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The growing complexity of real-world problems has motivated computer
scientists to search for efficient problem-solving methods. Metaheuristics
based on evolutionary computation and swarm intelligence are outstanding
examples of nature-inspired solution techniques. Inspired by the social
spiders, we propose a novel Social Spider Algorithm to solve global
optimization problems. This algorithm is mainly based on the foraging strategy
of social spiders, utilizing the vibrations on the spider web to determine the
positions of preys. Different from the previously proposed swarm intelligence
algorithms, we introduce a new social animal foraging strategy model to solve
optimization problems. In addition, we perform preliminary parameter
sensitivity analysis for our proposed algorithm, developing guidelines for
choosing the parameter values. The Social Spider Algorithm is evaluated by a
series of widely-used benchmark functions, and our proposed algorithm has
superior performance compared with other state-of-the-art metaheuristics.
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We propose to use the theory of phase transitions of Lee and Yang as a
practical tool to analyze long-range correlations in a finite-size system. We
apply it to the analysis of anisotropic flow in nucleus-nucleus collisions, and
show that this method is more reliable than any other used so far.
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In the era of advanced artificial intelligence and human-computer
interaction, identifying emotions in spoken language is paramount. This
research explores the integration of deep learning techniques in speech emotion
recognition, offering a comprehensive solution to the challenges associated
with speaker diarization and emotion identification. It introduces a framework
that combines a pre-existing speaker diarization pipeline and an emotion
identification model built on a Convolutional Neural Network (CNN) to achieve
higher precision. The proposed model was trained on data from five speech
emotion datasets, namely, RAVDESS, CREMA-D, SAVEE, TESS, and Movie Clips, out
of which the latter is a speech emotion dataset created specifically for this
research. The features extracted from each sample include Mel Frequency
Cepstral Coefficients (MFCC), Zero Crossing Rate (ZCR), Root Mean Square (RMS),
and various data augmentation algorithms like pitch, noise, stretch, and shift.
This feature extraction approach aims to enhance prediction accuracy while
reducing computational complexity. The proposed model yields an unweighted
accuracy of 63%, demonstrating remarkable efficiency in accurately identifying
emotional states within speech signals.
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Multidimensional scaling (MDS) is a dimensionality reduction tool used for
information analysis, data visualization and manifold learning. Most MDS
procedures embed data points in low-dimensional Euclidean (flat) domains, such
that distances between the points are as close as possible to given inter-point
dissimilarities. We present an efficient solver for classical scaling, a
specific MDS model, by extrapolating the information provided by distances
measured from a subset of the points to the remainder. The computational and
space complexities of the new MDS methods are thereby reduced from quadratic to
quasi-linear in the number of data points. Incorporating both local and global
information about the data allows us to construct a low-rank approximation of
the inter-geodesic distances between the data points. As a by-product, the
proposed method allows for efficient computation of geodesic distances.
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We investigate the fate of topological states on fractal lattices. Focusing
on a spinless chiral p-wave paired superconductor, we find that this model
supports two qualitatively distinct phases when defined on a Sierpinski gasket.
While the trivial phase is characterized by a self-similar spectrum with
infinitely many gaps and extended eigenstates, the novel "topological" phase
has a gapless spectrum and hosts chiral states propagating along edges of the
graph. Besides employing theoretical probes such as the real-space Chern
number, inverse participation ratio, and energy-level statistics in the
presence of disorder, we develop a simple physical picture capturing the
essential features of the model on the gasket. Extending this picture to other
fractal lattices and topological states, we show that the p+ip state admits a
gapped topological phase on the Sierpinski carpet and that a higher-order
topological insulator placed on this lattice hosts gapless modes localized on
corners.
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We study matrix models involving Pfaffian interactions as generalizations of
the standard $\beta = 1$ and $\beta = 4$ matrix models. We present the Pfaffian
formulas for the partition function and the characteristic polynomial averages.
We also explore the matrix chain with the Pfaffian interaction, which realizes
the BCD-type quiver matrix models.
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Indication of therapeutic hypothermia needs an accurate identification of
brain injury in the early neonatal period. Here, we aim to provide a simple
hypothermia decision-making tool for the term neonates with hypoxic-ischemic
encephalopathy (HIE) based on features of conventional electroencephalogram
(EEG) taken less than 6 hours from birth. EEG recordings from one hundred
full-term babies with HIE were included in the study. Each EEG recording was
graded by pediatric neurologists for HIE severity. Amplitude of each EEG
segment was analyzed in the slow frequency bands. Temporal fluctuations of
spectral power in delta (0.5 - 4 Hz) frequency band was used to characterize
each HIE grade. For each grade of abnormality, we estimated level and duration
(number of consecutive segments above a given level) probability densities for
power of delta oscillations. These 2D representation of EEG dynamics can
identify mild HIE group from those of requiring hypothermia. Our discrimination
system yielded an accuracy, recall, positive predictive value (precision),
negative predictive value, false alarm ratio and F1-score of 98%, 99%, 99%,
0.94%, 0.06 and 99%, respectively. These results provided an accurate
discrimination of mild versus moderate or severe HIE, and only one mild case
was erroneously detected as relevant for hypothermia. Quantized probability
densities of slow spectral features (delta power) from early conventional EEG
(withing 6 hours of birth) revealed significant differences in slow spectral
dynamics between infants with mild HIE grades and those relevant for
hypothermia.
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This is a survey of results in the enumeration of lattice paths.
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NGC1851 possibly shows a spread in [Fe/H], but the relation between this
spread and the division in the SGB is unknown. We obtained blue (3950-4600 A)
intermediate resolution (R~8,000) spectra for 47 stars on the bright and 30 on
the faint SGB of NGC 1851 (b-SGB and f-SGB, respectively). The determination of
the atmospheric parameters to extremely high internal accuracy leads to small
errors when comparing different stars in the cluster. We found that the b-SGB
is slightly more metal-poor than the f-SGB, with [Fe/H]=-1.227+/-0.009 and
[Fe/H]=-1.162+/- 0.012, respectively. This implies that the f-SGB is only
slightly older by ~0.6 Gyr than the b-SGB if the total CNO abundance is
constant. There are more C-normal stars in the b-SGB than in the f-SGB. This is
consistent with what is found for HB stars, if b-SGB are the progenitors of red
HB stars, and f-SGB those of blue HB ones. The abundances of the n-capture
elements Sr and Ba have a bimodal distribution, reflecting the separation
between f-SGB (Sr and Ba-rich) and b-SGB stars (Sr and Ba-poor). In both
groups, there is a clear correlation between [Sr/Fe] and [Ba/Fe], suggesting
that there is a real spread in the abundances of n-capture elements. There is
some correlation between C and Ba abundances, while the same correlation for Sr
is much more dubious. We identified six C-rich stars, which have a moderate
overabundance of Sr and Ba and rather low N abundances. This group of stars
might be the progenitors of these on the anomalous RGB in the (v, v-y) diagram.
These results are discussed within different scenarios for the formation of
NGC1851. It is possible that the two populations originated in different
regions of an inhomogeneous parent object. However, the striking similarity
with M22 calls for a similar evolution for these two clusters. Deriving
reliable CNO abundances for the two sequences would be crucial.
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Currently available temperature measurements or imaging at nano-micro scale
are limited to fluorescent molecules and luminescent nanocrystals, whose
spectral properties respond to temperature variation. The principle of
operation of these conventional temperature probes is typically related to
temperature induced multiphonon quenching or temperature dependent energy
transfers, therefore, above 12%/K sensitivity and high thermal resolution
remain a serious challenge. Here we demonstrate a novel class of highly
sensitive thermographic phosphors operating in room temperature range with
milikelvin thermal resolution, whose temperature readings are reproducible,
luminescence is photostable and brightness is not compromised by thermal
quenching. Corroborated with phase transition structural characterization and
high spatio-temporal temperature imaging, we demonstrated that optically active
europium ions are highly and smoothly susceptible to monoclinic to tetragonal
phase transition in LiYO2 host, which is evidenced by changed number and the
splitting of Stark components as well as by smooth variation of contribution
between magnetic and electric dipole transitions. Further, reducing the size of
phosphor from bulk to nanocrystalline matrix, shifted the phase transition
temperature from 100oC down to room temperature. These findings provide
insights into the mechanism underlaying phase transition based luminescence
nanothermometry and motivate future research toward new, highly sensitive, high
temporal and spatial resolution nano-thermometers aiming at precise studying
heat generation or diffusion in numerous biological and technology
applications.
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We report on observations of six giants in the globular cluster M15 (NGC
7078) using the Subaru Telescope to measure neutron-capture elemental
abundances. Our abundance analyses based on high-quality blue spectra confirm
the star-to-star scatter in the abundances of heavy neutron-capture elements
(e.g., Eu), and no significant s-process contribution to them, as was found in
previous studies. We have found, for the first time, that there are
anti-correlations between the abundance ratios of light to heavy
neutron-capture elements ([Y/Eu] and [Zr/Eu]) and heavy ones (e.g., Eu). This
indicates that light neutron-capture elements in these stars cannot be
explained by only a single r-process. Another process that has significantly
contributed to the light neutron-capture elements is required to have occurred
in M15. Our results suggest a complicated enrichment history for M15 and its
progenitor.
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The combination of soft responsive particles, such as microgels, with
nanoparticles (NPs) yields highly versatile complexes of great potential for
applications, from ad-hoc plasmonic sensors to controlled protocols for loading
and release. However, the assembly process between these microscale networks
and the co-dispersed nano-objects has not been investigated so far at the
microscopic level, preempting the possibility of designing such hybrid
complexes a priori. In this work, we combine state-of-the-art numerical
simulations with experiments, to elucidate the fundamental mechanisms taking
place when microgels-NPs assembly is controlled by electrostatic interactions.
We find a general behavior where, by increasing the number of interacting NPs,
the microgel deswells up to a minimum size, after which a plateau behavior
occurs. This occurs either when NPs are mainly adsorbed to the microgel corona
via the folding of the more external chains, or when NPs penetrate inside the
microgel, thereby inducing a collective reorganization of the polymer network.
By varying microgel properties, such as fraction of crosslinkers or charge, as
well as NPs size and charge, we further show that the microgel deswelling
curves can be rescaled onto a single master curve, for both experiments and
simulations, demonstrating that the process is entirely controlled by the
charge of the whole microgel-NPs complex. Our results thus have a direct
relevance in fundamental materials science and offer novel tools to tailor the
nanofabrication of hybrid devices of technological interest.
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Modern robots require accurate forecasts to make optimal decisions in the
real world. For example, self-driving cars need an accurate forecast of other
agents' future actions to plan safe trajectories. Current methods rely heavily
on historical time series to accurately predict the future. However, relying
entirely on the observed history is problematic since it could be corrupted by
noise, have outliers, or not completely represent all possible outcomes. To
solve this problem, we propose a novel framework for generating robust
forecasts for robotic control. In order to model real-world factors affecting
future forecasts, we introduce the notion of an adversary, which perturbs
observed historical time series to increase a robot's ultimate control cost.
Specifically, we model this interaction as a zero-sum two-player game between a
robot's forecaster and this hypothetical adversary. We show that our proposed
game may be solved to a local Nash equilibrium using gradient-based
optimization techniques. Furthermore, we show that a forecaster trained with
our method performs 30.14% better on out-of-distribution real-world lane change
data than baselines.
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We define a current-conserving approximation for the local conductivity
tensor of a disordered system which includes the effects of weak localization.
Using this approximation we show that the weak localization effect in
conductance is not obtained simply from the diagram corresponding to the
coherent back-scattering peak observed in optical experiments. Other diagrams
contribute to the effect at the same order and decrease its value. These
diagrams appear to have no semiclassical analogues, a fact which may have
implications for the semiclassical theory of chaotic systems. The effects of
discrete symmetries on weak localization in disordered conductors is evaluated
and and compared to results from chaotic scatterers.
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For the robots to achieve a desired behavior, we can program them directly,
train them, or give them an innate driver that makes the robots themselves
desire the targeted behavior. With the minimal surprise approach, we implant in
our robots the desire to make their world predictable. Here, we apply minimal
surprise to collective construction. Simulated robots push blocks in a 2D torus
grid world. In two variants of our experiment we either allow for emergent
behaviors or predefine the expected environment of the robots. In either way,
we evolve robot behaviors that move blocks to structure their environment and
make it more predictable. The resulting controllers can be applied in
collective construction by robots.
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We consider a planar waveguide with "twisted" boundary conditions. By
twisting we mean a special combination of Dirichlet and Neumann boundary
conditions. Assuming that the width of the waveguide goes to zero, we identify
the effective (limiting) operator as the width of the waveguide tends to zero,
establish the uniform resolvent convergence in various possible operator norms,
and give the estimates for the rates of convergence. We show that studying the
resolvent convergence can be treated as a certain threshold effect and we
present an elegant technique which justifies such point of view.
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It is shown that both the visibility ${\cal V} = 1/2$ predicted for
two-photon interference experiments with two independent
sources\textcolor{black}{, like the Hanbury Brown-Twiss experiment,} and the
visibility ${\cal V} = 1$ predicted for two-photon interference experiments
with a parametric down-conversion source\textcolor{black}{, like the
Ghosh-Mandel experiment,} can be explained \textcolor{black}{by a discrete
event simulation. This simulation approach reproduces the statistical
distributions of wave theory not by requiring the knowledge of the solution of
the wave equation of the whole system but by generating detection events
one-by-one according to an unknown distribution.} There is thus no need to
invoke quantum theory to explain the so-called nonclassical effects in the
interference of signal and idler photons in parametric down conversion. Hence,
a revision of the commonly accepted criterion of the nonclassical nature of
light\textcolor{black}{, ${\cal V} > 1/2$,} is called for.
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We describe a numerical scheme for exactly simulating the heat current
behavior in a quantum harmonic chain with self-consistent reservoirs.
Numerically-exact results are compared to classical simulations and to the
quantum behavior under the linear response approximation. In the classical
limit or for small temperature biases our results coincide with previous
calculations. At large bias and for low temperatures the quantum dynamics of
the system fundamentally differs from the close-to-equilibrium behavior,
revealing in particular the effect of thermal rectification for asymmetric
chains. Since this effect is absent in the classical analog of our model, we
conclude that in the quantum model studied here thermal rectification is a
purely quantum phenomenon, rooted in the quantum statistics.
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Coordination of multi-robot systems require some form of localization between
agents, but most methods today rely on some external infrastructure. Ultra Wide
Band (UWB) sensing has gained popularity in relative localization applications,
and we see many implementations that use cooperative agents augmenting UWB
range measurements with other sensing modalities (e.g., ViO, IMU, VSLAM) for
infrastructure-free relative localization. A lesser researched option is using
Angle of Arrival (AoA) readings obtained from UWB Antenna pairs to perform
relative localization. In this paper we present a UWB platform called ReLoki
that can be used for ranging and AoA-based relative localization in~3D. ReLoki
enables any message sent from a transmitting agent to be localized by using a
Regular Tetrahedral Antenna Array (RTA). As a full scale proof of concept, we
deploy ReLoki on a 3-robot system and compare its performance in terms of
accuracy and speed with prior methods.
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Radial-velocity (RV) jitter caused by stellar magnetic activity is an
important factor in state-of-the-art exoplanet discovery surveys such as
CARMENES. Stellar rotation, along with heterogeneities in the photosphere and
chromosphere caused by activity, can result in false-positive planet
detections. Hence, it is necessary to determine the stellar rotation period and
compare it to any putative planetary RV signature. Long-term measurements of
activity indicators such as the chromospheric emission in the Ca II H&K lines
enable the identification of magnetic activity cycles. In order to determine
stellar rotation periods and study the long-term behavior of magnetic activity
of the CARMENES guaranteed time observations (GTO) sample, it is advantageous
to extract Ca II H&K time series from archival data, since the CARMENES
spectrograph does not cover the blue range of the stellar spectrum containing
the Ca II H&K lines. We have assembled a catalog of 11634 archival spectra of
186 M dwarfs acquired by seven different instruments covering the Ca II H&K
regime: ESPADONS, FEROS, HARPS, HIRES, NARVAL, TIGRE, and UVES. The relative
chromospheric flux in these lines was directly extracted from the spectra by
rectification with PHOENIX synthetic spectra via narrow passbands around the Ca
ii H&K line cores. The combination of archival spectra from various instruments
results in time series for 186 stars from the CARMENES GTO sample. As an
example of the use of the catalog, we report the tentative discovery of three
previously unknown activity cycles of M dwarfs. We conclude that the method of
extracting Ca II H&K fluxes with the use of model spectra yields consistent
results for different instruments and that the compilation of this catalog will
enable the analysis of long-term activity time series for a large number of M
dwarfs.
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The optimal exponentials of the thickness in the geometry rigidity inequality
of shells represent the geometry rigidity of the shells. We obtain that the
lower bounds of the optimal exponentials are $4/3,$ $3/2,$ and $1,$ for the
hyperbolic shell, the parabolic shell, and the elliptic shell, respectively,
through the construction of the Ans\"{a}tze.
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The kinematic model for the planar Purcell's swimmer - a low Reynolds number
microswimmer is derived and used extensively in the literature. We revisit the
derivation and give the explicit expression of the local form of the connection
form in this note.
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Since an automotive driving vehicle is controlled by Advanced
Driver-Assistance Systems (ADAS) / Automated Driving (AD) functions, the
selected sensors for the perception process become a key component of the
system. Therefore, the necessity of ensuring precise data is crucial. But the
correctness of the data is not the only part that has to be ensured, the
limitations of the different technologies to accurately sense the reality must
be checked for an error-free decision making according to the current scenario.
In this context, this publication presents a comparison between two different
automotive radars through our self-developed robot mobile platform called
SPIDER, and how they can detect different kinds of objects in the tests carried
out at the ZalaZONE proving ground.
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We consider the online two-dimensional vector packing problem, showing a
lower bound of $11/5$ on the competitive ratio of any {\sc AnyFit} strategy for
the problem. We provide strategies with competitive ratio
$\max\!\left\{2,6\big/\big(1+3\tan(\pi/4-\gamma/2)\big)+\epsilon\right\}$ and
logarithmic advice, for any instance where all the input vectors are restricted
to have angles in the range $[\pi/4-\gamma/2,\pi/4+\gamma/2]$, for
$0\leq\gamma<\pi/3$ and
$\max\left\{5/2,4\big/\big(1+2\tan(\pi/4-\gamma/2)\big)+\epsilon\right\}$ and
logarithmic advice, for any instance where all the input vectors are restricted
to have angles in the range $[\pi/4-\gamma/2,\pi/4+\gamma/2]$, for
$0\leq\gamma\leq\pi/3$. In addition, we give a $5/2$-competitive strategy also
using logarithmic advice for the unrestricted vectors case. These results
should be contrasted to the currently best competitive strategy, FirstFit,
having competitive ratio~$27/10$.
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Magnetic moments strongly coupled to the spins of conduction electrons in a
nanostructure can confine the conduction-electron motion due to scattering at
almost localized Kondo singlets. We study the resulting local-moment formation
in the conduction-electron system and the magnetic exchange coupling mediated
by the Kondo singlets. Its distance dependence is oscillatory and induces
robust ferro- or antiferromagnetic order in multi-impurity systems.
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We give explicit estimates for the Stirling numbers of the second kind
$S(n,m)$. With a few exceptions, such estimates are asymptotically sharp. The
form of these estimates varies according to $m$ lying in the central or
non-central regions of $\{1,\ldots ,n\}$. In each case, we use a different
probabilistic representation of $S(n,m)$ in terms of well known random
variables to show the corresponding results.
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The CLAS detector was used to obtain the first ever measurement of the
electromagnetic decay of the $\Sigma^{*+}(1385)$ from the reaction $\gamma p
\to K^0 \Sigma^{*+}(1385)$. A real photon beam with a maximum energy of 3.8 GeV
was incident on a liquid-hydrogen target, resulting in the photoproduction of
the kaon and $\Sigma^*$ hyperon. Kinematic fitting was used to separate the
reaction channel from the background processes. The fitting algorithm exploited
a new method to kinematically fit neutrons in the CLAS detector, leading to the
partial width measurement of $250.0\pm56.9(stat)^{+34.3}_{-41.2}(sys)$ keV. A
U-spin symmetry test using the SU(3) flavor-multiplet representation yields
predictions for the $\Sigma^{*+}(1385)\to\Sigma^{+}\gamma$ and
$\Sigma^{*0}(1385)\to\Lambda\gamma$ partial widths that agree with the
experimental measurements.
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We introduce $\bar G$-fusions of local pointed groups on a block extension
$A=b\mathcal{O}G$, where $H$ is a normal subgroup of the finite group $G$,
$\bar G=G/H$, and $b$ is a $G$-invariant block of $\mathcal{O}H$. We show that
certain Clifford extensions associated to these pointed groups are invariant
under group graded basic Morita equivalences.
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We study phenomenologically the scenario in which the scalar top quark is
lighter than any other standard supersymmetric partner and also lighter than
the top quark, so that it decays to the gravitino via stop -> W^+ b G. In this
case, scalar top quark events would seem to be very difficult to separate from
top quark pair production. However, we show that, even at a hadron collider, it
is possible to distinguish these two reactions. We show also that the
longitudinal polarization of the final $W^+$ gives insight into the scalar top
and wino/Higgsino mixing parameters.
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Detecting test samples drawn sufficiently far away from the training
distribution statistically or adversarially is a fundamental requirement for
deploying a good classifier in many real-world machine learning applications.
However, deep neural networks with the softmax classifier are known to produce
highly overconfident posterior distributions even for such abnormal samples. In
this paper, we propose a simple yet effective method for detecting any abnormal
samples, which is applicable to any pre-trained softmax neural classifier. We
obtain the class conditional Gaussian distributions with respect to (low- and
upper-level) features of the deep models under Gaussian discriminant analysis,
which result in a confidence score based on the Mahalanobis distance. While
most prior methods have been evaluated for detecting either out-of-distribution
or adversarial samples, but not both, the proposed method achieves the
state-of-the-art performances for both cases in our experiments. Moreover, we
found that our proposed method is more robust in harsh cases, e.g., when the
training dataset has noisy labels or small number of samples. Finally, we show
that the proposed method enjoys broader usage by applying it to
class-incremental learning: whenever out-of-distribution samples are detected,
our classification rule can incorporate new classes well without further
training deep models.
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Elastic network models, simple structure-based representations of
biomolecules where atoms interact via short-range harmonic potentials, provide
great insight into a molecule's internal dynamics and mechanical properties at
extremely low computational cost. Their efficiency and effectiveness have made
them a pivotal instrument in the computer-aided study of proteins and, since a
few years, also of nucleic acids. In general, the coarse-grained sites, i.e.
those effective force centres onto which the all-atom structure is mapped, are
constructed based on intuitive rules: a typical choice for proteins is to
retain only the C$_\alpha$ atoms of each amino acid. However, a mapping
strategy relying only on the atom type and not the local properties of its
embedding can be suboptimal compared to a more careful selection. Here we
present a strategy in which the subset of atoms, each of which is mapped onto a
unique coarse-grained site of the model, is selected in a stochastic search
aimed at optimising a cost function. The latter is taken to be a simple measure
of the consistency between the harmonic approximation of an elastic network
model and the harmonic model obtained through exact integration of the
discarded degrees of freedom. The method is applied to two representatives of
structurally very different types of biomolecules: the protein Adenylate kinase
and the RNA molecule adenine riboswitch. Our analysis quantifies the
substantial impact that an algorithm-driven selection of coarse-grained sites
can have on a model's properties.
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Given a map $\mathcal M$ on a connected and closed orientable surface, the
delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal
M$ which captures some topological information of the embedding. We explore how
delta-matroids associated to dessins d'enfants behave under the action of the
absolute Galois group. Twists of delta-matroids are considered as well; they
correspond to the recently introduced operation of partial duality of maps.
Furthermore, we prove that every map has a partial dual defined over its field
of moduli. A relationship between dessins, partial duals and tropical curves
arising from the cartography groups of dessins is observed as well.
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In previous work, we have introduced a program aimed at studying the
birational geometry of locally symmetric varieties of Type IV associated to
moduli of certain projective varieties of K3 type. In particular, a concrete
goal of our program is to understand the relationship between GIT and
Baily-Borel compactifications for quartic K3 surfaces, K3's which are double
covers of a smooth quadric surface, and double EPW sextics. In our first paper
(arXiv:1607.01324), based on arithmetic considerations, we have given
conjectural decompositions into simple birational transformations of the period
maps from the GIT moduli spaces mentioned above to the corresponding
Baily-Borel compactifications. In our second paper (arXiv:1612.07432) we
studied the case of quartic K3's; we have given geometric meaning to this
decomposition and we have partially verified our conjectures. Here, we give a
full proof of our conjectures for the moduli space of K3's which are double
covers of a smooth quadric surface. The main new tool here is VGIT for (2,4)
complete intersection curves.
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For $d \in \mathbb{N}$ the well-known Schur-Cohn region $\mathcal{E}_d$
consists of all $d$-dimensional vectors $(a_1,\ldots,a_d)\in\mathbb{R}^d$
corresponding to monic polynomials $X^d+a_1X^{d-1}+\cdots+a_{d-1}X+a_d$ whose
roots all lie in the open unit disk. This region has been extensively studied
over decades. Recently, Akiyama and Peth\H{o} considered the subsets
$\mathcal{E}_d^{(s)}$ of the Schur-Cohn region that correspond to polynomials
of degree $d$ with exactly $s$ pairs of nonreal roots. They were especially
interested in the $d$-dimensional Lebesgue measures
$v_d^{(s)}:=\lambda_d(\mathcal{E}_d^{(s)})$ of these sets and their arithmetic
properties, and gave some fundamental results. Moreover, they posed two
conjectures that we prove in the present paper. Namely, we show that in the
totally complex case $d=2s$ the formula \[ \frac{v_{2s}^{(s)}}{v_{2s}^{(0)}} =
2^{2s(s-1)}\binom {2s}s \] holds for all $s\in\mathbb{N}$ and in the general
case the quotient $v_d^{(s)}/v_d^{(0)}$ is an integer for all choices $d\in
\mathbb{N}$ and $s\le d/2$. We even go beyond that and prove explicit
formul\ae{} for $v_d^{(s)} / v_d^{(0)}$ for arbitrary $d\in \mathbb{N}$, $s\le
d/2$. The ingredients of our proofs comprise Selberg type integrals,
determinants like the Cauchy double alternant, and partial Hilbert matrices.
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In the context of `Everything-as-a-Service', the transportation sector has
been evolving towards user-centric business models in which customized services
and mode-agnostic mobility resources are priced in a unified framework. Yet, in
the vast majority of studies on Mobility as a Service (MaaS) systems, mobility
resource pricing is based on segmented travel modes, e.g. private vehicle,
public transit and shared mobility services. This study attempts to address
this research gap by introducing innovative auction-based online MaaS
mechanisms where users can bid for any amount of mode-agnostic mobility
resources based on their willingness to pay and preferences. We take the
perspective of a MaaS regulator which aims to maximize social welfare by
allocating mobility resources to users. We propose two mechanisms which allow
users to either pay for the immediate use of mobility service (pay-as-you-go),
or to subscribe to mobility service packages (pay-as-a-package). We cast the
proposed auction-based mechanisms as online resource allocation problems where
users compete for MaaS resources and bid for travel time per trip. We propose
(integer-) linear programming formulations to accommodate user bids based on
available mobility resources in an online optimization approach. We show that
the proposed MaaS mechanisms are incentive-compatible, develop customized
online algorithms and derive performance bounds based on competitive analysis.
Extensive numerical simulations are conducted on large scale instances
generated from realistic mobility data, which highlight the benefits of the
proposed MaaS mechanisms and the effectiveness of the proposed online
optimization approaches.
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Since its formulation by Sir Isaac Newton, the problem of solving the
equations of motion for three bodies under their own gravitational force has
remained practically unsolved. Currently, the solution for a given
initialization can only be found by performing laborious iterative calculations
that have unpredictable and potentially infinite computational cost, due to the
system's chaotic nature. We show that an ensemble of solutions obtained using
an arbitrarily precise numerical integrator can be used to train a deep
artificial neural network (ANN) that, over a bounded time interval, provides
accurate solutions at fixed computational cost and up to 100 million times
faster than a state-of-the-art solver. Our results provide evidence that, for
computationally challenging regions of phase-space, a trained ANN can replace
existing numerical solvers, enabling fast and scalable simulations of many-body
systems to shed light on outstanding phenomena such as the formation of
black-hole binary systems or the origin of the core collapse in dense star
clusters.
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We consider a random walk on the fully-connected lattice with $N$ sites and
study the time evolution of the number of distinct sites $s$ visited by the
walker on a subset with $n$ sites. A record value $v$ is obtained for $s$ at a
record time $t$ when the walker visits a site of the subset for the first time.
The record time $t$ is a partial covering time when $v<n$ and a total covering
time when $v=n$. The probability distributions for the number of records $s$,
the record value $v$ and the record (covering) time $t$, involving $r$-Stirling
numbers, are obtained using generating function techniques. The mean values,
variances and skewnesses are deduced from the generating functions. In the
scaling limit the probability distributions for $s$ and $v$ lead to the same
Gaussian density. The fluctuations of the record time $t$ are also Gaussian at
partial covering, when $n-v={\mathrm O}(n)$. They are distributed according to
the type-I Gumbel extreme-value distribution at total covering, when $v=n$. A
discrete sequence of generalized Gumbel distributions, indexed by $n-v$, is
obtained at almost total covering, when $n-v={\mathrm O}(1)$. These generalized
Gumbel distributions are crossing over to the Gaussian distribution when $n-v$
increases.
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In this paper, we develop a two-stage distributed algorithm that enables
nodes in a graph to cooperatively estimate the spectrum of a matrix $W$
associated with the graph, which includes the adjacency and Laplacian matrices
as special cases. In the first stage, the algorithm uses a discrete-time linear
iteration and the Cayley-Hamilton theorem to convert the problem into one of
solving a set of linear equations, where each equation is known to a node. In
the second stage, if the nodes happen to know that $W$ is cyclic, the algorithm
uses a Lyapunov approach to asymptotically solve the equations with an
exponential rate of convergence. If they do not know whether $W$ is cyclic, the
algorithm uses a random perturbation approach and a structural controllability
result to approximately solve the equations with an error that can be made
small. Finally, we provide simulation results that illustrate the algorithm.
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Using a weak-disorder scheme and real-space renormalization-group techniques,
we obtain analytical results for the critical behavior of various q-state Potts
models with correlated disordered exchange interactions along d1 of d spatial
dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate
qualitative differences between the cases d-d1=1 (for which we find nonphysical
random fixed points, suggesting the existence of nonperturbative fixed
distributions) and d-d1>1 (for which we do find acceptable perturbartive random
fixed points), in agreement with previous numerical calculations by Andelman
and Aharony. We also rederive a criterion for relevance of correlated disorder,
which generalizes the usual Harris criterion.
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We obtain the gravitational emission from particles scattering via the Yukawa
interaction, presenting both classical and approximate quantum results. We also
estimate the contribution from the tensor part of the internucleon interaction.
This emission is the main source of a very-high frequency component to the
stochastic background in the Solar System and in neutron stars. The emission
from the Sun (allowing for Debye screening) and from a typical neutron star are
obtained. The gravitational wave luminosity of the Sun is $41 \pm 10$ MW.
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The Logarithmic Linear Relaxation (LLR) algorithm is an efficient method for
computing densities of states for systems with a continuous spectrum. A key
feature of this method is exponential error reduction, which allows us to
evaluate the density of states of a system over hundreds of thousands of orders
of magnitude with a fixed level of relative accuracy. As a consequence of
exponential error reduction, the LLR method provides a robust alternative to
traditional Monte Carlo calculations in cases in which states suppressed by the
Boltzmann weight play nevertheless a relevant role, e.g., as transition regions
between dominant configuration sets. After reviewing the algorithm, we will
show an application in U(1) Lattice Gauge Theory that has enabled us to obtain
the most accurate estimate of the critical coupling with modest computational
resources, defeating exponential tunneling times between metastable vacua. As a
further showcase, we will then present an application of the LLR method to the
decorrelation of the topological charge in SU(3) Lattice Gauge Theory near the
continuum limit. Finally, we will review in general applications of the LLR
algorithm to systems affected by a strong sign problem and discuss the case of
the Bose gas at finite chemical potential.
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We prove that for a one-dimensional infinite lattice, with long-range
coupling among sites, the diffusion of an initial delta-like pulse in the bulk,
is ballistic at all times. We obtain a closed-form expression for the mean
square displacement (MSD) as a function of time, and show some cases including
finite range coupling, exponentially decreasing coupling and power-law
decreasing coupling. For the case of an initial excitation at the edge of the
lattice, we find an approximate expression for the MSD that predicts ballistic
behavior at long times, in agreement with numerical results.
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A monopolist faces a partially uninformed population of consumers,
interconnected through a directed social network. In the network, the
monopolist offers rewards to informed consumers (influencers) conditional on
informing uninformed consumers (influenced). Rewards are needed to bear a
communication cost. We investigate the incentives for the monopolist to move to
a denser network and the impact of this decision on social welfare. Social
welfare increases in information diffusion which, for given communication
incentives, is higher in denser networks. However, the monopolist internalizes
transfers and thus may prefer an environment with less competition between
informed consumers. The presence of highly connected influencers (hubs) is the
main driver that aligns monopolist incentives and welfare.
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Bell's theorem implies that any completion of quantum mechanics which uses
hidden variables (that is, preexisting values of all observables) must be
nonlocal in the Einstein sense. This customarily indicates that knowledge of
the hidden variables would permit superluminal communication. Such superluminal
signaling, akin to the existence of a preferred reference frame, is to be
expected. However, here we provide a protocol that allows an observer with
knowledge of the hidden variables to communicate with her own causal past,
without superluminal signaling. That is, such knowledge would contradict
causality, irrespectively of the validity of relativity theory. Among the ways
we propose for bypassing the paradox there is the possibility of hidden
variables that change their values even when the state does not, and that means
that signaling backwards in time is prohibited in Bohmian mechanics.
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Non-ideal position estimation results in degraded performance of synchronous
motor drive systems due to reduction of the average capability of the drive as
well as torque harmonics of different orders. The signature and extent of the
performance degradation is further dependent, quite significantly, on the
current control architecture, i.e., feedforward or feedback control, employed.
This paper presents a comprehensive analysis of non-idealities or errors in
position estimation and their effects on the control performance of synchronous
motor drives. Analytical models capturing the error in various signals caused
by position sensing errors in the drive system for different control
architectures are presented and are validated with simulation and experimental
results on a prototype permanent magnet synchronous motor drive.
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We apply time-distance helioseismology, local correlation tracking and
Fourier spatial-temporal filtering methods to realistic supergranule scale
simulations of solar convection and compare the results with high-resolution
observations from the SOHO Michelson Doppler Imager (MDI). Our objective is to
investigate the surface and sub-surface convective structures and test
helioseismic measurements. The size and grid of the computational domain are
sufficient to resolve various convective scales from granulation to
supergranulation. The spatial velocity spectrum is approximately a power law
for scales larger than granules, with a continuous decrease in velocity
amplitude with increasing size. Aside from granulation no special scales exist,
although a small enhancement in power at supergranulation scales can be seen.
We calculate the time-distance diagram for f- and p-modes and show that it is
consistent with the SOHO/MDI observations. From the simulation data we
calculate travel time maps for surface gravity waves (f-mode). We also apply
correlation tracking to the simulated vertical velocity in the photosphere to
calculate the corresponding horizontal flows. We compare both of these to the
actual large-scale (filtered) simulation velocities. All three methods reveal
similar large scale convective patterns and provide an initial test of
time-distance methods.
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Manipulation in contrast to grasping is a trajectorial task that needs to use
dexterous hands. Improving the dexterity of robot hands, increases the
controller complexity and thus requires to use the concept of postural
synergies. Inspired from postural synergies, this research proposes a new
framework called kernelized synergies that focuses on the re-usability of the
same subspace for precision grasping and dexterous manipulation. In this work,
the computed subspace of postural synergies; parameterized by probabilistic
movement primitives, is treated with kernel to preserve its grasping and
manipulation characteristics and allows its reuse for new objects. The grasp
stability of the proposed framework is assessed with a force closure quality
index. For performance evaluation, the proposed framework is tested on two
different simulated robot hand models using the Syngrasp toolbox and
experimentally, four complex grasping and manipulation tasks are performed and
reported. The results confirm the hand agnostic approach of the proposed
framework and its generalization to distinct objects irrespective of their
shape and size.
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Standard Deontic Logic (SDL) has been used as the underlying logic to model
and reason over Multi-Agent Systems governed by norms (NorMAS). It is known
that SDL is not able to represent contrary-to-duty (CTD) scenarios in a
consistent way. That is the case, for example, of the so-called Chisholm
paradox, which models a situation in which a conditional obligation that
specifies what must be done when a primary obligation is violated holds. In
SDL, the set of sentences that represent the Chisholm paradox derives
inconsistent sentences. Due to the autonomy of the software agents of a NorMAS,
norms may be violated and the underlying logic used to model the NorMAS should
be able to represent violation scenarios. The contribution of this paper is
threefold: (i) we present how Kelsenian thinking, from his jurisprudence in the
context of legal ontologies, and Intuitionist Hybrid Logic can be adopted in
the modeling of NorMAS, (ii) discuss how this approach overcomes limitations of
the SDL and (iii) present a discussion about normative conflict identification
according to Hill's functional taxonomy, that generalizes from standard
identification by impossibility-of-joint-compliance test.
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Construction of the 12 GeV upgrade to the Continuous Electron Beam
Accelerator Facility (CEBAF) at the Thomas Jefferson National Accelerator
Facility is presently underway. This upgrade includes doubling the energy of
the electron beam to 12 GeV, the addition of a new fourth experimental hall,
and the construction of upgraded detector hardware. An overview of this upgrade
project is presented, along with highlights of the anticipated experimental
program.
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Identified particle spectra represent a crucial tool to understand the
behavior of the matter created in high-energy heavy-ion collisions. The
transverse momentum p_T distributions of identified hadrons contain
informations about the transverse expansion of the system and constrain the
freezeout properties of the matter created. The ALICE experiment has good
particle identification performance over a broad p_T range. In this
contribution the results for identified pions, kaons and protons in heavy-ion
collisions at 2.76 TeV center-of-mass energy are presented. These results are
compared with other identified particle measurements obtained by previous
experiments, and discussed in terms of the thermal and hydrodynamic pictures.
The status of extensions of this analysis, with the study of identified
particles as a function of event-by-event flow in Pb-Pb collisions, is also
discussed.
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Counting circular objects such as cell colonies is an important source of
information for biologists. Although this task is often time-consuming and
subjective, it is still predominantly performed manually. The aim of the
present work is to provide a new tool to enumerate circular objects from
digital pictures and video streams. Here, I demonstrate that the created
program, OpenCFU, is very robust, accurate and fast. In addition, it provides
control over the processing parameters and is implemented in an in- tuitive and
modern interface. OpenCFU is a cross-platform and open-source software freely
available at http://opencfu.sourceforge.net.
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Typically options with a path dependent payoff, such as Target Accumulation
Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper
describes a finite difference scheme for pricing a TARN option. Key steps in
the proposed scheme involve tracking of multiple one-dimensional finite
difference solutions, application of jump conditions at each cash flow exchange
date, and a cubic spline interpolation of results after each jump. Since a
finite difference scheme for TARN has significantly different features from a
typical finite difference scheme for options with a path independent payoff, we
give a step by step description on the implementation of the scheme, which is
not available in the literature. The advantages of the proposed finite
difference scheme over the Monte Carlo method are illustrated by examples with
three different knockout types. In the case of constant or time dependent
volatility models (where Monte Carlo requires simulation at cash flow dates
only), the finite difference method can be faster by an order of magnitude than
the Monte Carlo method to achieve the same accuracy in price. Finite difference
method can be even more efficient in comparison with Monte Carlo in the case of
local volatility model where Monte Carlo requires significantly larger number
of time steps. In terms of robust and accurate estimation of Greeks, the
advantage of the finite difference method will be even more pronounced.
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We study the compatibility of the quantum homogeneitiy and isotropy
hypothesis (QHIH), proposed by Ashtekar and Gupt to restrict the choice of
vacuum state for the cosmological perturbations in Loop Quantum Cosmology
(LQC), with the requirement that the selected vacuum should lead to a power
spectrum that does not oscillate. We inspect in close detail the procedure that
these authors followed to construct a set of states satisfying the QHIH, and
how a preferred vacuum can be determined within this set. We find a step that
is not univocally specified in this procedure, in relation with the replacement
of the set of states that was originally allowed by the QHIH with an
alternative set that is more manageable. In fact, the first of these sets does
not contain the state that has been used in most of the implementations of the
QHIH to the analysis of the power spectrum of the perturbations in LQC. We
focus our attention on the original set picked out by the QHIH and investigate
whether some of its elements may display a non-oscillatory behavior. We show
that, to the extent to which the techniques used in this paper apply, this
possibility is feasible. Thus, the two aforementioned criteria for the physical
restriction of the vacuum state in LQC are compatible with each other and not
exclusive.
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Let $H=(V,E)$ be a hypergraph, where $V$ is a set of vertices and $E$ is a
set of non-empty subsets of $V$ called edges. If all edges of $H$ have the same
cardinality $r$, then $H$ is a $r$-uniform hypergraph; if $E$ consists of all
$r$-subsets of $V$, then $H$ is a complete $r$-uniform hypergraph, denoted by
$K_n^r$, where $n=|V|$. A hypergraph $H'=(V',E')$ is called a subhypergraph of
$H=(V,E)$ if $V'\subseteq V$ and $E'\subseteq E$. A $r$-uniform hypergraph
$H=(V,E)$ is vertex-$k$-maximal if every subhypergraph of $H$ has
vertex-connectivity at most $k$, but for any edge $e\in E(K_n^r)\setminus
E(H)$, $H+e$ contains at least one subhypergraph with vertex-connectivity at
least $k+1$. In this paper, we first prove that for given integers $n,k,r$ with
$k,r\geq2$ and $n\geq k+1$, every vertex-$k$-maximal $r$-uniform hypergraph $H$
of order $n$ satisfies $|E(H)|\geq (^n_r)-(^{n-k}_r)$, and this lower bound is
best possible. Next, we conjecture that for sufficiently large $n$, every
vertex-$k$-maximal $r$-uniform hypergraph $H$ on $n$ vertices satisfies
$|E(H)|\leq(^n_r)-(^{n-k}_r)+(\frac{n}{k}-2)(^k_r)$, where $k,r\geq2$ are
integers. And the conjecture is verified for the case $r>k$.
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We revisit the corrections to black holes due to the $R^4$ terms in the
action. We discuss corrections to the metric and possible scalar fields, as
well as corrections to thermodynamic quantities. We also comment on the large
$D$ limit of the solutions.
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We present a direct method for solving the inverse problem of designing
isotropic potentials that cause self-assembly into target lattices. Each
potential is constructed by matching its energy spectrum to the reciprocal
representation of the lattice to guarantee that the desired structure is a
ground state. We use the method to self-assemble complex lattices not
previously achieved with isotropic potentials, such as a snub square tiling and
the kagome lattice. The latter is especially interesting because it provides
the crucial geometric frustration in several proposed spin liquids.
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In this paper, we extend the popular integral control technique to systems
evolving on Lie groups. More explicitly, we provide an alternative definition
of "integral action" for proportional(-derivative)-controlled systems whose
configuration evolves on a nonlinear space, where configuration errors cannot
be simply added up to compute a definite integral. We then prove that the
proposed integral control allows to cancel the drift induced by a constant bias
in both first order (velocity) and second order (torque) control inputs for
fully actuated systems evolving on abstract Lie groups. We illustrate the
approach by 3-dimensional motion control applications.
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We present a fully sampled map of the inner 3.2 kpc of the nearby spiral
galaxy NGC 2403 in the CO J=1-0 line. These data emphasize the relatively small
contribution of molecular hydrogen to the cold gas content of this galaxy, and
confirm that the gas surface densities in the inner 2.8 kpc of NGC 2403 lie
below the critical surface density for star formation under the theory proposed
by Kennicutt (1989). Since star formation is occurring throughout the inner
disk, the simple dynamical model used by Kennicutt cannot be the only important
process regulating star formation in galaxies. We suggest that stochastic star
formation processes are responsible for the star formation seen in these
regions, and thus that supercritical gas densities may not be a necessary
condition for star formation in the inner regions of galactic disks.
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Consider a set of images of a scene consisting of moving objects captured
using a hand-held camera. In this work, we propose an algorithm which takes
this set of multi-view images as input, detects the dynamic objects present in
the scene, and replaces them with the static regions which are being occluded
by them. The proposed algorithm scans the reference image in the row-major
order at the pixel level and classifies each pixel as static or dynamic. During
the scan, when a pixel is classified as dynamic, the proposed algorithm
replaces that pixel value with the corresponding pixel value of the static
region which is being occluded by that dynamic region. We show that we achieve
artifact-free removal of dynamic objects in multi-view images of several
real-world scenes. To the best of our knowledge, we propose the first method
which simultaneously detects and removes the dynamic objects present in
multi-view images.
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In the present work, a new computational framework for structural topology
optimization based on the concept of moving deformable components is proposed.
Compared with the traditional pixel or node point-based solution framework, the
proposed solution paradigm can incorporate more geometry and mechanical
information into topology optimization directly and therefore render the
solution process more flexible. It also has the great potential to reduce the
computational burden associated with topology optimization substantially. Some
representative examples are presented to illustrate the effectiveness of the
proposed approach.
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We discuss various aspects of the geometry of theta characteristics including
the birational geometry of the spin moduli space of curves, parametrization of
moduli via special K3 surfaces, as well as the relation with classical theta
function theory and string theory in the form of the superstring measure. A
historical view of the development of the subject is also presented.
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In this paper we obtain the rates of convergence of the algorithms given in
[13] and [14] for an automatic computation of the centered Hausdorff and
packing measures of a totally disconnected self-similar set. We evaluate these
rates empirically through the numerical analysis of three standard classes of
self-similar sets, namely, the families of Cantor type sets in the real line
and the plane and the class of Sierpinski gaskets. For these three classes and
for small contraction ratios, sharp bounds for the exact values of the
corresponding measures are obtained and it is shown how these bounds
automatically yield estimates of the corresponding measures, accurate in some
cases to as many as 14 decimal places. In particular, the algorithms accurately
recover the exact values of the measures in all cases in which these values are
known by geometrical arguments. Positive results, which confirm some
conjectural values given in [13] and [14] for the measures, are also obtained
for an intermediate range of larger contraction ratios. We give an argument
showing that, for this range of contraction ratios, the problem is inherently
computational in the sense that any theoretical proof, such as those mentioned
above, might be impossible, so that in these cases, our method is the only
available approach. For contraction ratios close to those of the connected case
our computational method becomes intractably time consuming, so the computation
of the exact values of the packing and centered Hausdorff measures in the
general case, with the open set condition, remains a challenging problem.
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We prove an analytic version of the stable graph regularity lemma from
\cite{MaSh}, which applies to stable functions $f\colon V\times W\to [0,1]$.
Our methods involve continuous model theory and, in particular, results on the
structure of local Keisler measures for stable continuous formulas. Along the
way, we develop some basic tools around ultraproducts of metric structures and
linear functionals on continuous formulas, and we also describe several
concrete families of examples of stable functions.
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The distance set $\Delta(E)$ of a set $E$ consists of all non-negative
numbers that represent distances between pairs of points in $E$. This paper
studies sparse (less than full-dimensional) Borel sets in $\mathbb R^d$, $d
\geq 2$ with a focus on properties of their distance sets. Our results are of
four types. First, we generalize a classical result of Steinhaus (1920) to
Borel sets $E \subseteq [0,1]^d$ with $s$-dimensional Hausdorff content larger
than $(1 - \rho)$, for small $\rho > 0$ and $s$ close to $d$. For such sets, we
show that $\Delta(E) \supseteq [a, b]$, where $0<a<b$ depend only on $d$ and
$\rho$. This leads to our second result, a quantitative formulation of a
theorem of Mattila and Sj$\ddot{\text{o}}$lin (1999). For an arbitrary Borel
set $E \subseteq [0,1]^d$ of large Hausdorff dimension, we show that
$\Delta(E)$ contains a union of intervals whose lengths are dictated by cubes
where $E$ holds high density. This structure theorem in turn yields a tool for
identifying abundance of distances; this is the third contribution of this
article. It allows us to formulate a size property of a set that guarantees all
sufficiently large distances, generalizing earlier work of Bourgain (1986). It
can also be used to construct examples of totally disconnected sparse sets with
this property. Finally, we explore special features of $\Delta(E)$ if $E$ is
assumed to have certain structural regularity in addition to large Hausdorff
dimension. The additional regularity is harnessed via $L^2$-Fourier asymptotics
of measures supported on $E$. Applications of this phenomenon give new
information on $\Delta(E)$ when $E$ is locally uniformly $s$-dimensional and
quasi-regular, in the terminology of Strichartz (1990). A number of new
examples, counterexamples and open problems are discussed.
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From fireflies to heart cells, many systems in Nature show the remarkable
ability to spontaneously fall into synchrony. By imitating Nature's success at
self-synchronizing, scientists have designed cost-effective methods to achieve
synchrony in the lab, with applications ranging from wireless sensor networks
to radio transmission. A similar story has occurred in the study of swarms,
where inspiration from the behavior flocks of birds and schools of fish has led
to 'low-footprint' algorithms for multi-robot systems. Here, we continue this
'bio-inspired' tradition, by speculating on the technological benefit of fusing
swarming with synchronization. The subject of recent theoretical work, minimal
models of so-called 'swarmalator' systems exhibit rich spatiotemporal patterns,
hinting at utility in 'bottom-up' robotic swarms. We review the theoretical
work on swarmalators, identify possible realizations in Nature, and discuss
their potential applications in technology.
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Cornerstone molecules (CO, H_2CO, CH_3OH, HCN, HNC, CN, CS, SO) were observed
toward seven sub-millimeter bright sources in the Orion molecular cloud in
order to quantify the range of conditions for which individual molecular line
tracers provide physical and chemical information. Five of the sources observed
were protostellar, ranging in energetics from 1 - 500L_sun, while the other two
sources were located at a shock front and within a photodissociation region
(PDR).
Statistical equilibrium calculations were used to deduce from the measured
line strengths the physical conditions within each source and the abundance of
each molecule. In all cases except the shock and the PDR, the abundance of CO
with respect to H_2 appears significantly below (factor of ten) the general
molecular cloud value of 10^-4. {Formaldehyde measurements were used to
estimate a mean temperature and density for the gas in each source. Evidence
was found for trends between the derived abundance of CO, H_2CO, CH_3OH, and CS
and the energetics of the source, with hotter sources having higher
abundances.} Determining whether this is due to a linear progression of
abundance with temperature or sharp jumps at particular temperatures will
require more detailed modeling. The observed methanol transitions require high
temperatures (T>50 K), and thus energetic sources, within all but one of the
observed protostellar sources. The same conclusion is obtained from
observations of the CS 7-6 transition. Analysis of the HCN and HNC 4-3
transitions provides further support for high densities n> 10^7 cm^-3 in all
the protostellar sources.
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Various first order approaches have been proposed in the literature to solve
Linear Programming (LP) problems, recently leading to practically efficient
solvers for large-scale LPs. From a theoretical perspective, linear convergence
rates have been established for first order LP algorithms, despite the fact
that the underlying formulations are not strongly convex. However, the
convergence rate typically depends on the Hoffman constant of a large matrix
that contains the constraint matrix, as well as the right hand side, cost, and
capacity vectors.
We introduce a first order approach for LP optimization with a convergence
rate depending polynomially on the circuit imbalance measure, which is a
geometric parameter of the constraint matrix, and depending logarithmically on
the right hand side, capacity, and cost vectors. This provides much stronger
convergence guarantees. For example, if the constraint matrix is totally
unimodular, we obtain polynomial-time algorithms, whereas the convergence
guarantees for approaches based on primal-dual formulations may have
arbitrarily slow convergence rates for this class. Our approach is based on a
fast gradient method due to Necoara, Nesterov, and Glineur (Math. Prog. 2019);
this algorithm is called repeatedly in a framework that gradually fixes
variables to the boundary. This technique is based on a new approximate version
of Tardos's method, that was used to obtain a strongly polynomial algorithm for
combinatorial LPs (Oper. Res. 1986).
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We construct the CP^n model on fuzzy sphere. The Bogomolny bound is saturated
by (anti-)self-dual solitons and the general solutions of BPS equation are
constructed. The dimension of moduli space describing the BPS solution on fuzzy
sphere is exactly the same as that of the commutative sphere or the
(noncommutative) plane. We show that in the soliton backgrounds, the number of
zero modes of Dirac operator on fuzzy sphere, Atiyah-Singer index, is exactly
given by the topological charge of the background solitons.
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Athermal disordered systems can exhibit a remarkable response to an applied
oscillatory shear: after a relatively few shearing cycles, the system falls
into a configuration that had already been visited in a previous cycle. After
this point the system repeats its dynamics periodically despite undergoing many
particle rearrangements during each cycle. We study the behavior of orbits as
we approach the jamming point in simulations of jammed particles subject to
oscillatory shear at fixed pressure and zero temperature. As the pressure is
lowered, we find that it becomes more common for the system to find periodic
states where it takes multiple cycles before returning to a previously visited
state. Thus, there is a proliferation of longer periods as the jamming point is
approached.
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Advanced Driver-Assistance Systems (ADAS) is one of the primary drivers
behind increasing levels of autonomy, driving comfort in this age of connected
mobility. However, the performance of such systems is a function of execution
rate which demands on-board platform-level support. With GPGPU platforms making
their way into automobiles, there exists an opportunity to adaptively support
high execution rates for ADAS tasks by exploiting architectural heterogeneity,
keeping in mind thermal reliability and long-term platform aging. We propose a
future-proof, learning-based adaptive scheduling framework that leverages
Reinforcement Learning to discover suitable scenario based task-mapping
decisions for accommodating increased task-level throughput requirements.
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In this paper, the Hook-Jews (HJ) optimization method is used to optimize a
3-phase Squirrel-Cage Induction Motor (SCIM) as an Electric Vehicle's (EV)
motor. Optimal designs with different numbers of poles, different nominal and
maximum speeds, and different numbers of grooves are compared and the best one
is selected. The optimization method used has advantages such as simple
programming, omission of gradients, short convergence times, and the
possibility of changing individual parameters. Design parameter variations for
optimal designs with rated speeds for 2-pole and 4-pole motors are shown and
explained. The results show that his 2-pole motor with the rectangular stator
and rotor slots and a rated speed of 1800 rpm has the highest efficiency.
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We have made a systematic numerical study of the 16 Wilf classes of length-5
classical pattern-avoiding permutations from their generating function
coefficients. We have extended the number of known coefficients in fourteen of
the sixteen classes. Careful analysis, including sequence extension, has
allowed us to estimate the growth constant of all classes, and in some cases to
estimate the sub-dominant power-law term associated with the exponential
growth.
In six of the sixteen classes we find the familiar power-law behaviour, so
that the coefficients behave like $s_n \sim C \cdot \mu^n \cdot n^g,$ while in
the remaining ten cases we find a stretched exponential as the most likely
sub-dominant term, so that the coefficients behave like $s_n \sim C \cdot \mu^n
\cdot \mu_1^{n^\sigma} \cdot n^g,$ where $0 < \sigma < 1.$ We have also
classified the 120 possible permutations into the 16 distinct classes.
We give compelling numerical evidence, and in one case a proof, that all 16
Wilf-class generating function coefficients can be represented as moments of a
non-negative measure on $[0,\infty).$ Such sequences are known as {\em
Stieltjes moment sequences}. They have a number of nice properties, such as
log-convexity, which can be used to provide quite strong rigorous lower bounds.
Stronger bounds still can be established under plausible monotonicity
assumptions about the terms in the continued-fraction expansion of the
generating functions implied by the Stieltjes property. In this way we provide
strong (non-rigorous) lower bounds to the growth constants, which are sometimes
within a few percent of the exact value.
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We discuss, on finite and infinite dimensional normed vector spaces, some
versions of Radstr\"{o}m cancellation law (or lemma) that are suited for
applications to set optimization problems. In this sense, we call our results
"conic" variants of the celebrated result of Radstr\"{o}m, since they involve
the presence of an ordering cone on the underlying space. Several adaptations
to this context of some topological properties of sets are studied and some
applications to subdifferential calculus associated to set-valued maps and to
necessary optimality conditions for constrained set optimization problems are
given. Finally, a stability problem is considered.
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Gaseous detectors with sense wires are still in use today in small
experiments as well as modern ones as those at the LHC. This short note is
about the construction of a small wire chamber with limited resources, which
could be used both as an educational tool and also as a tracker in small
experiments. The particular detector type selected for this work is the so
called "Delay Wire Chamber": it has only two output channels per plane and can
be made fully gas tight for educational operations. The design can be made with
free software tools, and the construction can be achieved by relatively simple
means.
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It is shown that the electric dipole moment of the tau lepton several orders
of magnitude larger than predicted by the standard model can be generated from
mixings in models with vector like mutiplets. The EDM of the tau lepton arises
from loops involving the exchange of the W, the charginos, the neutralinos, the
sleptons, the mirror leptons, and the mirror sleptons. The EDM of the Dirac tau
neutrino is also computed from loops involving the exhange of the W, the
charginos, the mirror leptons and mirror sleptons. A numerical analysis is
presented and it is shown that the EDMs of the tau lepton and of the tau
neutrino which lie just a couple of orders of magnitude below the sensitivity
of the current experiment can be achieved. Thus the predictions of the model
are testable in improved experiment on the EDM of the tau and of the tau
neutrino.
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This tutorial article introduces the physics of spin transfer torques in
magnetic devices. We provide an elementary discussion of the mechanism of spin
transfer torque, and review the theoretical and experimental progress in this
field. Our intention is to be accessible to beginning graduate students. This
is the introductory paper for a cluster of "Current Perspectives" articles on
spin transfer torques published in volume 320 of the Journal of Magnetism and
Magnetic Materials. This article is meant to set the stage for the others which
follow it in this cluster; they focus in more depth on particularly interesting
aspects of spin-torque physics and highlight unanswered questions that might be
productive topics for future research.
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To probe manifestations of multiband superconductivity in oxypnictides, we
measured the angular dependence of magnetic torque $\tau(\theta)$ in the mixed
state of SmO$_{0.8}$F$_{0.2}$FeAs single crystals as functions of temperature
$T$ and high magnetic field $H$ up to 30 T. We show that the effective mass
anisotropy parameter $\gamma$ extracted from $\tau(\theta)$, can be greatly
overestimated if the strong paramagnetism of Sm or Fe ions is not properly
taken into account. The correctly extracted $\gamma$ depends on both $T$ and
$H$, saturating at $\gamma \simeq 9$ at lower temperatures. Neither the London
penetration depth nor the superfluid density is affected by high fields fields
up to the upper critical field. Our results indicate two strongly-coupled
superconducting gaps of nearly equal magnitudes.
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We study the lower central series filtration L_k for a symplectic quotient
A=A_{2n}/<w> of the free algebra A_{2n} on 2n generators, where w=\sum
[x_i,x_{i+n}]. We construct an action of the Lie algebra H_{2n} of Hamiltonian
vector fields on the associated graded components of the filtration, and use
this action to give a complete description of the reduced first component
\bar{B}_1(A)= A/(L_2 + AL_3) and the second component B_2=L_2/L_3, and we
conjecture a description for the third component B_3=L_3/L_4.
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Finite-density QCD is difficult to study numerically because of the sign
problem. We prove that, in a certain region of the phase diagram, the phase
quenched approximation is exact to O(Nf/Nc). It is true for any physical
observables. We also consider the implications for the lattice simulations and
find a quantitative evidence for the validity of the phase quenching from
existing lattice QCD results at Nc=3. Our results show that the phase-quench
approximation is rather good already at Nc=3, and the 1/Nc correction can be
incorporated by the phase reweighting method without suffering from the overlap
problem. We also show the same equivalence in effective models and holographic
models.
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Many forms of programmable matter have been proposed for various tasks. We
use an abstract model of self-organizing particle systems for programmable
matter which could be used for a variety of applications, including smart paint
and coating materials for engineering or programmable cells for medical uses.
Previous research using this model has focused on shape formation and other
spatial configuration problems (e.g., coating and compression). In this work we
study foundational computational tasks that exceed the capabilities of the
individual constant size memory of a particle, such as implementing a counter
and matrix-vector multiplication. These tasks represent new ways to use these
self-organizing systems, which, in conjunction with previous shape and
configuration work, make the systems useful for a wider variety of tasks. They
can also leverage the distributed and dynamic nature of the self-organizing
system to be more efficient and adaptable than on traditional linear computing
hardware. Finally, we demonstrate applications of similar types of computations
with self-organizing systems to image processing, with implementations of image
color transformation and edge detection algorithms.
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Sequence labeling systems should perform reliably not only under ideal
conditions but also with corrupted inputs - as these systems often process
user-generated text or follow an error-prone upstream component. To this end,
we formulate the noisy sequence labeling problem, where the input may undergo
an unknown noising process and propose two Noise-Aware Training (NAT)
objectives that improve robustness of sequence labeling performed on perturbed
input: Our data augmentation method trains a neural model using a mixture of
clean and noisy samples, whereas our stability training algorithm encourages
the model to create a noise-invariant latent representation. We employ a
vanilla noise model at training time. For evaluation, we use both the original
data and its variants perturbed with real OCR errors and misspellings.
Extensive experiments on English and German named entity recognition benchmarks
confirmed that NAT consistently improved robustness of popular sequence
labeling models, preserving accuracy on the original input. We make our code
and data publicly available for the research community.
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We show that the horocyclic flow of an orientable compact higher genus
surface without conjugate points and with continuous Green bundles is uniquely
ergodic. The result applies to nonflat nonpositively curved surfaces and
generalizes a classical result of Furstenberg and Marcus in negative curvature.
The proof relies on the definition of a uniformly expanding parametrization on
the quotient by the strips of the surface.
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The purpose of this article is to provide a solution to the $m$-fold Laplace
equation in the half space $R_+^d$ under certain Dirichlet conditions. The
solutions we present are a series of $m$ boundary layer potentials. We give
explicit formulas for these layer potentials as linear combinations of powers
of the Laplacian applied to the Dirichlet data, with coefficients determined by
certain path counting problems.
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The fluctuation-dissipation relation (FDR) links thermal fluctuations and
dissipation at thermal equilibrium through temperature. Extending it beyond
equilibrium conditions in pursuit of broadening thermodynamics is often
feasible, albeit with system-dependent specific conditions. We demonstrate
experimentally that a generalized FDR holds for a harmonically trapped tracer
colliding with self-propelled walkers. The generalized FDR remains valid across
a large spectrum of active fluctuation frequencies, extending from underdamped
to critically damped dynamics, which we attribute to a single primary channel
for energy input and dissipation in our system.
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A probabilistic Markov Chain (MC) surrogate model for a two-dimensional
system of interacting particles within a square domain having inherent
symmetries is developed. Particles are assumed to be circular and identical,
colliding with each other and with rigid domain walls via perfectly elastic
collisions. Simulation results over many realizations are used to develop and
evaluate the surrogate MC model. The stationary quantity of interest (QoI) is
the number of particles within each of nine coarser subdomains, delineated via
three internal geometric symmetries. The surrogate model is used to quantify
QoI mean properties and uncertainty as the particle radius is varied.
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Recent advancements in multi-modal artificial intelligence (AI) have
revolutionized the fields of stock market forecasting and heart rate
monitoring. Utilizing diverse data sources can substantially improve prediction
accuracy. Nonetheless, additional data may not always align with the original
dataset. Interpolation methods are commonly utilized for handling missing
values in modal data, though they may exhibit limitations in the context of
sparse information. Addressing this challenge, we propose a Modality Completion
Deep Belief Network-Based Model (MC-DBN). This approach utilizes implicit
features of complete data to compensate for gaps between itself and additional
incomplete data. It ensures that the enhanced multi-modal data closely aligns
with the dynamic nature of the real world to enhance the effectiveness of the
model. We conduct evaluations of the MC-DBN model in two datasets from the
stock market forecasting and heart rate monitoring domains. Comprehensive
experiments showcase the model's capacity to bridge the semantic divide present
in multi-modal data, subsequently enhancing its performance. The source code is
available at: https://github.com/logan-0623/DBN-generate
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Most sequential recommendation (SR) systems employing graph neural networks
(GNNs) only model a user's interaction sequence as a flat graph without
hierarchy, overlooking diverse factors in the user's preference. Moreover, the
timespan between interacted items is not sufficiently utilized by previous
models, restricting SR performance gains. To address these problems, we propose
a novel SR system employing a hierarchical graph neural network (HGNN) to model
factorial user preferences. Specifically, a timespan-aware sequence graph (TSG)
for the target user is first constructed with the timespan among interacted
items. Next, all original nodes in TSG are softly clustered into factor nodes,
each of which represents a certain factor of the user's preference. At last,
all factor nodes' representations are used together to predict SR results. Our
extensive experiments upon two datasets justify that our HGNN-based factorial
user modeling obtains better SR performance than the state-of-the-art SR
models.
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We correct some tables and figures in [A.P. Bustamante and R.C. Calleja,
Physica D: Nonlinear Phenomena, 395 (2019), pp. 15-23, arXiv:1712.05476]. We
also report on the new computations that verify the accuracy of the data and
extend the results. The new computations have led us to find new patterns in
the data that were not noticed before. We formulate some more precise
conjectures.
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For an arbitrary ordinary second order differential equation a test is
constructed that checks if this equation is equivalent to Painleve I, II or
Painleve III with three zero parameters equations under the substitutions of
variables. If it is true then in case the Painleve equations I and II an
explicite change of variables is given that is written using the differential
invariants of the equation.
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It is a well-known fact that light rays do not follow the null geodesics of
the space-time in nonlinear electrodynamics; instead, they follow the null
geodesics of the so-called effective space-time. Taking this into account, in
this paper, we aim to discuss the possibility of distinguishing the type of
charge with which the black hole is endowed, via the motion of light rays. The
results show that, for any black hole being a charged solution of the field
equations of general relativity coupled to the nonlinear electrodynamics, one
cannot distinguish the two types of charge (magnetic or electric) through the
motion of light rays around it.
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The spatial localization or sequestering of motile cargo and their dispersal
within cells is an important process in a number of physiological contexts. The
morphology of the cytoskeletal network, along which active, motor-driven
intracellular transport takes place, plays a critical role in regulating such
transport phases. Here, we use a computational model to address the existence
and sensitivity of dynamic sequestering and how it depends on the parameters
governing the cytoskeletal network geometry, with a focus on filament lengths
and polarization away or toward the periphery. Our model of intracellular
transport solves for the time evolution of a probability distribution of cargo
that is transported by passive diffusion in the bulk cytoplasm and driven by
motors on explicitly rendered, polar cytoskeletal filaments with random
orientations. We show that depending on the lengths and polarizations of
filaments in the network, dynamic sequestering regions can form in different
regions of the cell. Furthermore, we find that, for certain parameters, the
residence time of cargo is non-monotonic with increasing filament length,
indicating an optimal regime for dynamic sequestration that is potentially
tunable via filament length. Our results are consistent with {\it in vivo}
observations and suggest that the ability to tunably control cargo
sequestration via cytoskeletal network regulation could provide a general
mechanism to regulate intracellular transport phases.
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Among the various attempts to understand collisionless absorption of intense
ultrashort laser pulses a variety of models has been invented to describe the
laser beam target interaction. In terms of basic physics collisionless
absorption is understood now as the interplay of the oscillating laser field
with the space charge field produced in the plasma. A first approach to this
idea is realized in Brunel's model the essence of which consists in the
formation of an oscillating charge cloud in the vacuum in front of the target.
The investigation of statistical ensembles of orbits shows that the absorption
process is localized at the ion-vacuum interface and in the skin layer: Single
electrons enter into resonance with the laser field thereby undergoing a phase
shift which causes orbit crossing and braking of Brunel's laminar flow. This
anharmonic resonance acts like an attractor for the electrons and leads to the
formation of a Maxwellian tail in the electron energy spectrum. Most remarkable
results of our investigations are the Brunel-like hot electron distribution at
the relativistic threshold; the minimum of absorption at $I\lambda^2 \cong
(0.3-1.2)\times 10^{21}$ W/cm$^2\mu$m$^2$, in the plasma target with the
electron density of $n_e \lambda^2\sim 10^{23}$cm$^{-3}\mu$m$^2;$ the drastic
reduction of the number of hot electrons in this domain and their reappearance
in the highly relativistic domain; strong coupling of the fast electron jets
with the return current through Cherenkov emission of plasmons. The hot
electron energy scaling shows a strong dependence on intensity in the
moderately relativistic domain $I\lambda^2 \cong (10^{18} - 10^{20})$
W/cm$^2\mu$m$^2$, a scaling in vague accordance with current published
estimates in the range $I\lambda^2 \cong (0.14-3.5)\times 10^{21}$
W/cm$^2\mu$m$^2$, and a distinct power increase beyond $I=3.5\times 10^{21}$
W/cm$^2\mu$m$^2$.
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We investigate the influence of quantum fluctuations upon dipolar Bose gases
by means of the Bogoliubov-de Gennes theory. Thereby, we make use of the local
density approximation to evaluate the dipolar exchange interaction between the
condensate and the excited particles. This allows to obtain the Bogoliubov
spectrum analytically in the limit of large particle numbers. After discussing
the condensate depletion and the ground-state energy correction, we derive
quantum corrected equations of motion for harmonically trapped dipolar Bose
gases by using superfluid hydrodynamics. These equations are subsequently
applied to analyze the equilibrium configuration, the low-lying oscillation
frequencies, and the time-of-flight dynamics. We find that both atomic magnetic
and molecular electric dipolar systems offer promising scenarios for detecting
beyond mean-field effects.
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Class imbalance occurs in many real-world applications, including image
classification, where the number of images in each class differs significantly.
With imbalanced data, the generative adversarial networks (GANs) leans to
majority class samples. The two recent methods, Balancing GAN (BAGAN) and
improved BAGAN (BAGAN-GP), are proposed as an augmentation tool to handle this
problem and restore the balance to the data. The former pre-trains the
autoencoder weights in an unsupervised manner. However, it is unstable when the
images from different categories have similar features. The latter is improved
based on BAGAN by facilitating supervised autoencoder training, but the
pre-training is biased towards the majority classes. In this work, we propose a
novel Conditional Variational Autoencoder with Balanced Pre-training for
Generative Adversarial Networks (CAPGAN) as an augmentation tool to generate
realistic synthetic images. In particular, we utilize a conditional
convolutional variational autoencoder with supervised and balanced pre-training
for the GAN initialization and training with gradient penalty. Our proposed
method presents a superior performance of other state-of-the-art methods on the
highly imbalanced version of MNIST, Fashion-MNIST, CIFAR-10, and two medical
imaging datasets. Our method can synthesize high-quality minority samples in
terms of Fr\'echet inception distance, structural similarity index measure and
perceptual quality.
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Graphene, a thinnest material in the world, can form moire structures on
different substrates, including graphite, h-BN, or metal surfaces. In such
systems the structure of graphene, i. e. its corrugation, as well as its
electronic and elastic properties are defined by the combination of the system
geometry and local interaction strength at the interface. The corrugation in
such structures on metals is heavily extracted from diffraction or local probe
microscopy experiments and can be obtained only via comparison with theoretical
data, which usually simulate the experimental findings. Here we show that
graphene corrugation on metals can be measured directly employing atomic force
spectroscopy and obtained value coincides with state-of-the-art theoretical
results. We also address the elastic reaction of the formed graphene nanodoms
on the indentation process by the scanning tip that is important for the
modeling and fabrication of graphene-based nanoresonators on the nanoscale.
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In this work, we calculate the solutions of the Rarita-Schwinger equation
with the inclusion of the eletromagnetic interaction. Our gauge and coupling
prescription choices lead to Dirac-type solutions. One of the consequences of
our results are the Landau level occupation of particles, quite different from
the usual spin 1/2 particle system occupation numbers.
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We investigate the entropy product formula for various gravitational
instantons. We speculate that due to the mass-independent features of the said
instantons they are \emph{universal} as well as they are \emph{quantized}. For
isolated Euclidean Schwarzschild black hole, these properties simply
\emph{fail}.
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This work provides an overview of gapped quantum spin systems, including
concepts, techniques, properties, and results. The basic framework and objects
of interest for quantum spin systems are introduced, and the main ideas behind
methods for proving spectral gaps for frustration-free models are outlined.
After reviewing recent progress on several spectral gap conjectures, we discuss
quasi-locality of the Heisenberg dynamics and its utility in proving properties
of gapped quantum spin systems. Lieb-Robinson bounds have played a central role
in establishing exponential decay of ground state correlations, an area law for
one-dimensional systems, a many-body adiabatic theorem, and spectral gap
stability. They also aided in the development of the quasi-adiabatic
continuation, which is a useful for investigating gapped ground state phases,
both of which are also discussed.
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Zero-field muon spin relaxation (ZF-$\mu$SR) measurements were undertaken on
under- and overdoped samples of superconducting YBa$_2$Cu$_3$O$_{6+x}$ to
determine the origin of the weak static magnetism recently reported in this
system. The temperature dependence of the muon spin relaxation rate in
overdoped crystals displays an unusual behavior in the superconducting state. A
comparison to the results of NQR and lattice structure experiments on highly
doped samples provides compelling evidence for strong coupling of charge, spin
and structural inhomogeneities.
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Large Language Models (LLMs) tend to be unreliable in the factuality of their
answers. To address this problem, NLP researchers have proposed a range of
techniques to estimate LLM's confidence over facts. However, due to the lack of
a systematic comparison, it is not clear how the different methods compare to
one another. To fill this gap, we present a survey and empirical comparison of
estimators of factual confidence. We define an experimental framework allowing
for fair comparison, covering both fact-verification and question answering.
Our experiments across a series of LLMs indicate that trained hidden-state
probes provide the most reliable confidence estimates, albeit at the expense of
requiring access to weights and training data. We also conduct a deeper
assessment of factual confidence by measuring the consistency of model behavior
under meaning-preserving variations in the input. We find that the confidence
of LLMs is often unstable across semantically equivalent inputs, suggesting
that there is much room for improvement of the stability of models' parametric
knowledge. Our code is available at
(https://github.com/amazon-science/factual-confidence-of-llms).
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