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In this paper, we compute finite sample bounds for data-driven approximations
of the solution to stochastic reachability problems. Our approach uses a
nonparametric technique known as kernel distribution embeddings, and provides
probabilistic assurances of safety for stochastic systems in a model-free
manner. By implicitly embedding the stochastic kernel of a Markov control
process in a reproducing kernel Hilbert space, we can approximate the safety
probabilities for stochastic systems with arbitrary stochastic disturbances as
simple matrix operations and inner products. We present finite sample bounds
for point-based approximations of the safety probabilities through construction
of probabilistic confidence bounds that are state- and input-dependent. One
advantage of this approach is that the bounds are responsive to non-uniformly
sampled data, meaning that tighter bounds are feasible in regions of the state-
and input-space with more observations. We numerically evaluate the approach,
and demonstrate its efficacy on a neural network-controlled pendulum system.
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A topological group $G$ is called extremely amenable if every continuous
action of $G$ on a compact space has a fixed point. This concept is linked with
geometry of high dimensions (concentration of measure). We show that a von
Neumann algebra is approximately finite-dimensional if and only if its unitary
group with the strong topology is the product of an extremely amenable group
with a compact group, which strengthens a result by de la Harpe. As a
consequence, a $C^\ast$-algebra $A$ is nuclear if and only if the unitary group
$U(A)$ with the relative weak topology is strongly amenable in the sense of
Glasner. We prove that the group of automorphisms of a Lebesgue space with a
non-atomic measure is extremely amenable with the weak topology and establish a
similar result for groups of non-singular transformations. As a consequence, we
prove extreme amenability of the groups of isometries of $L^p(0,1)$, $1\leq
p<\infty$, extending a classical result of Gromov and Milman ($p=2$). We show
that a measure class preserving equivalence relation $\mathcal R$ on a standard
Borel space is amenable if and only if the full group $[{\mathcal R}]$,
equipped with the uniform topology, is extremely amenable. Finally, we give
natural examples of concentration to a nontrivial space in the sense of Gromov
occuring in the automorphism groups of injective factors of type $III$.
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Instruction tuning aligns the response of large language models (LLMs) with
human preferences. Despite such efforts in human--LLM alignment, we find that
instruction tuning does not always make LLMs human-like from a cognitive
modeling perspective. More specifically, next-word probabilities estimated by
instruction-tuned LLMs are often worse at simulating human reading behavior
than those estimated by base LLMs. In addition, we explore prompting
methodologies for simulating human reading behavior with LLMs. Our results show
that prompts reflecting a particular linguistic hypothesis improve psychometric
predictive power, but are still inferior to small base models. These findings
highlight that recent advancements in LLMs, i.e., instruction tuning and
prompting, do not offer better estimates than direct probability measurements
from base LLMs in cognitive modeling. In other words, pure next-word
probability remains a strong predictor for human reading behavior, even in the
age of LLMs.
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Two-dimensional ferromagnetic electron gases subject to random scalar
potentials and Rashba spin-orbit interactions exhibit a striking quantum
criticality. As disorder strength $W$ increases, the systems undergo a
transition from a normal diffusive metal consisting of extended states to a
marginal metal consisting of critical states at a critical disorder $W_{c,1}$.
Further increase of $W$, another transition from the marginal metal to an
insulator occurs at $W_{c,2}$. Through highly accurate numerical procedures
based on the recursive Green's function method and the exact diagonalization,
we elucidate the nature of the quantum criticality and the properties of the
pertinent states. The intrinsic conductances follow an unorthodox
single-parameter scaling law: They collapse onto two branches of curves
corresponding to diffusive metal phase and insulating phase with correlation
lengths diverging exponentially as $\xi\propto\exp[\alpha/\sqrt{|W-W_c|}]$ near
transition points. Finite-size analysis of inverse participation ratios reveals
that the states within the critical regime $[W_{c,1},W_{c,2}]$ are fractals of
a universal fractal dimension $D=1.90\pm0.02$ while those in metallic
(insulating) regime spread over the whole system (localize) with $D=2$ ($D=0$).
A phase diagram in the parameter space illuminates the occurrence and evolution
of diffusive metals, marginal metals, and the Anderson insulators.
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To investigate how quantum effects might modify special relativity, we will
study a Lorentz transformation between classical and quantum reference frames
and express it in terms of the four-dimensional (4D) momentum of the quantum
reference frame. The transition from the classical expression of the Lorentz
transformation to a quantum-mechanical one requires us to symmetrize the
expression and replace all its dynamical variables with the corresponding
operators, from which we can obtain the same conclusion as that from quantum
field theory (given by Weinberg's formula): owing to the Heisenberg's
uncertainty relation, a particle (as a quantum reference frame) can propagate
over a spacelike interval.
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Sports broadcasters inject drama into play-by-play commentary by building
team and player narratives through subjective analyses and anecdotes. Prior
studies based on small datasets and manual coding show that such theatrics
evince commentator bias in sports broadcasts. To examine this phenomenon, we
assemble FOOTBALL, which contains 1,455 broadcast transcripts from American
football games across six decades that are automatically annotated with 250K
player mentions and linked with racial metadata. We identify major confounding
factors for researchers examining racial bias in FOOTBALL, and perform a
computational analysis that supports conclusions from prior social science
studies.
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We study the ferromagnetic phase transition in a randomly layered Heisenberg
model. A recent strong-disorder renormalization group approach [Phys. Rev. B
81, 144407 (2010)] predicted that the critical point in this system is of
exotic infinite-randomness type and is accompanied by strong power-law
Griffiths singularities. Here, we report results of Monte-Carlo simulations
that provide numerical evidence in support of these predictions. Specifically,
we investigate the finite-size scaling behavior of the magnetic susceptibility
which is characterized by a non-universal power-law divergence in the Griffiths
phase. In addition, we calculate the time autocorrelation function of the
spins. It features a very slow decay in the Griffiths phase, following a
non-universal power law in time.
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The probability of a projectile nucleon to traverse a target nucleus without
interaction is calculated for central Si-Pb collisions and compared to the data
of E814. The calculations are performed in two independent ways, via Glauber
theory and using the transport code UrQMD. For central collisions Glauber
predictions are about 30 to 50% higher than experiment, while the output of
UrQMD does not show the experimental peak of beam rapidity particles.
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The computational study of DNA and its interaction with ligands is a highly
relevant area of research, with significant consequences for developing new
therapeutic strategies. However, the computational description of such large
and complex systems requires considering interactions of different types. All
these considerations imply a real challenge for computational chemistry. Using
quantum methods for the entire system requires significant computational
resources, with improvements in parallelization and optimization of theoretical
strategies. Computational methods, such as LS-DFT and DLPNO-CCSD(T), may allow
performing ab initio QM calculations, including explicitly the electronic
structure for large biological systems, at a reasonable computing time. In this
work, we study the interaction of small molecules and cations with DNA
(duplex-DNA and G-quadruplexes), comparing different computational methods: a
linear-scaling DFT (LS-DFT) at LMKLL/DZDP level of theory, semi-empirical
methods (PM6-DH2 and PM7), mixed QM/MM, and DLPNO-CCSD(T). Our goal is to
demonstrate the adequacy of LS-DFT to treat the different types of interactions
present in DNA-dependent systems. We show that LMKLL/DZDP using SIESTA can
yield very accurate geometries and energetics in all the different systems
considered in this work: duplex DNA (dDNA), phenanthroline intercalating dDNA,
G-quadruplexes, and Metal-G-tetrads considering alkaline metals of different
sizes. As far as we know, this is the first time that full G-quadruplex
geometry optimizations have been carried out using a DFT method thanks to its
linear-scaling capabilities. Moreover, we show that LS-DFT provides
high-quality structures, and some semi-empirical Hamiltonian can also yield
suitable geometries. However, DLPNO-CCSD(T) and LS-DFT are the only methods
that accurately describe interaction energies for all the systems considered in
our study.
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Gravity-mediated SUSY breaking models with R-parity conservation give rise to
dark matter in the universe. I review neutralino dark matter in the minimal
supergravity model (mSUGRA), models with non-universal soft SUSY breaking terms
(NUSUGRA) which yield a well-tempered neutralino, and models with unified
Yukawa couplings at the GUT scale (as may occur in an SO(10) SUSY GUT theory).
These latter models have difficulty accommodating neutralino dark matter, but
work very well if the dark matter particles are axions and axinos.
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We investigate spin transport of heavy holes in III-V semiconductor quantum
wells in the presence of spin-orbit coupling of the Rashba type due to
structure-inversion asymmetry. Similarly to the case of electrons, the
longitudinal spin conductivity vanishes, whereas the off-diagonal elements of
the spin-conductivity tensor are finite giving rise to an intrinsic spin-Hall
effect. For a clean system we find a closed expression for the spin-Hall
conductivity depending on the length scale of the Rashba coupling and the hole
density. In this limit the spin-Hall conductivity is enhanced compared to its
value for electron systems, and it vanishes with increasing strength of the
impurity scattering. As an aside, we also derive explicit expressions for the
Fermi momenta and the densities of holes in the different dispersion branches
as a function of the spin-orbit coupling parameter and the total hole density.
These results are of relevance for the interpretation of possible Shubnikov-de
Haas measurements detecting the Rashba spin splitting.
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Magnons, the quanta of collective spin excitations in magnetically ordered
materials, have distinct properties that make them uniquely appealing for
quantum information applications. They can have ultra-small wavelengths down to
the nanometer scale even at microwave frequencies. They can provide coupling to
a diverse set of other quantum excitations, and their inherently gyrotropic
dynamics forms the basis for pronounced non-reciprocities. In this article we
discuss what the current research challenges are for integrating magnetic
materials into quantum information systems and provide a perspective on how to
address them.
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We consider settings where data are available on a nonparametric function and
various partial derivatives. Such circumstances arise in practice, for example
in the joint estimation of cost and input functions in economics. We show that
when derivative data are available, local averages can be replaced in certain
dimensions by nonlocal averages, thus reducing the nonparametric dimension of
the problem. We derive optimal rates of convergence and conditions under which
dimension reduction is achieved. Kernel estimators and their properties are
analyzed, although other estimators, such as local polynomial, spline and
nonparametric least squares, may also be used. Simulations and an application
to the estimation of electricity distribution costs are included.
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We give a two-parameter quantum deformation of the exterior plane and its
differential calculus without the use of any R-matrix and relate it to the
differential calculus with the R-matrix. We prove that there are two types of
solutions of the Yang-Baxter equation whose symmetry group is $GL_{p,q}(2)$. We
also give a two-parameter deformation of the fermionic oscillator algebra.
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Monodispersed strontium titanate nanoparticles were prepared and studied in
detail. It is found that ~10 nm as-prepared stoichiometric nanoparticles are in
a polar structural state (with possibly ferroelectric properties) over a broad
temperature range. A tetragonal structure, with possible reduction of the
electronic hybridization is found as the particle size is reduced. In the 10 nm
particles, no change in the local Ti-off centering is seen between 20 and 300
K. The results indicate that nanoscale motifs of SrTiO3 may be utilized in data
storage as assembled nano-particle arrays in applications where chemical
stability, temperature stability and low toxicity are critical issues.
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The structure of $3/2^{-}$ and $1/2^{+}$ states in $^{11}$B is investigated
with an $\alpha+\alpha+t$ orthogonality condition model (OCM) based on the
Gaussian expansion method. Full levels up to the $3/2^{-}_{3}$ and $1/2^{+}_2$
states around the $\alpha+\alpha+t$ threshold ($E_x$=11.1 MeV) are reproduced
consistently with the experimental energy levels. It is shown that the
$3/2_{3}^{-}$ state located around the $^{7}$Li+$\alpha$ threshold has an
$\alpha+\alpha+t$ cluster structure, whereas the $3/2_{1}^{-}$ and
$3/2_{2}^{-}$ states have a shell-model-like compact structure. We found that
the $3/2_{3}^{-}$ state does not possess an $\alpha$-condensate-like nature
similar to the $0^{+}_{2}$ state of $^{12}$C (Hoyle state) which has a dilute
$3\alpha$-condensate structure described by a $(0S_{\alpha})^3$ configuration
with about $70$\% probability, although the monopole transition strength of the
former is as large as that of the latter. We discuss the reasons why the
$3/2_{3}^{-}$ state does not have the condensate character. On the other hand,
the $1/2^{+}_{1}$ state just below the $^{7}$Li+$\alpha$ threshold has a
cluster structure which can be interpreted as a parity-doublet partner of the
$3/2^{-}_3$ state. We indicate that the $12.56$-MeV state
($J^{\pi}=1/2^{+}_{2}$) just above the $\alpha+\alpha+t$ threshold observed in
the $^7$Li($^{7}$Li,$^{11}$B$^*$)$t$ reaction etc. is of the
dilute-cluster-gas-like, and is a strong candidate for the Hoyle-analogue state
which has a configuration of $(0S_{\alpha})^{2}(0S_{t})$ with about $65$\%
probability from the analyses of the single-cluster motions in $^{11}$B. The
structure property of the $1/2^{+}$ resonant state is analyzed with the complex
scaling method.
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A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle,
two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a
double-well potential. This semiclassical description is based on the
`classical' dynamics of the mean-field Gross-Pitaevskii equation and is
expected to be valid for large N. We demonstrate the possibility to reconstruct
quantum properties of the N-particle system from the mean-field dynamics. The
resulting semiclassical eigenvalues and eigenstates are found to be in very
good agreement with the exact ones, even for small values of N, both for
subcritical and supercritical particle interaction strength where tunneling has
to be taken into account.
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This is the contribution to Quarks'2018 conference proceedings. This
contribution is devoted to the holographic description of chaos and quantum
complexity in the strongly interacting systems out of equilibrium. In the first
part of the talk we present different holographic complexity proposals in
out-of-equilibrium CFT following the local perturbation. The second part is
devoted to the chaotic growth of the local operator size at a finite chemical
potential. There are numerous results stating that the chemical potential may
lead to the chaos disappearance, and we confirm these results from holographic
viewpoint.
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In this work, we construct a new model for the collisional evolution of the
main asteroid belt. Our goals are to test the scaling law of Benz and Asphaug
(1999) and ascertain if it can be used for the whole belt. We want to find
initial size-frequency distributions (SFDs) for the considered six parts of the
belt (inner, middle, 'pristine', outer, Cybele zone, high-inclination region)
and to verify if the number of synthetic asteroid families created during the
simulation matches the number of observed families as well. We used new
observational data from the WISE satellite (Masiero et al., 2011) to construct
the observed SFDs. We simulate mutual collisions of asteroids with a modified
version of the Boulder code (Morbidelli et al., 2009), where the results of
hydrodynamic (SPH) simulations of Durda et al. (2007) and Benavidez et al.
(2012) are included. Because material characteristics can significantly affect
breakups, we created two models - for monolithic asteroids and for
rubble-piles. To explain the observed SFDs in the size range D = 1 to 10 km we
have to also account for dynamical depletion due to the Yarkovsky effect. The
assumption of (purely) rubble-pile asteroids leads to a significantly worse fit
to the observed data, so that we can conclude that majority of main-belt
asteroids are rather monolithic. Our work may also serve as a motivation for
further SPH simulations of disruptions of smaller targets (with a parent body
size of the order of 1 km).
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In this paper, we study the weighted sums of multiple t-values and of
multiple t-star values at even arguments. Some general weighted sum formulas
are given, where the weight coefficients are given by (symmetric) polynomials
of the arguments.
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We propose a quantum metrology scheme in a cavity QED setup to achieve the
Heisenberg limit. In our scheme, a series of identical two-level atoms randomly
pass through and interact with a dissipative single-mode cavity. Different from
the entanglement based Heisenberg limit metrology scheme, we do not need to
prepare the atomic entangled states before they enter into the cavity. We show
that the initial atomic coherence will induce an effective driving to the
cavity field, whose steady state is an incoherent superposition of orthogonal
states, with the superposition probabilities being dependent on the atom-cavity
coupling strength. By measuring the average photon number of the cavity in the
steady state, we demonstrate that the root-mean-square of the fluctuation of
the atom-cavity coupling strength is proportional to $1/N_c^2$ ($N_c$ is the
effective atom number interacting with the photon in the cavity during its
lifetime). It implies that we have achieved the Heisenberg limit in our quantum
metrology process. We also discuss the experimental feasibility of our
theoretical proposal. Our findings may find potential applications in quantum
metrology technology.
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We show that a thermal reservoir can effectively act as a squeezed reservoir
on atoms that are subject to energy-level modulation. For sufficiently fast and
strong modulation, for which the rotating-wave-approximation is broken, the
resulting squeezing persists at long times. These effects are analyzed by a
master equation that is valid beyond the rotating wave approximation. As an
example we consider a two-level-atom in a cavity with Lorentzian linewidth,
subject to sinusoidal energy modulation. A possible realization of these
effects is discussed for Rydberg atoms.
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Dilepton and photon production in heavy-ion collisions at SPS energies is
studied in the relativistic transport model that incorporates self-consistently
the change of hadron masses in dense matter. It is found that the dilepton
spectra in proton-nucleus reactions can be well described by the conventional
mechanisms of Dalitz decay, primary vector meson decay, decay of charmed
mesons, and the initial Drell-Yan processes. However, to provide a quantitative
explanation of the observed dilepton spectra in central heavy-ion collisions
requires contributions other than these direct decays and also various medium
effects. Introducing a decrease of vector meson masses in hot dense medium, we
find that the low-mass dilepton enhancement can be satisfactorily explained.
Furthermore, to explain the intermediate-mass dilepton enhancement in heavy-ion
collisions, secondary processes such as $\pi a_1\to l{\bar l}$ are found to be
very important. Finally, the single photon spectra in our calculations with
either free or in-medium meson masses do not exceed the upper limit measured by
the WA80 Collaboration.
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The Generalized Uncertainty Principle (GUP) has been directly applied to the
motion of (macroscopic) test bodies on a given space-time in order to compute
corrections to the classical orbits predicted in Newtonian Mechanics or General
Relativity. These corrections generically violate the Equivalence Principle.
The GUP has also been indirectly applied to the gravitational source by
relating the GUP modified Hawking temperature to a deformation of the
background metric. Such a deformed background metric determines new geodesic
motions without violating the Equivalence Principle. We point out here that the
two effects are mutually exclusive when compared with experimental bounds.
Moreover, the former stems from modified Poisson brackets obtained from a wrong
classical limit of the deformed canonical commutators.
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We study a type I see-saw scenario where the right-handed (RH) neutrinos,
responsible for the light neutrino mass generation, lie at the electroweak
scale. Under certain conditions, the strength of the charged and neutral
current weak interactions of the Standard Model particles with the heavy RH
neutrinos can be large enough to allow their production at the LHC, opening
also the possibility of observing other low energy signatures of the new
physics in the electroweak precision observables as well as in searches for
rare leptonic decays or neutrinoless double beta decay. We argue that in this
scenario the flavour structure of the neutrino Yukawa couplings is essentially
determined by the low energy neutrino parameters, leading to fairly strong
correlations among the new phenomena. In particular, we show that the present
bound on the $\mu \to e +\gamma$ decay rate makes very difficult the
observation of the heavy RH neutrinos at the LHC or the observation of
deviations from the Standard Model predictions in the electroweak precision
data. We also argue that all present experimental constraints on this scenario
still allow i) for an enhancement of the rate of neutrinoless double beta
decay, which thus can be in the range of sensitivity of the GERDA experiment
even when the light Majorana neutrinos possess a normal hierarchical mass
spectrum, and ii) for the predicted $\mu \to e+ \gamma$ decay rate to be within
the sensitivity range of the MEG experiment.
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Despite temperature rise being a first-order design constraint, traditional
thermal estimation techniques have severe limitations in modeling critical
aspects affecting the temperature in modern-day chips. Existing thermal
modeling techniques often ignore the effects of parameter variation, which can
lead to significant errors. Such methods also ignore the dependence of
conductivity on temperature and its variation. Leakage power is also
incorporated inadequately by state-of-the-art techniques. Thermal modeling is a
process that has to be repeated at least thousands of times in the design
cycle, and hence speed is of utmost importance.
To overcome these limitations, we propose VarSim, an ultrafast thermal
simulator based on Green's functions. Green's functions have been shown to be
faster than the traditional finite difference and finite element-based
approaches but have rarely been employed in thermal modeling. Hence we propose
a new Green's function-based method to capture the effects of leakage power as
well as process variation analytically. We provide a closed-form solution for
the Green's function considering the effects of variation on the process,
temperature, and thermal conductivity. In addition, we propose a novel way of
dealing with the anisotropicity introduced by process variation by splitting
the Green's functions into shift-variant and shift-invariant components. Since
our solutions are analytical expressions, we were able to obtain speedups that
were several orders of magnitude over and above state-of-the-art proposals with
a mean absolute error limited to 4% for a wide range of test cases.
Furthermore, our method accurately captures the steady-state as well as the
transient variation in temperature.
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Using Newman-Penrose formalism in tetrad and spinor notation, we perform
separation of variables in the wave equations for massless fields of various
spins s=1/2, 1, 3/2, 2 on the background of exact plane-fronted gravitational
wave metrics. Then, applying Wald's method of adjoint operators, we derive
equations for Debye potentials generating these fields and find inverse
projection operators expressing multicomponet fields in terms of scalar
potentials. For a number of shock wave backgrounds, as a special case of
non-vacuum pp-waves, the exact solutions for Debye potentials are constructed
explicitly. The possibility of generalization to the case of massive fields, in
particular, construction of exact solutions to the Dirac and Proca equations
are discussed. These results can be used in supergravity models on pp-wave
backgrounds.
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Image schema is a recurrent pattern of reasoning where one entity is mapped
into another. Image schema is similar to conceptual metaphor and is also
related to metaphoric gesture. Our main goal is to generate metaphoric gestures
for an Embodied Conversational Agent.
We propose a technique to learn the vector representation of image schemas.
As far as we are aware of, this is the first work which addresses that problem.
Our technique uses Ravenet et al's algorithm which we use to compute the image
schemas from the text input and also BERT and SenseBERT which we use as the
base word embedding technique to calculate the final vector representation of
the image schema. Our representation learning technique works by clustering:
word embedding vectors which belong to the same image schema should be
relatively closer to each other, and thus form a cluster.
With the image schemas representable as vectors, it also becomes possible to
have a notion that some image schemas are closer or more similar to each other
than to the others because the distance between the vectors is a proxy of the
dissimilarity between the corresponding image schemas. Therefore, after
obtaining the vector representation of the image schemas, we calculate the
distances between those vectors. Based on these, we create visualizations to
illustrate the relative distances between the different image schemas.
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It has been recently claimed that the symmetry group S4 yields to the
Tri-bimaximal neutrino mixing in a "natural" way from the group theory point of
view. Approving of this feature as an indication, we build a supersymmetric
model of lepton and quark masses based on this family symmetry group. In the
lepton sector, a correct mass hierarchy among the charged leptons is achieved
together to a neutrino mass matrix which can be diagonalized by the
Tri-bimaximal pattern. Our model results to be phenomenologically unequivalent
with respect to other proposals based on different flavour groups but still
predicting the Tri-bimaximal mixing. In the quark sector a realistic pattern
for masses and mixing angles is obtained. The flavour structures of the mass
matrices in both the sectors come from the spontaneously symmetry breaking of
S4, due to several scalar fields, which get non-zero vacuum expectation values.
A specific vacuum alignment is required and it is shown to be a natural results
of the minimization of the scalar potential and, moreover, to be stable under
the corrections from the higher order terms.
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Highly coherent wave is favorable for applications in which phase retrieval
is necessary, yet a high coherent wave is prone to encounter Rayleigh fading
phenomenon as it passes through a medium of random scatters. As an exemplary
case, phase-sensitive optical time-domain reflectometry (\Phi-OTDR) utilizes
coherent interference of backscattering light along a fiber to achieve
ultra-sensitive acoustic sensing, but sensing locations with fading won't be
functional. Apart from the sensing domain, fading is also ubiquitous in optical
imaging and wireless telecommunication, therefore it is of great interest. In
this paper, we theoretically describe and experimentally verify how the fading
phenomena in one-dimension optical scatters will be suppressed with arbitrary
number of independent probing channels. We initially theoretically explained
why fading would cause severe noise in the demodulated phase of \Phi-OTDR; then
M-degree summation of incoherent scattered light-waves is studied for the
purpose of eliminating fading. Finally, the gain of the retrieved phase
signal-to-noise-ratio and its fluctuations were analytically derived and
experimentally verified. This work provides a guideline for fading elimination
in one-dimension optical scatters, and it also provides insight for optical
imaging and wireless telecommunication.
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Two-dimensional representation of 3D anatomical structures is a simple and
intuitive way for analysing patient information across populations and image
modalities. It also allows convenient visualizations that can be included in
clinical reports for a fast overview of the whole structure. While cardiac
ventricles, especially the left ventricle, have an established standard
representation (e.g. bull's eye plot), the 2D depiction of the left atrium (LA)
is challenging due to its sub-structural complexity including the pulmonary
veins (PV) and the left atrial appendage (LAA). Quasi-conformal flattening
techniques, successfully applied to cardiac ventricles, require additional
constraints in the case of the LA to place the PV and LAA in the same
geometrical 2D location for different cases. Some registration-based methods
have been proposed but 3D (or 2D) surface registration is time-consuming and
prone to errors if the geometries are very different. We propose a novel atrial
flattening methodology where a quasi-conformal 2D map of the LA is obtained
quickly and without errors related to registration. In our approach, the LA is
divided into 5 regions which are then mapped to their analogue two-dimensional
regions. A dataset of 67 human left atria from magnetic resonance images (MRI)
was studied to derive a population-based 2D LA template representing the
averaged relative locations of the PVs and LAA. The clinical application of the
proposed methodology is illustrated on different use cases including the
integration of MRI and electroanatomical data.
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It is shown that (2+1)-dimensional QED reveals several unusual effects due to
the surface-term contributions. It is also shown that this system provides a
new pairing mechanism for the high-$T_c$ superconductivity on the plane.
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We initiate a study of positive multisections of Lefschetz fibrations via
positive factorizations in framed mapping class groups of surfaces. Using our
methods, one can effectively capture various interesting symplectic surfaces in
symplectic 4-manifolds as multisections, such as Seiberg-Witten basic classes
and exceptional classes, or branched loci of compact Stein surfaces as branched
coverings of the 4-ball. Various problems regarding the topology of symplectic
4-manifolds, such as the smooth classification of symplectic Calabi-Yau
4-manifolds, can be translated to combinatorial problems in this manner. After
producing special monodromy factorizations of Lefschetz pencils on symplectic
Calabi-Yau K3 and Enriques surfaces, and introducing monodromy substitutions
tailored for generating multisections, we obtain several novel applications,
allowing us to construct: new counter-examples to Stipsicz's conjecture on
fiber sum indecomposable Lefschetz fibrations, non-isomorphic Lefschetz pencils
of the same genera on the same new symplectic 4-manifolds, the very first
examples of exotic Lefschetz pencils, and new exotic embeddings of surfaces.
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We propose a one-loop induced neutrino mass model with hidden $U(1)$ gauge
symmetry, in which we successfully involve a bosonic dark matter (DM) candidate
propagating inside a loop diagram in neutrino mass generation to explain the
$e^+e^-$ excess recently reported by the DArk Matter Particle Explorer (DAMPE)
experiment. In our scenario dark matter annihilates into four leptons through
$Z'$ boson as DM DM $\to Z' Z' (Z' \to \ell^+ \ell^-)$ and $Z'$ decays into
leptons via one-loop effect. We then investigate branching ratios of $Z'$
taking into account lepton flavor violations and neutrino oscillation data.
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We made a 100 ks observation of the Sagittarius (Sgr) B1 region at (l, b) =
(0.5, -0.1) near to the Galactic center (GC) with the Suzaku/XIS. Emission
lines of S XV, Fe I, Fe XXV, and Fe XXVI were clearly detected in the spectrum.
We found that the Fe XXV and Fe XXVI line emissions smoothly distribute over
the Sgr B1 and B2 regions connecting from the GC. This result suggests that the
GC hot plasma extends at least up to the Sgr B region with a constant
temperature. There are two diffuse X-ray sources in the observed region. One of
the two (G0.42-0.04) is newly discovered, and exhibits a strong S XV Ka
emission line, suggesting a candidate for a supernova remnant located in the GC
region. The other one (M0.51-0.10), having a prominent Fe I Ka emission line
and a strongly absorbed continuum, is likely to be an X-ray reflection nebula.
There is no near source bright enough to irradiate M0.51-0.10. However, the Fe
I Ka emission can be explained if Sgr A* was ~ 10^6 times brighter 300 years
ago, the light travel time for 100 pc to M0.51-0.10, than it is at present.
|
The contribution of "hanged" diagrams into the reaction $np \rightarrow np
\pi^+ \pi^-$ was considered. It was shown that taking into account of these
diagrams permits to get better description of the effective mass spectrum of
$\pi^+\pi^-$-combinations.
|
The Gaussian graphical model is routinely employed to model the joint
distribution of multiple random variables. The graph it induces is not only
useful for describing the relationship between random variables but also
critical for improving statistical estimation precision. In high-dimensional
data analysis, despite an abundant literature on estimating this graph
structure, tests for the adequacy of its specification at a global level is
severely underdeveloped. To make progress, this paper proposes a novel
goodness-of-fit test that is computationally easy and theoretically tractable.
Under the null hypothesis, it is shown that asymptotic distribution of the
proposed test statistic follows a Gumbel distribution. Interestingly the
location parameter of this limiting Gumbel distribution depends on the
dependence structure under the null. We further develop a novel
consistency-empowered test statistic when the true structure is nested in the
postulated structure, by amplifying the noise incurred in estimation. Extensive
simulation illustrates that the proposed test procedure has the right size
under the null, and is powerful under the alternative. As an application, we
apply the test to the analysis of a COVID-19 data set, demonstrating that our
test can serve as a valuable tool in choosing a graph structure to improve
estimation efficiency.
|
We study the synchronization of Kuramoto oscillators with all-to-all coupling
in the presence of slow, noisy frequency adaptation. In this paper we develop a
new model for oscillators which adapt both their phases and frequencies. It is
found that this model naturally reproduces some observed phenomena that are not
qualitatively produced by the standard Kuramoto model, such as long waiting
times before the synchronization of clapping audiences. By assuming a
self-consistent steady state solution, we find three stability regimes for the
coupling constant k, separated by critical points k1 and k2: (i) for k<k1, only
the stable incoherent state exists; (ii) for k>k2, the incoherent state becomes
unstable and only the synchronized state exists; (iii) for k1<k<k2, both the
incoherent and synchronized states are stable. In the bistable regime
spontaneous transitions between the incoherent and synchronized states are
observed for finite ensembles. These transitions are well described as a
stochastic process on the order parameter r undergoing fluctuations due to the
system's finite size, leading to the following conclusions: (a) in the bistable
regime, the average waiting time of an incoherent-to-coherent transition can be
predicted by using Kramer's escape time formula and grows exponentially with
the number of oscillators; (b) when the incoherent state is unstable (k>k2),
the average waiting time grows logarithmically with the number of oscillators.
|
Deep convolutional neural networks trained on large datsets have emerged as
an intriguing alternative for compressing images and solving inverse problems
such as denoising and compressive sensing. However, it has only recently been
realized that even without training, convolutional networks can function as
concise image models, and thus regularize inverse problems. In this paper, we
provide further evidence for this finding by studying variations of
convolutional neural networks that map few weight parameters to an image. The
networks we consider only consist of convolutional operations, with either
fixed or parameterized filters followed by ReLU non-linearities. We demonstrate
that with both fixed and parameterized convolutional filters those networks
enable representing images with few coefficients. What is more, the
underparameterization enables regularization of inverse problems, in particular
recovering an image from few observations. We show that, similar to standard
compressive sensing guarantees, on the order of the number of model parameters
many measurements suffice for recovering an image from compressive
measurements. Finally, we demonstrate that signal recovery with a un-trained
convolutional network outperforms standard l1 and total variation minimization
for magnetic resonance imaging (MRI).
|
Extremely metal-poor star-forming galaxies (XMPs) represent one of our only
laboratories for study of the low-metallicity stars we expect to encounter at
early epochs. But as our understanding of the $z>6$ universe has improved, it
has become clear that the majority of known XMPs within 100 Mpc host
significantly less prominent massive star populations than their
reionization-era counterparts, severely limiting their utility as testbeds for
interpreting spectral features found at the highest redshifts. Here we present
a new photometric selection technique designed to identify nearby XMPs
dominated by young stellar populations comparable to those expected in the
reionization era. We apply our technique to uncover candidate XMPs in SDSS
imaging at magnitudes $16<i'<23$, extending significantly below the
completeness limits of the SDSS spectroscopic survey. Spectroscopic
observations with the MMT confirm that 32 of the 53 uniformly metal-poor and
high specific star formation rate targets we observed have gas-phase oxygen
abundances $12+\log\mathrm{O/H}<7.7$ ($Z/Z_\odot<0.1$), including two in the
range of the lowest-metallicity galaxies known, $Z/Z_\odot<0.05$. Our
observations shed new light onto the longstanding mystery of He II emission in
star-forming galaxies: we find that the equivalent width of the He II $\lambda
4686$ high-ionization emission line does not scale with that of H$\beta$ in our
sample, suggesting that binary evolution or other processes on $>10$ Myr
timescales contribute substantially to the $\mathrm{He^+}$-ionizing photon
budget in this metallicity regime. Applying such selection techniques coupled
with deep spectroscopy to next-generation photometric surveys like LSST may
eventually provide a basis for an empirical understanding of metal-poor massive
stars.
|
Two families of sets, nonstationary and stationary, are obtained. Each
nonstationary set $\psi_{p_v}$ consists of the solutions with the quantum
number $p_v=p^0v-p_3.$ It can be obtained from the nonstationary set
$\psi_{p_3}$ with quantum number $p_3$ by a boost along $x_3$-axis (along the
direction of the electric field) with velocity $-v$. Similarly, any stationary
set of solutions characterized by a quantum number $p_s=p^0-sp_3$ can be
obtained from stationary solutions with quantum number $p^0$ by the same boost
with velocity $-s$. All these sets are equivalent and the classification (i.e.
ascribing the frequency sign and in-, out- indexes) in any set is determined by
the classification in $\psi_{p_3}$-set, where it is beyond doubt.
|
It is argued that the twisted gauge theory is consistent provided it exhibits
also the standard noncommutative gauge symmetry.
|
In these notes we use the recently found relation between facets of tropical
Grassmannians and generalizations of Feynman diagrams to compute all "biadjoint
amplitudes" for $n=7$ and $k=3$. We also study scattering equations on
$X(3,7)$, the configuration space of seven points on $\mathbb{CP}^2$. We prove
that the number of solutions is $1272$ in a two-step process. In the first step
we obtain $1162$ explicit solutions to high precision using near-soft
kinematics. In the second step we compute the matrix of $360\times 360$
biadjoint amplitudes obtained by using the facets of ${\rm Trop}\, G(3,7)$,
subtract the result from using the $1162$ solutions and compute the rank of the
resulting matrix. The rank turns out to be $110$, which proves that the number
of solutions in addition to the $1162$ explicit ones is exactly $110$.
|
A semi-phenomenological model of a many-particle system of 4He atoms is
proposed, in which a helium atom is considered as a complex consisting of a
nucleus and a bound pair of electrons in the singlet state. At zero
temperature, there are two Bose-Einstein condensates of particles with opposite
charges, namely, a condensate of positively charged nuclei and a condensate of
negatively charged electron pairs. It is shown that in such a system there
exist two excitation branches: sound and optical. On the basis of this model an
interpretation of experiments on the study of the eltctrical activity of
superfluid heliun is proposed. The frequency at which the resonant absorption
of a microwave radiation is observed is interpreted as a gap in the optical
branch. It is shown that the distribution of the electric potential in a
standing wave in a resonator is similar to that observed experimentally.
|
Public health surveillance aims at lessening disease burden, e.g., in case of
infectious diseases by timely recognizing emerging outbreaks. Seen from a
statistical perspective, this implies the use of appropriate methods for
monitoring time series of aggregated case reports. This paper presents the
tools for such automatic aberration detection offered by the R package
surveillance. We introduce the functionality for the visualization, modelling
and monitoring of surveillance time series. With respect to modelling we focus
on univariate time series modelling based on generalized linear models (GLMs),
multivariate GLMs, generalized additive models and generalized additive models
for location, shape and scale. This ranges from illustrating implementational
improvements and extensions of the well-known Farrington algorithm, e.g, by
spline-modelling or by treating it in a Bayesian context. Furthermore, we look
at categorical time series and address overdispersion using beta-binomial or
Dirichlet-Multinomial modelling. With respect to monitoring we consider
detectors based on either a Shewhart-like single timepoint comparison between
the observed count and the predictive distribution or by likelihood-ratio based
cumulative sum methods. Finally, we illustrate how surveillance can support
aberration detection in practice by integrating it into the monitoring workflow
of a public health institution. Altogether, the present article shows how well
surveillance can support automatic aberration detection in a public health
surveillance context.
|
In this paper we begin to study the subalgebra lattice of a Leibniz algebra.
In particular, we deal with Leibniz algebras whose subalgebra lattice is
modular, upper semi-modular, lower semi-modular, distributive, or dually
atomistic. The fact that a non-Lie Leibniz algebra has fewer one-dimensional
subalgebras in general results in a number of lattice conditions being weaker
than in the Lie case.
|
We establish large deviation principles and phase transition results for both
quenched and annealed settings of nearest-neighbor random walks with constant
drift in random nonnegative potentials on $\mathbb Z^d$. We complement the
analysis of \cite{Zer}, where a shape theorem on the Lyapunov functions and a
large deviation principle in absence of the drift are achieved for the quenched
setting.
|
With the fast development of Deep Learning techniques, Named Entity
Recognition (NER) is becoming more and more important in the information
extraction task. The greatest difficulty that the NER task faces is to keep the
detectability even when types of NE and documents are unfamiliar. Realizing
that the specificity information may contain potential meanings of a word and
generate semantic-related features for word embedding, we develop a
distribution-aware word embedding and implement three different methods to make
use of the distribution information in a NER framework. And the result shows
that the performance of NER will be improved if the word specificity is
incorporated into existing NER methods.
|
This paper presents the $\mathrm{\mu}$Car, a 1:18 model-scale vehicle with
Ackermann steering geometry developed for experiments in networked and
autonomous driving in research and education. The vehicle is open source,
moderately costed and highly flexible, which allows for many applications. It
is equipped with an inertial measurement unit and an odometer and obtains its
pose via WLAN from an indoor positioning system. The two supported operating
modes for controlling the vehicle are (1) computing control inputs on external
hardware, transmitting them via WLAN and applying received inputs to the
actuators and (2) transmitting a reference trajectory via WLAN, which is then
followed by a controller running on the onboard Raspberry Pi Zero W. The design
allows identical vehicles to be used at the same time in order to conduct
experiments with a large amount of networked agents.
|
Given a compact K\"ahler manifold $X$, a quasiplurisubharmonic function is
called a Green function with pole at $p\in X$ if its Monge-Amp\`ere measure is
supported at $p$. We study in this paper the existence and properties of such
functions, in connection to their singularity at $p$. A full characterization
is obtained in concrete cases, such as (multi)projective spaces.
|
We study the spectrum of a quantum star graph with a non-selfadjoint Robin
condition at the central vertex. We first prove that, in the high frequency
limit, the spectrum of the Robin Laplacian is close to the usual spectrum
corresponding to the Kirchhoff condition. Then, we describe more precisely the
asymptotics of the difference in terms of the Barra-Gaspard measure of the
graph. This measure depends on the arithmetic properties of the lengths of the
edges. As a by-product, this analysis provides a Weyl Law for non-selfadjoint
quantum star graphs and it gives the asymptotic behaviour of the imaginary
parts of the eigenvalues.
|
Inspired by the Poisson Sigma Model and its relation to 2d gravity, we
consider models governing morphisms from TSigma to any Lie algebroid E, where
Sigma is regarded as d-dimensional spacetime manifold. We address the question
of minimal conditions to be placed on a bilinear expression in the 1-form
fields, S^ij(X) A_i A_j, so as to permit an interpretation as a metric on
Sigma. This becomes a simple compatibility condition of the E-tensor S with the
chosen Lie algebroid structure on E. For the standard Lie algebroid E=TM the
additional structure is identified with a Riemannian foliation of M, in the
Poisson case E=T^*M with a sub-Riemannian structure which is Poisson invariant
with respect to its annihilator bundle. (For integrable image of S, this means
that the induced Riemannian leaves should be invariant with respect to all
Hamiltonian vector fields of functions which are locally constant on this
foliation). This provides a huge class of new gravity models in d dimensions,
embedding known 2d and 3d models as particular examples.
|
The optical excitations in C$_{60}$ and higher fullerenes, including isomers
of C$_{76}$, C$_{78}$, and C$_{84}$, are theoretically investigated. We use a
tight binding model with long-range Coulomb interactions, treated by the
Hartree-Fock and configuration-interaction methods. We find that the optical
excitations in the energy region smaller than about 4 eV have most of their
amplitudes at the pentagons. The oscillator strengths of projected absorption
almost accord with those of the total absorption. Next, off-resonant third
order susceptibilities are investigated. We find that third order
susceptibilities of higher fullerenes are a few times larger than those of
C$_{60}$. The magnitude of nonlinearity increases as the optical gap decreases
in higher fullerenes. The nonlinearity is nearly proportional to the fourth
power of the carbon number when the onsite Coulomb repulsion is $2t$ or $4t$,
$t$ being the nearest neighbor hopping integral. This result, indicating
important roles of Coulomb interactions, agrees with quantum chemical
calculations of higher fullerenes.
|
Let $T$ be the regular tree in which every vertex has exactly $d\ge 3$
neighbours. Run a branching random walk on $T$, in which at each time step
every particle gives birth to a random number of children with mean $d$ and
finite variance, and each of these children moves independently to a uniformly
chosen neighbour of its parent. We show that, starting with one particle at
some vertex $0$ and conditionally on survival of the process, the time it takes
for every vertex within distance $r$ of $0$ to be hit by a particle of the
branching random walk is almost surely $r + \frac{2}{\log(3/2)}\log\log r +
o(\log\log r)$.
|
Through a homogeneous analysis of spectroscopic literature data of red giant
stars, we determine the radial metallicity profiles of 30 dwarf galaxies in the
Local Group. We explore correlations between the calculated metallicity
gradients and stellar mass, star formation history and environment, delivering
the largest compilation to date of this type. The dwarf galaxies in our sample
mostly show metallicity profiles decreasing with radius, with some exhibiting
rather steep profiles. The derived metallicity gradients as a function of the
half-light radius, $\nabla_{\rm [Fe/H]} (R/R_e)$, show no statistical
differences when compared with the galaxies' morphological type, nor with their
distance from the Milky Way or M31. No correlations are found with either
stellar mass or star formation timescales. In particular, we do not find the
linear relationship between $\nabla_{\rm [Fe/H]} (R/R_e)$ and the galaxies'
median age $t_{50}$, as instead shown in the literature for a set of simulated
systems. The presence of high angular momentum in some of our galaxies does not
seem to have an impact on the gradient values. The strongest gradients in our
sample are observed in systems that are likely to have experienced a past
merger event. By excluding them, the analysed dwarf galaxies show mild
gradients ($\sim -0.1$ dex $R_e^{-1}$) with little scatter between them,
regardless of their stellar mass, dynamical state, and star formation history.
These results are in good agreement with different sets of simulations
presented in the literature and analysed using the same method as for the
observed sample. The interplay between the multitude of factors that could
drive the formation of metallicity gradients in dwarf galaxies likely combine
in complex ways to produce in general comparable values.
|
The Ecological Civilization Pattern Recommendation System (ECPRS) aims to
recommend suitable ecological civilization patterns for target regions,
promoting sustainable development and reducing regional disparities. However,
the current representative recommendation methods are not suitable for
recommending ecological civilization patterns in a geographical context. There
are two reasons for this. Firstly, regions have spatial heterogeneity, and the
(ECPRS)needs to consider factors like climate, topography, vegetation, etc., to
recommend civilization patterns adapted to specific ecological environments,
ensuring the feasibility and practicality of the recommendations. Secondly, the
abstract features of the ecological civilization patterns in the real world
have not been fully utilized., resulting in poor richness in their embedding
representations and consequently, lower performance of the recommendation
system. Considering these limitations, we propose the ECPR-MML method.
Initially, based on the novel method UGPIG, we construct a knowledge graph to
extract regional representations incorporating spatial heterogeneity features.
Following that, inspired by the significant progress made by Large Language
Models (LLMs) in the field of Natural Language Processing (NLP), we employ
Large LLMs to generate multimodal features for ecological civilization patterns
in the form of text and images. We extract and integrate these multimodal
features to obtain semantically rich representations of ecological
civilization. Through extensive experiments, we validate the performance of our
ECPR-MML model. Our results show that F1@5 is 2.11% higher compared to
state-of-the-art models, 2.02% higher than NGCF, and 1.16% higher than UGPIG.
Furthermore, multimodal data can indeed enhance recommendation performance.
However, the data generated by LLM is not as effective as real data to a
certain extent.
|
Context. The most primitive metal-poor stars are important for studying the
conditions of the early galaxy and are also relevant to big bang
nucleosynthesis. Aims. Our objective is to find the brightest (V<14) most
metal-poor stars. Methods. Candidates were selected using a new method, which
is based on the mismatch between spectral types derived from colors and
observed spectral types. They were observed first at low resolution with EFOSC2
at the NTT/ESO to obtain an initial set of stellar parameters. The most
promising candidate, 2MASS J18082002-5104378 (V=11.9), was observed at high
resolution (R=50 000) with UVES at the VLT/ESO, and a standard abundance
analysis was performed. Results. We found that 2MASS J18082002-5104378 is an
ultra metal-poor star with stellar parameters Teff = 5440 K, log g = 3.0 dex,
vt = 1.5 km/s, [Fe/H] = -4.1 dex. The star has [C/Fe]<+0.9 in a 1D analysis, or
[C/Fe]<=+0.5 if 3D effects are considered; its abundance pattern is typical of
normal (non-CEMP) ultra metal-poor stars. Interestingly, the star has a binary
companion. Conclusions. 2MASS J1808-5104 is the brightest (V=11.9) metal-poor
star of its category, and it could be studied further with even higher S/N
spectroscopy to determine additional chemical abundances, thus providing
important constraints to the early chemical evolution of our Galaxy.
|
We prove that any C1-stably weakly shadowable volume-preserving
diffeomorphism defined on a compact manifold displays a dominated splitting E +
F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version
of this result for divergence-free vector fields. As a consequence, in low
dimensions, we obtain global hyperbolicity.
|
Metallic spin liquid has been reported in several correlated metals, but a
satisfactory theoretical description is not yet available. Here we propose a
potential route to realize the metallic spin liquid and construct an effective
$\mathbb{Z}_2$ gauge theory with charged fractionalized excitations on the
triangular Kondo lattice. This leads to a $\mathbb{Z}_2$ metallic spin liquid
featured with long-lived, heavy holon excitations of spin 0 and charge $+e$ and
a partially enlarged electron Fermi surface. It differs from the weak-coupling
FL$^*$ state proposed earlier and may be viewed as a fractionalized heavy
fermion liquid. Our theory provides a general framework to describe the
metallic spin liquid in frustrated Kondo lattice systems.
|
We prove a ballistic strong law of large numbers and an invariance principle
for random walks in strong mixing environments, under condition $(T)$ of
Sznitman (cf. \cite{Sz01}). This weakens by first time the Kalikow ballistic
assumption in mixing and proves finite moments of arbitrary order for the
approximate regeneration time of \cite{CZ02}. The main technical tool in the
proof is the introduction of renormalization schemes, which had only been
considered for i.i.d. environments.
|
We describe an algorithm computing the monodromy and the pole order
filtration on the Milnor fiber cohomology of any reduced projective plane curve
$C$. The relation to the zero set of Bernstein-Sato polynomial of the defining
homogeneous polynomial for $C$ is also discussed. When $C$ has some non
weighted homogeneous singularities, then we have to assume that a conjecture
holds in order to get some of our results. In all the examples computed so far
this conjecture holds.
|
We present new results based on high-resolution observations of Sgr A West at
the Galactic center with the VLA at 1.3 cm. We measured proper motions for 71
compact HII components. We also investigated radial velocities in the LSR
velocity using the H92a line data. Combining proper motion and radial velocity
measurements, we have determined the 3D velocity distribution in Sgr A West. We
find that the three ionized streams (Northern Arm, Eastern Arm, and Western
Arc) can be modeled with three bundles of Keplerian orbits around Sgr A*. We
determined the five orbital parameters for each of them using LSQ fitting to
the locii of the streams. Our results confirm earlier results on the streams in
the Western Arc and the Northern Arm to be in Keplerian orbits, suggesting that
the stream in the Eastern Arm is also consistent with an elliptical orbit. Both
the Northern and Eastern Arm streams have high eccentricities, while the
Western Arc stream is nearly circular. All three streams orbit around Sgr A* in
a counterclockwise sense (viewed from the Earth). We also report an ionized
nebula associated with IRS 8, including a bow shock in radio continuum emission
which shows excellent agreement with near IR observations. From the H92a line
data, we find evidence for interaction between the IRS 8 nebula and the
Northern Arm stream. Other new morphological features revealed in our
high-resolution image include: 1) a helical structure in the Northern Arm,
suggesting that MHD plays an important role in the motion of the ionized gas,
in addition to the dynamics determined by the central gravitational field and
2) a linear feature in the IRS 16 region, suggesting the compressed edge of the
Northern Arm may result from the collective winds and radiation pressure from
the high mass stars in the IRS16 cluster.
|
We systematically investigated the temperature behaviors of the electrical
conductivity and Hall coefficient of two series of amorphous indium gallium
zinc oxides (a-IGZO) films prepared by rf sputtering method. The two series of
films are $\sim$700\,nm and $\sim$25\,nm thick, respectively. For each film,
the conductivity increases with decreasing temperature from 300\,K to $T_{\rm
max}$, where $T_{\rm max}$ is the temperature at which the conductivity reaches
its maximum. Below $T_{\rm max}$, the conductivity decreases with decreasing
temperature. Both the conductivity and Hall coefficient vary linearly with $\ln
T$ at low temperature regime. The $\ln T$ behaviors of conductivity and Hall
coefficient cannot be explained by the traditional electron-electron
interaction theory, but can be quantitatively described by the current
electron-electron theory due to the presence of granularity. Combining with the
scanning electron microscopy images of the films, we propose that the
boundaries between the neighboring a-IGZO particles could make the film
inhomogeneous and play an important role in the electron transport processes.
|
Understanding body part geometry is crucial for precise medical diagnostics.
Curves effectively describe anatomical structures and are widely used in
medical imaging applications related to cardiovascular, respiratory, and
skeletal diseases. Traditional curve detection methods are often task-specific,
relying heavily on domain-specific features, limiting their broader
applicability. This paper introduces a novel approach for detecting
non-branching curves, which does not require prior knowledge of the object's
orientation, shape, or position. Our method uses neural networks to predict (1)
an attraction field, which offers subpixel accuracy, and (2) a closeness map,
which limits the region of interest and essentially eliminates outliers far
from the desired curve. We tested our curve detector on several clinically
relevant tasks with diverse morphologies and achieved impressive subpixel-level
accuracy results that surpass existing methods, highlighting its versatility
and robustness. Additionally, to support further advancements in this field, we
provide our private annotations of aortic centerlines and masks, which can
serve as a benchmark for future research. The dataset can be found at
https://github.com/neuro-ml/curve-detection.
|
We provide a new solution to the long-standing problem of inferring causality
from observations without modeling the unknown mechanisms. We show that the
evolution of any dynamical system is related to a predictive asymmetry that
quantifies causal connections from limited observations. A built-in
significance criterion obviates surrogate testing and drastically improves
computational efficiency. We validate our test on numerous synthetic systems
exhibiting behavior commonly occurring in nature, from linear and nonlinear
stochastic processes to systems exhibiting nonlinear deterministic chaos, and
on real-world data with known ground truths. Applied to the controversial
problem of glacial-interglacial sea level and CO$_{2}$ evolving in lock-step,
our test uncovers empirical evidence for CO$_{2}$ as a driver of sea level over
the last 800 thousand years. Our findings are relevant to any discipline where
time series are used to study natural systems.
|
We use conformal symmetry to constrain the shape of inflationary correlators
in the presence of long-lived vector field perturbations. Applying conformal
Ward identities, we derive general expressions, up to amplitudes and
normalization factors, for the two and three point correlators in the presence
of vector fields mediated by the interaction $f(\phi)\left(F_{\mu \nu}F^{\mu
\nu}+\alpha\tilde{F}_{\mu \nu}F^{\mu \nu}\right)$, where $f(\phi)$ is a
suitable coupling function between the scalar and the vector field. The
previous interaction allows for isotropy and parity symmetry breaking and is
consistent with super horizon conformal symmetry. As an application of the
conformal field theory techniques followed here, we evaluate the mixed
tensor-scalar $\langle \gamma \zeta \rangle$ and tensor-scalar-scalar $\langle
\gamma \zeta \zeta \rangle$ correlators which are interesting to look for
parity violating effects related with chiral gravitational waves. Finally, we
derive consistency relations for the three point correlators obtained.
|
A cocoon is a by-product of a propagating jet that results from shock heating
at the jet head. Herein, considering simultaneous cocoon formation, we study
the stability of relativistic jets propagating through the uniform ambient
medium. Using a simple analytic argument, we demonstrate that independent from
the jet launching condition, the effective inertia of the jet is larger than
that of the cocoon when the fully relativistic jet oscillates radially owing to
the pressure mismatch between jet and cocoon. In such situations, it is
expected that the onset condition for the oscillation-induced Rayleigh-Taylor
instability is satisfied at the jet interface, resulting in the destabilization
of the relativistic jet during its propagation. We have quantitatively verified
and confirmed our prior expectation by performing relativistic hydrodynamic
simulations in three dimensions. The possible occurrences of the
Richtmyer-Meshkov instability, oscillation-induced centrifugal instability, and
Kelvin-Helmholtz instability are also discussed.
|
We present hydrodynamical N-body simulations of clusters of galaxies with
feedback taken from semi-analytic models of galaxy formation. The advantage of
this technique is that the source of feedback in our simulations is a
population of galaxies that closely resembles that found in the real universe.
We demonstrate that, to achieve the high entropy levels found in clusters,
active galactic nuclei must inject a large fraction of their energy into the
intergalactic/intracluster media throughout the growth period of the central
black hole. These simulations reinforce the argument of Bower et al. (2008),
who arrived at the same conclusion on the basis of purely semi-analytic
reasoning.
|
An experiment to search for the electron electric dipole moment (\eEDM) on
the metastable $H^3\Delta_1$ state of ThO molecule was proposed and now in the
final stage of preparation by the ACME collaboration
[http://www.electronedm.org]. To interpret the experiment in terms of \eEDM\
and dimensionless constant $k_{T,P}$ characterizing the strength of the scalar
T,P-odd electron-nucleus neutral current interaction, an accurate theoretical
study of effective electric field on electron, Eeff, and $W_{T,P}$ constants is
required. We report calculation of \Eeff\ (84 GV/cm) and a parameter of T,P-odd
scalar neutral currents interaction, $W_{T,P}$ (116 kHz), together with the
hyperfine structure constant, molecule frame dipole moment and $H^3\Delta_1\to
X^1\Sigma^+$ transition energy, which can serve as a measure of reliability of
the obtained \Eeff\ and $W_{T,P}$ values. Besides, our results include a parity
assignment and evaluation of the electric-field dependence for the magnetic $g$
factors for the $\Omega$-doublets of $H^3\Delta_1$.
|
Modeling mixed-traffic motion and interactions is crucial to assess safety,
efficiency, and feasibility of future urban areas. The lack of traffic
regulations, diverse transport modes, and the dynamic nature of mixed-traffic
zones like shared spaces make realistic modeling of such environments
challenging. This paper focuses on the generalizability of the motion model,
i.e., its ability to generate realistic behavior in different environmental
settings, an aspect which is lacking in existing works. Specifically, our first
contribution is a novel and systematic process of formulating general motion
models and application of this process is to extend our Game-Theoretic Social
Force Model (GSFM) towards a general model for generating a large variety of
motion behaviors of pedestrians and cars from different shared spaces. Our
second contribution is to consider different motion patterns of pedestrians by
calibrating motion-related features of individual pedestrian and clustering
them into groups. We analyze two clustering approaches. The calibration and
evaluation of our model are performed on three different shared space data
sets. The results indicate that our model can realistically simulate a wide
range of motion behaviors and interaction scenarios, and that adding different
motion patterns of pedestrians into our model improves its performance.
|
In a Dynamic Solar Model (DSM) the temperature dependences of the pp cycle
neutrinos will be different from the ones determined by solar model
calculations with the luminosity constraint. Instead of the usual neutrino
fluxes pp ~ T^{-1/2}, Be ~ T^8, B ~ T^{18}, we determined by the nuclear
reaction rates formulas pp ~ T^{4.2}, Be ~ T^{-1/2}, B ~ T^{13.5}, for $\tau <
10^2$ years. These latter relations have high significance at estimating the
uncertainties of the solar central temperatures without assuming the luminosity
constraint. Although the purely astrophysical solutions seem to be ruled out,
this is not the case for a model in which astrophysical effects are included
besides the neutrino oscillations. Therefore a combined, DSM+MSW model is
suggested to calculate the observed solar neutrino fluxes. The combined SSM+MSW
fits to the rates+spectra+D/N changes give a bad fit to the total rates,
indicating the need to include the astrophysical factors besides the MSW
effect. The DSM suggest that the core dynamics is induced by intermittent
events of dissipation of rotational energy in the solar core, in relation to
angular momentum dissipation arising from the relative motion of the Sun and
the mass center of the Solar System, and it shifts the allowed ranges of the
MSW parameters into a more acceptable region. The role of the astrophysical
factors in the solar neutrino problem is behind the fact why the ``smoking
guns'' of neutrino oscillations are not found yet.
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Let X_n=(x_{ij}) be an n by p data matrix, where the n rows form a random
sample of size n from a certain p-dimensional population distribution.
Let R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that
is, the entry \rho_{ij} is the usual Pearson's correlation coefficient between
the ith column of X_n and jth column of X_n. For contemporary data both n and p
are large. When the population is a multivariate normal we study the test that
H_0: the p variates of the population are uncorrelated.
A test statistic is chosen as L_n=max_{i\ne j}|\rho_{ij}|. The asymptotic
distribution of L_n is derived by using the Chen-Stein Poisson approximation
method. Similar results for the non-Gaussian case are also derived.
|
We present the color-magnitude and color-stellar mass diagrams for galaxies
with z_phot < ~2, based on a K < 22 (AB) catalog of the Extended Chandra Deep
Field South (ECDFS) from the MUltiwavelength Survey by Yale-Chile (MUSYC). Our
main sample of 7840 galaxies contains 1297 M_* > 10^11 M_Sol galaxies in the
range 0.2 < z_phot < 1.8. We show empirically that this catalog is
approximately complete for M_* > 10^11 M_Sol galaxies for z_phot < 1.8. For
this mass-limited sample, we show that the locus of the red sequence
color-stellar mass relation evolves as Del(u-r) ~ (-0.44+/-0.02) z_phot for
z_phot < ~1.2. For z_phot > ~1.3, however, we are no longer able to reliably
distinguish red and blue subpopulations from the observed color distribution;
we show that this would require much deeper near infrared data. At 1.5 < z_phot
<1.8, the comoving number density of M_* > 10^11 M_Sol galaxies is ~50% of the
local value, with a red fraction of ~33%. Making a parametric fit to the
observed evolution, we find n_tot(z) ~ (1+z_phot)^(-0.52+/-0.12(+/-0.20)). We
find stronger evolution in the red fraction: f_red(z) ~
(1+z_phot)^(-1.17+/-0.18(+/-0.21)). Through a series of sensitivity analyses,
we show that the most important sources of systematic error are: 1. systematic
differences in the analysis of the z~0 and z>>0 samples; 2. systematic effects
associated with details of the photometric redshift calculation; and 3.
uncertainties in the photometric calibration. With this in mind, we show that
our results based on photometric redshifts are consistent with a completely
independent analysis which does not require redshift information for individual
galaxies. Our results suggest that, at most, 1/5 of local red sequence galaxies
with M_* >10^11 M_Sol were already in place at z ~ 2.
|
We examine an electric double layer containing an antagonistic salt in an
aqueous mixture, where the cations are small and hydrophilic but the anions are
large and hydrophobic. In this situation, a strong coupling arises between the
charge density and the solvent composition. As a result, the anions are trapped
in an oil-rich adsorption layer on a hydrophobic wall. % while the cations are
expelled from it. We then vary the surface charge density $\sigma$ on the wall.
For $\sigma>0$ the anions remain accumulated, but for $\sigma<0$ the cations
are attracted to the wall with increasing $|\sigma|$. Furthermore, the electric
potential drop $\Psi(\sigma)$ is nonmonotonic when the solvent interaction
parameter $\chi(T)$ exceeds a critical value $\chi_c$ determined by the
composition and the ion density in the bulk. This leads to a first order phase
transition between two kinds of electric double layers with different $\sigma$
and common $\Psi$. In equilibrium such two layer regions can coexist. The
steric effect due to finite ion sizes is crucial in these phenomena.
|
Testing extra dimensions at low-energies may lead to interesting effects. In
this work a test point charge is taken to move uniformly in the 3-dimensional
subspace of a (3+$n$)-brane embedded in a (3+$n$+1)-space with $n$ compact and
one warped infinite spatial extra dimensions. We found that the electromagnetic
potentials of the point charge match standard Liennard-Wiechert's at large
distances but differ from them close to it. These are finite at the position of
the charge and produce finite self-energies. We also studied a localized
Hydrogen atom and take the deviation from the standard Coulomb potential as a
perturbation. This produces a Lamb shift that is compared with known
experimental data to set bounds for the parameter of the model. This work
provides details and extends results reported in a previous Letter.
|
We report a study of the low-temperature thermal conductivity (\kappa) of
pure and Zn-doped LiCu_2O_2 single crystals. The \kappa(T) of pure LiCu_2O_2
single crystal shows a double-peak behavior, with two peaks locating at 48 K
and 14 K, respectively. The different dependences of the peaks on the Zn
concentration indicate that the high-T peak is likely due to the phonon
transport while the low-T one is attributed to the magnon transport in the spin
spiral ordering state. In addition, the magnetic field can gradually suppress
the low-T peak but does not affect the high-T one; this further confirms that
the low-T peak is originated from the magnon heat transport.
|
Hybrid quantum systems have the potential of mitigating current challenges in
developing a scalable quantum computer. Of particular interest is the
hybridization between atomic and superconducting qubits. We demonstrate a novel
experimental setup for transferring and trapping ultracold atoms inside a
millikelvin cryogenic environment, where interactions between atomic and
superconducting qubits can be established, paving the way for hybrid quantum
systems. $^{87}\text{Rb}$ atoms are prepared in a conventional magneto-optical
trap and transported via a magnetic conveyor belt into a UHV compatible
dilution refrigerator with optical access. We store $5\times10^{8}$ atoms with
a lifetime of 794 seconds in the vicinity of the millikelvin stage.
|
We demonstrate that the differential conductance, $dI/dV$, measured via
spectroscopic imaging scanning tunneling microscopy in the doped iron
chalcogenide FeSe$_{0.45}$Te$_{0.55}$, possesses a series of characteristic
features that allow one to extract the orbital structure of the superconducting
gaps. This yields nearly isotropic superconducting gaps on the two hole-like
Fermi surfaces, and a strongly anisotropic gap on the electron-like Fermi
surface. Moreover, we show that the pinning of nematic fluctuations by defects
can give rise to a dumbbell-like spatial structure of the induced impurity
bound states, and explains the related $C_2$-symmetry in the Fourier
transformed differential conductance.
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A new kind of cut diagram is introduced to sum Feynman diagrams with
nonabelian vertices. Unlike the Cutkosky diagrams which compute the
discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent
a resummation of both the real and the imaginary parts of Feynman diagrams
related by permutations. Several applications of the technique are reported,
including a resolution of the apparent inconsistency of the baryon problem in
large-$N_c$ QCD, a simplified calculation of high-energy low-order QCD
diagrams, and progress made with this technique on the unitarization of the
BFKL equation.
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We prove that a suitable asymptotic formula for the average number of
representations of integers $n=p_{1}^{3}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}$, where
$p_1,p_2,p_3,p_4$ are prime numbers, holds in intervals shorter than the the
ones previously known.
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Recent studies of atmospheric neutrinos and the results from CHOOZ and
Palo-Verde experiment call for new and more sensitive searches for neutrino
oscillations at reactors. The main goal of the project considered here is to
look for very small mixing angle oscillations of electron neutrinos in the
atmospheric neutrino mass parameter region around \Delta m^2 ~3 10^-3 eV^2 and
to define the element U_{e3} of the neutrino mixing matrix (U_{e3}is the
contribution of the mass-3 state to the electron neutrino flavor state). The
practical goal of the project is to decrease, relative to the CHOOZ, the
statistic and systematic errors as much as possible. To achieve this we plan to
use two identical antineutrino detectors each with a ~50-ton liquid
scintillator target located at ~1100 m and ~250 m from the underground reactor
(~600 mwe). Much attention is given to the detector calibration and monitoring
procedures. As a first step we consider two much smaller pilot detectors each
of ~ a 3 ton target mass stationed at ~20 m and 35-60 m from the reactor. The
goals of this first stage are: (i) to accumulate necessary experience and (ii)
to investigate with electron neutrinos the LSND mass parameter region.
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We consider degree-biased random walkers whose probability to move from a
node to one of its neighbors of degree $k$ is proportional to $k^{\alpha}$,
where $\alpha$ is a tuning parameter. We study both numerically and
analytically three types of characteristic times, namely: i) the time the
walker needs to come back to the starting node, ii) the time it takes to visit
a given node for the first time, and iii) the time it takes to visit all the
nodes of the network. We consider a large data set of real-world networks and
we show that the value of $\alpha$ which minimizes the three characteristic
times is different from the value $\alpha_{\rm min}=-1$ analytically found for
uncorrelated networks in the mean-field approximation. In addition to this, we
found that assortative networks have preferentially a value of $\alpha_{\rm
min}$ in the range $[-1,-0.5]$, while disassortative networks have $\alpha_{\rm
min}$ in the range $[-0.5, 0]$. We derive an analytical relation between the
degree correlation exponent $\nu$ and the optimal bias value $\alpha_{\rm
min}$, which works well for real-world assortative networks. When only local
information is available, degree-biased random walks can guarantee smaller
characteristic times than the classical unbiased random walks, by means of an
appropriate tuning of the motion bias.
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Information Reconciliation is an essential part of Quantum Key distribution
protocols that closely resembles Slepian-Wolf coding. The application of
nonbinary LDPC codes in the Information Reconciliation stage of a
high-dimensional discrete-variable Quantum Key Distribution setup is proposed.
We model the quantum channel using a $q$-ary symmetric channel over which
qudits are sent. Node degree distributions optimized via density evolution for
the Quantum Key Distribution setting are presented, and we show that codes
constructed using these distributions allow for efficient reconciliation of
large-alphabet keys.
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In this letter, the characteristics of noise and long-term stability of near-
and mid-infrared (near-IR and mid-IR) gas-filled fiber Raman lasers have been
investigated for the first time. The results reveal that an increase in Raman
pulse energy is associated with a decrease in noise, and that the relative
pulse peak intensity noise (RIN) is always lower than the relative pulse energy
noise (REN). We also demonstrate that long-term drift of the pulse energy and
peak power are directly linked with the high amount of heat release during the
Raman Stokes generation. The demonstrated noise and long-term stability
performance provide necessary references for potential spectroscopic
applications as well as further improvements of the emerging mid-IR gas-filled
hollow-core fiber (HCF) Raman laser technology.
|
The radiative transport equation for the Schr\"odinger equation in a periodic
potential with a weak random potential in electromagnetic fields is derived
using asymptotic expansion.
|
We have used the VLBA at 5 GHz to observe all galaxies with nuclear radio
flux densities above 3.5 mJy found in a VLA survey at 15 GHz of a sample of
nearby LINER galaxies. All galaxies were detected revealing high brightness
temperature ($T_{b} \ga 10^8$ K) radio sources. Free-free emission is unlikely
since it greatly overpredicts the soft X-ray luminosities. We infer the
presence of AGN-like, non-thermal radio emission most likely powered by
under-fed black holes. Together with our VLA sample we estimate from our
observations that at least half of LINER galaxies host genuine AGN. We find no
evidence for highly inverted radio cores as predicted in the ADAF model: the
(non-simultaneous) spectral indices are on average around $\alpha=0.0$. In the
two brightest sources we detect some extended emission, which appears to
originate in jets in at least one of these galaxies. Together with the spectral
indices this suggests that the nuclear emission at centimeter radio waves is
largely dominated by emission from radio jets, very similar to the situation in
more luminous AGN. The energy released in these jets could be a significant
fraction of the energy budget in the accretion flow.
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The factorization method by Kirsch (1998) provides a necessary and sufficient
condition for characterizing the shape and position of an unknown scatterer by
using far-field patterns of infinitely many time-harmonic plane waves at a
fixed frequency. This paper is concerned with the factorization method with a
single far-field pattern to recover a convex polygonal scatterer/source. Its
one-wave version relies on the absence of analytical continuation of the
scattered/radiated wave-fields in corner domains. It can be regarded as a
domain-defined sampling method and does not require forward solvers. In this
paper we provide a rigorous mathematical justification of the one-wave
factorization method and present some preliminary numerical examples. In
particular, the proposed scheme can be interpreted as a model-driven and
data-driven method, because it essentially depends on the scattering model and
a priori given \emph{sample data}.
|
'
The theory of KMS weights is based on a theorem of Combes and a theorem of
Kustermans. In applications to KMS states for flows on a unital $C^*$-algebra
the relation to KMS weights of the stabilized algebra has proved useful and
this relation hinges on a theorem of Laca and Neshveyev. The first three
chapters present proofs of these fundamental results that require a minimum of
prerequisites; in particular, they do not depend on the modular theory of von
Neumann algebras. In contrast, starting with chapter four the presented
material draws heavily on the modular theory of von Neumann algebras. Most
results are known from the work of N. V. Pedersen, J. Quaegebeur, J. Verding,
J. Kustermans, S. Vaes, A. Kishimoto, A. Kumjian and J. Christensen, but new
ones begin to surface. In chapter nine and the Appendices D and E the reader
can find a presentation of results obtained recently by the author, partly in
collaboration with G. A. Elliott and Y. Sato. This material is a natural
culmination of methods developed around 1980 by Bratteli, Elliott, Herman and
Kishimoto. Finally, in chapter ten there is a short presentation of the notion
of factor types for KMS weights and states.
|
Aims. We use the IBIS/ISGRI telescope on-board INTEGRAL to measure the
position of the centroid of the 20-200 keV emission from the Crab region.
Methods. We find that the astrometry of the IBIS telescope is affected by the
temperature of the IBIS mask during the observation. After correcting for this
effect, we show that the systematic errors in the astrometry of the telescope
are of the order of 0.5 arcsec. In the case of the Crab nebula and several
other bright sources, the very large number of photons renders the level of
statistical uncertainty in the centroid smaller or comparable to this value.
Results. We find that the centroid of the Crab nebula in hard X-rays (20-40
keV) is shifted by 8.0 arcsec with respect to the Crab pulsar in the direction
of the X-ray centroid of the nebula. A similar shift is also found at higher
energies (40-100 and 100-200 keV). We observe a trend of decreasing shift with
energy, which can be explained by an increase in the pulsed fraction. To
differentiate between the contribution of the pulsar and the nebula, we divide
our data into an on-pulse and off-pulse sample. Surprisingly, the nebular
emission (i.e., off-pulse) is located significantly away from the X-ray
centroid of the nebula. Conclusions. In all 3 energy bands (20-40, 40-100, and
100-200 keV), we find that the centroid of the nebula is significantly offset
from the predicted position. We interpret this shift in terms of a cut-off in
the electron spectrum in the outer regions of the nebula, which is probably the
origin of the observed spectral break around 100 keV. From a simple
spherically-symmetric model for the nebula, we estimate that the electrons in
the external regions of the torus (d ~ 0.35 pc from the pulsar) reach a maximal
energy slightly below 10^14 eV.
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We show that a new interpretation of quantum mechanics, in which the notion
of event is defined without reference to measurement or observers, allows to
construct a quantum general ontology based on systems, states and events.
Unlike the Copenhagen interpretation, it does not resort to elements of a
classical ontology. The quantum ontology in turn allows us to recognize that a
typical behavior of quantum systems exhibits strong emergence and ontological
non-reducibility. Such phenomena are not exceptional but natural, and are
rooted in the basic mathematical structure of quantum mechanics.
|
Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial
complex whose vertices are knot isotopy classes in $\mathbb{S}^3$. Later
Horiuchi and Ohyama defined Gordian complex of virtual knots using $v$-move and
forbidden moves. In this paper we discuss Gordian complex of knots by region
crossing change and Gordian complex of virtual knots by arc shift move. Arc
shift move is a local move in the virtual knot diagram which results in
reversing orientation locally between two consecutive crossings. We show the
existence of an arbitrarily high dimensional simplex in both the Gordian
complexes, i.e., by region crossing change and by the arc shift move. For any
given knot (respectively, virtual knot) diagram we construct an infinite family
of knots (respectively, virtual knots) such that any two distinct members of
the family have distance one by region crossing change (respectively, arc shift
move). We show that that the constructed virtual knots have the same affine
index polynomial.
|
The primary objective of this paper is to propose and analyze the notion of
dual cones associated with the metric projection and generalized projection in
Banach spaces. We show that the dual cones, related to the metric projection
and generalized metric projection, lose many important properties in
transitioning from Hilbert spaces to Banach spaces. We also propose and analyze
the notions of faces and visions in Banach spaces and relate them to the metric
projection and generalized projection. We provide many illustrative examples to
give insight into the given results.
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Nowadays, many visual scene understanding problems are addressed by dense
prediction networks. But pixel-wise dense annotations are very expensive (e.g.,
for scene parsing) or impossible (e.g., for intrinsic image decomposition),
motivating us to leverage cheap point-level weak supervision. However, existing
pointly-supervised methods still use the same architecture designed for full
supervision. In stark contrast to them, we propose a new paradigm that makes
predictions for point coordinate queries, as inspired by the recent success of
implicit representations, like distance or radiance fields. As such, the method
is named as dense prediction fields (DPFs). DPFs generate expressive
intermediate features for continuous sub-pixel locations, thus allowing outputs
of an arbitrary resolution. DPFs are naturally compatible with point-level
supervision. We showcase the effectiveness of DPFs using two substantially
different tasks: high-level semantic parsing and low-level intrinsic image
decomposition. In these two cases, supervision comes in the form of
single-point semantic category and two-point relative reflectance,
respectively. As benchmarked by three large-scale public datasets
PASCALContext, ADE20K and IIW, DPFs set new state-of-the-art performance on all
of them with significant margins.
Code can be accessed at https://github.com/cxx226/DPF.
|
We have shown that electron spin density can be generated by a dc current
flowing across a $pn$ junction with an embedded asymmetric quantum well. Spin
polarization is created in the quantum well by radiative electron-hole
recombination when the conduction electron momentum distribution is shifted
with respect to the momentum distribution of holes in the spin split valence
subbands. Spin current appears when the spin polarization is injected from the
quantum well into the $n$-doped region of the $pn$ junction. The accompanied
emission of circularly polarized light from the quantum well can serve as a
spin polarization detector.
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We consider the scattering of in-plane waves that interact with an edge of a
structured {penetrable (inertial)} line defect contained in a triangular
lattice, composed of periodically placed masses interconnected by massless
elastic rods. The steady state problem for time-harmonic excitation is
converted into a vector Wiener-Hopf equation using Fourier transform. The
matrix Wiener-Hopf kernel of this equation describes all dynamic phenomena
engaged in the scattering process, which includes instances where localised
interfacial waves can emerge along structured defect. This information is
exploited to identify the dependency of the existence of these waves on the
incident wave parameters and properties of the inertial defect. The symmetry in
the structure of scattering medium allows us to convert the vectorial problem
into a pair of scalar Wiener-Hopf equations posed along the lattice row
containing the defect. The solution embodies the exact representation of
scattered field, in terms of a contour integral in the complex plane, that
includes the contributions of evanescent and propagating waves. The solution
reveals that in the remote lattice, the reflected and transmitted components of
incident field are {accompanied by dynamic modes from three distinct symmetry
classes in addition to localised interfacial waves}. These classes correspond
to tensile modes acting transverse to the defected lattice row, shear modes
that act parallel to this row, and wave modes represented as a mixture of these
two responses. Benchmark finite element calculations are provided to validate
results against the obtained semi-analytical solution, which involve numerical
computations of the contour integrals. Graphical illustrations demonstrate
special dynamic responses encountered during the wave scattering process,
including dynamic anisotropy, negative reflection and negative refraction.
|
We show that the error term in the asymptotic formula for the Ces{\`a}ro mean
of the singular series in the Goldbach and the Hardy-Littlewood prime-pair
conjectures cannot be too small and oscillates.
|
In this paper, we consider the q-extensions of Boole polynomials. From those
polynomials, we derive some new and interesting properties and identities
related to special polynomials.
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The effect of small noise in a smooth dynamical system is negligible on any
finite time interval. Here we study situations when it persists on intervals
increasing to infinity. Such asymptotic regime occurs when the system starts
from initial condition, sufficiently close to an unstable fixed point. In this
case, under appropriate scaling, the trajectory converges to solution of the
unperturbed system, started from a certain {\em random} initial condition. In
this paper we consider the case of one dimensional diffusions on the positive
half line, which often arise as scaling limits in population dynamics.
|
In this paper, we study a class of generalized extensible beam equations with
a superlinear nonlinearity \begin{equation*} \left\{ \begin{array}{ll} \Delta
^{2}u-M\left( \Vert \nabla u\Vert _{L^{2}}^{2}\right) \Delta u+\lambda V(x)
u=f( x,u) & \text{ in }\mathbb{R}^{N}, \\ u\in H^{2}(\mathbb{R}^{N}), &
\end{array}% \right. \end{equation*}% where $N\geq 3$, $M(t) =at^{\delta }+b$
with $a,\delta >0$ and $b\in \mathbb{% R}$, $\lambda >0$ is a parameter, $V\in
C(\mathbb{R}^{N},\mathbb{R})$ and $% f\in C(\mathbb{R}^{N}\times
\mathbb{R},\mathbb{R}).$ Unlike most other papers on this problem, we allow the
constant $b$ to be nonpositive, which has the physical significance. Under some
suitable assumptions on $V(x)$ and $f(x,u)$, when $a$ is small and $\lambda$ is
large enough, we prove the existence of two nontrivial solutions $u_{a,\lambda
}^{(1)}$ and $% u_{a,\lambda }^{(2)}$, one of which will blow up as the
nonlocal term vanishes. Moreover, $u_{a,\lambda }^{(1)}\rightarrow
u_{\infty}^{(1)}$ and $% u_{a,\lambda }^{(2)}\rightarrow u_{\infty}^{(2)}$
strongly in $H^{2}(\mathbb{% R}^{N})$ as $\lambda\rightarrow\infty$, where
$u_{\infty}^{(1)}\neq u_{\infty}^{(2)}\in H_{0}^{2}(\Omega )$ are two
nontrivial solutions of Dirichlet BVPs on the bounded domain $\Omega$. It is
worth noting that the regularity of weak solutions $u_{\infty}^{(i)}(i=1,2)$
here is explored. Finally, the nonexistence of nontrivial solutions is also
obtained for $a$ large enough.
|
We excite an epicyclic motion, whose amplitude depends on the vertical
position, $z$, in a simulation of a turbulent accretion disc. An epicyclic
motion of this kind may be caused by a warping of the disc. By studying how the
epicyclic motion decays we can obtain information about the interaction between
the warp and the disc turbulence. A high amplitude epicyclic motion decays
first by exciting inertial waves through a parametric instability, but its
subsequent exponential damping may be reproduced by a turbulent viscosity. We
estimate the effective viscosity parameter, $\alpha_{\rm v}$, pertaining to
such a vertical shear. We also gain new information on the properties of the
disc turbulence in general, and measure the usual viscosity parameter,
$\alpha_{\rm h}$, pertaining to a horizontal (Keplerian) shear. We find that,
as is often assumed in theoretical studies, $\alpha_{\rm v}$ is approximately
equal to $\alpha_{\rm h}$ and both are much less than unity, for the field
strengths achieved in our local box calculations of turbulence. In view of the
smallness ($\sim 0.01$) of $\alpha_{\rm v}$ and $\alpha_{\rm h}$ we conclude
that for $\beta = p_{\rm gas}/p_{\rm mag} \sim 10$ the timescale for diffusion
or damping of a warp is much shorter than the usual viscous timescale. Finally,
we review the astrophysical implications.
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