multi-object densities. This algorithm: i) requires significantly less
processing time than multi-object density fusion methods; ii) achieves better
tracking accuracy by considering Optimal Sub-Pattern Assignment (OSPA) tracking
errors over several scans rather than a single scan; iii) is agnostic to local
multi-object tracking techniques, and only requires each node to provide a set
of estimated tracks. Thus, it is not necessary to assume that the nodes
maintain multi-object densities, and hence the fusion outcomes do not modify
local multi-object densities. Numerical experiments demonstrate our proposed
solution's real-time computational efficiency and accuracy compared to
state-of-the-art solutions in challenging scenarios. We also release source
code at https://github.com/AdelaideAuto-IDLab/Distributed-limitedFoV-MOT for
our fusion method to foster developments in DMOT algorithms.
|
Higher-order accuracy (order of $k+1$ in the $L^2$ norm) is one of the well
known beneficial properties of the discontinuous Galerkin (DG) method.
Furthermore, many studies have demonstrated the superconvergence property
(order of $2k+1$ in the negative norm) of the semi-discrete DG method. One can
take advantage of this superconvergence property by post-processing techniques
to enhance the accuracy of the DG solution. A popular class of post-processing
techniques to raise the convergence rate from order $k+1$ to order $2k+1$ in
the $L^2$ norm is the Smoothness-Increasing Accuracy-Conserving (SIAC)
filtering. In addition to enhancing the accuracy, the SIAC filtering also
increases the inter-element smoothness of the DG solution. The SIAC filtering
was introduced for the DG method of the linear hyperbolic equation by Cockburn
et al. in 2003. Since then, there are many generalizations of the SIAC
filtering have been proposed. However, the development of SIAC filtering has
never gone beyond the framework of using spline functions (mostly B-splines) to
construct the filter function. In this paper, we first investigate the general
basis function (beyond the spline functions) that can be used to construct the
SIAC filter. The studies of the general basis function relax the SIAC filter
structure and provide more specific properties, such as extra smoothness, etc.
Secondly, we study the basis functions' distribution and propose a new SIAC
filter called compact SIAC filter that significantly reduces the original SIAC
filter's support size while preserving (or even improving) its ability to
enhance the accuracy of the DG solution. We show that the proofs of the new
SIAC filters' ability to extract the superconvergence and provide numerical
results to confirm the theoretical results and demonstrate the new finding's
good numerical performance.
|
We propose a unifying rheological framework for dense suspensions of
non-Brownian spheres, predicting the onsets of particle friction and particle
inertia as distinct shear thickening mechanisms, while capturing quasistatic
and soft particle rheology at high volume fractions and shear rates
respectively. Discrete element method simulations that take suitable account of
hydrodynamic and particle-contact interactions corroborate the model
predictions, demonstrating both mechanisms of shear thickening, and showing
that they can occur concurrently with carefully selected particle surface
properties under certain flow conditions. Microstructural transitions
associated with frictional shear thickening are presented. We find very
distinctive divergences of both the microstructural and dynamic variables with
respect to volume fraction in the thickened and non-thickened states.
|
Fluctuations of conserved quantum numbers are associated with the
corresponding susceptibilities because of the symmetry of the system. The
underlying fact is that these fluctuations as defined through the static
correlators become identical to the direct calculation of these
susceptibilities defined through the thermodynamic derivatives, due to the
fluctuation-dissipation theorem. Through a rigorous exercise we explicitly show
that a diagrammatic calculation of the static correlators associated with the
conserved quark number fluctuations and the corresponding susceptibilities are
possible in case of mean field theories, if the implicit dependence of the mean
fields on the quark chemical potential are taken into account appropriately. As
an aside we also give an analytical prescription for obtaining the implicit
dependence of the mean fields on the quark chemical potential.
|
A novel framework for statistical learning is introduced which combines ideas
from regularization and ensembling. This framework is applied to learn an
ensemble of logistic regression models for high-dimensional binary
classification. In the new framework the models in the ensemble are learned
simultaneously by optimizing a multi-convex objective function. To enforce
diversity between the models the objective function penalizes overlap between
the models in the ensemble. Measures of diversity in classifier ensembles are
used to show how our method learns the ensemble by exploiting the
accuracy-diversity trade-off for ensemble models. In contrast to other
ensembling approaches, the resulting ensemble model is fully interpretable as a
logistic regression model, asymptotically consistent, and at the same time
yields excellent prediction accuracy as demonstrated in an extensive simulation
study and gene expression data applications. The models found by the proposed
ensemble methodology can also reveal alternative mechanisms that can explain
the relationship between the predictors and the response variable. An
open-source compiled software library implementing the proposed method is
briefly discussed.
|
IGR~J19149+1036 is a high mass X-ray binary detected by INTEGRAL in 2011 in
the hard X-ray domain. We have analyzed the BAT survey data of the first 103
months of the Swift mission detecting this source at a significance level of
~30 standard deviations. The timing analysis on the long term BAT light curve
reveals the presence of a strong sinusoidal intensity modulation of 22.25+/-
0.05 d, that we interpret as the orbital period of this binary system.
A broad band (0.3-150 keV) spectral analysis was performed combining the BAT
spectrum and the XRT spectra from the pointed follow up observations. The
spectrum is adequately modeled with an absorbed power law with a high energy
cutoff at ~24 keV and an absorption cyclotron feature at ~31 keV. Correcting
for the gravitational redshift, the inferred magnetic field at the neutron star
surface is B_surf ~ 3.6 x 10^12 gauss.
|
We analyze the implications of a Higgs discovery on possible ``new-physics''
scenarios, for $m_H$ up to $\sim 700$ GeV. For this purpose we critically
review lower and upper limits on the Higgs mass in the SM and in the MSSM,
respectively. Furthermore, we discuss the general features of possible
``heavy'' ($m_H \gsim 2 m_Z$) Higgs scenarios by means of a simple
heavy-fermion condensate model.
|
Studying the accretion process in very low-mass objects has important
implications for understanding their formation mechanism. Many nearby late-M
dwarfs that have previously been identified in the field are in fact young
brown dwarf members of nearby young associations. Some of them are still
accreting. They are therefore excellent targets for further studies of the
accretion process in the very low-mass regime at different stages.
We aim to search for accreting young brown dwarf candidates in a sample of 85
nearby late-M dwarfs.
Using photometric data from DENIS, 2MASS, and WISE, we constructed the
spectral energy distribution of the late-M dwarfs based on BT-Settl models to
detect infrared excesses. We then searched for lithium and H$\alpha$ emission
in candidates that exhibit infrared excesses to confirm their youth and the
presence of accretion.
Among the 85 late-M dwarfs, only DENIS-P J1538317$-$103850 (M5.5) shows
strong infrared excesses in WISE bands. The detection of lithium absorption in
the M5.5 dwarf and its Gaia trigonometric parallax indicate an age of $\sim$1
Myr and a mass of 47 $M_{\rm J}$. The H$\alpha$ emission line in the brown
dwarf shows significant variability that indicates sporadic accretion. This 1
Myr-old brown dwarf also exhibits intense accretion bursts with accretion rates
of up to $10^{-7.9}$$M_{\odot}$ yr$^{-1}$.
Our detection of sporadic accretion in one of the youngest brown dwarfs might
imply that sporadic accretion at early stages could play an important role in
the formation of brown dwarfs. Very low-mass cores would not be able to accrete
enough material to become stars, and thus they end up as brown dwarfs.
|
Measuring the similarity between data points often requires domain knowledge,
which can in parts be compensated by relying on unsupervised methods such as
latent-variable models, where similarity/distance is estimated in a more
compact latent space. Prevalent is the use of the Euclidean metric, which has
the drawback of ignoring information about similarity of data stored in the
decoder, as captured by the framework of Riemannian geometry. We propose an
extension to the framework of variational auto-encoders allows learning flat
latent manifolds, where the Euclidean metric is a proxy for the similarity
between data points. This is achieved by defining the latent space as a
Riemannian manifold and by regularising the metric tensor to be a scaled
identity matrix. Additionally, we replace the compact prior typically used in
variational auto-encoders with a recently presented, more expressive
hierarchical one---and formulate the learning problem as a constrained
optimisation problem. We evaluate our method on a range of data-sets, including
a video-tracking benchmark, where the performance of our unsupervised approach
nears that of state-of-the-art supervised approaches, while retaining the
computational efficiency of straight-line-based approaches.
|
Recurrent neural networks (RNNs) are known to be difficult to train due to
the gradient vanishing and exploding problems and thus difficult to learn
long-term patterns and construct deep networks. To address these problems, this
paper proposes a new type of RNNs with the recurrent connection formulated as
Hadamard product, referred to as independently recurrent neural network
(IndRNN), where neurons in the same layer are independent of each other and
connected across layers. Due to the better behaved gradient backpropagation,
IndRNN with regulated recurrent weights effectively addresses the gradient
vanishing and exploding problems and thus long-term dependencies can be
learned. Moreover, an IndRNN can work with non-saturated activation functions
such as ReLU (rectified linear unit) and be still trained robustly. Different
deeper IndRNN architectures, including the basic stacked IndRNN, residual
IndRNN and densely connected IndRNN, have been investigated, all of which can
be much deeper than the existing RNNs. Furthermore, IndRNN reduces the
computation at each time step and can be over 10 times faster than the commonly
used Long short-term memory (LSTM). Experimental results have shown that the
proposed IndRNN is able to process very long sequences and construct very deep
networks. Better performance has been achieved on various tasks with IndRNNs
compared with the traditional RNN, LSTM and the popular Transformer.
|
We present the biggest up-to-date sample of edge-on galaxies with B/PS bulges
and X-structures. The sample was prepared using images from the DESI Legacy
catalogue and contains about 2000 galaxies. To find suitable candidates in
catalogue, we made the assumption that the residues (original images minus
model) of galaxies with B/PS bulges should exhibit a characteristic X-shape.
Galaxies with such features were selected by eye and then used as input data
for a neural network training, which was applied to a bigger sample of edge-on
galaxies. Using the available data and the photometric models from the
literature, we investigated the observational and statistical properties of the
sample created. Comparing the $B/D$ ratios for galaxies with and without B/PS
bulges, we found that the $B/D$ ratio for galaxies from our sample is
statistically higher, with typical values in the range $\approx 0.2-0.5$
depending on the decomposition procedure. We studied how the opening angles
$\varphi$ of the X-structure and the length of its rays are distributed in the
formed sample and found them to be consistent with previous measurements and
predictions from $N$-body models, e.g. $\varphi \gtrsim 25~\deg$, but measured
here for a much larger number of galaxies. We found a sharp increase in the
B/PS bulge fraction for stellar masses $\log M_{\star} \gtrsim 10.4$, but for
edge-on galaxies, which complements the results of previous works. The sample
can be used in future work to test various bar models and their relationship
with B/PS bulges, as well as to study their stability and evolution.
|
We study the nonlinear Schr\"odinger equation with an arbitrary real
potential $V(x)\in (L^1+L^\infty)(\Gamma)$ on a star graph $\Gamma$. At the
vertex an interaction occurs described by the generalized Kirchhoff condition
with strength $-\gamma<0$. We show the existence of ground states
$\varphi_{\omega}(x)$ as minimizers of the action functional on the Nehari
manifold under additional negativity and decay conditions on $V(x)$. Moreover,
for $V(x)=-\dfrac{\beta}{x^\alpha}$, in the supercritical case, we prove that
the standing waves $e^{i\omega t}\varphi_{\omega}(x)$ are orbitally unstable in
$H^{1}(\Gamma)$ when $\omega$ is large enough. Analogous result holds for an
arbitrary $\gamma\in\mathbb{R}$ when the standing waves have symmetric profile.
|
For more than two decades it has been known that any compact Stein surface
(of real dimension four) admits a compatible Lefschetz fibration over a
two-disk. More recently, Giroux and Pardon have generalized this result by
giving a complex geometric proof for the existence of compatible Lefschetz
fibrations on Stein domains of any even dimension. As a preparatory step in
proving the former, Akbulut and Ozbagci have shown that there exist infinitely
many pairwise non-equivalent Lefschetz fibrations on the four-ball by using a
result of Lyon constructing fibrations on the complements of (p,q)-torus links
in the three-sphere. In this paper, we first extend this result to obtain
compatible Lefschetz fibrations on the six-ball whose pages are (p, q,
2)-Brieskorn varieties, and then construct a compatible 'relative' Lefschetz
fibrations on any Stein domain (of dimension six) which admit a certain
('admissible') 'relative Stein pair' structure. In particular, we provide a
purely topological proof for the existence of Lefschetz fibrations on specific
6-dimensional Stein domains.
|
In this thesis we develop generalized versions of the Chung-Feller theorem
for lattice paths constrained in the half plane. The beautiful cycle method
which was developed by Devoretzky and Motzkin as a means to prove the ballot
problem is modified and applied to generalize the classical Chung-Feller
theorem. We use Lagrange inversion to derive the generalized formulas. For the
generating function proof we study various ways of decomposing lattice paths.
We also show some results related to equidistribution properties in terms of
Narayana and Catalan generating functions. We then develop generalized
Chung-Feller theorems for Motzkin and Schroeder paths. Finally we study
generalized paths and the analogue of the Chung-Feller theorem for them.
|
This paper studies the light-tailed asymptotics of the stationary tail
probability vectors of a Markov chain of M/G/1 type. Almost all related studies
have focused on the typical case, where the transition block matrices in the
non-boundary levels have a dominant impact on the decay rate of the stationary
tail probability vectors and their decay is aperiodic. In this paper, we study
not only the typical case but also atypical cases such that the stationary tail
probability vectors decay periodically and/or their decay rate is determined by
the tail distribution of jump sizes from the boundary level. We derive
light-tailed asymptotic formulae for the stationary tail probability vectors by
locating the dominant poles of the generating function of the sequence of those
vectors. Further we discuss the positivity of the dominant terms of the
obtained asymptotic formulae.
|
A method of solving the time-dependent Schr\"odinger equation is presented,
in which a finite region of space is treated explicitly, with the boundary
conditions for matching the wave-functions on to the rest of the system
replaced by an embedding term added on to the Hamiltonian. This time-dependent
embedding term is derived from the Fourier transform of the energy-dependent
embedding potential, which embeds the time-independent Schr\"odinger equation.
Results are presented for a one-dimensional model of an atom in a time-varying
electric field, the surface excitation of this model atom at a jellium surface
in an external electric field, and the surface excitation of a bulk state.
|
The pioneer work of Krim and Widom unveiled the origin of the viscous nature
of friction at the atomic scale. This generated extensive experimental and
theoretical activity. However, fundamental questions remain open like the
relation between sliding friction and the topology of the substrate, as well as
the dependence on the temperature of the contact surface. Here we present
results, obtained using molecular dynamics, for the phononic friction
coefficient ($\eta_{ph}$) for a one dimensional model of an adsorbate-substrate
interface. Different commensuration relations between adsorbate and substrate
are investigated as well as the temperature dependence of $\eta_{ph}$. In all
the cases we studied $\eta_{ph}$ depends quadratically on the substrate
corrugation amplitude, but is a non-trivial function of the commensuration
ratio between substrate and adsorbate. The most striking result is a deep and
wide region of small values of $\eta_{ph}$ for substrate-adsorbate
commensuration ratios between $\approx 0.6-0.9$. Our results shed some light on
contradictory results for the relative size of phononic and electronic friction
found in the literature.
|
We show that if $K$ is an L-space twisted torus knot $T^{l,m}_{p,pk \pm 1}$
with $p \ge 2$, $k \ge 1$, $m \ge 1$ and $1 \le l \le p-1$, then the
fundamental group of the $3$-manifold obtained by $\frac{r}{s}$-surgery along
$K$ is not left-orderable whenever $\frac{r}{s} \ge 2 g(K) -1$, where $g(K)$ is
the genus of $K$.
|
Some well-known and less well-known or new notions related to group actions
are surveyed. Some of these notions are used to generalize affine spaces.
Actions are seen as functions with values in transformation monoids
|
Let $ \chi $ be a virtual (generalized) character of a finite group $ G $ and
$ L=L(\chi)$ be the image of $ \chi $ on $ G-\lbrace 1 \rbrace $. The pair $
(G, \chi) $ is said to be sharp of type $ L $ if $|G|=\prod _{ l \in L}
(\chi(1) - l) $. If the principal character of $G$ is not an irreducible
constituent of $\chi$, the pair $(G,\chi)$ is called normalized. In this paper,
we first provide some counterexamples to a conjecture that was proposed by
Cameron and Kiyota in $1988$. This conjecture states that if $(G,\chi)$ is
sharp and $|L|\geq 2$, then the inner product $(\chi,\chi)_G$ is uniquely
determined by $ L $. We then prove that this conjecture is true in the case
that $(G,\chi) $ is normalized, $\chi$ is a character of $ G $, and $ L $
contains at least an irrational value.
|
APN functions play a fundamental role in cryptography against attacks on
block ciphers. Several families of quadratic APN functions have been proposed
in the recent years, whose construction relies on the existence of specific
families of polynomials. A key question connected with such constructions is to
determine whether such APN functions exist for infinitely many dimensions or
not.
In this paper we consider a family of functions recently introduced by Li et
al. in 2021 showing that for any dimension $m\geq 3$ there exists an APN
function belonging to such a family.
Our main result is proved by a combination of different techniques arising
from both algebraic varieties over finite fields connected with linearized
permutation rational functions and {partial vector space partitions}, together
with investigations on the kernels of linearized polynomials.
|
The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to
interesting non-perturbative static spherically symmetric solutions which are
studied by mixed analitical and numerical methods. In the abelian sector of the
theory there are finite-energy magnetic and electric monopole solutions which
saturate the Bogomol'nyi bound. In the nonabelian sector there exist a
countable family of globally regular solutions which are purely magnetic but
have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is
bounded from above by the energy of the abelian magnetic monopole with unit
magnetic charge. The stability analysis demonstrates that the solutions are
saddle points of the energy functional with increasing number of unstable
modes. The existence and instability of these solutions are "explained" by the
Morse-theory argument recently proposed by Sudarsky and Wald.
|
Interaction graphs, such as those recording emails between individuals or
transactions between institutions, tend to be sparse yet structured, and often
grow in an unbounded manner. Such behavior can be well-captured by structured,
nonparametric edge-exchangeable graphs. However, such exchangeable models
necessarily ignore temporal dynamics in the network. We propose a dynamic
nonparametric model for interaction graphs that combine the sparsity of the
exchangeable models with dynamic clustering patterns that tend to reinforce
recent behavioral patterns. We show that our method yields improved held-out
likelihood over stationary variants, and impressive predictive performance
against a range of state-of-the-art dynamic interaction graph models.
|
This addendum provides results complementary to those obtained in [J. Phys.
G49, 055001 (2022)]. Specifically, an equivalent form of the relation, which
binds together the "spacelike" kernel functions for the hadronic vacuum
polarization contribution to the muon anomalous magnetic moment
$a^{\text{HVP}}_{\mu}$, is obtained. It is shown that the infrared limiting
value of the "spacelike" and "timelike" kernel functions, which enter the
representations for $a^{\text{HVP}}_{\mu}$ involving the Adler function and the
$R$-ratio, is identical to the corresponding QED contribution to the muon
anomalous magnetic moment of the preceding order in the electromagnetic
coupling. The next-to-leading order contributions $a^{\text{HVP}(3b)}_{\mu}$
(which includes the leptonic and hadronic insertions) and
$a^{\text{HVP}(3c)}_{\mu}$ (which includes the double hadronic insertion), are
studied. The three kernel functions appearing in the representations for
$a^{\text{HVP}(3b)}_{\mu}$, which involve the hadronic vacuum polarization
function, Adler function, and the $R$-ratio, are presented for the cases of the
electron and $\tau$-lepton loop insertions.
|
We report on experimental determinations of the temperature field in the
interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical
sample with aspect ratio (diameter over height) of 0.50, both in the classical
and in the ultimate state. The Prandtl number was close to 0.8. We find a
"logarithmic layer" in which the temperature varies as A*ln(z/L) + B with the
distance z from the bottom plate of the sample. The amplitude A varies with
radial position r. In the classical state these results are in good agreement
with direct numerical simulations (DNS); in the ultimate state there are as yet
no DNS. A close analogy between the temperature field in the classical state
and the "Law of the Wall" for the time-averaged down-stream velocity in shear
flow is discussed.
|
The dynamic nature of system gives rise to dynamical features of epidemic
spreading, such as oscillation and bistability. In this paper, by studying the
epidemic spreading in growing networks, in which susceptible nodes may
adaptively break the connections with infected ones yet avoid getting isolated,
we reveal a new phenomenon - \emph{epidemic reemergence}, where the number of
infected nodes is incubated at a low level for a long time and then bursts up
for a short time. The process may repeat several times before the infection
finally vanishes. Simulation results show that all the three factors, namely
the network growth, the connection breaking and the isolation avoidance, are
necessary for epidemic reemergence to happen. We present a simple theoretical
analysis to explain the process of reemergence in detail. Our study may offer
some useful insights helping explain the phenomenon of repeated epidemic
explosions.
|
Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.