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The classical Truncated Moment problem asks for necessary and sufficient
conditions so that a linear functional $L$ on $\mathcal{P}_{d}$, the vector
space of real $n$-variable polynomials of degree at most $d$, can be written as
integration with respect to a positive Borel measure $\mu$ on $\mathbb{R}^n$.
We work in a more general setting, where $L$ is a linear functional acting on a
finite dimensional vector space $V$ of Borel-measurable functions defined on a
$T_{1}$ topological space $S$. Using an iterative geometric construction, we
associate to $L$ a subset of $S$ called the \textit{core variety},
$\mathcal{CV}(L)$. Our main result is that $L$ has a representing measure $\mu$
if and only if $\mathcal{CV}(L)$ is nonempty. In this case, $L$ has a finitely
atomic representing measure, and the union of the supports of such measures is
precisely $\mathcal{CV}(L)$. We also use the core variety to describe the
facial decomposition of the cone of functionals in the dual space $V^{*}$
having representing measures. We prove a generalization of the Truncated
Riesz-Haviland Theorem of Curto-Fialkow, which permits us to solve a
generalized Truncated Moment Problem in terms of positive extensions of $L$.
These results are adapted to derive a Riesz-Haviland Theorem for a generalized
Full Moment Problem and to obtain a core variety theorem for the latter
problem.
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We find conditions which guarantee that a given flow on a closed smooth
manifold admits a smooth Lyapunov one-form lying in a prescribed de Rham
cohomology class. These conditions are formulated in terms of Schwartzman's
asymptotic cycles of the flow.
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Electromagnetic waves carry energy, linear momentum, and angular momentum.
When light (or other electromagnetic radiation) interacts with material media,
both energy and momentum are usually exchanged. The force and torque
experienced by material bodies in their interactions with the electromagnetic
field are such that the energy as well as the linear and angular momenta of the
overall system (i.e., the system of field plus matter) are conserved. Radiation
forces are now used routinely to trap and manipulate small objects such as
glass or plastic micro-beads and biological cells, to drive micro- and
nano-machines, and to contemplate interstellar travel with the aid of solar
sails. We discuss the properties of the electromagnetic field that enable such
wide-ranging applications.
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First, dark matter is introduced. Next, the Dirac negative energy state is
rediscussed. It is a negative matter with some new characteristics, which are
mainly the gravitation each other, but the repulsion with all positive matter.
Such the positive and negative matters are two regions of topological
separation in general case, and the negative matter is invisible. It is the
simplest candidate of dark matter, and can explain some characteristics of the
dark matter and dark energy. Recent phantom on dark energy is namely a negative
matter. We propose that in quantum fluctuations the positive matter and
negative matter are created at the same time, and derive an inflation cosmos,
which is created from nothing. The Higgs mechanism is possibly a product of
positive and negative matter. Based on a basic axiom and the two foundational
principles of the negative matter, we research its predictions and possible
theoretical tests, in particular, the season effect. The negative matter should
be a necessary development of Dirac theory. Finally, we propose the three basic
laws of the negative matter. The existence of four matters on positive,
opposite, and negative, negative-opposite particles will form the most perfect
symmetrical world.
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Providing an efficient strategy to navigate safely through unsignaled
intersections is a difficult task that requires determining the intent of other
drivers. We explore the effectiveness of Deep Reinforcement Learning to handle
intersection problems. Using recent advances in Deep RL, we are able to learn
policies that surpass the performance of a commonly-used heuristic approach in
several metrics including task completion time and goal success rate and have
limited ability to generalize. We then explore a system's ability to learn
active sensing behaviors to enable navigating safely in the case of occlusions.
Our analysis, provides insight into the intersection handling problem, the
solutions learned by the network point out several shortcomings of current
rule-based methods, and the failures of our current deep reinforcement learning
system point to future research directions.
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IceTop, the surface component of the IceCube Neutrino Observatory at the
South Pole, is an air shower array with an area of 1 km2. The detector allows a
detailed exploration of the mass composition of primary cosmic rays in the
energy range from about 100 TeV to 1 EeV by exploiting the correlation between
the shower energy measured in IceTop and the energy deposited by muons in the
deep ice. In this paper we report on the technical design, construction and
installation, the trigger and data acquisition systems as well as the software
framework for calibration, reconstruction and simulation. Finally the first
experience from commissioning and operating the detector and the performance as
an air shower detector will be discussed.
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We investigate the dependence of steady-state properties of Schelling's
segregation model on the agents' activation order. Our basic formalism is the
Pollicott-Weiss version of Schelling's segregation model. Our main result
modifies this baseline scenario by incorporating contagion in the decision to
move: (pairs of) agents are connected by a second, agent influence network.
Pair activation is specified by a random walk on this network.
The considered schedulers choose the next pair nonadaptively. We can
complement this result by an example of adaptive scheduler (even one that is
quite fair) that is able to preclude maximal segregation. Thus scheduler
nonadaptiveness seems to be required for the validity of the original result
under arbitrary asynchronous scheduling. The analysis (and our result) are part
of an adversarial scheduling approach we are advocating to evolutionary games
and social simulations.
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This paper addresses several unsettled issues associated with string creation
in systems of orthogonal Dp-D(8-p) branes. The interaction between the branes
can be understood either from the closed string or open string picture. In the
closed string picture it has been noted that the DBI action fails to capture an
extra RR exchange between the branes. We demonstrate how this problem persists
upon lifting to M-theory. These D-brane systems are analysed in the closed
string picture by using gauge-fixed boundary states in a non-standard lightcone
gauge, in which RR exchange can be analysed precisely. The missing piece in the
DBI action also manifests itself in the open string picture as a mismatch
between the Coleman-Weinberg potential obtained from the effective field theory
and the corresponding open string calculation. We show that this difference can
be reconciled by taking into account the superghosts in the (0+1)effective
theory of the chiral fermion, that arises from gauge fixing the spontaneously
broken world-line local supersymmetries.
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Unit testing is an essential activity in software development for verifying
the correctness of software components. However, manually writing unit tests is
challenging and time-consuming. The emergence of Large Language Models (LLMs)
offers a new direction for automating unit test generation. Existing research
primarily focuses on closed-source LLMs (e.g., ChatGPT and CodeX) with fixed
prompting strategies, leaving the capabilities of advanced open-source LLMs
with various prompting settings unexplored. Particularly, open-source LLMs
offer advantages in data privacy protection and have demonstrated superior
performance in some tasks. Moreover, effective prompting is crucial for
maximizing LLMs' capabilities. In this paper, we conduct the first empirical
study to fill this gap, based on 17 Java projects, five widely-used open-source
LLMs with different structures and parameter sizes, and comprehensive
evaluation metrics. Our findings highlight the significant influence of various
prompt factors, show the performance of open-source LLMs compared to the
commercial GPT-4 and the traditional Evosuite, and identify limitations in
LLM-based unit test generation. We then derive a series of implications from
our study to guide future research and practical use of LLM-based unit test
generation.
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In this paper, an important discovery has been found for nonconforming
immersed finite element (IFE) methods using the integral values on edges as
degrees of freedom for solving elliptic interface problems. We show that those
IFE methods without penalties are not guaranteed to converge optimally if the
tangential derivative of the exact solution and the jump of the coefficient are
not zero on the interface. A nontrivial counter example is also provided to
support our theoretical analysis. To recover the optimal convergence rates, we
develop a new nonconforming IFE method with additional terms locally on
interface edges. The new method is parameter-free which removes the limitation
of the conventional partially penalized IFE method. We show the IFE basis
functions are unisolvent on arbitrary triangles which is not considered in the
literature. Furthermore, different from multipoint Taylor expansions, we derive
the optimal approximation capabilities of both the Crouzeix-Raviart and the
rotated-$Q_1$ IFE spaces via a unified approach which can handle the case of
variable coefficients easily. Finally, optimal error estimates in both $H^1$-
and $L^2$- norms are proved and confirmed with numerical experiments.
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Scoring the driving performance of various drivers on a unified scale, based
on how safe or economical they drive on their daily trips, is essential for the
driver profile task. Connected vehicles provide the opportunity to collect
real-world driving data, which is advantageous for constructing scoring models.
However, the lack of pre-labeled scores impede the use of supervised regression
models and the data privacy issues hinder the way of traditionally
data-centralized learning on the cloud side for model training. To address
them, an unsupervised scoring method is presented without the need for labels
while still preserving fairness and objectiveness compared to subjective
scoring strategies. Subsequently, a federated learning framework based on
vehicle-cloud collaboration is proposed as a privacy-friendly alternative to
centralized learning. This framework includes a consistently federated version
of the scoring method to reduce the performance degradation of the global
scoring model caused by the statistical heterogeneous challenge of local data.
Theoretical and experimental analysis demonstrate that our federated scoring
model is consistent with the utility of the centrally learned counterpart and
is effective in evaluating driving performance.
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Optical diffraction tomography (ODT) has emerged as an important label-free
tool in biomedicine to measure the three-dimensional (3D) structure of a
biological sample. In this paper, we describe ODT using second-harmonic
generation (SHG) which is a coherent nonlinear optical process with a strict
symmetry selectivity and has several advantages over traditional fluorescence
methods. We report the tomographic retrieval of the 3D second-order nonlinear
optical susceptibility using two-dimensional holographic measurements of the
SHG fields at different illumination angles and polarization states. The method
is a generalization of the conventional linear ODT to the nonlinear scenario.
We demonstrate the method with a numerically simulated nanoparticle
distribution and an experiment with muscle tissue fibers. Our results show that
SHG ODT does not only provide an effective contrast mechanism for label-free
imaging but also due to the symmetry requirement enables the visualization of
properties that are not otherwise accessible.
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We propose the first practical learned lossless image compression system,
L3C, and show that it outperforms the popular engineered codecs, PNG, WebP and
JPEG 2000. At the core of our method is a fully parallelizable hierarchical
probabilistic model for adaptive entropy coding which is optimized end-to-end
for the compression task. In contrast to recent autoregressive discrete
probabilistic models such as PixelCNN, our method i) models the image
distribution jointly with learned auxiliary representations instead of
exclusively modeling the image distribution in RGB space, and ii) only requires
three forward-passes to predict all pixel probabilities instead of one for each
pixel. As a result, L3C obtains over two orders of magnitude speedups when
sampling compared to the fastest PixelCNN variant (Multiscale-PixelCNN).
Furthermore, we find that learning the auxiliary representation is crucial and
outperforms predefined auxiliary representations such as an RGB pyramid
significantly.
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Due to the rapid development technologies for small unmanned aircraft systems
(sUAS), the supply and demand market for sUAS is expanding globally. With the
great number of sUAS ready to fly in civilian airspace, an sUAS aircraft
traffic management system that can guarantee the safe and efficient operation
of sUAS is still at absence. In this paper, we propose a control protocol
design and analysis method for sUAS traffic management (UTM) which can safely
manage a large number of sUAS. The benefits of our approach are two folds: at
the top level, the effort for monitoring sUAS traffic (authorities) and
control/planning for each sUAS (operator/pilot) are both greatly reduced under
our framework; and at the low level, the behavior of individual sUAS is
guaranteed to follow the restrictions. Mathematical proofs and numerical
simulations are presented to demonstrate the proposed method.
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In a previous article for S&P magazine, we made a case for the new
intellectual challenges in the Internet of Things security research. In this
article, we revisit our earlier observations and discuss a few results from the
computer security community that tackle new issues. Using this sampling of
recent work, we identify a few broad general themes for future work.
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We introduce high-order dynamical decoupling strategies for open system
adiabatic quantum computation. Our numerical results demonstrate that a
judicious choice of high-order dynamical decoupling method, in conjunction with
an encoding which allows computation to proceed alongside decoupling, can
dramatically enhance the fidelity of adiabatic quantum computation in spite of
decoherence.
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The Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE) is a
blind narrow-band Halpha+[NII] imaging survey carried out with MegaCam at the
Canada-France-Hawaii Telescope. The survey covers the whole Virgo cluster
region from its core to one virial radius (104 deg^2). The sensitivity of the
survey is of f(Halpha) ~ 4 x 10^-17 erg sec-1 cm^-2 (5 sigma detection limit)
for point sources and Sigma (Halpha) ~ 2 x 10^-18 erg sec^-1 cm^-2 arcsec^-2 (1
sigma detection limit at 3 arcsec resolution) for extended sources, making
VESTIGE the deepest and largest blind narrow-band survey of a nearby cluster.
This paper presents the survey in all its technical aspects, including the
survey design, the observing strategy, the achieved sensitivity in both the
narrow-band Halpha+[NII] and in the broad-band r filter used for the stellar
continuum subtraction, the data reduction, calibration, and products, as well
as its status after the first observing semester. We briefly describe the
Halpha properties of galaxies located in a 4x1 deg^2 strip in the core of the
cluster north of M87, where several extended tails of ionised gas are detected.
This paper also lists the main scientific motivations of VESTIGE, which include
the study of the effects of the environment on galaxy evolution, the fate of
the stripped gas in cluster objects, the star formation process in nearby
galaxies of different type and stellar mass, the determination of the Halpha
luminosity function and of the Halpha scaling relations down to ~ 10^6 Mo
stellar mass objects, and the reconstruction of the dynamical structure of the
Virgo cluster. This unique set of data will also be used to study the HII
luminosity function in hundreds of galaxies, the diffuse Halpha+[NII] emission
of the Milky Way at high Galactic latitude, and the properties of emission line
galaxies at high redshift.
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In our paper [Markl, Shnider: Drinfel'd Algebra Deformations and the
Associahedra, IMRN 1994, no. 4, 169-176] we announced a construction of a
cohomology controlling deformations of quasi-coassociative (or Drinfel'd)
bialgebras. The full version of the paper will appear as [Markl, Shnider:
Drinfel'd Algebra Deformations, Homotopy Comodules and the Associahedra] in
Trans. Amer. Math. Soc. The construction in the paper was based on very
explicit arguments using deep combinatorial properties of the associahedra. The
present paper gives an alternative, general nonsense approach to the
construction. So, we just prove the existence of such a cohomology without
explicitly constructing it. This should be compared with the two approaches to
the cohomology of associative algebras: we either describe explicitly the
Hochschild complex and say "Behold! this is the cohomology" or we prove the
existence of a projective resolution and define the cohomology as the derived
functor.
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We prove that every del Pezzo surface of degree two over a finite field is
unirational, building on the work of Manin and an extension by Salgado, Testa,
and V\'arilly-Alvarado, who had proved this for all but three surfaces. Over
general fields of characteristic not equal to two, we state sufficient
conditions for a del Pezzo surface of degree two to be unirational.
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Through capturing spectral data from a wide frequency range along with the
spatial information, hyperspectral imaging (HSI) can detect minor differences
in terms of temperature, moisture and chemical composition. Therefore, HSI has
been successfully applied in various applications, including remote sensing for
security and defense, precision agriculture for vegetation and crop monitoring,
food/drink, and pharmaceuticals quality control. However, for condition
monitoring and damage detection in carbon fibre reinforced polymer (CFRP), the
use of HSI is a relatively untouched area, as existing non-destructive testing
(NDT) techniques focus mainly on delivering information about physical
integrity of structures but not on material composition. To this end, HSI can
provide a unique way to tackle this challenge. In this paper, with the use of a
near-infrared HSI camera, applications of HSI for the non-destructive
inspection of CFRP products are introduced, taking the EU H2020 FibreEUse
project as the background. Technical challenges and solutions on three case
studies are presented in detail, including adhesive residues detection, surface
damage detection and Cobot based automated inspection. Experimental results
have fully demonstrated the great potential of HSI and related vision
techniques for NDT of CFRP, especially the potential to satisfy the industrial
manufacturing environment.
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We calculate the nuclear dependence of direct photon production in
hadron-nucleus collisions. In terms of a multiple scattering picture, we
factorize the cross section for direct photon production into calculable
short-distance partonic parts times multiparton correlation functions in
nuclei. We present the hadron-nucleus cross section as $A^{\alpha}$ times the
hadron-nucleon cross section. Using information on the multiparton correlation
functions extracted from photon-nucleus experiments, we compute the value of
$\alpha$ as a function of transverse momentum of the direct photon. We also
compare our results with recent data from Fermilab experiment E706.
|
In this work we present a review of the most popular depth-averaged models to
simulate dry granular flows such as aerial avalanches. The classical
Savage-Hutter model and recent ones using a $\mu(I)$-rheology law are studied.
The objective is firstly to point out the advantages of each such models and
secondly to understand how the hypothesis considered in the derivation process
influence on the final system.
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I revisit some classic publications on modularity, to show what problems its
pioneers wanted to solve. These problems occur with spreadsheets too: to
recognise them may help us avoid them.
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We present VLT spectroscopic observations of 7 discovered galaxy groups
between 0.3<z<0.7. The groups were selected from the Strong Lensing Legacy
Survey (SL2S), a survey that consists in a systematic search for strong lensing
systems in the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). We give
details about the target selection, spectroscopic observations and data
reduction for the first release of confirmed SL2S groups. The dynamical
analysis of the systems reveals that they are gravitationally bound structures,
with at least 4 confirmed members and velocity dispersions between 300 and 800
km/s. Their virial masses are between 10^13 and 10^14 M_sun, and so can be
classified as groups or low mass clusters. Most of the systems are isolated
groups, except two of them that show evidence of an ongoing merger of two
sub-structures. We find a good agreement between the velocity dispersions
estimated from the analysis of the kinematics of group galaxies and the weak
lensing measurements, and conclude that the dynamics of baryonic matter is a
good tracer of the total mass content in galaxy groups.
|
We investigate the influence of the driving mechanism on the hysteretic
response of systems with athermal dynamics. In the framework of local-mean
field theory at finite temperature (but neglecting thermallly activated
processes), we compare the rate-independent hysteresis loops obtained in the
random field Ising model (RFIM) when controlling either the external magnetic
field $H$ or the extensive magnetization $M$. Two distinct behaviors are
observed, depending on disorder strength. At large disorder, the $H$-driven and
$M$-driven protocols yield identical hysteresis loops in the thermodynamic
limit. At low disorder, when the $H$-driven magnetization curve is
discontinuous (due to the presence of a macroscopic avalanche), the $M$-driven
loop is re-entrant while the induced field exhibits strong intermittent
fluctuations and is only weakly self-averaging. The relevance of these results
to the experimental observations in ferromagnetic materials, shape memory
alloys, and other disordered systems is discussed.
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Anticipating human motion depends on two factors: the past motion and the
person's intention. While the first factor has been extensively utilized to
forecast short sequences of human motion, the second one remains elusive. In
this work we approximate a person's intention via a symbolic representation,
for example fine-grained action labels such as walking or sitting down.
Forecasting a symbolic representation is much easier than forecasting the full
body pose with its complex inter-dependencies. However, knowing the future
actions makes forecasting human motion easier. We exploit this connection by
first anticipating symbolic labels and then generate human motion, conditioned
on the human motion input sequence as well as on the forecast labels. This
allows the model to anticipate motion changes many steps ahead and adapt the
poses accordingly. We achieve state-of-the-art results on short-term as well as
on long-term human motion forecasting.
|
Even though many of the experiments leading to the standard model of particle
physics were done at large accelerator laboratories in the US and at CERN, many
exciting developments happened in smaller national facilities all over the
world. In this report we highlight the history of accelerator facilities in
Germany.
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In the presence of large extra dimensions, the fundamental Planck scale can
be much lower than the apparent four-dimensional Planck scale. In this setup,
the weak gravity conjecture implies a much more stringent constraint on the UV
cutoff for the U(1) gauge theory in four dimensions. This new energy scale may
be relevant to LHC.
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In this note we study the dynamics of a model recently introduced by one of
us, that displays glassy phenomena in absence of energy barriers. Using an
adiabatic hypothesis we derive an equation for the evolution of the energy as a
function of time that describes extremely well the glassy behaviour observed in
Monte Carlo simulations.
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Transformer-based sequence-to-sequence architectures, while achieving
state-of-the-art results on a large number of NLP tasks, can still suffer from
overfitting during training. In practice, this is usually countered either by
applying regularization methods (e.g. dropout, L2-regularization) or by
providing huge amounts of training data. Additionally, Transformer and other
architectures are known to struggle when generating very long sequences. For
example, in machine translation, the neural-based systems perform worse on very
long sequences when compared to the preceding phrase-based translation
approaches (Koehn and Knowles, 2017).
We present results which suggest that the issue might also be in the mismatch
between the length distributions of the training and validation data combined
with the aforementioned tendency of the neural networks to overfit to the
training data. We demonstrate on a simple string editing task and a machine
translation task that the Transformer model performance drops significantly
when facing sequences of length diverging from the length distribution in the
training data. Additionally, we show that the observed drop in performance is
due to the hypothesis length corresponding to the lengths seen by the model
during training rather than the length of the input sequence.
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A locally decodable code encodes n-bit strings x in m-bit codewords C(x), in
such a way that one can recover any bit x_i from a corrupted codeword by
querying only a few bits of that word. We use a quantum argument to prove that
LDCs with 2 classical queries need exponential length: m=2^{Omega(n)}.
Previously this was known only for linear codes (Goldreich et al. 02). Our
proof shows that a 2-query LDC can be decoded with only 1 quantum query, and
then proves an exponential lower bound for such 1-query locally
quantum-decodable codes. We also show that q quantum queries allow more
succinct LDCs than the best known LDCs with q classical queries. Finally, we
give new classical lower bounds and quantum upper bounds for the setting of
private information retrieval. In particular, we exhibit a quantum 2-server PIR
scheme with O(n^{3/10}) qubits of communication, improving upon the O(n^{1/3})
bits of communication of the best known classical 2-server PIR.
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We study the propagation of null rays and massless fields in a black hole
fluctuating geometry. The metric fluctuations are induced by a small
oscillating incoming flux of energy. The flux also induces black hole mass
oscillations around its average value. We assume that the metric fluctuations
are described by a statistical ensemble. The stochastic variables are the
phases and the amplitudes of Fourier modes of the fluctuations. By averaging
over these variables, we obtain an effective propagation for massless fields
which is characterized by a critical length defined by the amplitude of the
metric fluctuations: Smooth wave packets with respect to this length are not
significantly affected when they are propagated forward in time. Concomitantly,
we find that the asymptotic properties of Hawking radiation are not severely
modified. However, backward propagated wave packets are dissipated by the
metric fluctuations once their blue shifted frequency reaches the inverse
critical length. All these properties bear many resemblences with those
obtained in models for black hole radiation based on a modified dispersion
relation. This strongly suggests that the physical origin of these models,
which were introduced to confront the trans-Planckian problem, comes from the
fluctuations of the black hole geometry.
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This paper introduces the implementation of steganography method called
StegIbiza, which uses tempo modulation as hidden message carrier. With the use
of Python scripting language, a bit string was encoded and decoded using WAV
and MP3 files. Once the message was hidden into a music files, an internet
radio was created to evaluate broadcast possibilities. No dedicated music or
signal processing equipment was used in this StegIbiza implementation
|
Measurements at the RHIC and the LHC have observed flavor dependence of
single-hadron suppression, which reveal the role played by quark masses in the
parton interactions with the quark-gluon plasma (QGP) medium. In this study, we
explore the manifestation of quark mass effect and flavor dependence in jet
observables. We approach this study using the LIDO transport model. Both
elastic and medium-induced radiative processes are implemented for hard parton
evolution in the medium. To guarantee energy-momentum conservation in the model
for the study of full jet observables, we also include a component that mimics
the energy-momentum transported by medium excitation. We first predict the
heavy-jet (B-jet, D-jet) and inclusive-jet nuclear modification factor $R_{AA}$
in central nuclear collisions at both the RHIC and the LHC beam energies. We
observe a flavor-dependent jet suppression as a function of jet transverse
momentum, which can be tested by future precision measurements of heavy jets.
We further investigate a novel observable that considers the angular
correlation between two hard objects: a D-meson and a jet, which provides model
constraints in addition to those imposed by inclusive measurements.
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This paper discusses emerging operational challenges associated with the
integration of solar photovoltaic (PV) in the All-Island power system (AIPS) of
Ireland and Northern Ireland. These include the impact of solar PV on: (i)
dispatch down levels; (ii) long-term frequency deviations; (iii) voltage
magnitude variations; and (iv) operational demand variations. A case study
based on actual data from the AIPS is used to analyze the above challenges. It
is shown that despite its (still) relatively low penetration compared to wind
power penetration, solar PV is challenging the real-time operation of the AIPS,
e.g., maintaining frequency within operational limits. EirGrid and SONI, the
transmission system operators (TSOs) of the AIPS, are working toward addressing
all the above challenges.
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Generative adversarial networks (GANs) offer an effective solution to the
image-to-image translation problem, thereby allowing for new possibilities in
medical imaging. They can translate images from one imaging modality to another
at a low cost. For unpaired datasets, they rely mostly on cycle loss. Despite
its effectiveness in learning the underlying data distribution, it can lead to
a discrepancy between input and output data. The purpose of this work is to
investigate the hypothesis that we can predict image quality based on its
latent representation in the GANs bottleneck. We achieve this by corrupting the
latent representation with noise and generating multiple outputs. The degree of
differences between them is interpreted as the strength of the representation:
the more robust the latent representation, the fewer changes in the output
image the corruption causes. Our results demonstrate that our proposed method
has the ability to i) predict uncertain parts of synthesized images, and ii)
identify samples that may not be reliable for downstream tasks, e.g., liver
segmentation task.
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We propose a novel transformer-style architecture called Global-Local Filter
Network (GLFNet) for medical image segmentation and demonstrate its
state-of-the-art performance. We replace the self-attention mechanism with a
combination of global-local filter blocks to optimize model efficiency. The
global filters extract features from the whole feature map whereas the local
filters are being adaptively created as 4x4 patches of the same feature map and
add restricted scale information. In particular, the feature extraction takes
place in the frequency domain rather than the commonly used spatial (image)
domain to facilitate faster computations. The fusion of information from both
spatial and frequency spaces creates an efficient model with regards to
complexity, required data and performance. We test GLFNet on three benchmark
datasets achieving state-of-the-art performance on all of them while being
almost twice as efficient in terms of GFLOP operations.
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Matrix game, which is also known as two person zero sum game, is a famous
model in game theory. There are some well established theories about it, such
as von Neumann minimax theorem. However, almost no literature have reported the
relationship between eigenvalue/eigenvector and properties of matrix game. In
this paper, we find such relation of some special matrices and try to extend
some conclusions to general matrix.
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We show that ultracold atoms can be controlled in multi-band optical lattices
through spatially periodic Raman pulses for investigation of a class of
strongly correlated physics related to the Kondo problem. The underlying
dynamics of this system is described by a spin-dependent fermionic or bosonic
Kondo-Hubbard lattice model even if we have only spin-independent atomic
collision interaction. We solve the bosonic Kondo-Hubbard lattice model through
a mean-field approximation, and the result shows a clear phase transition from
the ferromagnetic superfluid to the Kondo-signet insulator at the integer
filling.
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In this paper we study the representation theory of filtered algebras with
commutative associated graded whose spectrum has finitely many symplectic
leaves. Examples are provided by the algebras of global sections of
quantizations of symplectic resolutions, quantum Hamiltonian reductions,
spherical symplectic reflection algebras. We introduce the notion of holonomic
modules for such algebras. We show that the generalized Bernstein inequality
holds for simple modules and turns into equality for holonomic simples provided
the algebraic fundamental groups of all leaves are finite. Under the same
assumption, we prove that the associated variety of a simple holonomic module
is equi-dimensional. We also prove that, if the regular bimodule has finite
length or if the algebra in question is a quantum Hamiltonian reduction, then
any holonomic module has finite length. This allows to reduce the Bernstein
inequality for arbitrary modules to simple ones. We prove that the regular
bimodule has finite length for the global sections of quantizations of
symplectic resolutions and for Rational Cherednik algebras. The paper contains
a joint appendix by the author and Etingof that motivates the definition of a
holonomic module in the case of global sections of a quantization of a
symplectic resolution.
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Display technologies have evolved over the years. It is critical to develop
practical HDR capturing, processing, and display solutions to bring 3D
technologies to the next level. Depth estimation of multi-exposure stereo image
sequences is an essential task in the development of cost-effective 3D HDR
video content. In this paper, we develop a novel deep architecture for
multi-exposure stereo depth estimation. The proposed architecture has two novel
components. First, the stereo matching technique used in traditional stereo
depth estimation is revamped. For the stereo depth estimation component of our
architecture, a mono-to-stereo transfer learning approach is deployed. The
proposed formulation circumvents the cost volume construction requirement,
which is replaced by a ResNet based dual-encoder single-decoder CNN with
different weights for feature fusion. EfficientNet based blocks are used to
learn the disparity. Secondly, we combine disparity maps obtained from the
stereo images at different exposure levels using a robust disparity feature
fusion approach. The disparity maps obtained at different exposures are merged
using weight maps calculated for different quality measures. The final
predicted disparity map obtained is more robust and retains best features that
preserve the depth discontinuities. The proposed CNN offers flexibility to
train using standard dynamic range stereo data or with multi-exposure low
dynamic range stereo sequences. In terms of performance, the proposed model
surpasses state-of-the-art monocular and stereo depth estimation methods, both
quantitatively and qualitatively, on challenging Scene flow and differently
exposed Middlebury stereo datasets. The architecture performs exceedingly well
on complex natural scenes, demonstrating its usefulness for diverse 3D HDR
applications.
|
We investigate the possibility of achieving a slow signal field at the level
of single photons inside nanofibers by exploiting stimulated Brillouin
scattering, which involves a strong pump field and the vibrational modes of the
waveguide. The slow signal is significantly amplified for a pump field with a
frequency higher than that of the signal, and attenuated for a lower pump
frequency. We introduce a configuration for obtaining a propagating slow signal
without gain or loss and with a relatively wide bandwidth. This process
involves two strong pump fields with frequencies both higher and lower than
that of the signal, where the effects of signal amplification and attenuation
compensate each other. We account for thermal fluctuations due to the
scattering off thermal phonons and identify conditions under which thermal
contributions to the signal field are negligible. The slowing of light through
Brillouin optomechanics may serve as a vital tool for optical quantum
information processing and quantum communications within nanophotonic
structures.
|
We study the observation of a thin dust shell, radially freely falling to a
Reissner-Nordstrom black hole, by an observer who is also freely and radially
falling into this black hole. Considered and resolved are several common
paradoxes and fallacies peculiar for such problems. The results of this
analytical study are written as a numerical code that allows for calculating
all related effects of this model. The numerical result have been presented in
a few synthesized videos, making a colorful, quantitative and detailed
description of the occurring astrophysical phenomena, both above and below the
horizon.
|
This work demonstrates direct visual sensory-motor control using high-speed
CNN inference via a SCAMP-5 Pixel Processor Array (PPA). We demonstrate how
PPAs are able to efficiently bridge the gap between perception and action. A
binary Convolutional Neural Network (CNN) is used for a classic rock, paper,
scissors classification problem at over 8000 FPS. Control instructions are
directly sent to a servo motor from the PPA according to the CNN's
classification result without any other intermediate hardware.
|
We present the surface magnetic field conditions of the brightest pulsating
RV Tauri star, R Sct. Our investigation is based on the longest
spectropolarimetric survey ever performed on this variable star. The analysis
of high resolution spectra and circular polarization data give sharp
information on the dynamics of the atmosphere and the surface magnetism,
respectively. Our analysis shows that surface magnetic field can be detected at
different phases along a pulsating cycle, and that it may be related to the
presence of a radiative shock wave periodically emerging out of the photosphere
and propagating throughout the stellar atmosphere.
|
This paper is a compressed summary of some principal definitions and concepts
in the approach to the black box algebra being developed by the authors. We
suggest that black box algebra could be useful in cryptanalysis of homomorphic
encryption schemes, and that homomorphic encryption is an area of research
where cryptography and black box algebra may benefit from exchange of ideas.
|
We have examined the local structure of PMN-PT and PZN-PT solid solutions
using density functional theory. We find that the directions and magnitudes of
cation displacement can be explained by an interplay of cation-oxygen bonding,
electrostatic dipole-dipole interactions and short-range direct and through
oxygen Pb-B-cation repulsive interactions. We find that the Zn ions off-center
in the PZN-PT system, which also enables larger Pb and Nb/Ti displacements. The
off-centering behavior of Zn lessens Pb-B-cation repulsion, leading to a
relaxor to ferroelectric and a rhombohedral to tetragonal phase transition at
low PbTiO$_3$ content in the PZN-PT system. We also show that a simple
quadratic relationship exists between Pb and B-cation displacements and the
temperature maximum of dielectric constant, thus linking the enhanced
displacements in PZN-PT systems with the higher transition temperatures.
|
The Morse potential is relatively closed to the harmonic oscillator quantum
system. Thus, following the idea used for the latter, we study the possibility
of creating entanglement using squeezed coherent states of the Morse potential
as an input field of a beam splitter. We measure the entanglement with the
linear entropy for two types of such states and we study the dependence with
the coherence and squeezing parameters. The new results are linked with
observations made on probability densities and uncertainty relations of those
states. The dynamical evolution of the linear entropy is also explored.
|
Various methods of searching for supersymmetric dark matter are sensitive to
WIMPs with different properties. One consequence of this is that the
phenomenology of dark matter detection can vary dramatically in different
supersymmetric breaking scenarios.
In this paper, we consider the sensitivities to supersymmetric dark matter of
different detection methods and techniques in a wide variety of supersymmetric
breaking scenarios. We discuss the ability of various astrophysical
experiments, such as direct experiments, gamma-rays satellites, neutrino
telescopes and positron and anti-proton cosmic ray experiments, to test various
supersymmetry breaking scenarios. We also discuss what information can be
revealed about supersymmetry breaking by combining results from complementary
experiments. We place an emphasis on the differences between various
experimental techniques.
|
We study $L^p$-$L^q$ estimate for the spectral projection operator
$\Pi_\lambda$ associated to the Hermite operator $H=|x|^2-\Delta$ in $\mathbb
R^d$. Here $\Pi_\lambda$ denotes the projection to the subspace spanned by the
Hermite functions which are the eigenfunctions of $H$ with eigenvalue
$\lambda$. Such estimates were previously available only for $q=p'$,
equivalently with $p=2$ or $q=2$ (by $TT^*$ argument) except for the estimates
which are straightforward consequences of interpolation between those
estimates. As shown in the works of Karadzhov, Thangavelu, and Koch and Tataru,
the local and global estimates for $\Pi_\lambda$ are of different nature.
Especially, $\Pi_\lambda$ exhibits complicated behaviors near the set
$\sqrt\lambda\mathbb S^{d-1}$. Compared with the spectral projection operator
associated to the Laplacian, $L^p$-$L^q$ estimate for $\Pi_\lambda$ is not so
well understood up to now for general $p,q$. In this paper we consider
$L^p$--$L^q$ estimate for $\Pi_\lambda$ in a general framework including the
local and global estimates with $1\le p\le 2\le q\le \infty$ and undertake the
work of characterizing the sharp bounds on $\Pi_\lambda$. We establish various
new sharp estimates in extended ranges of $p,q$. First of all, we provide a
complete characterization of the local estimate for $\Pi_\lambda$ which was
first considered by Thangavelu. Secondly, for $d\ge5$, we prove the endpoint
$L^2$--$L^{2(d+3)/(d+1)}$ estimate for $\Pi_\lambda$ which has been left open
since the work of Koch and Tataru. Thirdly, we extend the range of $p,q$ for
which the operator $\Pi_\lambda$ is uniformly bounded from $L^p$ to $L^q$.
|
The photoluminescence dynamics of a microscopic gas of indirect excitons
trapped in coupled quantum wells is probed at very low bath temperature
(approximately 350 mK). Our experiments reveal the non linear energy relaxation
characteristics of indirect excitons. Particularly, we observe that the
excitons dynamics is strongly correlated with the screening of structural
disorder by repulsive exciton-exciton interactions. For our experiments where
two-dimensional excitonic states are gradually defined, the distinctive
enhancement of the exciton scattering rate towards lowest energy states with
increasing density does not reveal unambiguously quantum statistical effects
such as Bose stimulation.
|
We review the role of two-photon exchange (TPE) in electron-hadron
scattering, focusing in particular on hadronic frameworks suitable for
describing the low and moderate Q^2 region relevant to most experimental
studies. We discuss the effects of TPE on the extraction of nucleon form
factors and their role in the resolution of the proton electric to magnetic
form factor ratio puzzle. The implications of TPE on various other observables,
including neutron form factors, electroproduction of resonances and pions, and
nuclear form factors, are summarized. Measurements seeking to directly identify
TPE effects, such as through the angular dependence of polarization
measurements, nonlinear epsilon contributions to the cross sections, and via e+
p to e- p cross section ratios, are also outlined. In the weak sector, we
describe the role of TPE and gamma-Z interference in parity-violating electron
scattering, and assess their impact on the extraction of the strange form
factors of the nucleon and the weak charge of the proton.
|
In this paper we study the long time dynamics of the solutions to the
initial-boundary value problem for a scalar conservation law with a saturating
nonlinear diffusion. After discussing the existence of a unique stationary
solution and its asymptotic stability, we focus our attention on the phenomenon
of 'metastability', whereby the time-dependent solution develops into a layered
function in a relatively short time, and subsequently approaches a steady state
in a very long time interval. Numerical simulations illustrate the results.
|
For the first time we introduce an error estimator for the numerical
approximation of the equations describing the dynamics of sea ice. The idea of
the estimator is to identify different error contributions coming from spatial
and temporal discretization as well as from the splitting in time of the ice
momentum equations from further parts of the coupled system. The novelty of the
error estimator lies in the consideration of the splitting error, which turns
out to be dominant with increasing mesh resolution. Errors are measured in user
specified functional outputs like the total sea ice extent. The error estimator
is based on the dual weighted residual method that asks for the solution of an
additional dual problem for obtaining sensitivity information. Estimated errors
can be used to validate the accuracy of the solution and, more relevant, to
reduce the discretization error by guiding an adaptive algorithm that optimally
balances the mesh size and the time step size to increase the efficiency of the
simulation.
|
Motivations, emotions, and actions are inter-related essential factors in
human activities. While motivations and emotions have long been considered at
the core of exploring how people take actions in human activities, there has
been relatively little research supporting analyzing the relationship between
human mental states and actions. We present the first study that investigates
the viability of modeling motivations, emotions, and actions in language-based
human activities, named COMMA (Cognitive Framework of Human Activities). Guided
by COMMA, we define three natural language processing tasks (emotion
understanding, motivation understanding and conditioned action generation), and
build a challenging dataset Hail through automatically extracting samples from
Story Commonsense. Experimental results on NLP applications prove the
effectiveness of modeling the relationship. Furthermore, our models inspired by
COMMA can better reveal the essential relationship among motivations, emotions
and actions than existing methods.
|
The behavior of a massive scalar particle on the spacetime surrounding a
monopole is studied from a quantum mechanical point of view. All the boundary
conditions necessary to turn into self-adjoint the spatial portion of the wave
operator are found and their importance to the quantum interpretation of
singularities is emphasized.
|
Superradiant scattering of linear spin $s=0,\pm 1,\pm 2$ fields on Kerr black
hole background is investigated in the time domain by integrating numerically
the homogeneous Teukolsky master equation. The applied numerical setup has
already been used in studying long time evolution and tail behavior of
electromagnetic and metric perturbations on rotating black hole background
[arXiv:1905.09082v3]. To have a clear setup the initial data is chosen to be of
the compact support, while to optimize superradiance the frequency of the
initial data is fine tuned. Our most important finding is that the rate of
superradiance strongly depends on the relative position of the (compact)
support of the initial data and the ergoregion. When they are well-separated
then only a modest -- in case of $s=0$ scalar fields negligible --
superradiance occurs, whereas it can get to be amplified significantly whenever
the support of the initial data and the ergoregion overlap.
|
The Higgs mechanism well describes the electroweak symmetry breaking in
nature. We consider a possibility that the microscopic origin of the Higgs
field is UV physics of QCD. We construct a UV complete model of a higher
dimensional Yang-Mills theory as a deformation of a deconstructed (2,0) theory
in six dimensions, and couple the top and bottom (s)quarks to it. We see that
the Higgs fields appear as magnetic degrees of freedom. The model can naturally
explain the masses of the Higgs boson and the top quark. The rho meson-like
resonances with masses such as 1 TeV are predicted.
|
We consider an infinite spatial inhomogeneous random graph model with an
integrable connection kernel that interpolates nicely between existing spatial
random graph models. Key examples are versions of the weight-dependent random
connection model, the infinite geometric inhomogeneous random graph, and the
age-based random connection model. These infinite models arise as the local
limit of the corresponding finite models, see \cite{LWC_SIRGs_2020}. For these
models we identify the scaling of the \emph{local clustering} as a function of
the degree of the root in different regimes in a unified way. We show that the
scaling exhibits phase transitions as the interpolation parameter moves across
different regimes. In addition to the scaling we also identify the leading
constants of the clustering function. This allows us to draw conclusions on the
geometry of a \emph{typical} triangle contributing to the clustering in the
different regimes.
|
A classification is given of rank 3 group actions which are quasiprimitive
but not primitive. There are two infinite families and a finite number of
individual imprimitive examples. When combined with earlier work of Bannai,
Kantor, Liebler, Liebeck and Saxl, this yields a classification of all
quasiprimitive rank 3 permutation groups. Our classification is achieved by
first classifying imprimitive almost simple permutation groups which induce a
2-transitive action on a block system and for which a block stabiliser acts
2-transitively on the block. We also determine those imprimitive rank 3
permutation groups $G$ such that the induced action on a block is almost simple
and $G$ does not contain the full socle of the natural wreath product in which
$G$ embeds.
|
We construct a Dirac-Born-Infeld (DBI) action coupled to a two-form field in
four dimensional $\mathcal{N}=1$ supergravity. Our superconformal formulation
of the action shows a universal way to construct it in various Poincar\'e
supergravity formulations. We generalize the DBI action to that coupled to
matter sector. We also discuss duality transformations of the DBI action, which
are useful for phenomenological and cosmological applications.
|
We propose an experimentally accessible, objective measure for the
macroscopicity of superposition states in mechanical quantum systems. Based on
the observable consequences of a minimal, macrorealist extension of quantum
mechanics, it allows one to quantify the degree of macroscopicity achieved in
different experiments.
|
We present a Monte-Carlo algorithm for the simulation of the all-order strong
coupling expansion of the Z2 gauge theory. This random surface ensemble is
equivalent to the standard formulation, but allows to measure some quantities,
like Polyakov loop correlators or excess free energies, with an accuracy that
could not have been easily achieved with traditional simulation methods. One
interesting application of the algorithm is the investigation of effective
string theories.
|
The probability distribution of temperature of a blackbody can be determined
from its power spectrum. This technique is called blackbody radiation
inversion. In the present paper blackbody radiation inversion is applied on the
spectrum of the Sun. The probability distribution of temperature and the mean
temperature of the Sun are calculated without assuming a homogenous temperature
and without using Stefan-Boltzmann law. Different properties of this
distribution are characterized. This paper presents the very first mention and
investigation of the distortions present within the Sun's spectrum.
|
Driven by network intrusion detection, we propose a MultiResolution Anomaly
Detection (MRAD) method, which effectively utilizes the multiscale properties
of Internet features and network anomalies. In this paper, several theoretical
properties of the MRAD method are explored. A major new result is the
mathematical formulation of the notion that a two-scaled MRAD method has larger
power than the average power of the detection method based on the given two
scales. Test threshold is also developed. Comparisons between MRAD method and
other classical outlier detectors in time series are reported as well.
|
We give a Littlewood-Richardson type rule for expanding the product of a
row-strict quasisymmetric Schur function and a symmetric Schur function in
terms of row-strict quasisymmetric Schur functions. This expansion follows from
several new properties of an insertion algorithm defined by Mason and Remmel
(2010) which inserts a positive integer into a row-strict composition tableau.
|
We study the problem of learning individualized dose intervals using
observational data. There are very few previous works for policy learning with
continuous treatment, and all of them focused on recommending an optimal dose
rather than an optimal dose interval. In this paper, we propose a new method to
estimate such an optimal dose interval, named probability dose interval (PDI).
The potential outcomes for doses in the PDI are guaranteed better than a
pre-specified threshold with a given probability (e.g., 50%). The associated
nonconvex optimization problem can be efficiently solved by the
Difference-of-Convex functions (DC) algorithm. We prove that our estimated
policy is consistent, and its risk converges to that of the best-in-class
policy at a root-n rate. Numerical simulations show the advantage of the
proposed method over outcome modeling based benchmarks. We further demonstrate
the performance of our method in determining individualized Hemoglobin A1c
(HbA1c) control intervals for elderly patients with diabetes.
|
We study the formation of spin-1 symbiotic spinor solitons in a quasi-one-
(quasi-1D) and quasi-two-dimensional (quasi-2D) hyper-fine spin $F=1$
ferromagnetic Bose-Einstein condensate (BEC). The symbiotic solitons
necessarily have a repulsive intraspecies interaction and are bound due to an
attractive interspecies interaction. Due to a collapse instability in higher
dimensions, an additional spin-orbit coupling is necessary to stabilize a
quasi-2D symbiotic spinor soliton. Although a quasi-1D symbiotic soliton has a
simple Gaussian-type density distribution, novel spatial periodic structure in
density is found in quasi-2D symbiotic SO-coupled spinor solitons. For a weak
SO coupling, the quasi-2D solitons are of the $(-1, 0, +1)$ or $(+1, 0, -1)$
type with intrinsic vorticity and multi-ring structure, for Rashba or
Dresselhaus SO coupling, respectively, where the numbers in the parentheses are
angular momenta projections in spin components $F_z = +1, 0, -1$, respectively.
For a strong SO coupling, stripe and superlattice solitons, respectively, with
a stripe and square-lattice modulation in density, are found in addition to the
multi-ring solitons. The stationary states were obtained by imaginary-time
propagation of a mean-field model; dynamical stability of the solitons was
established by real-time propagation over a long period of time. The
possibility of the creation of such a soliton by removing the trap of a
confined spin-1 BEC in a laboratory is also demonstrated.
|
The autonomous control of unmanned aircraft is a highly safety-critical
domain with great economic potential in a wide range of application areas,
including logistics, agriculture, civil engineering, and disaster recovery. We
report on the development of a dynamic monitoring framework for the DLR ARTIS
(Autonomous Rotorcraft Testbed for Intelligent Systems) family of unmanned
aircraft based on the formal specification language RTLola. RTLola is a
stream-based specification language for real-time properties. An RTLola
specification of hazardous situations and system failures is statically
analyzed in terms of consistency and resource usage and then automatically
translated into an FPGA-based monitor. Our approach leads to highly efficient,
parallelized monitors with formal guarantees on the noninterference of the
monitor with the normal operation of the autonomous system.
|
We contribute to the program of proving lower bounds on the size of branching
programs solving the Tree Evaluation Problem introduced by Cook et. al. (2012).
Proving a super-polynomial lower bound for the size of nondeterministic thrifty
branching programs (NTBP) would separate $NL$ from $P$ for thrifty models
solving the tree evaluation problem. First, we show that {\em Read-Once NTBPs}
are equivalent to whole black-white pebbling algorithms thus showing a tight
lower bound (ignoring polynomial factors) for this model.
We then introduce a weaker restriction of NTBPs called {\em Bitwise
Independence}. The best known NTBPs (of size $O(k^{h/2+1})$) for the tree
evaluation problem given by Cook et. al. (2012) are Bitwise Independent. As our
main result, we show that any Bitwise Independent NTBP solving $TEP_{2}^{h}(k)$
must have at least $\frac{1}{2}k^{h/2}$ states. Prior to this work, lower
bounds were known for NTBPs only for fixed heights $h=2,3,4$ (See Cook et. al.
(2012)). We prove our results by associating a fractional black-white pebbling
strategy with any bitwise independent NTBP solving the Tree Evaluation Problem.
Such a connection was not known previously even for fixed heights.
Our main technique is the entropy method introduced by Jukna and Z{\'a}k
(2001) originally in the context of proving lower bounds for read-once
branching programs. We also show that the previous lower bounds given by Cook
et. al. (2012) for deterministic branching programs for Tree Evaluation Problem
can be obtained using this approach. Using this method, we also show tight
lower bounds for any $k$-way deterministic branching program solving Tree
Evaluation Problem when the instances are restricted to have the same group
operation in all internal nodes.
|
In this paper, we investigate a non-interacting scalar field cosmology with
an arbitrary potential using the $f$-deviser method that relies on the
differentiability properties of the potential. Using this alternative
mathematical approach, we present a unified dynamical system analysis at a
scalar field's background and perturbation levels with arbitrary potentials.
For illustration, we consider a monomial and double exponential potential.
These two classes of potentials comprise the asymptotic behaviour of several
classes of scalar field potentials, and, therefore, they provide the skeleton
for the typical behaviour of arbitrary potentials. Moreover, we analyse the
linear cosmological perturbations in the matterless case by considering three
scalar perturbations: the evolution of the Bardeen potentials, the comoving
curvature perturbation, the so-called Sasaki-Mukhanov variable, or the scalar
field perturbation in uniform curvature gauge. Finally, an exhaustive dynamical
system analysis for each scalar perturbation is presented, including the
evolution of Bardeen potentials in the presence of matter.
|
Motivated by experimental results on $\bar B\to D^{(*)}K^-K^{0}$, we use a
factorization approach to study these decays. Two mechanisms concerning kaon
pair production arise: current-produced (from vacuum) and transition (from the
$B$ meson). The kaon pair in the $\bar B {}^0\to D^{(*)+}K^-K^0$ decays can be
produced only by the vector current (current-produced), whose matrix element
can be extracted from $e^+e^-\to K\bar K$ processes via isospin relations. The
decay rates obtained this way are in good agreement with experiment. The
$B^-\to D^{(*)0}K^-K^0$ decays involve both current-produced and transition
processes. By using QCD counting rules and the measured $B^-\to D^{(*)0} K^-
K^0$ decay rates, the measured decay spectra can be understood.
|
The astronomy community has at its disposal a large back catalog of public
spectroscopic galaxy redshift surveys that can be used for the measurement of
luminosity functions. Utilizing the back catalog with new photometric surveys
to maximum efficiency requires modeling the color selection bias imposed on
selection of target galaxies by flux limits at multiple wavelengths. The
likelihood derived herein can address, in principle, all possible color
selection biases through the use of a generalization of the luminosity
function, $\Phi(L)$, over the space of all spectra: the spectro-luminosity
functional, $\Psi[L_\nu]$. It is, therefore, the first estimator capable of
simultaneously analyzing multiple redshift surveys in a consistent way. We also
propose a new way of parametrizing the evolution of the classic Shechter
function parameters, $L_\star$ and $\phi_\star$, that improves both the
physical realism and statistical performance of the model. The techniques
derived in this work will be used in an upcoming paper to measure the
luminosity function of galaxies at the rest frame wavelength of
$2.4\operatorname{\mu m}$ using the Widefield Infrared Survey Explorer (WISE).
|
We revisit the possibilities of accommodating the experimental indications of
the lepton flavor universality violation in $b$-hadron decays in the minimal
scenarios in which the Standard Model is extended by the presence of a single
$\mathcal{O}(1\,\mathrm{TeV})$ leptoquark state. To do so we combine the most
recent low energy flavor physics constraints, including
$R_{K^{(\ast)}}^\mathrm{exp}$ and $R_{D^{(\ast)}}^\mathrm{exp}$, and combine
them with the bounds on the leptoquark masses and their couplings to quarks and
leptons as inferred from the direct searches at the LHC and the studies of the
large $p_T$ tails of the $pp\to \ell\ell$ differential cross section. We find
that none of the scalar leptoquarks of $m_\mathrm{LQ} \simeq 1\div 2$ TeV can
accommodate the $B$-anomalies alone. Only the vector leptoquark, known as
$U_1$, can provide a viable solution which, in the minimal setup, provides an
interesting prediction, i.e. a lower bound to the lepton flavor violating $b\to
s\mu^\pm\tau^\mp$ decay modes, such as $\mathcal{B}(B\to K\mu\tau) \gtrsim
0.7\times 10^{-7}$.
|
The Volterra integral equations of the first kind with piecewise smooth
kernel are considered. Such equations appear in the theory of optimal control
of the evolving systems. The existence theorems are proved. The method for
constructing approximations of parametric families of solutions of such
equations is suggested. The parametric family of solutions is constructed in
terms of a logarithmic-power asymptotics.
|
Identifying the three-dimensional (3D) crystal-plane and strain-field
distributions of nanocrystals is essential for optical, catalytic, and
electronic applications. Here, we developed a methodology for visualizing the
3D information of chiral gold nanoparticles with concave gap structures by
Bragg coherent X-ray diffraction imaging. The distribution of the
high-Miller-index planes constituting the concave chiral gap was precisely
determined. The highly strained region adjacent to the chiral gaps was
resolved, which was correlated to the 432-symmetric morphology of the
nanoparticles and its corresponding plasmonic properties were numerically
predicted from the atomically defined structures. This approach can serve as a
general characterization platform for visualizing the 3D crystallographic and
strain distributions of nanoparticles, especially for applications where
structural complexity and local heterogeneity are major determinants, as
exemplified in plasmonics.
|
This paper deals with differential pencils possessing a term depending on the
unknown function with a fixed argument. We deduce the so called main equation
together with its fine structure for the spectral problem. Then, according to
the boundary conditions and the position of argument, we describe two cases:
degenerate and non-degenerate. For these two cases, the uniqueness of inverse
spectral problem are studied and a constructive procedure for reconstructing
the potentials along with necessary and sufficient conditions of its
solvability are obtained.
|
Transfer learning refers to machine learning techniques that focus on
acquiring knowledge from related tasks to improve generalization in the tasks
of interest. In MRI, transfer learning is important for developing strategies
that address the variation in MR images. Additionally, transfer learning is
beneficial to re-utilize machine learning models that were trained to solve
related tasks to the task of interest. Our goal is to identify research
directions, gaps of knowledge, applications, and widely used strategies among
the transfer learning approaches applied in MR brain imaging. We performed a
systematic literature search for articles that applied transfer learning to MR
brain imaging. We screened 433 studies and we categorized and extracted
relevant information, including task type, application, and machine learning
methods. Furthermore, we closely examined brain MRI-specific transfer learning
approaches and other methods that tackled privacy, unseen target domains, and
unlabeled data. We found 129 articles that applied transfer learning to brain
MRI tasks. The most frequent applications were dementia related classification
tasks and brain tumor segmentation. A majority of articles utilized transfer
learning on convolutional neural networks (CNNs). Only few approaches were
clearly brain MRI specific, considered privacy issues, unseen target domains or
unlabeled data. We proposed a new categorization to group specific, widely-used
approaches. There is an increasing interest in transfer learning within brain
MRI. Public datasets have contributed to the popularity of Alzheimer's
diagnostics/prognostics and tumor segmentation. Likewise, the availability of
pretrained CNNs has promoted their utilization. Finally, the majority of the
surveyed studies did not examine in detail the interpretation of their
strategies after applying transfer learning, and did not compare to other
approaches.
|
Ca$_{3}$Ru$_{2}$O$_{7}$ is a polar metal that belongs to the class of
multiferroic magnetic materials. Here, tiny amounts of Fe doping in the Ru
sites bring about dramatic changes in the electronic and magnetic properties
and generate a complex H-T phase diagram. To date, not much is known about the
ground state of such a system in the absence of magnetic field. By performing
muon-spin spectroscopy (${\mu}$SR) measurements in 5% Fe-doped
Ca$_{3}$Ru$_{2}$O$_{7}$ single crystals, we investigate its electronic
properties at a local level. Transverse-field ${\mu}$SR results indicate a very
sharp normal-to-antiferromagnetic transition at T$_{N}$ = 79.7(1) K, with a
width of only 1 K. Zero-field ${\mu}$SR measurements in the magnetically
ordered state allow us to determine the local fields B$_{i}$ at the muon
implantation sites. By symmetry, muons stopping close to the RuO$_{2}$ planes
detect only the weak nuclear dipolar fields, while those stopping next to
apical oxygens sense magnetic fields as high as 150 mT. In remarkable agreement
with the nominal Fe-doping, a $\sim$ 6% minority of the these muons feel
slightly lower fields, reflecting a local magnetic frustration induced by iron
ions. Finally, B$_{i}$ shows no significant changes across the
metal-to-insulator transition, close to 40 K. We ascribe this surprising lack
of sensitivity to the presence of crystal twinning.
|
We observed asteroid (596) Scheila and its ejecta cloud using the Swift
UV-optical telescope. We obtained photometry of the nucleus and the ejecta, and
for the first time measured the asteroid's reflection spectrum between 290 -
500 nm. Our measurements indicate significant reddening at UV wavelengths (13%
per 1000 {\AA}) and a possible broad, unidentified absorption feature around
380 nm. Our measurements indicate that the outburst has not permanently
increased the asteroid's brightness. We did not detect any of the gases that
are typically associated with either hypervolatile activity thought responsible
for cometary outbursts (CO+, CO2+), or for any volatiles excavated with the
dust (OH, NH, CN, C2, C3). We estimate that 6 x 10^8 kg of dust was released
with a high ejection velocity of 57 m/s (assuming 1 {\mu}m sized particles).
While the asteroid is red in color and the ejecta have the same color as the
Sun, we suggest that the dust does not contain any ice. Based on our
observations, we conclude that (596) Scheila was most likely impacted by
another main belt asteroid less than 100 meters in diameter.
|
We exploit the parquet formalism to derive exact flow equations for the
two-particle-reducible four-point vertices, the self-energy, and typical
response functions, circumventing the reliance on higher-point vertices. This
includes a concise, algebraic derivation of the multiloop flow equations, which
have previously been obtained by diagrammatic considerations. Integrating the
multiloop flow for a given input of the totally irreducible vertex is
equivalent to solving the parquet equations with that input. Hence, one can
tune systems from solvable limits to complicated situations by variation of
one-particle parameters, staying at the fully self-consistent solution of the
parquet equations throughout the flow. Furthermore, we use the resulting
differential form of the Schwinger-Dyson equation for the self-energy to
demonstrate one-particle conservation of the parquet approximation and to
construct a conserving two-particle vertex via functional differentiation of
the parquet self-energy. Our analysis gives a unified picture of the various
many-body relations and exact renormalization group equations.
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The second quantization of the quaternionic fermionic field is undertaken
using the real Hilbert space approach to quaternionic quantum mechanics
($\mathbbm H$QM). The solution responds to an open problem of quaternionic
quantum theory, and launches the basis to the development of the quaternionic
interaction theory.
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We obtain relaxation times for field theories with Lifshitz scaling and with
holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by
computing quasinormal modes of a bulk scalar field in the presence of Lifshitz
black branes. We determine the relation between relaxation time and dynamical
exponent z, for various values of boundary dimension d and operator scaling
dimension. It is found that for d>z+1, at zero momenta, the modes are
non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1
and zero momenta, we present analytical results.
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The goal of this paper is to provide a survey and application-focused atlas
of collective behavior coordination algorithms for multi-agent systems.
We survey the general family of collective behavior algorithms for
multi-agent systems and classify them according to their underlying
mathematical structure. In doing so, we aim to capture fundamental mathematical
properties of algorithms (e.g., scalability with respect to the number of
agents and bandwidth use) and to show how the same algorithm or family of
algorithms can be used for multiple tasks and applications.
Collectively, this paper provides an application-focused atlas of algorithms
for collective behavior of multi-agent systems, with three objectives:
1. to act as a tutorial guide to practitioners in the selection of
coordination algorithms for a given application;
2. to highlight how mathematically similar algorithms can be used for a
variety of tasks, ranging from low-level control to high-level coordination;
3. to explore the state-of-the-art in the field of control of multi-agent
systems and identify areas for future research.
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We present a new numerical scheme to study systems of non-convex, irregular,
and punctured particles in an efficient manner. We employ this method to
analyze regular packings of odd-shaped bodies, not only from a nanoparticle but
also both from a computational geometry perspective. Besides determining
close-packed structures for many shapes, we also discover a new denser
configuration for Truncated Tetrahedra. Moreover, we consider recently
synthesized nanoparticles and colloids, where we focus on the excluded volume
interactions, to show the applicability of our method in the investigation of
their crystal structures and phase behavior. Extensions to the presented scheme
include the incorporation of soft particle-particle interactions, the study of
quasicrystalline systems, and random packings.
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The use of random samples to approximate properties of geometric
configurations has been an influential idea for both combinatorial and
algorithmic purposes. This chapter considers two related
notions---$\epsilon$-approximations and $\epsilon$-nets---that capture the most
important quantitative properties that one would expect from a random sample
with respect to an underlying geometric configuration.
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We explore the critical fluctuations near the chiral critical endpoint (CEP)
in a chiral effective model and discuss possible signals of the CEP, recently
explored experimentally in nuclear collision. Particular attention is paid to
the dependence of such signals on the location of the phase boundary and the
CEP relative to the chemical freeze-out conditions in nuclear collisions. We
argue that in effective models, standard freeze-out fits to heavy-ion data
should not be used directly. Instead, the relevant quantities should be
examined on lines in the phase diagram that are defined self-consistently,
within the framework of the model. We discuss possible choices for such an
approach.
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When learning a mapping from an input space to an output space, the
assumption that the sample distribution of the training data is the same as
that of the test data is often violated. Unsupervised domain shift methods
adapt the learned function in order to correct for this shift. Previous work
has focused on utilizing unlabeled samples from the target distribution. We
consider the complementary problem in which the unlabeled samples are given
post mapping, i.e., we are given the outputs of the mapping of unknown samples
from the shifted domain. Two other variants are also studied: the two sided
version, in which unlabeled samples are give from both the input and the output
spaces, and the Domain Transfer problem, which was recently formalized. In all
cases, we derive generalization bounds that employ discrepancy terms.
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A full phonon intensity cancellation is reported in a longitudinal polarized
inelastic neutron scattering experiment performed on the magnetocaloric
compound MnFe$_{4}$Si$_{3}$, a ferromagnet with $T_{Curie}$ $\approx$ 305 K.
The TA[100] phonon polarized along the $c$-axis measured from the Brillouin
zone center $\textbf{G}$=(0, 0, 2) is observed only in one ($\sigma_{z}^{++}$)
of the two non-spin-flip polarization channels and is absent in the other one
($\sigma_{z}^{--}$) at low temperatures. This effect disappears at higher
temperatures, in the vicinity of $T_{Curie}$, where the phonon is measured in
both channels with nonetheless marked different intensities. The effect is
understood as originating from nuclear-magnetic interference between the
nuclear one-phonon and the magnetovibrational one-phonon scattering
cross-sections. The total cancellation reported is accidental, i.e. does not
correspond to a systematic effect, as established by measurements in different
Brillouin zones.
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The study of quantum thermal machines, and more generally of open quantum
systems, often relies on master equations. Two approaches are mainly followed.
On the one hand, there is the widely used, but often criticized, local
approach, where machine sub-systems locally couple to thermal baths. On the
other hand, in the more established global approach, thermal baths couple to
global degrees of freedom of the machine. There has been debate as to which of
these two conceptually different approaches should be used in situations out of
thermal equilibrium. Here we compare the local and global approaches against an
exact solution for a particular class of thermal machines. We consider
thermodynamically relevant observables, such as heat currents, as well as the
quantum state of the machine. Our results show that the use of a local master
equation is generally well justified. In particular, for weak inter-system
coupling, the local approach agrees with the exact solution, whereas the global
approach fails for non-equilibrium situations. For intermediate coupling, the
local and the global approach both agree with the exact solution and for strong
coupling, the global approach is preferable. These results are backed by
detailed derivations of the regimes of validity for the respective approaches.
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This technical report describes the training of nomic-embed-text-v1, the
first fully reproducible, open-source, open-weights, open-data, 8192 context
length English text embedding model that outperforms both OpenAI Ada-002 and
OpenAI text-embedding-3-small on short and long-context tasks. We release the
training code and model weights under an Apache 2 license. In contrast with
other open-source models, we release a training data loader with 235 million
curated text pairs that allows for the full replication of nomic-embed-text-v1.
You can find code and data to replicate the model at
https://github.com/nomic-ai/contrastors
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The fifth generation of mobile broadband is more than just an evolution to
provide more mobile bandwidth, massive machine-type communications, and
ultra-reliable and low-latency communications. It relies on a complex, dynamic
and heterogeneous environment that implies addressing numerous testing and
security challenges. In this paper we present 5Greplay, an open-source 5G
network traffic fuzzer that enables the evaluation of 5G components by
replaying and modifying 5G network traffic by creating and injecting network
scenarios into a target that can be a 5G core service (e.g., AMF, SMF) or a RAN
network (e.g., gNodeB). The tool provides the ability to alter network packets
online or offline in both control and data planes in a very flexible manner.
The experimental evaluation conducted against open-source based 5G platforms,
showed that the target services accept traffic being altered by the tool, and
that it can reach up to 9.56 Gbps using only 1 processor core to replay 5G
traffic.
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We calculated the longitudinal acoustic phonon limited electron mobility of
14 two dimensional semiconductors with composition of MX$_2$, where M (= Mo, W,
Sn, Hf, Zr and Pt) is the transition metal, and X is S, Se and Te. We treated
the scattering matrix by deformation potential approximation. We found that out
of the 14 compounds, MoTe$_2$, HfSe$_2$ and HfTe$_2$, are promising regarding
to the possible high mobility and finite band gap. The phonon limited mobility
can be above 2500 cm$^2$V$^{-1}$s$^{-1}$ at room temperature.
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We survey discrete and continuous model-theoretic notions which have
important connections to general topology. We present a self-contained
exposition of several interactions between continuous logic and $C_p$-theory
which have applications to a classification problem involving Banach spaces not
including $c_0$ or $l^p$, following recent results obtained by P. Casazza and
J. Iovino for compact continuous logics. Using $C_p$-theoretic results
involving Grothendieck spaces and double limit conditions, we extend their
results to a broader family of logics, namely those with a first countable
weakly Grothendieck space of types. We pose $C_p$-theoretic problems which have
model-theoretic implications.
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Effects of long-term atmospheric change were looked for in photometry
employing the Gemini North and South twin Multi-Object Spectrograph (GMOS-N and
GMOS-S) archival data. The whole GMOS imaging database, beginning from 2003,
was compared against the all-sky Gaia object catalog, yielding ~10^6 Sloan
r'-filter samples, ending in 2021. These were combined with reported sky and
meteorological conditions, versus a simple model of the atmosphere plus cloud
together with simulated throughputs. One exceptionally extincted episode in
2009 is seen, as is a trend (similar at both sites) of about 2 mmag worsening
attenuation per decade. This is consistent with solar-radiance transmissivity
records going back over six decades, aerosol density measurements, and more
than 0.2 deg C per decade rise in global air temperature, which has
implications for calibration of historic datasets or future surveys.
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The Discrete Light-Cone Quantization (DLCQ) of a supersymmetric SU(N) gauge
theory in 1+1 dimensions is discussed, with particular emphasis given to the
inclusion of all dynamical zero modes. Interestingly, the notorious `zero-mode
problem' is now tractable because of special supersymmetric cancellations. In
particular, we show that anomalous zero-mode contributions to the currents are
absent, in contrast to what is observed in the non-supersymmetric case. We find
that the supersymmetric partner of the gauge zero mode is the diagonal
component of the fermion zero mode. An analysis of the vacuum structure is
provided and it is shown that the inclusion of zero modes is crucial for
probing the phase properties of the vacua. In particular, we find that the
ground state energy is zero and N-fold degenerate, and thus consistent with
unbroken supersymmetry. We also show that the inclusion of zero modes for the
light-cone supercharges leaves the supersymmetry algebra unchanged. Finally, we
remark that the dependence of the light-cone Fock vacuum in terms of the gauge
zero is unchanged in the presence of matter fields.
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For a graph G, let f_{ij} be the number of spanning rooted forests in which
vertex j belongs to a tree rooted at i. In this paper, we show that for a path,
the f_{ij}'s can be expressed as the products of Fibonacci numbers; for a
cycle, they are products of Fibonacci and Lucas numbers. The {\em doubly
stochastic graph matrix} is the matrix F=(f_{ij})/f, where f is the total
number of spanning rooted forests of G and n is the number of vertices in G. F
provides a proximity measure for graph vertices. By the matrix forest theorem,
F^{-1}=I+L, where L is the Laplacian matrix of G. We show that for the paths
and the so-called T-caterpillars, some diagonal entries of F (which provides a
measure of the self-connectivity of vertices) converge to \phi^{-1} or to
1-\phi^{-1}, where \phi is the golden ratio, as the number of vertices goes to
infinity. Thereby, in the asymptotic, the corresponding vertices can be
metaphorically considered as "golden introverts" and "golden extroverts,"
respectively. This metaphor is reinforced by a Markov chain interpretation of
the doubly stochastic graph matrix, according to which F equals the overall
transition matrix of a random walk with a random number of steps on G.
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Music generation with the aid of computers has been recently grabbed the
attention of many scientists in the area of artificial intelligence. Deep
learning techniques have evolved sequence production methods for this purpose.
Yet, a challenging problem is how to evaluate generated music by a machine. In
this paper, a methodology has been developed based upon an interactive
evolutionary optimization method, with which the scoring of the generated
melodies is primarily performed by human expertise, during the training. This
music quality scoring is modeled using a Bi-LSTM recurrent neural network.
Moreover, the innovative generated melody through a Genetic algorithm will then
be evaluated using this Bi-LSTM network. The results of this mechanism clearly
show that the proposed method is able to create pleasurable melodies with
desired styles and pieces. This method is also quite fast, compared to the
state-of-the-art data-oriented evolutionary systems.
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In this paper, we find the energy-momentum distribution of stationary
axisymmetric spacetimes in the context of teleparallel theory by using
M$\ddot{o}$ller prescription. The metric under consideration is the
generalization of the Weyl metrics called the Lewis-Papapetrou metric. The
class of stationary axisymmetric solutions of the Einstein field equations has
been studied by Galtsov to include the gravitational effect of an {\it
external} source. Such spacetimes are also astrophysically important as they
describe the exterior of a body in equilibrium. The energy density turns out to
be non-vanishing and well-defined and the momentum becomes constant except
along $\theta$-direction. It is interesting to mention that the results reduce
to the already available results for the Weyl metrics when we take $\omega=0$.
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It is shown that the spectrum of the asymmetric rotor can be realized quantum
mechanically in terms of a system of interacting bosons. This is achieved in
the SU(3) limit of the interacting boson model by considering higher-order
interactions between the bosons. The spectrum corresponds to that of a rigid
asymmetric rotor in the limit of infinite boson number.
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