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Our current understanding of quantum chaos hinges on the random matrix
behavior (RMT) of typical states in quantum many-body systems, particularly
eigenstates and their energy level statistics. Although RMT has been remarkably
successful in describing `coarse' features of quantum states in chaotic
regimes, it fails to capture their `finer' features, particularly those arising
from spatial locality and symmetries. Here, we show that we can accurately
describe the behavior of eigenstate ensembles in physical systems by using RMT
ensembles with constraints that capture the key features of the physical
system. We demonstrate our approach on local spin Hamiltonians with a scalar
U(1) charge. By constructing constrained RMT ensembles that account for two
local scalar charges playing the role of energy and magnetization, we describe
the patterns of entanglement of mid-spectrum eigenstates at all lengthscales
and beyond their average behavior, analytically and numerically. When defining
the correspondence between quantum chaos and RMT, our work clarifies that RMT
ensembles must be constrained to account for all the features of the underlying
Hamiltonian, particularly spatial locality and symmetries.
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We present a model calculation of the generalized parton distributions where
the nucleon is described by a quark core surrounded by a mesonic cloud. In the
one-meson approximation, we expand the Fock state of the physical nucleon in a
series involving a bare nucleon and two-particle, meson-baryon, states. We
discuss the role of the different Fock-state components of the nucleon by
deriving a convolution formalism for the unpolarized generalized parton
distributions, and showing predictions at different kinematics.
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The Proceedings of the 2003 SLAC Workshops on flavor physics with a high
luminosity asymmetric e+e- collider. The sensitivity of flavor physics to
physics beyond the Standard Model is addressed in detail, in the context of the
improvement of experimental measurements and theoretical calculations.
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The coupling of cold atoms to the radiation field within a high-finesse
optical resonator, an optical cavity, induces long-range interactions which can
compete with an underlying optical lattice. The interplay between short- and
long-range interactions gives rise to new phases of matter including
supersolidity (SS) and density waves (DW), and interesting quantum dynamics.
Here it is shown that for hard-core bosons in one dimension the ground state
phase diagram and the quantum relaxation after sudden quenches can be
calculated exactly in the thermodynamic limit. Remanent DW order is observed
for quenches from a DW ground state into the superfluid (SF) phase below a
dynamical transition line. After sufficiently strong SF to DW quenches beyond a
static metastability line DW order emerges on top of remanent SF order, giving
rise to a dynamically generated supersolid state.
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Let $\ccM_{g,[n]}$, for $2g-2+n>0$, be the stack of genus $g$, stable
algebraic curves, endowed with $n$ unordered marked points.
Looijenga introduced the notion of Prym level structures in order to
construct smooth projective Galois coverings of the stack $\ccM_{g}$.
In \S 2 of this paper, we introduce the notion of Looijenga level structure
which generalizes Looijenga construction and provides a tower of Galois
coverings of $\ccM_{g,[n]}$ equivalent to the tower of all geometric level
structures over $\ccM_{g,[n]}$.
In \S 3, Looijenga level structures are interpreted geometrically in terms of
moduli of curves with symmetry. A byproduct of this characterization is a
simple criterion for their smoothness. As a consequence of this criterion, it
is shown that Looijenga level structures are smooth under mild hypotheses.
The second part of the paper, from \S 4, deals with the problem of describing
the D-M boundary of level structures. In \S 6, a description is given of the
nerve of the D-M boundary of abelian level structures. In \S 7, it is shown how
this construction can be used to "approximate" the nerve of Looijenga level
structures. These results are then applied to elaborate a new approach to the
congruence subgroup problem for the Teichm\"uller modular group.
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The vacuum energy of a scalar field in a spherically symmetric background
field is considered. It is expressed through the Jost function of the
corresponding scattering problem. The renormalization is discussed in detail
and performed using the uniform asymptotic expansion of the Jost function. The
method is demonstrated in a simple explicit example.
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There are many families of functions on partitions, such as the shifted
symmetric functions, for which the corresponding q-brackets are quasimodular
forms. We extend these families so that the corresponding q-brackets are
quasimodular for a congruence subgroup. Moreover, we find subspaces of these
families for which the q-bracket is a modular form. These results follow from
the properties of Taylor coefficients of strictly meromorphic quasi-Jacobi
forms around rational lattice points.
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We compare the results of measurements of the magnetic susceptibility Chi(T),
the linear coefficient of specific heat Gamma(T)=C(T)/T and 4f occupation
number nf(T) for the intermediate valence compounds YbXCu4 (X = Ag, Cd, In, Mg,
Tl, Zn) to the predictions of the Anderson impurity model, calculated in the
non-crossing approximation (NCA). The crossover from the low temperature Fermi
liquid state to the high temperature local moment state is substantially slower
in the compounds than predicted by the NCA; this corresponds to the
''protracted screening'' recently predicted for the Anderson Lattice. We
present results for the dynamic susceptibility, measured through neutron
scattering experiments, to show that the deviations between theory and
experiment are not due to crystal field effects, and we present
x-ray-absorption fine-structure (XAFS) results that show the local crystal
structure around the X atoms is well ordered, so that the deviations probably
do not arise from Kondo Disorder. The deviations may correlate with the
background conduction electron density, as predicted for protracted screening.
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The quasiparticle interference of the spectroscopic imaging scanning
tunneling microscopy has been investigated for the surface states of the large
gap topological insulator Bi$_2$Te$_3$ through the T-matrix formalism. Both the
scalar potential scattering and the spin-orbit scattering on the warped
hexagonal isoenergy contour are considered. While backscatterings are forbidden
by time-reversal symmetry, other scatterings are allowed and exhibit strong
dependence on the spin configurations of the eigenfunctions at k points over
the isoenergy contour. The characteristic scattering wavevectors found in our
analysis agree well with recent experiment results.
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Stars in disks of spiral galaxies are usually assumed to remain roughly at
their birth radii. This assumption is built into decades of modelling of the
evolution of stellar populations in our own Galaxy and in external systems. We
present results from self-consistent high-resolution $N$-body + Smooth Particle
Hydrodynamics simulations of disk formation, in which stars migrate across
significant galactocentric distances due to resonant scattering with transient
spiral arms, while preserving their circular orbits. We investigate the
implications of such migrations for observed stellar populations. Radial
migration provides an explanation for the observed flatness and spread in the
age-metallicity relation and the relative lack of metal poor stars in the solar
neighborhood. The presence of radial migration also prompts rethinking of
interpretations of extra-galactic stellar population data, especially for
determinations of star formation histories.
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We establish proof-theoretic, constructive and coalgebraic foundations for
proof search in coinductive Horn clause theories. Operational semantics of
coinductive Horn clause resolution is cast in terms of coinductive uniform
proofs; its constructive content is exposed via soundness relative to an
intuitionistic first-order logic with recursion controlled by the later
modality; and soundness of both proof systems is proven relative to a novel
coalgebraic description of complete Herbrand models.
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The eavesdropping scheme proposed by W\'{o}jcik [Phys. Rev. Lett. {\bf
90},157901(2003)] on the ping-pong protocol [Phys. Rev. Lett. {\bf 89},
187902(2002)] is improved by constituting a new set of attack operations. The
improved scheme has a zero eavesdropping-induced channel loss and produces
perfect anticorrelation. Therefore, the eavesdropper Eve can safely attack all
the transmitted bits and the eavesdropping information gain can always exceed
the legitimate user's information gain in the whole domain of the quantum
channel transmission efficiency $\eta$, i.e., [0,100%]. This means that the
ping-pong protocol can be completely eavesdropped in its original version. But
the improvement of the ping-pong protocol security produced by W\'{o}jcik is
also suitable for our eavesdropping attack.
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We argue that quantum fluctuations of the phase of the order parameter may
strongly affect the electron density of states (DOS) in ultrathin
superconducting wires. We demonstrate that the effect of such fluctuations is
equivalent to that of a quantum dissipative environment formed by sound-like
plasma modes propagating along the wire. We derive a non-perturbative
expression for the local electron DOS in superconducting nanowires which fully
accounts for quantum phase fluctuations. At any non-zero temperature these
fluctuations smear out the square-root singularity in DOS near the
superconducting gap and generate quasiparticle states at subgap energies.
Furthermore, at sufficiently large values of the wire impedance this
singularity is suppressed down to $T=0$ in which case DOS tends to zero at
subgap energies and exhibits the power-law behavior above the gap. Our
predictions can be directly tested in tunneling experiments with
superconducting nanowires.
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Let $\Phi = \{\phi_e\}_{e\in E}$ be a finitely irreducible conformal graph
directed Markov system (CGDMS) with symbolic representation $E_A^{\infty}$ and
limit set $J$. Under a mild condition on the system, we give a multifractal
analysis of level sets of Birkhoff averages with respect to Hausdorff dimension
for a large family of functions. We then apply these results to a few examples
in the case of both $E$ finite and $E$ countably infinite.
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Quantum mechanics provides several methods to generate and securely
distribute private lists of numbers suitably correlated to solve the Three
Byzantine Generals Problem. So far, these methods are based on three-qutrit
singlet states, four-qubit entangled states, and three or two pairwise quantum
key distribution channels. Here we show that the problem can be solved using a
single qutrit. This scheme presents some advantages over previous schemes, and
emphasizes the specific role of qutrits in basic quantum information
processing.
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In the {\sc Test Cover} problem we are given a hypergraph $H=(V,
\mathcal{E})$ with $|V|=n, |\mathcal{E}|=m$, and we assume that $\mathcal{E}$
is a test cover, i.e. for every pair of vertices $x_i, x_j$, there exists an
edge $e \in \mathcal{E}$ such that $|{x_i,x_j}\cap e|=1$. The objective is to
find a minimum subset of $\mathcal{E}$ which is a test cover. The problem is
used for identification across many areas, and is NP-complete. From a
parameterized complexity standpoint, many natural parameterizations of {\sc
Test Cover} are either $W[1]$-complete or have no polynomial kernel unless
$coNP\subseteq NP/poly$, and thus are unlikely to be solveable efficiently.
However, in practice the size of the edges is often bounded. In this paper we
study the parameterized complexity of {\sc Test-$r$-Cover}, the restriction of
{\sc Test Cover} in which each edge contains at most $r \ge 2$ vertices. In
contrast to the unbounded case, we show that the following below-bound
parameterizations of {\sc Test-$r$-Cover} are fixed-parameter tractable with a
polynomial kernel: (1) Decide whether there exists a test cover of size $n-k$,
and (2) decide whether there exists a test cover of size $m-k$, where $k$ is
the parameter. In addition, we prove a new lower bound $\lceil
\frac{2(n-1)}{r+1} \rceil$ on the minimum size of a test cover when the size of
each edge is bounded by $r$. {\sc Test-$r$-Cover} parameterized above this
bound is unlikely to be fixed-parameter tractable; in fact, we show that it is
para-NP-complete, as it is NP-hard to decide whether an instance of {\sc
Test-$r$-Cover} has a test cover of size exactly $\frac{2(n-1)}{r+1}$.
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Humans can robustly recognize and localize objects by integrating visual and
auditory cues. While machines are able to do the same now with images, less
work has been done with sounds. This work develops an approach for dense
semantic labelling of sound-making objects, purely based on binaural sounds. We
propose a novel sensor setup and record a new audio-visual dataset of street
scenes with eight professional binaural microphones and a 360 degree camera.
The co-existence of visual and audio cues is leveraged for supervision
transfer. In particular, we employ a cross-modal distillation framework that
consists of a vision `teacher' method and a sound `student' method -- the
student method is trained to generate the same results as the teacher method.
This way, the auditory system can be trained without using human annotations.
We also propose two auxiliary tasks namely, a) a novel task on Spatial Sound
Super-resolution to increase the spatial resolution of sounds, and b) dense
depth prediction of the scene. We then formulate the three tasks into one
end-to-end trainable multi-tasking network aiming to boost the overall
performance. Experimental results on the dataset show that 1) our method
achieves promising results for semantic prediction and the two auxiliary tasks;
and 2) the three tasks are mutually beneficial -- training them together
achieves the best performance and 3) the number and orientations of microphones
are both important. The data and code will be released to facilitate the
research in this new direction.
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Identification of the type of communication technology and/or modulation
scheme based on detected radio signal are challenging problems encountered in a
variety of applications including spectrum allocation and radio interference
mitigation. They are rendered difficult due to a growing number of emitter
types and varied effects of real-world channels upon the radio signal. Existing
spectrum monitoring techniques are capable of acquiring massive amounts of
radio and real-time spectrum data using compact sensors deployed in a variety
of settings. However, state-of-the-art methods that use such data to classify
emitter types and detect communication schemes struggle to achieve required
levels of accuracy at a computational efficiency that would allow their
implementation on low-cost computational platforms. In this paper, we present a
learning framework based on an LSTM denoising auto-encoder designed to
automatically extract stable and robust features from noisy radio signals, and
infer modulation or technology type using the learned features. The algorithm
utilizes a compact neural network architecture readily implemented on a
low-cost computational platform while exceeding state-of-the-art accuracy.
Results on realistic synthetic as well as over-the-air radio data demonstrate
that the proposed framework reliably and efficiently classifies received radio
signals, often demonstrating superior performance compared to state-of-the-art
methods.
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One major task of spoken language understanding (SLU) in modern personal
assistants is to extract semantic concepts from an utterance, called slot
filling. Although existing slot filling models attempted to improve extracting
new concepts that are not seen in training data, the performance in practice is
still not satisfied. Recent research collected question and answer annotated
data to learn what is unknown and should be asked, yet not practically scalable
due to the heavy data collection effort. In this paper, we incorporate
softmax-based slot filling neural architectures to model the sequence
uncertainty without question supervision. We design a Dirichlet Prior RNN to
model high-order uncertainty by degenerating as softmax layer for RNN model
training. To further enhance the uncertainty modeling robustness, we propose a
novel multi-task training to calibrate the Dirichlet concentration parameters.
We collect unseen concepts to create two test datasets from SLU benchmark
datasets Snips and ATIS. On these two and another existing Concept Learning
benchmark datasets, we show that our approach significantly outperforms
state-of-the-art approaches by up to 8.18%. Our method is generic and can be
applied to any RNN or Transformer based slot filling models with a softmax
layer.
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We explore the Mellin representation of correlation functions in conformal
field theories in the weak coupling regime. We provide a complete proof for a
set of Feynman rules to write the Mellin amplitude for a general tree level
Feynman diagram involving only scalar operators. We find a factorised form
involving beta functions associated to the propagators, similar to tree level
Feynman rules in momentum space for ordinary QFTs. We also briefly consider the
case where a generic scalar perturbation of the free CFT breaks conformal
invariance. Mellin space still has some utility and one can consider
non-conformal Mellin representations. In this context, we find that the beta
function corresponding to conformal propagator uplifts to a hypergeometric
function.
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Being light-weight and cost-effective, IR-based approaches for bug
localization have shown promise in finding software bugs. However, the accuracy
of these approaches heavily depends on their used bug reports. A significant
number of bug reports contain only plain natural language texts. According to
existing studies, IR-based approaches cannot perform well when they use these
bug reports as search queries. On the other hand, there is a piece of recent
evidence that suggests that even these natural language-only reports contain
enough good keywords that could help localize the bugs successfully. On one
hand, these findings suggest that natural language-only bug reports might be a
sufficient source for good query keywords. On the other hand, they cast serious
doubt on the query selection practices in the IR-based bug localization. In
this article, we attempted to clear the sky on this aspect by conducting an
in-depth empirical study that critically examines the state-of-the-art query
selection practices in IR-based bug localization. In particular, we use a
dataset of 2,320 bug reports, employ ten existing approaches from the
literature, exploit the Genetic Algorithm-based approach to construct optimal,
near-optimal search queries from these bug reports, and then answer three
research questions. We confirmed that the state-of-the-art query construction
approaches are indeed not sufficient for constructing appropriate queries (for
bug localization) from certain natural language-only bug reports although they
contain such queries. We also demonstrate that optimal queries and non-optimal
queries chosen from bug report texts are significantly different in terms of
several keyword characteristics, which has led us to actionable insights.
Furthermore, we demonstrate 27%--34% improvement in the performance of
non-optimal queries through the application of our actionable insights to them.
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In this paper, we will provide a method to compute the density of tautologies
among the set of well-formed formulae consisting of $m$ variables, the negation
symbol and the implication symbol; which has a possibility to be applied for
other logical systems. This paper contains computational numerical values of
the density of tautologies for two, three, and four variable cases. Also, for
certain quadratic systems, we will build a theory of the $s$-cut concept to
make a memory-time trade-off when we compute the ratio by brute-force counting,
and discover a fundamental relation between generating functions' values on the
singularity point and ratios of coefficients, which can be understood as
another interpretation of the Szeg\H{o} lemma for such quadratic systems. With
this relation, we will provide an asymptotic lower bound
$m^{-1}-(7/4)m^{-3/2}+O(m^{-2})$ of the density of tautologies in the logic
system with $m$ variables, the negation, and the implication, as $m$ goes to
the infinity
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Photometric classification of supernovae (SNe) is imperative as recent and
upcoming optical time-domain surveys, such as the Large Synoptic Survey
Telescope (LSST), overwhelm the available resources for spectrosopic follow-up.
Here we develop a range of light curve classification pipelines, trained on 518
spectroscopically-classified SNe from the Pan-STARRS1 Medium-Deep Survey
(PS1-MDS): 357 Type Ia, 93 Type II, 25 Type IIn, 21 Type Ibc, and 17 Type I
SLSNe. We present a new parametric analytical model that can accommodate a
broad range of SN light curve morphologies, including those with a plateau, and
fit this model to data in four PS1 filters (griz). We test a number of feature
extraction methods, data augmentation strategies, and machine learning
algorithms to predict the class of each SN. Our best pipelines result in 90%
average accuracy, 70% average purity, and 80% average completeness for all SN
classes, with the highest success rates for Type Ia SNe and SLSNe and the
lowest for Type Ibc SNe. Despite the greater complexity of our classification
scheme, the purity of our Type Ia SN classification, 95%, is on par with
methods developed specifically for Type Ia versus non-Type Ia binary
classification. As the first of its kind, this study serves as a guide to
developing and training classification algorithms for a wide range of SN types
with a purely empirical training set, particularly one that is similar in its
characteristics to the expected LSST main survey strategy. Future work will
implement this classification pipeline on ~3000 PS1/MDS light curves that lack
spectroscopic classification.
|
I present an extension of the phase distance correlation periodogram to
two-dimensional astrometric data. I show that this technique is more suitable
than previously proposed approaches to detect eccentric Keplerian orbits, and
that it overcomes the inherent bias of the joint periodogram to circular
orbits. This new technique might prove to be essential in the context of future
astrometric space missions such as Theia.
|
We present observations of the giant HII region complex N159 in the LMC using
IRAC on the {\it Spitzer Space Telescope}. One of the two objects previously
identified as protostars in N159 has an SED consistent with classification as a
Class I young stellar object (YSO) and the other is probably a Class I YSO as
well, making these two stars the youngest stars known outside the Milky Way. We
identify two other sources that may also be Class I YSOs. One component,
N159AN, is completely hidden at optical wavelengths, but is very prominent in
the infrared. The integrated luminosity of the entire complex is L $\approx
9\times10^6$L$_{\odot}$, consistent with the observed radio emission assuming a
normal Galactic initial mass function (IMF). There is no evidence for a red
supergiant population indicative of an older burst of star formation. The N159
complex is 50 pc in diameter, larger in physical size than typical HII regions
in the Milky Way with comparable luminosity. We argue that all of the
individual components are related in their star formation history. The
morphology of the region is consistent with a wind blown bubble $\approx
1-2Myr-old that has initiated star formation now taking place at the rim. Other
than its large physical size, star formation in N159 appears to be
indistinguishable from star formation in the Milky Way.
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Statistical models that involve latent Markovian state processes have become
immensely popular tools for analysing time series and other sequential data.
However, the plethora of model formulations, the inconsistent use of
terminology, and the various inferential approaches and software packages can
be overwhelming to practitioners, especially when they are new to this area.
With this review-like paper, we thus aim to provide guidance for both
statisticians and practitioners working with latent Markov models by offering a
unifying view on what otherwise are often considered separate model classes,
from hidden Markov models over state-space models to Markov-modulated Poisson
processes. In particular, we provide a roadmap for identifying a suitable
latent Markov model formulation given the data to be analysed. Furthermore, we
emphasise that it is key to applied work with any of these model classes to
understand how recursive techniques exploiting the models' dependence structure
can be used for inference. The R package LaMa adapts this unified view and
provides an easy-to-use framework for very fast (C++ based) evaluation of the
likelihood of any of the models discussed in this paper, allowing users to
tailor a latent Markov model to their data using a Lego-type approach.
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Quasi-free photoproduction of eta-mesons from the deuteron has been measured
at the tagged photon facility of the Mainz microtron MAMI with the photon
spectrometer TAPS for incident photon energies from the production threshold at
630 MeV up to 820 MeV. In a fully exclusive measurement eta-mesons and recoil
nucleons were detected in coincidence. At incident photon energies above the
production threshold on the free nucleon, where final state interaction effects
are negligible, an almost constant ratio of sigma(n)/sigma(p)=0.66+/-0.10 was
found. At lower incident photon energies the ratio rises due to re-scattering
effects. The average ratio agrees with the value extracted from a comparison of
the inclusive d(gamma,eta)X cross section to the free proton cross section via
a participant - spectator model for the deuteron cross section
(sigma(n)/sigma(p)=0.67+/-0.07). The angular dependence of the ratio agrees
with the expected small deviation of neutron and proton cross section from
isotropy due to the influence of the D13(1520) resonance. The energy dependence
of the ratio in the excitation energy range of the S11(1535) resonance
disfavors model predictions which try to explain this resonance as K-Sigma
bound state.
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In this paper we explore some categorical results of 2-crossed module of
commutative algebras extending work of Porter in [18]. We also show that the
forgetful functor from the category of 2-crossed modules to the category of
k-algebras, taking {L, M, P, \partial_2, \partial_1} to the base algebra P, is
fibred and cofibred considering the pullback (coinduced) and induced 2-crossed
modules constructions, respectively. Also we consider free 2- crossed modules
as an application of induced 2-crossed modules.
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We discuss in detail different future long baseline neutrino oscillation
setups and we show the remarkable potential for very precise measurements of
mass splittings and mixing angles. Furthermore it will be possible to make
precise tests of coherent forward scattering and MSW effects, which allow to
determine the sign of $\Delta m^2$. Finally strong limits or measurements of
leptonic CP violation will be possible, which is very interesting since it is
most likely connected to the baryon asymmetry of the universe.
|
The mean ground state occupation number and condensate fluctuations of
interacting and non-interacting Bose gases confined in a harmonic trap are
considered by using a canonical ensemble approach. To obtain the mean ground
state occupation number and the condensate fluctuations, an analytical
description for the probability distribution function of the condensate is
provided directly starting from the analysis of the partition function of the
system. For the ideal Bose gas, the probability distribution function is found
to be a Gaussian one for the case of the harmonic trap. For the interacting
Bose gas, using a unified approach the condensate fluctuations are calculated
based on the lowest-order perturbation method and on Bogoliubov theory. It is
found that the condensate fluctuations based on the lowest-order perturbation
theory follow the law $<delta^{2}N_{\bf 0}>\sim N$, while the fluctuations
based on Bogoliubov theory behave as $N^{4/3}$.
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This paper has two parts, on Baumslag-Solitar groups and on general G-trees.
In the first part we establish bounds for stable commutator length (scl) in
Baumslag-Solitar groups. For a certain class of elements, we further show that
scl is computable and takes rational values. We also determine exactly which of
these elements admit extremal surfaces.
In the second part we establish a universal lower bound of 1/12 for scl of
suitable elements of any group acting on a tree. This is achieved by
constructing efficient quasimorphisms. Calculations in the group BS(2,3) show
that this is the best possible universal bound, thus answering a question of
Calegari and Fujiwara. We also establish scl bounds for acylindrical tree
actions.
Returning to Baumslag-Solitar groups, we show that their scl spectra have a
uniform gap: no element has scl in the interval (0, 1/12).
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This is a treatise on finite point configurations spanning a fixed volume to
be found in a single color-class of an arbitrary finite (measurable) coloring
of the Euclidean space $\mathbb{R}^n$, or in a single large measurable subset
$A\subseteq\mathbb{R}^n$. More specifically, we study vertex-sets of simplices,
rectangular boxes, and parallelotopes, attempting to make progress on several
open problems posed in the 1970s and the 1980s. As one of the highlights, we
give the negative answer to a question of Erd\H{o}s and Graham, by coloring the
Euclidean plane $\mathbb{R}^2$ in $25$ colors without creating monochromatic
rectangles of unit area. More generally, we construct a finite coloring of the
Euclidean space $\mathbb{R}^n$ such that no color-class contains the $2^m$
vertices of any (possibly rotated) $m$-dimensional rectangular box of volume
$1$. A positive result is still possible if rectangular boxes of merely
sufficiently large volumes are sought in a single color-class of a finite
measurable coloring of $\mathbb{R}^n$, and we establish it under an additional
assumption $n\geq m+1$. Also, motivated by a question of Graham on reasonable
bounds in his result on monochromatic axes-aligned right-angled $m$-dimensional
simplices, we establish its measurable coloring and density variants with
polylogarithmic bounds, again in dimensions $n\geq m+1$. Next, we generalize a
result of Erd\H{o}s and Mauldin, by constructing an infinite measure set
$A\subseteq\mathbb{R}^n$ such that every $n$-parallelotope with vertices in $A$
has volume strictly smaller than $1$. Finally, some results complementing the
literature on isometric embeddings of hypercube graphs and on the hyperbolic
analogue of the Hadwiger--Nelson problem also follow as byproducts of our
approaches.
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It has recently been claimed that analysis of Greenwich sunspot data over 120
years reveals that sunspot activity clusters around two longitudes separated by
180 degrees (``active longitudes'') with clearly defined differential rotation
during activity cycles.In the present work we extend this critical examination
of methodology to the actual Greenwich sunspot data and also consider newly
proposed methods of analysis claiming to confirm the original identification of
active longitudes. Our analysis revealed that values obtained for the
parameters of differential rotation are not stable across different methods of
analysis proposed to track persistent active longitudes. Also, despite a very
thorough search in parameter space, we were unable to reproduce results
claiming to reveal the century-persistent active longitudes. We can therefore
say that strong and well substantiated evidence for an essential and
century-scale persistent nonaxisymmetry in the sunspot distribution does not
exist.
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We present a new study of the Virgo Cluster galaxies M86, M84, NGC 4338, and
NGC 4438 using a mosaic of five separate pointings with XMM-Newton. Our
observations allow for robust measurements of the temperature and metallicity
structure of each galaxy along with the entire ~ 1 degree region between these
galaxies. When combined with multiwavelength observations, the data suggest
that all four of these galaxies are undergoing ram pressure stripping by the
Intracluster Medium (ICM). The manner in which the stripped gas trailing the
galaxies interacts with the ICM, however, is observably distinct. Consistent
with previous observations, M86 is observed to have a long tail of ~ 1 keV gas
trailing to the north-west for distances of ~ 100-150 kpc. However, a new site
of ~ 0.6 keV thermal emission is observed to span to the east of M86 in the
direction of the disturbed spiral galaxy NGC 4438. This region is spatially
coincident with filaments of H-alpha emission, likely originating in a recent
collision between the two galaxies. We also resolve the thermodynamic structure
of stripped ~ 0.6 keV gas to the south of M84, suggesting that this galaxy is
undergoing both AGN feedback and ram pressure stripping simultaneously. These
four sites of stripped X-ray gas demonstrate that the nature of ram pressure
stripping can vary significantly from site to site.
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Arikan's polar codes are capable of achieving the Shannon's capacity at a low
encoding and decoding complexity, while inherently supporting rate adaptation.
By virtue of these attractive features, polar codes have provided fierce
competition to both the turbo as well as the Low Density Parity Check (LDPC)
codes, making its way into the 5G New Radio (NR). Realizing the significance of
polar codes, in this paper we provide a comprehensive survey of polar codes,
highlighting the major milestones achieved in the last decade. Furthermore, we
also provide tutorial insights into the polar encoder, decoders as well as the
code construction methods. We also extend our discussions to quantum polar
codes with an emphasis on the underlying quantum-to-classical isomorphism and
the syndrome-based quantum polar codes.
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In this paper, we study weakly classical 1-absorbing prime submodules of a
nonzero unital module $M$ over a commutative ring $R$ having a nonzero
identity. A proper submodule $N$ of $M$ is said to be a weakly classical
1-absorbing prime submodule, if for each $m\in M$ and nonunits $a,b,c\in R,$
$0\neq abcm\in N$ implies that $abm\in N$ or $cm\in N$. We give various
examples and properties of weakly classical 1-absorbing prime submodules. Also,
we investiage the weakly classical 1-absorbing prime submodules of tensor
product $F\otimes M$ of a (faithfully) flat $R$-module $F$ and any $R$-module
$M.$ Also, we prove that if every proper submodule of an $R$-module $M$ is
weakly classical 1-absorbing prime, then $Jac(R)^{3}M=0$. In terms of this
result, we characterize modules over local rings in which every proper
submodule is weakly classical 1-absorbing prime.
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Using an analogy between the Brauer groups in algebra and the Whitehead
groups in topology, we first use methods of algebraic K-theory to give a
natural definition of Brauer spectra for commutative rings, such that their
homotopy groups are given by the Brauer group, the Picard group and the group
of units. Then, in the context of structured ring spectra, the same idea leads
to two-fold non-connected deloopings of the spectra of units.
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The measurement of the azimuthal-correlation function of prompt D mesons with
charged particles in pp collisions at $\sqrt{s}$ = 5.02 TeV and p-Pb collisions
at $\sqrt{s_{\rm NN}}$ = 5.02 TeV with the ALICE detector at the LHC is
reported. The D$^{\rm 0}$, D$^{\rm +}$, and D$^{\rm *+}$ mesons, together with
their charge conjugates, were reconstructed at midrapidity in the transverse
momentum interval 3 < $p_{\rm T}$ < 24 GeV/c and correlated with charged
particles having $p_{\rm T}$ > 0.3 GeV/c and pseudorapidity $|\eta| <$ 0.8. The
properties of the correlation peaks appearing in the near- and away-side
regions (for $\Delta \varphi \approx$ 0 and $\Delta \varphi \approx \pi$,
respectively) were extracted via a fit to the azimuthal correlation functions.
The shape of the correlation functions and the near- and away-side peak
features are found to be consistent in pp and p-Pb collisions, showing no
modifications due to nuclear effects within uncertainties. The results are
compared with predictions from Monte Carlo simulations performed with the
PYTHIA, POWHEG+PYTHIA, HERWIG, and EPOS 3 event generators.
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Designing complex physical systems, including photonic structures, is
typically a tedious trial-and-error process that requires extensive simulations
with iterative sweeps in multi-dimensional parameter space. To circumvent this
conventional approach and substantially expedite the discovery and development
of photonic structures, here we develop a framework leveraging both a deep
generative model and a modified evolution strategy to automate the inverse
design of engineered nanophotonic materials. The capacity of the proposed
methodology is tested through the application to a case study, where
metasurfaces in either continuous or discrete topologies are generated in
response to customer-defined spectra at the input. Through a variational
autoencoder, all potential patterns of unit nanostructures are encoded into a
continuous latent space. An evolution strategy is applied to vectors in the
latent space to identify an optimized vector whose nanostructure pattern
fulfills the design objective. The evaluation shows that over 95% accuracy can
be achieved for all the unit patterns of the nanostructure tested. Our scheme
requires no prior knowledge of the geometry of the nanostructure, and, in
principle, allows joint optimization of the dimensional parameters. As such,
our work represents an efficient, on-demand, and automated approach for the
inverse design of photonic structures with subwavelength features.
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We analyze theoretically the interplay between the torsional and the
rotational motion of an aligned biphenyl-like molecule. To do so, we consider a
transition between two electronic states with different internal torsional
potentials, induced by means of a resonant laser pulse. The change in the
internal torsional potential provokes the motion of the torsional wavepacket in
the excited electronic state, modifying the structure of the molecule, and
hence, its inertia tensor. We find that this process has a strong impact on the
rotational wave function, displaying different behavior depending on the
electronic states involved and their associated torsional potentials. We
describe the dynamics of the system by considering the degree of alignment and
the expectations values of the angular momentum operators for the overall
rotation of the molecule.
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We present a neural network architecture to predict a point in color space
from the sequence of characters in the color's name. Using large scale
color--name pairs obtained from an online color design forum, we evaluate our
model on a "color Turing test" and find that, given a name, the colors
predicted by our model are preferred by annotators to color names created by
humans. Our datasets and demo system are available online at colorlab.us.
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Thanks to the wide range of features offered by web browsers, modern websites
include various types of content such as JavaScript and CSS in order to create
interactive user interfaces. Browser vendors also provided extensions to
enhance web browsers with additional useful capabilities that are not
necessarily maintained or supported by default.
However, included content can introduce security risks to users of these
websites, unbeknownst to both website operators and users. In addition, the
browser's interpretation of the resource URLs may be very different from how
the web server resolves the URL to determine which resource should be returned
to the browser. The URL may not correspond to an actual server-side file system
structure at all, or the web server may internally rewrite parts of the URL.
This semantic disconnect between web browsers and web servers in interpreting
relative paths (path confusion) could be exploited by Relative Path Overwrite
(RPO). On the other hand, even tough extensions provide useful additional
functionality for web browsers, they are also an increasingly popular vector
for attacks. Due to the high degree of privilege extensions can hold,
extensions have been abused to inject advertisements into web pages that divert
revenue from content publishers and potentially expose users to malware.
In this thesis, I propose novel research into understanding and mitigating
the security risks of content inclusion in web browsers to protect website
publishers as well as their users.
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Using density functional tight-binding method, we studied the elastic
properties, deformation and failure of armchair (AC) and zigzag (ZZ)
phosphorene nano tubes (PNTs) under uniaxial tensile strain. We found that the
deformation and failure of PNTs are very anisotropic. For ZZ PNTs, three
deformation phases are recognized: The primary linear elastic phase, which is
associated with the interactions between the neighboring puckers, succeeded by
the bond rotation phase, where the puckered configuration of phosphorene is
smoothed via bond rotation, and lastly the bond elongation phase, where the P-P
bonds are directly stretched up to the maximally allowed limit and the failure
is initiated by the rupture of the most stretched bonds.
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One of important questions concerning particles which compose the Dark Matter
(DM) is their average speed. We consider the model of relativistic weakly
interacting massive particles and try to impose an upper bound on their actual
and past warmness through the analysis of density perturbations and comparison
with the LSS data. It is assumed that the DM can be described by the recently
invented model of reduced relativistic gas (RRG). The equation of state of the
RRG model is closely reproducing the one of the Maxwell distribution, while
being much simpler. This advantage of the RRG model makes our analysis very
efficient. As a result we arrive at the rigid and model-independent bound for
the DM warmness without using the standard (much more sophisticated) approach
based on the Einstein-Boltzmann system of equations.
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X-ray as well as electron diffraction are powerful tools for structure
determination of molecules. Studies on randomly oriented molecules in the
gas-phase address cases in which molecular crystals cannot be generated or the
interaction-free molecular structure is to be addressed. Such studies usually
yield partial geometrical information, such as interatomic distances. Here, we
present a complementary approach, which allows obtaining insight to the
structure, handedness and even detailed geometrical features of molecules in
the gas phase. Our approach combines Coulomb explosion imaging, the information
that is encoded in the molecular frame diffraction pattern of core-shell
photoelectrons and ab initio computations. Using a loop-like analysis scheme we
are able to deduce specific molecular coordinates with sensitivity even to the
handedness of chiral molecules and the positions of individual atoms, as, e.g.,
protons.
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We examine the impact of the combination of a static electric field and a non
resonant linearly polarized laser field on an asymmetric top molecule. Within
the rigid rotor approximation, we analyze the symmetries of the Hamiltonian for
all possible field configurations. For each irreducible representation, the
Schr\"odinger equation is solved by a basis set expansion in terms of a linear
combination of Wigner functions respecting the corresponding symmetries, which
allows us to distinguish avoided crossings from genuine ones. Using the
fluorobenzene and pyridazine molecules as prototypes, the rotational spectra
and properties are analyzed for experimentally accessible static field
strengths and laser intensities. Results for energy shifts, orientation,
alignment and hybridization of the angular motion are presented as the field
parameters are varied. We demonstrate that a proper selection of the fields
gives rise to a constrained rotational motion in the three Euler angles, the
wave function being oriented along the electrostatic field direction, and
aligned in the other two angles.
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This chapter focuses on the self-driving technology from a control
perspective and investigates the control strategies used in autonomous vehicles
and advanced driver-assistance systems from both theoretical and practical
viewpoints. First, we introduce the self-driving technology as a whole,
including perception, planning and control techniques required for
accomplishing the challenging task of autonomous driving. We then dwell upon
each of these operations to explain their role in the autonomous system
architecture, with a prime focus on control strategies. The core portion of
this chapter commences with detailed mathematical modeling of autonomous
vehicles followed by a comprehensive discussion on control strategies. The
chapter covers longitudinal as well as lateral control strategies for
autonomous vehicles with coupled and de-coupled control schemes. We as well
discuss some of the machine learning techniques applied to autonomous vehicle
control task. Finally, we briefly summarize some of the research works that our
team has carried out at the Autonomous Systems Lab and conclude the chapter
with a few thoughtful remarks.
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The example provided in the comment [arXiv:0803.2241] concerns a situation
where the system is initially at negative temperature. It is known that in such
cases the Law of Entropy Decrease holds. Nevertheless, this does not challenge
the validity of the Second Law of Thermodynamics.
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The problem of unicellular-multicellular transition is one of the main issues
that is discussing in evolutionary biology. In [1] the fitness of a colony of
cells is considered in terms of its two basic components, viability and
fecundity. Intrinsic trade-off function of each cell defines a type of cell. We
elaborate models providing in [1]. Assuming that all intrinsic trade-off
functions are linear, we construct a model with different cell types and show
that the differentiation of these types tends to full specialization. In
addition, we attempt to consider the fact that environmental factors influence
on the fitness of the colony. Thus, we introduce an energy restriction to the
model and show that in optimum we get situations in which there exists a set of
states, each of them allowing colony to achieve the same maximum level of
fitness. In some states arbitrary chosen cell may be specialized, in some -
unspecialized, but fecundity and viability of each cell belong to limited
ranges (which are unique for each cell). It is worth pointing out that the
models from [1] are not robust. We try to overcome this disadvantage.
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This paper presents a slot antenna array with a reconfigurable radar cross
section (RCS). The antenna system is formed by combining a liquid absorber with
a 2*2 slot antenna array. The liquid absorber consists of a polymethyl
methacrylate (PMMA) container, a 45% ethanol layer, and a metal ground,which is
attached to the surface of the slot antenna array. The incident wave can be
absorbed by the absorber rather than reflected in other directions when the
PMMA container is filled with ethanol, which reduces the monostatic and
bistatic RCS. Thus the RCS of the antenna can be changed by injecting and
extracting ethanol while the antenna's radiation performance in terms of
bandwidth, radiation patterns and gain is well sustained. In a complex
communication system, this can be used to switch between detection and stealth
mode. The mechanism of the absorber is investigated. The simulated results show
that the antenna with this absorber has monostatic and bistatic RCS reduction
bands from 2.0 GHz to 18.0 GHz, a maximum RCS reduction of 35 dB with an
average RCS reduction of 13.28 dB. The antenna's operating band is 100 MHz.
Without ethanol, the antenna has a realized gain of 12.1 dBi, and it drops by 2
dB when the lossy ethanol is injected. The measured results agree well with the
simulated ones.
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In recent years, multimodal large language models (MLLMs) have shown strong
potential in real-world applications. They are developing rapidly due to their
remarkable ability to comprehend multimodal information and their inherent
powerful cognitive and reasoning capabilities. Among MLLMs, vision language
models (VLM) stand out for their ability to understand vision information.
However, the scaling trend of VLMs under the current mainstream paradigm has
not been extensively studied. Whether we can achieve better performance by
training even larger models is still unclear. To address this issue, we
conducted experiments on the pretraining stage of MLLMs. We conduct our
experiment using different encoder sizes and large language model (LLM) sizes.
Our findings indicate that merely increasing the size of encoders does not
necessarily enhance the performance of VLMs. Moreover, we analyzed the effects
of LLM backbone parameter size and data quality on the pretraining outcomes.
Additionally, we explored the differences in scaling laws between LLMs and
VLMs.
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We analyze signatures of the dynamical quantum phase transitions in physical
observables. In particular, we show that both the expectation value and various
out of time order correlation functions of the finite length product or string
operators develop cusp singularities following quench protocols, which become
sharper and sharper as the string length increases. We illustrated our ideas
analyzing both integrable and nonintegrable one-dimensional Ising models
showing that these transitions are robust both to the details of the model and
to the choice of the initial state.
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The similarity of the absolute luminosity profiles of Type Ia supernovae
(SNIe), as one kind of distance indicator, has led their use in extragalactic
astronomy as secondary standard candles. In general, the empirical relationship
of SNIa on the absolute peak magnitude $M_{\rm B}$ is calibrated by Cepheid
variables in the near distance scale and directly extrapolated to much farther
distances. Two main problems arise. First, their calibration, in particular the
determination of $M_{\rm B}$, depends on the empirical relationship of Cepheid
variables, which suffers from various uncertainties. The second is related to
the homogeneity of SNIa in their true $M_{\rm B}$, which is known to be poor in
different environments. The observed GW signal of the coalescence of compact
binary systems and their electromagnetic counterparts provide the novel and
model-independent way to address these two problems. In the era of
second-generation GW detectors, the low-redshift GW sources provide a novel
method to calibrate the empirical relationship of SNIa, using their
self-calibrated distances. Here, we use the event GW170817 to calibrate the
empirical relationship in different low redshift ranges, and find that the
calibration results are consistent with the ones derived from the Cepheid
variables. Moreover, the uncertainties of $M_{\rm B}$ in both methods are also
comparable. By the observations of third-generation GW detectors, GW sources
can also be used to measure the values of $M_{\rm B}$ for the high-redshift
SNIe, which provides a unique opportunity to study the dependence of $M_{\rm
B}$ on the local environment, strength of gravity, and the intrinsic properties
of the explosion, in addition to test the homogeneity of standard candles. We
find that the uncertainties of $M_{\rm B}$ in both high and low redshifts are
more than one order of magnitude smaller than the current accuracy.
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Two candidates for "almost-invariant" toroidal surfaces passing through
magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost
surfaces, use families of periodic pseudo-orbits (i.e. paths for which the
action is not exactly extremal). QFMin pseudo-orbits, which are
coordinate-dependent, are field lines obtained from a modified magnetic field,
and ghost-surface pseudo-orbits are obtained by displacing closed field lines
in the direction of steepest descent of magnetic action, $\oint
\vec{A}\cdot\mathbf{dl}$. A generalized Hamiltonian definition of ghost
surfaces is given and specialized to the usual Lagrangian definition. A
modified Hamilton's Principle is introduced that allows the use of Lagrangian
integration for calculation of the QFMin pseudo-orbits. Numerical calculations
show QFMin and Lagrangian ghost surfaces give very similar results for a
chaotic magnetic field perturbed from an integrable case, and this is explained
using a perturbative construction of an auxiliary poloidal angle for which
QFMin and Lagrangian ghost surfaces are the same up to second order. While
presented in the context of 3-dimensional magnetic field line systems, the
concepts are applicable to defining almost-invariant tori in other $1{1/2}$
degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.
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We calculate the neutrino energy emission rate due to singlet-state pairing
of protons in the neutron star cores taking into account the relativistic
correction to the non-relativistic rate. The non-relativistic rate is
numerically small, and the relativistic correction appears to be about 10 -- 50
times larger. It plays thus the leading role, reducing great difference between
the neutrino emissions due to pairing of protons and neutrons. The results are
important for simulations of neutron star cooling.
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Inequalities are key tools to prove FDR control of a multiple test. The
present paper studies upper and lower bounds for the FDR under various
dependence structures of p-values, namely independence, reverse martingale
dependence and positive regression dependence on the subset (PRDS) of true null
hypotheses. The inequalities are based on exact finite sample formulas which
are also of interest for independent uniformly distributed p-values under the
null. As applications the asymptotic worst case FDR of step up and step down
tests coming from an non-decreasing rejection curve is established. In
addition, new step up tests are established and necessary conditions for the
FDR control are discussed. The reverse martingale models yield sharper FDR
results than the PRDS models. Already in certain multivariate normal dependence
models the familywise error rate of the Benjamini Hochberg step up test can be
different from the desired level alpha. The second part of the paper is devoted
to adaptive step up tests under dependence. The well-known Storey estimator is
modified so that the corresponding step up test has finite sample control for
various block wise dependent p-values. These results may be applied to
dependent genome data. Within each chromosome the p-values may be reverse
martingale dependent while the chromosomes are independent.
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The Dynamical-gap formation in Weyl semimetals modulated by intense
elliptically polarized light is addressed through the solution of the
time-dependent Schr\"odinger equation for the Weyl Hamiltonian via the Floquet
theorem. The time-dependent wave functions and the quasi-energy spectrum of the
two-dimensional Weyl Hamiltonian under normal incidence of elliptically
polarized electromagnetic waves are obtained using a non-perturbative approach.
In it, the Weyl equation is reduced to an ordinary second-order differential
Mathieu equation. It is shown that the stability conditions of the Mathieu
functions are directly inherited by the wave function resulting in a
quasiparticle spectrum consisting of bands and gaps determined by dynamical
diffraction and resonance conditions between the electron and the
electromagnetic wave. Estimations of the electromagnetic field intensity and
frequency, as well as the magnitude of the generated gap are obtained for the
$8-Pmmn$ phase of borophene. We provide with a simple method that enables to
predict the formation of dynamical-gaps of unstable wave functions and their
magnitudes. This method can readily be adapted to other Weyl semimetals.
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The use of photonic crystal and negative refractive index materials is known
to improve resolution of optical microscopy and lithography devices down to 80
nm level. Here we demonstrate that utilization of well-known digital image
recovery techniques allows us to further improve resolution of optical
microscope down to 30 nm level. Our microscope is based on a flat dielectric
mirror deposited onto an array of nanoholes in thin gold film. This
two-dimensional photonic crystal mirror may have either positive or negative
effective refractive index as perceived by surface plasmon polartions in the
visible frequency range. The optical images formed by the mirror are enhanced
using simple digital filters.
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In this paper we extend earlier results regarding the effects of the lower
layer of the ocean (below the thermocline) on the baroclinic instability within
the upper layer (above the thermocline). We confront quasigeostrophic
baroclinic instability properties of a 2.5-layer model with those of a 3-layer
model with a very thick deep layer, which has been shown to predict spectral
instability for basic state parameters for which the 2.5-layer model predicts
nonlinear stability. We compute and compare maximum normal-mode perturbation
growth rates, as well as rigorous upper bounds on the nonlinear growth of
perturbations to unstable basic states, paying particular attention to the
region of basic state parameters where the stability properties of the 2.5- and
3-layer model differ substantially. We found that normal-mode perturbation
growth rates in the 3-layer model tend to maximize in this region. We also
found that the size of state space available for eddy-amplitude growth tends to
minimize in this same region. Moreover, we found that for a large spread of
parameter values in this region the latter size reduces to only a small
fraction of the total enstrophy of the system, thereby allowing us to make
assessments of the significance of the instabilities.
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A growing number of researchers are conducting randomized experiments to
analyze causal relationships in network settings where units influence one
another. A dominant methodology for analyzing these experiments is
design-based, leveraging random treatment assignments as the basis for
inference. In this paper, we generalize this design-based approach to
accommodate complex experiments with a variety of causal estimands and
different target populations. An important special case of such generalized
network experiments is a bipartite network experiment, in which treatment is
randomized among one set of units, and outcomes are measured on a separate set
of units. We propose a broad class of causal estimands based on stochastic
interventions for generalized network experiments. Using a design-based
approach, we show how to estimate these causal quantities without bias and
develop conservative variance estimators. We apply our methodology to a
randomized experiment in education where participation in an anti-conflict
promotion program is randomized among selected students. Our analysis estimates
the causal effects of treating each student or their friends among different
target populations in the network. We find that the program improves the
overall conflict awareness among students but does not significantly reduce the
total number of such conflicts.
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In this paper, we aimed to provide a review and tutorial for researchers in
the field of medical imaging using language models to improve their tasks at
hand. We began by providing an overview of the history and concepts of language
models, with a special focus on large language models. We then reviewed the
current literature on how language models are being used to improve medical
imaging, emphasizing different applications such as image captioning, report
generation, report classification, finding extraction, visual question
answering, interpretable diagnosis, and more for various modalities and organs.
The ChatGPT was specially highlighted for researchers to explore more potential
applications. We covered the potential benefits of accurate and efficient
language models for medical imaging analysis, including improving clinical
workflow efficiency, reducing diagnostic errors, and assisting healthcare
professionals in providing timely and accurate diagnoses. Overall, our goal was
to bridge the gap between language models and medical imaging and inspire new
ideas and innovations in this exciting area of research. We hope that this
review paper will serve as a useful resource for researchers in this field and
encourage further exploration of the possibilities of language models in
medical imaging.
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Cosmic Dark Fluid is considered as a non-stationary medium, in which
electromagnetic waves propagate, and magneto-electric field structures emerge
and evolve. A medium - type representation of the Dark Fluid allows us to
involve into analysis the concepts and mathematical formalism elaborated in the
framework of classical covariant electrodynamics of continua, and to
distinguish dark analogs of well-known medium-effects, such as optical
activity, pyro-electricity, piezo-magnetism, electro- and magneto-striction and
dynamo-optical activity. The Dark Fluid is assumed to be formed by a duet of a
Dark Matter (a pseudoscalar axionic constituent) and Dark Energy (a scalar
element); respectively, we distinguish electrodynamic effects induced by these
two constituents of the Dark Fluid. The review contains discussions of ten
models, which describe electrodynamic effects induced by Dark Matter and/or
Dark Energy. The models are accompanied by examples of exact solutions to the
master equations, correspondingly extended; applications are considered for
cosmology and space-times with spherical and pp-wave symmetries. In these
applications we focused the attention on three main electromagnetic phenomena
induced by the Dark Fluid: first, emergence of Longitudinal Magneto-Electric
Clusters; second, generation of anomalous electromagnetic responses; third,
formation of Dark Epochs in the Universe history.
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We present a new measurement principle to determine the absolute time delay
of a waveform from an optical reference plane to an electrical reference plane
and vice versa. We demonstrate a method based on this principle with 2 ps
uncertainty. This method can be used to perform accurate time delay
determinations of optical transceivers used in fibre-optic time-dissemination
equipment. As a result the time scales in optical and electrical domain can be
related to each other with the same uncertainty. We expect this method to break
new grounds in high-accuracy time transfer and absolute calibration of
time-transfer equipment.
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Although significant advances have been made in face recognition (FR), FR in
unconstrained environments remains challenging due to the domain gap between
the semi-constrained training datasets and unconstrained testing scenarios. To
address this problem, we propose a controllable face synthesis model (CFSM)
that can mimic the distribution of target datasets in a style latent space.
CFSM learns a linear subspace with orthogonal bases in the style latent space
with precise control over the diversity and degree of synthesis. Furthermore,
the pre-trained synthesis model can be guided by the FR model, making the
resulting images more beneficial for FR model training. Besides, target dataset
distributions are characterized by the learned orthogonal bases, which can be
utilized to measure the distributional similarity among face datasets. Our
approach yields significant performance gains on unconstrained benchmarks, such
as IJB-B, IJB-C, TinyFace and IJB-S (+5.76% Rank1).
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The effect of edge and corner diffusions on the morphology and on the density
of islands nucleated irreversibly on a flat substrate surface is studied.
Without edge and corner diffusion, islands are fractal. As an edge diffusion
constant $D_e$ increases, islands tend to take a cross shape with four needles
in the $< 10 >$ direction. Additional corner diffusion with a diffusion
constant $D_c$ yields square islands. When $D_e$ is small relative to the
surface diffusion constant $D_s$, the square corner shows the Berg instability
to produce hopper growth in the $<11>$ direction. The corner diffusion
influences the island number density $n$. At a deposition flux $F$ with a small
$D_c$, mainly monomers are mobile and $n \propto (F/D_s)^{1/3}$. At large
$D_c$, dimers and trimers are also mobile and $n \propto F^{3/7} D_s^{-5/21}
D_c^{-4/21}$. The $F$ dependence is in good agreement to the rate equation
analysis, but the dependence on $D_c$ cannot be explained by the theory.
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In the tight-binding approximation the Harper like equation describing an
electron in 3D crystal subject to a uniform magnetic field is obtained. It is
supposed that the vector H can be oriented along several directions in the
lattice. The Fermi surfaces relevant to a magnetic flux p/q=1/2 in a simple
cubic lattice are built. The quantization rules in magnetic fields slightly
distinguished from p/q=1/2 are investigated.
|
We show that integral monodromy groups of Kloosterman $\ell$-adic sheaves of
rank $n\ge 2$ on $\mathbb{G}_m/\mathbb{F}_q$ are as large as possible when the
characteristic $\ell$ is large enough, depending only on the rank. This variant
of Katz's results over $\mathbb{C}$ was known by works of Gabber, Larsen, Nori
and Hall under restrictions such as $\ell$ large enough depending on
$\operatorname{char}(\mathbb{F}_q)$ with an ineffective constant, which is
unsuitable for applications. We use the theory of finite groups of Lie type to
extend Katz's ideas, in particular the classification of maximal subgroups of
Aschbacher and Kleidman-Liebeck. These results will apply to study reductions
of hyper-Kloosterman sums in forthcoming work.
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Bohmian trajectories on the toroidal surface T^2 are determined from
eigenfunctions of the Schrodinger equation. An expression for the monodromy
matrix M(t) on a curved surface is developed and eigenvalues of M(t) on T^2
calculated. Lyapunov exponents for trajectories on T^2 are found for some
trajectories to be of order unity.
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We present a conjectural formula describing the cokernel of the Albanese map
of zero-cycles of smooth projective varieties $X$ over $p$-adic fields in terms
of the N\'eron-Severi group and provide a proof under additional assumptions on
an integral model of $X$. The proof depends on a non-degeneracy result of
Brauer-Manin pairing due to Saito-Sato and on Gabber-de Jong's comparison
result of cohomological- and Azumaya-Brauer groups. We will also mention the
local-global problem of the Albanese-cokernel; the abelian group on the "local
side" turns out to be a finite group.
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Physics simulation is ubiquitous in robotics. Whether in model-based
approaches (e.g., trajectory optimization), or model-free algorithms (e.g.,
reinforcement learning), physics simulators are a central component of modern
control pipelines in robotics. Over the past decades, several robotic
simulators have been developed, each with dedicated contact modeling
assumptions and algorithmic solutions. In this article, we survey the main
contact models and the associated numerical methods commonly used in robotics
for simulating advanced robot motions involving contact interactions. In
particular, we recall the physical laws underlying contacts and friction (i.e.,
Signorini condition, Coulomb's law, and the maximum dissipation principle), and
how they are transcribed in current simulators. For each physics engine, we
expose their inherent physical relaxations along with their limitations due to
the numerical techniques employed. Based on our study, we propose theoretically
grounded quantitative criteria on which we build benchmarks assessing both the
physical and computational aspects of simulation. We support our work with an
open-source and efficient C++ implementation of the existing algorithmic
variations. Our results demonstrate that some approximations or algorithms
commonly used in robotics can severely widen the reality gap and impact target
applications. We hope this work will help motivate the development of new
contact models, contact solvers, and robotic simulators in general, at the root
of recent progress in motion generation in robotics.
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We derive a compact analytical solution of the $n$th-order equal-time
correlation functions by using scattering matrix ($S$ matrix) under a weak
coherent state input. Our solution applies to any dissipative quantum system
that respects the U(1) symmetry. We further extend our analytical solution into
two categories depending on whether the input and output channels are
identical. The first category provides a different path for studying
cross-correlation and multiple-drive cases, while the second category is
instrumental in studying waveguide quantum electrodynamics systems. Our
analytical solution allows for easy investigation of the statistical properties
of multiple photons even in complex systems. Furthermore, we have developed a
user-friendly open-source library in Python known as the quantum correlation
solver, and this tool provides a convenient means to study various dissipative
quantum systems that satisfy the above-mentioned criteria. Our study enables
using $S$ matrix to study the photonic correlation and advance the
possibilities for exploring complex systems.
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We study the complete electrode model boundary condition for second order
elliptic PDE. A specific case of this is the PDE describing the electrostatic
potential for a conductive body into which current is injected through
electrodes that touch the boundary. We obtain the optimal description of the
gradient of the electrostatic potential upon approach to the edge of the
electrodes.
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We obtain in this work a sharp estimate on the left tail of the distribution
of the so-called derivative martingale in the $L^4$ phase, answering a
conjecture by H. Lacoin, R. Rhodes & V. Vargas in the framework of the Gaussian
branching random walk.
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The continuous advance of the automotive industry is leading to the emergence
of more advanced driver assistance systems that enable the automation of
certain tasks and that are undoubtedly aimed at achieving vehicles in which the
driving task can be completely delegated. All these advances will bring changes
in the paradigm of the automotive market, as is the case of insurance. For this
reason, CESVIMAP and the Universidad Carlos III de Madrid are working on an
Autonomous Testing pLatform for insurAnce reSearch (ATLAS) to study this
technology and obtain first-hand knowledge about the responsibilities of each
of the agents involved in the development of the vehicles of the future. This
work gathers part of the advancements made in ATLAS, which have made it
possible to have an autonomous vehicle with which to perform tests in real
environments and demonstrations bringing the vehicle closer to future users. As
a result of this work, and in collaboration with the Johannes Kepler University
Linz, the impact, degree of acceptance and confidence of users in autonomous
vehicles has been studied once they have taken a trip on board a fully
autonomous vehicle such as ATLAS. This study has found that, while most users
would be willing to use an autonomous vehicle, the same users are concerned
about the use of this type of technology. Thus, understanding the reasons for
this concern can help define the future of autonomous cars.
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We study baryons as three-body systems using the QCD degrees of freedom in
the framework of covariant Bethe-Salpeter equations. The interaction among
quarks is reduced to a vector-vector interaction via a single dressed-gluon
exchange (Rainbow-Ladder truncation). The formalism allows for the study of the
hadron spectrum as well as their internal properties. We will present the
calculation of electromagnetic properties of spin-3/2 baryons. The model
independent features of our results are assessed using two different models for
the dressings.
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In many domains, the previous decade was characterized by increasing data
volumes and growing complexity of computational workloads, creating new demands
for highly data-parallel computing in distributed systems. Effective operation
of these systems is challenging when facing uncertainties about the performance
of jobs and tasks under varying resource configurations, e.g., for scheduling
and resource allocation. We survey predictive performance modeling (PPM)
approaches to estimate performance metrics such as execution duration, required
memory or wait times of future jobs and tasks based on past performance
observations. We focus on non-intrusive methods, i.e., methods that can be
applied to any workload without modification, since the workload is usually a
black-box from the perspective of the systems managing the computational
infrastructure. We classify and compare sources of performance variation,
predicted performance metrics, required training data, use cases, and the
underlying prediction techniques. We conclude by identifying several open
problems and pressing research needs in the field.
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Accurate forecasts for COVID-19 are necessary for better preparedness and
resource management. Specifically, deciding the response over months or several
months requires accurate long-term forecasts which is particularly challenging
as the model errors accumulate with time. A critical factor that can hinder
accurate long-term forecasts, is the number of unreported/asymptomatic cases.
While there have been early serology tests to estimate this number, more tests
need to be conducted for more reliable results. To identify the number of
unreported/asymptomatic cases, we take an epidemiology data-driven approach. We
show that we can identify lower bounds on this ratio or upper bound on actual
cases as a factor of reported cases. To do so, we propose an extension of our
prior heterogeneous infection rate model, incorporating unreported/asymptomatic
cases. We prove that the number of unreported cases can be reliably estimated
only from a certain time period of the epidemic data. In doing so, we construct
an algorithm called Fixed Infection Rate method, which identifies a reliable
bound on the learned ratio. We also propose two heuristics to learn this ratio
and show their effectiveness on simulated data. We use our approaches to
identify the upper bounds on the ratio of actual to reported cases for New York
City and several US states. Our results demonstrate with high confidence that
the actual number of cases cannot be more than 35 times in New York, 40 times
in Illinois, 38 times in Massachusetts and 29 times in New Jersey, than the
reported cases.
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I review quark momentum distributions in the nucleon at large momentum
fractions x. Particular attention is paid to the impact of nuclear effects in
deuterium on the d/u quark distribution ratio as x -> 1. A new global study of
parton distributions, using less restrictive kinematic cuts in Q^2 and W^2,
finds strong suppression of the d quark distribution once nuclear corrections
are accounted for.
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Let $G$ be a simple algebraic group of type $G_2$ over an algebraically
closed field of characteristic $2$. We give an example of a finite group
$\Gamma$ with Sylow $2$-subgroup $\Gamma_2$ and an infinite family of pairwise
non-conjugate homomorphisms $\rho\colon \Gamma\rightarrow G$ whose restrictions
to $\Gamma_2$ are all conjugate. This answers a question of Burkhard
K\"ulshammer from 1995. We also give an action of $\Gamma$ on a connected
unipotent group $V$ such that the map of 1-cohomologies ${\rm
H}^1(\Gamma,V)\rightarrow {\rm H}^1(\Gamma_p,V)$ induced by restriction of
1-cocycles has an infinite fibre.
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We prove that, given $\alpha>0$, if $M$ is a complete Riemannian manifold
which Ricci curvature
satisfies.\[\operatorname*{Ric}\nolimits_{x}(v)\geq\alpha\operatorname{sech}^{2}
(r(x)))\] or \[ \operatorname*{Ric}\nolimits_{x}(v)\geq-\frac{{h_{\alpha}}
(r(x))}{r(x)^{2}}, \] where \[ {h_{\alpha}}(r) =
\frac{\alpha(\alpha+1)r(x)^{\alpha }}{r(x)^{\alpha }-1}, \] for all $x\in
M\backslash B_{R}(o)$ and for all $v\in T_{x}M,$ $\left\Vert v\right\Vert =1,$
where \ $o$ is a fixed point of $M$, $r(x)=d(o,x)$, $d$ the Riemannian distance
in $M$ and $B_{R}(o)$ the geodesic ball of $M$ centered at $o$ with radius
$R>0$, then $M$ is $p-$parabolic for any $p>1$, if satisfies the first
inequality, and $M$ is $p-$parabolic, for any $p\geq(\alpha+1)(n-1)+1$, if
satisfies the second inequality.
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In search for mathematically tractable models of anomalous diffusion, we
introduce a simple dynamical system consisting of a chain of coupled maps of
the interval whose Lyapunov exponents vanish everywhere. The volume preserving
property and the vanishing Lyapunov exponents are intended to mimic the
dynamics of polygonal billiards, which are known to give rise to anomalous
diffusion, but which are too complicated to be analyzed as thoroughly as
desired. Depending on the value taken by a single parameter \alpha, our map
experiences sub-diffusion, super-diffusion or normal diffusion. Therefore its
transport properties can be compared with those of given L\'evy walks
describing transport in quenched disordered media. Fixing \alpha\ so that the
mean square displacement generated by our map and that generated by the
corresponding L\'evy walk asymptotically coincide, we prove that all moments of
the corresponding asymptotic distributions coincide as well, hence all
observables which are expressed in terms of the moments coincide.
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In this work, we present a method to compute the Kantorovich-Wasserstein
distance of order one between a pair of two-dimensional histograms. Recent
works in Computer Vision and Machine Learning have shown the benefits of
measuring Wasserstein distances of order one between histograms with $n$ bins,
by solving a classical transportation problem on very large complete bipartite
graphs with $n$ nodes and $n^2$ edges. The main contribution of our work is to
approximate the original transportation problem by an uncapacitated min cost
flow problem on a reduced flow network of size $O(n)$ that exploits the
geometric structure of the cost function. More precisely, when the distance
among the bin centers is measured with the 1-norm or the $\infty$-norm, our
approach provides an optimal solution. When the distance among bins is measured
with the 2-norm: (i) we derive a quantitative estimate on the error between
optimal and approximate solution; (ii) given the error, we construct a reduced
flow network of size $O(n)$. We numerically show the benefits of our approach
by computing Wasserstein distances of order one on a set of grey scale images
used as benchmark in the literature. We show how our approach scales with the
size of the images with 1-norm, 2-norm and $\infty$-norm ground distances, and
we compare it with other two methods which are largely used in the literature.
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The dependence of the photocurrent generated in a Pd/graphene/Ti junction
device on the incident photon polarization is studied. Spatially resolved
photocurrent images were obtained as the incident photon polarization is
varied. The photocurrent is maximum when the polarization direction is
perpendicular to the graphene channel direction and minimum when the two
directions are parallel. This polarization dependence can be explained as being
due to the anisotropic electron-photon interaction of Dirac electrons in
graphene.
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Motivated by the current interest in the understanding of the Mott insulators
away from half filling, observed in many perovskite oxides, we study the Mott
metal-insulator transition (MIT) in the doped Hubbard-Holstein model using the
Hatree-Fock mean field theory. The Hubbard-Holstein model is the simplest model
containing both the Coulomb and the electron-lattice interactions, which are
important ingredients in the physics of the perovskite oxides. In contrast to
the half-filled Hubbard model, which always results in a single phase (either
metallic or insulating), our results show that away from half-filling, a mixed
phase of metallic and insulating regions occur. As the dopant concentration is
increased, the metallic part progressively grows in volume, until it exceeds
the percolation threshold, leading to percolative conduction. This happens
above a critical dopant concentration $\delta_c$, which, depending on the
strength of the electron-lattice interaction, can be a significant fraction of
unity. This means that the material could be insulating even for a substantial
amount of doping, in contrast to the expectation that doped holes would destroy
the insulating behavior of the half-filled Hubbard model. Our theory provides a
framework for the understanding of the density-driven metal-insulator
transition observed in many complex oxides.
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Recent neutron scattering, nuclear magnetic resonance, and scanning tunneling
microscopy experiments have yielded valuable new information on the interplay
between charge and spin density wave order and superconductivity in the cuprate
superconductors, by using an applied perpendicular magnetic field to tune the
ground state properties. We compare the results of these experiments with the
predictions of a theory which assumed that the ordinary superconductor was
proximate to a quantum transition to a superconductor with co-existing
spin/charge density wave order.
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We propose an efficient method to generate multiparticle entangled states of
NV centers in a spin mechanical system, where the spins interact through a
collective coupling of the Lipkin-Meshkov-Glick (LMG) type. We show that,
through adiabatic transitions in the ground state of the LMG Hamiltonian, the
Greenberger-Horne-Zeilinger (GHZ)-type or the W-type entangled states of the NV
spins can be generated with this hybrid system from an initial product state.
Because of adiabaticity, this scheme is robust against practical noise and
experimental imperfection, and may be useful for quantum information
processing.
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We describe the population-based SEIR (susceptible, exposed, infected,
removed) model developed by the Irish Epidemiological Modelling Advisory Group
(IEMAG), which advises the Irish government on COVID-19 responses. The model
assumes a time-varying effective contact rate (equivalently, a time-varying
reproduction number) to model the effect of non-pharmaceutical interventions. A
crucial technical challenge in applying such models is their accurate
calibration to observed data, e.g., to the daily number of confirmed new cases,
as the past history of the disease strongly affects predictions of future
scenarios. We demonstrate an approach based on inversion of the SEIR equations
in conjunction with statistical modelling and spline-fitting of the data, to
produce a robust methodology for calibration of a wide class of models of this
type.
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We consider string theory on a background of the form AdS_3 x N. Our aim is
to give a description of the dual CFT in a general set up. With the requirement
that we have N=2 supersymmetry in spacetime, we provide evidence that the dual
CFT is in the moduli space of a certain symmetric product M^p/S_p. On the way
to show this, we reproduce some recent results on string propagation on AdS_3
and extend them to the superstring.
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In this paper we use the Batalin-Fradkin-Vilkovisky formalism to study a
recently proposed nonlocal symmetry of QED. In the BFV extended phase space we
show that this symmetry stems from a canonical transformation in the ghost
sector.
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Simple economic and performance arguments suggest appropriate lifetimes for
main memory pages and suggest optimal page sizes. The fundamental tradeoffs are
the prices and bandwidths of RAMs and disks. The analysis indicates that with
today's technology, five minutes is a good lifetime for randomly accessed
pages, one minute is a good lifetime for two-pass sequentially accessed pages,
and 16 KB is a good size for index pages. These rules-of-thumb change in
predictable ways as technology ratios change. They also motivate the importance
of the new Kaps, Maps, Scans, and $/Kaps, $/Maps, $/TBscan metrics.
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We study the eigenstates of two opposite spin fermions on a one-dimensional
lattice with finite range interaction. The eigenstates are projected onto the
set of Fock eigenstates of the noninteracting case. We find antiresonances for
symmetric eigenstates, which eliminate the interaction between two symmetric
Fock states when satisfying a corresponding selection rule.
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Vircators (Virtual Cathode Oscillators) are sources of short-pulsed, high
power, microwave (GHz) radiation. An essentially dimensional argument relates
their radiated power, pulse energy and oscillation frequency to their driving
voltage and fundamental physical constants. For a diode of width and gap 10 cm
and for voltages of a few hundred keV the peak radiated power cannot exceed
${\cal O} (\text{30 GW})$ and the broad-band single cycle radiated energy
cannot exceed ${\cal O}(\text{3 J})$. If electrons can be accelerated to
relativistic energies higher powers and radiated energies may be possible.
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Linde in hep-th/0611043 shows that some (though not all) versions of the
global (volume-weighted) description avoid the "Boltzmann brain" problem raised
in hep-th/0610079 if the universe does not have a decay time less than 20 Gyr.
Here I give an apparently natural version of the volume-weighted description in
which the problem persists, highlighting the ambiguity of taking the ratios of
infinite volumes that appear to arise from eternal inflation.
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This paper describes the design and implementation of mechanisms for
light-weight inclusion of formal mathematics in informal mathematical writings,
particularly in a Web-based setting. This is conceptually done in three stages:
(i) by choosing a suitable representation layer (based on RDF) for encoding the
information about available resources of formal mathematics, (ii) by exporting
this information from formal libraries, and (iii) by providing syntax and
implementation for including formal mathematics in informal writings.
We describe the use case of an author referring to formal text from an
informal narrative, and discuss design choices entailed by this use case.
Furthermore, we describe an implementation of the use case within the Agora
prototype: a Wiki for collaborating on formalized mathematics.
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Multi-modal entity alignment (MMEA) aims to identify equivalent entities
between two multi-modal knowledge graphs for integration. Unfortunately, prior
arts have attempted to improve the interaction and fusion of multi-modal
information, which have overlooked the influence of modal-specific noise and
the usage of labeled and unlabeled data in semi-supervised settings. In this
work, we introduce a Pseudo-label Calibration Multi-modal Entity Alignment
(PCMEA) in a semi-supervised way. Specifically, in order to generate holistic
entity representations, we first devise various embedding modules and attention
mechanisms to extract visual, structural, relational, and attribute features.
Different from the prior direct fusion methods, we next propose to exploit
mutual information maximization to filter the modal-specific noise and to
augment modal-invariant commonality. Then, we combine pseudo-label calibration
with momentum-based contrastive learning to make full use of the labeled and
unlabeled data, which improves the quality of pseudo-label and pulls aligned
entities closer. Finally, extensive experiments on two MMEA datasets
demonstrate the effectiveness of our PCMEA, which yields state-of-the-art
performance.
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The existence of a spatially thin, kinematically coherent Disk of Satellites
(DoS) around the Milky Way (MW), is a problem that often garners vivacious
debate in the literature or at scientific meetings. One of the most recent
incarnations of this wrangle occurred with two papers by Maji et al, who argued
that these structures "maybe a misinterpretation of the data". These claims are
in stark contrast to previous works. Motivated by this and other recent
publications on this problem, we discuss necessary considerations to make,
observational effects to consider, and pitfalls to avoid when investigating
satellite galaxy planes such as the MW's DoS. In particular, we emphasize that
conclusions need to have a statistical basis including a determination of the
significance of satellite alignments, observational biases must not be ignored,
and measurement errors (e.g. for proper motions) need to be considered. We
discuss general problems faced by attempts to determine the dynamical stability
of the DoS via orbit integrations of MW satellite galaxies, and demonstrate
that to interpret simulations, it is helpful to compare them with a null case
of isotropically distributed satellite positions and velocities. Based on these
criteria, we find that the conclusions of Maji et al. do not hold up to
scrutiny, and that their hydrodynamic cosmological simulation of a single host
shows no evidence for a significant kinematic coherence among the simulated
satellite galaxies, in contrast to the observed MW system.
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Drone cell (DC) is an emerging technique to offer flexible and cost-effective
wireless connections to collect Internet-of-things (IoT) data in uncovered
areas of terrestrial networks. The flying trajectory of DC significantly
impacts the data collection performance. However, designing the trajectory is a
challenging issue due to the complicated 3D mobility of DC, unique DC-to-ground
(D2G) channel features, limited DC-to-BS (D2B) backhaul link quality, etc. In
this paper, we propose a 3D DC trajectory design for the DC-assisted IoT data
collection where multiple DCs periodically fly over IoT devices and relay the
IoT data to the base stations (BSs). The trajectory design is formulated as a
mixed integer non-linear programming (MINLP) problem to minimize the average
user-to-DC (U2D) pathloss, considering the state-of-the-art practical D2G
channel model. We decouple the MINLP problem into multiple quasi-convex or
integer linear programming (ILP) sub-problems, which optimizes the user
association, user scheduling, horizontal trajectories and DC flying altitudes
of DCs, respectively. Then, a 3D multi-DC trajectory design algorithm is
developed to solve the MINLP problem, in which the sub-problems are optimized
iteratively through the block coordinate descent (BCD) method. Compared with
the static DC deployment, the proposed trajectory design can lower the average
U2D pathloss by 10-15 dB, and reduce the standard deviation of U2D pathloss by
56%, which indicates the improvements in both link quality and user fairness.
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In this paper we introduce the concept of random time changes in dynamical
systems. The subordination principle may be applied to study the long time
behavior of the random time systems. We show, under certain assumptions on the
class of random time, that the subordinated system exhibits a slower time decay
which is determined by the random time characteristics. In the path asymptotic
a random time change is reflected in the new velocity of the resulting
dynamics.
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We propose an extension to the recently proposed extranatural or gauge
inflation scenario in which the radius modulus field around which the Wilson
loop is wrapped assists inflation as it shrinks. We discuss how this might lead
to more generic initial conditions for inflation.
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The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal
masses and equal or unequal populations are described at zero and finite
temperatures in the strong attraction limit. In this limit, the Fermi-Fermi
mixture can be described by a weakly interacting Bose-Fermi mixture, where the
bosons correspond to Feshbach molecules and the fermions correspond to excess
atoms. First, we discuss the three and four fermion scattering processes, and
use the exact boson-fermion and boson-boson scattering lengths to generate the
phase diagrams in terms of the underlying fermion-fermion scattering length. In
three dimensions, in addition to the normal and uniform superfluid phases, we
find two stable non-uniform states corresponding to (1) phase separation
between pure unpaired (excess) and pure paired fermions (molecular bosons); and
(2) phase separation between pure excess fermions and a mixture of excess
fermions and molecular bosons. Lastly, we also discuss the effects of the
trapping potential in the density profiles of condensed and non-condensed
molecular bosons, and excess fermions at zero and finite temperatures, and
discuss possible implications of our findings to experiments involving mixtures
of ultracold fermions.
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Subsets and Splits