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The spatial symmetry property of truncated birth-death processes studied in
Di Crescenzo [6] is extended to a wider family of continuous-time Markov
chains. We show that it yields simple expressions for first-passage-time
densities and avoiding transition probabilities, and apply it to a bilateral
birth-death process with jumps. It is finally proved that this symmetry
property is preserved within the family of strongly similar Markov chains.
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We answer a question of Zadrozny.
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Cosmic inflation is commonly assumed to be driven by quantum fields. Quantum
mechanics predicts phenomena such as quantum fluctuations and tunneling of the
field. Here we show an example of a quantum interference effect which goes
beyond the semi-classical treatment and which may be of relevance in the early
universe. We study the quantum coherent dynamics for a tilted, periodic
potential, which results in genuine quantum oscillations of the inflaton field,
analogous to Bloch oscillations in condensed matter and atomic systems. Our
results show that quantum interference phenomena may be of relevance in
cosmology.
|
Sponsored search represents a major source of revenue for web search engines.
This popular advertising model brings a unique possibility for advertisers to
target users' immediate intent communicated through a search query, usually by
displaying their ads alongside organic search results for queries deemed
relevant to their products or services. However, due to a large number of
unique queries it is challenging for advertisers to identify all such relevant
queries. For this reason search engines often provide a service of advanced
matching, which automatically finds additional relevant queries for advertisers
to bid on. We present a novel advanced matching approach based on the idea of
semantic embeddings of queries and ads. The embeddings were learned using a
large data set of user search sessions, consisting of search queries, clicked
ads and search links, while utilizing contextual information such as dwell time
and skipped ads. To address the large-scale nature of our problem, both in
terms of data and vocabulary size, we propose a novel distributed algorithm for
training of the embeddings. Finally, we present an approach for overcoming a
cold-start problem associated with new ads and queries. We report results of
editorial evaluation and online tests on actual search traffic. The results
show that our approach significantly outperforms baselines in terms of
relevance, coverage, and incremental revenue. Lastly, we open-source learned
query embeddings to be used by researchers in computational advertising and
related fields.
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Choosing a uniformly sampled simple directed graph realization of a degree
sequence has many applications, in particular in social networks where
self-loops are commonly not allowed. It has been shown in the past that one can
perform a Markov chain arc-switching algorithm to sample a simple directed
graph uniformly by performing two types of switches: a 2-switch and a directed
3-cycle reorientation. This paper discusses under what circumstances a directed
3-cycle reorientation is required. In particular, the class of degree sequences
where this is required is a subclass of the directed 3-cycle anchored degree
sequences. An important implication of this result is a reduced Markov chain
algorithm that uses only 2-switches.
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Observations of powerful radio waves from neutron star magnetospheres raise
the question of how strong waves interact with particles in a strong background
magnetic field $B_{bg}$. This problem is examined by solving the particle
motion in the wave. Remarkably, waves with amplitudes $E_0>B_{bg}$ pump
particle energy via repeating resonance events, quickly reaching the radiation
reaction limit. As a result, the wave is scattered with a huge cross section.
This fact has implications for models of fast radio bursts and magnetars.
Particles accelerated in the wave emit gamma-rays, which can trigger an $e^\pm$
avalanche and, instead of silent escape, the wave will produce X-ray fireworks.
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Let $\mathcal{C}$ be a clutter with a perfect matching $e_1,...,e_g$ of
K\"onig type and let $\Delta_\mathcal{C}$ be the Stanley-Reisner complex of the
edge ideal of $\mathcal{C}$. If all c-minors of $\mathcal{C}$ have a free
vertex and $\mathcal{C}$ is unmixed, we show that $\Delta_\mathcal{C}$ is pure
shellable. We are able to describe, in combinatorial and algebraic terms, when
$\Delta_\mathcal{C}$ is pure. If $\mathcal{C}$ has no cycles of length 3 or 4,
then it is shown that $\Delta_\mathcal{C}$ is pure if and only if
$\Delta_\mathcal{C}$ is pure shellable (in this case $e_i$ has a free vertex
for all $i$), and that $\Delta_\mathcal{C}$ is pure if and only if for any two
edges $f_1,f_2$ of $\mathcal{C}$ and for any $e_i$, one has that $f_1\cap
e_i\subset f_2\cap e_i$ or $f_2\cap e_i\subset f_1\cap e_i$. It is also shown
that this ordering condition implies that $\Delta_\mathcal{C}$ is pure
shellable, without any assumption on the cycles of $\mathcal{C}$. Then we prove
that complete admissible uniform clutters and their Alexander duals are
unmixed. In addition, the edge ideals of complete admissible uniform clutters
are facet ideals of shellable simplicial complexes, they are Cohen-Macaulay,
and they have linear resolutions. Furthermore if $ \mathcal{C}$ is admissible
and complete, then $\mathcal{C}$ is unmixed. We characterize certain conditions
that occur in a Cohen-Macaulay criterion for bipartite graphs of Herzog and
Hibi, and extend some results of Faridi--on the structure of unmixed simplicial
trees--to clutters with the K\"onig property without 3-cycles or 4-cycles.
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Following a `bottom-up approach' in understanding many-particle effects and
dynamics we provide a systematic ab initio study of the dependence of the
breathing dynamics of ultracold bosons in a 1D harmonic trap on the number of
bosons ranging from few to many. To this end, we employ the Multi-Layer
Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) which
has been developed very recently [S. Kr\"onke, L. Cao, O. Vendrell and P.
Schmelcher. {\it New J. Phys.} {\bf 15}, 063018 (2013)]. The beating behavior
for two bosons is found numerically and consequently explained by an analytical
approach. Drawing on this, we show how to compute the complete breathing mode
spectrum in this case. We examine how the two-mode breathing behavior of two
bosons evolves to the single-frequency behavior of the many-particle limit when
adding more particles. In the limit of many particles, we numerically study the
dependence of the breathing mode frequency on both the interaction strength as
well as on the particle number. We provide an estimate for the parameter region
in which Gross-Pitaevskii theory is well applicable.
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A distributed denial-of-service (DDoS) attack is an attack wherein multiple
compromised computer systems flood the bandwidth and/or resources of a target,
such as a server, website or other network resource, and cause a denial of
service for users of the targeted resource. The flood of incoming messages,
connection requests or malformed packets to the target system forces it to slow
down or even crash and shut down, thereby denying service to legitimate users
or systems. This paper presents a literature review of DDoS attacks and the
common defense mechanisms available. It also presents a literature review of
the defenses for low-rate DDoS attacks that have not been handled effectively
hitherto.
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Speech segmentation is an essential part of speech translation (ST) systems
in real-world scenarios. Since most ST models are designed to process speech
segments, long-form audio must be partitioned into shorter segments before
translation. Recently, data-driven approaches for the speech segmentation task
have been developed. Although the approaches improve overall translation
quality, a performance gap exists due to a mismatch between the models and ST
systems. In addition, the prior works require large self-supervised speech
models, which consume significant computational resources. In this work, we
propose a segmentation model that achieves better speech translation quality
with a small model size. We propose an ASR-with-punctuation task as an
effective pre-training strategy for the segmentation model. We also show that
proper integration of the speech segmentation model into the underlying ST
system is critical to improve overall translation quality at inference time.
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The IDP knowledge base system currently uses MiniSAT(ID) as its backend
Constraint Programming (CP) solver. A few similar systems have used a Mixed
Integer Programming (MIP) solver as backend. However, so far little is known
about when the MIP solver is preferable. This paper explores this question. It
describes the use of CPLEX as a backend for IDP and reports on experiments
comparing both backends.
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Collateral circulation results from specialized anastomotic channels which
are capable of providing oxygenated blood to regions with compromised blood
flow caused by ischemic injuries. The quality of collateral circulation has
been established as a key factor in determining the likelihood of a favorable
clinical outcome and goes a long way to determine the choice of stroke care
model - that is the decision to transport or treat eligible patients
immediately.
Though there exist several imaging methods and grading criteria for
quantifying collateral blood flow, the actual grading is mostly done through
manual inspection of the acquired images. This approach is associated with a
number of challenges. First, it is time-consuming - the clinician needs to scan
through several slices of images to ascertain the region of interest before
deciding on what severity grade to assign to a patient. Second, there is a high
tendency for bias and inconsistency in the final grade assigned to a patient
depending on the experience level of the clinician.
We present a deep learning approach to predicting collateral flow grading in
stroke patients based on radiomic features extracted from MR perfusion data.
First, we formulate a region of interest detection task as a reinforcement
learning problem and train a deep learning network to automatically detect the
occluded region within the 3D MR perfusion volumes. Second, we extract radiomic
features from the obtained region of interest through local image descriptors
and denoising auto-encoders. Finally, we apply a convolutional neural network
and other machine learning classifiers to the extracted radiomic features to
automatically predict the collateral flow grading of the given patient volume
as one of three severity classes - no flow (0), moderate flow (1), and good
flow (2)...
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We analyse the concept of active gravitational mass for Reissner-Nordstrom
spacetime in terms of scalar polynomial invariants and the Karlhede
classification. We show that while the Kretschmann scalar does not produce the
expected expression for the active gravitational mass, both scalar polynomial
invariants formed from the Weyl tensor, and the Cartan scalars, do.
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The nonlinear Markov processes are the measure-valued dynamical systems which
preserve positivity. They can be represented as the law of large numbers limits
of general Markov models of interacting particles. In physics, the kinetic
equations allow Lyapunov functionals (entropy, free energy, etc.). This may be
considered as a sort of inheritance of the Lyapunov functionals from the
microscopic master equations. We study nonlinear Markov processes that inherit
thermodynamic properties from the microscopic linear Markov processes. We
develop the thermodynamics of nonlinear Markov processes and analyze the
asymptotic assumption, which are sufficient for this inheritance.
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The study of twisted representations of graded vertex algebras is important
for understanding orbifold models in conformal field theory. In this paper we
consider the general set-up of a vertex algebra $V$, graded by $\G/\Z$ for some
subgroup $\G$ of $\R$ containing $\Z$, and with a Hamiltonian operator $H$
having real (but not necessarily integer) eigenvalues. We construct the
directed system of twisted level $p$ Zhu algebras $\zhu_{p, \G}(V)$, and we
prove the following theorems: For each $p$ there is a bijection between the
irreducible $\zhu_{p, \G}(V)$-modules and the irreducible $\G$-twisted positive
energy $V$-modules, and $V$ is $(\G, H)$-rational if and only if all its Zhu
algebras $\zhu_{p, \G}(V)$ are finite dimensional and semisimple. The main
novelty is the removal of the assumption of integer eigenvalues for $H$. We
provide an explicit description of the level $p$ Zhu algebras of a universal
enveloping vertex algebra, in particular of the Virasoro vertex algebra
$\vir^c$ and the universal affine Kac-Moody vertex algebra $V^k(\g)$ at
non-critical level. We also compute the inverse limits of these directed
systems of algebras.
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We present a new framework for characterizing quasinormal modes (QNMs) or
resonant states for the wave equation on asymptotically flat spacetimes,
applied to the setting of extremal Reissner-Nordstr\"om black holes. We show
that QNMs can be interpreted as honest eigenfunctions of generators of time
translations acting on Hilbert spaces of initial data, corresponding to a
suitable time slicing. The main difficulty that is present in the
asymptotically flat setting, but is absent in the previously studied cases of
asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes,
is that $L^2$-based Sobolev spaces are not suitable Hilbert space choices.
Instead, we consider Hilbert spaces of functions that are additionally Gevrey
regular at infinity and at the event horizon. We introduce $L^2$-based Gevrey
estimates for the wave equation that are intimately connected to the existence
of conserved quantities along null infinity and the event horizon. We relate
this new framework to the traditional interpretation of quasinormal frequencies
as poles of the meromorphic continuation of a resolvent operator and obtain new
quantitative results in this setting.
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Ongoing or upcoming surveys such as Gaia, ZTF, or LSST will observe
light-curves of billons or more astronomical sources. This presents new
challenges for identifying interesting and important types of variability.
Collecting a sufficient number of labelled data for training is difficult,
however, especially in the early stages of a new survey. Here we develop a
single-band light-curve classifier based on deep neural networks, and use
transfer learning to address the training data paucity problem by conveying
knowledge from one dataset to another. First we train a neural network on 16
variability features extracted from the light-curves of OGLE and EROS-2
variables. We then optimize this model using a small set (e.g. 5%) of periodic
variable light-curves from the ASAS dataset in order to transfer knowledge
inferred from OGLE/EROS-2 to a new ASAS classifier. With this we achieve good
classification results on ASAS, thereby showing that knowledge can be
successfully transferred between datasets. We demonstrate similar transfer
learning using Hipparcos and ASAS-SN data. We therefore find that it is not
necessary to train a neural network from scratch for every new survey, but
rather that transfer learning can be used even when only a small set of
labelled data is available in the new survey.
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We introduce Artinian Gorenstein algebras defined by the face posets of
regular polyhedra. We consider the strong Lefschetz property and Hodge--Riemann
relation for the algebras. We show the strong Lefschetz property of the
algebras for all Platonic solids. On the other hand, for some Platonic solids,
we show that the algebras do not satisfy the Hodge--Riemann relation with
respect to some strong Lefschetz elements.
|
Picking up multiple objects at once is a grasping skill that makes a human
worker efficient in many domains. This paper presents a system to pick a
requested number of objects by only picking once (OPO). The proposed
Only-Pick-Once System (OPOS) contains several graph-based algorithms that
convert the layout of objects into a graph, cluster nodes in the graph, rank
and select candidate clusters based on their topology. OPOS also has a
multi-object picking predictor based on a convolutional neural network for
estimating how many objects would be picked up with a given gripper location
and orientation. This paper presents four evaluation metrics and three
protocols to evaluate the proposed OPOS. The results show OPOS has very high
success rates for two and three objects when only picking once. Using OPOS can
significantly outperform two to three times single object picking in terms of
efficiency. The results also show OPOS can generalize to unseen size and shape
objects.
|
Applications of high-dimensional regression often involve multiple sources or
types of covariates. We propose methodology for this setting, emphasizing the
"wide data" regime with large total dimensionality p and sample size n<<p. We
focus on a flexible ridge-type prior with shrinkage levels that are specific to
each data type or source and that are set automatically by empirical Bayes. All
estimation, including setting of shrinkage levels, is formulated mainly in
terms of inner product matrices of size n x n. This renders computation
efficient in the wide data regime and allows scaling to problems with millions
of features. Furthermore, the proposed procedures are free of user-set tuning
parameters. We show how sparsity can be achieved by post-processing of the
Bayesian output via constrained minimization of a certain Kullback-Leibler
divergence. This yields sparse solutions with adaptive, source-specific
shrinkage, including a closed-form variant that scales to very large p. We
present empirical results from a simulation study based on real data and a case
study in Alzheimer's disease involving millions of features and multiple data
sources.
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We consider a system of interacting particles with random initial conditions.
Continuum approximations of the system, based on truncations of the BBGKY
hierarchy, are described and simulated for various initial distributions and
types of interaction. Specifically, we compare the Mean Field Approximation
(MFA), the Kirkwood Superposition Approximation (KSA), and a recently developed
truncation of the BBGKY hierarchy (the Truncation Approximation - TA). We show
that KSA and TA perform more accurately than MFA in capturing approximate
distributions (histograms) obtained from Monte Carlo simulations. Furthermore,
TA is more numerically stable and less computationally expensive than KSA.
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S stars are transition objects between M-type giants and carbon stars on the
asymptotic giant branch (AGB). They are characterized by overabundances of
s-process elements. Roughly half of them are enhanced in technetium (Tc), an
s-process element with no stable isotope, while the other half lack technetium.
This dichotomy arises from the fact that Tc-rich S stars are intrinsically
producing s-process elements and have undergone third dredge-up (TDU) events,
while Tc-poor S stars owe their s-process overabundances to a past pollution by
a former AGB companion. Our aim is to analyse the abundances of S stars and
gain insights into their evolutionary status and on the nucleosynthesis of
heavy s-process elements taking place in their interior. In particular, the
location of extrinsic and intrinsic S stars in the HR diagram will be compared
with the theoretical onset of the TDU on the thermally-pulsing AGB. A sample of
19 S-type stars was analysed by combining HERMES high-resolution spectra,
accurate Gaia Data Release 2 (GDR2) parallaxes, stellar-evolution models, and
newly-designed MARCS model atmospheres for S-type stars. Combining the derived
parameters with GDR2 parallaxes allows a joint analysis of the location of the
stars in the Hertzsprung-Russell diagram and of their surface abundances. For
all 19 stars, Zr and Nb abundances are derived, complemented by abundances of
other s-process elements for the three Tc-rich S stars. These abundances agree
within the uncertainties with nucleosynthesis predictions for stars of
corresponding mass, metallicity and evolutionary stage. Most extrinsic S stars
lie close to the tip of the red giant branch (RGB), and a few are located along
the early AGB. The location of intrinsic S stars in the HR diagram is
compatible with them being thermally-pulsing AGB stars.
|
While wormholes are as good a prediction of Einstein's theory as black holes,
they are subject to severe restrictions from quantum field theory. In
particular, holding a wormhole open requires a violation of the null energy
condition, calling for the existence of exotic matter. The Casimir effect has
shown that this physical requirement can be met on a small scale, thereby
solving a key conceptual problem. The Casimir effect does not, however,
guarantee that the small-scale violation is sufficient for supporting a
macroscopic wormhole. The purpose of this paper is to connect the Casimir
effect to noncommutative geometry, which also aims to accommodate small-scale
effects, the difference being that these can now be viewed as intrinsic
properties of spacetime. As a result, the noncommutative effects can be
implemented by modifying only the energy momentum tensor in the Einstein field
equations, while leaving the Einstein tensor unchanged. The wormhole can
therefore be macroscopic in spite of the small Casimir effect.
|
In this Article, we review a novel, rapidly developing field of modern light
science named all-dielectric nanophotonics. This branch of nanophotonics is
based on the properties of high-index dielectric nanoparticles which allow for
controlling both magnetic and electric responses of a nanostructured matter.
Here, we discuss optical properties of high-index dielectric nanoparticles,
methods of their fabrication, and recent advances in practical applications,
including the quantum source emission engineering, Fano resonances in
all-dielectric nanoclusters, surface enhanced spectroscopy and sensing,
coupled-resonator optical waveguides, metamaterials and metasurfaces, and
nonlinear nanophotonics.
|
Renewable energy forecasting is attaining greater importance due to its
constant increase in contribution to the electrical power grids. Solar energy
is one of the most significant contributors to renewable energy and is
dependent on solar irradiation. For the effective management of electrical
power grids, forecasting models that predict solar irradiation, with high
accuracy, are needed. In the current study, Machine Learning techniques such as
Linear Regression, Extreme Gradient Boosting and Genetic Algorithm Optimization
are used to forecast solar irradiation. The data used for training and
validation is recorded from across three different geographical stations in the
United States that are part of the SURFRAD network. A Global Horizontal Index
(GHI) is predicted for the models built and compared. Genetic Algorithm
Optimization is applied to XGB to further improve the accuracy of solar
irradiation prediction.
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Distributional fixed points of a Poisson shot noise transform (for
nonnegative, nonincreasing response functions bounded by 1) are characterized.
The tail behavior of fixed points is described. Typically they have either
exponential moments or their tails are proportional to a power function, with
exponent greater than -1. The uniqueness of fixed points is also discussed.
Finally, it is proved that in most cases fixed points are absolutely
continuous, apart from the possible atom at zero.
|
In the rapidly changing healthcare landscape, the implementation of offline
reinforcement learning (RL) in dynamic treatment regimes (DTRs) presents a mix
of unprecedented opportunities and challenges. This position paper offers a
critical examination of the current status of offline RL in the context of
DTRs. We argue for a reassessment of applying RL in DTRs, citing concerns such
as inconsistent and potentially inconclusive evaluation metrics, the absence of
naive and supervised learning baselines, and the diverse choice of RL
formulation in existing research. Through a case study with more than 17,000
evaluation experiments using a publicly available Sepsis dataset, we
demonstrate that the performance of RL algorithms can significantly vary with
changes in evaluation metrics and Markov Decision Process (MDP) formulations.
Surprisingly, it is observed that in some instances, RL algorithms can be
surpassed by random baselines subjected to policy evaluation methods and reward
design. This calls for more careful policy evaluation and algorithm development
in future DTR works. Additionally, we discussed potential enhancements toward
more reliable development of RL-based dynamic treatment regimes and invited
further discussion within the community. Code is available at
https://github.com/GilesLuo/ReassessDTR.
|
The sterile insect technique consists in massive release of sterilized males
in the aim to reduce the size of mosquitoes population or even eradicate it. In
this work, we investigate the feasability of using the sterile insect technique
as a barrier against reinvasion. More precisely, we provide some numerical
simulations and mathematical results showing that performing the sterile insect
technique on a band large enough may stop reinvasion.
|
In this short note we employ the Briot-Bouquet differential subordination to
determine the best possible inclusion relation within a certain family of
analytic functions defined by the Salagean derivative.
|
A novel linear integration rule called $\textit{control neighbors}$ is
proposed in which nearest neighbor estimates act as control variates to speed
up the convergence rate of the Monte Carlo procedure on metric spaces. The main
result is the $\mathcal{O}(n^{-1/2} n^{-s/d})$ convergence rate -- where $n$
stands for the number of evaluations of the integrand and $d$ for the dimension
of the domain -- of this estimate for H\"older functions with regularity $s \in
(0,1]$, a rate which, in some sense, is optimal. Several numerical experiments
validate the complexity bound and highlight the good performance of the
proposed estimator.
|
We investigate known mechanisms for enhancing nuclear fusion rates at ambient
temperatures and pressures in solid-state environments. In deuterium fusion, on
which the paper is focused, an enhancement of >40 orders of magnitude would be
needed to achieve observable fusion. We find that mechanisms for fusion rate
enhancement up to 30 orders of magnitude each are known across the domains of
atomic physics, nuclear physics, and quantum dynamics. Cascading such
mechanisms could lead to an overall enhancement of 40 orders of magnitude and
more. We present a roadmap with examples of how hypothesis-driven research
could be conducted in -- and across -- each domain to probe the plausibility of
technologically-relevant fusion in the solid state.
|
We have developed a new on-axis digital holographic technique, heterodyne
holography. The resolution of this technique is limited mainly by the amount of
data recorded on two-dimensional photodetectors, i.e., the number of pixels and
their size. We demonstrate that it is possible to increase the resolution
linearly with the amount of recorded data by aperture synthesis as done in the
radar technique but with an optical holographic field.
|
We study composite D-wave superconductors consisting of randomly oriented and
randomly distributed superconducting droplets embedded into a matrix. In a
certain range of parameters the application of a small magnetic field enhances
the superconductivity in these materials while larger fields suppress
superconductivity as usual in conventional superconductors. We investigate the
magnetic field dependence of the superfluid density and the critical
temperature of such superconductors.
|
This work develops optimal preconditioners for the discrete H(curl) and
H(div) problems on two-dimensional surfaces by nodal auxiliary space
preconditioning [R. Hiptmair, J. Xu: SIAM J. Numer. Anal. \textbf{45},
2483-2509 (2007)]. In particular, on unstructured triangulated surfaces, we
develop fast and user-friendly preconditioners for the edge and face element
discretizations of curl-curl and grad-div problems based on inverting several
discrete surface Laplacians. The proposed preconditioners lead to efficient
iterative methods for computing harmonic tangential vector fields on discrete
surfaces. Numerical experiments on two- and three-dimensional hypersurfaces are
presented to test the performance of those surface preconditioners.
|
We develop the theory of canonical-dissipative systems, based on the
assumption that both the conservative and the dissipative elements of the
dynamics are determined by invariants of motion. In this case, known solutions
for conservative systems can be used for an extension of the dynamics, which
also includes elements such as the take-up/dissipation of energy. This way, a
rather complex dynamics can be mapped to an analytically tractable model, while
still covering important features of non-equilibrium systems. In our paper,
this approach is used to derive a rather general swarm model that considers (a)
the energetic conditions of swarming, i.e. for active motion, (b) interactions
between the particles based on global couplings. We derive analytical
expressions for the non-equilibrium velocity distribution and the mean squared
displacement of the swarm. Further, we investigate the influence of different
global couplings on the overall behavior of the swarm by means of
particle-based computer simulations and compare them with the analytical
estimations.
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We consider the decision problem for quantifier-free formulas whose atoms are
linear inequalities interpreted over the reals or rationals. This problem may
be decided using satisfiability modulo theory (SMT), using a mixture of a SAT
solver and a simplex-based decision procedure for conjunctions.
State-of-the-art SMT solvers use simplex implementations over rational numbers,
which perform well for typical problems arising from model-checking and program
analysis (sparse inequalities, small coefficients) but are slow for other
applications (denser problems, larger coefficients). We propose a simple
preprocessing phase that can be adapted on existing SMT solvers and that may be
optionally triggered. Despite using floating-point computations, our method is
sound and complete - it merely affects efficiency. We implemented the method
and provide benchmarks showing that this change brings a naive and slow
decision procedure ("textbook simplex" with rational numbers) up to the
efficiency of recent SMT solvers, over test cases arising from model-checking,
and makes it definitely faster than state-of-the-art SMT solvers on dense
examples.
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A broad range of membrane proteins display anomalous diffusion on the cell
surface. Different methods provide evidence for obstructed subdiffusion and
diffusion on a fractal space, but the underlying structure inducing anomalous
diffusion has never been visualized due to experimental challenges. We
addressed this problem by imaging the cortical actin at high resolution while
simultaneously tracking individual membrane proteins in live mammalian cells.
Our data confirm that actin introduces barriers leading to compartmentalization
of the plasma membrane and that membrane proteins are transiently confined
within actin fences. Furthermore, superresolution imaging shows that the
cortical actin is organized into a self-similar meshwork. These results present
a hierarchical nanoscale picture of the plasma membrane.
|
Electronic Design Automation (EDA) industry heavily reuses third party IP
cores. These IP cores are vulnerable to insertion of Hardware Trojans (HTs) at
design time by third party IP core providers or by malicious insiders in the
design team. State of the art research has shown that existing HT detection
techniques, which claim to detect all publicly available HT benchmarks, can
still be defeated by carefully designing new sophisticated HTs. The reason
being that these techniques consider the HT landscape to be limited only to the
publicly known HT benchmarks, or other similar (simple) HTs. However the
adversary is not limited to these HTs and may devise new HT design principles
to bypass these countermeasures.
In this paper, we discover certain crucial properties of HTs which lead to
the definition of an exponentially large class of Deterministic Hardware
Trojans $H_D$ that an adversary can (but is not limited to) design. The
discovered properties serve as HT design principles, based on which we design a
new HT called 'XOR-LFSR' and present it as a 'proof-of-concept' example from
the class $H_D$. These design principles help us understand the tremendous ways
an adversary has to design a HT, and show that the existing publicly known HT
benchmarks are just the tip of the iceberg on this huge landscape. This work,
therefore, stresses that instead of guaranteeing a certain (low) false negative
rate for a small constant set of publicly known HTs, a rigorous HT detection
tool should take into account these newly discovered HT design principles and
hence guarantee the detection of an exponentially large class (exponential in
number of wires in IP core) of HTs with negligible false negative rate.
|
Machine learning models are widely used for real-world applications, such as
document analysis and vision. Constrained machine learning problems are
problems where learned models have to both be accurate and respect constraints.
For continuous convex constraints, many works have been proposed, but learning
under combinatorial constraints is still a hard problem. The goal of this paper
is to broaden the modeling capacity of constrained machine learning problems by
incorporating existing work from combinatorial optimization. We propose first a
general framework called BaGeL (Branch, Generate and Learn) which applies
Branch and Bound to constrained learning problems where a learning problem is
generated and trained at each node until only valid models are obtained.
Because machine learning has specific requirements, we also propose an extended
table constraint to split the space of hypotheses. We validate the approach on
two examples: a linear regression under configuration constraints and a
non-negative matrix factorization with prior knowledge for latent semantics
analysis.
|
We propose a multi-dimensional structured state space (S4) approach to speech
enhancement. To better capture the spectral dependencies across the frequency
axis, we focus on modifying the multi-dimensional S4 layer with whitening
transformation to build new small-footprint models that also achieve good
performance. We explore several S4-based deep architectures in time (T) and
time-frequency (TF) domains. The 2-D S4 layer can be considered a particular
convolutional layer with an infinite receptive field although it utilizes fewer
parameters than a conventional convolutional layer. Evaluated on the
VoiceBank-DEMAND data set, when compared with the conventional U-net model
based on convolutional layers, the proposed TF-domain S4-based model is 78.6%
smaller in size, yet it still achieves competitive results with a PESQ score of
3.15 with data augmentation. By increasing the model size, we can even reach a
PESQ score of 3.18.
|
There continues to be enormous interest in the BCS to BEC transition as there
still is no exact theory. We recently reported a revealing reinterpretation of
the condensed phase Boson-Fermion Model (BFM) by comparing it to a cold atom
formulation [1]. While the ground and singly excited states appear to remain
continuous in all models we have examined, the collective modes contain a
singularity due to a Feshbach resonance (tuned by doping) causing a breakdown
of the Migdal theorem. As a result of vertex corrections, there is a
fundamental change in the nature of the superconductivity due to the formation
of preformed pairs as the previously suggested location [1] of a quantum
critical point in the fulleride phase diagram is passed. The result is a
quantum phase transition (QPT) between BCS and BEC-like (or Feshbach resonance)
superconductivity (SC).
We discuss features of the resonance and the role of the experimentally
observed preformed pair formation in fullerides, essential to the Boson-Fermion
Model (BFM), and often speculated since the work of Nozieres and Schmitt-Rink
[17]. Here, we present arguments to establish a model of the preformed pair
which can be favorably compared to a circular charge density wave (CDW)
isolated on a fulleride molecule. The binding is much larger than a Cooper
pair. The CDW seems to be stabalized by splitting of the Jahn-Teller active
vibrational modes to reduce Coulomb repulsions. Our conclusions are: 1) the
doping of two electrons into triply degenerate orbitals results in the
experimentally observed singlet state (CDW); and 2) this CDW (preformed pair)
has a dual role as doping is varied: suppression of BCS SC and enabling a
Feshbach resonance form of SC.
|
Nonlinear spin precession has been observed in 3He-B in large counterflow of
the normal and superfluid fractions. The new precessing state is stabilized at
high rf excitation level and displays frequency-locked precession over a large
range of frequency shifts, with the magnetization at its equilibrium value.
Comparison to analytical and numerical calculation indicates that in this state
the orbital angular momentum L of the Cooper pairs is oriented transverse to
the external magnetic field in a ``non-Leggett'' configuration with broken
spin-orbit coupling. The resonance shift depends on the tipping angle theta of
the magnetization as omega - omega_L = (Omega_B^2 / 2 omega_L)(cos(theta) -
1/5). The phase diagram of the precessing modes with arbitrary orientation of L
is constructed.
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A detailed study of the evolution of the magnetoresistance was performed on
electrodeposited Co/Cu multilayers with Cu layer thicknesses ranging from 0.5
nm to 4.5 nm. For thin Cu layers (up to 1.5 nm), anisotropic magnetoresistance
(AMR) was observed whereas multilayers with thicker Cu layers exhibited clear
giant magnetoresistance (GMR) behaviour. The GMR magnitude increased up to
about 3.5 to 4 nm Cu layer thickness and slightly decreased afterwards.
According to magnetic measurements, all samples exhibited ferromagnetic (FM)
behaviour. The relative remanence turned out to be about 0.75 for both AMR and
GMR type multilayers. This clearly indicates the absence of an
antiferromagnetic (AF) coupling between adjacent magnetic layers for Cu layers
even above 1.5 nm where the GMR effect occurs. The AMR behaviour at low spacer
thicknesses indicates the presence of strong FM coupling (due to, e.g.,
pin-holes in the spacer and/or areas of the Cu layer where the layer thickness
is very small). With increasing spacer thickness, the pin-hole density reduces
and/or the layer thickness uniformity improves which both lead to a weakening
of the FM coupling. This improvement in multilayer structure quality results in
a better separation of magnetic layers and the weaker coupling (or complete
absence of interlayer coupling) enables a more random magnetization orientation
of adjacent layers, all this leading to an increase of the GMR. Coercive field
and zero-field resistivity measurements as well as the results of a structural
study reported earlier on the same multilayers provide independent evidence for
the microstructural features established here. The large GMR reported
previously on such Co/Cu multilayers at Cu layer thicknesses around 1 nm can be
attributed to the presence of a fairly large superparamagnetic (SPM) fraction
rather than being due to a strong AF coupling.
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Teaching Unix to new students is a common tasks in many higher schools. This
paper presents an approach to such course where the students progress
autonomously with the help of the teacher. The traditional textbook is
complemented with a wiki, and the main thread of the course is a game, in the
form of a treasure hunt. The course finishes with a lab exam, where students
have to perform practical manipulations similar to the ones performed during
the treasure hunt. The exam is graded fully automatically. This paper discusses
the motivations and advantages of the approach, and gives an overall view of
the tools we developed. The tools are available from the web, and open-source,
hence re-usable outside the Ensimag.
|
We solve the one-dimensional Dirac equation by taking into account the
possibility of position-dependence in the mass function. We also take the Fermi
velocity to act as a local variable and examine the combined effects of the two
on the solvability of the Dirac equation with respect to the Morse potential.
Our results for the wave functions and the energy levels corresponding to such
an extended scheme are furnished in closed forms.
|
Geometric phase has been proposed as one of the promising methodologies to
perform fault tolerant quantum computations. However, since decoherence plays a
crucial role in such studies, understanding of mixed state geometric phase has
become important. While mixed state geometric phase was first introduced
mathematically by Uhlmann, recently Sjoqvist et al. [Phys. Rev. Lett. 85(14),
2845 (2000)] have described the mixed state geometric phase in the context of
quantum interference and shown theoretically that the visibility as well as the
shift of the interference pattern are functions of geometric phase and the
purity of the mixed state. Here we report the first experimental study of the
dependence of interference visibility and shift of the interference pattern on
the mixed state geometric phase by Nuclear Magnetic Resonance.
|
We will consider P-graph complexes, where P is a cyclic operad. P-graph
complexes are natural generalizations of Kontsevich's graph complexes -- for P
= the operad for associative algebras it is the complex of ribbon graphs, for P
= the operad for commutative associative algebras, the complex of all graphs.
We construct a `universal class' in the cohomology of the graph complex with
coefficients in a theory. The Kontsevich-type invariant is then an evaluation,
on a concrete cyclic algebra, of this class. We also explain some results of M.
Penkava and A. Schwarz on the construction of an invariant from a cyclic
deformation of a cyclic algebra. Our constructions are illustrated by a `toy
model' of tree complexes.
|
Lorenz values and the Gini index are popular quantities in Mathematical
Economics, and are used here in the context of quantum systems with
finite-dimensional Hilbert space. They quantify the uncertainty in the
probability distribution related to an orthonormal basis. It is shown that
Lorenz values are superadditive functions and the Gini indices are subadditive
functions. The supremum over all density matrices of the sum of the two Gini
indices with respect to position and momentum states, is used to define an
uncertainty coefficient which quantifies the uncertainty in the quantum system.
It is shown that the uncertainty coefficient is positive, and an upper bound
for it is given. Various examples demonstrate these ideas.
|
A model of key processes influencing the evolution of a hydrocarbon grain of
an arbitrary size under astrophysical conditions corresponding to ionized
hydrogen regions (HII regions) and supernova remnants is presented. The
considered processes include aromatization and photodestruction, sputtering by
electrons and ions, and shattering due to collisions between grains. The model
can be used to simulate the grain size distribution and the aromatization
degree during the evolution of HII regions and supernova remnants for a
specified radiation field, relative velocity of gas and dust, etc. The
contribution of various processes to the evolution of hydrocarbon dust grains
for parameters typical for the interstellar medium of our Galaxy is presented.
Small grains (less than 50 carbon atoms) should be fully aromatized in the
general interstellar medium. If larger grains initially have an aliphatic
structure, it is preserved to a substantial extent. Variations in the size
distribution of the grains due to their mutual collisions depend appreciably on
the adopted initial size distribution. For the MRN initial distribution a
significant redistribution of grain sizes is obtained, which increases the mass
fraction of smaller grains. Characteristic for an initial distribution from the
work of Jones et al. (2013), with high initial fraction of small grains, is a
general decrease in the number of grains of all sizes.
|
In this paper, we present two adaptive methods for the basis enrichment of
the mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving the
flow problem in heterogeneous media. We develop an a-posteriori error indicator
which depends on the norm of a local residual operator. Based on this
indicator, we construct an offline adaptive method to increase the number of
basis functions locally in coarse regions with large local residuals. We also
develop an online adaptive method which iteratively enriches the function space
by adding new functions computed based on the residual of the previous solution
and special minimum energy snapshots. We show theoretically and numerically the
convergence of the two methods. The online method is, in general, better than
the offline method as the online method is able to capture distant effects (at
a cost of online computations), and both methods have faster convergence than a
uniform enrichment. Analysis shows that the online method should start with
certain number of initial basis functions in order to have the best
performance. The numerical results confirm this and show further that with
correct selection of initial basis functions, the convergence of the online
method can be independent of the contrast of the medium. We consider cases with
both very high and very low conducting inclusions and channels in our numerical
experiments.
|
It is well known that weakly $p$-summable sequences in a Banach space $E$ are
associated to bounded operators from $\ell_{p^*}$ to $E$, and unconditionally
$p$-summable sequences in $E$ are associated to compact operators from
$\ell_{p^*}$ to $E$. Generalizing these results to a quite wide environment, we
characterize the classes of Banach spaces-valued sequences that are associated
to (or represented by) some Banach operator ideal. Using these
characterizations, we decide, among all sequence classes that usually appear in
the literature, which are represented by some Banach operator ideal and which
are not. Moreover, to each class that is represented by some Banach operator
ideal, we show an ideal that represents it. Illustrative examples and
additional applications are provided.
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The nonmesonic decay of $\Lambda$-hypernuclei provides access to the
nonleptonic weak decay process $\Lambda N \to NN$, which is achievable only
through the observation of hypernuclear ground-state decays. We continue the
discussion of some specific cases which make it possible to detect a few
exclusive transitions, namely, the stripping of nucleon from the ground state
results in a resonance state decaying via emission of two clusters. Delayed
clusters accompanying weak decay of light hypernuclei give a unique information
on spin dependence of the weak decay matrix elements.
|
Machine learning based data-driven technologies have shown impressive
performances in a variety of application domains. Most enterprises use data
from multiple sources to provide quality applications. The reliability of the
external data sources raises concerns for the security of the machine learning
techniques adopted. An attacker can tamper the training or test datasets to
subvert the predictions of models generated by these techniques. Data poisoning
is one such attack wherein the attacker tries to degrade the performance of a
classifier by manipulating the training data.
In this work, we focus on label contamination attack in which an attacker
poisons the labels of data to compromise the functionality of the system. We
develop Gradient-based Data Subversion strategies to achieve model degradation
under the assumption that the attacker has limited-knowledge of the victim
model. We exploit the gradients of a differentiable convex loss function
(residual errors) with respect to the predicted label as a warm-start and
formulate different strategies to find a set of data instances to contaminate.
Further, we analyze the transferability of attacks and the susceptibility of
binary classifiers. Our experiments show that the proposed approach outperforms
the baselines and is computationally efficient.
|
We prove the complete asymptotic expansion of the spectral function (the
integral kernel of the spectral projection) of a Schrodinger operator
$H=-\Delta+b$ acting in $R^d$ when the potential $b$ is real and either smooth
periodic, or generic quasi-periodic (finite linear combination of
exponentials), or belongs to a wide class of almost-periodic functions.
|
The overlap between the spectroscopic Galactic Archaeology with HERMES
(GALAH) survey & $Gaia$ provides a high-dimensional chemodynamical space of
unprecedented size. We present a first analysis of a subset of this overlap, of
7066 dwarf, turn-off, & sub-giant stars. [...] We investigate correlations
between chemical compositions, ages, & kinematics for this sample. Stellar
parameters & elemental abundances are derived from the GALAH spectra with the
spectral synthesis code SME. [...] We report Li, C, O, Na, Mg, Al, Si, K, Ca,
Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Y, as well as Ba & we note that we employ
non-LTE calculations for Li, O, Al, & Fe. We show that the use of astrometric &
photometric data improves the accuracy of the derived spectroscopic parameters,
especially $\log g$. [...] we recover the result that stars of the
high-$\alpha$ sequence are typically older than stars in the low-$\alpha$
sequence, the latter spanning $-0.7<$[Fe/H]$<+0.5$. While these two sequences
become indistinguishable in [$\alpha$/Fe] vs. [Fe/H] at the metal-rich regime,
we find that age can be used to separate stars from the extended high-$\alpha$
& the low-$\alpha$ sequence even in this regime. [...] we find that the old
stars ($>8$ Gyr have lower angular momenta $L_z$ than the Sun, which implies
that they are on eccentric orbits & originate from the inner disk. Contrary to
some previous smaller scale studies we find a continuous evolution in the
high-$\alpha$-sequence up to super-solar [Fe/H] rather than a gap, which has
been interpreted as a separate "high-$\alpha$ metal-rich" population. Stars in
our sample that are younger than 10 Gyr, are mainly found on the low
$\alpha$-sequence & show a gradient in $L_z$ from low [Fe/H]
($L_z>L_{z,\odot}$) towards higher [Fe/H] ($L_z<L_{z,\odot}$), which implies
that the stars at the ends of this sequence are likely not originating from the
close solar vicinity.
|
We start from a static, spherically symmetric space-time in the presence of
an electrostatic field and construct the mini-superspace Lagrangian that
reproduces the well known Reissner - Nordstr\"om solution. We identify the
classical integrals of motion that are to be mapped to quantum observables and
which are associated with the mass and charge. Their eigenvalue equations are
used as supplementary conditions to the Wheeler-DeWitt equation and a link is
provided between the existence of an horizon and to whether the spectrum of the
observables is fully discrete or not. For each case we provide an orthonormal
basis of states as emerges through the process of canonical quantization.
|
We consider a planar SIS-type Josephson junction between diffusive
superconductors (S) through an insulating tunnel interface (I). We construct
fully self-consistent perturbation theory with respect to the interface
conductance. As a result, we find correction to the first Josephson harmonic
and calculate the second Josephson harmonic. At arbitrary temperatures, we
correct previous results for the nonsinusoidal current-phase relation in
Josephson tunnel junctions, which were obtained with the help of conjectured
form of solution. Our perturbation theory also describes the difference between
the phases of the order parameter and of the anomalous Green functions.
|
In a previous paper, it has been shown that the entropy of non-extremal black
holes in Warped Anti-de Sitter (WAdS) spaces in massive gravity can be computed
microscopically in terms of a dual conformal field theory. Here, we extend this
computation to a set of asymptotic boundary conditions that, while still
gathering the WAdS$_3$ black holes, also allow for new solutions that are not
locally equivalent to WAdS$_3$ space, and therefore are associated to the local
degrees of freedom of the theory (bulk massive gravitons). After presenting
explicit examples of such geometries, we compute the asymptotic charge algebra
and show that it is generated by the semi-direct sum of Virasoro algebra and an
affine Kac-Moody algebra. The value of the central charge turns out to be
exactly the one that leads to reproduce the entropy of the WAdS$_3$ black
holes. This result probes the WAdS$_3$/CFT$_2$ correspondence in presence of
bulk gravitons.
|
A unique three-band patch antenna for high accuracy ranging between nodes in
open-loop coherent distributed antenna arrays is presented. Open-loop coherent
distributed operations require accurate relative position knowledge between
nodes to enable distributed beamforming operations. For the highest accuracy,
the inter-node ranging will typically occur at frequencies higher than the
frequency of the signal transmitted by the distributed array (the coherent
action signal) to enable wider bandwidth signals to be used, however it is
important that the inter-node ranging measure the distance between the antennas
transmitting the coherent action signal. In this work, a three-band antenna is
presented that is designed to support distributed beamforming at 1.88 GHz and
high-accuracy ranging using a sparse, two-tone waveform operating near 9.5 and
10.5 GHz. The two-tone waveform is supported by a slotted patch antenna
surrounded by a larger patch antenna supporting the 1.88 GHz array signal. The
antennas are concentrically designed to ensure that the phase centers of the
ranging antenna and the coherent action antenna are closely aligned. Simulated
and measured performance shows phase center displacement of approximately
lambda/10 relative to the coherent action signal, while maintaining S11 below
-10 dB at each band.
|
We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting
quantum interference device (SQUID) phase qubit with a 100 um^2 area junction
acquired over a range of microwave drive power and frequency detuning. Given
the slightly anharmonic level structure of the device, several excited states
play an important role in the qubit dynamics, particularly at high power. To
investigate the effects of these levels, multiphoton Rabi oscillations were
monitored by measuring the tunneling escape rate of the device to the voltage
state, which is particularly sensitive to excited state population. We compare
the observed oscillation frequencies with a simplified model constructed from
the full phase qubit Hamiltonian and also compare time-dependent escape rate
measurements with a more complete density-matrix simulation. Good quantitative
agreement is found between the data and simulations, allowing us to identify a
shift in resonance (analogous to the ac Stark effect), a suppression of the
Rabi frequency, and leakage to the higher excited states.
|
Chemically non-equilibrated quark-antiquark matter is studied within the
Nambu-Jona-Lasinio model. The equations of state of non-strange (q=u,d) and
strange (q=s) quark-antiquark systems are calculated in the mean-field
approximation. The existence of metastable bound states with zero pressure is
predicted at finite densities and temperatures less than about 50 MeV. It is
shown that the minimum energy per particle occurs for symmetric systems, with
equal densities of quarks and antiquarks. At T=0 these metastable states have
quark number densities of about 0.5 fm^-3 for q=u,d and of 1 fm^-3 for q=s. A
first order chiral phase transition is found at finite densities and
temperatures. The critical temperature for this phase transition is
approximately 75 MeV (90 MeV) for the non-strange (strange) baryon-free
quark-antiquark matter. For realistic choices of parameters, the model does not
predict the phase transition in chemically equilibrated systems. Possible decay
channels of the metastable quark-antiquark droplets and their signatures in
relativistic heavy-ion collisions are discussed.
|
We report the results of a mm-wave molecular line survey of the nearby (D ~
70 pc), 12 Myr-old system V4046 Sgr -- a tight (9 R_sun separation),
short-period (2.42 day) binary with nearly equal component masses of ~0.9 M_sun
-- conducted with the 30 m telescope of the Institut de Radio Astronomie
Millimetrique (IRAM). We detected rotational transitions of 12CO 13CO, HCN, CN,
and HCO+. The double-peaked CO line profiles of V4046 Sgr are well fit by a
model invoking a Keplerian disk with outer radius of ~250 AU that is viewed at
an inclination i = 35 degrees. We infer minimum disk gas and dust masses of ~13
and ~20 Earth masses from the V4046 Sgr CO line and submm continuum fluxes,
respectively. The actual disk gas mass could be much larger if the gas-phase CO
is highly depleted and/or 13CO is very optically thick. The overall similarity
of the circumbinary disk of V4046 Sgr to the disk orbiting the single, ~8
Myr-old star TW Hya -- a star/disk system often regarded as representative of
the early solar nebula -- indicates that gas giant planets are likely
commonplace among close binary star systems. Given the relatively advanced age
and proximity of V4046 Sgr, these results provide strong motivation for future
high-resolution imaging designed to ascertain whether a planetary system now
orbits its twin suns.
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We discuss some results around the following question: Let $f$ be a
nonconstant complex entire function and $a$, $b$ two distinct complex numbers.
If $f$ and its derivative $f'$ share their simple $a$-points and also share the
value $b$, does this imply $f\equiv f'$?
|
Here we propose a new design paradigm for a superconducting nanowire single
photon detector that uses a multi-layer architecture that places the electric
leads beneath the nanowires. This allows for a very large number of detector
elements, which we will call pixels in analogy to a conventional CCD camera, to
be placed in close proximity. This leads to significantly better photon number
resolution than current single and multi-nanowire meanders, while maintaining
similar detection areas. We discuss the reset time of the pixels and how the
design can be modified to avoid the latching failure seen in extremely short
superconducting nanowires. These advantages give a multi-layer superconducting
number-resolving photon detector significant advantages over the current design
paradigm of long superconducting nanowire meanders. Such advantages are
desirable in a wide array of photonics applications.
|
We demonstrate temperature measurement of a sample attached to the end of a
cantilever using cantilever magnetometry of solid air ``contamination'' of the
sample surface. In experiments like our Magnetic Resonance Force Microscopy
(MRFM), the sample is mounted at the end of a thin cantilever with small
thermal conductance. Thus, the sample can be at a significantly different
temperature than the bulk of the instrument. Using cantilever magnetometry of
the oxygen paramagnetism in solid air provides the temperature of the sample,
without any modifications to our MRFM (Magnetic Resonance Force Microscopy)
apparatus.
|
We investigate the metal-insulator Mott transition in a generalized version
of the periodic Anderson model, in which a band of itinerant electrons is
hybridrized with a narrow and strongly correlated band. Using dynamical
mean-field theory, we show that the precondition for a Mott transition is an
integer total filling of the two bands, while for an integer constant
occupation of the correlated band the system remains a correlated metal at
arbitrary large interaction strength. We picture the transition at a
non-integer filling of the correlated orbital as the Mott localization of the
singlet states between itinerant and strongly interacting electrons, having
occupation of one per lattice site. We show that the Mott transition is of the
first-order and we characterize the nature of the resulting insulating state
with respect to relevant physical parameters, such as the charge-transfer
energy.
|
Since Artificial Intelligence (AI) software uses techniques like deep
lookahead search and stochastic optimization of huge neural networks to fit
mammoth datasets, it often results in complex behavior that is difficult for
people to understand. Yet organizations are deploying AI algorithms in many
mission-critical settings. To trust their behavior, we must make AI
intelligible, either by using inherently interpretable models or by developing
new methods for explaining and controlling otherwise overwhelmingly complex
decisions using local approximation, vocabulary alignment, and interactive
explanation. This paper argues that intelligibility is essential, surveys
recent work on building such systems, and highlights key directions for
research.
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Simulations of pulverised coal combustion rely on various models, required in
order to correctly approximate the flow, chemical reactions, and behavior of
solid particles. These models, in turn, rely on multiple model parameters,
which are determined through experiments or small-scale simulations and contain
a certain level of uncertainty. The competing effects of transport, particle
physics, and chemistry give rise to various scales and disparate dynamics,
making it a very challenging problem to analyse. Therefore, the steady
combustion process of a single solid particle is considered as a starting point
for this study. As an added complication, the large number of parameters
present in such simulations makes a purely forward approach to sensitivity
analysis very expensive and almost infeasible. Therefore, the use of
adjoint-based algorithms, to identify and quantify the underlying sensitivities
and uncertainties, is proposed. This adjoint framework bears a great advantage
in this case, where a large input space is analysed, since a single forward and
backward sweep provides sensitivity information with respect to all parameters
of interest. In order to investigate the applicability of such methods, both
discrete and continuous adjoints are considered, and compared to the
conventional approaches, such as finite differences, and forward sensitivity
analysis. Various quantities of interest are considered, and sensitivities with
respect to the relevant combustion parameters are reported for two different
freestream compositions, describing air and oxy-atmospheres. This study serves
as a benchmark for future research, where unsteady and finally turbulent cases
will be considered.
|
We present WFPC2 images in the F450W, F606W and F814W filters of the
interacting pair of galaxies NGC 454. Our data indicate that the system is in
the early stages of interaction. A population of young star-clusters has formed
around the late component, and substantial amounts of gas have sunk into the
center of the earlier component, where it has not yet produced significant
visible star formation or nuclear activity. We have photometric evidence that
the star-clusters have strong line emission, which indicate the presence of a
substantial component of hot, massive stars which formed less than 5-10 Myrs
ago.
|
We define new algebras, local bimodules, and bimodule maps in the spirit of
Ozsvath-Szabo's bordered knot Floer homology. We equip them with the structure
of 2-representations of the categorified negative half U^- of U_q(gl(1|1)),
1-morphisms of such, and 2-morphisms respectively, and show that they
categorify representations of U_q(gl(1|1)^-) and maps between them. Unlike with
Ozsvath-Szabo's algebras, the algebras considered here can be built from a
higher tensor product operation recently introduced by Rouquier and the author.
Our bimodules are all motivated by holomorphic disk counts in Heegaard
diagrams; for positive and negative crossings, the bimodules can also be
expressed as mapping cones involving a singular-crossing bimodule and the
identity bimodule. In fact, they arise from an action of the monoidal category
of Soergel bimodules via Rouquier complexes in the usual way, the first time
(to the author's knowledge) such an expression has been obtained for braiding
bimodules in Heegaard Floer homology.
Furthermore, the singular crossing bimodule naturally factors into two
bimodules for trivalent vertices; such bimodules have not appeared in previous
bordered-Floer approaches to knot Floer homology. The action of the Soergel
category comes from an action of categorified quantum gl(2) on the
2-representation 2-category of U^- in line with the ideas of skew Howe duality,
where the trivalent vertex bimodules are associated to 1-morphisms E, F in
categorified quantum gl(2).
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Confinement of filamentary objects is ubiquitous in numerous biological,
medical, and engineering scenarios. Quantitatively determining the mechanical
interaction between flexible filaments and surface confinement is particularly
challenging due to the unknown contact force induced by elasticity interacting
with geometric constraints. Here, we consider a simplified model of confined
filamentary object: an elastic curve under surface confinement. Local force and
moment balance equation incorporating the role of contact is utilized to derive
the contact force exerted by surface on the confined elastic curve. It reveals
the relation between contact force and local geometry at balanced state and
provides a route to obtain the contact force from local confined geometry
directly. Examples are provided to illustrate how to calculate contact force
from obtained geometries. We believe that our results contribute to future
efforts in the mechanics of filamentary objects under surface confinement.
|
The spectra of heavy quarkonia are studied in two approaches: with the use of
the Afonin-Pusenkov representation of the Regge trajectory for the squared
excitation energy $E^2(nl)$ (ERT), and using the relativistic Hamiltonian with
the universal interaction. The parameters of the ERTs are extracted from
experimental mass differences and their values in bottomonium: the intercept
$a(b\bar b)=0.131\,$GeV$^2$, the slope of the orbital ERT $b_l(b\bar b)
=0.50$\,GeV$^2$, and the slope of the radial ERT, $b_n(b\bar
b)=0.724$\,GeV$^2$, appear to be smaller than those in charmonium, where
$a(c\bar c)=0.381$\,GeV$^2$, $b_l(c\bar c)=0.686$\,GeV$^2$, and the radial
slope $b_n(c\bar c)= 1.074$\,GeV$^2$, which value is close to that in light
mesons, $b_n(q\bar q)=1.1(1)$\,GeV$^2$. For the resonances above the $D\bar D$
threshold the masses of the $\chi_{c0}(nP)$ with $n=2,3,4$, equal to 4218\,MeV,
4503\,MeV, 4754\,MeV, are obtained, while above the $B\bar B$ threshold the
resonances $\Upsilon(3\,^3D_1)$ with the mass 10693\,MeV and
$\chi_{b1}(4\,^3P_1)$ with the mass 10756\,MeV are predicted.
|
The enrichment history of $r$-process elements has been imprinted on the
stellar abundances that change in accordance with increasing metallicity in
galaxies. Close examination of the [Eu/Fe] feature caused by stars in nearby
galaxies, including the Large Magellanic Cloud (LMC), shows its perplexity. The
decreasing trend of the [Eu/Fe] feature is followed by a nearly constant value;
this trend is generally attributed to an onset of the delayed Fe release from
type Ia supernovae (SNe Ia), which is the same interpretation of the
[$\alpha$/Fe] feature. However, this feature appears in the LMC at [Fe/H] of
approximately -0.7, which is significantly higher than that for the [alpha/Fe]
case ($\approx$ -2). This result potentially indicates the presence of an
overlooked property of the $r$-process site that remains unseen in the study of
the Milky Way. Here, we propose that this [Eu/Fe]-knee feature is created by a
fade-out of core-collapse SNe producing $r$-process elements; these elements
along with neutron star mergers (NSMs) promote the $r$-process enrichment under
the condition for this specific SNe such that their occurrence is limited to a
low-metallicity environment. This metallicity threshold for the occurrence rate
of $r$-process SNe at a subsolar is nearly identical to that for long gamma-ray
bursts whose origin may be connected to fast-rotating massive stars. Moreover,
we reason that the contribution of Eu from NSMs is crucial to maintain a high
[Eu/Fe] at an early stage in dwarf galaxies by a balance with Fe from SNe Ia;
both enrichments via NSMs and SNe Ia proceed with similar delay time
distributions.
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Among the symmetries in physics, the rotation symmetry is most familiar to
us. It is known that the spherical harmonics serve useful purposes when the
world is rotated. Squeeze transformations are also becoming more prominent in
physics, particularly in optical sciences and in high-energy physics. As can be
seen from Dirac's light-cone coordinate system, Lorentz boosts are squeeze
transformations. Thus the squeeze transformation is one of the fundamental
transformations in Einstein's Lorentz-covariant world. It is possible to define
a complete set of orthonormal functions defined for one Lorentz frame. It is
shown that the same set can be used for other Lorentz frames. Transformation
properties are discussed. Physical applications are discussed in both optics
and high-energy physics. It is shown that the Lorentz harmonics provide the
mathematical basis for squeezed states of light. It is shown also that the same
set of harmonics can be used for understanding Lorentz-boosted hadrons in
high-energy physics. It is thus possible to transmit physics from one branch of
physics to the other branch using the mathematical basis common to them.
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We construct an entanglement measure that coincides with the generalized
concurrence for a general pure bipartite state based on wedge product.
Moreover, we construct an entanglement measure for pure multi-qubit states,
which are entanglement monotone. Furthermore, we generalize our result on a
general pure multipartite state.
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We study the dynamics of kinks in the $\phi^4$ model subjected to a
parametric ac force, both with and without damping, as a paradigm of solitary
waves with internal modes. By using a collective coordinate approach, we find
that the parametric force has a non-parametric effect on the kink motion.
Specifically, we find that the internal mode leads to a resonance for
frequencies of the parametric driving close to its own frequency, in which case
the energy of the system grows as well as the width of the kink. These
predictions of the collective coordinate theory are verified by numerical
simulations of the full partial differential equation. We finally compare this
kind of resonance with that obtained for non-parametric ac forces and conclude
that the effect of ac drivings on solitary waves with internal modes is exactly
the opposite of their character in the partial differential equation.
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We find new solutions to the five-dimensional Einstein-Maxwell-dilaton theory
with cosmological constant where the dilaton field couples to the
electromagnetic field as well as to the cosmological term with two different
coupling constants. The five-dimensional spacetime is non-stationary and is a
conformally regular spacetime, everywhere. Both the dilaton field and the
electromagnetic field depends on time and two spatial directions. The
cosmological constant takes positive, negative or zero value, depending on the
value of coupling constant. We study the physical properties of the spacetime
and show that the solutions are unique in five dimensions and can't be uplifted
to higher-dimensional Einstein-Maxwell theory or Einstein gravity in presence
of cosmological constant. Moreover, we construct new solutions to the theory
where both coupling constants are equal.
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The temperature dependences of the galvanomagnetic and thermoelectric
transport coefficients within a generic hot-spot model are reconsidered.
Despite the recent success in explaining ac Hall effect data in
YBa_{2}Cu_{3}O_{7}, a general feature of this model is a departure from the
approximately universal temperature dependences observed for normal state
transport in the optimally doped cuprates. In this paper, we discuss such
systematic deviations and illustrate some of their effects through a concrete
numerical example using the calculated band structure for YBa_{2}Cu_{3}O_{7}.
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Speaker verification (SV) suffers from unsatisfactory performance in
far-field scenarios due to environmental noise andthe adverse impact of room
reverberation. This work presents a benchmark of multichannel speech
enhancement for far-fieldspeaker verification. One approach is a deep neural
network-based, and the other is a combination of deep neural network andsignal
processing. We integrated a DNN architecture with signal processing techniques
to carry out various experiments. Ourapproach is compared to the existing
state-of-the-art approaches. We examine the importance of enrollment in
pre-processing,which has been largely overlooked in previous studies.
Experimental evaluation shows that pre-processing can improve the SVperformance
as long as the enrollment files are processed similarly to the test data and
that test and enrollment occur within similarSNR ranges. Considerable
improvement is obtained on the generated and all the noise conditions of the
VOiCES dataset.
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Block copolymers provide a wonderful platform in studying the soft condensed
matter systems. Many fascinating ordered structures have been discovered in
bulk and confined systems. Among various theories, the self-consistent field
theory (SCFT) has been proven to be a powerful tool for studying the
equilibrium ordered structures. Many numerical methods have been developed to
solve the SCFT model. However, most of these focus on the bulk systems, and
little work on the confined systems, especially on general curved surfaces. In
this work, we developed a linear surface finite element method, which has a
rigorous mathematical theory to guarantee numerical precsion, to study the
self-assembled phases of block copolymers on general curved surfaces based on
the SCFT. Furthermore, to capture the consistent surface for a given
self-assembled pattern, an adaptive approach to optimize the size of the
general curved surface has been proposed. To demonstrate the power of this
approach, we investigate the self-assembled patterns of diblock copolymers on
several distinct curved surfaces, including five closed surfaces and an
unclosed surface. Numerical results illustrate the efficiency of the proposed
method. The obtained ordered structures are consistent with the previous
results on standard surfaces, such as sphere and torus. Certainly, the proposed
numerical framework has the capability of studying the phase behaviors on
general surfaces precisely.
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We present comprehensive observational results of the metallicity effect on
the fraction of globular clusters (GC) that contain low-mass X-ray binaries
(LMXB), by utilizing all available data obtained with Chandra for LMXBs and HST
ACS for GCs. Our primary sample consists of old elliptical galaxies selected
from the ACS Virgo and Fornax surveys. To improve statistics at both the lowest
and highest X-ray luminosity, we also use previously reported results from
other galaxies. It is well known that the LMXB fraction is considerably higher
in red, metal-rich, than in blue, metal-poor GCs. In this paper, we test
whether this metallicity effect is X-ray luminosity-dependent, and find that
the effect holds uniformly in a wide luminosity range. This result is
statistically significant (at >= 3 sigma) in LMXBs with luminosities in the
range LX = 2 x 10^37 - 5 x 10^38 erg s-1, where the ratio of LMXB fractions in
metal-rich to metal-poor GCs is R = 3.4 +- 0.5. A similar ratio is also found
at lower (down to 10^36 erg s-1) and higher luminosities (up to the ULX
regime), but with less significance (~2 sigma confidence). Because different
types of LMXBs dominate in different luminosities, our finding requires a new
explanation for the metallicity effect in dynamically formed LMXBs. We confirm
that the metallicity effect is not affected by other factors such as stellar
age, GC mass, stellar encounter rate, and galacto-centric distance.
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By adopting the empirical constraints related to the estimates of Helium
enhancement ($\Delta Y$), present mass ratio between first and second stellar
generations ($M_{1G}/M_{2G}$) and the actual mass of Galactic globular clusters
($M_{GC}$), we envisage a possible scenario for the formation of these stellar
systems. Our approach allows for the possible loss of stars through evaporation
or tidal interactions and different star formation efficiencies. In our
approach the star formation efficiency of the first generation
($\epsilon_{1G}$) is the central factor that links the stellar generations as
it not only defines both the mass in stars of the first generation and the
remaining mass available for further star formation, but it also fixes the
amount of matter required to contaminate the second stellar generation. In this
way, $\epsilon_{1G}$ is fully defined by the He enhancement between successive
generations in a GC. We also show that globular clusters fit well within a
$\Delta Y$ {\it vs} $M_{1G}/M_{2G}$ diagram which indicates three different
evolutionary paths. The central one is for clusters that have not loss stars,
through tidal interactions, from either of their stellar generations, and thus
their present $M_{GC}$ value is identical to the amount of low mass stars ($M_*
\le$ 1 M$_\odot$) that resulted from both stellar generations. Other possible
evolutions imply either the loss of first generation stars or the combination
of a low star formation efficiency in the second stellar generation and/or a
loss of stars from the second generation. From these considerations we derive a
lower limit to the mass ($M_{tot}$) of the individual primordial clouds that
gave origin to globular clusters.
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We propose an application of sequence generative adversarial networks
(SeqGAN), which are generative adversarial networks for discrete sequence
generation, for creating polyphonic musical sequences. Instead of a monophonic
melody generation suggested in the original work, we present an efficient
representation of a polyphony MIDI file that simultaneously captures chords and
melodies with dynamic timings. The proposed method condenses duration, octaves,
and keys of both melodies and chords into a single word vector representation,
and recurrent neural networks learn to predict distributions of sequences from
the embedded musical word space. We experiment with the original method and the
least squares method to the discriminator, which is known to stabilize the
training of GANs. The network can create sequences that are musically coherent
and shows an improved quantitative and qualitative measures. We also report
that careful optimization of reinforcement learning signals of the model is
crucial for general application of the model.
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We propose an innovative Parallel Quantum Local Search (PQLS) methodology
that leverages the capabilities of small-scale quantum computers to efficiently
address complex combinatorial optimization problems. Traditional Quantum Local
Search (QLS) methods face limitations due to the sequential nature of solving
sub-problems, which arises from dependencies between their solutions. Our
approach transcends this constraint by simultaneously executing multiple QLS
pathways and aggregating their most effective outcomes at certain intervals to
establish a ``generation''. Each subsequent generation commences with the
optimal solution from its predecessor, thereby significantly accelerating the
convergence towards an optimal solution. Our findings demonstrate the profound
impact of parallel quantum computing in enhancing the resolution of Ising
problems, which are synonymous with combinatorial optimization challenges.
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We consider a discrete-time, linear state equation with delay which arises as
a model for a trader's account value when buying and selling a risky asset in a
financial market. The state equation includes a nonnegative feedback gain
$\alpha$ and a sequence $v(k)$ which models asset returns which are within
known bounds but otherwise arbitrary. We introduce two thresholds, $\alpha_-$
and $\alpha_+$, depending on these bounds, and prove that for $\alpha <
\alpha_-$, state positivity is guaranteed for all time and all asset-return
sequences; i.e., bankruptcy is ruled out and positive solutions of the state
equation are continuable indefinitely. On the other hand, for $\alpha >
\alpha_+$, we show that there is always a sequence of asset returns for which
the state fails to be positive for all time; i.e., along this sequence,
bankruptcy is certain and the solution of the state equation ceases to be
meaningful after some finite time. Finally, this paper also includes a
conjecture which says that for the "gap" interval $\alpha_- \leq \alpha \leq
\alpha_+,$ state positivity is also guaranteed for all time. Support for the
conjecture, both theoretical and computational, is provided.
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A search for leptoquarks has been performed in 310 pb-1 of data from ppbar
collisions at a center-of-mass energy of 1.96 TeV, collected by the D0 detector
at the Fermilab Tevatron Collider. The topology analyzed consists of acoplanar
jets with missing transverse energy. The data show good agreement with standard
model expectations, and a lower mass limit of 136 GeV has been set at the 95%
C.L. for a scalar leptoquark decaying exclusively into a quark and a neutrino.
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Intensive longitudinal data (ILD) collected in mobile health (mHealth)
studies contain rich information on multiple outcomes measured frequently over
time that have the potential to capture short-term and long-term dynamics.
Motivated by an mHealth study of smoking cessation in which participants
self-report the intensity of many emotions multiple times per day, we describe
a dynamic factor model that summarizes the ILD as a low-dimensional,
interpretable latent process. This model consists of two submodels: (i) a
measurement submodel--a factor model--that summarizes the multivariate
longitudinal outcome as lower-dimensional latent variables and (ii) a
structural submodel--an Ornstein-Uhlenbeck (OU) stochastic process--that
captures the temporal dynamics of the multivariate latent process in continuous
time. We derive a closed-form likelihood for the marginal distribution of the
outcome and the computationally-simpler sparse precision matrix for the OU
process. We propose a block coordinate descent algorithm for estimation.
Finally, we apply our method to the mHealth data to summarize the dynamics of
18 different emotions as two latent processes. These latent processes are
interpreted by behavioral scientists as the psychological constructs of
positive and negative affect and are key in understanding vulnerability to
lapsing back to tobacco use among smokers attempting to quit.
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A symplectic cut of a manifold M with a Hamiltonian circle action is a
symplectic quotient of M x C. If M is Kaehler then, since C is Kaehler, the cut
space is Kaehler as well. The symplectic structure on the cut is well
understood. In this paper we describe the complex structure (and hence the
metric) on the cut. We then generalize the construction to the case where M has
a torus action and C is replaced by a toric Kaehler manifold.
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We show that the density and temperature dependences of the
$\alpha$-relaxation time of several glassforming polymers can be described
through a single scaling variable $X=e(\rho)/T$, where $e(\rho)$ is well fitted
by a power law $\rho^x$, $x$ being a species-specific parameter. This implies
that ``fragility'' is an intrinsic, density-independent property of a
glassformer characterizing its super-Arrhenius slowing down of relaxations, and
it leads us to propose a modification of the celebrated Angell plot.
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Depth estimation provides an alternative approach for perceiving 3D
information in autonomous driving. Monocular depth estimation, whether with
single-frame or multi-frame inputs, has achieved significant success by
learning various types of cues and specializing in either static or dynamic
scenes. Recently, these cues fusion becomes an attractive topic, aiming to
enable the combined cues to perform well in both types of scenes. However,
adaptive cue fusion relies on attention mechanisms, where the quadratic
complexity limits the granularity of cue representation. Additionally, explicit
cue fusion depends on precise segmentation, which imposes a heavy burden on
mask prediction. To address these issues, we propose the GSDC Transformer, an
efficient and effective component for cue fusion in monocular multi-frame depth
estimation. We utilize deformable attention to learn cue relationships at a
fine scale, while sparse attention reduces computational requirements when
granularity increases. To compensate for the precision drop in dynamic scenes,
we represent scene attributes in the form of super tokens without relying on
precise shapes. Within each super token attributed to dynamic scenes, we gather
its relevant cues and learn local dense relationships to enhance cue fusion.
Our method achieves state-of-the-art performance on the KITTI dataset with
efficient fusion speed.
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We study the properties of the 3-dimensional and projected shapes of haloes
using high resolution numerical simulations and observational data where the
latter comes from the 2PIGG (Eke et al. 2004) and SDSS-DR3GC group catalogues
(Merchan & Zandivarez 2005). We investigate the dependence of halo shape on
characteristics such as mass and number of members. In the 3-dimensional case,
we find a significant correlation between the mass and halo shape; massive
systems are more prolate than small haloes. We detect a source of strong
systematics in estimates of the triaxiality of a halo, which is found to be a
strong function of the number of members; LCDM haloes usually characterised by
triaxial shapes, slightly bent toward prolate forms, appear more oblate when
taking only a small subset of the halo particles. The ellipticities of observed
2PIGG and SDSS-DR3GC groups are found to be strongly dependent on the number of
group members, so that poor groups appear more elongated than rich ones.
However, this is again an artifact caused by poor statistics and not an
intrinsic property of the galaxy groups, nor an effect from observational
biases. We interpret these results with the aid of a GALFORM mock 2PIGG
catalogue. When comparing the group ellipticities in mock and real catalogues,
we find an excellent agreement between the trends of shapes with number of
group members. When carefully taking into account the effects of low number
statistics, we find that more massive groups are consistent with more elongated
shapes. Finally, our studies find no significant correlations between the shape
of observed 2PIGG or SDSS-DR3GC groups with the properties of galaxy members
such as colour or spectral type index.
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The generalization of the Jessen-Marcinkiewicz-Zygmund-type theorem for the
abstract space with measure was obtained in current paper. Some applications to
classical harmonic analysis were reviewed.
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We study the distortions induced by peculiar velocities on the redshift-space
correlation function of galaxies of different morphological types in the
Pisces-Perseus redshift survey. Redshift-space distortions affect early- and
late-type galaxies in different ways. In particular, at small separations, the
dominant effect comes from virialized cluster cores, where ellipticals are the
dominant population. The net result is that a meaningful comparison of the
clustering strength of different morphological types can be performed only in
real space, i.e., after projecting out the redshift distortions on the
two-point correlation function xi(r_p,pi). A power-law fit to the projected
function w_p(r_p) on scales smaller than 10/h Mpc gives r_o =
8.35_{-0.76}^{+0.75} /h Mpc, \gamma = 2.05_{-0.08}^{+0.10} for the early-type
population, and r_o = 5.55_{-0.45}^{+0.40} /h Mpc, \gamma =
1.73_{-0.08}^{+0.07} for spirals and irregulars. These values are derived for a
sample luminosity brighter than M_{Zw} = -19.5. We detect a 25% increase of r_o
with luminosity for all types combined, from M_{Zw} = -19 to -20. In the
framework of a simple stable-clustering model for the mean streaming of pairs,
we estimate sigma_12(1), the one-dimensional pairwise velocity dispersion
between 0 and 1 /h Mpc, to be 865^{+250}_{-165} km/s for early-type galaxies
and 345^{+95}_{-65} km/s for late types. This latter value should be a fair
estimate of the pairwise dispersion for ``field'' galaxies; it is stable with
respect to the presence or absence of clusters in the sample, and is consistent
with the values found for non-cluster galaxies and IRAS galaxies at similar
separations.
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We consider sequences of operators $U_n:L^1(X)\to M(X)$, where $X$ is a space
of homogeneous type. Under certain conditions on the operators $U_n$ we give a
complete characterization of convergence (divergence) sets of functional
sequences $U_n(f)$, where $f\in L^p(X)$, $1\le p\le \infty$. The results are
applied to characterize convergence sets of some specific operator sequences in
classical analysis.
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Shape restrictions such as monotonicity on functions often arise naturally in
statistical modeling.
We consider a Bayesian approach to the problem of estimation of a monotone
regression function and testing for monotonicity. We construct a prior
distribution using piecewise constant functions. For estimation, a prior
imposing monotonicity of the heights of these steps is sensible, but the
resulting posterior is harder to analyze theoretically. We consider a
``projection-posterior'' approach, where a conjugate normal prior is used, but
the monotonicity constraint is imposed on posterior samples by a projection map
on the space of monotone functions. We show that the resulting posterior
contracts at the optimal rate $n^{-1/3}$ under the $L_1$-metric and at a nearly
optimal rate under the empirical $L_p$-metrics for $0<p\le 2$. The
projection-posterior approach is also computationally more convenient. We also
construct a Bayesian test for the hypothesis of monotonicity using the
posterior probability of a shrinking neighborhood of the set of monotone
functions. We show that the resulting test has a universal consistency property
and obtain the separation rate which ensures that the resulting power function
approaches one.
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In the classical obstacle problem, the free boundary can be decomposed into
"regular" and "singular" points. As shown by Caffarelli in his seminal papers
\cite{C77,C98}, regular points consist of smooth hypersurfaces, while singular
points are contained in a stratified union of $C^1$ manifolds of varying
dimension. In two dimensions, this $C^1$ result has been improved to
$C^{1,\alpha}$ by Weiss \cite{W99}.
In this paper we prove that, for $n=2$ singular points are locally contained
in a $C^2$ curve. In higher dimension $n\ge 3$, we show that the same result
holds with $C^{1,1}$ manifolds (or with countably many $C^2$ manifolds), up to
the presence of some "anomalous" points of higher codimension. In addition, we
prove that the higher dimensional stratum is always contained in a
$C^{1,\alpha}$ manifold, thus extending to every dimension the result in
\cite{W99}.
We note that, in terms of density decay estimates for the contact set, our
result is optimal. In addition, for $n\ge3$ we construct examples of very
symmetric solutions exhibiting linear spaces of anomalous points, proving that
our bound on their Hausdorff dimension is sharp.
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A number of merging galaxy clusters show the presence of large-scale radio
emission associated with the intra-cluster medium (ICM). These synchrotron
sources are generally classified as radio haloes and radio relics. Whilst it is
commonly accepted that mergers play a crucial role in the formation of radio
haloes and relics, not all the merging clusters show the presence of giant
diffuse radio sources and this provides important information concerning
current models. The Abell 781 complex is a spectacular system composed of an
apparent chain of clusters on the sky. Its main component is undergoing a
merger and hosts peripheral emission that is classified as a candidate radio
relic and a disputed radio halo. We used new LOw Frequency ARay (LOFAR)
observations at 143 MHz and archival Giant Metrewave Radio Telescope (GMRT)
observations at 325 and 610 MHz to study radio emission from non-thermal
components in the ICM of Abell 781. Complementary information came from
XMM-Newton data, which allowed us to investigate the connection with the
thermal emission and its complex morphology. The origin of the peripheral
emission is still uncertain. We speculate that it is related to the interaction
between a head tail radio galaxy and shock. However, the current data allow us
only to set an upper limit of $\mathcal{M} < 1.4$ on the Mach number of this
putative shock. Instead, we successfully characterise the surface brightness
and temperature jumps of a shock and two cold fronts in the main cluster
component of Abell 781. Their positions suggest that the merger is involving
three substructures. We do not find any evidence for a radio halo either at the
centre of this system or in the other clusters of the chain. We place an upper
limit to the diffuse radio emission in the main cluster of Abell 781 that is a
factor of 2 below the current radio power-mass relation for giant radio haloes.
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Given a pretrained encoder-based language model, how can we accurately
compress it without retraining? Retraining-free structured pruning algorithms
are crucial in pretrained language model compression due to their significantly
reduced pruning cost and capability to prune large language models. However,
existing retraining-free algorithms encounter severe accuracy degradation, as
they fail to handle pruning errors, especially at high compression rates. In
this paper, we propose K-prune (Knowledge-preserving pruning), an accurate
retraining-free structured pruning algorithm for pretrained encoder-based
language models. K-prune focuses on preserving the useful knowledge of the
pretrained model to minimize pruning errors through a carefully designed
iterative pruning process composed of knowledge measurement,
knowledge-preserving mask search, and knowledge-preserving weight-tuning. As a
result, K-prune shows significant accuracy improvements up to 58.02%p higher F1
score compared to existing retraining-free pruning algorithms under a high
compression rate of 80% on the SQuAD benchmark without any retraining process.
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We discuss a model metallic glass in which Barkhausen Noise can be studied in
exquisite detail, free of thermal effects and of the rate of ramping of the
magnetic field. The mechanism of the jumps in magnetic moment that cause the
Barkhausen Noise can be fully understood as consecutive instabilities where an
eigenvalue of the Hessian matrix hits zero, leading to a magnetization jump
$\Delta m$ which is simultaneous with a stress and energy changes $\Delta
\sigma$ and $\Delta U$ respectively. Contrary to common belief we find no
"movements of magnetic domain boundaries" across pinning sites, no fractal
domains, no self-organized criticality and no exact scaling behaviour. We
present a careful numerical analysis of the statistical properties of the
phenomenon, and show that with every care taken this analysis is tricky, and
easily misleading. Without a guiding theory it is almost impossible to get the
right answer for the statistics of Barkhausen Noise. We therefore present an
analytic theory, showing that the probability distribution function (pdf) of
Barkhausen Noise is not a power law times an exponential cutoff.
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The pure spinor formalism for the superstring has the advantage over the more
conventional Ramond-Neveu-Schwarz formalism of being manifestly spacetime
supersymmetric, which simplifies the computation of multiparticle and multiloop
amplitudes and allows the description of Ramond-Ramond backgrounds. In addition
to the worldsheet variables of the Green-Schwarz-Siegel action, the pure spinor
formalism includes bosonic ghost variables which are constrained spacetime
spinors and are needed for covariant quantization using a nilpotent BRST
operator.
In this review, several applications of the formalism are described including
the explicit computation in D=10 superspace of the general disk amplitude with
an arbitrary number of external massless states, genus one amplitudes with up
to seven external states, genus two amplitudes with up to five external states,
and the low-energy limit of the genus three amplitude with up to four external
states. The pure spinor formalism has also been used to covariantly quantize
the superstring in an $AdS_5\times S^5$ background and might be useful for
proving the AdS-CFT correspondence in the limit of small AdS radius.
This is an overview written for the "Handbook of Quantum Gravity", eds. C.
Bambi, L. Modesto and I. Shapiro.
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