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Let $T_m$ be a noncommutative Fourier multiplier. In recent work, Mei and
Ricard introduced a noncommutative analogue of Cotlar's identity in order to
prove that certain multipliers are bounded on the non-commutative $L_p$-spaces
of a free group. Here, we study Cotlar type identities in full generality,
giving a closed characterization for them in terms of $m$:
\[
\big( m(g h) - m(g) \big) \, \big( m(g^{-1}) - m(h) \big) = 0,
\; \forall g \in \mathrm{G} \setminus \{e\}, h \in \mathrm{G}.
\] We manage to prove, using a geometric argument, that if $X$ is a tree --
or more generally an $\mathbb{R}$-tree -- on which $\mathrm{G}$ acts and $m$
lifts to a function $\widetilde{m}: X \to \mathbb{C}$ that is constant on the
connected subsets of $X \setminus \{x_0\}$, then $m$ satisfies Cotlar's
identity and thus $T_m$ is bounded in $L_p$ for $1 < p < \infty$. This result
establishes a new connection between groups actions on $\mathbb{R}$-trees and
Fourier multipliers. We show that $m$ is trivial when the action has global
fixed points. This machinery allows us to simultaneously generalize the free
group transforms of Mei and Ricard and the theory of Hilbert transforms in
left-orderable groups, which follows from Arveson's subdiagonal algebras. Using
Bass-Serre theory, we construct new examples of Fourier multipliers in groups.
Those include new families like Baumslag-Solitar groups. We also show that a
natural Hilbert transform in $\mathrm{PSL}_2(\mathbb{C})$ satisfies Cotlar's
identity when restricted to the Bianchi group
$\mathrm{PSL}_2(\mathbb{Z}[\sqrt{-1}])$.
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Graphene nano-ribbons junctions based electronic devices are proposed in this
Letter. Non-equilibrium Green function calculations show that nano-ribbon
junctions tailored from single layer graphene with different edge shape and
width can act as metal-semiconductor junctions and quantum dots can be
implemented. In virtue of the possibilities of patterning monolayer graphene
down to atomic precision, these structures, quite different from the previously
reported two-dimensional bulk graphene or carbon nanotube devices, are expected
to be used as the building blocks of the future nano-electronics.
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We study the Topological Casimir effect, in which extra vacuum energy emerges
as a result of the topological features of the theory, rather than due to the
conventional fluctuations of the physical propagating degrees of freedom. We
compute the corresponding topological term in quantum Maxwell theory defined on
a compact manifold. Numerically, the topological effect is much smaller than
the conventional Casimir effect. However, we argue that the Topological Casimir
Effect is highly sensitive to an external magnetic field, which may help to
discriminate it from the conventional Casimir effect. It is quite amazing that
the external magnetic field plays the role of the $\theta$ state, similar to a
$\theta$ vacuum in QCD, or $\theta=\pi$ in topological insulators.
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We have measured the CP asymmetry A_CP = [BF(b -> s gamma) - BF(bbar -> sbar
gamma)]/ [BF(b -> s gamma) + BF(bbar -> sbar gamma)] to be A_CP = (-0.079 +/-
0.108 +/- 0.022)(1.0 +/- 0.030), implying that, at 90% confidence level, A_CP
lies between -0.27 and +0.10. These limits rule out some extreme non-Standard
Model predictions, but are consistent with most, as well as with the Standard
Model.
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We calculate the dynamic structure factor S(q,omega) of a one-dimensional
(1D) interacting Bose gas confined in a harmonic trap. The effective
interaction depends on the strength of the confinement enforcing the 1D motion
of atoms; interaction may be further enhanced by superimposing an optical
lattice on the trap potential. In the compressible state, we find that the
smooth variation of the gas density around the trap center leads to softening
of the singular behavior of S(q,omega) at Lieb-1 mode compared to the behavior
predicted for homogeneous 1D systems. Nevertheless, the density-averaged
response remains a non-analytic function of q and omega at Lieb-1 mode in the
limit of weak trap confinement. The exponent of the power-law non-analyticity
is modified due to the inhomogeneity in a universal way, and thus, bears
unambiguously the information about the (homogeneous) Lieb-Liniger model. A
strong optical lattice causes formation of Mott phases. Deep in the Mott
regime, we predict a semi-circular peak in S(q,\omega) centered at the on-site
repulsion energy, omega=U. Similar peaks of smaller amplitudes exist at
multiples of U as well. We explain the suppression of the dynamic response with
entering into the Mott regime, observed recently by D. Clement et al., Phys.
Rev. Lett. v. 102, p. 155301 (2009), based on an f-sum rule for the
Bose-Hubbard model.
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The rise of large language models (LLMs) is revolutionizing information
retrieval, question answering, summarization, and code generation tasks.
However, in addition to confidently presenting factually inaccurate information
at times (known as "hallucinations"), LLMs are also inherently limited by the
number of input and output tokens that can be processed at once, making them
potentially less effective on tasks that require processing a large set or
continuous stream of information. A common approach to reducing the size of
data is through lossless or lossy compression. Yet, in some cases it may not be
strictly necessary to perfectly recover every detail from the original data, as
long as a requisite level of semantic precision or intent is conveyed.
This paper presents three contributions to research on LLMs. First, we
present the results from experiments exploring the viability of approximate
compression using LLMs, focusing specifically on GPT-3.5 and GPT-4 via ChatGPT
interfaces. Second, we investigate and quantify the capability of LLMs to
compress text and code, as well as to recall and manipulate compressed
representations of prompts. Third, we present two novel metrics -- Exact
Reconstructive Effectiveness (ERE) and Semantic Reconstruction Effectiveness
(SRE) -- that quantify the level of preserved intent between text compressed
and decompressed by the LLMs we studied. Our initial results indicate that
GPT-4 can effectively compress and reconstruct text while preserving the
semantic essence of the original text, providing a path to leverage
$\sim$5$\times$ more tokens than present limits allow.
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We introduce an effective theory which extends hydrodynamics into a regime
where the critical slowing down would otherwise make hydrodynamics
inapplicable.
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G349.7 + 00.2 is a young Galactic supernova remnant (SNR) with a mushroom
morphology in radio and X-rays, and it has been detected across the entire
electromagnetic spectrum from radio to high energy $\gamma$-rays. Moreover, the
remnant is interacting with a molecular cloud based on the observations in the
radio and infrared band. The reason for the formation of the periphery and the
dynamical evolution of the remnant are investigated using 3D hydrodynamical
(HD) simulations. Under the assumption that the supernova ejecta is evolved in
the medium with a density gradient, the shell is composed of two hemispheres
with different radiuses, and the smaller hemisphere is in relatively dense
media. The resulting periphery of remnant is consistent with detected ones, and
it can be concluded that the peculiar periphery of G349.7+00.2 can be
reproduced as the remnants interacting with the medium with a density gradient.
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In this note we take a new look at the local convergence of alternating
optimization methods for low-rank matrices and tensors. Our abstract
interpretation as sequential optimization on moving subspaces yields insightful
reformulations of some known convergence conditions that focus on the interplay
between the contractivity of classical multiplicative Schwarz methods with
overlapping subspaces and the curvature of low-rank matrix and tensor
manifolds. While the verification of the abstract conditions in concrete
scenarios remains open in most cases, we are able to provide an alternative and
conceptually simple derivation of the asymptotic convergence rate of the
two-sided block power method of numerical algebra for computing the dominant
singular subspaces of a rectangular matrix. This method is equivalent to an
alternating least squares method applied to a distance function. The
theoretical results are illustrated and validated by numerical experiments.
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As a contribution to an eventual solution of the problem of the determination
of the maximal subgroups of the Monster we show that there is no subgroup
isomorphic to Sz(8). The proof is largely, though not entirely, computer-free.
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Observations of white dwarfs in dark matter-rich environments can provide
strong limits on the strength of dark matter interactions. Here we apply the
recently improved formalism of the dark matter capture rate in white dwarfs to
a general model in which dark matter interacts with the white dwarf ion
components via a light scalar mediator. We compute the dark matter capture rate
in the optically thin limit in a cold white dwarf from the globular cluster
Messier. We then estimate the threshold cross-section, which significantly
varies as a function of the light scalar mediator mass $m_\phi$ in the range of
$0.05\, m_\chi<m_\phi<m_\chi$ and becomes constant when $m_\phi>m_\chi$. We
also show that the bounds obtained from the dark matter capture in a white
dwarf from the globular cluster Messier 4 are complementary to direct detection
experiments and particularly strong in the sub-GeV regime.
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Effective connectivity can describe the causal patterns among brain regions.
These patterns have the potential to reveal the pathological mechanism and
promote early diagnosis and effective drug development for cognitive disease.
However, the current methods utilize software toolkits to extract empirical
features from brain imaging to estimate effective connectivity. These methods
heavily rely on manual parameter settings and may result in large errors during
effective connectivity estimation. In this paper, a novel brain
imaging-to-graph generation (BIGG) framework is proposed to map functional
magnetic resonance imaging (fMRI) into effective connectivity for mild
cognitive impairment (MCI) analysis. To be specific, the proposed BIGG
framework is based on the diffusion denoising probabilistic models (DDPM),
where each denoising step is modeled as a generative adversarial network (GAN)
to progressively translate the noise and conditional fMRI to effective
connectivity. The hierarchical transformers in the generator are designed to
estimate the noise at multiple scales. Each scale concentrates on both spatial
and temporal information between brain regions, enabling good quality in noise
removal and better inference of causal relations. Meanwhile, the
transformer-based discriminator constrains the generator to further capture
global and local patterns for improving high-quality and diversity generation.
By introducing the diffusive factor, the denoising inference with a large
sampling step size is more efficient and can maintain high-quality results for
effective connectivity generation. Evaluations of the ADNI dataset demonstrate
the feasibility and efficacy of the proposed model. The proposed model not only
achieves superior prediction performance compared with other competing methods
but also predicts MCI-related causal connections that are consistent with
clinical studies.
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The rapid development of the Large Language Model (LLM) presents huge
opportunities for 6G communications, e.g., network optimization and management
by allowing users to input task requirements to LLMs by nature language.
However, directly applying native LLMs in 6G encounters various challenges,
such as a lack of private communication data and knowledge, limited logical
reasoning, evaluation, and refinement abilities. Integrating LLMs with the
capabilities of retrieval, planning, memory, evaluation and reflection in
agents can greatly enhance the potential of LLMs for 6G communications. To this
end, we propose a multi-agent system with customized communication knowledge
and tools for solving communication related tasks using natural language,
comprising three components: (1) Multi-agent Data Retrieval (MDR), which
employs the condensate and inference agents to refine and summarize
communication knowledge from the knowledge base, expanding the knowledge
boundaries of LLMs in 6G communications; (2) Multi-agent Collaborative Planning
(MCP), which utilizes multiple planning agents to generate feasible solutions
for the communication related task from different perspectives based on the
retrieved knowledge; (3) Multi-agent Evaluation and Reflecxion (MER), which
utilizes the evaluation agent to assess the solutions, and applies the
reflexion agent and refinement agent to provide improvement suggestions for
current solutions. Finally, we validate the effectiveness of the proposed
multi-agent system by designing a semantic communication system, as a case
study of 6G communications.
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Fitted interatomic potentials are widely used in atomistic simulations thanks
to their ability to compute the energy and forces on atoms quickly. However,
the simulation results crucially depend on the quality of the potential being
used. Force matching is a method aimed at constructing reliable and
transferable interatomic potentials by matching the forces computed by the
potential as closely as possible, with those obtained from first principles
calculations. The potfit program is an implementation of the force-matching
method that optimizes the potential parameters using a global minimization
algorithm followed by a local minimization polish. We extended potfit in two
ways. First, we adapted the code to be compliant with the KIM Application
Programming Interface (API) standard (part of the Knowledgebase of Interatomic
Models Project). This makes it possible to use potfit to fit many KIM potential
models, not just those prebuilt into the potfit code. Second, we incorporated
the geodesic Levenberg--Marquardt (LM) minimization algorithm into potfit as a
new local minimization algorithm. The extended potfit was tested by generating
a training set using the KIM Environment-Dependent Interatomic Potential (EDIP)
model for silicon and using potfit to recover the potential parameters from
different initial guesses. The results show that EDIP is a "sloppy model" in
the sense that its predictions are insensitive to some of its parameters, which
makes fitting more difficult. We find that the geodesic LM algorithm is
particularly efficient for this case. The extended potfit code is the first
step in developing a KIM-based fitting framework for interatomic potentials for
bulk and two dimensional materials. The code is available for download via
https://www.potfit.net.
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Strong coupling of photons and materials in semiconductor nanocavity systems
has been investigated because of its potentials in quantum information
processing and related applications, and has been testbeds for cavity quantum
electrodynamics (QED). Interesting phenomena such as coherent exchange of a
single quantum between a single quantum dot and an optical cavity, called
vacuum Rabi oscillation, and highly efficient cavity QED lasers have been
reported thus far. The coexistence of vacuum Rabi oscillation and laser
oscillation appears to be contradictory in nature, because the fragile
reversible process may not survive in laser oscillation. However, recently, it
has been theoretically predicted that the strong-coupling effect could be
sustained in laser oscillation in properly designed semiconductor systems.
Nevertheless, the experimental realization of this phenomenon has remained
difficult since the first demonstration of the strong-coupling, because an
extremely high cavity quality factor and strong light-matter coupling are both
required for this purpose. Here, we demonstrate the onset of laser oscillation
in the strong-coupling regime in a single quantum dot (SQD)-cavity system. A
high-quality semiconductor optical nanocavity and strong SQD-field coupling
enabled to the onset of lasing while maintaining the fragile coherent exchange
of quanta between the SQD and the cavity. In addition to the interesting
physical features, this device is seen as a prototype of an ultimate solid
state light source with an SQD gain, which operates at ultra-low power, with
expected applications in future nanophotonic integrated systems and monolithic
quantum information devices.
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The paper aims to apply the complex-octonions to explore the variable
gravitational mass and energy gradient of several particles in the external
ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the
algebra of quaternions to study the physical properties of electromagnetic
fields. Some scholars follow up this method in the field theories. Nowadays,
they employ the complex-octonions to analyze simultaneously the physical
quantities of electromagnetic and gravitational fields, including the field
potential, field strength, field source, linear momentum, angular momentum,
torque, and force. When the octonion force is equal to zero, it is able to
deduce eight independent equilibrium equations, especially the force
equilibrium equation, precession equilibrium equation, mass continuity
equation, and current continuity equation. In the force equilibrium equation,
the gravitational mass is variable. The gravitational mass is the sum of the
inertial mass and a few tiny terms. These tiny terms will be varied with not
only the fluctuation of field strength and of potential energy, but also the
spatial dimension of velocity. The study reveals that it is comparatively
untoward to attempt to measure directly the variation of these tiny terms of
gravitational mass in the ultra-strong magnetic field. However it is not such
difficult to measure the energy gradient relevant to the variation of these
tiny terms of gravitational mass. In the complex-octonion space, the
gravitational mass is a sort of variable physical quantity, rather than an
intrinsic property of any physical object. And this inference is accordant with
the academic thought of `the mass is not an intrinsic property any more' in the
unified electro-weak theory.
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Generative models have shown a giant leap in synthesizing photo-realistic
images with minimal expertise, sparking concerns about the authenticity of
online information. This study aims to develop a universal AI-generated image
detector capable of identifying images from diverse sources. Existing methods
struggle to generalize across unseen generative models when provided with
limited sample sources. Inspired by the zero-shot transferability of
pre-trained vision-language models, we seek to harness the nontrivial
visual-world knowledge and descriptive proficiency of CLIP-ViT to generalize
over unknown domains. This paper presents a novel parameter-efficient
fine-tuning approach, mixture of low-rank experts, to fully exploit CLIP-ViT's
potential while preserving knowledge and expanding capacity for transferable
detection. We adapt only the MLP layers of deeper ViT blocks via an integration
of shared and separate LoRAs within an MoE-based structure. Extensive
experiments on public benchmarks show that our method achieves superiority over
state-of-the-art approaches in cross-generator generalization and robustness to
perturbations. Remarkably, our best-performing ViT-L/14 variant requires
training only 0.08% of its parameters to surpass the leading baseline by +3.64%
mAP and +12.72% avg.Acc across unseen diffusion and autoregressive models. This
even outperforms the baseline with just 0.28% of the training data. Our code
and pre-trained models will be available at
https://github.com/zhliuworks/CLIPMoLE.
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Given a quadratic module, we construct its universal C*-algebra, and then use
methods and notions from the theory of C*-algebras to study the quadratic
module. We define residually finite-dimensional quadratic modules, and
characterize them in various ways, in particular via a Positivstellensatz. We
give unified proofs for several existing strong Positivstellens\"atze, and
prove some new ones. Our approach also leads naturally to interesting new
examples in free convexity. We show that the usual notion of a free convex hull
is not able to detect residual finite-dimensionality. We thus propose a new
notion of free convexity, which is coordinate-free. We characterize
semialgebraicity of free convex hulls of semialgebraic sets, and show that they
are not always semialgebraic, even at scalar level. This also shows that the
membership problem for quadratic modules has a negative answer in the
non-commutative setup.
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We aim to combine asteroseismology, spectroscopy, and evolutionary models to
establish a comprehensive picture of the evolution of Galactic blue supergiant
stars (BSG). To start such an investigation, we selected three BSG candidates
for our analysis: HD 42087 (PU Gem), HD 52089 ($\epsilon$ CMa) and HD 58350
($\eta$ CMa). These stars show pulsations and were suspected to be in an
evolutionary stage either preceding or succeding the red supergiant (RSG)
stage.
For our analysis, we utilized the 2-min cadence TESS data to study the
photometric variability and obtained new spectroscopic observations at the
CASLEO observatory. We calculated CMFGEN non-LTE radiative transfer models and
derived stellar and wind parameters using the iterative spectral analysis
pipeline XTGRID. The spectral modeling was limited to changing only the
effective temperature, surface gravity, CNO abundances, and mass-loss rates.
Finally, we compared the derived metal abundances with predictions from Geneva
stellar evolution models. The frequency spectra of all three stars show either
stochastic oscillations, nonradial strange modes, or a rotational splitting.
We conclude that the rather short sectoral observing windows of TESS prevent
establishing a reliable mode identification of low frequencies connected to
mass-loss variabilities. The spectral analysis confirmed gradual changes in the
mass-loss rates and the derived CNO abundances comply with the values reported
in the literature. We were able to achieve a quantitative match with stellar
evolution models for the stellar masses and luminosities. However, the
spectroscopic surface abundances turned out to be inconsistent with theoretical
predictions. The stars show N enrichment, typical for CNO cycle processed
material, but the abundance ratios do not reflect the associated levels of C
and O depletion.
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Spectral dimensionality reduction algorithms are widely used in numerous
domains, including for recognition, segmentation, tracking and visualization.
However, despite their popularity, these algorithms suffer from a major
limitation known as the "repeated Eigen-directions" phenomenon. That is, many
of the embedding coordinates they produce typically capture the same direction
along the data manifold. This leads to redundant and inefficient
representations that do not reveal the true intrinsic dimensionality of the
data. In this paper, we propose a general method for avoiding redundancy in
spectral algorithms. Our approach relies on replacing the orthogonality
constraints underlying those methods by unpredictability constraints.
Specifically, we require that each embedding coordinate be unpredictable (in
the statistical sense) from all previous ones. We prove that these constraints
necessarily prevent redundancy, and provide a simple technique to incorporate
them into existing methods. As we illustrate on challenging high-dimensional
scenarios, our approach produces significantly more informative and compact
representations, which improve visualization and classification tasks.
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III-V tunneling field-effect transistors (TFETs) offer great potentials in
future low-power electronics application due to their steep subthreshold slope
and large "on" current. Their 3D quantum transport study using non-equilibrium
Green's function method is computationally very intensive, in particular when
combined with multiband approaches such as the eight-band K.P method. To reduce
the numerical cost, an efficient reduced-order method is developed in this
article and applied to study homojunction InAs and heterojunction GaSb-InAs
nanowire TFETs. Device performances are obtained for various channel widths,
channel lengths, crystal orientations, doping densities, source pocket lengths,
and strain conditions.
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We investigate the photometric modulation induced by magnetic activity cycles
and study the relationship between rotation period and activity cycle(s) in
late-type (FGKM) stars. We analyse light-curves spanning up to 9 years of 125
nearby stars provided by the ASAS survey. The sample is mainly conformed by
low-activity main sequence late A to mid M-type stars. A search is performed
for short (days) and long-term (years) periodic variations in the photometry.
We modelled with combinations of sinusoids the light-curves to measure the
properties of these periodic signals. To provide a better statistical
interpretation of our results we complement them with the results from previous
similar works. We have been able to measure long-term photometric cycles of 47
stars. Rotational modulation was also detected and rotational periods measured
in 36 stars. For 28 stars we have simultaneous measurements of both, activity
cycles and rotational periods, being 17 of them M-type stars. From sinusoidal
fits we measured both photometric amplitudes and periods. The measured cycle
periods range from 2 up to 14 yr with photometric amplitudes in the range of
5-20 mmag. We have found that the distribution of cycle lengths for the
different spectral types is similar. On the other hand the distribution of
rotation periods is completely different, trending to longer periods for later
type stars. The amplitudes induced by magnetic cycles and rotation show a clear
correlation. A trend of photometric amplitudes with rotation period is also
outlined in the data. For a given activity index the amplitudes of the
photometric variability induced by activity cycles of main sequence GK stars
are lower than those of early and mid-M dwarfs. Using spectroscopic data we
also provide an update in the empirical relationship between the level of
chromospheric activity as given by log(Rhk) and the rotation periods.
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We present a study of the multi-wavelength properties, from the mid-infrared
to the hard X-rays, of a sample of 255 spectroscopically identified X-ray
selected Type-2 AGN from the XMM-COSMOS survey. Most of them are obscured the
X-ray absorbing column density is determined by either X-ray spectral analyses
(for the 45% of the sample), or from hardness ratios. Spectral Energy
Distributions (SEDs) are computed for all sources in the sample. The average
SEDs in the optical band is dominated by the host-galaxy light, especially at
low X-ray luminosities and redshifts. There is also a trend between X-ray and
mid-infrared luminosity: the AGN contribution in the infrared is higher at
higher X-ray luminosities. We calculate bolometric luminosities, bolometric
corrections, stellar masses and star formation rates (SFRs) for these sources
using a multi-component modeling to properly disentangle the emission
associated to stellar light from that due to black hole accretion. For 90% of
the sample we also have the morphological classifications obtained with an
upgraded version of the Zurich Estimator of Structural Types (ZEST+). We find
that on average Type-2 AGN have lower bolometric corrections than Type-1 AGN.
Moreover, we confirm that the morphologies of AGN host-galaxies indicate that
there is a preference for these Type-2 AGN to be hosted in bulge-dominated
galaxies with stellar masses greater than 10^10 solar masses.
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Molecular dynamics simulations, with full Coulomb interaction and
self-consistent field emission, are used to examine mutual space-charge
interactions between beams originating from several emitter areas, in a planar
infinite diode. The simulations allow observation of the trajectory of each
individual electron through the diode gap. Results show that when the
center-to-center spacing between emitters is greater than half of the gap
spacing the emitters are essentially independent. For smaller spacing the
mutual space-charge effect increases rapidly and should not be discounted. A
simple qualitative explanation for this effect is given.
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Spin-orbit torque (SOT) induced magnetisation switching in CoFeB/Ta/CoFeB
trilayer with two CoFeB layers exhibiting in-plane magnetic anisotropy (IPMA)
and perpendicular magnetic anisotropy (PMA) is investigated. Interlayer
exchange coupling (IEC), measured using ferromagnetic resonance technique is
modified by varying thickness of Ta spacer. The evolution of the IEC leads to
different orientation of the magnetic anisotropy axes of two CoFeB layers: for
thicker Ta layer where magnetisation prefers antiferromagnetic ordering and for
thinner Ta layer where ferromagnetic coupling exists. Magnetisation state of
the CoFeB layer exhibiting PMA is controlled by the spin-polarized current
originating from SOT in $\mu m$ sized Hall bars. The evolution of the critical
SOT current density with Ta thickness is presented, showing an increase with
decreasing $t_\mathrm{Ta}$, which coincides with the coercive field dependence.
In a narrow range of $t_\mathrm{Ta}$ corresponding to the ferromagnetic IEC,
the field-free SOT-induced switching is achieved.
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Paradoxes in the Boltzmann kinetic theory are presented. Firstly, it is
pointed out that the usual notion concerning the perfect continuity of
distribution function is not generally valid; in many important situations
using certain types of discontinuous distribution functions is an absolute
must. Secondly, it is revealed that there is no time reversibility in terms of
beam-to-beam collisions and, in connection with this, there are intrinsic
difficulties in formulating the net change of molecular density due to
collisions, either in the three-dimensional velocity space or in the
six-dimensional phase space. With help of simple examples, the paradoxes
manifest themselves clearly.
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We investigate sensing of magnetic fields using quantum spin chains at finite
temperature and exploit quantum phase crossovers to improve metrological bounds
on the estimation of the chain parameters. In particular, we analyze the $ XX $
spin chain and show that the magnetic sensitivity of this system is dictated by
its adiabatic magnetic susceptibility, which scales extensively (linearly) in
the number of spins $ N $. Next, we introduce an iterative feedforward protocol
that actively exploits features of quantum phase crossovers to enable
super-extensive scaling of the magnetic sensitivity. Moreover, we provide
experimentally realistic observables to saturate the quantum metrological
bounds. Finally, we also address magnetic sensing in the Heisenberg $ XY $ spin
chain.
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In the present paper we report on the combined experimental and theoretical
study of the Sr6-xEuxBP5O20 (x=0.01; 0.03; 0.05; 0.07; 0.09; 0.11; 0.13; 0.15)
phosphors. Details of the samples preparation and spectroscopic measurements
are followed by the analysis of the room-temperature absorption and emission
spectra, which yielded the main parameters of the electron-phonon coupling,
such as Huang-Rhys factor, Stokes shift, effective phonon energy, and
zero-phonon line position were determined for the first time for the studied
system. The obtained parameters were used to model the emission band shapes,
which perfectly reproduce the experimental results for all samples.
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Feebly Interacting Particles (FIPs) might offer the solution to (some of) the
open questions beyond the Standard Models of particle physics and cosmology. At
DESY in Hamburg, three non-accelerator-based experiments will search for FIPs
as dark matter candidates (ALPS II, BabyIAXO) or constituting the dark matter
in our home galaxy (MADMAX).
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Humans exhibit outstanding learning, planning and adaptation capabilities
while performing different types of industrial tasks. Given some knowledge
about the task requirements, humans are able to plan their limbs motion in
anticipation of the execution of specific skills. For example, when an operator
needs to drill a hole on a surface, the posture of her limbs varies to
guarantee a stable configuration that is compatible with the drilling task
specifications, e.g. exerting a force orthogonal to the surface. Therefore, we
are interested in analyzing the human arms motion patterns in industrial
activities. To do so, we build our analysis on the so-called manipulability
ellipsoid, which captures a posture-dependent ability to perform motion and
exert forces along different task directions. Through thorough analysis of the
human movement manipulability, we found that the ellipsoid shape is task
dependent and often provides more information about the human motion than
classical manipulability indices. Moreover, we show how manipulability patterns
can be transferred to robots by learning a probabilistic model and employing a
manipulability tracking controller that acts on the task planning and execution
according to predefined control hierarchies.
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The parameter space of the Constrained Minimal supersymmetric Standard Model
is considered. It is shown that for the particular choice of parameters there
are some regions where long-living charged superparticles exist. Two regions of
interest are the co-annihilation region with light staus, and the region with
large negative trilinear scalar coupling A distinguished by light stops. The
phenomenology of long-living superparticles is briefly discussed.
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We propose a decentralized Maximum Likelihood solution for estimating the
stochastic renewable power generation and demand in single bus Direct Current
(DC) MicroGrids (MGs), with high penetration of droop controlled power
electronic converters. The solution relies on the fact that the primary control
parameters are set in accordance with the local power generation status of the
generators. Therefore, the steady state voltage is inherently dependent on the
generation capacities and the load, through a non-linear parametric model,
which can be estimated. To have a well conditioned estimation problem, our
solution avoids the use of an external communication interface and utilizes
controlled voltage disturbances to perform distributed training. Using this
tool, we develop an efficient, decentralized Maximum Likelihood Estimator (MLE)
and formulate the sufficient condition for the existence of the globally
optimal solution. The numerical results illustrate the promising performance of
our MLE algorithm.
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We investigate $L^1\to L^\infty$ dispersive estimates for the three
dimensional Dirac equation with a potential. We also classify the structure of
obstructions at the thresholds of the essential spectrum as being composed of a
two dimensional space of resonances and finitely many eigenfunctions. We show
that, as in the case of the Schr\"odinger evolution, the presence of a
threshold obstruction generically leads to a loss of the natural $t^{-\frac32}$
decay rate. In this case we show that the solution operator is composed of a
finite rank operator that decays at the rate $t^{-\frac12}$ plus a term that
decays at the rate $t^{-\frac32}$.
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Local linearization is highlighted to explain the success of the orbital
approximation in positive response to Scerri's comments on the electronic
configuration model. The relevance of Rydberg states is made clear.
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Let K be a complete algebraically closed p-adic field of characteristic zero.
Let f, g be two transcendental meromorphic functions in the whole field K or
meromorphic functions in an open disk that are not quotients of bounded
analytic functions. Let P be a polynomial of uniqueness for meromorphic
functions in K or in an open disk and let $\alpha$ be a small meromorphic
function with regards to f and g. If f'P'(f) and g'P'(g) share $\alpha$
counting multiplicity, then we show that f=g provided that the multiplicity
order of zeroes of P' satisfy certain inequalities. If $\alpha$ is a Moebius
function or a non-zero constant, we can obtain more general results on P.
|
X-ray images and gas temperatures taken from a deep ~200 ks Chandra
observation of the Centaurus cluster are presented. Multiple inner bubbles and
outer semicircular edges are revealed, together with wispy filaments of soft
X-ray emitting gas. The frothy central structure and eastern edge are likely
due to the central radio source blowing bubbles in the intracluster gas. The
semicircular edges to the surface brightness maps 32kpc to the east and 17.5kpc
to the west are marked by sharp temperature increases and abundance drops. The
edges could be due to sloshing motions of the central potential, or are
possibly enhanced by earlier radio activity. The high abundance of the
innermost gas (about 2.5 times Solar) limits the amount of diffusion and mixing
taking place.
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We discuss in a compact way how the implicit relations between spatiotemporal
relatedness of information items, spatiotemporal relatedness of users, social
relatedness of users and semantic relatedness of information items may be
exploited for an information retrieval architecture that operates along the
lines of human ways of searching. The decentralized and agent oriented
architecture mirrors emerging trends such as upcoming mobile and decentralized
social networking as a new paradigm in social computing and is targetted to
satisfy broader and more subtly interlinked information demands beyond
immediate information needs which can be readily satisfied with current IR
services. We briefly discuss why using spatio-temporal references as primary
information criterion implicitly conserves other relations and is thus suitable
for such an architecture. We finally shortly point to results from a large
evaluation study using Wikipedia articles.
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We study the supersymmetry generators Q, S on the 1-loop vectorless sector of
N=4 Super Yang-Mills, by reduction to the plane-wave matrix model. Using a
coherent basis in the su(2|2) sector, a comparison with the algebra given by
Beisert in nlin/0610017 is presented, and some parameters (up to one-loop) are
determined. We make a final comparison of these supercharges with the results
that can be obtained from the string action by working in the light-cone-gauge
and discretizing the string.
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In these proceedings, we summarise our recent calculations of next-to-leading
order electroweak corrections to Higgs boson pair and Higgs boson plus jet
production. The calculations are divided into different regions. In the
high-energy region, we analytically calculate the Higgs boson contribution to
the leading two-loop Yukawa corrections for $gg\to HH$. These corrections are
generated by a single virtual Higgs boson exchange within the top quark loop.
Our high-energy expansion yields precise predictions for the region where the
Higgs boson transverse momenta $p_T > 120 $ GeV. In the low-energy region, we
compute the complete two-loop electroweak corrections to $gg\to HH$ and $gg \to
gH$. We obtain analytic results through the large top quark mass expansion,
covering all sectors of the Standard Model.
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We consider a model for the evolution of an interface in a heterogeneous
environment governed by a parabolic equation. The heterogeneity is introduced
as obstacles exerting a localized dry friction. Our main result establishes the
emergence of a rate-independent hysteresis for suitable randomly distributed
obstacles, i.e., interfaces are pinned by the obstacles until a certain
critical applied driving force is exceeded. The treatment of such a model in
the context of pinning and depinning requires a comparison principle. We prove
this property and hence the existence of viscosity solutions. Moreover, under
reasonable assumptions, we show that viscosity solutions are equivalent to weak
solutions.
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We combine the DPW method and Opening Nodes to construct embedded surfaces of
positive constant mean curvature with Delaunay ends in euclidean space, with no
limitation to the genus or number of ends.
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Transition-metal compounds represent a fascinating playground for exploring
the intricate relationship between structural distortions, electronic
properties, and magnetic behaviour, holding significant promise for
technological advancements. Among these compounds, YBaCo$_4$O$_{7}$ (Y114) is
attractive due to its manifestation of a ferrimagnetic component at low
temperature intertwined with distortion effect due to the charge
disproportionation on Co ions, exerting profound impact on its magnetic
properties. In this perspective paper, we study the structural and magnetic
intricacies of the Y114 crystal. Traditionally, the investigation of such
materials has relied heavily on computational modelling using
density-functional theory (DFT) with the on-site Coulomb interaction correction
$U$ (DFT+$U$) based on the Hubbard model (sometimes including Hund's exchange
coupling parameter $J$, DFT+$U$+$J$) to unravel their complexities. Herein, we
analysed the spurious effects of magnetic-moment delocalisation and spillover
to non-magnetic ions in the lattice on electronic structure and magnetic
properties of Y114. To overcome this problem we have applied constrained DFT
(cDFT) based on the potential self-consistency approach, and comprehensively
explore the Y114 crystal's characteristics in its ferrimagnetic order. We find
that cDFT yields magnetic moments of Co ions much closer to the experimental
values than LDA+$U$+$J$ with the parameters $U$ and $J$ fitted to reproduce
experimental lattice constants. cDFT allows for an accurate prediction of
magnetic properties using oxidation states of magnetic ions as well-defined
parameters. Through this perspective, we not only enhance our understanding of
the magnetic interactions in Y114 crystal, but also pave the way for future
investigations into magnetic materials.
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We examine the time dependent defect fluctuations and lifetimes for a
bidisperse disordered assembly of Yukawa particles. At high temperatures, the
noise spectrum of fluctuations is white and the coordination number lifetimes
have a stretched exponential distribution. At lower temperatures, the system
dynamically freezes, the defect fluctuations exhibit a 1/f spectrum, and there
is a power law distribution of the coordination number lifetimes. Our results
indicate that topological defect fluctuations may be a useful way to
characterize systems exhibiting dynamical heterogeneities.
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Evolutionary game theory has proven to be an elegant framework providing many
fruitful insights in population dynamics and human behaviour. Here, we focus on
the aspect of behavioural plasticity and its effect on the evolution of
populations. We consider games with only two strategies in both well-mixed
infinite and finite populations settings. We assume that individuals might
exhibit behavioural plasticity referred to as incompetence of players. We study
the effect of such heterogeneity on the outcome of local interactions and,
ultimately, on global competition. For instance, a strategy that was dominated
before can become desirable from the selection perspective when behavioural
plasticity is taken into account. Furthermore, it can ease conditions for a
successful fixation in infinite populations' invasions. We demonstrate our
findings on the examples of Prisoners' Dilemma and Snowdrift game, where we
define conditions under which cooperation can be promoted.
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Social media has become an important channel for publicizing academic
research. Employing a dataset of about 10 million tweets of 584,264 scientific
papers from 2012 to 2018, this study investigates the differential diffusion of
influential and non-influential papers (divided by Average journal impact
factor percentile). We find that non-influential papers shows a diffusion trend
with multiple rounds, sparse, short-duration and small-scale bursts. In
contrast, the bursts of influential journals are characterized by a small
number of persistent, dense and large-scale bursts. Influential papers are
generally disseminated to many loosely connected communities, while
non-influential papers are diffused to several densely connected communities.
|
In a discrete group generated by hyperplane reflections in the
$n$-dimensional hyperbolic space, the reflection length of an element is the
minimal number of hyperplane reflections in the group that suffices to factor
the element. For a Coxeter group that arises in this way and does not split
into a direct product of spherical and affine reflection groups, the reflection
length is unbounded. The action of the Coxeter group induces a tessellation of
the hyperbolic space. After fixing a fundamental domain, there exists a
bijection between the tiles and the group elements. We describe certain points
in the visual boundary of the $n$-dimensional hyperbolic space for which every
neighbourhood contains tiles of every reflection length. To prove this, we show
that two disjoint hyperplanes in the $n$-dimensional hyperbolic space without
common boundary points have a unique common perpendicular.
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Recent observations suggest that $\gamma$-ray bursts (GRBs) and their
afterglows are produced by jets of highly relativistic cannonballs (CBs),
emitted in supernova (SN) explosions. The CBs, reheated by their collision with
the shell, emit radiation that is collimated along their direction of motion
and Doppler-boosted to the typical few-hundred keV energy of the GRB.
Accompanying the GRB, there should be an intense burst of neutrinos of a few
hundreds of GeV energy, made by the decay of charged pions produced in the
collisions of the CBs with the SN shell . The neutrino beam carries almost all
of the emitted energy, but is much narrower than the GRB beam and should only
be detected in coincidence with the small fraction of GRBs whose CBs are moving
very close to the line of sight. The neutral pions made in the transparent
outskirts of the SN shell decay into energetic $\gamma$-rays (EGRs) of energy
of ${\cal{O}}$(100) GeV. The EGR beam, whose energy fluence is comparable to
that of the companion GRB, is as wide as the GRB beam and should be observable,
in coincidence with GRBs, with existing or planned detectors. We derive in
detail these predictions of the CB model.
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We have studied quasielastic charged current hyperon production induced by
$\bar\nu_\mu$ on free nucleon and the nucleons bound inside the nucleus.
The calculations are performed for several nuclear targets like $^{12}C$,
$^{40}Ar$, $^{56}Fe$ and $^{208}Pb$ which are presently being used in various
oscillation experiments using accelerator neutrinos. The inputs are the
hyperon-nucleon transition form factors determined from neutrino-nucleon
scattering as well as from semileptonic decays of neutron and hyperons using
SU(3) symmetry. The calculations for the nuclear targets are done in local
density approximation. The nuclear medium effects(NME) due to Fermi motion and
final state interaction(FSI) effect due to hyperon-nucleon scattering have been
taken into account.
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We give a proof of the openness conjecture of Demailly and Koll\'ar for
positively curved singular metrics on ample line bundles over projective
varieties. As a corollary it follows that the openness conjecture for
plurisubharmonic functions with isolated sigularities holds.
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Incremental learning methods can learn new classes continually by distilling
knowledge from the last model (as a teacher model) to the current model (as a
student model) in the sequentially learning process. However, these methods
cannot work for Incremental Implicitly-Refined Classification (IIRC), an
incremental learning extension where the incoming classes could have two
granularity levels, a superclass label and a subclass label. This is because
the previously learned superclass knowledge may be occupied by the subclass
knowledge learned sequentially. To solve this problem, we propose a novel
Multi-Teacher Knowledge Distillation (MTKD) strategy. To preserve the subclass
knowledge, we use the last model as a general teacher to distill the previous
knowledge for the student model. To preserve the superclass knowledge, we use
the initial model as a superclass teacher to distill the superclass knowledge
as the initial model contains abundant superclass knowledge. However,
distilling knowledge from two teacher models could result in the student model
making some redundant predictions. We further propose a post-processing
mechanism, called as Top-k prediction restriction to reduce the redundant
predictions. Our experimental results on IIRC-ImageNet120 and IIRC-CIFAR100
show that the proposed method can achieve better classification accuracy
compared with existing state-of-the-art methods.
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We investigate the Kerr and magneto-optical effects for a probe laser field
with two orthogonally polarized components, propagating in a cold Rydberg
atomic gas with an inverted-Y-type level configuration via double
electromagnetically induced transparency (EIT). Through an approach beyond both
mean-field and ground-state approximations, we make detailed calculations on
third-order nonlinear optical susceptibilities and show that the system
possesses giant nonlocal selfand cross-Kerr nonlinearities contributed by
Rydberg-Rydberg interaction. The theoretical result of the cross-Kerr
nonlinearity obtained for 85Rb atomic gas is very close to the experimental one
reported recently. Moreover, we demonstrate that the probe laser field can
acquire a very large magnetooptical rotation via the double EIT, which may be
used to design atomic magnetometers with high precision. The results presented
here are promising not only for the development of nonlocal nonlinear
magneto-optics but also for applications in precision measurement and optical
information processing and transmission based on Rydberg atomic gases.
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Planar superconducting junctions with a large effective Josephson coupling
constant and a pronounced interface pair breaking are shown to represent weak
links with small critical currents and strongly anharmonic current-phase
relations. The supercurrent near Tc is described taking into account the
interface pair breaking as well as the current depairing and the Josephson
coupling-induced pair breaking of arbitrary strengths. A new analytical
expression for the anharmonic supercurrent, which is in excellent agreement
with the numerical data presented, is obtained. In junctions with a large
effective Josephson coupling constant and a pronounced interface pair breaking,
the current-induced depairing is substantially enhanced in the vicinity of the
interface thus having a crucial influence on the current-phase relation despite
a small depairing in the bulk.
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A differential calculus on Cuntz algebra with three generators coming from
the action of rotation group in three dimensions is introduced. The
differential calculus is shown to satisfy Assumptions I-IV of [1] so that
Levi-Civita Connection exists uniquely for any pseudo-Riemannian metric in the
sense of [1]. Scalar curvature is computed for the Levi-Civita connection
corresponding to the canonical bilinear metric.
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We discuss systems which have some, but not all of the hallmarks of
topological phases. These systems' topological character is not fully captured
by a local order parameter, but they are also not fully described at low
energies by topological quantum field theories. For such systems, we formulate
the concepts of quasi-topological phases (to be contrasted with true
topological phases), and symmetry-protected quasi-topological phases. We
describe examples of systems in each class and discuss the implications for
topological protection of information and operations. We explain why
topological phases and quasi-topological phases have greater stability than is
sometimes appreciated. In the examples that we discuss, we focus on Ising-type
(a.k.a. Majorana) systems particularly relevant to recent theoretical advances
and experimental efforts.
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While synthesizing the single crystals of novel materials is not always
feasible, orienting the layered polycrystals becomes an attractive method in
the studies of angular dependencies of inelastic scattering of x-rays or
neutrons. Putting in use the Rietveld analysis of layered structures in novel
manganites and cuprates we develop the studies of their anisotropic properties
with oriented powders instead of single crystals. Densities of phonon states
(DOS) and atomic thermal displacememts (ATD) are anisotropic in the A-site
ordered manganites LnBaMn2Oy of both y=5 and y=6 series (Ln=Y, La, Sm, Gd). We
establish the angular dependence of DOS on textures of arbitrary strengths,
link the textures observed by x-ray and gamma-ray techniques, and solve the
problem of disentanglement of Goldanskii-Karyagin effect (GKE) and texture in
Moessbauer spectra.
|
Frequency-domain expressions are found for gradiometer and
satellite-to-satellite tracking measurements of a point source on the surface
of the Earth. The maximum signal-to-noise ratio as a function of noise in the
measurement apparatus is computed, and from that the minimum detectable point
mass is inferred. A point mass of magnitude M_3=100 Gt gives a signal-to-noise
ratio of 3 when a GOCE-like gradiometer passes directly over the mass. On the
satellite-to-satellite tracking mission GRACE-FO M_3=1.3 Gt for the microwave
instrument and M_3=0.5 Gt for the laser ranging interferometer. The sensitivity
of future GRACE-like missions with different orbital parameters and improved
accelerometer sensitivity is explored, and the optimum spacecraft separation
for detecting point-like sources is found. The future-mission benefit of
improving the accelerometer sensitivity for measurement of non-gravitational
disturbances is shown by the resulting reduction of M_3 to as small as 7 Mt for
500 km orbital altitude and optimized satellite separation of 900 km.
|
The effect of the symmetry energy on the properties of compact stars is
discussed. It is shown that, for stars with masses above 1 $M_\odot$, the
radius of the star varies linearly with the symmetry energy slope $L$. The
dependence of the hyperon content and onset density of the direct Urca process
on the symmetry energy and meson coupling parametrization are also analyzed.
|
A quasi-free quantum particle endowed with Heaviside position dependent mass
jump is observed to experience scattering effects manifested by its by-product
introduction of the derivative of the Dirac's-delta point dipole interaction.
Using proper parametric mappings, the reflection and transmission coefficients
are obtained. A new ordering ambiguity parameters set, as the only feasibly
admissible within the current methodical proposal, is suggested.
|
Neural compression algorithms are typically based on autoencoders that
require specialized encoder and decoder architectures for different data
modalities. In this paper, we propose COIN++, a neural compression framework
that seamlessly handles a wide range of data modalities. Our approach is based
on converting data to implicit neural representations, i.e. neural functions
that map coordinates (such as pixel locations) to features (such as RGB
values). Then, instead of storing the weights of the implicit neural
representation directly, we store modulations applied to a meta-learned base
network as a compressed code for the data. We further quantize and entropy code
these modulations, leading to large compression gains while reducing encoding
time by two orders of magnitude compared to baselines. We empirically
demonstrate the feasibility of our method by compressing various data
modalities, from images and audio to medical and climate data.
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We investigate the dynamics of Rydberg electrons excited from the ground
state of ultracold atoms trapped in an optical lattice. We first consider a
lattice comprising an array of double-well potentials, where each double well
is occupied by two ultracold atoms. We demonstrate the existence of molecular
states with equilibrium distances of the order of experimentally attainable
inter-well spacings and binding energies of the order of 10^3 GHz. We also
consider the situation whereby ground-state atoms trapped in an optical lattice
are collectively excited to Rydberg levels, such that the charge-density
distributions of neighbouring atoms overlap. We compute the hopping rate and
interaction matrix elements between highly-excited electrons separated by
distances comparable to typical lattice spacings. Such systems have tunable
interaction parameters and a temperature ~10^{-4} times smaller than the Fermi
temperature, making them potentially attractive for the study and simulation of
strongly correlated electronic systems.
|
Oscillating integrals often arise in the theoretical description of phenomena
in chemical physics, in particular in atomic and molecular collisions, and in
spectroscopy. A computer code for the numerical evaluation of the oscillatory
cuspoid canonical integrals and their first-order partial derivatives is
described. The code uses a novel adaptive contour algorithm, which chooses a
contour in the complex plane that avoids the violent oscillatory and
exponential natures of the integrand and modifies its choice as necessary.
Applications are made to the swallowtail canonical integral and to a bessoid
integral.
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Agile software development is nowadays a widely adopted practise in both
open-source and industrial software projects. Agile teams typically heavily
rely on issue management tools to document new issues and keep track of
outstanding ones, in addition to storing their technical details, effort
estimates, assignment to developers, and more. Previous work utilised the
historical information stored in issue management systems for various purposes;
however, when researchers make their empirical data public, it is usually
relevant solely to the study's objective. In this paper, we present a more
holistic and versatile dataset containing a wealth of information on more than
500,000 issues from 44 open-source Agile software, making it well-suited to
several research avenues, and cross-analyses therein, including effort
estimation, issue prioritization, issue assignment and many more. We make this
data publicly available on GitHub to facilitate ease of use, maintenance, and
extensibility.
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Communication at high carrier frequencies such as millimeter wave (mmWave)
and terahertz (THz) requires channel estimation for very large bandwidths at
low SNR. Hence, allocating an orthogonal pilot tone for each coherence
bandwidth leads to excessive number of pilots. We leverage generative
adversarial networks (GANs) to accurately estimate frequency selective channels
with few pilots at low SNR. The proposed estimator first learns to produce
channel samples from the true but unknown channel distribution via training the
generative network, and then uses this trained network as a prior to estimate
the current channel by optimizing the network's input vector in light of the
current received signal. Our results show that at an SNR of -5 dB, even if a
transceiver with one-bit phase shifters is employed, our design achieves the
same channel estimation error as an LS estimator with SNR = 20 dB or the LMMSE
estimator at 2.5 dB, both with fully digital architectures. Additionally, the
GAN-based estimator reduces the required number of pilots by about 70% without
significantly increasing the estimation error and required SNR. We also show
that the generative network does not appear to require retraining even if the
number of clusters and rays change considerably.
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The dispersion surfaces of printed periodic structures in layered media are
efficiently computed using a full-wave method based on the periodic Method of
Moments (MoM). The geometry of the dispersion surface is estimated after
mapping the determinant of the periodic MoM impedance matrix over a range of
frequencies and impressed phase shifts. For lossless periodic structures in the
long-wavelength regime, such as lossless metasurfaces, a tracking algorithm is
proposed to represent the dispersion surface as a superposition of
parameterized iso-frequency curves. The mapping process of the determinant is
accelerated using a specialized interpolation technique with respect to the
frequency and impressed phase shifts. The algorithm combines a fast evaluation
of the rapidly varying part of the periodic impedance matrix and the
interpolation of the computationally intensive but slowly varying remainder.
The mapping is further accelerated through the use of Macro basis functions
(MBFs). The method has been first tested on lossless metasurface-type
structures and validated using the commercial software CST. The specialized
technique enables a drastic reduction of the number of periodic impedance
matrices that needs to be explicitly computed. In the two examples considered,
only 12 matrices are required to cover any phase shift and a frequency band
larger than one octave. An important advantage of the proposed method is that
it does not entail any approximation, so that it can be used for lossy
structure and leaky waves, as demonstrated through two additional examples.
|
We reconsider the problem of the birefringence of electromagnetic (EM) waves
in a medium consisting of a plasma and a $\nu\bar{\nu}$-gas within the Standard
Model of particle physics. The considered effect arises in such a medium due to
the parity violation for the electroweak neutrino-electron interaction. Our
recent calculations of the electroweak correction to the photon polarization
operator in the electroweak plasma allow us to significantly improve some
previous estimates of such effect in astrophysics. We estimate the rotary power
for EM waves propagating in a non-relativistic plasma in the intergalactic
space and interacting with the gas of relic neutrinos and antineutrinos there.
We show that, in presence of a plasma, the EM wave birefringence effect in a
$\nu\bar{\nu}$-gas exceeds significantly that effect in a $\nu\bar{\nu}$-gas in
empty space considered earlier. These previous treatments of the birefringence
relied on the calculations of the refraction index for on-shell photons in
vacuum using the forward scattering amplitude $\gamma\nu\to \gamma\nu$ with
virtual charged leptons in Feynman diagrams. The possibility to observe
experimentally the new effect suggested here is discussed.
|
We establish a local null controllability result for following the nonlinear
parabolic equation: $$u_t-\left(b\left(x,\int_0^1u \ \right)u_x
\right)_x+f(t,x,u)=h\chi_\omega,\ (t,x)\in (0,T)\times (0,1) $$ where
$b(x,r)=\ell(r)a(x)$ is a function with separated variables that defines an
operator which degenerates at $x=0$ and has a nonlocal term. Our approach
relies on an application of Liusternik's inverse mapping theorem that demands
the proof of a suitable Carleman estimate.
|
Ill-conditioning of the system matrix is a well-known complication in
immersed finite element methods and trimmed isogeometric analysis. Elements
with small intersections with the physical domain yield problematic eigenvalues
in the system matrix, which generally degrades efficiency and robustness of
iterative solvers. In this contribution we investigate the spectral properties
of immersed finite element systems treated by Schwarz-type methods, to
establish the suitability of these as smoothers in a multigrid method. Based on
this investigation we develop a geometric multigrid preconditioner for immersed
finite element methods, which provides mesh-independent and
cut-element-independent convergence rates. This preconditioning technique is
applicable to higher-order discretizations, and enables solving large-scale
immersed systems in parallel, at a computational cost that scales linearly with
the number of degrees of freedom. The performance of the preconditioner is
demonstrated for conventional Lagrange basis functions and for isogeometric
discretizations with both uniform B-splines and locally refined approximations
based on truncated hierarchical B-splines.
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Cosmic shear is one of the primary probes to test gravity with current and
future surveys. There are two main techniques to analyse a cosmic shear survey;
a tomographic method, where correlations between the lensing signal in
different redshift bins are used to recover redshift information, and a 3D
approach, where the full redshift information is carried through the entire
analysis. Here we compare the two methods, by forecasting cosmological
constraints for future surveys like Euclid. We extend the 3D formalism for the
first time to theories beyond the standard model, belonging to the Horndeski
class. This includes the majority of universally coupled extensions to
$\Lambda$CDM with one scalar degree of freedom in addition to the metric, still
in agreement with current observations. Given a fixed background, the evolution
of linear perturbations in Horndeski gravity is described by a set of four
functions of time only. We model their time evolution assuming proportionality
to the dark energy density fraction and place Fisher matrix constraints on the
proportionality coefficients. We find that a 3D analysis can constrain
Horndeski theories better than a tomographic one, in particular with a decrease
in the errors of the order of 20$\%$. This paper shows for the first time a
quantitative comparison on an equal footing between Fisher matrix forecasts for
both a fully 3D and a tomographic analysis of cosmic shear surveys. The
increased sensitivity of the 3D formalism comes from its ability to retain
information on the source redshifts along the entire analysis.
|
High-throughput data analyses are becoming common in biology, communications,
economics and sociology. The vast amounts of data are usually represented in
the form of matrices and can be considered as knowledge networks. Spectra-based
approaches have proved useful in extracting hidden information within such
networks and for estimating missing data, but these methods are based
essentially on linear assumptions. The physical models of matching, when
applicable, often suggest non-linear mechanisms, that may sometimes be
identified as noise. The use of non-linear models in data analysis, however,
may require the introduction of many parameters, which lowers the statistical
weight of the model. According to the quality of data, a simpler linear
analysis may be more convenient than more complex approaches.
In this paper, we show how a simple non-parametric Bayesian model may be used
to explore the role of non-linearities and noise in synthetic and experimental
data sets.
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In this paper, we consider the distributed filtering problem over sensor
networks such that all sensors cooperatively track unknown time-varying
parameters by using local information. A distributed forgetting factor least
squares (FFLS) algorithm is proposed by minimizing a local cost function
formulated as a linear combination of accumulative estimation error. Stability
analysis of the algorithm is provided under a cooperative excitation condition
which contains spatial union information to reflect the cooperative effect of
all sensors. Furthermore, we generalize theoretical results to the case of
Markovian switching directed graphs. The main difficulties of theoretical
analysis lie in how to analyze properties of the product of non-independent and
non-stationary random matrices. Some techniques such as stability theory,
algebraic graph theory and Markov chain theory are employed to deal with the
above issue. Our theoretical results are obtained without relying on the
independency or stationarity assumptions of regression vectors which are
commonly used in existing literature.
|
We study the geometry of the space of measures of a compact ultrametric space
X, endowed with the L^p Wasserstein distance from optimal transportation. We
show that the power p of this distance makes this Wasserstein space affinely
isometric to a convex subset of l^1. As a consequence, it is connected by
1/p-H\"older arcs, but any a-H\"older arc with a>1/p must be constant. This
result is obtained via a reformulation of the distance between two measures
which is very specific to the case when X is ultrametric; howeverthanks to the
Mendel-Naor Ultrametric Skeleton it has consequences even when X is a general
compact metric space. More precisely, we use it to estimate the size of
Wasserstein spaces, measured by an analogue of Hausdorff dimension that is
adapted to (some) infinite-dimensional spaces. The result we get generalizes
greatly our previous estimate that needed a strong rectifiability assumption.
The proof of this estimate involves a structural theorem of independent
interest: every ultrametric space contains large co-Lipschitz images of
\emph{regular} ultrametric spaces, i.e. spaces of the form {1,...,k}^N with a
natural ultrametric. We are also lead to an example of independent interest: a
space of positive lower Minkowski dimension, all of whose proper closed subsets
have vanishing lower Minkowski dimension.
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In this paper, we study the problem of optimal data collection for policy
evaluation in linear bandits. In policy evaluation, we are given a target
policy and asked to estimate the expected reward it will obtain when executed
in a multi-armed bandit environment. Our work is the first work that focuses on
such optimal data collection strategy for policy evaluation involving
heteroscedastic reward noise in the linear bandit setting. We first formulate
an optimal design for weighted least squares estimates in the heteroscedastic
linear bandit setting that reduces the MSE of the value of the target policy.
We then use this formulation to derive the optimal allocation of samples per
action during data collection. We then introduce a novel algorithm SPEED
(Structured Policy Evaluation Experimental Design) that tracks the optimal
design and derive its regret with respect to the optimal design. Finally, we
empirically validate that SPEED leads to policy evaluation with mean squared
error comparable to the oracle strategy and significantly lower than simply
running the target policy.
|
Recent results reported in Science by Schon et al. using field-effect doping
to study ladders and fullerenes are here described.
|
Recent advancements in Natural Language Processing (NLP), particularly in
Large Language Models (LLMs), associated with deep learning-based computer
vision techniques, have shown substantial potential for automating a variety of
tasks. One notable model is Visual ChatGPT, which combines ChatGPT's LLM
capabilities with visual computation to enable effective image analysis. The
model's ability to process images based on textual inputs can revolutionize
diverse fields. However, its application in the remote sensing domain remains
unexplored. This is the first paper to examine the potential of Visual ChatGPT,
a cutting-edge LLM founded on the GPT architecture, to tackle the aspects of
image processing related to the remote sensing domain. Among its current
capabilities, Visual ChatGPT can generate textual descriptions of images,
perform canny edge and straight line detection, and conduct image segmentation.
These offer valuable insights into image content and facilitate the
interpretation and extraction of information. By exploring the applicability of
these techniques within publicly available datasets of satellite images, we
demonstrate the current model's limitations in dealing with remote sensing
images, highlighting its challenges and future prospects. Although still in
early development, we believe that the combination of LLMs and visual models
holds a significant potential to transform remote sensing image processing,
creating accessible and practical application opportunities in the field.
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In this paper we give a linear time algorithm for computing the number of
spanninig trees in double nested graphs.
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Non-Markovian quantum processes exhibit different memory effects when
measured in different ways; an unambiguous characterization of memory length
requires accounting for the sequence of instruments applied to probe the system
dynamics. This instrument-specific notion of quantum Markov order displays
stark differences to its classical counterpart. Here, we explore the structure
of quantum stochastic processes with finite length memory in detail. We begin
by examining a generalized collision model with memory, before framing this
instance within the general theory. We detail the constraints that are placed
on the underlying system-environment dynamics for a process to exhibit finite
Markov order with respect to natural classes of probing instruments, including
deterministic (unitary) operations and sequences of generalized quantum
measurements with informationally-complete preparations. Lastly, we show how
processes with vanishing quantum conditional mutual information form a special
case of the theory. Throughout, we provide a number of representative,
pedagogical examples to display the salient features of memory effects in
quantum processes.
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In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR)
seeks to optimize the reward obtained by sensing an underlying $N$ dimensional
random vector, by collecting at most $K$ arbitrary projections of it. The $N$
components of the latent vector represent sub-channels states, that change
dynamically from "busy" to "idle" and vice versa, as a Markov chain that is
biased towards producing sparse vectors. To identify the optimal strategy we
formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem,
generalizing the popular Cognitive Spectrum Sensing model, in which the CR can
sense $K$ out of the $N$ sub-channels, as well as the typical static setting of
Compressive Sensing, in which the CR observes $K$ linear combinations of the
$N$ dimensional sparse vector. The CR opportunistic choice of the sensing
matrix should balance the desire of revealing the state of as many dimensions
of the latent vector as possible, while not exceeding the limits beyond which
the vector support is no longer uniquely identifiable.
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In this paper, we expand the methodology presented in Mertens et. al (2020,
Biometrical Journal) to the study of life-time (survival) outcome which is
subject to censoring and when imputation is used to account for missing values.
We consider the problem where missing values can occur in both the calibration
data as well as newly - to-be-predicted - observations (validation). We focus
on the Cox model. Methods are described to combine imputation with predictive
calibration in survival modeling subject to censoring. Application to
cross-validation is discussed. We demonstrate how conclusions broadly confirm
the first paper which restricted to the study of binary outcomes only.
Specifically prediction-averaging appears to have superior statistical
properties, especially smaller predictive variation, as opposed to a direct
application of Rubin's rules. Distinct methods for dealing with the baseline
hazards are discussed when using Rubin's rules-based approaches.
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We experimentally demonstrate the orbital angular momentum (OAM) conversion
by the coupled nonlinear optical processes in a quasi-periodically poled LiTaO3
crystal. In such crystal, third-harmonic generation (THG) is realized by the
coupled second-harmonic generation (SHG) and sum-frequency generation (SFG)
processes, i.e., SHG is dependent on SFG and vice versa. The OAMs of the
interacting waves are proved to be conserved in such coupled nonlinear optical
processes. As increasing the input OAM in the experiment, the conversion
efficiency decreases because of the reduced fundamental power intensity. Our
results provide better understanding for the OAM conversions, which can be used
to efficiently produce an optical OAM state at a short wavelength.
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I show that the dynamical determinant, associated to an Anosov
diffeomorphism, is the Fredholm determinant of the corresponding
Ruelle-Perron-Frobenius transfer operator acting on appropriate Banach spaces.
As a consequence it follows, for example, that the zeroes of the dynamical
determinant describe the eigenvalues of the transfer operator and the Ruelle
resonances and that, for $\Co^\infty$ Anosov diffeomorphisms, the dynamical
determinant is an entire function.
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In this paper, we prove four-moment theorems for multidimensional free
Poisson limits on free Wigner chaos or the free Poisson algebra. We prove that,
under mild technical conditions, a bi-indexed sequence of free stochastic
integrals in free Wigner algebra or free Poisson algebra converges to a free
sequence of free Poisson random variables if and only if the moments with order
not greater than four of the sequence converge to the corresponding moments of
the limit sequence of random variables. Similar four-moment theorems hold when
the limit sequence is not free, but has a multidimensional free Poisson
distribution with parameters $\lambda>0$ and $\alpha=\{\alpha_i: 0\ne
\alpha_i\in \mathbb{R}, i=1, 2, \cdots\}$.
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Artificial reverberation (AR) models play a central role in various audio
applications. Therefore, estimating the AR model parameters (ARPs) of a
reference reverberation is a crucial task. Although a few recent
deep-learning-based approaches have shown promising performance, their
non-end-to-end training scheme prevents them from fully exploiting the
potential of deep neural networks. This motivates the introduction of
differentiable artificial reverberation (DAR) models, allowing loss gradients
to be back-propagated end-to-end. However, implementing the AR models with
their difference equations "as is" in the deep learning framework severely
bottlenecks the training speed when executed with a parallel processor like GPU
due to their infinite impulse response (IIR) components. We tackle this problem
by replacing the IIR filters with finite impulse response (FIR) approximations
with the frequency-sampling method. Using this technique, we implement three
DAR models -- differentiable Filtered Velvet Noise (FVN), Advanced Filtered
Velvet Noise (AFVN), and Delay Network (DN). For each AR model, we train its
ARP estimation networks for analysis-synthesis (RIR-to-ARP) and blind
estimation (reverberant-speech-to-ARP) task in an end-to-end manner with its
DAR model counterpart. Experiment results show that the proposed method
achieves consistent performance improvement over the non-end-to-end approaches
in both objective metrics and subjective listening test results.
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We present the systematic-error study of the neutrino flux in the NO{\nu}A
experiment. Systematic errors on the flux at the near detector (ND), far
detector (FD), and the ratio FD/ND, due to the beam-transport and
hadro-production are estimated. Prospects of constraining the {\nu}{\mu} and
{\nu}e flux using data from ND are outlined.
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The recent experiments reported by Borisenko et al. (cond-mat/0305179 v2),
are examined in light of the conditions to be satisfied in the search for
time-reversal violation by circularly polarized ARPES. Two principal problems
are found: (1) A lack of any evidence for the magnitude of the pseudogap or the
temperature of its onset in the samples studied. (2) A difference in the
dichroic signal at low and high temperatures. The difference is greater than
the stated error bars and is contrary to the conclusions reached in the paper.
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Many one--dimensional quantum systems, in particular interacting electron and
spin systems, can be described a Luttinger liquids. Here, some basic ideas of
this picture of one--dimensional systems are briefly reviewed. I then discuss
the effect of interchain coupling for a finite number of parallel chains. In
the case of spin chains coupled by exchange interactions, the low--energy
properties are radically different according to whether the number of coupled
chains is even or odd: even number of chains have a gap in the spin
excitations, whereas odd numbers of chains are gapless. The effect of
interchain tunneling is analyzed for two and three coupled chains of itinerant
fermions: for repulsive interactions, the two--chain system is ``universally''
found to be a d--wave superconductor, with a gap in the spin excitation
spectrum. On the other hand, for three chains the ground state depends both on
the boundary conditions in the transverse direction and on the strength of the
interactions. Weak repulsive interactions in all cases lead to dominant
superconducting pairing of d--type. An example of a three--leg spin ladder with
a spin gap is proposed. A general scheme to keep track of fermion
anticommutation in the bosonization technique is developed.
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The cosmic web is a highly complex geometrical pattern, with galaxy clusters
at the intersection of filaments and filaments at the intersection of walls.
Identifying and describing the filamentary network is not a trivial task due to
the overwhelming complexity of the structure, its connectivity and the
intrinsic hierarchical nature. To detect and quantify galactic filaments we use
the Bisous model, which is a marked point process built to model
multi-dimensional patterns. The Bisous filament finder works directly with the
galaxy distribution data and the model intrinsically takes into account the
connectivity of the filamentary network. The Bisous model generates the visit
map (the probability to find a filament at a given point) together with the
filament orientation field. Using these two fields, we can extract filament
spines from the data. Together with this paper we publish the computer code for
the Bisous model that is made available in GitHub. The Bisous filament finder
has been successfully used in several cosmological applications and further
development of the model will allow to detect the filamentary network also in
photometric redshift surveys, using the full redshift posterior. We also want
to encourage the astro-statistical community to use the model and to connect it
with all other existing methods for filamentary pattern detection and
characterisation.
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As deep neural models in NLP become more complex, and as a consequence
opaque, the necessity to interpret them becomes greater. A burgeoning interest
has emerged in rationalizing explanations to provide short and coherent
justifications for predictions. In this position paper, we advocate for a
formal framework for key concepts and properties about rationalizing
explanations to support their evaluation systematically. We also outline one
such formal framework, tailored to rationalizing explanations of increasingly
complex structures, from free-form explanations to deductive explanations, to
argumentative explanations (with the richest structure). Focusing on the
automated fact verification task, we provide illustrations of the use and
usefulness of our formalization for evaluating explanations, tailored to their
varying structures.
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Results on dissipative isoscalar modes of a hot and dilute nuclear droplet
are presented. As compared to the adiabatic limit (part I), realistic
dissipation yields a substantial reduction of the growth rates for all unstable
modes, while the area of spinodal instability in the ($\varrho$,T)-plane
remains unchanged. The qualitative features of multifragmentation through
spinodal decomposition as obtained in the adiabatic limit are not significantly
affected by dissipation.
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Semi-labeled trees are phylogenies whose internal nodes may be labeled by
higher-order taxa. Thus, a leaf labeled Mus musculus could nest within a
subtree whose root node is labeled Rodentia, which itself could nest within a
subtree whose root is labeled Mammalia. Suppose we are given collection
$\mathcal P$ of semi-labeled trees over various subsets of a set of taxa. The
ancestral compatibility problem asks whether there is a semi-labeled tree
$\mathcal T$ that respects the clusterings and the ancestor/descendant
relationships implied by the trees in $\mathcal P$. We give a
$\tilde{O}(M_{\mathcal{P}})$ algorithm for the ancestral compatibility problem,
where $M_{\mathcal{P}}$ is the total number of nodes and edges in the trees in
$\mathcal P$. Unlike the best previous algorithm, the running time of our
method does not depend on the degrees of the nodes in the input trees.
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This article presents a holistic compound Poisson regression model framework
to forecast number of corner kicks taken in association football. Corner kick
taken events are often decisive in the match outcome and inherently arrive in
batch with serial clustering pattern. Providing parameter estimates with
intuitive interpretation, a class of compound Poisson regression including a
Bayesian implementation of geometric-Poisson distribution is introduced. With a
varying shape parameter, the corner counts serial correlation between matches
is handled naturally within the Bayesian model. In this study, information
elicited from cross-market betting odds was used to improve the model
predictability. Margin application methods to adjust market inefficiency in raw
odds are also discussed.
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Minimum Bisection denotes the NP-hard problem to partition the vertex set of
a graph into two sets of equal sizes while minimizing the width of the
bisection, which is defined as the number of edges between these two sets. We
first consider this problem for trees and prove that the minimum bisection
width of every tree $T$ on $n$ vertices satisfies $MinBis(T) \leq 8 n \Delta(T)
/ diam(T)$. Second, we generalize this to arbitrary graphs with a given tree
decomposition $(T,X)$ and give an upper bound on the minimum bisection width
that depends on the structure of $(T,X)$. Moreover, we show that a bisection
satisfying our general bound can be computed in time proportional to the
encoding length of the tree decomposition when the latter is provided as input.
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Until recently, uncertainty quantification in low energy nuclear theory was
typically performed using frequentist approaches. However in the last few
years, the field has shifted toward Bayesian statistics for evaluating
confidence intervals. Although there are statistical arguments to prefer the
Bayesian approach, no direct comparison is available. In this work, we compare,
directly and systematically, the frequentist and Bayesian approaches to
quantifying uncertainties in direct nuclear reactions. Starting from identical
initial assumptions, we determine confidence intervals associated with the
elastic and the transfer process for both methods, which are evaluated against
data via a comparison of the empirical coverage probabilities. Expectedly, the
frequentist approach is not as flexible as the Bayesian approach in exploring
parameter space and often ends up in a different minimum. We also show that the
two methods produce significantly different correlations. In the end, the
frequentist approach produces significantly narrower uncertainties on the
considered observables than the Bayesian. Our study demonstrates that the
uncertainties on the reaction observables considered here within the Bayesian
approach represent reality more accurately than the much narrower uncertainties
obtained using the standard frequentist approach.
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We present the generalized quasiclassical theory of the long-range
superconducting proximity effect in heterostructures with strong ferromagnets,
where the exchange splitting is of the order of Fermi energy. In the
ferromagnet the propagation of spin-triplet Cooper pairs residing on the
spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian
gauge field which results either from the spin-orbital coupling or from the
magnetic texture. The additional gauge field enters into the quasiclassical
equations in superposition with the usual electromagnetic vector potential and
results in the generation of spontaneous superconducting currents and phase
shifts in various geometries which provide the sources of long-range
spin-triplet correlations. We derive the Usadel equations and boundary
conditions for the strong ferromagnet and consider several generic examples of
the Josephson systems supporting spontaneous currents.
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Non-critical string cosmologies may be viewed as the analogue of
off-equilibrium models arising within string theory as a result of a cosmically
catastrophic event in the early Universe. Such models entail relaxing-to-zero
dark energies provided by a rolling dilaton field at late times. We discuss
fits of such non-critical models to high-redshift supernovae data, including
the recent ones by HST and ESSENCE and compare the results with those of a
conventional model with Cold Dark Matter and a cosmological constant and a
model invoking super-horizon perturbations.
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Neurodevelopmental disorders (NDD), encompassing conditions like Intellectual
Disability, Attention Deficit Hyperactivity Disorder, and Autism Spectrum
Disorder, present challenges across various cognitive capacities. Attention
deficits are often common in individuals with NDD due to the sensory system
dysfunction that characterizes these disorders. Consequently, limited attention
capability can affect the overall quality of life and the ability to transfer
knowledge from one circumstance to another. The literature has increasingly
recognized the potential benefits of virtual reality (VR) in supporting NDD
learning and rehabilitation due to its interactive and engaging nature, which
is critical for consistent practice. In previous studies, we explored the usage
of a VR application called Wildcard to enhance attention skills in persons with
NDD. The application has been redesigned in this study, exploiting eye-tracking
technology to enable novel and more fine-grade interactions. A four-week
experiment with 38 NDD participants was conducted to evaluate its usability and
effectiveness in improving Visual Attention Skills. Results show the usability
and effectiveness of Wildcard in enhancing attention skills, advocating for
continued exploration of VR and eye-tracking technology's potential in NDD
interventions.
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We formulate Dirac fermions on a (1+1)-dimensional lattice based on a
Hamiltonian formalism. The species doubling problem of the lattice fermion is
resolved by introducing hopping interactions that mix left- and right-handed
fermions around the momentum boundary. Approximate chiral symmetry is realized
on the lattice. The deviation of the fermion propagator from the continuum one
is small.
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This study proposes a data condensation method for multivariate kernel
density estimation by genetic algorithm. First, our proposed algorithm
generates multiple subsamples of a given size with replacement from the
original sample. The subsamples and their constituting data points are regarded
as $\it{chromosome}$ and $\it{gene}$, respectively, in the terminology of
genetic algorithm. Second, each pair of subsamples breeds two new subsamples,
where each data point faces either $\it{crossover}$, $\it{mutation}$, or
$\it{reproduction}$ with a certain probability. The dominant subsamples in
terms of fitness values are inherited by the next generation. This process is
repeated generation by generation and brings the sparse representation of
kernel density estimator in its completion. We confirmed from simulation
studies that the resulting estimator can perform better than other well-known
density estimators.
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We study a new variant of the vehicle routing problem, called the Mobile
Production Vehicle Routing Problem (MoP-VRP). In this problem, vehicles are
equipped with 3D printers, and production takes place on the way to the
customer. The objective is to minimize the weighted cost incurred by travel and
delay of service. We formulate a Mixed Integer Programming (MIP) model and
develop an Adaptive Large Neighbourhood Search (ALNS) heuristic for this
problem. To show the advantage of mobile production, we compare the problem
with the Central Production Vehicle Routing Problem (CP-VRP), where production
takes place in a central depot. We also propose an efficient ALNS for the
CP-VRP. We generate benchmark instances based on Vehicle Routing Problem with
Time Windows (VRPTW) benchmark instances, and realistic instances based on
real-life data provided by the Danish Company 3D Printhuset. Overall, the
proposed ALNS for both problems are efficient, and we solve instances up to 200
customers within a short computational time. We test different scenarios with
varying numbers of machines in each vehicle, as well as different production
time. The results show that these are the key factors that influence travel and
delay costs. The key advantage of mobile production is flexibility: it can
shorten the time span from the start of production to the delivery of products,
and at the same time lower delivery costs. Moreover, long-term cost estimations
show that this technology has low operation costs and thus is feasible in real
life practice.
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We study the Minimum Crossing Number problem: given an $n$-vertex graph $G$,
the goal is to find a drawing of $G$ in the plane with minimum number of edge
crossings. This is one of the central problems in topological graph theory,
that has been studied extensively over the past three decades. The first
non-trivial efficient algorithm for the problem, due to Leighton and Rao,
achieved an $O(n\log^4n)$-approximation for bounded degree graphs. This
algorithm has since been improved by poly-logarithmic factors, with the best
current approximation ratio standing on $O(n \poly(d) \log^{3/2}n)$ for graphs
with maximum degree $d$. In contrast, only APX-hardness is known on the
negative side.
In this paper we present an efficient randomized algorithm to find a drawing
of any $n$-vertex graph $G$ in the plane with $O(OPT^{10}\cdot \poly(d \log
n))$ crossings, where $OPT$ is the number of crossings in the optimal solution,
and $d$ is the maximum vertex degree in $G$. This result implies an
$\tilde{O}(n^{9/10} \poly(d))$-approximation for Minimum Crossing Number, thus
breaking the long-standing $\tilde{O}(n)$-approximation barrier for
bounded-degree graphs.
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Most novel view synthesis methods such as NeRF are unable to capture the true
high dynamic range (HDR) radiance of scenes since they are typically trained on
photos captured with standard low dynamic range (LDR) cameras. While the
traditional exposure bracketing approach which captures several images at
different exposures has recently been adapted to the multi-view case, we find
such methods to fall short of capturing the full dynamic range of indoor
scenes, which includes very bright light sources. In this paper, we present
PanDORA: a PANoramic Dual-Observer Radiance Acquisition system for the casual
capture of indoor scenes in high dynamic range. Our proposed system comprises
two 360{\deg} cameras rigidly attached to a portable tripod. The cameras
simultaneously acquire two 360{\deg} videos: one at a regular exposure and the
other at a very fast exposure, allowing a user to simply wave the apparatus
casually around the scene in a matter of minutes. The resulting images are fed
to a NeRF-based algorithm that reconstructs the scene's full high dynamic
range. Compared to HDR baselines from previous work, our approach reconstructs
the full HDR radiance of indoor scenes without sacrificing the visual quality
while retaining the ease of capture from recent NeRF-like approaches.
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