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Although Potent purports to use only radial velocities in reconstructing the
potential velocity field of galaxies, the derivation of transverse components
is implicit in the smoothing procedures adopted. Thus the possibility arises of
using nonradial line integrals to derive a smoothed velocity field. For an
inhomogeneous galaxy distribution the optimal path for integration need not be
radial, and can be obtained using max-flow algorithms. In this paper we
describe how one may use Dijkstra's algorithm to obtain this optimal path and
velocity field, and present the results of applying the algorithm to a
realistic spatial distribution of galaxies. These results show that the method
has limited effect due to the large smoothing scales employed in Potent.
However, the viability of the technique is demonstrated and, finally, we
discuss other possible methods involving averaging over an ensemble of
non-radial paths for improving a potential velocity field derived from
redshifts.
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Hyperpolarized 13C-MRI allows real time observation of metabolism in vivo.
Imaging sequences have been developed to follow the metabolism of [1-13C]
pyruvate and extract reaction kinetics, which can show tumour treatment
response. We applied the fitting model and algorithm for the imaging data of
mice tumour models and determined error estimates for the parameters of
interest. Data was least-squares fitted onto a two-site exchange model in
MATLAB, followed by statistic computation to assess model performance.
Inference through the application of MCMC was also performed. The modelling and
inference process extracted quantitative information satisfactorily and
reproducibly, demonstrating metabolic activity and intratumour heterogeneity.
Finally, novel fitting methods were evaluated and further recommendations were
made.
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It has been observed by several authors that well-known periodization
strategies like tent or Chebychev transforms lead to remarkable results for the
recovery of multivariate functions from few samples. So far, theoretical
guarantees are missing. The goal of this paper is twofold. On the one hand, we
give such guarantees and briefly describe the difficulties of the involved
proof. On the other hand, we combine these periodization strategies with recent
novel constructive methods for the efficient subsampling of finite frames in
$\mathbb{C}$. As a result we are able to reconstruct non-periodic multivariate
functions from very few samples. The used sampling nodes are the result of a
two-step procedure. Firstly, a random draw with respect to the Chebychev
measure provides an initial node set. A further sparsification technique
selects a significantly smaller subset of these nodes with equal approximation
properties. This set of sampling nodes scales linearly in the dimension of the
subspace on which we project and works universally for the whole class of
functions. The method is based on principles developed by Batson, Spielman, and
Srivastava and can be numerically implemented. Samples on these nodes are then
used in a (plain) least-squares sampling recovery step on a suitable hyperbolic
cross subspace of functions resulting in a near-optimal behavior of the
sampling error. Numerical experiments indicate the applicability of our
results.
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We study the near horizon 2d gravity theory which captures the near extremal
thermodynamics of BTZ with excess mass $\delta M$ and excess angular momentum
$\delta J =\mathcal{L}\, \delta M$ over extremality. We find that the
Jackiw-Teitelboim theory is able to capture such departures from extremality
with an additional parameter $\mathcal{L}$ relating it to the near extremal BTZ
configuration. We are able to show this by obtaining new simultaneous near
horizon near extremal limits of the BTZ geometry parametrized by $\mathcal{L}$.
The resulting Jackiw-Teitelboim theory captures the near extremal
thermodynamics of such BTZ geometries provided we identify the temperature
$T^{(2)}_H$ of the $AdS_2$ geometry in the Jackiw-Teitelboim theory to be
$T^{(2)}_H=T_H/(1-\mu\,\mathcal{L})$ where $T_H$ is the BTZ temperature and
$\mu$ its chemical potential with $\mu\,\mathcal{L}<1$.
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$\alpha$-Sn is an elemental topological material, whose topological phases
can be tuned by strain and magnetic field. Such tunability offers a substantial
potential for topological electronics. However, InSb substrates, commonly used
to stabilize $\alpha$-Sn allotrope, suffer from parallel conduction,
restricting transport investigations and potential applications. Here, the
successful MBE growth of high-quality $\alpha$-Sn layers on insulating, hybrid
CdTe/GaAs(001) substrates, with bulk electron mobility approaching 20000
cm$^2$V$^{-1}$s$^{-1}$ is reported. The electronic properties of the samples
are systematically investigated by independent complementary techniques,
enabling thorough characterization of the 3D Dirac (DSM) and Weyl (WSM)
semimetal phases induced by the strains and magnetic field, respectively.
Magneto-optical experiments, corroborated with band structure modeling, provide
an exhaustive description of the bulk states in the DSM phase. The modeled
electronic structure is directly observed in angle-resolved photoemission
spectroscopy, which reveals linearly dispersing bands near the Fermi level. The
first detailed study of negative longitudinal magnetoresistance relates this
effect to the chiral anomaly and, consequently, to the presence of WSM.
Observation of the $\pi$ Berry phase in Shubnikov-de Haas oscillations agrees
with the topologically non-trivial nature of the investigated samples. Our
findings establish $\alpha$-Sn as an attractive topological material for
exploring relativistic physics and future applications.
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Using the Yukawa couplings of the minimal supersymmetric SU(5) model, the
rates for $\mu \to e\gamma$, $\mu \to e$ conversion and $\tau \to \mu \gamma$
are computed. For a selectron mass of 100 GeV, and without exploring the full
parameter space, we find rates which are one order of magnitude beneath present
experimental bounds. It is argued that these relatively large rates have a wide
applicability, so that lepton flavor violating signals provide a more general
test of supersymmetric unification than can be obtained from either proton
decay or neutrino masses.
|
Unconventional quasiparticles emerging in the fractional quantum Hall regime
present the challenge of observing their exotic properties unambiguously.
Although the fractional charge of quasiparticles has been demonstrated since
nearly three decades, the first convincing evidence of their anyonic quantum
statistics has only recently been obtained and, so far, the so-called scaling
dimension that determines the quasiparticles propagation dynamics remains
elusive. In particular, while the non-linearity of the tunneling quasiparticle
current should reveal their scaling dimension, the measurements fail to match
theory, arguably because this observable is not robust to non-universal
complications. Here we achieve an unambiguous measurement of the scaling
dimension from the thermal to shot noise cross-over, and observe a long-awaited
agreement with expectations. Measurements are fitted to the predicted finite
temperature expression involving both the quasiparticles scaling dimension and
their charge, in contrast to previous charge investigations focusing on the
high bias shot noise regime. A systematic analysis, repeated on multiple
constrictions and experimental conditions, consistently matches the theoretical
scaling dimensions for the fractional quasiparticles emerging at filling
factors 1/3, 2/5 and 2/3. This establishes a central property of fractional
quantum Hall anyons, and demonstrates a powerful and complementary window into
exotic quasiparticles.
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For each positive integer $m$, the $m$th order harmonic numbers are given by
$$H_n^{(m)}=\sum_{0<k\le n}\frac1{k^m}\ \ (n=0,1,2,\ldots).$$ We discover exact
values of some series involving harmonic numbers of order not exceeding three.
For example, we conjecture that
$$\sum_{k=0}^\infty(6k+1)\frac{\binom{2k}k^3}{256^k}\left(H_{2k}^{(3)}-\frac{7}{64}H_{k}^{(3)}\right)
=\frac{25\zeta(3)}{8\pi}-G,$$
where $G$ denotes the Catalan constant $\sum_{k=0}^\infty(-1)^k/(2k+1)^2$.
This paper contains $66$ conjectures posed by the author since October 2022.
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There is a known analogy between growth questions for class groups and for
Selmer groups. If $p$ is a prime, then the $p$-torsion of the ideal class group
grows unboundedly in $\mathbb{Z}/p\mathbb{Z}$-extensions of a fixed number
field $K$, so one expects the same for the $p$-Selmer group of a nonzero
abelian variety over $K$. This Selmer group analogue is known in special cases
and we prove it in general, along with a version for arbitrary global fields.
|
There are significant benefits to serve deep learning models from relational
databases. First, features extracted from databases do not need to be
transferred to any decoupled deep learning systems for inferences, and thus the
system management overhead can be significantly reduced. Second, in a
relational database, data management along the storage hierarchy is fully
integrated with query processing, and thus it can continue model serving even
if the working set size exceeds the available memory. Applying model
deduplication can greatly reduce the storage space, memory footprint, cache
misses, and inference latency. However, existing data deduplication techniques
are not applicable to the deep learning model serving applications in
relational databases. They do not consider the impacts on model inference
accuracy as well as the inconsistency between tensor blocks and database pages.
This work proposed synergistic storage optimization techniques for duplication
detection, page packing, and caching, to enhance database systems for model
serving. We implemented the proposed approach in netsDB, an object-oriented
relational database. Evaluation results show that our proposed techniques
significantly improved the storage efficiency and the model inference latency,
and serving models from relational databases outperformed existing deep
learning frameworks when the working set size exceeds available memory.
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For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in
Perkins (1990) that if the underlying spatial motion belongs to a certain class
of L\'evy processes that admit jumps, then with probability one the closed
support of $X_t$ is the whole space for almost all $t>0$ before extinction, the
so-called ``instantaneous propagation'' property. In this paper for
superprocesses on $\mathbb{R}^1$ whose spatial motion is the symmetric stable
process of index $\alpha \in (0,2/3)$, we prove that there exist exceptional
times at which the support is compact and nonempty. Moreover, we show that the
set of exceptional times is dense with full Hausdorff dimension. Besides, we
prove that near extinction, the support of the superprocess is concentrated
arbitrarily close to the distinction point, thus upgrading the corresponding
results in Tribe (1992) from $\alpha \in (0,1/2)$ to $\alpha \in (0,2/3)$, and
we further show that the set of such exceptional times also admits a full
Hausdorff dimension.
|
High-speed railway is playing an important role in mass transportation, due
to its lower energy consumption, less environmental pollution, larger capacity
and higher safety features. The development of high-speed railway makes
people's life more and more convenient. Meanwhile, providing high quality of
service broadband communications for fast-moving users still remains unsolved,
despite the fact that new solutions of incremental improvements are keeping up
with this unprecedented communication requirement growth. This article proposes
a communication system infrastructure based on airborne relay for high-speed
trains in the further Cyber-Physical Systems. Comparisons and feasibility
analysis are provided as well as discussions of key wireless technologies and
obstacles in this system.
|
Our understanding of various states of matter usually relies on the
assumption of thermodynamic equilibrium. However, the transitions between
different phases of matter can be strongly affected by non-equilibrium
phenomena. Here we demonstrate and explain an example of non-equilibrium
stalling of a continuous, second-order phase transition. We create a
superheated atomic Bose gas, in which a Bose-Einstein condensate (BEC) persists
above the equilibrium critical temperature, $T_c$, if its coupling to the
surrounding thermal bath is reduced by tuning interatomic interactions. For
vanishing interactions the BEC persists in the superheated regime for a minute.
However, if strong interactions are suddenly turned on, it rapidly "boils"
away. Our observations can be understood within a two-fluid picture, treating
the condensed and thermal components of the gas as separate equilibrium systems
with a tuneable inter-component coupling. We experimentally reconstruct a
non-equilibrium phase diagram of our gas, and theoretically reproduce its main
features.
|
We prove higher regularity for nonlinear nonlocal equations with possibly
discontinuous coefficients of VMO-type in fractional Sobolev spaces. While for
corresponding local elliptic equations with VMO coefficients it is only
possible to obtain higher integrability, in our nonlocal setting we are able to
also prove a substantial amount of higher differentiability, so that our result
is in some sense of purely nonlocal type. By embedding, we also obtain higher
H\"older regularity for such nonlocal equations.
|
We show that there is a canonical, order preserving map $\psi$ of lattices of
subgroups, which maps the lattice $\Sub(A)$ of subgroups of the ideal class
group of a galois number field $\K$ into the lattice $\Sub(\KH/\K)$ of
subfields of the Hilbert class field. Furthermore, this map is a capitulation
map in the sense that all the primes in the classes of $A' \subset A$
capitulate in $\psi(A')$. In particular we have a new, strong version of the
generalized Hilbert 94 Theorem, which confirms the result of Myiake and adds
more structure to (part) of the capitulation kernel of subfields of $\KH$.
|
The valley-Chern and spin-valley-Chern numbers are the key concepts in
valleytronics. They are topological numbers in the Dirac theory but not in the
tight-binding model. We analyze the bulk-edge correspondence between the two
phases which have the same Chern and spin-Chern numbers but different
valley-Chern and spin-valley-Chern numbers. The edge state between them is
topologically trivial in the tight-binding model but is shown to be as robust
as the topological edge. We construct Y-junctions made of topological edges.
They satisfy the topological Kirchhoff law, where the topological charges are
conserved at the junction. We may interpret a Y-junction as a scattering
process of particles which have four topological numbers. It would be a
milestone of future topological electronics.
|
The hyperbolic space $ \H^d$ can be defined as a pseudo-sphere in the $(d+1)$
Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of
linear isometries of the Minkowski space such that $\H^d/\Gamma$ is a compact
manifold. We introduce Fuchsian convex bodies, which are closed convex sets in
Minkowski space, globally invariant for the action of a Fuchsian group. A
volume can be associated to each Fuchsian convex body, and, if the group is
fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be
studied in the same manner as convex bodies of Euclidean space in the classical
Brunn--Minkowski theory. For example, support functions can be defined, as
functions on a compact hyperbolic manifold instead of the sphere.
The main result is the convexity of the associated volume (it is log concave
in the classical setting). This implies analogs of Alexandrov--Fenchel and
Brunn--Minkowski inequalities. Here the inequalities are reversed.
|
In this article, we investigate various physical implications of quantum
circuit complexity using squeezed state formalism of Primordial Gravitational
Waves (PGW). Recently quantum information theoretic concepts, such as
entanglement entropy, and complexity are playing a pivotal role to understand
the dynamics of quantum system even in the diverse fields such as, high energy
physics and cosmology. This paper is devoted in studying quantum circuit
complexity of PGW for various cosmological models, such as de Sitter,
inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas
model etc. We compute complexity measure using both Covariance and Nielsen's
wave function method for three different choices of quantum initial vacua:
Motta-Allen, $\alpha$ and Bunch-Davies. Besides computing circuit complexity,
we have also computed Von-Neumann entanglement entropy. By making the
comparison of complexity with entanglement entropy, we are able to probe
various features regarding the dynamics of evolution for different cosmological
models. Because entanglement entropy is independent of the squeezing angle, we
are able to understand more details of the system using Nielsen's measure of
complexity which is dependent on both squeezing parameter and angle. This
implies that quantum complexity could indeed be a useful probe to study quantum
features in cosmological scale. Quantum complexity is also becoming a powerful
technique to understand the chaotic behaviour and random fluctuations of
quantum fields. Using the growth of complexity, we are able to compute quantum
Lyapunov exponent for various cosmological models and comment on it's chaotic
nature.
|
We give combinatorial models for complex, smooth, non-spherical, generic,
irreducible representations of the group G=PGL(2,F), where F is a
non-archimedean locally compact field. They use the graphs X_k lying above the
tree of G, introduced in a previous work. We show that such representations may
be realized as quotients of the cohomology of X_k for some k, or equivalently
as spaces of discrete harmonic forms on X_k. For supercuspidal representations
these models are unique.
|
The Loewner equation describes the time development of an analytic map into
the upper half of the complex plane in the presence of a "forcing", a defined
singularity moving around the real axis. The applications of this equation use
the trace, the locus of singularities in the upper half plane. This note
discusses the structure of the trace for the case in which the forcing
function, xi(t), is proportional to (-t)^beta with beta in the interval (0,
1/2). In this case, the trace is a simple curve, gamma(t), which touches the
real axis twice. It is computed by using matched asymptotic analysis to compute
the trajectory of the Loewner evolution in the neighborhood of the singularity,
and then assuming a smooth mapping of these trajectories away from the
singularity. Near the t=0 singularity, the trace has a shape given by
[ Re(gamma(t)-gamma(0)) ]^(1-beta) ~ [ beta*Im(gamma(t)) ]^beta ~
O(xi(t))^(1-beta).
A numerical calculation of the trace provides support for the asymptotic
theory.
|
Video data is explosively growing. As a result of the "big video data",
intelligent algorithms for automatic video summarization have re-emerged as a
pressing need. We develop a probabilistic model, Sequential and Hierarchical
Determinantal Point Process (SH-DPP), for query-focused extractive video
summarization. Given a user query and a long video sequence, our algorithm
returns a summary by selecting key shots from the video. The decision to
include a shot in the summary depends on the shot's relevance to the user query
and importance in the context of the video, jointly. We verify our approach on
two densely annotated video datasets. The query-focused video summarization is
particularly useful for search engines, e.g., to display snippets of videos.
|
Liquid crystals with molecules constrained to the tangent bundle of a curved
surface show interesting phenomena resulting from the tight coupling of the
elastic and bulk free energies of the liquid crystal with geometric properties
of the surface. We derive thermodynamically consistent Frank-Oseen-Helfrich and
Landau-de Gennes-Helfrich models which consider the simultaneous relaxation of
the director/Q-tensor fields and the surface. The resulting systems of vector-
or tensor-valued surface partial differential equation and geometric evolution
laws are numerically solved to tackle the rich dynamics of these systems and to
compute the resulting equilibrium shapes. The results strongly depend on the
intrinsic and extrinsic curvature contributions and can lead to unexpected
asymmetric shapes.
|
The two-dimensional (2D) material Cr$_2$Ge$_2$Te$_6$ is a member of the class
of insulating van der Waals magnets. Here, using high resolution angle-resolved
photoemission spectroscopy in a detailed temperature dependence study, we
identify a clear response of the electronic structure to a dimensional
crossover in the form of two distinct temperature scales marking onsets of
modifications in the electronic structure. Specifically, we observe Te
$p$-orbital-dominated bands to undergo changes at the Curie transition
temperature T$_C$ while the Cr $d$-orbital-dominated bands begin evolving at a
higher temperature scale. Combined with neutron scattering, density functional
theory calculations, and Monte Carlo simulations, we find that the electronic
system can be consistently understood to respond sequentially to the distinct
temperatures at which in-plane and out-of-plane spin correlations exceed a
characteristic length scale. Our findings reveal the sensitivity of the
orbital-selective electronic structure for probing the dynamical evolution of
local moment correlations in vdW insulating magnets.
|
We present a photoluminescence study of single-layer MoS2 flakes on SiO2
surfaces. We demonstrate that the luminescence peak position of flakes prepared
from natural MoS2, which varies by up to 25 meV between individual as-prepared
flakes, can be homogenized by annealing in vacuum, which removes adsorbates
from the surface. We use HfO2 and Al2O3 layers prepared by atomic layer
deposition to cover some of our flakes. We clearly observe a suppression of the
low-energy luminescence peak observed for as-prepared flakes at low
temperatures, indicating that this peak originates from excitons bound to
surface adsorbates. We also observe different temperature-induced shifts of the
luminescence peaks for the oxide-covered flakes. This effect stems from the
different thermal expansion coefficients of the oxide layers and the MoS2
flakes. It indicates that the single-layer MoS2 flakes strongly adhere to the
oxide layers and are therefore strained.
|
Recent advances in deep learning have enabled complex real-world use cases
comprised of multiple vision tasks and detection tasks are being shifted to the
edge side as a pre-processing step of the entire workload. Since running a deep
model on resource-constraint devices is challenging, techniques for efficient
inference methods are demanded. In this paper, we present an objectness-aware
object detection method to reduce computational cost by sparsifying activation
values on background regions where target objects don't exist. Sparsified
activation can be exploited to increase inference speed by software or hardware
accelerated sparse convolution techniques. To accomplish this goal, we
incorporate a light-weight objectness mask generation (OMG) network in front of
an object detection (OD) network so that it can zero out unnecessary background
areas of an input image before being fed into the OD network. In experiments,
by switching background activation values to zero, the average number of zero
values increases further from 36% to 68% on MobileNetV2-SSDLite even with ReLU
activation while maintaining accuracy on MS-COCO. This result indicates that
the total MAC including both OMG and OD networks can be reduced to 62% of the
original OD model when only non-zero multiply-accumulate operations are
considered. Moreover, we show a similar tendency in heavy networks (VGG and
RetinaNet) and an additional dataset (PASCAL VOC).
|
We develop a theory of superconducting pairing in low-density Strontium
titanate due to quadratic coupling of electron density to soft transverse
optical phonons. It leads to static attractive potential between electrons
which decay length scales inversely with soft optical gap. For low electron
densities attraction between electrons is local and transition temperature Tc
was found. The Tc(n) dependence in agreement with experimental data for low
doping was calculated. Next, we show that suppression of Tc by hydrostatic
pressure and strong increase of Tc due to isotop substitution are explained
within our theory.
|
This paper formulates a penalized empirical likelihood (PEL) method for
inference on the population mean when the dimension of the observations may
grow faster than the sample size. Asymptotic distributions of the PEL ratio
statistic is derived under different component-wise dependence structures of
the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii)
short-range dependence. It follows that the limit distribution of the proposed
PEL ratio statistic can vary widely depending on the correlation structure, and
it is typically different from the usual chi-squared limit of the empirical
likelihood ratio statistic in the fixed and finite dimensional case. A unified
subsampling based calibration is proposed, and its validity is established in
all three cases, (i)-(iii). Finite sample properties of the method are
investigated through a simulation study.
|
We demonstrate the multiplexing of a classical coherent and a quantum state
of light in a single telecommunciation fiber. For this purpose we make use of
spontaneous parametric down conversion and quantum frequency conversion to
generate photon pairs at 854 nm and the telecom O-band. The herald photon
triggers a telecom C-band laser pulse. The telecom single photon and the laser
pulse are combined and coupled to a standard telecom fiber. Low background time
correlation of the classical and quantum signal behind the fiber shows
successful telecommunication channel multiplexing.
|
We present a complete algebraic classification for the curvature tensor in
Weyl-Cartan geometry, by applying methods of eigenvalues and principal null
directions on its irreducible decomposition under the group of global Lorentz
transformations, thus providing a full invariant characterisation of all the
possible algebraic types of the torsion and nonmetricity field strength tensors
in Weyl-Cartan space-times. As an application, we show that in the framework of
Metric-Affine Gravity the field strength tensors of a dynamical torsion field
cannot be doubly aligned with the principal null directions of the Riemannian
Weyl tensor in scalar-flat, slowly rotating, stationary and axisymmetric
space-times.
|
This paper explores the integration of cross-polarized stimulated Brillouin
scattering (XP-SBS) with Kerr and quadratic nonlinearities in lithium niobate
(LN) to enhance photonic device performance. Three novel applications are
demonstrated: (i) a reconfigurable stimulated Brillouin laser (SBL) with 0.7-Hz
narrow linewidth and 40-nm tunability, enabled by XP-SBS's thermo-optic phase
matching; (ii) an efficient coherent mode converter achieving 55% conversion
efficiency via intracavity Brillouin-enhanced four-wave mixing; (iii) a
Brillouin-quadratic laser and frequency comb operational in near-infrared and
visible bands, benefiting from the interaction between XP-SBS and quadratic
nonlinearity. These advancements promise significant improvements in photonic
technologies, including narrow-linewidth laser, microcomb generation, and
optical signal processing, paving the way for more robust and versatile
applications.
|
In this paper we prove an invariant Harnack inequality on
Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot
groups. The proof relies on an "abstract" formulation of a technique recently
introduced by Caffarelli and Silvestre. In addition, we write explicitly the
Poisson kernel for a class of degenerate subelliptic equations in product-type
Carnot groups.
|
Conditional independence (CI) tests are widely used in statistical data
analysis, e.g., they are the building block of many algorithms for causal graph
discovery. The goal of a CI test is to accept or reject the null hypothesis
that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in
\mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional
independence testing under the constraint of differential privacy. We design
two private CI testing procedures: one based on the generalized covariance
measure of Shah and Peters (2020) and another based on the conditional
randomization test of Cand\`es et al. (2016) (under the model-X assumption). We
provide theoretical guarantees on the performance of our tests and validate
them empirically. These are the first private CI tests with rigorous
theoretical guarantees that work for the general case when $Z$ is continuous.
|
Fine-grained annotations---e.g. dense image labels, image segmentation and
text tagging---are useful in many ML applications but they are labor-intensive
to generate. Moreover there are often systematic, structured errors in these
fine-grained annotations. For example, a car might be entirely unannotated in
the image, or the boundary between a car and street might only be coarsely
annotated. Standard ML training on data with such structured errors produces
models with biases and poor performance. In this work, we propose a novel
framework of Error-Correcting Networks (ECN) to address the challenge of
learning in the presence structured error in fine-grained annotations. Given a
large noisy dataset with commonly occurring structured errors, and a much
smaller dataset with more accurate annotations, ECN is able to substantially
improve the prediction of fine-grained annotations compared to standard
approaches for training on noisy data. It does so by learning to leverage the
structures in the annotations and in the noisy labels. Systematic experiments
on image segmentation and text tagging demonstrate the strong performance of
ECN in improving training on noisy structured labels.
|
We prove that to store n bits x so that each prefix-sum query Sum(i) :=
sum_{k < i} x_k can be answered by non-adaptively probing q cells of log n
bits, one needs memory > n + n/log^{O(q)} n. Our bound matches a recent upper
bound of n + n/log^{Omega(q)} n by Patrascu (FOCS 2008), also non-adaptive. We
also obtain a n + n/log^{2^{O(q)}} n lower bound for storing a string of
balanced brackets so that each Match(i) query can be answered by non-adaptively
probing q cells. To obtain these bounds we show that a too efficient data
structure allows us to break the correlations between query answers.
|
This paper proposes a method to reconstruct the neural radiance field with
equirectangular omnidirectional images. Implicit neural scene representation
with a radiance field can reconstruct the 3D shape of a scene continuously
within a limited spatial area. However, training a fully implicit
representation on commercial PC hardware requires a lot of time and computing
resources (15 $\sim$ 20 hours per scene). Therefore, we propose a method to
accelerate this process significantly (20 $\sim$ 40 minutes per scene). Instead
of using a fully implicit representation of rays for radiance field
reconstruction, we adopt feature voxels that contain density and color features
in tensors. Considering omnidirectional equirectangular input and the camera
layout, we use spherical voxelization for representation instead of cubic
representation. Our voxelization method could balance the reconstruction
quality of the inner scene and outer scene. In addition, we adopt the
axis-aligned positional encoding method on the color features to increase the
total image quality. Our method achieves satisfying empirical performance on
synthetic datasets with random camera poses. Moreover, we test our method with
real scenes which contain complex geometries and also achieve state-of-the-art
performance. Our code and complete dataset will be released at the same time as
the paper publication.
|
Significant progress has been made with artistic robots. However, existing
robots fail to produce high-quality portraits in a short time. In this work, we
present a drawing robot, which can automatically transfer a facial picture to a
vivid portrait, and then draw it on paper within two minutes averagely. At the
heart of our system is a novel portrait synthesis algorithm based on deep
learning. Innovatively, we employ a self-consistency loss, which makes the
algorithm capable of generating continuous and smooth brush-strokes. Besides,
we propose a componential sparsity constraint to reduce the number of
brush-strokes over insignificant areas. We also implement a local sketch
synthesis algorithm, and several pre- and post-processing techniques to deal
with the background and details. The portrait produced by our algorithm
successfully captures individual characteristics by using a sparse set of
continuous brush-strokes. Finally, the portrait is converted to a sequence of
trajectories and reproduced by a 3-degree-of-freedom robotic arm. The whole
portrait drawing robotic system is named AiSketcher. Extensive experiments show
that AiSketcher can produce considerably high-quality sketches for a wide range
of pictures, including faces in-the-wild and universal images of arbitrary
content. To our best knowledge, AiSketcher is the first portrait drawing robot
that uses neural style transfer techniques. AiSketcher has attended a quite
number of exhibitions and shown remarkable performance under diverse
circumstances.
|
Smooth pseudodifferential operators on $\mathbb{R}^n$ can be characterized by
their mapping properties between $L^p-$Sobolev spaces due to Beals and
Ueberberg. In applications such a characterization would also be useful in the
non-smooth case, for example to show the regularity of solutions of a partial
differential equation. Therefore, we will show that every linear operator $P$,
which satisfies some specific continuity assumptions, is a non-smooth
pseudodifferential operator of the symbol-class $C^{\tau}
S^m_{1,0}(\mathbb{R}^n \times \mathbb{R}^n)$. The main new difficulties are the
limited mapping properties of pseudodifferential operators with non-smooth
symbols.
|
Milner (1984) defined a process semantics for regular expressions. He
formulated a sound proof system for bisimilarity of process interpretations of
regular expressions, and asked whether this system is complete.
We report conceptually on a proof that shows that Milner's system is
complete, by motivating, illustrating, and describing all of its main steps. We
substantially refine the completeness proof by Grabmayer and Fokkink (2020) for
the restriction of Milner's system to `1-free' regular expressions. As a
crucial complication we recognize that process graphs with empty-step
transitions that satisfy the layered loop-existence/elimination property LLEE
are not closed under bisimulation collapse (unlike process graphs with LLEE
that only have proper-step transitions). We circumnavigate this obstacle by
defining a LLEE-preserving `crystallization procedure' for such process graphs.
By that we obtain `near-collapsed' process graphs with LLEE whose strongly
connected components are either collapsed or of `twin-crystal' shape. Such
near-collapsed process graphs guarantee provable solutions for bisimulation
collapses of process interpretations of regular expressions.
|
Code writing is repetitive and predictable, inspiring us to develop various
code intelligence techniques. This survey focuses on code search, that is, to
retrieve code that matches a given query by effectively capturing the semantic
similarity between the query and code. Deep learning, being able to extract
complex semantics information, has achieved great success in this field.
Recently, various deep learning methods, such as graph neural networks and
pretraining models, have been applied to code search with significant progress.
Deep learning is now the leading paradigm for code search. In this survey, we
provide a comprehensive overview of deep learning-based code search. We review
the existing deep learning-based code search framework which maps query/code to
vectors and measures their similarity. Furthermore, we propose a new taxonomy
to illustrate the state-of-the-art deep learning-based code search in a
three-steps process: query semantics modeling, code semantics modeling, and
matching modeling which involves the deep learning model training. Finally, we
suggest potential avenues for future research in this promising field.
|
In this article, we study the uniqueness problem for the generalized gauss
maps of minimal surfaces (with the same base) immersed in $\mathbb R^{n+1}$
which have the same inverse image of some hypersurfaces in a projective
subvariety $V\subset\mathbb P^n(\mathbb C)$. As we know, this is the first time
the unicity of generalized gauss maps on minimal surfaces sharing hypersurfaces
in a projective varieties is studied. Our results generalize and improve the
previous results in this field.
|
We demonstrate sensing of inhomogeneous dc magnetic fields by employing
entangled trapped ions, which are shuttled in a segmented Paul trap. As
\textit{sensor states}, we use Bell states of the type
$\left|\uparrow\downarrow\right>+\text{e}^{\text{i}\varphi}\left|\downarrow\uparrow\right>$
encoded in two $^{40}$Ca$^+$ ions stored at different locations. Due to the
linear Zeeman effect, the relative phase $\varphi$ serves to measure the
magnetic field difference between the constituent locations, while common-mode
fluctuations are rejected. Consecutive measurements on sensor states encoded in
the $\text{S}_{1/2}$ ground state and in the $\text{D}_{5/2}$ metastable state
are used to separate an ac Zeeman shift from the linear dc Zeeman effect. We
measure magnetic field differences over distances of up to $6.2~\text{mm}$,
with accuracies of around 300~fT, sensitivities down to $12~\text{pT} /
\sqrt{\text{Hz}}$, and spatial resolutions down to $10~\text{nm}$. For
optimizing the information gain while maintaining a high dynamic range, we
implement an algorithm for Bayesian frequency estimation.
|
We present results concerning the light and strange quark contents of the
nucleon using $N_f=2+1+1$ flavours of maximally twisted mass fermions. The
corresponding $\sigma$-terms are casting light on the origin of the nucleon
mass and their values are important to interpret experimental data from direct
dark matter searches. We discuss our strategy to estimate systematic
uncertainties arising in our computations. Our preliminary results for the
$\sigma-$terms read $\sigma_{\pi N} = 37(2.6)(24.7) \mev$ and
$\sigma_s=28(8)(10) \mev$. We present our recent final analysis of the $y_N$
parameter and found $y_N=0.135(46)$ including
systematics\cite{Alexandrou:2013nda}.
|
We introduce a scale of anisotropic Sobolev spaces defined through a
three-parameter family of Fourier multipliers and study their functional
analytic properties. These spaces arise naturally in PDE when studying
traveling wave solutions, and we give some simple applications of the spaces in
this direction.
|
This paper is about the wireless sensor network in environmental monitoring
applications. A Wireless Sensor Network consists of many sensor nodes and a
base station. The number and type of sensor nodes and the design protocols for
any wireless sensor network is application specific. The sensor data in this
application may be light intensity, temperature, pressure, humidity and their
variations .Clustering and routing are the two areas which are given more
attention in this paper.
|
We discuss the superluminal problem in the diffusion of ultra high energy
protons with energy losses taken into account. The phenomenological solution of
this problem is found with help of the generalized J\"uttner propagator,
originally proposed for relativization of the Maxwellian gas distribution. It
is demonstrated that the generalized J\"uttner propagator gives the correct
expressions in the limits of diffusive and rectilinear propagation of the
charged particles in the magnetic fields, together with the intermediate
regime, in all cases without superluminal velocities. This solution, very
general for the diffusion, is considered for two particular cases: diffusion
inside the stationary objects, like e.g. galaxies, clusters of galaxies etc,
and for expanding universe. The comparison with the previously obtained
solutions for propagation of UHE protons in magnetic fields is performed.
|
We initiate the study of non-interactive zero-knowledge (NIZK) arguments for
languages in QMA. Our first main result is the following: if Learning With
Errors (LWE) is hard for quantum computers, then any language in QMA has an
NIZK argument with preprocessing. The preprocessing in our argument system
consists of (i) the generation of a CRS and (ii) a single
(instance-independent) quantum message from verifier to prover. The
instance-dependent phase of our argument system involves only a single
classical message from prover to verifier. Importantly, verification in our
protocol is entirely classical, and the verifier needs not have quantum memory;
its only quantum actions are in the preprocessing phase. Our second
contribution is to extend the notion of a classical proof of knowledge to the
quantum setting. We introduce the notions of arguments and proofs of quantum
knowledge (AoQK/PoQK), and we show that our non-interactive argument system
satisfies the definition of an AoQK. In particular, we explicitly construct an
extractor which can recover a quantum witness from any prover which is
successful in our protocol. Finally, we show that any language in QMA has an
(interactive) proof of quantum knowledge.
|
In this paper we introduce color Hom-Akivis algebras and prove that the
commutator of any color non-associative Hom-algebra structure map leads to a
color Hom-akivis algebra. We give various constructions of color Hom-Akivis
algebras. Next we study flexible and alternative color Hom-Akivis algebras.
Likewise color Hom-Akivis algebras, we introduce non-commutative color
Hom-Leibniz-Poisson algebras and presente several constructions. Moreover we
give the relationship between Hom-dialgebras and Hom-Leibniz-Poisson algebras;
i.e. a Hom-dialgebras give rise to a Hom-Leibniz-Poisson algebra. Finally we
show that twisting a color Hom-Leibniz module structure map by a color
Hom-Leibniz algebra endomorphism, we get another one.
|
We show that every simple transitive $2$-representation of the $2$-category
of projective functors for a certain quotient of the quadratic dual of the
preprojective algebra associated with a tree is equivalent to a cell
$2$-representation.
|
We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev
space $W^{1,\varphi}(\mathbb{R}^n)$. Under some natural assumptions on
$\varphi$ we show that the maximal function is bounded and continuous in
$W^{1,\varphi}(\mathbb{R}^n)$.
|
The influence of a constant homogeneous external magnetic field $H$ on the
formation and stability of quark droplets is investigated within a simple Nambu
-- Jona-Lasinio model by using a thermodynamic approach. For a vanishing
magnetic field stable quark droplets, which are schematically the bags of
massless quarks, are allowed to exist only at $G>G_{bag}$, where $G$ is the
quark coupling constant, $G_{bag}=1.37G_{crit}$, and $G_{crit}$ is the value of
the coupling constant above which chiral symmetry is spontaneously broken down.
On the other hand, a nonvanishing external magnetic field can induce the
stability of quark droplets so that they may exist even at $G<G_{bag}$. In this
case, depending on the value of $H$, quark droplets are composed either of
massive or massless quarks.
|
We report topography-free materials contrast imaging on a nano-fabricated
Boron-doped Silicon sample measured with a Near-field Scanning Microwave
Microscope over a broad frequency range. The Boron doping was performed using
the Focus Ion Beam technique on a Silicon wafer with nominal resistivity of 61
Ohm.cm. A topography-free doped region varies in sheet resistance from
1000Ohm/Square to about 400kOhm/Square within a lateral distance of 4
micrometer. The qualitative spatial-resolution in sheet resistance imaging
contrast is no worse than 100 nm as estimated from the frequency shift signal.
|
Developers of low-level systems code providing core functionality for
operating systems and kernels must address hardware-level features of modern
multicore architectures. A particular feature is pipelined "out-of-order
execution" of the code as written, the effects of which are typically
summarised as a "weak memory model" - a term which includes further
complicating factors that may be introduced by compiler optimisations. In many
cases, the nondeterminism inherent in weak memory models can be expressed as
micro-parallelism, i.e., parallelism within threads and not just between them.
Fortunately Jones' rely/guarantee reasoning provides a compositional method for
shared-variable concurrency, whether that be in terms of communication between
top-level threads or micro-parallelism within threads. In this paper we provide
an in-depth verification of the lock algorithm used in the seL4 microkernel,
using rely/guarantee to handle both interthread communication as well as
micro-parallelism introduced by weak memory models.
|
The exact distributed controllability of the semilinear wave equation
$y_{tt}-y_{xx} + g(y)=f \,1_{\omega}$, assuming that $g$ satisfies the growth
condition $\vert g(s)\vert /(\vert s\vert \log^{2}(\vert s\vert))\rightarrow 0$
as $\vert s\vert \rightarrow \infty$ and that $g^\prime\in
L^\infty_{loc}(\mathbb{R})$ has been obtained by Zuazua in the nineties. The
proof based on a Leray-Schauder fixed point argument makes use of precise
estimates of the observability constant for a linearized wave equation. It does
not provide however an explicit construction of a null control. Assuming that
$g^\prime\in L^\infty_{loc}(\mathbb{R})$, that $\sup_{a,b\in \mathbb{R},a\neq
b} \vert g^\prime(a)-g^{\prime}(b)\vert/\vert a-b\vert^r<\infty $ for some
$r\in (0,1]$ and that $g^\prime$ satisfies the growth condition $\vert
g^\prime(s)\vert/\log^{2}(\vert s\vert)\rightarrow 0$ as $\vert s\vert
\rightarrow \infty$, we construct an explicit sequence converging strongly to a
null control for the solution of the semilinear equation. The method, based on
a least-squares approach guarantees the convergence whatever the initial
element of the sequence may be. In particular, after a finite number of
iterations, the convergence is super linear with rate $1+r$. This general
method provides a constructive proof of the exact controllability for the
semilinear wave equation.
|
We discuss the possibility of utilizing the ultra-high energy neutrino beam
(about 1000 TeV) to detect and destroy the nuclear bombs wherever they are and
whoever possess them.
|
On grounds of the discussed material, we reason about possible future
development of quantum game theory and its impact on information processing and
the emerging information society. The idea of quantum artificial intelligence
is explained.
|
How does the number of collaborators affect individual productivity? Results
of prior research have been conflicting, with some studies reporting an
increase in individual productivity as the number of collaborators grows, while
other studies showing that the {free-rider effect} skews the effort invested by
individuals, making larger groups less productive. The difference between these
schools of thought is substantial: if a super-scaling effect exists, as
suggested by former studies, then as groups grow, their productivity will
increase even faster than their size, super-linearly improving their
efficiency. We address this question by studying two planetary-scale
collaborative systems: GitHub and Wikipedia. By analyzing the activity of over
2 million users on these platforms, we discover that the interplay between
group size and productivity exhibits complex, previously-unobserved dynamics:
the productivity of smaller groups scales super-linearly with group size, but
saturates at larger sizes. This effect is not an artifact of the heterogeneity
of productivity: the relation between group size and productivity holds at the
individual level. People tend to do more when collaborating with more people.
We propose a generative model of individual productivity that captures the
non-linearity in collaboration effort. The proposed model is able to explain
and predict group work dynamics in GitHub and Wikipedia by capturing their
maximally informative behavioral features, and it paves the way for a
principled, data-driven science of collaboration.
|
Exchange-coupling between soft- and hard-magnetic phases plays an important
role in the engineering of novel magnetic materials. To achieve exchange
coupling, a two-phase microstructure is necessary. This interface effect is
further enhanced if both phase dimensions are reduced to the nanometer scale.
At the same time, it is challenging to obtain large sample dimensions. In this
study, powder blends and ball-milled powder blends of Fe-SmCo$_{5}$ are
consolidated and are deformed by high-pressure torsion (HPT), as this technique
allows us to produce bulk magnetic materials of reasonable sizes. Additionally,
the effect of severe deformation by ball-milling and severe plastic deformation
by HPT on exchange coupling in Fe-SmCo$_{5}$ composites is investigated. Due to
the applied shear deformation, it is possible to obtain a texture in both
phases, resulting in an anisotropic magnetic behavior and an improved magnetic
performance.
|
We demonstrate that the gravity wave background amplitude implies a robust
upper bound on the ratio: \lambda / H^{-1} < e^60, where \lambda is the proper
wavelength of fluctuations of interest and H^{-1} is the horizon at the end of
inflation. The bound holds as long as the energy density of the universe does
not drop faster than radiation subsequent to inflation. This limit implies that
the amount of expansion between the time the scales of interest leave the
horizon and the end of inflation, denoted by e^N, is also bounded from above,
by about e^60 times a factor that involves an integral over the first slow-roll
parameter. In other words, the bound on N is model dependent -- we show that
for vast classes of slow-roll models, N < 67. The quantities, \lambda / H^{-1}
or N, play an important role in determining the nature of inflationary scalar
and tensor fluctuations. We suggest ways to incorporate the above bounds when
confronting inflation models with observations. As an example, this bound
solidifies the tension between observations of cosmic microwave background
(CMB) anisotropies and chaotic inflation with a \phi^4 potential by closing the
escape hatch of large N (< 62).
|
Generally, turn-to-turn power fluctuations of incoherent spontaneous
synchrotron radiation in a storage ring depend on the 6D phase-space
distribution of the electron bunch. In some cases, if only one parameter of the
distribution is unknown, this parameter can be determined from the measured
magnitude of these power fluctuations. In this Letter, we report an absolute
measurement (no free parameters or calibration) of a small vertical emittance
(5--15 nm rms) of a flat beam by this method, under conditions, when it is
unresolvable by a conventional synchrotron light beam size monitor.
|
Identifying and extracting data elements such as study descriptors in
publication full texts is a critical yet manual and labor-intensive step
required in a number of tasks. In this paper we address the question of
identifying data elements in an unsupervised manner. Specifically, provided a
set of criteria describing specific study parameters, such as species, route of
administration, and dosing regimen, we develop an unsupervised approach to
identify text segments (sentences) relevant to the criteria. A binary
classifier trained to identify publications that met the criteria performs
better when trained on the candidate sentences than when trained on sentences
randomly picked from the text, supporting the intuition that our method is able
to accurately identify study descriptors.
|
We apply topological methods to obtain global continuation results for
harmonic solutions of some periodically perturbed ordinary differential
equations on a $k$-dimensional differentiable manifold $M \subseteq
\mathbb{R}^m$. We assume that $M$ is globally defined as the zero set of a
smooth map and, as a first step, we determine a formula which reduces the
computation of the degree of a tangent vector field on $M$ to the Brouwer
degree of a suitable map in $\mathbb{R}^m$. As further applications, we study
the set of harmonic solutions to periodic semi-esplicit differential-algebraic
equations.
|
The aim of this paper is to propose an alternative method to solve a Fault
Tolerant Control problem. The model is a linear system affected by a
disturbance term: this represents a large class of technological faulty
processes. The goal is to make the system able to tolerate the undesired
perturbation, i.e., to remove or at least reduce its negative effects; such a
task is performed in three steps: the detection of the fault, its
identification and the consequent process recovery. When the disturbance
function is known to be \emph{quantized} over a finite number of levels, the
detection can be successfully executed by a recursive \emph{decoding}
algorithm, arising from Information and Coding Theory and suitably adapted to
the control framework. This technique is analyzed and tested in a flight
control issue; both theoretical considerations and simulations are reported.
|
We prove that under mild positivity assumptions the entropy rate of a hidden
Markov chain varies analytically as a function of the underlying Markov chain
parameters. A general principle to determine the domain of analyticity is
stated. An example is given to estimate the radius of convergence for the
entropy rate. We then show that the positivity assumptions can be relaxed, and
examples are given for the relaxed conditions. We study a special class of
hidden Markov chains in more detail: binary hidden Markov chains with an
unambiguous symbol, and we give necessary and sufficient conditions for
analyticity of the entropy rate for this case. Finally, we show that under the
positivity assumptions the hidden Markov chain {\em itself} varies
analytically, in a strong sense, as a function of the underlying Markov chain
parameters.
|
Large language models (LLMs) have offered new opportunities for emotional
support, and recent work has shown that they can produce empathic responses to
people in distress. However, long-term mental well-being requires emotional
self-regulation, where a one-time empathic response falls short. This work
takes a first step by engaging with cognitive reappraisals, a strategy from
psychology practitioners that uses language to targetedly change negative
appraisals that an individual makes of the situation; such appraisals is known
to sit at the root of human emotional experience. We hypothesize that
psychologically grounded principles could enable such advanced psychology
capabilities in LLMs, and design RESORT which consists of a series of
reappraisal constitutions across multiple dimensions that can be used as LLM
instructions. We conduct a first-of-its-kind expert evaluation (by clinical
psychologists with M.S. or Ph.D. degrees) of an LLM's zero-shot ability to
generate cognitive reappraisal responses to medium-length social media messages
asking for support. This fine-grained evaluation showed that even LLMs at the
7B scale guided by RESORT are capable of generating empathic responses that can
help users reappraise their situations.
|
Theories of quantum gravity suggest the existence of a minimal length scale.
We study the consequences of a particular implementation of the idea of a
minimal length scale in the model of large extra dimensions, the ADD model. To
do this we have looked at real graviton production in association with a jet at
hadron colliders. In the minimal length scenario, the bounds on the effective
string scale are significantly less stringent than those derived in the
conventional ADD model, both at the upgraded Tevatron and at the Large Hadron
Collider.
|
Maximal signal and peak of high-frequency relic gravitational waves (GW's),
recently expected by quintessential inflationary models, may be firmly
localized in the GHz region, the energy density of the relic gravitons in
critical units (i.e., $ h_0^2 \Omega_{GW}$) is of the order $10^{-6}$, roughly
eight orders of magnitude larger than in ordinary inflationary models. This is
just right best frequency band of the electromagnetic (EM) response to the
high-frequency GW's in smaller EM detecting systems. We consider the EM
response of a Gaussian beam passing through a static magnetic field to a
high-frequency relic GW. It is found that under the synchroresonance condition,
the first-order perturbative EM power fluxes will contain "left circular wave"
and "right circular wave" around the symmetrical axis of the Gaussian beam, but
the perturbative effects produced by the states of + polarization and $\times$
polarization of the relic GW have different properties, and the perturbations
on behavior are obviously different from that of the background EM fields in
the local regions. For the high-frequency relic GW with the typical parameters
$ \nu_g = 10^{10}Hz$, $ h = 10^{- 30} $ in the quintessential inflationary
models, the corresponding perturbative photon flux passing through the region $
10^{- 2} m^{2} $ would be expected to be $ 10^{3}s^{-1} $. This is largest
perturbative photon flux we recently analyzed and estimated using the typical
laboratory parameters. In addition, we also discuss geometrical phase shift
generated by the high-frequency relic GW in the Gaussian beam and estimate
possible physical effects.
|
The Chandra X-ray Observatory is providing fascinating new views of massive
star-forming regions, revealing all stages in the life cycles of massive stars
and their effects on their surroundings. I present a Chandra tour of some of
the most famous of these regions: M17, NGC 3576, W3, Tr14 in Carina, and 30
Doradus. Chandra highlights the physical processes that characterize the lives
of these clusters, from the ionizing sources of ultracompact HII regions (W3)
to superbubbles so large that they shape our views of galaxies (30 Dor). X-ray
observations usually reveal hundreds of pre-main sequence (lower-mass) stars
accompanying the OB stars that power these great HII region complexes, although
in one case (W3 North) this population is mysteriously absent. The most massive
stars themselves are often anomalously hard X-ray emitters; this may be a new
indicator of close binarity. These complexes are sometimes suffused by soft
diffuse X-rays (M17, NGC 3576), signatures of multi-million-degree plasmas
created by fast O-star winds. In older regions we see the X-ray remains of the
deaths of massive stars that stayed close to their birthplaces (Tr14, 30 Dor),
exploding as cavity supernovae within the superbubbles that these clusters
created.
|
Recently, a coherent picture of the quantum mechanics of an evaporating black
hole has been presented which reconciles unitarity with the predictions of the
equivalence principle. The thermal nature of a black hole as viewed in a
distant reference frame arises from entanglement between the hard and soft
modes, generated by the chaotic dynamics at the string scale. In this paper, we
elaborate on this picture, particularly emphasizing the importance of the
chaotic nature of the string (UV) dynamics across all low energy species in
generating large (IR) spacetime behind the horizon. Implications of this UV/IR
relation include O(1) breaking of global symmetries at the string scale and a
self-repair mechanism of black holes restoring the smoothness of their
horizons. We also generalize the framework to other systems, including Rindler,
de Sitter, and asymptotically flat spacetimes, and find a consistent picture in
each case. Finally, we discuss the origin of the particular construction
adopted in describing the black hole interior as well as the outside of a de
Sitter horizon. We argue that the construction is selected by the
quantum-to-classical transition, in particular the applicability of the Born
rule in a quantum mechanical world.
|
We use numerical simulations to study the dynamics of surface discharges,
which are common in high-voltage engineering. We simulate positive streamer
discharges that propagate towards a dielectric surface, attach to it, and then
propagate over the surface. The simulations are performed in air with a
two-dimensional plasma fluid model, in which a flat dielectric is placed
between two plate electrodes. Electrostatic attraction is the main mechanism
that causes streamers to grow towards the dielectric. Due to the net charge in
the streamer head, the dielectric gets polarized, and the electric field
between the streamer and the dielectric is increased. Compared to streamers in
bulk gas, surface streamers have a smaller radius, a higher electric field, a
higher electron density, and higher propagation velocity. A higher applied
voltage leads to faster inception and faster propagation of the surface
discharge. A higher dielectric permittivity leads to more rapid attachment of
the streamer to the surface and a thinner surface streamer. Secondary emission
coefficients are shown to play a modest role, which is due to relatively strong
photoionization in air. In the simulations, a high electric field is present
between the positive streamers and the dielectric surface. We show that the
magnitude and decay of this field are affected by the positive ion mobility.
|
The cosmic ray spectrum at $10^{19}{\rm eV}-10^{20}{\rm eV}$, reported by the
Fly's Eye and the AGASA experiments, is shown to be consistent with a
cosmological distribution of sources of protons, with a power law generation
spectrum ${\rm d}\ln N/{\rm d}\ln E=-2.3\pm0.5$ and energy production rate of
$4.5\pm1.5\times10^{44}{\rm erg}\ {\rm Mpc}^{-3}\ {\rm yr}^{-1}$. The two
events measured above $10^{20}{\rm eV}$ are not inconsistent with this model.
Verifying the existence of a ``black-body cutoff'', currently observed with low
significance, would require $\sim30$ observation-years with existing
experiments, but only $\sim1$ year with the proposed $\sim5000\ {\rm km}^2$
detectors. For a cosmological source distribution, no anisotropy is expected in
the angular distribution of events with energies up to $\sim5\times10^{19}{\rm
eV}$.
|
This note is devoted, after the result of Harui, arXiv:1306.5842, to solve
some natural questions for non-singular plane curves of degree $d$ over an
algebraically closed field $K$ of zero characteristic.
|
Many real-world networks such as the gene networks, protein-protein
interaction networks and metabolic networks exhibit community structures,
meaning the existence of groups of densely connected vertices in the networks.
Many local similarity measures in the networks are closely related to the
concept of the community structures, and may have positive effect on community
detection in the networks. Here, various local similarity measures are used to
extract the local structural information and then are applied to community
detection in the networks by using the edge-reweighting strategy. The effect of
the local similarity measures on community detection is carefully investigated
and compared in various networks. The experimental results show that the local
similarity measures are crucial to the improvement for the community detection
methods, while the positive effect of the local similarity measures is closely
related to the networks under study and the applied community detection
methods.
|
We propose a globally convergent numerical method to compute solutions to a
general class of quasi-linear PDEs with both Neumann and Dirichlet boundary
conditions. Combining the quasi-reversibility method and a suitable Carleman
weight function, we define a map of which fixed point is the solution to the
PDE under consideration. To find this fixed point, we define a recursive
sequence with an arbitrary initial term using the same manner as in the proof
of the contraction principle. Applying a Carleman estimate, we show that the
sequence above converges to the desired solution. On the other hand, we also
show that our method delivers reliable solutions even when the given data are
noisy. Numerical examples are presented.
|
Multiparameter estimation, which aims to simultaneously determine multiple
parameters in the same measurement procedure, attracts extensive interests in
measurement science and technologies. Here, we propose a multimode many-body
quantum interferometry for simultaneously estimating linear and quadratic
Zeeman coefficients via an ensemble of spinor atoms. Different from the scheme
with individual atoms, by using an $N$-atom multimode GHZ state, the
measurement precisions of the two parameters can simultaneously attain the
Heisenberg limit, and they respectively depend on the hyperfine spin number $F$
in the form of $\Delta p \propto 1/(FN)$ and $\Delta q \propto 1/(F^2N)$.
Moreover, the simultaneous estimation can provide better precision than the
individual estimation. Further, by taking a three-mode interferometry with Bose
condensed spin-1 atoms for an example, we show how to perform the simultaneous
estimation of $p$ and $q$. Our scheme provides a novel paradigm for
implementing multiparameter estimation with multimode quantum correlated
states.
|
The main objective of the electrical stimulation of the brain is to generate
action potentials from the application of electromagnetic fields. Among the
available techniques, transcranial electrical stimulation (TES) represents a
popular method of administration that has the advantage of being non-invasive
and economically more affordable. This article aims to briefly introduce the
reader into the understanding of TES in terms of the physics involved as well
as for some of the relevant results of studies applying this technique.
|
In this paper, uniqueness and uniform structural stability of Poiseuille
flows in an infinitely long pipe with Navier boundary conditions are
established for axisymmetric solutions of steady Navier-Stokes system. The
crucial point is that the estimate is uniform with respect both the flux of
flows and slip coefficient which appeared in Navier boundary conditions. With
the aid of special structure of Navier-Stokes system and the refined estimate
for some quantities such as radial velocity, the uniqueness and existence of
steady solutions of Navier-Stokes system can be obtained even when the external
forces are large as long as the fluxes of flows are large. The delicate
decomposition in the two dimensional plane for slip coefficient and frequency
corresponding to Fourier variable in the axial direction plays a key role to
achieve these estimates.
|
We present the discovery of a luminous X-ray transient, serendipitously
detected by Swift's X-ray Telescope (XRT) on 2020 February 5, located in the
nucleus of the galaxy SDSS J143359.16+400636.0 at z=0.099 (luminosity distance
$D_{\rm L}=456$ Mpc). The transient was observed to reach a peak luminosity of
$\sim10^{44}$ erg s$^{-1}$ in the 0.3--10 keV X-ray band, which was $\sim20$
times more than the peak optical/UV luminosity. Optical, UV, and X-ray
lightcurves from the Zwicky Transient Facility (ZTF) and Swift show a decline
in flux from the source consistent with $t^{-5/3}$, and observations with
NuSTAR and Chandra show a soft X-ray spectrum with photon index
$\Gamma=2.9\pm0.1$. The X-ray/UV properties are inconsistent with well known
AGN properties and have more in common with known X-ray tidal disruption events
(TDE), leading us to conclude that it was likely a TDE. The broadband spectral
energy distribution (SED) can be described well by a disk blackbody model with
an inner disk temperature of $7.3^{+0.3}_{-0.8}\times10^{5}$ K, with a large
fraction ($>40$%) of the disk emission up-scattered into the X-ray band. An
optical spectrum taken with Keck/LRIS after the X-ray detection reveals LINER
line ratios in the host galaxy, suggesting low-level accretion on to the
supermassive black hole prior to the event, but no broad lines or other
indications of a TDE were seen. The stellar velocity dispersion implies the
mass of the supermassive black hole powering the event is log($M_{\rm
BH}$/$M_{\odot}$)$=7.41\pm0.41$, and we estimate that at peak the Eddington
fraction of this event was $\sim$50%. This likely TDE was not identified by
wide-field optical surveys, nor optical spectroscopy, indicating that more
events like this would be missed without wide-field UV or X-ray surveys.
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Nonassociative commutative algebras $A$ generated by idempotents $e$ whose
adjoint operators ${\rm ad}_e\colon A \rightarrow A$, given by $x \mapsto xe$,
are diagonalizable and have few eigenvalues are of recent interest. When
certain fusion (multiplication) rules between the associated eigenspaces are
imposed, the structure of these algebras remains rich yet rather rigid. For
example vertex operator algebras give rise to such algebras. The connection
between the Monster algebra and Monster group extends to many axial algebras
which then have interesting groups of automorphisms.
Axial algebras of Jordan type $\eta$ are commutative algebras generated by
idempotents whose adjoint operators have a minimal polynomial dividing
$(x-1)x(x-\eta)$, where $\eta \notin \{0,1\}$ is fixed, with well-defined and
restrictive fusion rules. The case of $\eta \neq \frac{1}{2}$ was thoroughly
analyzed by Hall, Rehren, and Shpectorov in a recent paper, in which axial
algebras were introduced. Here we focus on the case where $\eta=\frac{1}{2}$,
which is much less understood and is of a different nature.
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We study the imaginary part of the effective $ac$ conductivity as well as its
distribution probability for vanishing losses in 2D composites. This
investigation showed that the effective medium theory provides only
informations about the average conductivity, while its fluctuations which
correspond to the field energy in this limit are neglected by this theory.
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Following the development of fuzzy logic theory by Lotfi Zadeh, its
applications were investigated by researchers in different fields. Presenting
and working with uncertain data is a complex problem. To solve for such a
complex problem, the structure of relationships and operators dependent on such
relationships must be repaired. The fuzzy database has integrity limitations
including data dependencies. In this paper, first fuzzy multivalued dependency
based semantic proximity and its problems are studied. To solve these problems,
the semantic proximity's formula is modified, and fuzzy multivalued dependency
based on the concept of extension of semantic proximity with \alpha degree is
defined in fuzzy relational database which includes Crisp, NULL and fuzzy
values, and also inference rules for this dependency are defined, and their
completeness is proved. Finally, we will show that fuzzy functional dependency
based on this concept is a special case of fuzzy multivalued dependency in
fuzzy relational database.
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In order to identify the Higgs sector realized in nature, the predictions for
Higgs boson masses, production cross sections and decay widths have to be
compared with experimental results. We give a brief overview about computer
codes for the evaluation of the properties of charged Higgs bosons, mostly
focusing on the case of the Minimal Supersymmetric Standard Model (MSSM). We
briefly review the relevance of the various contributions to the charged MSSM
Higgs boson mass arising at the one-loop level.
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In this work we propose and analyze a novel approach for group sparse
recovery. It is based on regularized least squares with an $\ell^0(\ell^2)$
penalty, which penalizes the number of nonzero groups. One distinct feature of
the approach is that it has the built-in decorrelation mechanism within each
group, and thus can handle challenging strong inner-group correlation. We
provide a complete analysis of the regularized model, e.g., existence of a
global minimizer, invariance property, support recovery, and properties of
block coordinatewise minimizers. Further, the regularized problem admits an
efficient primal dual active set algorithm with a provable finite-step global
convergence. At each iteration, it involves solving a least-squares problem on
the active set only, and exhibits a fast local convergence, which makes the
method extremely efficient for recovering group sparse signals. Extensive
numerical experiments are presented to illustrate salient features of the model
and the efficiency and accuracy of the algorithm. A comparative study indicates
its competitiveness with existing approaches.
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We extend standard k.p theory to take into account periodic perturbations
which are rapidly oscillating with a wavelength of a few lattice constants. Our
general formalism allows us to explicitly consider the Bragg reflections due to
the perturbation-induced periodicity. As an example we calculate the effective
masses in the lowest two conduction bands of spontaneously ordered GaInP_2 as a
function of the degree of ordering. Comparison of our results for the lowest
conduction band to available experimental data and to first principle
calculations shows good agreement.
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Co-saliency detection aims to discover common and salient objects in an image
group containing more than two relevant images. Moreover, depth information has
been demonstrated to be effective for many computer vision tasks. In this
paper, we propose a novel co-saliency detection method for RGBD images based on
hierarchical sparsity reconstruction and energy function refinement. With the
assistance of the intra saliency map, the inter-image correspondence is
formulated as a hierarchical sparsity reconstruction framework. The global
sparsity reconstruction model with a ranking scheme focuses on capturing the
global characteristics among the whole image group through a common foreground
dictionary. The pairwise sparsity reconstruction model aims to explore the
corresponding relationship between pairwise images through a set of pairwise
dictionaries. In order to improve the intra-image smoothness and inter-image
consistency, an energy function refinement model is proposed, which includes
the unary data term, spatial smooth term, and holistic consistency term.
Experiments on two RGBD co-saliency detection benchmarks demonstrate that the
proposed method outperforms the state-of-the-art algorithms both qualitatively
and quantitatively.
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This is a sequel to \cite{osy} and \cite{sxy}. Associated with $G:=\GL_n$ and
its rational representation $(\rho, M)$ over an algebraically closed filed
$\bk$, we define an enhanced algebraic group $\uG:=G\ltimes_\rho M$ which is a
product variety $\GL_n\times M$, endowed with an enhanced cross product. In
this paper, we first show that the nilpotent cone $\ucaln:=\caln(\ugg)$ of the
enhanced Lie algebra $\ugg:=\Lie(\uG)$ has finite nilpotent orbits under
adjoint $\uG$-action if and only if up to tensors with one-dimensional modules,
$M$ is isomorphic to one of the three kinds of modules: (i) a one-dimensional
module, (ii) the natural module $\bk^n$, (iii) the linear dual of $\bk^n$ when
$n>2$; and $M$ is an irreducible module of dimension not bigger than $3$ when
$n=2$. We then investigate the geometry of enhanced nilpotent orbits when the
finiteness occurs. Our focus is on the enhanced group
$\uG=\GL(V)\ltimes_{\eta}V$ with the natural representation $(\eta, V)$ of
$\GL(V)$, for which we give a precise classification of finite nilpotent orbits
via a finite set $\scrpe$ of so-called enhanced partitions of $n=\dim V$, then
give a precise description of the closures of enhanced nilpotent orbits via
constructing so-called enhanced flag varieties. Finally, the $\uG$-equivariant
intersection cohomology decomposition on the nilpotent cone of $\ugg$ along the
closures of nilpotent orbits is established.
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We briefly review several models of heavy quarkonium production in hadronic
collisions, and discuss the status of QCD factorization for these production
models.
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We present a study of the second-order nonlinear optical properties of
metal-based metamaterials. A hydrodynamic model for electronic response is
used, in which nonlinear surface contributions are expressed in terms of the
bulk polarization. The model is in good agreement with published experimental
results, and clarifies the mechanisms contributing to the nonlinear response.
In particular, we show that the reported enhancement of second-harmonic in
split-ring resonator based media is driven by the electric rather than the
magnetic properties of the structure.
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Measurement results of photoproduced excited hyperon states using the CLAS
detector at Jefferson Lab are shown. The invariant mass distribution of the
Lambda(1405) has recently been shown to be different for each of the three
Sigma pi channels that it decays to, showing that there is prominent
interference between the isospin I=0 and I=1 isospin amplitudes. Measurements
of the differential and total cross sections of the three hyperons
Lambda(1405), Sigma0(1385), and Lambda(1520) are presented and compared.
Prospects of future studies using a 12 GeV beam with the GlueX detector are
briefly given.
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The task of 3D semantic scene completion with monocular cameras is gaining
increasing attention in the field of autonomous driving. Its objective is to
predict the occupancy status of each voxel in the 3D scene from partial image
inputs. Despite the existence of numerous methods, many of them overlook the
issue of accurate alignment between spatial and depth information. To address
this, we propose DepthSSC, an advanced method for semantic scene completion
solely based on monocular cameras. DepthSSC combines the ST-GF (Spatial
Transformation Graph Fusion) module with geometric-aware voxelization, enabling
dynamic adjustment of voxel resolution and considering the geometric complexity
of 3D space to ensure precise alignment between spatial and depth information.
This approach successfully mitigates spatial misalignment and distortion issues
observed in prior methods. Through evaluation on the SemanticKITTI dataset,
DepthSSC not only demonstrates its effectiveness in capturing intricate 3D
structural details but also achieves state-of-the-art performance. We believe
DepthSSC provides a fresh perspective on monocular camera-based 3D semantic
scene completion research and anticipate it will inspire further related
studies.
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Self-supervised learning (SSL) has emerged as a powerful technique for
learning rich representations from unlabeled data. The data representations are
able to capture many underlying attributes of data, and be useful in downstream
prediction tasks. In real-world settings, spurious correlations between some
attributes (e.g. race, gender and age) and labels for downstream tasks often
exist, e.g. cancer is usually more prevalent among elderly patients. In this
paper, we investigate SSL in the presence of spurious correlations and show
that the SSL training loss can be minimized by capturing only a subset of the
conspicuous features relevant to those sensitive attributes, despite the
presence of other important predictive features for the downstream tasks. To
address this issue, we investigate the learning dynamics of SSL and observe
that the learning is slower for samples that conflict with such correlations
(e.g. elder patients without cancer). Motivated by these findings, we propose a
learning-speed aware SSL (LA-SSL) approach, in which we sample each training
data with a probability that is inversely related to its learning speed. We
evaluate LA-SSL on three datasets that exhibit spurious correlations between
different attributes, demonstrating that it improves the robustness of
pretrained representations on downstream classification tasks.
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We study the visibility of sunspots and its influence on observed values of
sunspot region parameters. We use Virtual Observatory tools provided by
AstroGrid to analyse a sample of 6862 sunspot regions. By studying the
distributions of locations where sunspots were first and last observed on the
solar disk, we derive the visibility function of sunspots, the rate of magnetic
flux emergence and the ratio between the durations of growth and decay phases
of solar active regions. We demonstrate that the visibility of small sunspots
has a strong center-to-limb variation, far larger than would be expected from
geometrical (projection) effects. This results in a large number of young spots
being invisible: 44% of new regions emerging in the West of the Sun go
undetected. For sunspot regions that are detected, large differences exist
between actual locations and times of flux emergence, and the apparent ones
derived from sunspot data. The duration of the growth phase of solar regions
has been up to now underestimated.
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NGC 7129 FIRS 2 is a young intermediate-mass (IM) protostar, which is
associated with two energetic bipolar outflows and displays clear signs of the
presence of a hot core. It has been extensively observed with ground based
telescopes and within the WISH Guaranteed Time Herschel Key Program. We present
new observations of the C18O 3-2 and the HDO 3_{12}-2_{21} lines towards NGC
7129 FIRS 2. Combining these observations with Herschel data and modeling their
emissions, we constrain the C18O and HDO abundance profiles across the
protostellar envelope. In particular, we derive the abundance of C18O and HDO
in the hot core. The intensities of the C18O lines are well reproduced assuming
that the C18O abundance decreases through the protostellar envelope from the
outer edge towards the centre until the point where the gas and dust reach the
CO evaporation temperature (~20-25 K) where the C18O is released back to the
gas phase. Once the C18O is released to the gas phase, the modelled C18O
abundance is found to be ~1.6x10^{-8}, which is a factor of 10 lower than the
reference abundance. This result is supported by the non-detection of C18O 9-8,
which proves that even in the hot core (T_k>100 K) the CO abundance must be 10
times lower than the reference value. Several scenarios are discussed to
explain this C18O deficiency. One possible explanation is that during the
pre-stellar and protostellar phase, the CO is removed from the grain mantles by
reactions to form more complex molecules. Our HDO modeling shows that the
emission of HDO 3_{12}-2_{21} line is maser and comes from the hot core
(T_k>100 K). Assuming the physical structure derived by Crimier et al. (2010),
we determine a HDO abundance of ~0.4 - 1x10^{-7} in the hot core of this IM
protostar, similar to that found in the hot corinos NGC 1333 IRAS 2A and IRAS
16293-2422.
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We present a treatment of many-body Fermionic systems that facilitates an
expression of the well-known quantities in a series expansion of the Planck's
constant. The ensuing semiclassical result contains to a leading order of the
response function the classical time correlation function of the observable
followed by the Weyl-Wigner series, on top of these terms are the
periodic-orbit correction terms. The treatment given here starts from linear
response assumption of the many-body theory and in its connection with
semiclassical theory, it makes no assumption of the integrability of classical
dynamics underlying the one-body quantal system. Applications of the framework
are also discussed.
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We study the transfer operators for a family $F_r:[0,1] \to [0,1]$ depending
on the parameter $r\in [0,1]$, which interpolates between the tent map and the
Farey map. In particular, considering the action of the transfer operator on a
suitable Hilbert space, we can define a family of infinite matrices associated
to the operators and study their spectrum by numerical methods.
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The rare $B \to K^{(*)} \bar{\ell} \ell$ decays exhibit a long-standing
tension with Standard Model (SM) predictions, which can be attributed to a
lepton-universal short-distance $b \to s \bar{\ell} \ell$ interaction. We
present two novel methods to disentangle this effect from long-distance
dynamics: one based on the determination of the inclusive $b \to s \bar{\ell}
\ell$ rate at high dilepton invariant mass ($q^2\geq 15~{\rm GeV}^2$), the
other based on the analysis of the $q^2$ spectrum of the exclusive modes $B \to
K^{(*)} \bar{\ell} \ell$ (in the entire $q^2$ range).
Using the first method, we show that the SM prediction for the inclusive $b
\to s \bar{\ell} \ell$ rate at high dilepton invariant mass is in good
agreement with the result obtained summing the SM predictions for one- and
two-body modes ($K$, $K^*$, $K\pi$). This observation allows us to perform a
direct comparison of the inclusive $b \to s \bar{\ell} \ell$ rate with data.
This comparison shows a significant deficit ($\sim 2\sigma$) in the data, fully
compatible with the deficit observed at low-$q^2$ on the exclusive modes. This
provides independent evidence of an anomalous $b \to s \bar{\ell} \ell$
short-distance interaction, free from uncertainties on the hadronic form
factors. To test the short-distance nature of this effect we use a second
method, where we analyze the exclusive $B \to K^{(*)} \bar{\ell} \ell$ data in
the entire $q^2$ region. Here, after using a dispersive parametrization of the
charmonia resonances, we extract the non-SM contribution to the universal
Wilson coefficient $C_9$ for every bin in $q^2$ and for every polarization. The
$q^2$- and polarization-independence of the result, and its compatibility with
the inclusive determination, provide a consistency check of the short-distance
nature of this effect.
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Intelligent vehicles have demonstrated excellent capabilities in many
transportation scenarios. The inference capabilities of neural networks using
cameras limit the accuracy of accident detection in complex transportation
systems. This paper presents AccidentBlip2, a pure vision-based multi-modal
large model Blip2 for accident detection. Our method first processes the
multi-view images through ViT-14g and sends the multi-view features into the
cross-attention layer of Q-Former. Different from Blip2's Q-Former, our Motion
Q-Former extends the self-attention layer with the temporal-attention layer. In
the inference process, the queries generated from previous frames are input
into Motion Q-Former to aggregate temporal information. Queries are updated
with an auto-regressive strategy and are sent to a MLP to detect whether there
is an accident in the surrounding environment. Our AccidentBlip2 can be
extended to a multi-vehicle cooperative system by deploying Motion Q-Former on
each vehicle and simultaneously fusing the generated queries into the MLP for
auto-regressive inference. Our approach outperforms existing video large
language models in detection accuracy in both single-vehicle and multi-vehicle
systems.
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It is shown that for every $p\in (2,\infty)$ there exists a doubling subset
of $L_p$ that does not admit a bi-Lipschitz embedding into $\R^k$ for any $k\in
\N$.
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Optimal state-feedback controllers, capable of changing between different
objective functions, are advantageous to systems in which unexpected situations
may arise. However, synthesising such controllers, even for a single objective,
is a demanding process. In this paper, we present a novel and straightforward
approach to synthesising these policies through a combination of trajectory
optimisation, homotopy continuation, and imitation learning. We use numerical
continuation to efficiently generate optimal demonstrations across several
objectives and boundary conditions, and use these to train our policies.
Additionally, we demonstrate the ability of our policies to effectively learn
families of optimal state-feedback controllers, which can be used to change
objective functions online. We illustrate this approach across two trajectory
optimisation problems, an inverted pendulum swingup and a spacecraft orbit
transfer, and show that the synthesised policies, when evaluated in simulation,
produce trajectories that are near-optimal. These results indicate the benefit
of trajectory optimisation and homotopy continuation to the synthesis of
controllers in dynamic-objective contexts.
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We have used nanoelectromechanical resonators to probe superfluid $^4$He at
different temperature regimes, spanning over four orders of magnitude in
damping. These regimes are characterized by the mechanisms which provide the
dominant contributions to damping and the shift of the resonance frequency:
tunneling two level systems at the lowest temperatures, ballistic phonons and
rotons at few hundred mK, and laminar drag in the two-fluid regime below the
superfluid transition temperature as well as in the normal fluid. Immersing the
nanoelectromechanical resonators in fluid increases their effective mass
substantially, decreasing their resonance frequency. Dissipationless superflow
gives rise to a unique possibility to dramatically change the mechanical
resonance frequency in situ, allowing rigorous tests on different damping
models in mechanical resonators. We apply this method to characterize tunneling
two-level system losses and magnetomotive damping in the devices.
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In this paper we present a mathematical analysis for a steady-state laminar
boundary layer flow, governed by the Ostwald-de Wael power-law model of an
incompressible non- Newtonian fluid past a semi-infinite power-law stretched
flat plate with uniform free stream velocity. A generalization of the usual
Blasius similarity transformation is used to find similarity solutions [1].
Under appropriate assumptions, partial differential equations are transformed
into an autonomous third-order nonlinear degenerate ordinary differential
equation with boundary conditions. Using a shooting method, we establish the
existence of an infinite number of global unbounded solutions. The asymptotic
behavior is also discussed. Some properties of those solutions depend on the
viscosity power-law index.
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