text
stringlengths 6
128k
|
|---|
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.
|
Let $K$ be a centrally symmetric spherical and simplicial polytope, whose
vertices form a $\frac{1}{4n}-$net in the unit sphere in $\mathbb{R}^n$. We
prove a uniform lower bound on the norms of all hyperplane projections $P: X
\to X$, where $X$ is the $n$-dimensional normed space with the unit ball $K$.
The estimate is given in terms of the determinant function of vertices and
faces of $K$. In particular, if $N \geq n^{4n}$ and $K = \conv \{ \pm x_1, \pm
x_2, \ldots, \pm x_N \}$, where $x_1, x_2, \ldots, x_N$ are independent random
points distributed uniformly in the unit sphere, then every hyperplane
projection $P: X \to X$ satisfies an inequality $\|P\|_X \geq
1+c_nN^{-(2n^2+4n+6)}$ (for some explicit constant $c_n$), with the probability
at least $1 - \frac{3}{N}.$
|
Recently, there has been an increased interest in studying quantum
entanglement and quantum coherence. Since both of these properties are
attributed to the existence of quantum superposition, it would be useful to
determine if some type of correlation between them exists. Hence, the purpose
of this paper is to explore the type of the correlation in several systems with
different types of anisotropy. The focus will be on the XY spin chains with the
Dzyaloshinskii-Moriya interaction and the type of the mentioned bond will be
explored using the quantum renormalization group method.
|
In this short note, we describe the so-called homogeneous involution on
finite-dimensional graded-division algebra over an algebraically closed field.
We also compute their graded polynomial identities with involution. As pointed
out by L. Fonseca and T. de Mello, a homogeneous involution naturally appears
when dealing with graded polynomial identities and a compatible involution.
|
It is sometimes argued that observation of tensor modes from inflation would
provide the first evidence for quantum gravity. However, in the usual
inflationary formalism, also the scalar modes involve quantised metric
perturbations. We consider the issue in a semiclassical setup in which only
matter is quantised, and spacetime is classical. We assume that the state
collapses on a spacelike hypersurface, and find that the spectrum of scalar
perturbations depends on the hypersurface. For reasonable choices, we can
recover the usual inflationary predictions for scalar perturbations in
minimally coupled single-field models. In models where non-minimal coupling to
gravity is important and the field value is sub-Planckian, we do not get a
nearly scale-invariant spectrum of scalar perturbations. As gravitational waves
are only produced at second order, the tensor-to-scalar ratio is negligible. We
conclude that detection of inflationary gravitational waves would indeed be
needed to have observational evidence of quantisation of gravity.
|
We demonstrate a one-dimensional optical lattice clock with ultracold 171Yb
atoms, which is free from the linear Zeeman effect. The absolute frequency of
the 1S0(F = 1/2) - 3P0(F = 1/2) clock transition in 171Yb is determined to be
518 295 836 590 864(28) Hz with respect to the SI second.
|
The issue concerning the nature and the role of microstructural
inhomogeneities in iron chalcogenide superconducting crystals of FeTe0.65Se0.35
and their correlation with transport properties of this system was addressed.
Presented data demonstrate that chemical disorder originating from the kinetics
of the crystal growth process significantly influences the superconducting
properties of an Fe-Te-Se system. Transport measurements of the transition
temperature and critical current density performed for microscopic bridges
allow us to deduce the local properties of a superconductor with
microstructural inhomogeneities, and significant differences were noted. The
variances observed in the local properties were explained as a consequence of
weak superconducting links existing in the studied crystals. The results
confirm that inhomogeneous spatial distribution of ions and small hexagonal
symmetry nanoscale regions with nanoscale phase separation also seem to enhance
the superconductivity in this system with respect to the values of the critical
current density. Magnetic measurements confirm the conclusions drawn from the
transport measurements.
|
We show that for most pairs of surfaces, there exists a finite subgraph of
the flip graph of the first surface so that any injective homomorphism of this
finite subgraph into the flip graph of the second surface can be extended
uniquely to an injective homomorphism between the two flip graphs. Combined
with a result of Aramayona-Koberda-Parlier, this implies that any such
injective homomorphism of this finite set is induced by an embedding of the
surfaces. We also include images of several flip graphs in an appendix.
|
We present the results of a detailed analysis of the XMM-Newton observation
of the galaxy cluster Abell 3921. The X-ray morphology of the cluster is
elliptical, with the centroid offset from the brightest cluster galaxy by 17
arcsec, and with a pronounced extension toward the NW. Subtraction of a 2D beta
model fit to the main cluster emission reveals a large scale, irregular
residual structure in the direction of the extension, containing both diffuse
emission from the intra cluster medium, and extended emission from the second
and third-brightest cluster galaxies (BG2 and BG3). The greatest concentration
of galaxies in the subcluster lies at the extreme northern edge of the
residual. The cluster exhibits a remarkable temperature structure, in
particular a bar of significantly hotter gas, oriented SE-NW and stretching
from the centre of the cluster towards BG2 and BG3. Our detailed study of the
morphological and thermal structure points to an off-axis merger between a main
cluster and a less massive galaxy cluster infalling from the SE. From
comparison of the temperature map with numerical simulations, and with
independent calculations based on simple physical assumptions, we conclude that
the merging event is ~0.5 Gyr old. The cluster is thus perhaps the best X-ray
observed candidate so far of an intermediate mass ratio, moderate impact
parameter merger.
|
We study the possibility of probing dark energy behaviour using gravitational
wave experiments like LISA and Advanced LIGO. Using two popular
parameterizations for dark energy equation of state, we show that with current
sensitivities of LISA and Advanced LIGO to detect the stochastic gravitational
waves, it is possible to probe a large section of parameter space for the dark
energy equation of state which is allowed by present cosmological observations.
|
We present our analysis on the photon structure functions at small Bjorken
variable x in the framework of the holographic QCD. In the kinematic region, a
photon can fluctuate into vector mesons and behaves like a hadron rather than a
pointlike particle. Assuming the Pomeron exchange dominance, the dominant
hadronic contribution to the structure functions is computed by convoluting the
probe and target photon density distributions obtained from the wave functions
of the U(1) vector field in the five-dimensional AdS space and the
Brower-Polchinski-Strassler-Tan Pomeron exchange kernel. Our calculations are
in agreement with both the experimental data from OPAL collaboration at LEP and
those calculated from the parton distribution functions of the photon proposed
by Gl\"uck, Reya, and Schienbein. The predictions presented here will be tested
at future linear colliders, such as the planned International Linear Collider.
|
The precise value of the neutron lifetime is of fundamental importance to
particle physics and cosmology. The neutron lifetime recently obtained, 878.5
+/- 0.7stat +/- 0.3sys s, is the most accurate one to date. The new result for
the neutron lifetime differs from the world average value by 6.5 standard
deviations. The impact of the new result on testing of Standard Model and on
data analysis for the primordial nucleosynthesis model is scrutinized.
|
We present a realization of quantized charge pumping. A lateral quantum dot
is defined by metallic split gates in a GaAs/AlGaAs heterostructure. A surface
acoustic wave whose wavelength is twice the dot length is used to pump single
electrons through the dot at a frequency f=3GHz. The pumped current shows a
regular pattern of quantization at values I=nef over a range of gate voltage
and wave amplitude settings. The observed values of n, the number of electrons
transported per wave cycle, are determined by the number of electronic states
in the quantum dot brought into resonance with the fermi level of the electron
reservoirs during the pumping cycle.
|
Despite their importance in a wide variety of applications, the estimation of
ionization cross sections for large molecules continues to present challenges
for both experiment and theory. Machine learning algorithms have been shown to
be an effective mechanism for estimating cross section data for atomic targets
and a select number of molecular targets. We present an efficient machine
learning model for predicting ionization cross sections for a broad array of
molecular targets. Our model is a 3-layer neural network that is trained using
published experimental datasets. There is minimal input to the network, making
it widely applicable. We show that with training on as few as 10 molecular
datasets, the network is able to predict the experimental cross sections of
additional molecules with an accuracy similar to experimental uncertainties in
existing data. As the number of training molecular datasets increased, the
network's predictions became more accurate and, in the worst case, were within
30% of accepted experimental values. In many cases, predictions were within 10%
of accepted values. Using a network trained on datasets for 25 different
molecules, we present predictions for an additional 27 molecules, including
alkanes, alkenes, molecules with ring structures, and DNA nucleotide bases.
|
The rearrangement step of nuclear fission occurs within 0.17 yoctosecond, in
a new state of nuclear matter characterized by the formation of closed shells
of nucleons. The determination of its lifetime is now based on the prompt
neutron emission law. The width of isotopic distributions measures the
uncertainty in the neutron number of the fragments. Magic mass numbers, 82 and
126, play a major role in the mass distributions. Arguments are presented in
favour of an all-neutron state. The boson field responsible for the new
collective interaction has to be searched for.
|
We show that gravitational interactions between massless thermal modes and a
nucleating Coleman-de Luccia bubble may lead to efficient decoherence and
strongly suppress metastable vacuum decay for bubbles that are small compared
to the Hubble radius. The vacuum decay rate including gravity and thermal
photon interactions has the exponential scaling $\Gamma\sim\Gamma_{CDL}^{2}$,
where $\Gamma_{CDL}$ is the Coleman-de Luccia decay rate neglecting photon
interactions. For the lowest metastable initial state an efficient quantum Zeno
effect occurs due to thermal radiation of temperatures as low as the de Sitter
temperature. This strong decoherence effect is a consequence of gravitational
interactions with light external mode. We argue that efficient decoherence does
not occur for the case of Hawking-Moss decay. This observation is consistent
with requirements set by Poincare recurrence in de Sitter space.
|
I will present a method for providing initial guesses to a linear solver for
systems with multiple shifts. This can also be extended to the case of multiple
sources each with a different shift.
|
Many re-ranking strategies in search systems rely on stochastic ranking
policies, encoded as Doubly-Stochastic (DS) matrices, that satisfy desired
ranking constraints in expectation, e.g., Fairness of Exposure (FOE). These
strategies are generally two-stage pipelines: \emph{i)} an offline re-ranking
policy construction step and \emph{ii)} an online sampling of rankings step.
Building a re-ranking policy requires repeatedly solving a constrained
optimization problem, one for each issued query. Thus, it is necessary to
recompute the optimization procedure for any new/unseen query. Regarding
sampling, the Birkhoff-von-Neumann decomposition (BvND) is the favored approach
to draw rankings from any DS-based policy. However, the BvND is too costly to
compute online. Hence, the BvND as a sampling solution is memory-consuming as
it can grow as $\gO(N\, n^2)$ for $N$ queries and $n$ documents.
This paper offers a novel, fast, lightweight way to predict fair stochastic
re-ranking policies: Constrained Meta-Optimal Transport (CoMOT). This method
fits a neural network shared across queries like a learning-to-rank system. We
also introduce Gumbel-Matching Sampling (GumMS), an online sampling approach
from DS-based policies. Our proposed pipeline, CoMOT + GumMS, only needs to
store the parameters of a single model, and it generalizes to unseen queries.
We empirically evaluated our pipeline on the TREC 2019 and 2020 datasets under
FOE constraints. Our experiments show that CoMOT rapidly predicts fair
re-ranking policies on held-out data, with a speed-up proportional to the
average number of documents per query. It also displays fairness and ranking
performance similar to the original optimization-based policy. Furthermore, we
empirically validate the effectiveness of GumMS to approximate DS-based
policies in expectation.
|
It is well-known that the action of a quantum channel on a state can be
represented, using an auxiliary space, as the partial trace of an associated
bipartite state. Recently, it was observed that for the bipartite state
associated with the optimal average input of the channel, the entanglement of
formation is simply the entropy of the reduced density matrix minus the Holevo
capacity. It is natural to ask if every bipartite state can be associated with
some channel in this way. We show that the answer is negative.
|
Possible saturation of betatron acceleration of dust particles behind strong
shock fronts from supernovae is considered. It is argued that the efficiency of
the nonthermal dust destruction should be substantially lower than the value
estimated from a traditional description of betatron acceleration of dust
grains behind radiative shock waves. The inhibition of the nonthermal
destruction can be connected with the mirror instability developed in the dust
component behind strong shocks with the velocity 3 times exceeding the Alfv\'en
speed. The instability develops on characteristic time scales much shorter the
age of a supernova remnant, thus its influence on the efficiency of dust
destruction can be substantial: in the range of shock velocities 100 km
s$^{-1}<v_s<300$ km s$^{-1}$ the destruction efficiency can be an order of
magnitude lower that normally estimated.
|
Two-photon photopolymerization of UV curing resins is an attractive method
for the fabrication of microscopic transparent objects with size in the tens of
micrometers range. We have been using this method to produce three-dimensional
structures for optical micromanipulation, in an optical system based on a
femtosecond laser. By carefully adjusting the laser power and the exposure time
we were able to create micro-objects with well-defined 3D features and with
resolution below the diffraction limit of light. We discuss the performance and
capabilities of a microfabrication system, with some examples of its products.
|
The present era has witnessed a new dawn in technology innovations with the
entry and use of nanomaterials in the industries and in the products used and
to be used in day-to-day life creating a huge possibility of ending up in the
food chain. Several studies in the past has highlighted toxicity of
nanomaterials due to their size. However, we cannot stop technological
advancements provided by the nanomaterials fulfilling human needs but can find
a solution to the toxicity of the nanomaterials for a better future and safe
environment. In this study, we propose capping of nanomaterials to reduce the
toxicity without compromising their functionality. Capping of the nanomaterials
is used to passivate nanomaterials but the same capping also helps in the
reduction of surface reactivity leading to low toxicity. We studied
phytotoxicity in the presence of one of the most extensively used metal
nanoparticles (copper nanoparticles) on Eleusine corcana G. (finger millet) and
Paspalum scrobiculatum L. (Kodo millet). Copper nanoparticles were synthesized
by the hydrometallurgical methods. Ethylenediaminetetraacetic acid (EDTA) was
used to cap the nanoparticles during the synthesis. In vitro studies results
showed that the toxicity of copper nanoparticles is significantly reduced after
capping. Anti-bacterial activity studies showed no change in efficacy of copper
nanoparticles after capping. This study highlights the use of capping to reduce
the toxicity of nanomaterials without sacrificing their required applicability.
|
Despite rapid progress in increasing the language coverage of automatic
speech recognition, the field is still far from covering all languages with a
known writing script. Recent work showed promising results with a zero-shot
approach requiring only a small amount of text data, however, accuracy heavily
depends on the quality of the used phonemizer which is often weak for unseen
languages. In this paper, we present MMS Zero-shot a conceptually simpler
approach based on romanization and an acoustic model trained on data in 1,078
different languages or three orders of magnitude more than prior art. MMS
Zero-shot reduces the average character error rate by a relative 46% over 100
unseen languages compared to the best previous work. Moreover, the error rate
of our approach is only 2.5x higher compared to in-domain supervised baselines,
while our approach uses no labeled data for the evaluation languages at all.
|
We present the results of ground-based imaging spectroscopy of the [Ne II]
12.8 micron line emitted from the ultracompact (UC) H II regions; W51d,
G45.12+0.13, G35.20-1.74 and Monoceros R2, with 2arcsec spatial resolution. We
found that the overall distribution of the [Ne II] emission is generally in
good agreement with the radio (5 or 15 GHz) VLA distribution for each source.
The Ne+ abundance ([Ne+/H+]) distributions are also derived from the [Ne II]
and the radio maps. As for G45.12+0.13 and W51d, the Ne+ abundance decreases
steeply from the outer part of the map toward the radio peak. On the other
hand, the Ne+ abundance distributions of G35.20-1.74 and Mon R2 appear rather
uniform. These results can be interpreted by the variation of ionizing
structures of neon, which is primarily determined by the spectral type of the
ionizing stars. We have evaluated the effective temperature of the ionizing
star by comparing the Ne+ abundance averaged over the whole observed region
with that calculated by H II region models based on recent non-LTE stellar
atmosphere models: 39,100 (+1100, -500) K (O7.5V-O8V) for W51d, 37,200 (+1000,
-700) K (O8V-O8.5V) for G45.12+0.13, 35,000-37,600 (+1500, -600) K (O8V-O9V)
for G35.20-1.74, and < 34,000 K (< B0V) for Mon R2. These effective
temperatures are consistent with those inferred from the observed Ne+ abundance
distributions.
|
An integral criterion for the existence of an invariant measure of an It\^{o}
process is developed. This new criterion is based on the probabilistic symbol
of the It\^{o} process. In contrast to the standard integral criterion for
invariant measures of Markov processes based on the generator, no test
functions and hence no information on the domain of the generator is needed.
|
The dominantly orbital state method allows a semiclassical description of
quantum systems. At the origin, it was developed for two-body relativistic
systems. Here, the method is extended to treat two-body Hamiltonians and
systems with three identical particles, in $D\ge 2$ dimensions, with arbitrary
kinetic energy and potential. This method is very easy to implement and can be
used in a large variety of fields. Results are expected to be reliable for
large values of the orbital angular momentum and small radial excitations, but
information about the whole spectrum can also be obtained in some very specific
cases.
|
We calculate the magnetic response of a buckled honeycomb lattice with
intrinsic spin-orbit coupling (such as silicene) which supports valley-spin
polarized energy bands when subjected to a perpendicular electric field $E_z$.
By changing the magnitude of the external electric field, the size of the two
band gaps involved can be tuned, and a transition from a topological insulator
(TI) to a trivial band insulator (BI) is induced as one of the gaps becomes
zero, and the system enters a valley-spin polarized metallic state (VSPM). In
an external magnetic field ($B$), a distinct signature of the transition is
seen in the derivative of the magnetization with respect to chemical potential
($\mu$) which gives the quantization of the Hall plateaus through the Streda
relation. When plotted as a function of the external electric field, the
magnetization has an abrupt change in slope at its minimum which signals the
VSPM state. The magnetic susceptibility ($\chi$) shows jumps as a function of
$\mu$ when a band gap is crossed which provides a measure of the gaps'
variation as a function of external electric field. Alternatively, at fixed
$\mu$, the susceptibility displays an increasingly large diamagnetic response
as the electric field approaches the critical value of the VSPM phase. In the
VSPM state, magnetic oscillations exist for any value of chemical potential
while for the TI, and BI state, $\mu$ must be larger than the minimum gap in
the system. When $\mu$ is larger than both gaps, there are two fundamental
cyclotron frequencies (which can also be tuned by $E_z$) involved in the
de-Haas van-Alphen oscillations which are close in magnitude. This causes a
prominent beating pattern to emerge.
|
System reliability analysis aims at computing the probability of failure of
an engineering system given a set of uncertain inputs and limit state
functions. Active-learning solution schemes have been shown to be a viable tool
but as of yet they are not as efficient as in the context of component
reliability analysis. This is due to some peculiarities of system problems,
such as the presence of multiple failure modes and their uneven contribution to
failure, or the dependence on the system configuration (e.g., series or
parallel). In this work, we propose a novel active learning strategy designed
for solving general system reliability problems. This algorithm combines subset
simulation and Kriging/PC-Kriging, and relies on an enrichment scheme tailored
to specifically address the weaknesses of this class of methods. More
specifically, it relies on three components: (i) a new learning function that
does not require the specification of the system configuration, (ii) a
density-based clustering technique that allows one to automatically detect the
different failure modes, and (iii) sensitivity analysis to estimate the
contribution of each limit state to system failure so as to select only the
most relevant ones for enrichment. The proposed method is validated on two
analytical examples and compared against results gathered in the literature.
Finally, a complex engineering problem related to power transmission is solved,
thereby showcasing the efficiency of the proposed method in a real-case
scenario.
|
This note develops Rio's proof [C. R. Math. Acad. Sci. Paris, 1995] of the
rate of convergence in the Marcinkiewicz--Zygmund strong law of large numbers
to the case of sums of dependent random variables with regularly varying
normalizing constants. It allows us to obtain a complete convergence result for
dependent sequences under uniformly bounded moment conditions. This result is
new even when the underlying random variables are independent. The main
theorems are applied to three different dependence structures: (i) $m$-pairwise
negatively dependent random variables, (ii) $m$-extended negatively dependent
random variables, and (iii) $\varphi$-mixing sequences. To our best knowledge,
the results for cases (i) and (ii) are the first results in the literature on
complete convergence for sequences of $m$-pairwise negatively dependent random
variables and $m$-extended negatively dependent random variables under the
optimal moment conditions even when $m=1$. While the results for cases (i) and
(iii) unify and improve many existing ones, the result for case (ii)
complements the main result of Chen et al. [J. Appl. Probab., 2010].
Affirmative answers to open questions raised by Chen et al. [J. Math. Anal.
Appl., 2014] and Wu and Rosalsky [Glas. Mat. Ser. III, 2015] are also given. An
example illustrating the sharpness of the main result is presented.
|
In this paper we study several issues related to the generation of
superpotential induced by background Ramond-Ramond fluxes in compactification
of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons
with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we
propose a general formula for the superpotential and justify it comparing the
supersymmetry conditions in D=2 and D=10 supergravity theories. We also suggest
a geometric interpretation to the supersymmetric index in the two-dimensional
effective theory in terms of topological invariants of the Calabi-Yau
four-fold, and estimate the asymptotic growth of these invariants from BTZ
black hole entropy. Finally, we explicitly construct new supersymmetric vacua
for Type IIA string theory compactification on a Calabi-Yau four-fold with
Ramond-Ramond fluxes.
|
We study the computation of Gaussian orthant probabilities, i.e. the
probability that a Gaussian falls inside a quadrant. The
Geweke-Hajivassiliou-Keane (GHK) algorithm [Genz, 1992; Geweke, 1991;
Hajivassiliou et al., 1996; Keane, 1993], is currently used for integrals of
dimension greater than 10. In this paper we show that for Markovian covariances
GHK can be interpreted as the estimator of the normalizing constant of a state
space model using sequential importance sampling (SIS). We show for an AR(1)
the variance of the GHK, properly normalized, diverges exponentially fast with
the dimension. As an improvement we propose using a particle filter (PF). We
then generalize this idea to arbitrary covariance matrices using Sequential
Monte Carlo (SMC) with properly tailored MCMC moves. We show empirically that
this can lead to drastic improvements on currently used algorithms. We also
extend the framework to orthants of mixture of Gaussians (Student, Cauchy
etc.), and to the simulation of truncated Gaussians.
|
The possibility of interpreting baryons containing a single heavy quark as
bound states of solitons (that arise in the nonlinear sigma model) and heavy
mesons is explored. Particular attention is paid to the parity of the bound
states and to the role of heavy quark symmetry.
|
We derive a quadratic recursion relation for the linear Hodge integrals of
the form $\langle\tau_2^n\lambda_k\rangle$. These numbers are used in a formula
for Masur-Veech volumes of moduli spaces of quadratic differentials discovered
by Chen, M\"oller, and Sauvaget. Therefore, our recursion provides an efficient
way of computing these volumes.
|
This paper addresses the problem of estimating the 3-DoF camera pose for a
ground-level image with respect to a satellite image that encompasses the local
surroundings. We propose a novel end-to-end approach that leverages the
learning of dense pixel-wise flow fields in pairs of ground and satellite
images to calculate the camera pose. Our approach differs from existing methods
by constructing the feature metric at the pixel level, enabling full-image
supervision for learning distinctive geometric configurations and visual
appearances across views. Specifically, our method employs two distinct
convolution networks for ground and satellite feature extraction. Then, we
project the ground feature map to the bird's eye view (BEV) using a fixed
camera height assumption to achieve preliminary geometric alignment. To further
establish content association between the BEV and satellite features, we
introduce a residual convolution block to refine the projected BEV feature.
Optical flow estimation is performed on the refined BEV feature map and the
satellite feature map using flow decoder networks based on RAFT. After
obtaining dense flow correspondences, we apply the least square method to
filter matching inliers and regress the ground camera pose. Extensive
experiments demonstrate significant improvements compared to state-of-the-art
methods. Notably, our approach reduces the median localization error by 89%,
19%, 80% and 35% on the KITTI, Ford multi-AV, VIGOR and Oxford RobotCar
datasets, respectively.
|
Offline reinforcement learning has emerged as a promising technology by
enhancing its practicality through the use of pre-collected large datasets.
Despite its practical benefits, most algorithm development research in offline
reinforcement learning still relies on game tasks with synthetic datasets. To
address such limitations, this paper provides autonomous driving datasets and
benchmarks for offline reinforcement learning research. We provide 19 datasets,
including real-world human driver's datasets, and seven popular offline
reinforcement learning algorithms in three realistic driving scenarios. We also
provide a unified decision-making process model that can operate effectively
across different scenarios, serving as a reference framework in algorithm
design. Our research lays the groundwork for further collaborations in the
community to explore practical aspects of existing reinforcement learning
methods. Dataset and codes can be found in https://sites.google.com/view/ad4rl.
|
Heath and Pemmaraju conjectured that the queue-number of a poset is bounded
by its width and if the poset is planar then also by its height. We show that
there are planar posets whose queue-number is larger than their height,
refuting the second conjecture. On the other hand, we show that any poset of
width $2$ has queue-number at most $2$, thus confirming the first conjecture in
the first non-trivial case. Moreover, we improve the previously best known
bounds and show that planar posets of width $w$ have queue-number at most
$3w-2$ while any planar poset with $0$ and $1$ has queue-number at most its
width.
|
We find Mask2Former also achieves state-of-the-art performance on video
instance segmentation without modifying the architecture, the loss or even the
training pipeline. In this report, we show universal image segmentation
architectures trivially generalize to video segmentation by directly predicting
3D segmentation volumes. Specifically, Mask2Former sets a new state-of-the-art
of 60.4 AP on YouTubeVIS-2019 and 52.6 AP on YouTubeVIS-2021. We believe
Mask2Former is also capable of handling video semantic and panoptic
segmentation, given its versatility in image segmentation. We hope this will
make state-of-the-art video segmentation research more accessible and bring
more attention to designing universal image and video segmentation
architectures.
|
Document Layout Analysis is a fundamental step in Handwritten Text Processing
systems, from the extraction of the text lines to the type of zone it belongs
to. We present a system based on artificial neural networks which is able to
determine not only the baselines of text lines present in the document, but
also performs geometric and logic layout analysis of the document. Experiments
in three different datasets demonstrate the potential of the method and show
competitive results with respect to state-of-the-art methods.
|
In many real-world applications such as business planning and sensor data
monitoring, one important, yet challenging, the task is to rank objects(e.g.,
products, documents, or spatial objects) based on their ranking scores and
efficiently return those objects with the highest scores. In practice, due to
the unreliability of data sources, many real-world objects often contain noises
and are thus imprecise and uncertain. In this paper, we study the problem of
probabilistic top-k dominating(PTD) query on such large-scale uncertain data in
a distributed environment, which retrieves k uncertain objects from distributed
uncertain databases(on multiple distributed servers), having the largest
ranking scores with high confidences. In order to efficiently tackle the
distributed PTD problem, we propose a MapReduce framework for processing
distributed PTD queries over distributed uncertain databases. In this MapReduce
framework, we design effective pruning strategies to filter out false alarms in
the distributed setting, propose cost-model-based index distribution mechanisms
over servers, and develop efficient distributed PTD query processing
algorithms. Extensive experiments have demonstrated the efficiency and
effectiveness of our proposed distributed PTD approach on both real and
synthetic data sets through various experimental settings.
|
Generalizing S. Gelfand's classical construction of a Novikov algebra from a
commutative differential algebra, a deformation family $(A,\circ_q)$, for
scalars $q$, of Novikov algebras is constructed from what we call an admissible
commutative differential algebra, by adding a second linear operator to the
commutative differential algebra with certain admissibility condition. The case
of $(A,\circ_0)$ recovers the construction of S. Gelfand. This admissibility
condition also ensures a bialgebra theory of commutative differential algebras,
enriching the antisymmetric infinitesimal bialgebra. This way, a deformation
family of Novikov bialgebras is obtained, under the further condition that the
two operators are bialgebra derivations. As a special case, we obtain a
bialgebra variation of S. Gelfand's construction with an interesting twist:
every commutative and cocommutative differential antisymmetric infinitesimal
bialgebra gives rise to a Novikov bialgebra whose underlying Novikov algebra is
$(A,\circ_{-\frac{1}{2}})$ instead of $(A,\circ_0)$. The close relations of the
classical bialgebra theories with Manin triples, classical Yang-Baxter type
equations, $\mathcal{O}$-operators, and pre-structures are expanded to the two
new bialgebra theories, in a way that is compatible with the just established
connection between the two bialgebras. As an application, Novikov bialgebras
are obtained from admissible differential Zinbiel algebras.
|
Deep learning methods have been considered promising for accelerating
molecular screening in drug discovery and material design. Due to the limited
availability of labelled data, various self-supervised molecular pre-training
methods have been presented. While many existing methods utilize common
pre-training tasks in computer vision (CV) and natural language processing
(NLP), they often overlook the fundamental physical principles governing
molecules. In contrast, applying denoising in pre-training can be interpreted
as an equivalent force learning, but the limited noise distribution introduces
bias into the molecular distribution. To address this issue, we introduce a
molecular pre-training framework called fractional denoising (Frad), which
decouples noise design from the constraints imposed by force learning
equivalence. In this way, the noise becomes customizable, allowing for
incorporating chemical priors to significantly improve molecular distribution
modeling. Experiments demonstrate that our framework consistently outperforms
existing methods, establishing state-of-the-art results across force
prediction, quantum chemical properties, and binding affinity tasks. The
refined noise design enhances force accuracy and sampling coverage, which
contribute to the creation of physically consistent molecular representations,
ultimately leading to superior predictive performance.
|
Stoichiometric Sr2IrO4 is a ferromagnetic Jeff = 1/2 Mott insulator driven by
strong spin-orbit coupling. Introduction of very dilute oxygen vacancies into
single-crystal Sr2IrO4-delta with delta < 0.04 leads to significant changes in
lattice parameters and an insulator-to-metal transition at TMI = 105 K. The
highly anisotropic electrical resistivity of the low-temperature metallic state
for delta ~ 0.04 exhibits anomalous properties characterized by non-Ohmic
behavior and an abrupt current-induced transition in the resistivity at T* = 52
K, which separates two regimes of resisitive switching in the nonlinear I-V
characteristics. The novel behavior illustrates an exotic ground state and
constitutes a new paradigm for devices structures in which electrical
resistivity is manipulated via low-level current densities ~ 10 mA/cm2
(compared to higher spin-torque currents ~ 107-108 A/cm2) or magnetic
inductions ~ 0.1-1.0 T.
|
Graphene nanoribbons are a promising candidate for fault-tolerant quantum
electronics. In this scenario, qubits are realised by localised states that can
emerge on junctions in hybrid ribbons formed by two armchair nanoribbons of
different widths. We derive an effective theory based on a tight-binding ansatz
for the description of hybrid nanoribbons and use it to make accurate
predictions of the energy gap and nature of the localisation in various hybrid
nanoribbon geometries. We use quantum Monte Carlo simulations to demonstrate
that the effective theory remains applicable in the presence of Hubbard
interactions. We discover, in addition to the well known localisations on
junctions, which we call `Fuji', a new type of `Kilimanjaro' localisation
smeared out over a segment of the hybrid ribbon. We show that Fuji
localisations in hybrids of width $N$ and $N+2$ armchair nanoribbons occur
around symmetric junctions if and only if $N\pmod3=1$, while edge-aligned
junctions never support strong localisation. This behaviour cannot be explained
relying purely on the topological $Z_2$ invariant, which has been believed the
origin of the localisations to date.
|
Semantic communication serves as a novel paradigm and attracts the broad
interest of researchers. One critical aspect of it is the multi-user semantic
communication theory, which can further promote its application to the
practical network environment. While most existing works focused on the design
of end-to-end single-user semantic transmission, a novel non-orthogonal
multiple access (NOMA)-based multi-user semantic communication system named
NOMASC is proposed in this paper. The proposed system can support semantic
tranmission of multiple users with diverse modalities of source information. To
avoid high demand for hardware, an asymmetric quantizer is employed at the end
of the semantic encoder for discretizing the continuous full-resolution
semantic feature. In addition, a neural network model is proposed for mapping
the discrete feature into self-learned symbols and accomplishing intelligent
multi-user detection (MUD) at the receiver. Simulation results demonstrate that
the proposed system holds good performance in non-orthogonal transmission of
multiple user signals and outperforms the other methods, especially at
low-to-medium SNRs. Moreover, it has high robustness under various simulation
settings and mismatched test scenarios.
|
In this paper we continue the study of non-relativistic p+1 dimensional
theories that we started at arXiv:0904.1343. We extend the analysis presented
there to the case of stable and unstable Dp-branes.
|
Clustering analysis has become a ubiquitous information retrieval tool in a
wide range of domains, but a more automatic framework is still lacking. Though
internal metrics are the key players towards a successful retrieval of
clusters, their effectiveness on real-world datasets remains not fully
understood, mainly because of their unrealistic assumptions underlying
datasets. We hypothesized that capturing {\it traces of information gain}
between increasingly complex clustering retrievals---{\it InfoGuide}---enables
an automatic clustering analysis with improved clustering retrievals. We
validated the {\it InfoGuide} hypothesis by capturing the traces of information
gain using the Kolmogorov-Smirnov statistic and comparing the clusters
retrieved by {\it InfoGuide} against those retrieved by other commonly used
internal metrics in artificially-generated, benchmarks, and real-world
datasets. Our results suggested that {\it InfoGuide} can enable a more
automatic clustering analysis and may be more suitable for retrieving clusters
in real-world datasets displaying nontrivial statistical properties.
|
In this work, we investigate the size, thermal inertia, surface roughness and
geometric albedo of 10 Vesta family asteroids by using the Advanced
Thermophysical Model (ATPM), based on the thermal infrared data acquired by
mainly NASA's Wide-field Infrared Survey Explorer (WISE). Here we show that the
average thermal inertia and geometric albedo of the investigated Vesta family
members are 42 $\rm J m^{-2} s^{-1/2} K^{-1}$ and 0.314, respectively, where
the derived effective diameters are less than 10 km. Moreover, the family
members have a relatively low roughness fraction on their surfaces. The
similarity in thermal inertia and geometric albedo among the V-type Vesta
family member may reveal their close connection in the origin and evolution. As
the fragments of the cratering event of Vesta, the family members may have
undergone similar evolution process, thereby leading to very close thermal
properties. Finally, we estimate their regolith grain sizes with different
volume filling factors.
|
It has become clear during the last decades that the interaction between the
supernova ejecta and the circumstellar medium is playing a major role both for
the observational properties of the supernova and for understanding the
evolution of the progenitor star leading up to the explosion. In addition, it
provides an opportunity to understand the shock physics connected to both
thermal and non-thermal processes, including relativistic particle
acceleration, radiation processes and the hydrodynamics of shock waves. This
chapter has an emphasis on the information we can get from radio and X-ray
observations, but also their connection to observations in the optical and
ultraviolet. We first review the different physical processes involved in
circumstellar interaction, including hydrodynamics, thermal X-ray emission,
acceleration of relativistic particles and non-emission processes in the radio
and X-ray ranges. Finally, we discuss applications of these to different types
of supernovae.
|
We review measurements of semileptonic and leptonic charm meson decays
performed by the Belle experiment, and we use these results to estimate the
sensitivity of the follow-on Belle II experiment to these decays.
|
The use of machine learning to develop intelligent software tools for
interpretation of radiology images has gained widespread attention in recent
years. The development, deployment, and eventual adoption of these models in
clinical practice, however, remains fraught with challenges. In this paper, we
propose a list of key considerations that machine learning researchers must
recognize and address to make their models accurate, robust, and usable in
practice. Namely, we discuss: insufficient training data, decentralized
datasets, high cost of annotations, ambiguous ground truth, imbalance in class
representation, asymmetric misclassification costs, relevant performance
metrics, generalization of models to unseen datasets, model decay, adversarial
attacks, explainability, fairness and bias, and clinical validation. We
describe each consideration and identify techniques to address it. Although
these techniques have been discussed in prior research literature, by freshly
examining them in the context of medical imaging and compiling them in the form
of a laundry list, we hope to make them more accessible to researchers,
software developers, radiologists, and other stakeholders.
|
The large ttbar production cross-section at the LHC suggests the use of top
quark decays to calibrate several critical parts of the detectors, such as the
trigger system, the jet energy scale and b-tagging.
|
Geodesic equations of timelike and null charged particles in the Ernst metric
are studied. We consider two distinct forms of the Ernst solution where the
Maxwell potential represents either a uniform electric or magnetic field.
Circular orbits in various configurations are considered, as well as their
perturbations and stability. We find that the electric field strength must be
below a certain charge-dependent critical value for these orbits to be stable.
The case of the magnetic Ernst metric contains a limit which reduces to the
Melvin magnetic universe. In this case the equations of motion are solved to
reveal cycloidlike or trochoidlike motion, similar to those found by Frolov and
Shoom around black holes immersed in test magnetic fields.
|
We study the effect of disorder and doping on the metal-insulator transition
in a repulsive Hubbard model on a square lattice using the determinant quantum
Monte Carlo method. First, with the aim of making our results reliable, we
compute the sign problem with various parameters such as temperature, disorder,
on-site interactions, and lattice size. We show that in the presence of
randomness in the hopping elements, the metal-insulator transition occurs and
the critical disorder strength differs at different fillings. We also
demonstrate that doping is a driving force behind the metal-insulator
transition.
|
Risk assessment is a major challenge for supply chain managers, as it
potentially affects business factors such as service costs, supplier
competition and customer expectations. The increasing interconnectivity between
organisations has put into focus methods for supply chain cyber risk
management. We introduce a general approach to support such activity taking
into account various techniques of attacking an organisation and its suppliers,
as well as the impacts of such attacks. Since data is lacking in many respects,
we use structured expert judgment methods to facilitate its implementation. We
couple a family of forecasting models to enrich risk monitoring. The approach
may be used to set up risk alarms, negotiate service level agreements, rank
suppliers and identify insurance needs, among other management possibilities.
|
We study the tau-function and theta-divisor of an isomonodromic family of
linear differential (2x2)-systems with non-resonant irregular singularities. In
some particular case the estimates for pole orders of the coefficient matrices
of the family are applied.
|
Conversational recommender systems (CRS) that are able to interact with users
in natural language often utilize recommendation dialogs which were previously
collected with the help of paired humans, where one plays the role of a seeker
and the other as a recommender. These recommendation dialogs include items and
entities that indicate the users' preferences. In order to precisely model the
seekers' preferences and respond consistently, CRS typically rely on item and
entity annotations. A recent example of such a dataset is INSPIRED, which
consists of recommendation dialogs for sociable conversational recommendation,
where items and entities were annotated using automatic keyword or pattern
matching techniques. An analysis of this dataset unfortunately revealed that
there is a substantial number of cases where items and entities were either
wrongly annotated or annotations were missing at all. This leads to the
question to what extent automatic techniques for annotations are effective.
Moreover, it is important to study impact of annotation quality on the overall
effectiveness of a CRS in terms of the quality of the system's responses. To
study these aspects, we manually fixed the annotations in INSPIRED. We then
evaluated the performance of several benchmark CRS using both versions of the
dataset. Our analyses suggest that the improved version of the dataset, i.e.,
INSPIRED2, helped increase the performance of several benchmark CRS,
emphasizing the importance of data quality both for end-to-end learning and
retrieval-based approaches to conversational recommendation. We release our
improved dataset (INSPIRED2) publicly at
https://github.com/ahtsham58/INSPIRED2.
|
We report several recent updates from the BABAR Collaboration on the matrix
elements $|V_{cb}|$, $|V_{ub}|$, and $|V_{td}|$ of the
Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix, and the angles $\beta$ and
$\alpha$ of the unitarity triangle. Most results presented here are using the
full BABAR $\Upsilon(4S)$ data set.
|
Recent works have revealed that Transformers are implicitly learning the
syntactic information in its lower layers from data, albeit is highly dependent
on the quality and scale of the training data. However, learning syntactic
information from data is not necessary if we can leverage an external syntactic
parser, which provides better parsing quality with well-defined syntactic
structures. This could potentially improve Transformer's performance and sample
efficiency. In this work, we propose a syntax-guided localized self-attention
for Transformer that allows directly incorporating grammar structures from an
external constituency parser. It prohibits the attention mechanism to
overweight the grammatically distant tokens over close ones. Experimental
results show that our model could consistently improve translation performance
on a variety of machine translation datasets, ranging from small to large
dataset sizes, and with different source languages.
|
We analyze the statistical properties and dynamical implications of galaxy
distributions in phase space for samples selected from the 2MASS Extended
Source Catalog. The galaxy distribution is decomposed into modes $\delta({\bf
k, x})$ which describe the number density perturbations of galaxies in phase
space cell given by scale band $\bf k$ to ${\bf k}+\Delta {\bf k}$ and spatial
range $\bf x$ to ${\bf x}+\Delta {\bf x}$. In the nonlinear regime,
$\delta({\bf k, x})$ is highly non-Gaussian. We find, however, that the
correlations between $\delta({\bf k, x})$ and $\delta({\bf k', x'})$ are always
very weak if the spatial ranges (${\bf x}$, ${\bf x}+\Delta {\bf x}$) and
(${\bf x'}$, ${\bf x'}+\Delta {\bf x'}$) don't overlap. This feature is due to
the fact that the spatial locality of the initial perturbations is memorized
during hierarchical clustering. The highly spatial locality of the 2MASS galaxy
correlations is a strong evidence for the initial perturbations of the cosmic
mass field being spatially localized, and therefore, consistent with a Gaussian
initial perturbations on scales as small as about 0.1 h$^{-1}$ Mpc. Moreover,
the 2MASS galaxy spatial locality indicates that the relationship between
density perturbations of galaxies and the underlying dark matter should be
localized in phase space. That is, for a structure consisting of perturbations
on scales from $k$ to $ k+\Delta {k}$, the nonlocal range in the relation
between galaxies and dark matter should {\it not} be larger than $|{\Delta {\bf
x}}|=2\pi/|\Delta {\bf k}|$. The stochasticity and nonlocality of the bias
relation between galaxies and dark matter fields should be no more than the
allowed range given by the uncertainty relation $|{\Delta {\bf x}|| \Delta{\bf
k}}|=2\pi$.
|
We report results of zero-field muon spin relaxation experiments on the
filled-skutterudite superconductors~Pr$_{1-x}$Ce$_{x}$Pt$_4$Ge$_{12}$, $x = 0$,
0.07, 0.1, and 0.2, to investigate the effect of Ce doping on broken
time-reversal symmetry (TRS) in the superconducting state. In these alloys
broken TRS is signaled by the onset of a spontaneous static local magnetic
field~$B_s$ below the superconducting transition temperature. We find that
$B_s$ decreases linearly with $x$ and $\to 0$ at $x \approx 0.4$, close to the
concentration above which superconductivity is no longer observed. The
(Pr,Ce)Pt$_4$Ge$_{12}$ and isostructural (Pr,La)Os$_4$Sb$_{12}$ alloy series
both exhibit superconductivity with broken TRS, and in both the decrease of
$B_s$ is proportional to the decrease of Pr concentration. This suggests that
Pr-Pr intersite interactions are responsible for the broken<EMAIL_ADDRESS>The two
alloy series differ in that the La-doped alloys are superconducting for all La
concentrations, suggesting that in (Pr,Ce)Pt$_4$Ge$_{12}$ pair-breaking by Ce
doping suppresses superconductivity. For all $x$ the dynamic muon spin
relaxation rate decreases somewhat in the superconducting state. This may be
due to Korringa relaxation by conduction electrons, which is reduced by the
opening of the superconducting energy gap.
|
We obtain a lower bound for the coarse Ricci curvature of continuous time
pure jump Markov processes, with an emphasis on interacting particle systems.
Applications to several models are provided, with a detailed study of the herd
behavior of a simple model of interacting agents.
|
We prove that insertion-elimination Lie algebra of Feynman graphs, in the
ladder case, has a natural interpretation in terms of a certain algebra of
infinite dimensional matrices. We study some aspects of its representation
theory and we discuss some relations with the representation of the Heisenberg
algebra
|
Self-consistent field theory (SCFT) has established that for cubic network
phases in diblock copolymer melts, the double-gyroid (DG) is thermodynamically
stable relative to the competitor double-diamond (DD) and double-primitive (DP)
phases, and exhibits a window of stability intermediate to the classical
lamellar and columnar phases. This competition is widely thought to be
controlled by "packing frustration" -- the incompatibility of uniformly filling
melts with a locally preferred chain packing motif. Here, we reassess the
thermodynamics of cubic network formation in strongly-segregated diblock melts,
based on a recently developed medial strong segregation theory ("mSST")
approach that directly connects the shape and thermodynamics of chain packing
environments to the medial geometry of tubular network surfaces. We first show
that medial packing significantly relaxes prior SST upper bounds on the free
energy of network phases, which we attribute to the spreading of terminal chain
ends within network nodal regions. Exploring geometric and thermodynamic
metrics of chain packing in network phases, we show that mSST reproduces
effects dependent on the elastic asymmetry of the blocks that are consistent
with SCFT at large $\chi N$. We then characterize geometric frustration in
terms of the spatially-variant distributions of local entropic and enthalpic
costs throughout the morphologies, extracted from mSST predictions. We find
that the DG morphology, due to its unique medial geometry in the nodal regions,
is stabilized by the incorporation of favorable, quasi-lamellar packing over
much of its morphology, motifs which are inaccessible to DD and DP morphologies
due to "interior corners" in their medial geometries. Finally, we use our
results to analyze "hot spots" of chain stretching and discuss implications for
network susceptibility to the uptake of guest molecules.
|
For the fermion transformation in the space all books of quantum mechanics
propose to use the unitary operator $\widehat{U}_{\vec
n}(\varphi)=\exp{(-i\frac\varphi2(\widehat\sigma\cdot\vec n))}$, where
$\varphi$ is angle of rotation around the axis $\vec{n}$. But this operator
turns the spin in inverse direction presenting the rotation to the left. The
error of defining of $\widehat{U}_{\vec n}(\varphi)$ action is caused because
the spin supposed as simple vector which is independent from
$\widehat\sigma$-operator a priori. In this work it is shown that each fermion
marked by number $i$ has own Pauli-vector $\widehat\sigma_i$ and both of them
change together. If we suppose the global $\widehat\sigma$-operator and using
the Bloch Sphere approach define for all fermions the common quantization axis
$z$ the spin transformation will be the same: the right hand rotation around
the axis $\vec{n}$ is performed by the operator $\widehat{U}^+_{\vec
n}(\varphi)=\exp{(+i\frac\varphi2(\widehat\sigma\cdot\vec n))}$.
|
A new optimized extreme learning machine- (ELM-) based method for power
system transient stability prediction (TSP) using synchrophasors is presented
in this paper. First, the input features symbolizing the transient stability of
power systems are extracted from synchronized measurements. Then, an ELM
classifier is employed to build the TSP model. And finally, the optimal
parameters of the model are optimized by using the improved particle swarm
optimization (IPSO) algorithm. The novelty of the proposal is in the fact that
it improves the prediction performance of the ELM-based TSP model by using IPSO
to optimize the parameters of the model with synchrophasors. And finally, based
on the test results on both IEEE 39-bus system and a large-scale real power
system, the correctness and validity of the presented approach are verified.
|
The influence of a Gaussian environment on a quantum system can be described
by effectively replacing the continuum with a discrete set of ancillary quantum
and classical degrees of freedom. This defines a pseudomode model which can be
used to classically simulate the reduced system dynamics. Here, we consider an
alternative point of view and analyze the potential benefits of an analog or
digital quantum simulation of the pseudomode model itself. Superficially, such
a direct experimental implementation is, in general, impossible due to the
unphysical properties of the effective degrees of freedom involved. However, we
show that the effects of the unphysical pseudomode model can still be
reproduced using measurement results over an ensemble of physical systems
involving ancillary harmonic modes and an optional stochastic driving field.
This is done by introducing an extrapolation technique whose efficiency is
limited by stability against imprecision in the measurement data. We examine
how such a simulation would allow us to (i) perform accurate quantum simulation
of the effects of complex non-perturbative and non-Markovian environments in
regimes that are challenging for classical simulation, (ii) conversely,
mitigate potential unwanted non-Markovian noise present in quantum devices, and
(iii) restructure some of some of the properties of a given physical bath, such
as its temperature.
|
The conventional mesh-based Level of Detail (LoD) technique, exemplified by
applications such as Google Earth and many game engines, exhibits the
capability to holistically represent a large scene even the Earth, and achieves
rendering with a space complexity of O(log n). This constrained data
requirement not only enhances rendering efficiency but also facilitates dynamic
data fetching, thereby enabling a seamless 3D navigation experience for users.
In this work, we extend this proven LoD technique to Neural Radiance Fields
(NeRF) by introducing an octree structure to represent the scenes in different
scales. This innovative approach provides a mathematically simple and elegant
representation with a rendering space complexity of O(log n), aligned with the
efficiency of mesh-based LoD techniques. We also present a novel training
strategy that maintains a complexity of O(n). This strategy allows for parallel
training with minimal overhead, ensuring the scalability and efficiency of our
proposed method. Our contribution is not only in extending the capabilities of
existing techniques but also in establishing a foundation for scalable and
efficient large-scale scene representation using NeRF and octree structures.
|
We report preliminary results for 2D massive QED with two flavours of Wilson
fermions, using the Hermitean variant of L\"uscher's bosonization technique.
The chiral condensate and meson masses are obtained. The simplicity of the
model allows for high statistics simulations close to the chiral and continuum
limit, both in the quenched approximation and with dynamical fermions.
|
Given one quasi-smooth derived space cut out of another by a section of a
2-term complex of bundles, we give two formulae for its virtual cycle.
They are modelled on the the $p$-fields construction of Chang-Li and the
Quantum Lefschetz principle, and recover these when applied to moduli spaces of
(stable or quasi-) maps. When the complex is a single bundle we recover results
of Kim-Kresch-Pantev.
|
A well-known question asks whether the spectrum of the Laplacian on a
Riemannian manifold $(M,g)$ determines the Riemannian metric $g$ up to
isometry. A similar question is whether the energy spectrum of all harmonic
maps from a given Riemannian manifold $(\Sigma,h)$ to $M$ determines the
Riemannian metric on the target space. We consider this question in the case of
harmonic maps between flat tori. In particular, we show that the two
isospectral, non-isometric $16$-dimensional flat tori found by Milnor cannot be
distinguished by the energy spectrum of harmonic maps from $d$-dimensional flat
tori for $d\leq 3$, but can be distinguished by certain flat tori for $d\geq
4$. This is related to a property of the Siegel theta series in degree $d$
associated to the $16$-dimensional lattices in Milnor's example.
|
We review non-linear sigma-models with (2,1) and (2,2) supersymmetry. We
focus on off-shell closure of the supersymmetry algebra and give a complete
list of (2,2) superfields. We provide evidence to support the conjecture that
all N=(2,2) non-linear sigma-models can be described by these fields. This in
its turn leads to interesting consequences about the geometry of the target
manifolds. One immediate corollary of this conjecture is the existence of a
potential for hyper-Kahler manifolds, different from the Kahler potential,
which does not only allow for the computation of the metric, but of the three
fundamental two-forms as well. Several examples are provided: WZW models on
SU(2) x U(1) and SU(2) x SU(2) and four-dimensional special hyper-Kahler
manifolds.
|
We present the kinematic anaylsis of $246$ stars within $4^\prime$ from the
center of Orion Nebula Cluster (ONC), the closest massive star cluster with
active star formation across the full mass range, which provides valuable
insights in the the formation and evolution of star cluster on an
individual-star basis. High-precision radial velocities and surface
temperatures are retrieved from spectra acquired by the NIRSPEC instrument used
with adaptive optics (NIRSPAO) on the Keck II 10-m telescope. A
three-dimensional kinematic map is then constructed by combining with the
proper motions previously measured by the Hubble Space Telescope (HST)
ACS/WFPC2/WFC3IR and Keck II NIRC2. The measured root-mean-squared velocity
dispersion is $2.26\pm0.08~\mathrm{km}\,\mathrm{s}^{-1}$, significantly higher
than the virial equilibrium's requirement of
$1.73~\mathrm{km}\,\mathrm{s}^{-1}$, suggesting that the ONC core is
supervirial, consistent with previous findings. Energy equipartition is not
detected in the cluster. Most notably, the velocity of each star relative to
its neighbors is found to be negatively correlated with stellar mass. Low-mass
stars moving faster than their surrounding stars in a supervirial cluster
suggests that the initial masses of forming stars may be related to their
initial kinematic states. Additionally, a clockwise rotation preference is
detected. A weak sign of inverse mass segregation is also identified among
stars excluding the Trapezium stars, though it could be a sample bias. Finally,
this study reports the discovery of four new candidate spectroscopic binary
systems.
|
We introduce the circumcenter mapping induced by a set of (usually
nonexpansive) operators. One prominent example of a circumcenter mapping is the
celebrated Douglas--Rachford splitting operator. Our study is motivated by the
Circumcentered--Douglas--Rachford method recently introduced by Behling, Bello
Cruz, and Santos in order to accelerate the Douglas--Rachford method for
solving certain classes of feasibility problems. We systematically explore the
properness of the circumcenter mapping induced by reflectors or projectors.
Numerous examples are presented. We also present a version of Browder's
demiclosedness principle for circumcenter mappings.
|
To facilitate the evolution of edge intelligence in ever-changing
environments, we study on-device incremental learning constrained in limited
computation resource in this paper. Current on-device training methods just
focus on efficient training without considering the catastrophic forgetting,
preventing the model getting stronger when continually exploring the world. To
solve this problem, a direct solution is to involve the existing incremental
learning mechanisms into the on-device training framework. Unfortunately, such
a manner cannot work well as those mechanisms usually introduce large
additional computational cost to the network optimization process, which would
inevitably exceed the memory capacity of the edge devices. To address this
issue, this paper makes an early effort to propose a simple but effective
edge-friendly incremental learning framework. Based on an empirical study on
the knowledge intensity of the kernel elements of the neural network, we find
that the center kernel is the key for maximizing the knowledge intensity for
learning new data, while freezing the other kernel elements would get a good
balance on the model's capacity for overcoming catastrophic forgetting. Upon
this finding, we further design a center-sensitive kernel optimization
framework to largely alleviate the cost of the gradient computation and
back-propagation. Besides, a dynamic channel element selection strategy is also
proposed to facilitate a sparse orthogonal gradient projection for further
reducing the optimization complexity, upon the knowledge explored from the new
task data. Extensive experiments validate our method is efficient and
effective, e.g., our method achieves average accuracy boost of 38.08% with even
less memory and approximate computation compared to existing on-device training
methods, indicating its significant potential for on-device incremental
learning.
|
We derive the central charge and BPS equations from the low-energy effective
action for N=2 SU(2) Yang-Mills theory in the Coulomb phase, using a
systematic, canonical procedure. We then obtain solutions for monopole and dyon
BPS states, whose core structure is described by a dual Lagrangian containing
the monopole or dyon as a fundamental field. Spherically symmetric states
possess a shell of charge at a characteristic radius.
|
All possible symmetry-determined nonlinear normal modes (also called by
simple periodic orbits, one-mode solutions etc.) in both hard and soft
Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying
their stability in the thermodynamic limit, as well as its application for each
of the above nonlinear normal modes are presented.
|
We study a bosonic string with one end free and the other confined to a
D-brane. Only the odd oscillator modes are allowed, which leads to a Virasoro
algebra of even Virasoro modes only. The theory is quantized in a gauge where
world-sheet time and ordinary time are identified. There are no negative or
null norm states, and no tachyon. The Regge slope is twice that of the open
string; this can serve as a test of the usefulness of the the model as a
semi-quantitative description of mesons with one light and one extremely heavy
quark when such higher spin mesons are found. The Virasoro conditions select
specific SO(D-1) irreps. The asymptotic density of states can be estimated by
adapting the Hardy-Ramanujan analysis to a partition of odd integers; the
estimate becomes exact as D goes to infinity.
|
The spin rate \Omega of neutron stars at a given temperature T is constrained
by the interplay between gravitational-radiation instabilities and viscous
damping. Navier-Stokes theory has been used to calculate the viscous damping
timescales and produce a stability curve for r-modes in the (\Omega,T) plane.
In Navier-Stokes theory, viscosity is independent of vorticity, but kinetic
theory predicts a coupling of vorticity to the shear viscosity. We calculate
this coupling and show that it can in principle significantly modify the
stability diagram at lower temperatures. As a result, colder stars can remain
stable at higher spin rates.
|
We show that the algebraic automorphism group of the SL(2,C) character
variety of a closed orientable surface with negative Euler characteristic is a
finite extension of its mapping class group. Along the way, we provide a simple
characterization of the valuations on the character algebra coming from
measured laminations.
|
Through experiments, we studied defect turbulence, a type of spatiotemporal
chaos in planar systems of nematic liquid crystals, to clarify the chaotic
advection of weak turbulence. In planar systems of large aspect ratio,
structural relaxation which is characterized by the dynamic structure factor
exhibits a long-period oscillation that is described well by a combination of a
simple exponential relaxation and underdamped oscillation. The simple
relaxation arises as a result of the roll modulation while the damped
oscillation is manifest in the repetitive gliding of defect pairs in a local
area. Each relaxation is derived analytically by the projection operator method
that separates turbulent transport into a macroscopic contribution and
fluctuations. The analysis proposes that the two relaxations are not
correlated. The nonthermal fluctuations of defect turbulence are consequently
separated into two independent Markov processes. Our approach sheds light on
diversity and universality from a unified viewpoint for weak turbulence.
|
Two reactions, pp->ppX and pp->p\pi^+X, are used to study the 1.47<M<1.68 GeV
baryonic mass range. Three different final states are considered in the
invariant masses: N^* or \Delta^+, p\pi^0, and p\eta. The last two channels are
defined by software cuts applied to the missing mass of the first reaction.
Several narrow structures are extracted with widths \sigma(\Gamma) varying
between 3 and 9 MeV. Some structures are observed in one channel but not in
others. Such nonobservation may be due either to the spectrometer momenta
limits or to the physics (e.g. no such disintegration channel is allowed from
the narrow state considered).
We tentatively conclude that the broad Particle Data Group (PDG) baryonic
resonances N(1520)D13, N(1535)S11, Delta(1600)P33, and N(1675)D15 are
collective states built from several narrow and weakly excited resonances, each
having a (much) smaller width than the one reported by PDG.
|
A ribbon is a surface swept out by a line segment turning as it moves along a
central curve. For narrow magnetic ribbons, for which the length of the line
segment is much less than the length of the curve, the anisotropy induced by
the magnetostatic interaction is biaxial, with hard axis normal to the ribbon
and easy axis along the central curve. The micromagnetic energy of a narrow
ribbon reduces to that of a one-dimensional ferromagnetic wire, but with
curvature, torsion and local anisotropy modified by the rate of turning. These
general results are applied to two examples, namely a helicoid ribbon, for
which the central curve is a straight line, and a M\"obius ribbon, for which
the central curve is a circle about which the line segment executes a
$180^\circ$ twist. In both examples, for large positive tangential anisotropy,
the ground state magnetization lies tangent to the central curve. As the
tangential anisotropy is decreased, the ground state magnetization undergoes a
transition, acquiring an in-surface component perpendicular to the central
curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy,
below which the ground state is uniformly perpendicular to the central curve.
The transition for the M\"obius ribbon is more subtle; it occurs at a positive
critical value of the anisotropy, below which the ground state is nonuniform.
For the helicoid ribbon, the dispersion law for spin wave excitations about the
tangential state is found to exhibit an asymmetry determined by the geometric
and magnetic chiralities.
|
The silicon-strip tracker of the China Seismo-Electromagnetic Satellite
(CSES) consists of two double-sided silicon strip detectors (DSSDs) which
provide incident particle tracking information. The low-noise analog ASIC VA140
was used in this study for DSSD signal readout. A beam test on the DSSD module
was performed at the Beijing Test Beam Facility of the Beijing Electron
Positron Collider (BEPC) using a 400~800 MeV/c proton beam. The pedestal
analysis results, RMSE noise, gain correction, and particle incident position
reconstruction of the DSSD module are presented.
|
Let $\Sigma_g$ denote the closed orientable surface of genus $g$ and fix an
arbitrary simplicial triangulation of $\Sigma_g$. We construct and study a
natural surjective group homomorphism from the surface braid group on $n$
strands on $\Sigma_g$ to the first singular homology group of $\Sigma_g$ with
integral coefficients. In particular, we show that the kernel of this
homomorphism is generated by canonical braids which arise from the
triangulation of $\Sigma_g$. This provides a simple description of natural
subgroups of surface braid groups which are closely tied to the homology groups
of the surfaces $\Sigma_g$.
|
We study the abelianization of Kontsevich's Lie algebra associated with the
Lie operad and some related problems. Calculating the abelianization is a
long-standing unsolved problem, which is important in at least two different
contexts: constructing cohomology classes in $H^k(\mathrm{Out}(F_r);\mathbb Q)$
and related groups as well as studying the higher order Johnson homomorphism of
surfaces with boundary. The abelianization carries a grading by "rank," with
previous work of Morita and Conant-Kassabov-Vogtmann computing it up to rank
$2$. This paper presents a partial computation of the rank $3$ part of the
abelianization, finding lots of irreducible $\mathrm{SP}$-representations with
multiplicities given by spaces of modular forms. Existing conjectures in the
literature on the twisted homology of $\mathrm{SL}_3(\mathbb Z)$ imply that
this gives a full account of the rank $3$ part of the abelianization in even
degrees.
|
In the present work we study non-thermal leptogenesis and baryon asymmetry in
the universe in different neutrino mass models discussed recently. For each
model we obtain a formula relating the reheating temperature after inflation to
the inflaton mass. It is shown that all but four cases are excluded and that in
the cases which survive the inflaton mass and the reheating temperature after
inflation are bounded from below and from above.
|
The theory of a massless two-dimensional scalar field with a periodic
boundary interaction is considered. At a critical value of the period this
system defines a conformal field theory and can be re-expressed in terms of
free fermions, which provide a simple realization of a hidden $SU(2)$ symmetry
of the original theory. The partition function and the boundary $S$-matrix can
be computed exactly as a function of the strength of the boundary interaction.
We first consider open strings with one interacting and one Dirichlet boundary,
and then with two interacting boundaries. The latter corresponds to motion in a
periodic tachyon background, and the spectrum exhibits an interesting band
structure which interpolates between free propagation and tight binding as the
interaction strength is varied.
|
Matrices whose adjoint is a low rank perturbation of a rational function of
the matrix naturally arise when trying to extend the well known
Faber-Manteuffel theorem, which provides necessary and sufficient conditions
for the existence of a short Arnoldi recurrence. We show that an orthonormal
Krylov basis for this class of matrices can be generated by a short recurrence
relation based on GMRES residual vectors. These residual vectors are computed
by means of an updating formula. Furthermore, the underlying Hessenberg matrix
has an accompanying low rank structure, which we will investigate closely.
|
We propose a geometric algorithm for topic learning and inference that is
built on the convex geometry of topics arising from the Latent Dirichlet
Allocation (LDA) model and its nonparametric extensions. To this end we study
the optimization of a geometric loss function, which is a surrogate to the
LDA's likelihood. Our method involves a fast optimization based weighted
clustering procedure augmented with geometric corrections, which overcomes the
computational and statistical inefficiencies encountered by other techniques
based on Gibbs sampling and variational inference, while achieving the accuracy
comparable to that of a Gibbs sampler. The topic estimates produced by our
method are shown to be statistically consistent under some conditions. The
algorithm is evaluated with extensive experiments on simulated and real data.
|
We consider waves, which obey the semilinear Klein-Gordon equation,
propagating in the Friedmann-Lemaitre-Robertson-Walker spacetimes. The
equations in the de Sitter and Einstein-de Sitter spacetimes are the important
particular cases.
We show the global in time existence in the energy class of solutions of the
Cauchy problem.
|
An important question in the derivation of the acceleration radiation, which
also arises in Hawking's derivation of black hole radiance, is the need to
invoke trans-Planckian physics for the quantum field that originates the
created quanta. We point out that this issue can be further clarified by
reconsidering the analysis in terms of particle detectors, transition
probabilities, and local two-point functions. By writing down separate
expressions for the spontaneous- and induced-transition probabilities of a
uniformly accelerated detector, we show that the bulk of the effect comes from
the natural (non trans-Planckian) scale of the problem, which largely
diminishes the importance of the trans-Planckian sector. This is so, at least,
when trans-Planckian physics is defined in a Lorentz invariant way. This
analysis also suggests how to define and estimate the role of trans-Planckian
physics in the Hawking effect itself.
|
A long-standing issue in mathematical finance is the speed-up of pricing
options, especially multi-asset options. A recent study has proposed to use
tensor train learning algorithms to speed up Fourier transform (FT)-based
option pricing, utilizing the ability of tensor networks to compress
high-dimensional tensors. Another usage of the tensor network is to compress
functions, including their parameter dependence. In this study, we propose a
pricing method, where, by a tensor learning algorithm, we build tensor trains
that approximate functions appearing in FT-based option pricing with their
parameter dependence and efficiently calculate the option price for the varying
input parameters. As a benchmark test, we run the proposed method to price a
multi-asset option for the various values of volatilities and present asset
prices. We show that, in the tested cases involving up to 11 assets, the
proposed method is comparable to or outperforms Monte Carlo simulation with
$10^5$ paths in terms of computational complexity, keeping the comparable
accuracy.
|
We study Malliavin differentiability of solutions to sub-critical singular
parabolic stochastic partial differential equations (SPDEs) and we prove the
existence of densities for a class of singular SPDEs. Both of these results are
implemented in the setting of regularity structures. For this we construct
renormalized models in situations where some of the driving noises are replaced
by deterministic Cameron-Martin functions, and we show Lipschitz continuity of
these models with respect to the Cameron-Martin norm. In particular, in many
interesting situations we obtain a convergence and stability result for lifts
of $L^2$-functions to models, which is of independent interest. The proof also
involves two separate algebraic extensions of the regularity structure which
are carried out in rather large generality.
|
Let $R$ be a commutative additively idempotent semiring. In this paper, some
properties and characterizations for permanents of matrices over $R$ are
established, and several inequalities for permanents are given. Also, the
adjiont matrices of matriecs over $R$ are considered. Partial results obtained
in this paper generalize the corresponding ones on fuzzy matrices, on lattice
matrices and on incline matrices.
|
Modern smart home control systems utilize real-time occupancy and activity
monitoring to ensure control efficiency, occupants' comfort, and optimal energy
consumption. Moreover, adopting machine learning-based anomaly detection models
(ADMs) enhances security and reliability. However, sufficient system knowledge
allows adversaries/attackers to alter sensor measurements through stealthy
false data injection (FDI) attacks. Although ADMs limit attack scopes, the
availability of information like occupants' location, conducted activities, and
alteration capability of smart appliances increase the attack surface.
Therefore, performing an attack space analysis of modern home control systems
is crucial to design robust defense solutions. However, state-of-the-art
analyzers do not consider contemporary control and defense solutions and
generate trivial attack vectors. To address this, we propose a control and
defense-aware novel attack analysis framework for a modern smart home control
system, efficiently extracting ADM rules. We verify and validate our framework
using a state-of-the-art dataset and a prototype testbed.
|
We conjecture an equivalence between the Gromov-Witten theory of 3-folds and
the holomorphic Chern-Simons theory of Donaldson-Thomas. For Calabi-Yau
3-folds, the equivalence is defined by the change of variables, exp(iu)=-q,
where u is the genus parameter of GW theory and q is charge parameter of DT
theory. The conjecture is proven for local Calabi-Yau toric surfaces.
|
The Ising exchange interaction is a limiting case of strong exchange
anisotropy and represents a key property of many magnetic materials. Here we
find necessary and sufficient conditions to achieve Ising exchange interaction
for metal sites with unquenched orbital moments. Contrary to current views, the
rules established here narrow much the range of lanthanide and actinide ions
which can exhibit Ising exchange interaction. It is shown that the arising
Ising interaction can be of two distinct types: (i) coaxial, with magnetic
moments directed along the anisotropy axes on the metal sites and (ii)
non-coaxial, with arbitrary orientation of one of magnetic moments. These
findings will contribute to purposeful design of lanthanide and actinide based
materials.
|
Measurements of the low-frequency (f<= 100 kHz) permittivity at T<= 160 K and
dc resistivity (T<= 430 K) are reported for La(1-x)Ca(x)MnO(3) (0<= x<= 0.15).
Static dielectric constants are determined from the low-T limiting behavior of
the permittivity. The estimated polarizability for bound holes ~ 10^{-22}
cm^{-3} implies a radius comparable to the interatomic spacing, consistent with
the small polaron picture established from prior transport studies near room
temperature and above on nearby compositions. Relaxation peaks in the
dielectric loss associated with charge-carrier hopping yield activation
energies in good agreement with low-T hopping energies determined from
variable-range hopping fits of the dc resistivity. The doping dependence of
these energies suggests that the orthorhombic, canted antiferromagnetic ground
state tends toward an insulator-metal transition that is not realized due to
the formation of the ferromagnetic insulating state near Mn(4+) concentration ~
0.13.
|
We study the problem of designing interval-valued observers that
simultaneously estimate the system state and learn an unknown dynamic model for
partially unknown nonlinear systems with dynamic unknown inputs and bounded
noise signals. Leveraging affine abstraction methods and the existence of
nonlinear decomposition functions, as well as applying our previously developed
data-driven function over-approximation/abstraction approach to over-estimate
the unknown dynamic model, our proposed observer recursively computes the
maximal and minimal elements of the estimate intervals that are proven to
contain the true augmented states. Then, using observed output/measurement
signals, the observer iteratively shrinks the intervals by eliminating
estimates that are not compatible with the measurements. Finally, given new
interval estimates, the observer updates the over-approximation of the unknown
model dynamics. Moreover, we provide sufficient conditions for uniform
boundedness of the sequence of estimate interval widths, i.e., stability of the
designed observer, in the form of tractable (mixed-)integer programs with
finitely countable feasible sets.
|
The goal of the paper is to lay the foundation for the qualitative analogue
of the classical, quantitative sparse graph limit theory. In the first part of
the paper we introduce the qualitative analogues of the Benjamini-Schramm and
local-global graph limit theories for sparse graphs. The natural limit objects
are continuous actions of finitely generated groups on totally disconnected
compact metric spaces. We prove that the space of weak equivalent classes of
free Cantor actions is compact and contains a smallest element, as in the
measurable case. We will introduce and study various notions of almost
finiteness, the qualitative analogue of hyperfiniteness, for classes of bounded
degree graphs. We prove the almost finiteness of a new class of \'etale
groupoids associated to Cantor actions and construct an example of a
nonamenable, almost finite totally disconnected \'etale groupoid, answering a
query of Suzuki. Motivated by the notions and results on qualitative graph
limits, in the second part of our paper we give a precise definition of
constant-time distributed algorithms on sparse graphs. We construct such
constant-time algorithms for various approximation problems for hyperfinite and
almost finite graph classes. We also prove the Hausdorff convergence of the
spectra of convergent graph sequences in the strongly almost finite category.
|
Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.