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Sigmoid semilogarithmic functions with shape of Boltzmann equations, have
become extremely popular to describe diverse biological situations. Part of the
popularity is due to the easy avail- ability of software which fits Boltzmann
functions to data, without much knowledge of the fitting procedure or the
statistical properties of the parameters derived from the procedure. The
purpose of this paper is to explore the plasticity of the Boltzmann function to
fit data, some aspects of the optimization procedure to fit the function to
data and how to use this plastic function to differentiate the effect of
treatment on data and to attest the statistical significance of treatment
effect on the data.
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The automatic generation of high-quality mathematical problems is practically
valuable in many educational scenarios. Large multimodal model provides a novel
technical approach for the mathematical problem generation because of its wide
success in cross-modal data scenarios. However, the traditional method of
separating problem solving from problem generation and the mainstream
fine-tuning framework of monotonous data structure with homogeneous training
objectives limit the application of large multimodal model in mathematical
problem generation. Addressing these challenges, this paper proposes COMET, a
"Cone of Experience" enhanced large multimodal model for mathematical problem
generation. Firstly, from the perspective of mutual ability promotion and
application logic, we unify stem generation and problem solving into
mathematical problem generation. Secondly, a three-stage fine-turning framework
guided by the "Cone of Experience" is proposed. The framework divides the
fine-tuning data into symbolic experience, iconic experience, and direct
experience to draw parallels with experiences in the career growth of teachers.
Several fine-grained data construction and injection methods are designed in
this framework. Finally, we construct a Chinese multimodal mathematical problem
dataset to fill the vacancy of Chinese multimodal data in this field. Combined
with objective and subjective indicators, experiments on multiple datasets
fully verify the effectiveness of the proposed framework and model.
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We study the optical appearance of Schwarzschild-de Sitter and
Reissner-Nordstr\"{o}m-de Sitter black holes viewed by distant observers inside
cosmological horizons. Unlike their asymptotically flat counterparts, due to
the positive cosmological constant, there are outermost stable circular orbits
in the spacetimes, resulting in significant outer edges in the images. Besides,
when the Reissner-Nordstr\"{o}m-de Sitter black hole has a stable Cauchy
horizon, the photons from the preceding companion universe can be received by
the observer in our universe. These rays create a multi-ring structure in the
image. Since the stable Cauchy horizon violates the strong cosmic censorship
conjecture, this novel image shed some light on the test of the conjecture by
astronomical observations.
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Let $p_n(y)=\sum_k\hat{\alpha}_k\phi(y-k)+\sum_{l=0}^{j_n-1}\sum_k\hat
{\beta}_{lk}2^{l/2}\psi(2^ly-k)$ be the linear wavelet density estimator, where
$\phi$, $\psi$ are a father and a mother wavelet (with compact support),
$\hat{\alpha}_k$, $\hat{\beta}_{lk}$ are the empirical wavelet coefficients
based on an i.i.d. sample of random variables distributed according to a
density $p_0$ on $\mathbb{R}$, and $j_n\in\mathbb{Z}$, $j_n\nearrow\infty$.
Several uniform limit theorems are proved: First, the almost sure rate of
convergence of $\sup_{y\in\mathbb{R}}|p_n(y)-Ep_n(y)|$ is obtained, and a law
of the logarithm for a suitably scaled version of this quantity is established.
This implies that $\sup_{y\in\mathbb{R}}|p_n(y)-p_0(y)|$ attains the optimal
almost sure rate of convergence for estimating $p_0$, if $j_n$ is suitably
chosen. Second, a uniform central limit theorem as well as strong invariance
principles for the distribution function of $p_n$, that is, for the stochastic
processes $\sqrt{n}(F_n
^W(s)-F(s))=\sqrt{n}\int_{-\infty}^s(p_n-p_0),s\in\mathbb{R}$, are proved; and
more generally, uniform central limit theorems for the processes
$\sqrt{n}\int(p_n-p_0)f$, $f\in\mathcal{F}$, for other Donsker classes
$\mathcal{F}$ of interest are considered. As a statistical application, it is
shown that essentially the same limit theorems can be obtained for the hard
thresholding wavelet estimator introduced by Donoho et al. [Ann. Statist. 24
(1996) 508--539].
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We propose a dark matter model in which the dark sector is gauged under a new
SU(2) group. The dark sector consists of SU(2) dark gauge fields, two triplet
dark Higgs fields, and two dark fermion doublets (dark matter candidates in
this model). The dark sector interacts with the SM sector through kinetic and
mass mixing operators. The model explains both PAMELA and Fermi LAT data very
well and also satisfies constraints from both the DM relic density and Standard
Model precision observables. The phenomenology of the model at the LHC is also
explored.
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The present contribution focuses on the effect of adherend surface roughness
on the strength of adhesive joints, which are particularly cost-effective and
extensively applied in a wide range of industrial applications. However, the
reliability of such solutions is a critical concern for the integrity of
commercial products. To gain a deeper understanding on the effect of roughness,
an extensive experimental campaign is proposed, where thermoplastic substrates
are produced with a specified roughness, whose characterization has been
performed using a confocal profilometer. Elastic strips are then bonded onto
such substrates using Silicone adhesive while controlling the adhesive
thickness. Peeling tests are finally carried out and the effects of joint
parameters such as surface roughness, adhesive thickness, and loading rate are
discussed in detail. Eventually, it is demonstrated that the surface roughness
can increase the adhesion energy of joints depending on the value of a ratio
between the adhesive thickness and the root mean square elevation of roughness.
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In this work we analyze the stochastic dynamics of the Kauffman model
evolving under the influence of noise. By considering the average crossing time
between two distinct trajectories, we show that different Kauffman models
exhibit a similar kind of behavior, even when the structure of their basins of
attraction is quite different. This can be considered as a robust property of
these models. We present numerical results for the full range of noise level
and obtain approximate analytic expressions for the above crossing time as a
function of the noise in the limit cases of small and large noise levels.
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We consider a class of multi-robot motion planning problems where each robot
is associated with multiple objectives and decoupled task specifications. The
problems are formulated as an open-loop non-cooperative differential game. A
distributed anytime algorithm is proposed to compute a Nash equilibrium of the
game. The following properties are proven: (i) the algorithm asymptotically
converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the
price of stability equals one; (iii) for the worst case, the computational
complexity and communication cost are linear in the robot number.
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Many factors influence biomolecules binding, and its assessment constitutes
an elusive challenge in computational structural biology. In this respect, the
evaluation of shape complementarity at molecular interfaces is one of the main
factors to be considered. We focus on the particular case of antibody-antigen
complexes to quantify the complementarities occurring at molecular interfaces.
We relied on a method we recently developed, which employs the 2D Zernike
descriptors, to characterize investigated regions with an ordered set of
numbers summarizing the local shape properties. Collected a structural dataset
of antibody-antigen complexes, we applied this method and we statistically
distinguished, in terms of shape complementarity, pairs of interacting regions
from non-interacting ones. Thus, we set up a novel computational strategy based
on \textit{in-silico} mutagenesis of antibody binding site residues. We
developed a Monte Carlo procedure to increase the shape complementarity between
the antibody paratope and a given epitope on a target protein surface. We
applied our protocol against several molecular targets in SARS-CoV-2 spike
protein, known to be indispensable for viral cell invasion. We, therefore,
optimized the shape of template antibodies for the interaction with such
regions. As the last step of our procedure, we performed an independent
molecular docking validation of the results of our Monte Carlo simulations.
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We propose in this paper a combined model of Long Short Term Memory and
Convolutional Neural Networks (LSTM-CNN) that exploits word embeddings and
positional embeddings for cross-sentence n-ary relation extraction. The
proposed model brings together the properties of both LSTMs and CNNs, to
simultaneously exploit long-range sequential information and capture most
informative features, essential for cross-sentence n-ary relation extraction.
The LSTM-CNN model is evaluated on standard dataset on cross-sentence n-ary
relation extraction, where it significantly outperforms baselines such as CNNs,
LSTMs and also a combined CNN-LSTM model. The paper also shows that the
LSTM-CNN model outperforms the current state-of-the-art methods on
cross-sentence n-ary relation extraction.
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Non-linear effects have become increasingly relevant in modern circular
particle accelerators, and in recent years a change of paradigm has appeared,
the attitude towards nonlinear effects having shifted from fighting them to
exploiting them with the goal of devising new beam manipulations, such as the
splitting of the beam in the transverse phase space by crossing a stable
resonance. In the field of hadron accelerators, well-established operational
techniques based on nonlinear effects exist, whereas for the case of
synchrotron light sources these new techniques are only beginning their way
into the field. In this paper, we discuss novel techniques aimed at providing
split beams in synchrotron light sources that are obtained by using stable
islands in the transverse phase space or unsplit beams with AC dipoles to
generate periodic closed orbits. The results of detailed numerical simulations,
which support the proposed methods, are presented and discussed in this paper,
together with possible applications.
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Recently, Cai and Su [Phys. Rev. D {\bf 81}, 103514 (2010)] found that the
sign of interaction $Q$ in the dark sector changed in the approximate redshift
range of $0.45\,\lsim\, z\,\lsim\, 0.9$, by using a model-independent method to
deal with the observational data. In fact, this result raises a remarkable
problem, since most of the familiar interactions cannot change their signs in
the whole cosmic history. Motivated by the work of Cai and Su, we have proposed
a new type of interaction in a previous work [H. Wei, Nucl. Phys. B {\bf 845},
381 (2011)]. The key ingredient is the deceleration parameter $q$ in the
interaction $Q$, and hence the interaction $Q$ can change its sign when our
universe changes from deceleration ($q>0$) to acceleration ($q<0$). In the
present work, we consider the cosmological constraints on this new type of
sign-changeable interactions, by using the latest observational data. We find
that the cosmological constraints on the model parameters are fairly tight. In
particular, the key parameter $\beta$ can be constrained to a narrow range.
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We have studied the Gamow-Teller (GT) transitions from $N=Z+2$ neighbors to
$N=Z=$ odd nuclei in $p$-shell region by using isospin-projected and
$\beta\gamma$-constraint antisymmetrized molecular dynamics combined with
generator coordinate method. The calculated GT transition strengths from $0^+1$
states to $1^+0$ states such as ${}^{6} \textrm{He}(0_1^+1)\rightarrow{}^{6}
\textrm{Li}(1_1^+0)$, ${}^{10} \textrm{Be}(0_1^+1)\rightarrow{}^{10}
\textrm{B}(1_1^+0)$, and ${}^{14} \textrm{C}(0_1^+1)\rightarrow{}^{14}
\textrm{N}(1_2^+0)$ exhaust more than 50\% of the sum rule. These $N=Z+2$
initial states and $N=Z=$ odd final states are found to dominantly have
$S=0,T=1$ $nn$ pairs and $S=1,T=0$ $pn$ pairs, respectively. Based on
two-nucleon ($NN$) pair picture, we can understand the concentration of the GT
strengths as the spin-isospin-flip transition $nn(S=0,T=1)\rightarrow
pn(S=1,T=0)$ in $LS$-coupling scheme. The GT transition can be a good probe to
identify the spin-isospin partner states with $nn$ pairs and $pn$ pairs of
$N=Z+2$ and $N=Z=$ odd nuclei, respectively.
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Deep neural networks are typically too computationally expensive to run in
real-time on consumer-grade hardware and low-powered devices. In this paper, we
investigate reducing the computational and memory requirements of neural
networks through network pruning and quantisation. We examine their efficacy on
large networks like AlexNet compared to recent compact architectures:
ShuffleNet and MobileNet. Our results show that pruning and quantisation
compresses these networks to less than half their original size and improves
their efficiency, particularly on MobileNet with a 7x speedup. We also
demonstrate that pruning, in addition to reducing the number of parameters in a
network, can aid in the correction of overfitting.
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A mechanical electroscope based on a change in the resonant frequency of a
cantilever one micron in size in the presence of charge has recently been
fabricated. We derive the decoherence rate of a charge superposition during
measurement with such a device using a master equation theory adapted from
quantum optics. We also investigate the information produced by such a
measurement, using a quantum trajectory approach. Such instruments could be
used in mesoscopic electronic systems, and future solid-state quantum
computers, so it is useful to know how they behave when used to measure quantum
superpositions of charge.
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Rotary dynamics of polarized composite particles as dipole rigid bodies is
considered. It is described the Euler equations singularly perturbed by the
radiation reaction torque. The Schott term is taken into account, and the
reduction procedure lowering higher derivatives is applied. Asymptotic methods
of nonlinear mechanics are used to analyze the rotary dynamics of
askew-polarized spinning top. Numerical estimates are relevant to the
hypothetical DAST-nanocrystals that might possess a huge dipole moment.
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We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with
massive particles and show that we recover in this limit Feynman graph
amplitudes (with Hadamard propagator) expressed as an abelian spin foam model.
We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be
resummed. This leads to the conclusion that the dynamics of quantum particles
coupled to quantum 3d gravity can be expressed in terms of an effective new non
commutative field theory which respects the principles of doubly special
relativity. We discuss the construction of Lorentzian spin foam models
including Feynman propagators
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With much advancement in the field of nanotechnology, bioengineering and
synthetic biology over the past decade, microscales and nanoscales devices are
becoming a reality. Yet the problem of engineering a reliable communication
system between tiny devices is still an open problem. At the same time, despite
the prevalence of radio communication, there are still areas where traditional
electromagnetic waves find it difficult or expensive to reach. Points of
interest in industry, cities, and medical applications often lie in embedded
and entrenched areas, accessible only by ventricles at scales too small for
conventional radio waves and microwaves, or they are located in such a way that
directional high frequency systems are ineffective. Inspired by nature, one
solution to these problems is molecular communication (MC), where chemical
signals are used to transfer information. Although biologists have studied MC
for decades, it has only been researched for roughly 10 year from a
communication engineering lens. Significant number of papers have been
published to date, but owing to the need for interdisciplinary work, much of
the results are preliminary. In this paper, the recent advancements in the
field of MC engineering are highlighted. First, the biological, chemical, and
physical processes used by an MC system are discussed. This includes different
components of the MC transmitter and receiver, as well as the propagation and
transport mechanisms. Then, a comprehensive survey of some of the recent works
on MC through a communication engineering lens is provided. The paper ends with
a technology readiness analysis of MC and future research directions.
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Within linear continuum theory, no magnetic texture can propagate faster than
the maximum group velocity of its spin waves. Here we report a transient regime
due to the appearance of additional antiferromagnetic textures that breaks the
Lorentz translational invariance of the magnetic system by atomistic spin
dynamics simulations. This dynamical regime is akin to domain wall
Walker-breakdown in ferromagnets and involves the nucleation of an
antiferromagnetic domain wall pair. Subsequently, one of the nucleated
180$^{\circ}$ domain wall creates with the original domain wall a 360$^{\circ}$
spin-rotation which remains static even under the action of the spin-orbit
field. The other 180$^{\circ}$ domain wall becomes accelerated to
super-magnonic speeds. Under large spin-orbit fields, multiple domain wall
generation and recombination is obtained which may explain the recently
experimentally observed current pulse induce shattering of large domain
structures into small fragmented domains and the subsequent slow recreation of
large-scale domain formation prior current pulse.
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Our purpose is to investigate properties for processes with stationary and
independent increments under $G$-expectation. As applications, we prove the
martingale characterization to $G$-Brownian motion and present a decomposition
for generalized $G$-Brownian motion.
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Data-hunger and data-imbalance are two major pitfalls in many deep learning
approaches. For example, on highly optimized production lines, defective
samples are hardly acquired while non-defective samples come almost for free.
The defects however often seem to resemble each other, e.g., scratches on
different products may only differ in a few characteristics. In this work, we
introduce a framework, Defect Transfer GAN (DT-GAN), which learns to represent
defect types independent of and across various background products and yet can
apply defect-specific styles to generate realistic defective images. An
empirical study on the MVTec AD and two additional datasets showcase DT-GAN
outperforms state-of-the-art image synthesis methods w.r.t. sample fidelity and
diversity in defect generation. We further demonstrate benefits for a critical
downstream task in manufacturing -- defect classification. Results show that
the augmented data from DT-GAN provides consistent gains even in the few
samples regime and reduces the error rate up to 51% compared to both
traditional and advanced data augmentation methods.
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In this paper, a study is carried out on the $e^-p \to e^-\gamma^* p \to p
W^+\gamma \nu_e$ production to probe quartic $W^+W^-\gamma\gamma$ couplings
using 10, 100 ${\rm fb^{-1}}$ of $e^-p$ collisions data at $\sqrt{s}$= 1.30,
1.98 GeV at the Large Hadron electron Collider (LHeC) and 100, 1000 ${\rm
fb^{-1}}$ with $\sqrt{s}$= 3.46, 5.29 GeV at the Future Circular
Collider-hadron electron (FCC-he). Production cross-sections are determined for
both at leptonic and hadronic decay channel of the $W$-boson. With the data
from future $e^-p$ colliders, it is possible to obtain sensitivity measures at
$95\%$ C.L. on the anomalous $f_ {M,i}/\Lambda^4$ and $ f_ {T,i}/\Lambda^4$
couplings which are competitive with the limits obtained by the LHC, as well as
with others limits reported in the literature. The production mode $e^-p \to
e^-\gamma^* p \to p W^+\gamma \nu_e $ in $e^-p$ collisions offers a window for
study the quartic $W^+W^-\gamma\gamma$ electroweak bosons couplings at the LHeC
and the FCC-he, which provides a much cleaner collision environment than the
LHC.
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We show that the time-1 map of an Anosov flow, whose strong-unstable
foliation is $C^2$ smooth and minimal, is $C^2$ close to a diffeomorphism
having positive central Lyapunov exponent Lebesgue almost everywhere and a
unique physical measure with full basin, which is $C^r$ stably ergodic. Our
method is perturbative and does not rely on preservation of a smooth measure.
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The purpose of the comment is to point out that the leading term of the
Ginzburg-Landau nonanalytical correction to the interface tension of
Bose-Einstein condensates with strong segregation and the surface tension of
extreme type-I superconductors are described by a common coefficient derived
from the universal equation for the phase boundary. The agreement between the
numerical value of the coefficients gives a hint that this can be an exact
result which deserves to be checked. The outcome will be of interest for
physicists working in both fields.
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This study develops a framework for testing hypotheses on structural
parameters in incomplete models. Such models make set-valued predictions and
hence do not generally yield a unique likelihood function. The model structure,
however, allows us to construct tests based on the least favorable pairs of
likelihoods using the theory of Huber and Strassen (1973). We develop tests
robust to model incompleteness that possess certain optimality properties. We
also show that sharp identifying restrictions play a role in constructing such
tests in a computationally tractable manner. A framework for analyzing the
local asymptotic power of the tests is developed by embedding the least
favorable pairs into a model that allows local approximations under the limits
of experiments argument. Examples of the hypotheses we consider include those
on the presence of strategic interaction effects in discrete games of complete
information. Monte Carlo experiments demonstrate the robust performance of the
proposed tests.
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The master equation of quantum optical density operator is transformed to the
equation of characteristic function. The parametric amplification and amplitude
damping as well as the phase damping are considered. The solution for the most
general initial quantum state is obtained for parametric amplification and
amplitude damping. The purity of one mode Gaussian system and the entanglement
of two mode Gaussian system are studied.
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Coherent states of light, and methods for distinguishing between them, are
central to all applications of laser light. We obtain the ultimate quantum
limit on the error probability exponent for discriminating among any M
multimode coherent-state waveforms via the quantum Chernoff exponent in M-ary
multi-copy state discrimination. A receiver, i.e., a concrete realization of a
quantum measurement, called the Sequential Waveform Nulling (SWN) receiver, is
proposed for discriminating an arbitrary coherent-state ensemble using only
auxiliary coherent-state fields, beam splitters, and non-number-resolving
single photon detectors. An explicit error probability analysis of the SWN
receiver is used to show that it achieves the quantum limit on the error
probability exponent, which is shown to be a factor of four greater than the
error probability exponent of an ideal heterodyne-detection receiver on the
same ensemble. We generalize the philosophy of the SWN receiver, which is
itself adapted from some existing coherent-state receivers, and propose a
receiver -- the Sequential Testing (ST) receiver-- for discriminating n copies
of M pure quantum states from an arbitrary Hilbert space. The ST receiver is
shown to achieve the quantum Chernoff exponent in the limit of a large number
of copies, and is remarkable in requiring only local operations and classical
communication (LOCC) to do so. In particular, it performs adaptive copy-by-copy
binary projective measurements. Apart from being of fundamental interest, these
results are relevant to communication, sensing, and imaging systems that use
laser light and to photonic implementations of quantum information processing
protocols in general.
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We consider a problem in Multi-Task Learning (MTL) where multiple linear
models are jointly trained on a collection of datasets ("tasks"). A key novelty
of our framework is that it allows the sparsity pattern of regression
coefficients and the values of non-zero coefficients to differ across tasks
while still leveraging partially shared structure. Our methods encourage models
to share information across tasks through separately encouraging 1) coefficient
supports, and/or 2) nonzero coefficient values to be similar. This allows
models to borrow strength during variable selection even when non-zero
coefficient values differ across tasks. We propose a novel mixed-integer
programming formulation for our estimator. We develop custom scalable
algorithms based on block coordinate descent and combinatorial local search to
obtain high-quality (approximate) solutions for our estimator. Additionally, we
propose a novel exact optimization algorithm to obtain globally optimal
solutions. We investigate the theoretical properties of our estimators. We
formally show how our estimators leverage the shared support information across
tasks to achieve better variable selection performance. We evaluate the
performance of our methods in simulations and two biomedical applications. Our
proposed approaches appear to outperform other sparse MTL methods in variable
selection and prediction accuracy. We provide the sMTL package on CRAN.
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Molecular Relational Learning (MRL), aiming to understand interactions
between molecular pairs, plays a pivotal role in advancing biochemical
research. Recently, the adoption of large language models (LLMs), known for
their vast knowledge repositories and advanced logical inference capabilities,
has emerged as a promising way for efficient and effective MRL. Despite their
potential, these methods predominantly rely on the textual data, thus not fully
harnessing the wealth of structural information inherent in molecular graphs.
Moreover, the absence of a unified framework exacerbates the issue of
information underutilization, as it hinders the sharing of interaction
mechanism learned across diverse datasets. To address these challenges, this
work proposes a novel LLM-based multi-modal framework for Molecular inTeraction
prediction following Chain-of-Thought (CoT) theory, termed MolTC, which
effectively integrate graphical information of two molecules in pair. To train
MolTC efficiently, we introduce a Multi-hierarchical CoT concept to refine its
training paradigm, and conduct a comprehensive Molecular Interactive
Instructions dataset for the development of biochemical LLMs involving MRL. Our
experiments, conducted across various datasets involving over 4,000,000
molecular pairs, exhibit the superiority of our method over current GNN and
LLM-based baselines. Code is available at https://github.com/MangoKiller/MolTC.
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Spin-orbit coupling plays a large role in stabilizing the low-temperature
orthorhombic phase of La$_{2-x}$Sr$_x$CuO$_4$. It splits the degeneracy of the
van Hove singularities (thereby stabilizing the distorted phase) and completely
changes the shape of the Fermi surfaces, potentially introducing diabolical
points into the band structure. The present paper gives a detailed account of
the resulting electronic structure.
A slave boson calculation shows how these results are modified in the
presence of strong correlation effects. A scaling regime, found very close to
the metal-insulator transition, allows an analytical determination of the
crossover, in the limit of zero oxygen-oxygen hopping, $t_{OO}\rightarrow 0$.
Extreme care must exercised in chosing the parameters of the three-band model.
In particular, $t_{OO}$ is renormalized from its LDA value. Furthermore, it is
suggested that the slave boson model be spin-corrected, in which case the
system is close to a metal-insulator transition at half filling.
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A key feature of intelligent behaviour is the ability to learn abstract
strategies that scale and transfer to unfamiliar problems. An abstract strategy
solves every sample from a problem class, no matter its representation or
complexity -- like algorithms in computer science. Neural networks are powerful
models for processing sensory data, discovering hidden patterns, and learning
complex functions, but they struggle to learn such iterative, sequential or
hierarchical algorithmic strategies. Extending neural networks with external
memories has increased their capacities in learning such strategies, but they
are still prone to data variations, struggle to learn scalable and transferable
solutions, and require massive training data. We present the Neural Harvard
Computer (NHC), a memory-augmented network based architecture, that employs
abstraction by decoupling algorithmic operations from data manipulations,
realized by splitting the information flow and separated modules. This
abstraction mechanism and evolutionary training enable the learning of robust
and scalable algorithmic solutions. On a diverse set of 11 algorithms with
varying complexities, we show that the NHC reliably learns algorithmic
solutions with strong generalization and abstraction: perfect generalization
and scaling to arbitrary task configurations and complexities far beyond seen
during training, and being independent of the data representation and the task
domain.
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The classical Weyl Law says that if $N_M(\lambda)$ denotes the number of
eigenvalues of the Laplace operator on a $d$-dimensional compact manifold $M$
without a boundary that are less than or equal to $\lambda$, then $$
N_M(\lambda)=c\lambda^d+O(\lambda^{d-1}).$$
In this paper, we show Duistermaat and Guillemin's result allows us to
replace the $O(\lambda^{d-1})$ error with $o(\lambda^{d-1})$ if $M$ is a
product manifold. We quantify this bound in the case of Cartesian product of
spheres by reducing the problem to the study of the distribution of weighted
integer lattice points in Euclidean space and formulate a conjecture in the
general case reminiscent of the sum-product phenomenon in additive
combinatorics.
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The signless Laplacian spectral radius of a graph $G$, denoted by $q(G)$, is
the largest eigenvalue of its signless Laplacian matrix. In this paper, we
investigate extremal signless Laplacian spectral radius for graphs without
short cycles or long cycles. Let $\mathcal{G}(m,g)$ be the family of graphs on
$m$ edges with girth $g$ and $\mathcal{H}(m,c)$ be the family of graphs on $m$
edges with circumference $c$. More precisely, we obtain the unique extremal
graph with maximal $q(G)$ in $\mathcal{G}(m,g)$ and $\mathcal{H}(m,c)$,
respectively.
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We discuss kinematical correlations between charged leptons from semileptonic
decays of open charm/bottom, leptons produced in the Drell-Yan mechanism as
well as some other mechanisms not included so far in the literature in
proton-proton scattering at BNL RHIC. The distributions of charm and bottom
quarks/antiquarks are calculated in the framework of the $k_t$-factorization
approach. For this calculation we use the Kwieci\'nski unintegrated parton
distributions. The hadronization of heavy quarks is done by means of Peterson
et al. fragmentation function. We use semileptonic decay functions found by
fitting recent semileptonic data obtained by the CLEO and BABAR collaborations.
The Drell-Yan processes were calculated including transverse momenta of quarks
and antiquarks, also using the Kwieci\'nski parton distributions. We have also
took into consideration reactions initiated by purely QED
$\gamma^*\gamma^*$-fusion in elastic and inelastic pp collisions as well as
recently proposed diffractive mechanism of exclusive charm-anticharm
production. The contribution of the later mechanism is rather small. We get
good description of the dilepton invariant mass spectrum measured recently by
the PHENIX collaboration and present predictions for the dilepton pair
transverse momentum distribution as well as distribution in azimuthal angle
between electron and positron.
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Different measures of heart rate variability and particularly of respiratory
sinus arrhythmia are widely used in research and clinical applications.
Inspired by the ideas from the theory of coupled oscillators, we use
simultaneous measurements of respiratory and cardiac activity to perform a
nonlinear decomposition of the heart rate variability into the
respiratory-related component and the rest. We suggest to exploit the technique
as a universal preprocessing tool, both for the analysis of respiratory
influence on the heart rate as well as in cases when effects of other factors
on the heart rate variability are in focus. The theoretical consideration is
illustrated by the analysis of 25 data sets from healthy subjects.
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Optimizing non-convex functions is of primary importance in the vast majority
of machine learning algorithms. Even though many gradient descent based
algorithms have been studied, successive convex approximation based algorithms
have been recently empirically shown to converge faster. However, such
successive convex approximation based algorithms can get stuck in a first-order
stationary point. To avoid that, we propose an algorithm that perturbs the
optimization variable slightly at the appropriate iteration. In addition to
achieving the same convergence rate results as the non-perturbed version, we
show that the proposed algorithm converges to a second order stationary point.
Thus, the proposed algorithm escapes the saddle point efficiently and does not
get stuck at the first order saddle points.
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Low-rank tensor approximation error bounds are proposed for the case of noisy
input data that depend on low-rank representation type, rank and the
dimensionality of the tensor. The bounds show that high-dimensional low-rank
structured approximations provide superior noise-filtering properties compared
to matrices with the same rank and total element count.
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Video processing solutions for motion analysis are key tasks in many computer
vision applications, ranging from human activity recognition to object
detection. In particular, speed estimation algorithms may be relevant in
contexts such as street monitoring and environment surveillance. In most
realistic scenarios, the projection of a framed object of interest onto the
image plane is likely to be affected by dynamic changes mainly related to
perspectival transformations or periodic behaviours. Therefore, advanced speed
estimation techniques need to rely on robust algorithms for object detection
that are able to deal with potential geometrical modifications. The proposed
method is composed of a sequence of pre-processing operations, that aim to
reduce or neglect perspetival effects affecting the objects of interest,
followed by the estimation phase based on the Maximum Likelihood (ML)
principle, where the speed of the foreground objects is estimated. The ML
estimation method represents, indeed, a consolidated statistical tool that may
be exploited to obtain reliable results. The performance of the proposed
algorithm is evaluated on a set of real video recordings and compared with a
block-matching motion estimation algorithm. The obtained results indicate that
the proposed method shows good and robust performance.
|
We consider a simple Higgs portal dark matter model, where the Standard Model
is supplemented with a complex scalar whose imaginary part plays the role of
WIMP dark matter (DM). We show that the direct DM detection cross section
vanishes at tree level and zero momentum transfer due to a cancellation by
virtue of a softly broken symmetry. This cancellation is operative for any
mediator masses. As a result, our electroweak scale dark matter satisfies all
of the phenomenological constraints quite naturally.
|
We use weak-value amplification to enhance the polarization-sensitive
fast-light effect from induced Raman absorption in hot rubidium vapor. We
experimentally demonstrate that projecting the output signal into an
appropriate polarization state enables a pulse advancement of 4.2 {\mu}s, which
is 15 times larger than that naturally caused by dispersion. More
significantly, we show that combining weak-value amplification with the
dispersive response of an atomic system provides a clear advantage in terms of
the maximum pulse advancement achievable for a given value of loss. This
technique has potential applications for designing novel
quantum-information-processing gates and optical buffers for telecommunication
systems.
|
The Accretion-Ejection Instability has been proposed to explain the low
frequency Quasi-Periodic Oscillation (QPO) observed in low-mass X-Ray Binaries,
in particular Black-Hole candidates. Its frequency, typically a fraction of the
Keplerian frequency at the disk inner radius, is exactly in the range indicated
by observations. The variations of the frequency with the disk inner radius
(extracted from spectral fits of the X-ray emission) might thus be a useful
test. In this paper we discuss how changes in the rotation curve, due to
relativistic effects when the disk approaches the central object, affect the
physics of the instability, and thus this frequency-inner radius relation. We
find that the relationship between the frequency of the mode and the Keplerian
frequency at the inner disk radius ($r_{int}$) departs from the one obtained in
a Keplerian disk, when $r_{int}$ approaches the last stable orbit. This might
agree with the recently published results, showing a discrepancy between the
behavior of the QPO in the micro quasar GRO J1655, compared to other sources
such as XTE J1550 and GRS 1915.
In a companion paper (Rodriguez et al., 2002, hereafter Paper I) we have
presented detailed observational results for GRO J1655 and GRS 1915. We show
how the opposite correlations found in these sources between the disk color
radius (assumed to be close to its inner radius) and the QPO frequency could
indeed be explained by our theoretical result.
|
When photons from distant galaxies and stars pass through our neighboring
environment, the wavelengths of the photons would be shifted by our local
gravitational potential. This local gravitational redshift effect can
potentially have an impact on the measurement of cosmological distance-redshift
relation. Using available supernovae data, Wojtak et al [1] found seemingly
large biases of cosmological parameters for some extended models (non-flat
$\Lambda$CDM, $w$CDM, etc.). Huang [2] pointed out that, however, the biases
can be reduced to a negligible level if cosmic microwave background (CMB) data
are added to break the strong degeneracy between parameters in the extended
models. In this article we forecast the cosmological bias due to local
gravitational redshifts for a future WFIRST-like supernovae survey. We find
that the local gravitational redshift effect remains negligible, provided that
CMB data or some future redshift survey data are added to break the degeneracy
between parameters.
|
The fluctuation exchange (FLEX) approximation is applied to study the
Holstein-Hubbard model. Due to the retarded nature of the phonon-mediated
electron-electron interaction, neither fast Fourier transform (FFT) nor
previously developed NRG methods for Hubbard-type purely electronic models are
applicable, while brute force solutions are limited by the demands on
computational time and storage which increase rapidly at low temperature $T$.
Here,we describe a new numerical renormalization group (NRG) technique to solve
the FLEX equations efficiently. Several orders of magnitude of CPU time and
storage can be saved at low $T$ ($\sim 80K$). To test our approach, we compare
our NRG results to brute force calculations on small lattices at elevated
temperatures. Both s-wave and d-wave superconducting phase diagrams are then
obtained by applying the NRG approach at low $T$. The isotope effect for s-wave
pairing is BCS-like in a realistic phonon frequency range, but vanishes at
unphysically large phonon frequency ($\sim $ band width). For d-wave pairing,
the isotope exponent is negative and small compared to the typical observed
values in non-optimally doped cuprates.
|
This is an extended version of a series of lectures given in St Flour. It
includes a discussion of relations between the occupation field of Markov loops
with the corresponding free field.
|
A conjectural expression of the asymptotic gap between the rate-distortion
function of an arbitrary generalized Gaussian multiterminal source coding
system and that of its centralized counterpart in the high-resolution regime is
proposed. The validity of this expression is verified when the number of
sources is no more than 3.
|
Following its flyby and first imaging the Pluto-Charon binary, the New
Horizons spacecraft visited the Kuiper-Belt-Object (KBO) (486958) 2014 MU69
(Arrokoth). Imaging showed MU69 to be a contact-binary, made of two individual
lobes connected by a narrow neck, rotating at low spin period (15.92 h), and
having high obliquity (~98 deg), similar to other KBO contact-binaries inferred
through photometric observations. The origin of such peculiar configurations is
puzzling, and all scenarios suggested for the origins of contact-binaries fail
to reproduce such properties and their likely high frequency. Here we show that
semi-secular perturbations operating only on ultra-wide (~0.1-0.4 Hill-radius)
KBO-binaries can robustly lead to gentle, slow-speed binary mergers at
arbitrarily high obliquities, but low rotational velocities, that can reproduce
MU69's (and similar oblique contact binaries) characteristics. Using N-body
simulations, we find that ~15% of all ultra-wide binaries with cosine-uniform
inclination distribution are likely to merge through this process. Moreover, we
find that such mergers are sufficiently gentle as to only slightly deform the
KBO shape, and can produce the measured rotation speed of MU69. The
semi-secular contact-binary formation channel not only explains the observed
properties of MU69, but could also apply for other Kuiper/asteroid belt
binaries, and for Solar/extra-solar moon systems.
|
Motivation: We investigate whether a template-based classification pipeline
could be used to identify immunophenotypes in (and thereby classify) a
heterogeneous disease with many subtypes. The disease we consider here is Acute
Myeloid Leukemia, which is heterogeneous at the morphologic, cytogenetic and
molecular levels, with several known subtypes. The prognosis and treatment for
AML depends on the subtype.
Results: We apply flowMatch, an algorithmic pipeline for flow cytometry data
created in earlier work, to compute templates succinctly summarizing classes of
AML and healthy samples. We develop a scoring function that accounts for
features of the AML data such as heterogeneity to identify immunophenotypes
corresponding to various AML subtypes, including APL. All of the AML samples in
the test set are classified correctly with high confidence.
Availability: flowMatch is available at
www.bioconductor.org/packages/devel/bioc/html/flowMatch.html; programs specific
to immunophenotyping AML are at www.cs.purdue.edu/homes/aazad/software.html.
|
The Maxwell and Maxwell-de Rham equations can be solved exactly to first
order in an external gravitational field. The gravitational background induces
phases in the wave functions of spin-1 particles. These phases yield the optics
of the particles without requiring any thin lens approximation.
|
Photon correlation measurements reveal memory effects in the optical emission
of single InAs quantum dots with timescales from 10 to 800 ns. With above-band
optical excitation, a long-timescale negative correlation (antibunching) is
observed, while with quasi-resonant excitation, a positive correlation
(blinking) is observed. A simple model based on long-lived charged states is
presented that approximately explains the observed behavior, providing insight
into the excitation process. Such memory effects can limit the internal
efficiency of light emitters based on single quantum dots, and could also be
problematic for proposed quantum-computation schemes.
|
We report the first electron paramagnetic resonance studies of single
crystals and powders of Pr_{0.6}Ca_{0.4}MnO_{3} in the 300-4.2 K range,
covering the charge ordering transition at ~ 240 K and antiferromagnetic
transition (T_N) at ~ 170 K. The asymmetry parameter for the Dysonian single
crystal spectra shows anomalous increase at T_{co}. Below T_{co} the g-value
increases continuously, suggesting a gradual strengthening of orbital ordering.
The linewidth undergoes a sudden increase at T_{co} and continues to increase
down to T_N. The intensity increases as the temperature is decreased till
T_{co} due to the renormalization of magnetic susceptibility arising from the
build up of ferromagnetic correlations. The value of the exchange constant, J,
is estimated to be 154 K.
|
This paper explores the potential of large language models (LLMs) to make the
Aeronautical Regulations of Colombia (RAC) more accessible. Given the
complexity and extensive technicality of the RAC, this study introduces a novel
approach to simplifying these regulations for broader understanding. By
developing the first-ever RAC database, which contains 24,478 expertly labeled
question-and-answer pairs, and fine-tuning LLMs specifically for RAC
applications, the paper outlines the methodology for dataset assembly,
expert-led annotation, and model training. Utilizing the Gemma1.1 2b model
along with advanced techniques like Unsloth for efficient VRAM usage and flash
attention mechanisms, the research aims to expedite training processes. This
initiative establishes a foundation to enhance the comprehensibility and
accessibility of RAC, potentially benefiting novices and reducing dependence on
expert consultations for navigating the aviation industry's regulatory
landscape.
You can visit the dataset
(https://huggingface.co/somosnlp/gemma-1.1-2b-it_ColombiaRAC_FullyCurated_format_chatML_V1)
and the model
(https://huggingface.co/datasets/somosnlp/ColombiaRAC_FullyCurated) here.
|
Data association is one of the fundamental problems in multi-sensor systems.
Most current techniques rely on pairwise data associations which can be
spurious even after the employment of outlier rejection schemes. Considering
multiple pairwise associations at once significantly increases accuracy and
leads to consistency. In this work, we propose two fully decentralized methods
for consistent global data association from pairwise data associations. The
first method is a consensus algorithm on the set of doubly stochastic matrices.
The second method is a decentralization of the spectral method proposed by
Pachauri et al.. We demonstrate the effectiveness of both methods using
theoretical analysis and experimental evaluation.
|
Though convolutional neural networks are widely used in different tasks, lack
of generalization capability in the absence of sufficient and representative
data is one of the challenges that hinder their practical application. In this
paper, we propose a simple, effective, and plug-and-play training strategy
named Knowledge Distillation for Domain Generalization (KDDG) which is built
upon a knowledge distillation framework with the gradient filter as a novel
regularization term. We find that both the ``richer dark knowledge" from the
teacher network, as well as the gradient filter we proposed, can reduce the
difficulty of learning the mapping which further improves the generalization
ability of the model. We also conduct experiments extensively to show that our
framework can significantly improve the generalization capability of deep
neural networks in different tasks including image classification,
segmentation, reinforcement learning by comparing our method with existing
state-of-the-art domain generalization techniques. Last but not the least, we
propose to adopt two metrics to analyze our proposed method in order to better
understand how our proposed method benefits the generalization capability of
deep neural networks.
|
We discuss the thermal evolution of the spurion and messenger fields of
ordinary gauge mediation models taking into account the Standard Model degrees
of freedom. It is shown that for thermalized messengers the metastable susy
breaking vacuum becomes thermally selected provided that the susy breaking
sector is sufficiently weakly coupled to messengers or to any other observable
field.
|
The RGB-D camera maintains a limited range for working and is hard to
accurately measure the depth information in a far distance. Besides, the RGB-D
camera will easily be influenced by strong lighting and other external factors,
which will lead to a poor accuracy on the acquired environmental depth
information. Recently, deep learning technologies have achieved great success
in the visual SLAM area, which can directly learn high-level features from the
visual inputs and improve the estimation accuracy of the depth information.
Therefore, deep learning technologies maintain the potential to extend the
source of the depth information and improve the performance of the SLAM system.
However, the existing deep learning-based methods are mainly supervised and
require a large amount of ground-truth depth data, which is hard to acquire
because of the realistic constraints. In this paper, we first present an
unsupervised learning framework, which not only uses image reconstruction for
supervising but also exploits the pose estimation method to enhance the
supervised signal and add training constraints for the task of monocular depth
and camera motion estimation. Furthermore, we successfully exploit our
unsupervised learning framework to assist the traditional ORB-SLAM system when
the initialization module of ORB-SLAM method could not match enough features.
Qualitative and quantitative experiments have shown that our unsupervised
learning framework performs the depth estimation task comparable to the
supervised methods and outperforms the previous state-of-the-art approach by
$13.5\%$ on KITTI dataset. Besides, our unsupervised learning framework could
significantly accelerate the initialization process of ORB-SLAM system and
effectively improve the accuracy on environmental mapping in strong lighting
and weak texture scenes.
|
Establishing a predictive ab initio method for solid systems is one of the
fundamental goals in condensed matter physics and computational materials
science. The central challenge is how to encode a highly-complex
quantum-many-body wave function compactly. Here, we demonstrate that artificial
neural networks, known for their overwhelming expressibility in the context of
machine learning, are excellent tool for first-principles calculations of
extended periodic materials. We show that the ground-state energies in real
solids in one-, two-, and three-dimensional systems are simulated precisely,
reaching their chemical accuracy. The highlight of our work is that the
quasiparticle band spectra, which are both essential and peculiar to
solid-state systems, can be efficiently extracted with a computational
technique designed to exploit the low-lying energy structure from neural
networks. This work opens up a path to elucidate the intriguing and complex
many-body phenomena in solid-state systems.
|
The paper deals with the controllability of finite-dimensional linear
difference delay equations, i.e., dynamics for which the state at a given time
$t$ is obtained as a linear combination of the control evaluated at time $t$
and of the state evaluated at finitely many previous instants of time
$t-\Lambda_1,\dots,t-\Lambda_N$. Based on the realization theory developed by
Y.Yamamoto for general infinite-dimensional dynamical systems, we obtain
necessary and sufficient conditions, expressed in the frequency domain, for the
approximate controllability in finite time in $L^q$ spaces, $q \in [1,
+\infty)$. We also provide a necessary condition for $L^1$ exact
controllability, which can be seen as the closure of the $L^1$ approximate
controllability criterion. Furthermore, we provide an explicit upper bound on
the minimal times of approximate and exact controllability, given by
$d\max\{\Lambda_1,\dots,\Lambda_N\}$, where $d$ is the dimension of the state
space.
|
ZnGeN2 and other heterovalent ternary semiconductors have important potential
applications in optoelectronics, but ordering of the cation sublattice, which
can affect the band gap, lattice parameters, and phonons, is not yet well
understood. Here the effects of growth and processing conditions on the
ordering of the ZnGeN2 cation sublattice were investigated using x-ray
diffraction and Raman spectroscopy. Polycrystalline ZnGeN2 was grown by
exposing solid Ge to Zn and NH3 vapors at temperatures between 758 degree C and
914 degree C. Crystallites tended to be rod-shaped, with growth rates higher
along the c-axis. The degree of ordering, from disordered, wurtzite-like x-ray
diffraction spectra to orthorhombic, with space group Pna21, increased with
increasing growth temperature, as evidenced by the appearance of superstructure
peaks and peak splittings in the diffraction patterns. Annealing disordered,
low-temperature-grown ZnGeN2 at 850 degree C resulted in increased cation
ordering. Growth of ZnGeN2 on a liquid Sn-Ge-Zn alloy at 758 degree C showed an
increase in the tendency for cation ordering at a lower growth temperature, and
resulted in hexagonal platelet-shaped crystals. The trends shown here may help
to guide understanding of the synthesis and characterization of other
heterovalent ternary nitride semiconductors as well as ZnGeN2.
|
It is shown that the $n$-point functions of scalar massive free fields on the
noncommutative Minkowski space are distributions which are boundary values of
analytic functions. Contrary to what one might expect, this construction does
not provide a connection to the popular traditional Euclidean approach to
noncommutative field theory (unless the time variable is assumed to commute).
Instead, one finds Schwinger functions with twistings involving only momenta
that are on the mass-shell. This explains why renormalization in the
traditional Euclidean noncommutative framework crudely differs from
renormalization in the Minkowskian regime.
|
The properties of galaxies depend on their environment: red, passive
elliptical galaxies are usually located in denser environments than blue,
star-forming spiral galaxies. This difference in galaxy populations can be
detected at all scales from groups of galaxies to superclusters. In this paper,
we will discuss the effect of the large-scale environment on galaxies. Our
results suggest that galaxies in superclusters are more likely to be passive
than galaxies in voids even when they belong to groups with the same richness.
In addition, the galaxies in superclusters are also affected by the morphology
of the supercluster: filament-type superclusters contain relatively more red,
passive galaxies than spider-type superclusters. These results suggest that the
evolution of a galaxy is not determined by its local environment alone, but the
large-scale environment also affects.
|
We study the fluid inclusion of both Lennard-Jones particles and particles
with competing interaction ranges --short range attractive and long range
repulsive (SALR)-- in a disordered porous medium constructed as a controlled
pore glass in two dimensions. With the aid of a full two-dimensional
Ornstein-Zernike approach, complemented by a Replica Ornstein-Zernike integral
equation, we explicitly obtain the spatial density distribution of the fluid
adsorbed in the porous matrix and a good approximation for the average
fluid-matrix correlations. The results illustrate the remarkable differences
between the adsorbed Lennard-Jones (LJ) and SALR systems. In the latter
instance, particles tend to aggregate in clusters which occupy pockets and bays
in the porous structure, whereas the LJ fluid uniformly wets the porous walls.
A comparison with Molecular Dynamics simulations shows that the two-dimensional
Ornstein-Zernike approach with a Hypernetted Chain closure together with a
sensible approximation for the fluid-fluid correlations can provide an accurate
picture of the spatial distribution of adsorbed fluids for a given
configuration of porous material.
|
It is shown that the probabilities for the spin singlet can be reproduced
through classical resources, with no communication between the distant parties,
by using merely shared (pseudo-)randomness. If the parties are conscious beings
aware of both the hidden-variables and the random mechanism, then one has a
conspiracy. If the parties are aware of only the random variables, they may be
induced to believe that they are able to send instantaneous information to one
another. It is also possible to reproduce the correlations at the price of
reducing the detection efficiency. It is further demonstrated that the same
probability decomposition could be realized through action-at-a-distance,
provided it existed.
|
We show that the $\g$-vector of the interval subdivision of a simplicial
complex with a nonnegative and symmetric $h$-vector is nonnegative. In
particular, we prove that such $\g$-vector is the $f$-vector of some balanced
simplicial complex. Moreover, we show that the local $\g$-vector of the
interval subdivision of a simplex is nonnegative; answering a question by
Juhnke-Kubitzke et al.
|
Traditional syntax models typically leverage part-of-speech (POS) information
by constructing features from hand-tuned templates. We demonstrate that a
better approach is to utilize POS tags as a regularizer of learned
representations. We propose a simple method for learning a stacked pipeline of
models which we call "stack-propagation". We apply this to dependency parsing
and tagging, where we use the hidden layer of the tagger network as a
representation of the input tokens for the parser. At test time, our parser
does not require predicted POS tags. On 19 languages from the Universal
Dependencies, our method is 1.3% (absolute) more accurate than a
state-of-the-art graph-based approach and 2.7% more accurate than the most
comparable greedy model.
|
Recent work has shown that either (1) increasing the input length or (2)
increasing model size can improve the performance of Transformer-based neural
models. In this paper, we present a new model, called LongT5, with which we
explore the effects of scaling both the input length and model size at the same
time. Specifically, we integrated attention ideas from long-input transformers
(ETC), and adopted pre-training strategies from summarization pre-training
(PEGASUS) into the scalable T5 architecture. The result is a new attention
mechanism we call {\em Transient Global} (TGlobal), which mimics ETC's
local/global attention mechanism, but without requiring additional side-inputs.
We are able to achieve state-of-the-art results on several summarization tasks
and outperform the original T5 models on question answering tasks.
|
In this paper, we propose a spatial modulation (SM) scheme referred to as
complex quadrature spatial modulation (CQSM). In contrast to quadrature spatial
modulation (QSM), CQSM transmits two complex signal constellation symbols on
the real and quadrature spatial dimensions at each channel use, increasing the
spectral efficiency. To this end, signal symbols transmitted at any given time
instant are drawn from two different modulation sets. The first modulation set
is any of the conventional QAM/PSK alphabets, while the second is a rotated
version of it. The optimal rotation angle is obtained through simulations for
several modulation schemes and analytically proven for the case of QPSK, where
both results coincide. Simulation results showed that CQSM outperformed QSM and
generalized SM (GSM) by approximately 5 and 4.5 dB, respectively, for the same
transmission rate. Its performance was similar to that of QSM; however, it
achieved higher transmission rates. It was additionally shown numerically and
analytically that CQSM outperformed QSM for a relatively large number of
transmit antennas.
|
The Wilson contour integral approach is applied to resum the soft gluon
radiative correctins to the quark form factors in the Sudakov regime. The
one-loop order results for the quark-photon (color singlet form factor) and
quark-gluon (color non-singlet form factor) vertices are presented. The
explicit expressions for the vacuum averaged contour integrals in $g^2$
accuracy are derived for an arbitrary gauge field. The corresponding one-loop
cusp anomalous dimensions are found in the case of perturbative gluon field in
arbitrary covariant gauge. It is shown that the gauge dependence drops out from
the leading high energy behavior.
|
In a generic supersymmetric extension of the Standard Model, whether unified
or not, a simple and well motivated U(2) symmetry, acting on the lightest two
generations, completely solves the flavour changing problem and necessarily
leads to a predictive texture for the Yukawa couplings.
|
Given an invertible sheaf on a fibre space between projective varieties of
positive characteristic, we show that fibrewise semi-ampleness implies relative
semi-ampleness. The same statement fails in characteristic zero.
|
We analyze the high-resolution X-ray spectrum of the Seyfert 1 galaxy NGC
5548, for the full 0.1-10 keV band, using improved calibration results of the
Chandra-LETGS instrument. The warm absorber consists of at least three
ionization components, namely one with a low, medium and high ionization
parameter. The X-ray absorbing material, from an outflowing wind, covers the
full range of velocity components found from UV absorption lines. The presence
of redshifted emission components for the strongest blue-shifted resonance
absorption lines indicate that the absorber is located at a distance larger
than the edge of the accretion disk. We derive an upper limit to the edge of
the accretion disk of 1 light year. Absorption lines from ions of at least ten
chemical elements have been detected, and in general for these elements there
are no strong deviations from solar abundances. The narrow emission lines from
the O VII and Ne IX forbidden and intercombination lines probably originate
from much larger distances to the black hole. We find evidence for weak
relativistically broadened oxygen and nitrogen emission lines from the inner
parts of the accretion disk, but at a much smaller flux level than those
observed in some other active galactic nuclei. In addition, there is a broad,
non-relativistic C VI Ly alpha emission line that is consistent with emission
lines from the inner part of the optical/UV broad line region.
|
We use Toponogov's triangle comparison theorem from Riemannian geometry along
with quantitative scale oriented variants of classical propagation of
singularities arguments to obtain logarithmic improvements of the
Kakeya-Nikodym norms introduced in \cite{SKN} for manifolds of nonpositive
sectional curvature. Using these and results from our paper \cite{BS15} we are
able to obtain log-improvements of $L^p(M)$ estimates for such manifolds when
$2<p<\tfrac{2(n+1)}{n-1}$. These in turn imply $(\log\lambda)^{\sigma_n}$,
$\sigma_n\approx n$, improved lower bounds for $L^1$-norms of eigenfunctions of
the estimates of the second author and Zelditch~\cite{SZ11}, and using a result
from Hezari and the second author~\cite{HS}, under this curvature assumption,
we are able to improve the lower bounds for the size of nodal sets of Colding
and Minicozzi~\cite{CM} by a factor of $(\log \lambda)^{\mu}$ for any
$\mu<\tfrac{2(n+1)^2}{n-1}$, if $n\ge3$.
|
We address second-order optimality conditions for optimal control problems
involving sparsity functionals which induce spatio-temporal sparsity patterns.
We employ the notion of (weak) second subderivatives. With this approach, we
are able to reproduce the results from Casas, Herzog, and Wachsmuth (ESAIM
COCV, 23, 2017, p. 263-295). Our analysis yields a slight improvement of one of
these results and also opens the door for the sensitivity analysis of this
class of problems.
|
Doubly heavy baryons $\left(QQq\right)$ and singly heavy antimesons
$\left(\bar{Q}q\right)$ are related by the heavy quark-diquark (HQDQ) symmetry
because in the $m_Q \to \infty$ limit, the light degrees of freedom in both the
hadrons are expected to be in identical configurations. Hyperfine splittings of
the ground states in both systems are nonvanishing at $O(1/m_Q)$ in the heavy
quark mass expansion and HQDQ symmetry relates the hyperfine splittings in the
two sectors. In this paper, working within the framework of Non-Relativistic
QCD (NRQCD), we point out the existence of an operator that couples four heavy
quark fields to the chromomagnetic field with a coefficient that is enhanced by
a factor from Coulomb exchange. This operator gives a correction to doubly
heavy baryon hyperfine splittings that scales as $1/m_Q^2 \times \alpha_S/r$,
where $r$ is the separation between the heavy quarks in the diquark. This
correction can be calculated analytically in the extreme heavy quark limit in
which the potential between the quarks in the diquark is Coulombic. In this
limit, the correction is $O(\alpha_s^2/m_Q)$ and comes with a small
coefficient. For values of $\alpha_s$ relevant to doubly charm and doubly
bottom systems, the correction to the hyperfine splittings in doubly heavy
baryons is only a few percent or smaller. We also argue that nonperturbative
corrections to the prediction for the hyperfine splittings are suppressed by
$\Lambda^2_{\rm QCD}/m_Q^2$ rather than $\Lambda_{\rm QCD}/m_Q$. Corrections
should be $\approx 10\%$ in the charm sector and smaller in heavier systems.
|
Hot-carrier cooling (HCC) in metal halide perovskites in the high-density
regime is significantly slower compared to conventional semiconductors. This
effect is commonly attributed to a hot-phonon bottleneck but the influence of
the lattice properties on the HCC behaviour is poorly understood. Using
pressure-dependent transient absorption spectroscopy (fs-TAS) we find that at
an excitation density below Mott transition, pressure does not affect the HCC.
On the contrary, above Mott transition, HCC in methylammonium lead iodide
(MAPbI3) is around two times as fast at 0.3 GPa compared to ambient pressure.
Our electron-phonon coupling calculations reveal about two times stronger
electron-phonon coupling for the inorganic cage mode at 0.3 GPa. However, our
experiments reveal that pressure promotes faster HCC only above Mott
transition. Altogether, these findings suggest a change in the nature of
excited carriers in the high-density regime, providing insights on the
electronic behavior of devices operating at such high charge-carrier density.
|
Efficient optical quantum memories are a milestone required for several
quantum technologies including repeater-based quantum key distribution and
on-demand multi-photon generation. We present an efficiency optimization of an
optical electromagnetically induced transparency (EIT) memory experiment in a
warm cesium vapor using a genetic algorithm and analyze the resulting
waveforms. The control pulse is represented either as a Gaussian or free-form
pulse, and the results from the optimization are compared. We see an
improvement factor of 3(7)\% when using optimized free-form pulses. By limiting
the allowed pulse energy in a solution, we show an energy-based optimization
giving a 30% reduction in energy, with minimal efficiency loss.
|
With the advent of high precision neutrino scattering experiments comes the
need for improved radiative corrections. We present a phenomenological analysis
of some contributions to the production of photons in neutrino neutral current
scattering that are relevant to experiments subsuming the 1% level.
|
The most pristine remnants of the Solar system's planet formation epoch orbit
the Sun beyond Neptune, the small bodies of the trans-Neptunian object
populations. The bulk of the mass is in ~100 km objects, but objects at smaller
sizes have undergone minimal collisional processing, with New Horizons recently
revealing that ~20 km effective diameter body (486958) Arrokoth appears to be a
primordial body, not a collisional fragment. This indicates bodies at these
sizes (and perhaps smaller) retain a record of how they were formed, and are
the most numerous record of that epoch. However, such bodies are impractical to
find by optical surveys due to their very low brightnesses. Their presence can
be inferred from the observed cratering record of Pluto and Charon, and
directly measured by serendipitous stellar occultations. These two methods
produce conflicting results, with occultations measuring roughly ten times the
number of ~km bodies inferred from the cratering record. We use numerical
models to explore how these observations can be reconciled with evolutionary
models of the outer Solar system. We find that models where the initial size of
bodies decreases with increasing semimajor axis of formation, and models where
the surface density of bodies increases beyond the 2:1 mean-motion resonance
with Neptune can produce both sets of observations, though comparison to
various observational tests favours the former mechanism. We discuss how to
evaluate the astrophysical plausibility of these solutions, and conclude
extended serendipitous occultation surveys with broad sky coverage are the most
practical approach.
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In this work, we study the effects on the relevant observational parameters
of an inflationary universe from a chaotic potential with a step. We
numerically evolve the perturbation equations within both cold inflation and
warm inflation. On the one hand, in a cold inflation scenario we analyse the
scalar power spectrum $P_{\mathcal{R}}$ in terms of the number of e-folds
$N_{e}$, and in terms of the ratio $k/k_{0}$, where $k_{0}$ is our pivot scale.
We show how $P_{\mathcal{R}}$ oscillates around $0.2< k/k_{0} < 20$.
Additionally, we present the evolution of two relevant parameters: the scalar
spectral index $n_\mathrm{s}$ and the tensor-to-scalar ratio $r$. In fact, more
than one region of $(n_\mathrm{s},r)$ lies within the observable window (Planck
2018). On the other hand, in the warm inflationary case, we also examine the
evolution of $P_{\mathcal{R}}$ in terms of $N_{e}$ and $k/k_{0}$. Perturbations
are amplified in WI; in fact, $P_{\mathcal{R}}$ can be much larger than the CMB
value $P_{\mathcal{R}}> 2.22\times 10^{-9}$. This time, the spectral index
$n_\mathrm{s}$ is clearly blue-tilted, at smaller scales, and the
tensor-to-scalar ratio $r$ becomes too low. However, $n_\mathrm{s}$ can change
from blue-tilted towards red-tilted, since $P_{\mathcal{R}}$ starts oscillating
around $k/k_{0}\sim 40$. Indeed, the result from the step potential skims the
Planck contours. Finally, one key aspect of this research was to contrast the
features of an inflationary potential between both paradigms, and, in fact,
they show similarities and differences. Due to a featured background and a
combined effect of entropy fluctuations (only in warm inflation), in both
scenarios certain fluctuation scales are not longer ``freeze in'' on
super-horizon scales.
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This paper proposes a novel Stochastic Split Linearized Bregman Iteration
($S^{2}$-LBI) algorithm to efficiently train the deep network. The $S^{2}$-LBI
introduces an iterative regularization path with structural sparsity. Our
$S^{2}$-LBI combines the computational efficiency of the LBI, and model
selection consistency in learning the structural sparsity. The computed
solution path intrinsically enables us to enlarge or simplify a network, which
theoretically, is benefited from the dynamics property of our $S^{2}$-LBI
algorithm. The experimental results validate our $S^{2}$-LBI on MNIST and
CIFAR-10 dataset. For example, in MNIST, we can either boost a network with
only 1.5K parameters (1 convolutional layer of 5 filters, and 1 FC layer),
achieves 98.40\% recognition accuracy; or we simplify $82.5\%$ of parameters in
LeNet-5 network, and still achieves the 98.47\% recognition accuracy. In
addition, we also have the learning results on ImageNet, which will be added in
the next version of our report.
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Although significant recent progress has been made in improving the
multi-core scalability of high throughput transactional database systems,
modern systems still fail to achieve scalable throughput for workloads
involving frequent access to highly contended data. Most of this inability to
achieve high throughput is explained by the fundamental constraints involved in
guaranteeing ACID --- the addition of cores results in more concurrent
transactions accessing the same contended data for which access must be
serialized in order to guarantee isolation. Thus, linear scalability for
contended workloads is impossible. However, there exist flaws in many modern
architectures that exacerbate their poor scalability, and result in throughput
that is much worse than fundamentally required by the workload.
In this paper we identify two prevalent design principles that limit the
multi-core scalability of many (but not all) transactional database systems on
contended workloads: the multi-purpose nature of execution threads in these
systems, and the lack of advanced planning of data access. We demonstrate the
deleterious results of these design principles by implementing a prototype
system, ORTHRUS, that is motivated by the principles of separation of database
component functionality and advanced planning of transactions. We find that
these two principles alone result in significantly improved scalability on
high-contention workloads, and an order of magnitude increase in throughput for
a non-trivial subset of these contended workloads.
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We calculate the effects of finite density of isospin asymmetric strange
hadronic matter, for different strangeness fractions, on the in-medium
properties of vector $\left( D^{\ast}, D_{s}^{\ast}, B^{\ast},
B_{s}^{\ast}\right)$ and axial-vector $\left( D_{1}, D_{1s}, B_{1},
B_{1s}\right)$ mesons using chiral hadronic SU(3) model and QCD sum rules. We
focus on the evaluation of in-medium mass-shift and shift of decay constant of
above vector and axial vector mesons. In QCD sum rule approach the properties
e.g. masses and decay constants of vector and axial vector mesons are written
in terms of quark and gluon condensates. These quarks and gluon condensates are
evaluated in the present work using chiral SU(3) model through the medium
modification of scalar-isoscalar fields $\sigma$ and $\zeta$, the
scalar-isovector field
$\delta$ and scalar dilaton field $\chi$ in strange hadronic medium which
includes both nucleons as well as hyperons. As we shall see in detail the
masses and decay constants of heavy vector and axial vector mesons are affected
significantly due to isospin asymmetry and strangeness fraction of the medium
and these modifications may influence the experimental observables produced in
heavy ion collision experiments. The results of present investigations of
in-medium properties of vector and axial-vector mesons at finite density of
strange hadronic medium may be helpful for understanding the experimental data
from heavy-ion collision experiments in-particular for the Compressed Baryonic
Matter (CBM) experiment of FAIR facility at GSI, Germany.
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We enumerate interlaced pairs of parking functions whose underlying Dyck path
has a bounded height. We obtain an explicit formula for this enumeration in the
form of a quotient of analogs of Chebicheff polynomials having coefficients in
the ring of symmetric functions.
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We generalize Moore's nonstandard proof of the Spectral theorem for bounded
self-adjoint operators to the case of unbounded operators. The key step is to
use a definition of the nonstandard hull of an internally bounded self-adjoint
operator due to Raab.
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The radiative capture process $n p \to d \gamma$ is considered within the
framework of a recently developed six-quark dressed-bag model for the
nucleon-nucleon interaction. The calculations presented here include both the
nucleon current and the meson-exchange current contributions. The latter uses
short-range hadronic form factors for the pion exchange currents consistent
with the soft cut-off parameter $\Lambda_{\pi NN}$ from the $NN$-potential.
Contributions of the pion exchange current and $\Delta$-isobar current to the
total cross section still cannot explain the discrepancy between the
theoretical and experimental cross sections. Possibilities for new types of
meson exchange currents associated with chiral fields inside multi-quark
dressed-bag states in nuclei are discussed.
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Careful prompt design is critical to the use of large language models in
zero-shot or few-shot learning. As a consequence, there is a growing interest
in automated methods to design optimal prompts. In this work, we propose
Test-time Prompt Editing using Reinforcement learning (TEMPERA). In contrast to
prior prompt generation methods, TEMPERA can efficiently leverage prior
knowledge, is adaptive to different queries and provides an interpretable
prompt for every query. To achieve this, we design a novel action space that
allows flexible editing of the initial prompts covering a wide set of
commonly-used components like instructions, few-shot exemplars, and
verbalizers. The proposed method achieves significant gains compared with
recent SoTA approaches like prompt tuning, AutoPrompt, and RLPrompt, across a
variety of tasks including sentiment analysis, topic classification, natural
language inference, and reading comprehension. Our method achieves 5.33x on
average improvement in sample efficiency when compared to the traditional
fine-tuning methods.
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The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum
foundations, arising from the lack of local realistic description of quantum
mechanics. The EPR paradox has stimulated an important concept of "quantum
nonlocality", which manifests itself by three different types: quantum
entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality
is more often used to show the "quantum nonlocality", the original EPR paradox
is essentially a steering paradox. In this work, we formulate the original EPR
steering paradox into a contradiction equality,thus making it amenable to an
experimental verification. We perform an experimental test of the steering
paradox in a two-qubit scenario. Furthermore, by starting from the steering
paradox, we generate a generalized linear steering inequality and transform
this inequality into a mathematically equivalent form, which is more friendly
for experimental implementation, i.e., one may only measure the observables in
$x$-, $y$-, or $z$-axis of the Bloch sphere, rather than other arbitrary
directions. We also perform experiments to demonstrate this scheme. Within the
experimental errors, the experimental results coincide with the theoretical
predictions. Our results deepen the understanding of quantum foundations and
provide an efficient way to detect the steerability of quantum states.
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We often seek to estimate the causal effect of an exposure on a particular
outcome in both randomized and observational settings. One such estimation
method is the covariate-adjusted residuals estimator, which was designed for
individually or cluster randomized trials. In this manuscript, we study the
properties of this estimator and develop a new estimator that utilizes both
covariate adjustment and inverse probability weighting We support our
theoretical results with a simulation study and an application in an infectious
disease setting. The covariate-adjusted residuals estimator is an efficient and
unbiased estimator of the average treatment effect in randomized trials;
however, it is not guaranteed to be unbiased in observational studies. Our
novel estimator, the covariate-adjusted residuals estimator with inverse
probability weighting, is unbiased in randomized and observational settings,
under a reasonable set of assumptions. Furthermore, when these assumptions
hold, it provides efficiency gains over inverse probability weighting in
observational studies. The covariate-adjusted residuals estimator is valid for
use in randomized trials, but should not be used in observational studies. The
covariate-adjusted residuals estimator with inverse probability weighting
provides an efficient alternative for use in randomized and observational
settings.
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It is shown that for a certain class of the Kato functions the Trotter-Kato
product formulae converge in Dixmier ideal C 1,$\infty$ in topology, which is
defined by the $\times$ 1,$\infty$-norm. Moreover, the rate of convergence in
this topology inherits the error-bound estimate for the corresponding
operator-norm convergence. 1 since [24], [14]. Note that a subtle point of this
program is the question about the rate of convergence in the corresponding
topology. Since the limit of the Trotter-Kato product formula is a strongly
continuous semigroup, for the von Neumann-Schatten ideals this topology is the
trace-norm $\times$ 1 on the trace-class ideal C 1 (H). In this case the limit
is a Gibbs semigroup [25]. For self-adjoint Gibbs semigroups the rate of
convergence was estimated for the first time in [7] and [9]. The authors
considered the case of the Gibbs-Schr{\"o}dinger semigroups. They scrutinised
in these papers a dependence of the rate of convergence for the (exponential)
Trotter formula on the smoothness of the potential in the Schr{\"o}dinger
generator. The first abstract result in this direction was due to [19]. In this
paper a general scheme of lifting the operator-norm rate convergence for the
Trotter-Kato product formulae was proposed and advocated for estimation the
rate of the trace-norm
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We prove a new global existence result for the asymptotically flat,
spherically symmetric Einstein-Vlasov system which describes in the framework
of general relativity an ensemble of particles which interact by gravity. The
data are such that initially all the particles are moving radially outward and
that this property can be bootstrapped. The resulting non-vacuum spacetime is
future geodesically complete.
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The terrestrial fossil record shows that the exponential rise in biodiversity
since the Precambrian period has been punctuated by large extinctions, at
intervals of 40 to 140 Myr. These mass extinctions represent extremes over a
background of smaller events and the natural process of species extinction. We
point out that the non-terrestrial phenomena proposed to explain these events,
such as boloidal impacts (a candidate for the end-Cretaceous extinction), and
nearby supernovae, are collectively far more effective during the solar
system's traversal of spiral arms. Using the best available data on the
location and kinematics of the Galactic spiral structure (including distance
scale and kinematic uncertainties), we present evidence that arm crossings
provide a viable explanation for the timing of the large extinctions.
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The photoluminescence (PL) spectrum of a two-dimensional electron gas (2DEG)
in the fractional quantum Hall regime is studied. The response of the 2DEG to
an optically injected valence hole depends on the separation d between the
electron and hole layers. At d smaller than the magnetic length lambda, the PL
spectrum shows recombination of neutral (X) and charged (X-) excitons. At
d>lambda, the hole binds one or two Laughlin quasielectrons (QE) of the 2DEG to
form fractionally charged excitons (FCX), hQE or hQE2. Different FCX states
have different optical properties, and their stability depends critically on
the presence of QE's in the 2DEG. This explains discontinuities observed in the
PL spectrum at such (Laughlin) filling factors as nu=1/3 or 2/3.
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We study the effect of varying sound speed on clustering dark energy in the
Dirac-Born-Infeld (DBI) scenario. The DBI action is included in the class of
$k$-essence models, and it has an important role in describing the effective
degrees of freedom of D-branes in the string theory. In the DBI setup, we take
the anti-de Sitter (AdS) warp factor $f(\phi)=f_0\, \phi^{-4}$, and investigate
the self-interacting quartic potential $V(\phi)=\lambda\phi^{4}/4$. We
calculate the full expression of the effective sound speed for our model, and
show that it can evolve with time during the cosmological evolution. Besides,
the adiabatic sound speed evolves with time here, and this influences the
background dynamics to some extent. We show that the effective sound speed is
very close to the adiabatic sound speed. We examine the effect of the variable
sound speed on growth of the perturbations in both the linear and non-linear
regimes. In the linear regime, we apply the Pseudo-Newtonian formalism, and
show that dark energy suppresses the growth of perturbations at low redshifts.
From study the Integrated Sachs-Wolf (ISW) effect in our setup, we see that the
model manifests some deviation from the concordance $\Lambda$CDM model. In the
non-linear regime, we follow the approach of spherical collapse model, and
calculate the linear overdensity, the virial overdensity, overdensity at the
turn around and the rate of expansion of collapsed region. We further compute
relative number density of halo objects above a given mass in our setting, and
show that the number of structures with respect to the $\Lambda$CDM model is
reduced more in the high mass tail at high redshifts.
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We apply the Adversarial NLI dataset to train the NLI model and show that the
model has the potential to enhance factual correctness in abstract
summarization. We follow the work of Falke et al. (2019), which rank multiple
generated summaries based on the entailment probabilities between an source
document and summaries and select the summary that has the highest entailment
probability. The authors' earlier study concluded that current NLI models are
not sufficiently accurate for the ranking task. We show that the Transformer
models fine-tuned on the new dataset achieve significantly higher accuracy and
have the potential of selecting a coherent summary.
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The synthesis of antimonene, which is a promising group-V 2D material for
both fundamental studies and technological applications, remains highly
challenging. Thus far, it has been synthesized only by exfoliation or growth on
a few substrates. In this study, we show that thin layers of antimonene can be
grown on Ag (111) by molecular beam epitaxy. High-resolution scanning tunneling
microscopy combined with theoretical calculations revealed that the
submonolayer Sb deposited on a Ag (111) surface forms a layer of AgSb2 surface
alloy upon annealing. Further deposition of Sb on the AgSb2 surface alloy
causes an epitaxial layer of Sb to form, which is identified as antimonene with
a buckled honeycomb structure. More interestingly, the lattice constant of the
epitaxial antimonene (5 {\AA}) is much larger than that of freestanding
antimonene, indicating a high tensile strain of more than 20%. This kind of
large strain is expected to make the antimonene a highly promising candidate
for room-temperature quantum spin Hall material.
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The Time Projection Chamber (TPC) has been recognized as a potentially
powerful detector for the search of WIMPs by measuring the directions of
nuclear recoils, in which the most convincing signature of WIMPs, caused by the
Earth's motion around the Galaxy, appears.
We report on the first results of a performance study of the neutron exposure
of our prototype micro-TPC with Ar-C$_2$H$_6$ (90:10) and CF$_4$ gas of 150
Torr.
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The short coherence lengths characteristic of low-dimensional superconductors
are associated with usefully high critical fields or temperatures.
Unfortunately, such materials are often sensitive to disorder and suffer from
phase fluctuations in the superconducting order parameter which diverge with
temperature $T$, magnetic field $H$ or current $I$. We propose an approach to
overcome synthesis and fluctuation problems: building superconductors from
inhomogeneous composites of nanofilaments. Macroscopic crystals of
quasi-one-dimensional Na$_{2-\delta}$Mo$_6$Se$_6$ featuring Na vacancy disorder
($\delta\approx$~0.2) are shown to behave as percolative networks of
superconducting nanowires. Long range order is established via transverse
coupling between individual one-dimensional filaments, yet phase coherence
remains unstable to fluctuations and localization in the zero-($T$,$H$,$I$)
limit. However, a region of reentrant phase coherence develops upon raising
($T$,$H$,$I$). We attribute this phenomenon to an enhancement of the transverse
coupling due to electron delocalization. Our observations of reentrant phase
coherence coincide with a peak in the Josephson energy $E_J$ at non-zero
($T$,$H$,$I$), which we estimate using a simple analytical model for a
disordered anisotropic superconductor. Na$_{2-\delta}$Mo$_6$Se$_6$ is therefore
a blueprint for a future generation of nanofilamentary superconductors with
inbuilt resilience to phase fluctuations at elevated ($T$,$H$,$I$).
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A weakly consecutive sequence (WCS) is a permutation $\sigma$ of $\{1,
\ldots, k\}$ such that if an integer $d$ divides $\sigma(i)$, then $d$ also
divides $\sigma(i \pm d)$ insofar as these are defined. The structure of weakly
consecutive sequences is surprisingly rich, and it is difficult to find a
formula for the number $N(k)$ of WCS's of length $k$. However, for a given $k$
we describe four starting sequences, to each of which we can apply three
\emph{rules} or operations to generate new WCS's. We conjecture that any WCS
can be constructed by applying these rules, which depend in an intricate way on
the primality of $k$ and surrounding integers. We find bounds for $N(k)$ by
analyzing these rules.
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I develop an extension of the usual three-flavor quark model to four flavors
(u, d, s and c), and discuss the classification of pentaquark states with
hidden charm. This work is motivated by the recent observation of such states
by the LHCb Collatoration at CERN.
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We have investigated the cross-over from Zener tunneling of single charge
carriers to avalanche type of bunched electron transport in a suspended
graphene Corbino disk in the zeroth Landau level. At low bias, we find a
tunneling current that follows the gyrotropic Zener tunneling behavior. At
larger bias, we find avalanche type of transport that sets in at a smaller
current the larger the magnetic field is. The low-frequency noise indicates
strong bunching of the electrons in the avalanches. On the basis of the
measured low-frequency switching noise power, we deduce the characteristic
switching rates of the avalanche sequence. The simultaneous microwave shot
noise measurement also reveals intrinsic correlations within the avalanche
pulses and indicate decrease of correlations with increasing bias.
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We present the Evolving Graph Fourier Transform (EFT), the first invertible
spectral transform that captures evolving representations on temporal graphs.
We motivate our work by the inadequacy of existing methods for capturing the
evolving graph spectra, which are also computationally expensive due to the
temporal aspect along with the graph vertex domain. We view the problem as an
optimization over the Laplacian of the continuous time dynamic graph.
Additionally, we propose pseudo-spectrum relaxations that decompose the
transformation process, making it highly computationally efficient. The EFT
method adeptly captures the evolving graph's structural and positional
properties, making it effective for downstream tasks on evolving graphs. Hence,
as a reference implementation, we develop a simple neural model induced with
EFT for capturing evolving graph spectra. We empirically validate our
theoretical findings on a number of large-scale and standard temporal graph
benchmarks and demonstrate that our model achieves state-of-the-art
performance.
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