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High quality lithium niobate thin film microresonators provide an ideal
platform for on-chip nonlinear optics applications. However, the phase matching
condition for efficient parametric process sets a high requirement for
fabrication control. Here we demonstrate a photonic molecular structure
composed of two strongly coupled lithium niobate microdisks of different
diameters fabricated using femtosecond laser micromachining and focused ion
beam milling. With a continuous wave excitation, rich nonlinear optical
processes including cascaded four-wave mixing and stimulated Raman scattering
were observed around the second harmonic wavelength. Our results indicate that
the coupled microdisks form a superior system for nonlinear optical process.
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We show that the entanglement between the internal (spin) and external
(position) degrees of freedom of a qubit in a random (dynamically disordered)
one-dimensional discrete time quantum random walk (QRW) achieves its maximal
possible value asymptotically in the number of steps, outperforming the
entanglement attained by using ordered QRW. The disorder is modeled by
introducing an extra random aspect to QRW, a classical coin that randomly
dictates which quantum coin drives the system's time evolution. We also show
that maximal entanglement is achieved independently of the initial state of the
walker, study the number of steps the system must move to be within a small
fixed neighborhood of its asymptotic limit, and propose two experiments where
these ideas can be tested.
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Indoor air pollution is a major issue in developing countries such as India
and Bangladesh, exacerbated by factors like traditional cooking methods,
insufficient ventilation, and cramped living conditions, all of which elevate
the risk of health issues like lung infections and cardiovascular diseases.
With the World Health Organization associating around 3.2 million annual deaths
globally to household air pollution, the gravity of the problem is clear. Yet,
extensive empirical studies exploring these unique patterns and indoor
pollutions extent are missing. To fill this gap, we carried out a six months
long field study involving over 30 households, uncovering the complexity of
indoor air pollution in developing countries, such as the longer lingering time
of VOCs in the air or the significant influence of air circulation on the
spatiotemporal distribution of pollutants. We introduced an innovative IoT air
quality sensing platform, the Distributed Air QuaLiTy MONitor (DALTON ),
explicitly designed to meet the needs of these nations, considering factors
like cost, sensor type, accuracy, network connectivity, power, and usability.
As a result of a multi-device deployment, the platform identifies pollution
hot-spots in low and middle-income households in developing nations. It
identifies best practices to minimize daily indoor pollution exposure. Our
extensive qualitative survey estimates an overall system usability score of
2.04, indicating an efficient system for air quality monitoring.
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The accelerated progress in manufacturing noisy intermediate-scale quantum
(NISQ) computing hardware has opened the possibility of exploring its
application in transforming approaches to solving computationally challenging
problems. The important limitations common among all NISQ computing
technologies are the absence of error correction and the short coherence time,
which limit the computational power of these systems. Shortening the required
time of a single run of a quantum algorithm is essential for reducing
environment-induced errors and for the efficiency of the computation. We have
investigated the ability of a variational version of adiabatic quantum
computation (AQC) to generate an accurate state more efficiently compared to
existing adiabatic methods. The standard AQC method uses a time-dependent
Hamiltonian, connecting the initial Hamiltonian with the final Hamiltonian. In
the current approach, a navigator Hamiltonian is introduced which has a
non-zero amplitude only in the middle of the annealing process. Both the
initial and navigator Hamiltonians are determined using variational methods. A
hermitian cluster operator, inspired by coupled-cluster theory and truncated to
single and double excitations/de-excitations, is used as a navigator
Hamiltonian. A comparative study of our variational algorithm (VanQver) with
that of standard AQC, starting with a Hartree--Fock Hamiltonian, is presented.
The results indicate that the introduction of the navigator Hamiltonian
significantly improves the annealing time required to achieve chemical accuracy
by two to three orders of magnitude. The efficiency of the method is
demonstrated in the ground-state energy estimation of molecular systems,
namely, H$_2$, P4, and LiH.
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We elaborate on Abelian complex scalar models, which are dictated by natural
actions (all couplings are of order one), at fixed and large global $U(1)$
charge in an arbitrary number of dimensions. The ground state $|
\upsilon\rangle$ is coherently constructed by the zero modes and the appearance
of a centrifugal potential is quantum mechanically verified. Using the path
integral formulation we systematically analyze the quantum fluctuations around
$| \upsilon\rangle$ in order to derive an effective action for the Goldstone
mode, which becomes perturbatively meaningful when the charge is large. In this
regime we explicitly show that the whole construction is stable against quantum
corrections, in the sense that any higher derivative couplings to Goldstone's
tree-level action are suppressed by appropriate powers of the large charge.
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We point out a potential relevance between the Krein-Gupta-Bleuler (KGB)
vacuum leading to a fully covariant quantum field theory for gravity in de
Sitter (dS) spacetime and the observable smallness of the cosmological
constant. This may provide a formulation of linear quantum gravity in a
framework amenable to developing a more complete theory determining the value
of the cosmological constant.
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Relativistic AGN jets exhibit multi-timescale variability and a broadband
non-thermal spectrum extending from radio to gamma-rays. These highly
magnetized jets are prone to undergo several Magneto-hydrodynamic (MHD)
instabilities during their propagation in space and could trigger jet radiation
and particle acceleration. This work aims to study the implications of
relativistic kink mode instability on the observed long-term variability in the
context of the twisting in-homogeneous jet model. To achieve this, we
investigate the physical configurations preferable for forming kink mode
instability by performing high-resolution 3D relativistic MHD simulations of a
portion of highly magnetized jets. In particular, we perform simulations of
cylindrical plasma column with Lorentz factor $\geq 5$ and study the effects of
magnetization values and axial wave-numbers with decreasing pitch on the onset
and growth of kink instability. We have confirmed the impact of axial
wave-number on the dynamics of the plasma column including the growth of the
instability. In this work, we have further investigated the connection between
the dynamics of the plasma column with its time-varying emission features. From
our analysis, we find a correlated trend between the growth rate of kink mode
instability and the flux variability obtained from the simulated light curve.
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The quantized Knizhnik-Zamolodchikov equations associated with the
trigonometric R-matrix or the rational R-matrix of the A-type are considered.
Jackson integral representations for solutions of these equations are
described. Asymptotic solutions for a holonomic system of difference equations
are constructed. Relations between the integral representations and the Bethe
ansatz are indicated.
|
Image registration is important for medical imaging, the estimation of the
spatial transformation between different images. Many previous studies have
used learning-based methods for coarse-to-fine registration to efficiently
perform 3D image registration. The coarse-to-fine approach, however, is limited
when dealing with the different motions of nearby objects. Here we propose a
novel Motion-Aware (MA) structure that captures the different motions in a
region. The MA structure incorporates a novel Residual Aligner (RA) module
which predicts the multi-head displacement field used to disentangle the
different motions of multiple neighbouring objects. Compared with other deep
learning methods, the network based on the MA structure and RA module achieve
one of the most accurate unsupervised inter-subject registration on the 9
organs of assorted sizes in abdominal CT scans, with the highest-ranked
registration of the veins (Dice Similarity Coefficient / Average surface
distance: 62\%/4.9mm for the vena cava and 34\%/7.9mm for the portal and
splenic vein), with a half-sized structure and more efficient computation.
Applied to the segmentation of lungs in chest CT scans, the new network
achieves results which were indistinguishable from the best-ranked networks
(94\%/3.0mm). Additionally, the theorem on predicted motion pattern and the
design of MA structure are validated by further analysis.
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AmbSAT (or AmoebaSAT) is a biologically-inspired stochastic local search
(SLS) solver to explore solutions to the Boolean satisfiability problem (SAT).
AmbSAT updates multiple variables in parallel at every iteration step, and thus
AmbSAT can find solutions with a fewer number of iteration steps than some
other conventional SLS solvers for a specific set of SAT instances. However,
the parallelism of AmbSAT is not compatible with general-purpose
microprocessors in that many clock cycles are required to execute each
iteration; thus, AmbSAT requires special hardware that can exploit the
parallelism of AmbSAT to quickly find solutions. In this paper, we propose a
circuit model (hardware-friendly algorithm) that explores solutions to SAT in a
similar way to AmbSAT, which we call circuit-level AmbSAT (CL-AmbSAT). We
conducted numerical simulation to evaluate the search performance of CL-AmbSAT
for a set of randomly generated SAT instances that was designed to estimate the
scalability of our approach. Simulation results showed that CL-AmbSAT finds
solutions with a fewer iteration number than a powerful SLS solver, ProbSAT,
and outperforms even AmbSAT. Since CL-AmbSAT uses simple combinational logic to
update variables, CL-AmbSAT can be easily implemented in various hardware.
|
Perovskite solar cells (PSC) are shown to behave as coupled ionic-electronic
conductors with strong evidence that the ionic environment moderates both the
rate of electron-hole recombination and the band offsets in planar PSC.
Numerous models have been presented to explain the behavior of perovskite solar
cells, but to date no single model has emerged that can explain both the
frequency and time dependent response of the devices. Here we present a
straightforward coupled ionic-electronic model that can be used to explain the
large amplitude transient behavior and the impedance response of PSC.
|
This paper provides a thorough exploration of the absolute value equations
$Ax-|x|=b$, a seemingly straightforward concept that has gained heightened
attention in recent years. It is an NP-hard and nondifferentiable problem and
equivalent with the standard linear complementarity problem. Offering a
comprehensive review of existing literature, the study delves into theorems
concerning the existence and nonexistence of solutions to the absolute value
equations, along with numerical methods for effectively addressing this complex
equation. Going beyond conventional approaches, the paper investigates
strategies for obtaining solutions with minimal norms, techniques for
correcting infeasible systems, and other pertinent topics. By pinpointing
challenging issues and emphasizing open problems, this paper serves as a
valuable guide for shaping the future research trajectory in this dynamic and
multifaceted field.
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This paper presents a series of results on the interplay between quantum
estimation, cloning and finite de Finetti theorems. First, we consider the
measure-and-prepare channel that uses optimal estimation to convert M copies
into k approximate copies of an unknown pure state and we show that this
channel is equal to a random loss of all but s particles followed by cloning
from s to k copies. When the number k of output copies is large with respect to
the number M of input copies the measure-and-prepare channel converges in
diamond norm to the optimal universal cloning. In the opposite case, when M is
large compared to k, the estimation becomes almost perfect and the
measure-and-prepare channel converges in diamond norm to the partial trace over
all but k systems. This result is then used to derive de Finetti-type results
for quantum states and for symmetric broadcast channels, that is, channels that
distribute quantum information to many receivers in a permutationally invariant
fashion. Applications of the finite de Finetti theorem for symmetric broadcast
channels include the derivation of diamond-norm bounds on the asymptotic
convergence of quantum cloning to state estimation and the derivation of bounds
on the amount of quantum information that can be jointly decoded by a group of
k receivers at the output of a symmetric broadcast channel.
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Several recent spectroscopic investigations have presented conflicting
results on the existence of Na-rich asymptotic giant branch (AGB) stars in the
Galactic globular cluster M4 (NGC6121). The studies disagree on whether or not
Na-rich red giant branch (RGB) stars evolve to the AGB. For a sample of
previously published HER- MES/AAT AGB and RGB stellar spectra we present a
re-analysis of O, Na, and Fe abundances, and a new analysis of Mg and Al
abundances; we also present CN band strengths for this sample, derived from
low-resolution AAOmega spectra. Following a detailed literature comparison, we
find that the AGB samples of all studies consistently show lower abundances of
Na and Al, and are weaker in CN, than RGB stars in the cluster. This is similar
to recent observations of AGB stars in NGC 6752 and M 62. In an attempt to
explain this result, we present new theoretical stellar evolutionary models for
M 4; however, these predict that all stars, including Na-rich RGB stars, evolve
onto the AGB. We test the robustness of our abundance results using a variety
of atmospheric models and spectroscopic methods; however, we do not find
evidence that systematic modelling uncertainties can explain the apparent lack
of Na- rich AGB stars in M4. We conclude that an unexplained, but robust,
discordance between observations and theory remains for the AGB stars in M 4.
|
A helical CR structure is a decomposition of a real Euclidean space into an
even-dimensional horizontal subspace and its orthogonal vertical complement,
together with an almost complex structure on the horizontal space and a marked
vector in the vertical space. We prove an equivalence between such structures
and step two Carnot groups equipped with a distinguished normal geodesic, and
also between such structures and smooth real curves whose derivatives have
constant Euclidean norm. As a consequence, we relate step two Carnot groups
equipped with sub-Riemannian geodesics with this family of curves. The
restriction to the unit circle of certain planar homogeneous polynomial
mappings gives an instructive class of examples. We describe these examples in
detail.
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Let $f(z) = \sum A(n) n^{(k-1)/2} e(nz)$ be a cusp form of weight $k \geq 3$
on $\Gamma_0(N)$ with character $\chi$. By studying a certain shifted
convolution sum, we prove that $\sum_{n \leq X} A(n^2+h) = c_{f,h} X +
O_{f,h,\epsilon}(X^{\frac{3}{4}+\epsilon})$ for $\epsilon>0$, which improves a
result of Blomer from 2008 with error $X^{\frac{6}{7}+\epsilon}$.
This includes an appendix due to Raphael S. Steiner, proving stronger bounds
for certain spectral averages.
|
We study on which classes of graphs first-order logic (FO) and monadic
second-order logic (MSO) have the same expressive power. We show that for all
classes C of graphs that are closed under taking subgraphs, FO and MSO have the
same expressive power on C if, and only if, C has bounded tree depth. Tree
depth is a graph invariant that measures the similarity of a graph to a star in
a similar way that tree width measures the similarity of a graph to a tree. For
classes just closed under taking induced subgraphs, we show an analogous result
for guarded second-order logic (GSO), the variant of MSO that not only allows
quantification over vertex sets but also over edge sets. A key tool in our
proof is a Feferman-Vaught-type theorem that is constructive and still works
for unbounded partitions.
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We propose sparsemax, a new activation function similar to the traditional
softmax, but able to output sparse probabilities. After deriving its
properties, we show how its Jacobian can be efficiently computed, enabling its
use in a network trained with backpropagation. Then, we propose a new smooth
and convex loss function which is the sparsemax analogue of the logistic loss.
We reveal an unexpected connection between this new loss and the Huber
classification loss. We obtain promising empirical results in multi-label
classification problems and in attention-based neural networks for natural
language inference. For the latter, we achieve a similar performance as the
traditional softmax, but with a selective, more compact, attention focus.
|
The connection between the time-dependent physical spectrum of light and the
phase space overlap of Wigner functions is investigated for optical pulses.
Time and frequency properties of optical pulses with chirp are analyzed using
the phase space Wigner and Ambiguity distribution functions. It is shown that
optical pulses can exhibit interesting phenomena, very much reminiscent of
quantum mechanical interference, quantum entanglement of wave packets, and
quantum sub-Planck structures of the time and frequency phase space.
|
This short note is devoted to the study of the Hamiltonian formalism and the
integrability of the bosonic model introduced in [hep-th/0612079]. We calculate
Poisson bracket of spatial components of Lax connection and we argue that its
structure implies classical integrability of the theory.
|
We study higher statistical moments of Distortion for randomized social
choice in a metric implicit utilitarian model. The Distortion of a social
choice mechanism is the expected approximation factor with respect to the
optimal utilitarian social cost (OPT). The $k^{th}$ moment of Distortion is the
expected approximation factor with respect to the $k^{th}$ power of OPT. We
consider mechanisms that elicit alternatives by randomly sampling voters for
their favorite alternative. We design two families of mechanisms that provide
constant (with respect to the number of voters and alternatives) $k^{th}$
moment of Distortion using just $k$ samples if all voters can then participate
in a vote among the proposed alternatives, or $2k-1$ samples if only the
sampled voters can participate. We also show that these numbers of samples are
tight. Such mechanisms deviate from a constant approximation to OPT with
probability that drops exponentially in the number of samples, independent of
the total number of voters and alternatives. We conclude with simulations on
real-world Participatory Budgeting data to qualitatively complement our
theoretical insights.
|
For the isotropic Lam\'e system, we prove in dimensions three or larger that
both Lam\'e coefficients are uniquely recovered from partial Cauchy data on an
arbitrary open subset of the boundary provided that the coefficient $\mu$ is a
priori close to a constant.
|
We consider nonlocal linear Schr\"odinger-type critical systems of the type
\begin{equation}\label{eqabstr}
\Delta^{1/4} v=\Omega\, v~~~\mbox{in $\R\,.$} \
\end{equation} where $\Omega$ is antisymmetric potential in $L^2(\R,so(m))$,
$v$ is a ${\R}^m$ valued map and $\Omega\, v$ denotes the matrix
multiplication. We show that every solution $v\in L^2(\R,\R^m)$ of
\rec{eqabstr} is in fact in $L^p_{loc}(\R,\R^m)$, for every $2\le p<+\infty$,
in other words, we prove that the system (\ref{eqabstr}) which is a-priori only
critical in $L^2$ happens to have a subcritical behavior for antisymmetric
potentials.
As an application we obtain the $C^{0,\alpha}_{loc}$ regularity of weak
$1/2$-harmonic maps into $C^2$ compact manifold without boundary.
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We study quasi-geostrophic turbulence and plasma drift turbulence within the
Charney-Hasegawa-Mima (CHM) model. We focus, theoretically and using numerical
simulations, on conservation of {\em zonostrophy} and on its role in the
formation of the zonal jets. The zonostrophy invariant was first predicted in
\cite{perm,BNZ_invariant} in two special cases -- large-scale turbulence and
anisotropic turbulence. Papers \cite{perm,BNZ_invariant} also predicted that
the three invariants, energy, enstrophy and zonostrophy, will cascade
anisotropically into non-intersecting sectors in the $k$-space, so that the
energy cascade is "pushed" into the large-scale zonal scales. In the present
paper, we consider the scales much less than the Rossby deformation radius and
generalise the Fj{\o}rtoft argument of \cite{perm,BNZ_invariant} to find the
directions of the three cascades in this case. For the first time, we
demonstrate numerically that zonostrophy is well conserved by the CHM model,
and that the energy, enstrophy and zonostrophy cascade as prescribed by the
Fj{\o}rtoft argument if the nonlinearity is sufficiently weak. Moreover,
numerically we observe that zonostrophy is conserved surprisingly well at late
times and the triple-cascade picture is rather accurate even if the initial
nonlinearity is strong.
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We report calculations of the electronic structure of FeO in the LDA and
LDA+U approximation with and without rhombohedral distortion. In both cases LDA
renders an antiferromagnetic metal, and LDA+U opens a Hubbard gap. However, the
character of the gap is qualitatively different in the two structure, and the
difference can be traced down to underlying LDA band structure. An analysis of
the calculations gives a new insight on the origin of the insulating gap in 3d
monoxides and on the role of the k-dependency of U, missing in the contemporary
LDA+U method.
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Let $M$ be a compact K\"ahler manifold equipped with a pre-quantum line
bundle $L$. In [9], using $T$-symmetry, we constructed a polarization
$\mathcal{P}_{\mathrm{mix}}$ on $M$, which generalizes real polarizations on
toric manifolds. In this paper, we obtain the following results for the quantum
space $\mathcal{H}_{\mathrm{mix}}$ associated to $\mathcal{P}_{\mathrm{mix}}$.
First, $\mathcal{H}_{\mathrm{mix}}$ consists of distributional sections of $L$
with supports inside $\mu^{-1}(\mathfrak{t}^{*}_{\mathbb{Z}})$. This gives
$\mathcal{H}_{\mathrm{mix}}=\bigoplus_{\lambda \in
\mathfrak{t}^{*}_{\mathbb{Z}} } \mathcal{H}_{\mathrm{mix}, \lambda}$. Second,
the above decomposition of $\mathcal{H}_{\mathrm{mix}}$ coincides with the
weight decomposition for the $T$-symmetry. Third, an isomorphism
$\mathcal{H}_{\mathrm{mix}, \lambda} \cong H^{0}( M//_{\lambda}T,
L//_{\lambda}T)$, for regular $\lambda$. Namely, geometric quantization
commutes with symplectic reduction.
|
The milestone discovery of GW 170817-GRB 170817A-AT 2017gfo has shown that
gravitational wave (GW) could be produced during the merger of neutron
star-neutron star/black hole and that in electromagnetic (EM) wave a gamma-ray
burst (GRB) and a kilonova (KN) are generated in sequence after the merger.
Observationally, however, EM property before the merger phase is still unclear.
Here we report a peculiar precursor in a KN-associated long-duration GRB
211211A, providing evidence of the EM before the merger. This precursor lasts
$\sim$ 0.2 s, and the waiting time between the precursor and the main burst is
$\sim$ 1 s, comparable to that between GW 170817 and GRB 170817A. The spectrum
of the precursor could be well fit with a non-thermal cutoff power-law model
instead of a blackbody. Especially, a $\sim$22 Hz Quasi-Periodic Oscillation
candidate ($\sim 3\sigma$) is detected in the precursor. These temporal and
spectral properties indicate that this precursor is probably produced by a
catastrophic flare accompanying with magnetoelastic or crustal oscillations of
a magnetar in binary compact merger. The strong magnetic field of the magnetar
can also account for the prolonged duration of GRB 211211A. However, it poses a
challenge to reconcile the rather short lifetime of a magnetar with the rather
long spiraling time of a binary neutron star system only by the GW radiation
before merger.
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Massive Nambu-Goldstone (mNG) bosons are quasiparticles whose gap is
determined exactly by symmetry. They appear whenever a symmetry is broken
spontaneously in the ground state of a quantum many-body system, and at the
same time explicitly by the system's chemical potential. In this paper, we
revisit mNG bosons and show that apart from their gap, symmetry also protects
their scattering amplitudes. Just like for ordinary gapless NG bosons, the
scattering amplitudes of mNG bosons vanish in the long-wavelength limit. Unlike
for gapless NG bosons, this statement holds for any scattering process
involving one or more external mNG states; there are no kinematic singularities
associated with the radiation of a soft mNG boson from an on-shell initial or
final state.
|
Results are presented from a search for a narrow, spin-2 resonance decaying
into a pair of Z bosons, with one Z-boson decaying into leptons (e+e- or
mu+mu-) and the other into jets. An example of such a resonance is the
Kaluza--Klein graviton, G[KK], predicted in Randall--Sundrum models. The
analysis is based on a 4.9 inverse femtobarn sample of proton-proton collisions
at a center-of-mass energy of 7 TeV, collected with the CMS detector at the
LHC. Kinematic and topological properties including decay angular distributions
are used to discriminate between signal and background. No evidence for a
resonance is observed, and upper limits on the production cross sections times
branching fractions are set. In two models that predict Z-boson spin
correlations in graviton decays, graviton masses are excluded lower than a
value which varies between 610 and 945 GeV, depending on the model and the
strength of the graviton couplings.
|
The problem of (non)random distribution of points on sphere and in space is
investigated. The procedure for obtaining preferred direction (and plane) for
points on the sphere (in the sky) and in the space is discussed.
At present, directions of perihelia of the observed long-period comets cannot
be considered to be distributed uniformly in the sky (contrary of the statement
made by Neslu\v{s}an 1996). The action of galactic disk should increase the
concentration in the zone of galactic latitude $b \approx 0^{\circ}$, unless
the observational selection effects play an important role.
|
We obtain a relativistically covariant wave equation for neutrinos in dense
matter and electromagnetic field, which describes both flavor oscillations and
neutrino spin rotation. Using this equation we construct a quasi-classical
theory of these phenomena. We obtain the probabilities of arbitrary spin-flavor
transitions assuming the external conditions to be constant. We demonstrate
that the resonance behavior of the transition probabilities is possible only
when the neutrino flavor states cannot be described as superpositions of the
mass eigenstates. We discover that a resonance, which is similar to the
Mikheev-Smirnov-Wolfenstein resonance, takes place for neutrinos in magnetic
field due to the transition magnetic moments. This resonance gives an
opportunity to determine, whether neutrinos are Dirac or Majorana particles.
|
The Fast Lyapunov Indicators are functions defined on the tangent fiber of
the phase-space of a discrete (or continuous) dynamical system, by using a
finite number of iterations of the dynamics. In the last decade, they have been
largely used in numerical computations to localize the resonances in the
phase-space and, more recently, also the stable and unstable manifolds of
normally hyperbolic invariant manifolds. In this paper, we provide an analytic
description of the growth of tangent vectors for orbits with initial conditions
which are close to the stable-unstable manifolds of a hyperbolic saddle point
of an area-preserving map. The representation explains why the Fast Lyapunov
Indicator detects the stable-unstable manifolds of all fixed points which
satisfy a certain condition. If the condition is not satisfied, a suitably
modified Fast Lyapunov Indicator can be still used to detect the
stable-unstable manifolds. The new method allows for a detection of the
manifolds with a number of precision digits which increases linearly with
respect to the integration time. We illustrate the method on the critical
problem of detection of the so-called tube manifolds of the Lyapunov orbits of
L1,L2 in the circular restricted three-body problem.
|
We prove the existence of nonnegative martingale solutions to a class of
stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension
driven thin-film flow influenced by thermal noise. The construction applies to
a range of mobilites including the cubic one which occurs under the assumption
of a no-slip condition at the liquid-solid interface. Since their introduction
more than 15 years ago, by Davidovitch, Moro, and Stone and by Gr\"un, Mecke,
and Rauscher, the existence of solutions to stochastic thin-film equations for
cubic mobilities has been an open problem, even in the case of sufficiently
regular noise. Our proof of global-in-time solutions relies on a careful
combination of entropy and energy estimates in conjunction with a tailor-made
approximation procedure to control the formation of shocks caused by the
nonlinear stochastic scalar conservation law structure of the noise.
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Water's viscosity dependence on pressure was also not affected by O-GNFs,
except at 10 ppm, where the shuttle effect may have increased the presence of
hydrophobic methane bubbles in the solution. Under high pressure, the relative
viscosity of the system remained non-Einsteinian at all temperatures except 2C.
This may have been because the density anomaly of water was shifted to a colder
temperature as the hydrogen bonding network was weaker. The phase transition
from liquid to hydrate was identical to that of pure water, indicating that the
presence of different stages of growth was not affected by the presence of
O-GNF. However, the times to reach a maximum viscosity were faster in O-GNF
systems compared to pure water. This said, the hydrate formation limitations
inherent to the measurement system were not overcome by the presence of O-GNFs.
The times to application-relevant viscosity values were maximized in the 1 ppm
system at 49.75 % (200 mPa.s) and 31.93 % (500 mPa.s) faster than the baseline.
Therefore, the presence of O-GNFs allowed for shorter times to desired
viscosities and at lower driving forces than the baseline, improving the
viability of the hydrate technologies to which they can be added.
|
Transferring knowledge from a teacher neural network pretrained on the same
or a similar task to a student neural network can significantly improve the
performance of the student neural network. Existing knowledge transfer
approaches match the activations or the corresponding hand-crafted features of
the teacher and the student networks. We propose an information-theoretic
framework for knowledge transfer which formulates knowledge transfer as
maximizing the mutual information between the teacher and the student networks.
We compare our method with existing knowledge transfer methods on both
knowledge distillation and transfer learning tasks and show that our method
consistently outperforms existing methods. We further demonstrate the strength
of our method on knowledge transfer across heterogeneous network architectures
by transferring knowledge from a convolutional neural network (CNN) to a
multi-layer perceptron (MLP) on CIFAR-10. The resulting MLP significantly
outperforms the-state-of-the-art methods and it achieves similar performance to
the CNN with a single convolutional layer.
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A rigorous analytical approach is applied to solve the eigenvalue problem for
a pair of circular dielectric cylinders with complex permittivity. This
approach relies on field expansion in terms of two sets of orthogonal azimuthal
modes, which are coupled due to finite distance between the cylinders. We
investigate the ability of a gain-dielectric cylinder operated in the
fundamental TM mode to compensate material losses of a larger cylinder operated
in the higher-order radial TM mode. To achieve such a loss compensation
phenomenon, a simple design strategy is developed. It is shown that this
phenomenon can be achieved for a certain distance between the cylinders, which
is associated with the exceptional point of the system. For smaller distances,
the adverse impact of high-order azimuthal (hybrid) modes are found to be
essential. The results obtained are validated against full-wave simulations.
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This paper presents a highly robust space-frequency block coded (SFBC)
multiple-input multiple-output (MIMO) orthogonal frequency division
multiplexing (OFDM) system. The proposed system is based on applying a short
block length Walsh Hadamard transform (WHT) after the SFBC encoder. The main
advantage of the proposed system is that the channel frequency responses over
every two adjacent subcarriers become equal. Such interesting result provides
an exceptional operating conditions for SFBC-OFDM systems transmitting over
time and frequencyselective fading channels. Monte Carlo simulation is used to
evaluate the bit error rate (BER) performance of the proposed system using
various wireless channels with different degrees of frequency selectivity and
Doppler spreads. The simulation results demonstrated that the proposed scheme
substantially outperforms the standard SFBC-OFDM and the space-time block coded
(STBC) OFDM systems in severe time-varying frequency-selective fading channels.
Moreover, the proposed system has very low complexity because it is based on
short block length WHT.
|
Recent years have seen a phenomenal rise in performance and applications of
transformer neural networks. The family of transformer networks, including
Bidirectional Encoder Representations from Transformer (BERT), Generative
Pretrained Transformer (GPT) and Vision Transformer (ViT), have shown their
effectiveness across Natural Language Processing (NLP) and Computer Vision (CV)
domains. Transformer-based networks such as ChatGPT have impacted the lives of
common men. However, the quest for high predictive performance has led to an
exponential increase in transformers' memory and compute footprint. Researchers
have proposed techniques to optimize transformer inference at all levels of
abstraction. This paper presents a comprehensive survey of techniques for
optimizing the inference phase of transformer networks. We survey techniques
such as knowledge distillation, pruning, quantization, neural architecture
search and lightweight network design at the algorithmic level. We further
review hardware-level optimization techniques and the design of novel hardware
accelerators for transformers. We summarize the quantitative results on the
number of parameters/FLOPs and accuracy of several models/techniques to
showcase the tradeoff exercised by them. We also outline future directions in
this rapidly evolving field of research. We believe that this survey will
educate both novice and seasoned researchers and also spark a plethora of
research efforts in this field.
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The microscopic mechanism of heavy band formation, relevant for
unconventional superconductivity in CeCoIn$_5$ and other Ce-based heavy fermion
materials, depends strongly on the efficiency with which $f$ electrons are
delocalized from the rare earth sites and participate in a Kondo lattice.
Replacing Ce$^{3+}$ ($4f^1$, $J=5/2$) with Sm$^{3+}$ ($4f^5$, $J=5/2$), we show
that a combination of crystal field and on-site Coulomb repulsion causes
SmCoIn$_5$ to exhibit a $\Gamma_7$ ground state similar to CeCoIn$_5$ with
multiple $f$ electrons. Remarkably, we also find that with this ground state,
SmCoIn$_5$ exhibits a temperature-induced valence crossover consistent with a
Kondo scenario, leading to increased delocalization of $f$ holes below a
temperature scale set by the crystal field, $T_v$ $\approx$ 60 K. Our result
provides evidence that in the case of many $f$ electrons, the crystal field
remains the most important tuning knob in controlling the efficiency of
delocalization near a heavy fermion quantum critical point, and additionally
clarifies that charge fluctuations play a general role in the ground state of
"115" materials.
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We study spaces and moduli spaces of Riemannian metrics with non-negative
Ricci or non-negative sectional curvature on closed and open manifolds. We
construct, in particular, the first classes of manifolds for which these moduli
spaces have non-trivial rational homotopy, homology and cohomology groups. We
also show that in every dimension at least seven (respectively, at least eight)
there exist closed (respectively, open) manifolds for which the space and
moduli space of Riemannian metrics with non-negative sectional curvature has
infinitely many path components. A completely analogous statement holds for
spaces and moduli spaces of non-negative Ricci curvature metrics.
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Context: Being dominated by non-thermal emission from aligned relativistic
jets, blazars allow us to elucidate the physics of extragalactic jets, and,
ltimately, how the energy is extracted from the central black hole in
radio-loud active galactic nuclei. Aims: Crucial information is provided by
broad-band spectral energy distributions (SEDs), their trends with luminosity
and correlated multi-frequency variability. With this study we plan to obtain a
database of contemporaneous radio-to-optical spectra of a sample of blazars,
which are and will be observed by current and future high-energy satellites.
Methods: Since December 2004 we are performing a monthly multi-frequency radio
monitoring of a sample of 35 blazars at the antennas in Medicina and Noto.
Contemporaneous near-IR and optical observations for all our observing epochs
are organised. Results: Until June 2006 about 4000 radio measurements and 5500
near-IR and optical measurements were obtained. Most of the sources show
significant variability in all observing bands. Here we present the
multi-frequency data acquired during the first eighteen months of the project,
and construct the SEDs for the best-sampled sources.
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Although the mathematical study on the synchronization of wave equations at
finite horizon has been well developed, there was few results on the
synchronization of wave equations for long-time horizon. The aim of the paper
is to investigate the uniform synchronization at the infinite horizon for one
abstract linear second order evolution system in a Hilbert space.
First, using the classical compact perturbation theory on the uniform
stability of semigroups of contractions, we will establish a lower bound on the
number of damping, necessary for the uniform synchronization of the considered
system. Then, under the minimum number of damping, we clarify the algebraic
structure of the system as well as the necessity of the conditions of
compatibility on the coupling matrices. We then establish the uniform
synchronization by the compact perturbation method and then give the dynamics
of the asymptotic orbit. Various applications are given for the system of wave
equations with boundary feedback or (and) locally distributed feedback, and for
the system of Kirchhoff plate with distributed feedback. Some open questions
are raised at the end of the paper for future development.
The study is based on the synchronization theory and the compact perturbation
of semigroups.
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In our world with full of uncertainty, debates and argumentation contribute
to the progress of science and society. Despite of the increasing attention to
characterize human arguments, most progress made so far focus on the debate
outcome, largely ignoring the dynamic patterns in argumentation processes. This
paper presents a study that automatically analyzes the key factors in argument
persuasiveness, beyond simply predicting who will persuade whom. Specifically,
we propose a novel neural model that is able to dynamically track the changes
of latent topics and discourse in argumentative conversations, allowing the
investigation of their roles in influencing the outcomes of persuasion.
Extensive experiments have been conducted on argumentative conversations on
both social media and supreme court. The results show that our model
outperforms state-of-the-art models in identifying persuasive arguments via
explicitly exploring dynamic factors of topic and discourse. We further analyze
the effects of topics and discourse on persuasiveness, and find that they are
both useful - topics provide concrete evidence while superior discourse styles
may bias participants, especially in social media arguments. In addition, we
draw some findings from our empirical results, which will help people better
engage in future persuasive conversations.
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We show that the Fourier transform of Patterson-Sullivan measures associated
to convex cocompact groups of isometries of real hyperbolic space decays
polynomially quickly at infinity. The proof is based on the $L^2$-flattening
theorem obtained in prior work of the author, combined with a method based on
dynamical self-similarity for ruling out the sparse set of potential
frequencies where the Fourier transform can be large.
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Code Smell Detection (CSD) plays a crucial role in improving software quality
and maintainability. And Deep Learning (DL) techniques have emerged as a
promising approach for CSD due to their superior performance. However, the
effectiveness of DL-based CSD methods heavily relies on the quality of the
training data. Despite its importance, little attention has been paid to
analyzing the data preparation process. This systematic literature review
analyzes the data preparation techniques used in DL-based CSD methods. We
identify 36 relevant papers published by December 2023 and provide a thorough
analysis of the critical considerations in constructing CSD datasets, including
data requirements, collection, labeling, and cleaning. We also summarize seven
primary challenges and corresponding solutions in the literature. Finally, we
offer actionable recommendations for preparing and accessing high-quality CSD
data, emphasizing the importance of data diversity, standardization, and
accessibility. This survey provides valuable insights for researchers and
practitioners to harness the full potential of DL techniques in CSD.
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We report on the realisation of a chip-based multipole ion trap manufactured
using micro-electromechanical systems (MEMS) technology. It provides ion
confinement in an almost field-free volume between two planes of radiofrequency
electrodes, deposited on glass substrates, which allows for optical access to
the trap. An analytical model of the effective trapping potential is presented
and compared with numerical calculations. Stable trapping of argon ions is
achieved and a lifetime of 16s is measured. Electrostatic charging of the chip
surfaces is studied and found to agree with a numerical estimate.
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We address estimation of intervention effects in experimental designs in
which (a) interventions are assigned at the cluster level; (b) clusters are
selected to form pairs, matched on observed characteristics; and (c)
intervention is assigned to one cluster at random within each pair. One goal of
policy interest is to estimate the average outcome if all clusters in all pairs
are assigned control versus if all clusters in all pairs are assigned to
intervention. In such designs, inference that ignores individual level
covariates can be imprecise because cluster-level assignment can leave
substantial imbalance in the covariate distribution between experimental arms
within each pair. However, most existing methods that adjust for covariates
have estimands that are not of policy interest. We propose a methodology that
explicitly balances the observed covariates among clusters in a pair, and
retains the original estimand of interest. We demonstrate our approach through
the evaluation of the Guided Care program.
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The Polaris Flare cloud region contains a great deal of extended emission. It
is at high declination and high Galactic latitude. It was previously seen
strongly in IRAS Cirrus emission at 100 microns. We have detected it with both
PACS and SPIRE on Herschel. We see filamentary and low-level structure. We
identify the five densest cores within this structure. We present the results
of a temperature, mass and density analysis of these cores. We compare their
observed masses to their virial masses, and see that in all cases the observed
masses lie close to the lower end of the range of estimated virial masses.
Therefore, we cannot say whether they are gravitationally bound prestellar
cores. Nevertheless, these are the best candidates to be potentialprestellar
cores in the Polaris cloud region.
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In this work, we have studied the behavior of null geodesics within a
rotating wormhole space-time in non-magnetized pressure-less plasma. By
focusing on the dispersion relation of the plasma and disregarding its direct
gravitational effects, we examine how light rays traverse in the mentioned
space-time. A key highlight of the work is the necessity of a specific plasma
distribution profile to establish a generalized Carter's constant, shedding
light on the importance of this parameter. Furthermore, we have derived
analytical formulas to distinguish the shadow boundary across various plasma
profiles, uncovering a fascinating trend of diminishing shadow size as plasma
density increases. Intriguingly, certain limits of the plasma parameters result
in the complete disappearance of the shadow. When calculating the deflection
angle by a wormhole in plasma space-time, we observe a distinct pattern: the
angle decreases as the plasma parameter rises in non-homogeneous plasma
space-time, diverging from the behavior observed in homogeneous plasma
space-time. Also, leveraging observational data from M$87^{\ast}$, we establish
constraints on the throat radius. Furthermore, minimum shadow diameters provide
valuable constraints for the radial and latitudinal plasma parameters.
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For each natural number $m\ge 3$, let $P_m(x)$ denote the generalized
$m$-gonal number $\frac{(m-2)x^2-(m-4)x}{2}$ with $x\in\mathbb{Z}$. In this
paper, with the help of the congruence theta function, we establish conditions
on $a$, $b$, $c$ for which the sum $P_a(x)+P_b(y)+P_c(z)$ represents all but
finitely many positive integers.
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Systematic choice of the Hecke eigenforms of half-integral weight is an
interesting problem in the theory of modular forms. In this paper, we find all
Dedekind-eta products of half-integral weight which are Hecke eigenforms up to
weight 15/2 with varying levels. Proof is based on the Shimura lift.
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Let $K$ be a finite extension of $\mathbf{Q}_p$ and let $G_K =
\mathrm{Gal}(\bar{\mathbf{Q}}_p/K)$. There is a very useful classification of
$p$-adic representations of $G_K$ in terms of cyclotomic
$(\varphi,\Gamma)$-modules (cyclotomic means that $\Gamma={\rm
Gal}(K_\infty/K)$ where $K_\infty$ is the cyclotomic extension of $K$). One
particularly convenient feature of the cyclotomic theory is the fact that any
$(\varphi,\Gamma)$-module is overconvergent.
Questions pertaining to the $p$-adic local Langlands correspondence lead us
to ask for a generalization of the theory of $(\varphi,\Gamma)$-modules, with
the cyclotomic extension replaced by an infinitely ramified $p$-adic Lie
extension $K_\infty / K$. It is not clear what shape such a generalization
should have in general. Even in the case where we have such a generalization,
namely the case of a Lubin-Tate extension, most $(\varphi,\Gamma)$-modules fail
to be overconvergent.
In this article, we develop an approach that gives a solution to both
problems at the same time, by considering the locally analytic vectors for the
action of $\Gamma$ inside some big modules defined using Fontaine's rings of
periods. We show that, in the cyclotomic case, we recover the ususal
overconvergent $(\varphi,\Gamma)$-modules. In the Lubin-Tate case, we can
prove, as an application of our theory, a folklore conjecture in the field
stating that $(\varphi,\Gamma)$-modules attached to $F$-analytic
representations are overconvergent.
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The ParaOpt algorithm was recently introduced as a time-parallel solver for
optimal-control problems with a terminal-cost objective, and convergence
results have been presented for the linear diffusive case with implicit-Euler
time integrators. We reformulate ParaOpt for tracking problems and provide
generalized convergence analyses for both objectives. We focus on linear
diffusive equations and prove convergence bounds that are generic in the time
integrators used. For large problem dimensions, ParaOpt's performance depends
crucially on having a good preconditioner to solve the arising linear systems.
For the case where ParaOpt's cheap, coarse-grained propagator is linear, we
introduce diagonalization-based preconditioners inspired by recent advances in
the ParaDiag family of methods. These preconditioners not only lead to a
weakly-scalable ParaOpt version, but are themselves invertible in parallel,
making maximal use of available concurrency. They have proven convergence
properties in the linear diffusive case that are generic in the time
discretization used, similarly to our ParaOpt results. Numerical results
confirm that the iteration count of the iterative solvers used for ParaOpt's
linear systems becomes constant in the limit of an increasing processor count.
The paper is accompanied by a sequential MATLAB implementation.
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Reinforcement learning (RL) methods usually treat reward functions as black
boxes. As such, these methods must extensively interact with the environment in
order to discover rewards and optimal policies. In most RL applications,
however, users have to program the reward function and, hence, there is the
opportunity to make the reward function visible -- to show the reward
function's code to the RL agent so it can exploit the function's internal
structure to learn optimal policies in a more sample efficient manner. In this
paper, we show how to accomplish this idea in two steps. First, we propose
reward machines, a type of finite state machine that supports the specification
of reward functions while exposing reward function structure. We then describe
different methodologies to exploit this structure to support learning,
including automated reward shaping, task decomposition, and counterfactual
reasoning with off-policy learning. Experiments on tabular and continuous
domains, across different tasks and RL agents, show the benefits of exploiting
reward structure with respect to sample efficiency and the quality of resultant
policies. Finally, by virtue of being a form of finite state machine, reward
machines have the expressive power of a regular language and as such support
loops, sequences and conditionals, as well as the expression of temporally
extended properties typical of linear temporal logic and non-Markovian reward
specification.
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We prove the birational rigidity of Fano complete intersections of index 1
with a singular point of high multiplicity, which can be close to the degree of
the variety. In particular, the groups of birational and biregular
automorphisms of these varieties are equal, and they are non-rational. The
proof is based on the techniques of the method of maximal singularities, the
generalized $4n^2$-inequality for complete intersection singularities and the
technique of hypertangent divisors.
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We investigate the validity of the Linear Elastic Fracture Mechanics approach
to dynamic fracture. We first test the predictions in a lattice simulation,
using a formula of Eshelby for the time-dependent Stress Intensity Factor.
Excellent agreement with the theory is found. We then use the same method to
analyze the experiment of Sharon and Fineberg. The data here is not consistent
with the theoretical expectation.
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We consider the exact superpotential of N=1 super Yang-Mills theory with
gauge group SO(N) and arbitrary tree-level polynomial superpotential of one
adjoint Higgs field. A field-theoretic derivation of the glueball
superpotential is given, based on factorization of the N=2 Seiberg-Witten
curve. Following the conjecture of Dijkgraaf and Vafa, the result is matched
with the corresponding SO(N) matrix model prediction. The verification involves
an explicit solution of the first non-trivial loop equation, relating the
spherical free energy to that of the non-orientable surfaces with topology
$RP^2$.
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We consider the question of Quantum Unique Ergodicity for quasimodes on
surfaces of constant negative curvature, and conjecture the order of quasimodes
that should satisfy QUE. We then show that this conjecture holds for Eisenstein
series on the modular surface, extending results of Luo-Sarnak and Jakobson.
Moreover, we observe that the equidistribution results of Luo-Sarnak and
Jakobson extend to quasimodes of much weaker order--- for which QUE is known to
fail on compact surfaces--- though in this scenario the total mass of the limit
measures will decrease. We interpret this stronger equidistribution property in
the context of arithmetic QUE, in light of recent joint work with E.
Lindenstrauss on joint quasimodes.
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In this paper, we discuss how to efficiently evaluate and assemble general
finite element variational forms on H(div) and H(curl). The proposed strategy
relies on a decomposition of the element tensor into a precomputable reference
tensor and a mesh-dependent geometry tensor. Two key points must then be
considered: the appropriate mapping of basis functions from a reference
element, and the orientation of geometrical entities. To address these issues,
we extend here a previously presented representation theorem for affinely
mapped elements to Piola-mapped elements. We also discuss a simple numbering
strategy that removes the need to contend with directions of facet normals and
tangents. The result is an automated, efficient, and easy-to-use implementation
that allows a user to specify finite element variational forms on H(div) and
H(curl) in close to mathematical notation.
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Let $U_q(\hat{\cal G})$ be a quantized affine Lie algebra. It is proven that
the universal R-matrix $R$ of $U_q(\hat{\cal G})$ satisfies the celebrated
conjugation relation $R^\dagger=TR$ with $T$ the usual twist map. As
applications, braid generators are shown to be diagonalizable on arbitrary
tensor product modules of integrable irreducible highest weight $U_q(\hat{\cal
G})$-module and a spectral decomposition formula for the braid generators is
obtained which is the generalization of Reshetikhin's and Gould's forms to the
present affine case. Casimir invariants are constructed and their eigenvalues
computed by means of the spectral decomposition formula. As a by-product, an
interesting identity is found.
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Pandharipande-Pixton-Zvonkine's proof of Pixton's generalized Faber-Zagier
relations in the tautological ring of $\overline M_{g, n}$ has started the
study of tautological relations from semisimple cohomological field theories.
In this article we compare the relations obtained in the examples of the
equivariant Gromov-Witten theory of projective spaces and of spin structures.
We prove an equivalence between the $\mathbb P^1$- and 3-spin relations, and
more generally between restricted $\mathbb P^m$-relations and similarly
restricted (m + 2)-spin relations. We also show that the general $\mathbb
P^m$-relations imply the (m + 2)-spin relations.
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Primordial Black Holes (PBHs) are of interest in many cosmological contexts.
PBHs lighter than about 1012 kg are predicted to be directly detectable by
their Hawking radiation. This radiation should produce both a diffuse
extragalactic gamma-ray background from the cosmologically-averaged
distribution of PBHs and gamma-ray burst signals from individual light black
holes. The Fermi, Milagro, Veritas, HESS and HAWC observatories, in combination
with new burst recognition methodologies, offer the greatest sensitivity for
the detection of such black holes or placing limits on their existence.
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A recent measurement of the proper motion of PSR J0908-4913 shows that it is
a fast moving object at a distance of some 3 kpc. Here we present evidence that
the pulsar is located at the edge of a previously unknown, filled-centre
supernova remnant, G270.4-1.0. The velocity vector of the pulsar points
directly away from the centre of the remnant. The putative association of the
pulsar with SNR G270.4-1.0 implies the pulsar is ~12kyr old, significantly less
than its characteristic age of 110kyr. We show that the rotation axis of the
pulsar points in the direction of the proper motion. Rotation measure and
dispersion measure variations are seen over time, likely indicating the pulsar
is passing behind a filament of the remnant.
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We find the first three most general Minkowski or Hsiung-Minkowski identities
relating the total mean curvatures $H_i$, of degrees $i=1,2,3$, of a closed
hypersurface $N$ immersed in a given orientable Riemannian manifold $M$ endowed
with any given vector field $P$. Then we specialise the three identities to the
case when $P$ is a position vector field. We further obtain that the classical
Minkowski identity is natural to all Riemannian manifolds and, moreover, that a
corresponding 1st degree Hsiung-Minkowski identity holds true for all Einstein
manifolds. We apply the result to hypersurfaces with constant $H_1,H_2$.
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Due to its low bandgap and high optical efficiency, tellurium is considered
an important material candidate for mid-infrared applications. Taking advantage
of its structural anisotropy, we fabricated tellurium nanowire devices and
investigated the radiative interaction of charge carriers by the
polarization-resolved photoconductivity spectra under mid-infrared
illumination. The intensity of the photoresponse shows sensitive dependence on
temperature and could be significantly boosted by positive voltage bias from
the back gate.
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We present a detection of a broad Ly-alpha absorber (BLA) with a matching O
VI line in the nearby universe. The BLA is detected at z = 0.01028 in the high
S/N spectrum of Mrk 290 obtained using the Cosmic Origins Spectrograph. The
Ly-alpha absorption has two components, with b(HI) = 55 +/- 1 km/s and b(HI) =
33 +/- 1 km/s, separated in velocity by v ~ 115 km/s. The O VI, detected by
FUSE at z = 0.01027, has a b(OVI) = 29 +/- 3 km/s and is kinematically well
aligned with the broader HI component. The different line widths of the BLA and
OVI suggest a temperature of T = 1.4 x 10^5 K in the absorber. The observed
line strength ratios and line widths favor an ionization scenario in which both
ion-electron collisions and UV photons contribute to the ionization in the gas.
Such a model requires a low-metallicity of -1.7 dex, ionization parameter of
log U ~ -1.4, a large total hydrogen column density of N(H) ~ 4 x 10^19 cm^-2,
and a path length of 400 kpc. The line of sight to Mrk 290 intercepts at the
redshift of the absorber, a megaparsec scale filamentary structure extending
over 20 deg in the sky, with several luminous galaxies distributed within 1.5
Mpc projected distance from the absorber. The collisionally ionized gas in this
absorber is likely tracing a shock-heated gaseous structure, consistent with a
few different scenarios for the origin, including an over-dense region of the
WHIM in the galaxy filament or highly ionized gas in the extended halo of one
of the galaxies in the filament. In general, BLAs with metals provide an
efficient means to study T ~ 10^5 - 10^6 K gas in galaxy halos and in the
intergalactic medium. A substantial fraction of the baryons "missing" from the
present universe is predicted to be in such environments in the form of highly
ionized plasma.
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Deep convolutional neural networks (CNNs) are broadly considered to be
state-of-the-art generic end-to-end image classification systems. However, they
are known to underperform when training data are limited and thus require data
augmentation strategies that render the method computationally expensive and
not always effective. Rather than using a data augmentation strategy to encode
invariances as typically done in machine learning, here we propose to
mathematically augment a nearest subspace classification model in
sliced-Wasserstein space by exploiting certain mathematical properties of the
Radon Cumulative Distribution Transform (R-CDT), a recently introduced image
transform. We demonstrate that for a particular type of learning problem, our
mathematical solution has advantages over data augmentation with deep CNNs in
terms of classification accuracy and computational complexity, and is
particularly effective under a limited training data setting. The method is
simple, effective, computationally efficient, non-iterative, and requires no
parameters to be tuned. Python code implementing our method is available at
https://github.com/rohdelab/mathematical_augmentation. Our method is integrated
as a part of the software package PyTransKit, which is available at
https://github.com/rohdelab/PyTransKit.
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Election manifestos document the intentions, motives, and views of political
parties. They are often used for analysing a party's fine-grained position on a
particular issue, as well as for coarse-grained positioning of a party on the
left--right spectrum. In this paper we propose a two-stage model for
automatically performing both levels of analysis over manifestos. In the first
step we employ a hierarchical multi-task structured deep model to predict fine-
and coarse-grained positions, and in the second step we perform post-hoc
calibration of coarse-grained positions using probabilistic soft logic. We
empirically show that the proposed model outperforms state-of-art approaches at
both granularities using manifestos from twelve countries, written in ten
different languages.
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Prevalent ungrammatical expressions and disfluencies in spontaneous speech
from second language (L2) learners pose unique challenges to Automatic Speech
Recognition (ASR) systems. However, few datasets are tailored to L2 learner
speech. We publicly release LearnerVoice, a dataset consisting of 50.04 hours
of audio and transcriptions of L2 learners' spontaneous speech. Our linguistic
analysis reveals that transcriptions in our dataset contain L2S (L2 learner's
Spontaneous speech) features, consisting of ungrammatical expressions and
disfluencies (e.g., filler words, word repetitions, self-repairs, false
starts), significantly more than native speech datasets. Fine-tuning
whisper-small.en with LearnerVoice achieves a WER of 10.26%, 44.2% lower than
vanilla whisper-small.en. Furthermore, our qualitative analysis indicates that
54.2% of errors from the vanilla model on LearnerVoice are attributable to L2S
features, with 48.1% of them being reduced in the fine-tuned model.
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In the present work we describe a model-independent method of developing a
plot of scale factor versus lookback time from the usual Hubble diagram of
modulus data against redshift. This is the first plot of this type. We follow
the model-independent methodology of Daly and Djorgovski (2004) used for their
radio-galaxy data. Once the data plot is completed, any model can be applied
and will display accordingly as described in standard literature. We then
compile an extensive data set to z = 1.8 by combining SNe Ia data from SNLS3 of
Conley et al. (2011), High-z SNe data of Riess et al. (2004) and radio-galaxy
data of Daly & Djorgovski (2004) to be used to validate the new plot. We first
display these data on a standard Hubble diagram to confirm the best fit for
LCDM cosmology and thus validate the joined data set. The scale factor plot is
then developed from the data and the LCDM model is again displayed from a
least-squares fit. The fit parameters are in agreement with the Hubble diagram
fit confirming the validity of the new plot. Of special interest is the
transition-time of the universe which in the scale factor plot will appear as
an inflection point in the data set. Noise is more visible on this presentation
which is particularly sensitive to inflection points of any model displayed on
the plot unlike on a modulus-z diagram where there are no inflection points and
the transition-z is not at all obvious by inspection. We obtain a lower limit
of z >0.6. It is evident from this presentation that there is a dearth of SNe
data in the range, z = 1-2, exactly the range necessary to confirm a LCDM
transition-z in the neighborhood of z = 0.76.
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We derive the new identity in homotopy algebras which directly corresponds to
the Schwinger-Dyson equations in quantum field theory. As an application, we
derive the Ward-Takahashi identities. We demonstrate that the Ward-Takahashi
identities are reproduced in several examples. In general, our formula contains
divergence. We mediate this problem by introducing stubs known in the context
of string field theory. With the regularization, we can calculate the anomaly
such as axial U(1) anomaly in vector-like U(1) gauge theory.
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In this paper we present a model to calculate the stringy product on twisted
orbifold K-theory of Adem-Ruan-Zhang for abelian complex orbifolds.
In the first part we consider the non-twisted case on an orbifold presented
as the quotient of a manifold acted by a compact abelian Lie group. We give an
explicit description of the obstruction bundle, we explain the relation with
the product defined by Jarvis-Kaufmann-Kimura and, via a Chern character map,
with the Chen-Ruan cohomology, and we explicitely calculate the stringy product
for a weighted projective orbifold.
In the second part we consider orbifolds presented as the quotient of a
manifold acted by a finite abelian group and twistings coming from the group
cohomology. We show a decomposition formula for twisted orbifold K-theory that
is suited to calculate the stringy product and we use this formula to calculate
two examples when the group is $(\integer/2)^3$.
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We consider a one-dimensional diffusion in a stable L\'evy environment. We
show that the normalized local time process refocused at the bottom of the
standard valley with height $\log t$, $(L_X(t,\mathfrak m_{\log t}+x)/t,x\in
\R)$, converges in law to a functional of two independent L\'evy processes
conditioned to stay positive. To prove this result, we show that the law of the
standard valley is close to a two-sided L\'evy process conditioned to stay
positive. We also obtain the limit law of the supremum of the normalized local
time. This result has been obtained by Andreoletti and Diel in the case of a
Brownian environment.
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Envy-freeness is a widely studied notion in resource allocation, capturing
some aspects of fairness. The notion of envy being inherently subjective
though, it might be the case that an agent envies another agent, but that she
objectively has no reason to do so. The difficulty here is to define the notion
of objectivity, since no ground-truth can properly serve as a basis of this
definition. A natural approach is to consider the judgement of the other agents
as a proxy for objectivity. Building on previous work by Parijs (who introduced
"unanimous envy") we propose the notion of approval envy: an agent $a_i$
experiences approval envy towards $a_j$ if she is envious of $a_j$, and
sufficiently many agents agree that this should be the case, from their own
perspectives. Some interesting properties of this notion are put forward.
Computing the minimal threshold guaranteeing approval envy clearly inherits
well-known intractable results from envy-freeness, but (i) we identify some
tractable cases such as house allocation; and (ii) we provide a general method
based on a mixed integer programming encoding of the problem, which proves to
be efficient in practice. This allows us in particular to show experimentally
that existence of such allocations, with a rather small threshold, is very
often observed.
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Recent analyses of several isospin effects in heavy-ion reactions have
allowed us to constrain the density dependence of nuclear symmetry energy at
sub-saturation densities within a narrow range. Combined with constraints on
the Equation of State (EOS) of symmetric nuclear matter obtained previously
from analyzing the elliptic flow in relativistic heavy-ion collisions, the EOS
of neutron-rich nuclear matter is thus partially constrained. Here we report
effects of the partially constrained EOS of neutron-rich nuclear matter on the
mass-radius correlation, moment of inertia, elliptical deformation and
gravitational radiation of (rapidly) rotating neutron stars.
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We consider hyperbolic and partially hyperbolic diffeomorphisms on compact
manifolds. Associated with invariant foliation of these systems, we define some
topological invariants and show certain relationships between these topological
invariants and the geometric and Lyapunov growths of these foliations. As an
application, we show examples of systems with persistent non- absolute
continuous center and weak unstable foliations. This generalizes the remarkable
results of Shub and Wilkinson to cases where the center manifolds are not
compact.
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Domain Adaptive Object Detection (DAOD) focuses on improving the
generalization ability of object detectors via knowledge transfer. Recent
advances in DAOD strive to change the emphasis of the adaptation process from
global to local in virtue of fine-grained feature alignment methods. However,
both the global and local alignment approaches fail to capture the topological
relations among different foreground objects as the explicit dependencies and
interactions between and within domains are neglected. In this case, only
seeking one-vs-one alignment does not necessarily ensure the precise knowledge
transfer. Moreover, conventional alignment-based approaches may be vulnerable
to catastrophic overfitting regarding those less transferable regions (e.g.
backgrounds) due to the accumulation of inaccurate localization results in the
target domain. To remedy these issues, we first formulate DAOD as an open-set
domain adaptation problem, in which the foregrounds and backgrounds are seen as
the ``known classes'' and ``unknown class'' respectively. Accordingly, we
propose a new and general framework for DAOD, named Foreground-aware
Graph-based Relational Reasoning (FGRR), which incorporates graph structures
into the detection pipeline to explicitly model the intra- and inter-domain
foreground object relations on both pixel and semantic spaces, thereby endowing
the DAOD model with the capability of relational reasoning beyond the popular
alignment-based paradigm. The inter-domain visual and semantic correlations are
hierarchically modeled via bipartite graph structures, and the intra-domain
relations are encoded via graph attention mechanisms. Empirical results
demonstrate that the proposed FGRR exceeds the state-of-the-art performance on
four DAOD benchmarks.
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We formulate nonlinear nonlocal integro-PDE with memory, biloaded (boundary
integrals load the ambient space, and the ambient space loads the boundary),
and the associated optimal control problems. We derive part of the necessary
conditions for optimality in the form of Hamilton-Euler-Lagrange loaded
integro-PDEs. In the process, we introduce an agglomeration of new differential
operators. Our results have relevance to optimal amelioration of flooded areas,
remediation of sites of contaminated groundwater, and active control methods
for optimally extinguishing forest fires.
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We consider the Kudla-Millson theta series associated to a quadratic space of
signature $(N,N)$. By combining a `see-saw' argument with the Siegel-Weil
formula, we show that its (regularized) integral along a torus attached to a
totally real field of degree $N$ is the diagonal restriction of an Eisenstein
series. It allows us to express the Fourier coefficients of the diagonal
restriction as intersection numbers, which generalizes a result of
Darmon-Pozzi-Vonk to totally real fields.
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We suggest a modification of the operator exponential method for the
numerical solving the difference linear initial boundary value problems. The
scheme is based on the representation of the difference operator for given
boundary conditions as the perturbation of the same operator for periodic ones.
We analyze the error, stability and efficiency of the scheme for a model
example of the one-dimensional operator of second difference.
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Magic state resources or non-stabilizerness quantify the beyond-Clifford
operations necessary for universal quantum computing. How rapidly are magic
resources generated by generic many-body dynamics under constraints of
locality? We address this problem by exploring magic spreading in brick-wall
random unitary circuits. Inspired by the algebraic structure of the Clifford
group, we propose a scalable measure of non-stabilizerness, the
Calderbank-Shor-Steane entropy, which generalizes the notion of stabilizer
entropy and mirrors its qualitative behavior. This metric enables the
investigation of non-stabilizerness dynamics for systems of up to N = 1024
qudits. Our main finding is that magic resources equilibrate on timescales
logarithmic in system size N, akin to anticoncentration and Hilbert space
delocalization measures, but differently from entanglement entropy. We
conjecture that our findings describe the phenomenology of non-stabilizerness
growth in a broad class of chaotic many-body systems.
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The technological singularity refers to a hypothetical scenario in which
technological advances virtually explode. The most popular scenario is the
creation of super-intelligent algorithms that recursively create ever higher
intelligences. It took many decades for these ideas to spread from science
fiction to popular science magazines and finally to attract the attention of
serious philosophers. David Chalmers' (JCS 2010) article is the first
comprehensive philosophical analysis of the singularity in a respected
philosophy journal. The motivation of my article is to augment Chalmers' and to
discuss some issues not addressed by him, in particular what it could mean for
intelligence to explode. In this course, I will (have to) provide a more
careful treatment of what intelligence actually is, separate speed from
intelligence explosion, compare what super-intelligent participants and
classical human observers might experience and do, discuss immediate
implications for the diversity and value of life, consider possible bounds on
intelligence, and contemplate intelligences right at the singularity.
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With the proliferation of generative AI and the increasing volume of
generative data (also called as synthetic data), assessing the fidelity of
generative data has become a critical concern. In this paper, we propose a
discriminative approach to estimate the total variation (TV) distance between
two distributions as an effective measure of generative data fidelity. Our
method quantitatively characterizes the relation between the Bayes risk in
classifying two distributions and their TV distance. Therefore, the estimation
of total variation distance reduces to that of the Bayes risk. In particular,
this paper establishes theoretical results regarding the convergence rate of
the estimation error of TV distance between two Gaussian distributions. We
demonstrate that, with a specific choice of hypothesis class in classification,
a fast convergence rate in estimating the TV distance can be achieved.
Specifically, the estimation accuracy of the TV distance is proven to
inherently depend on the separation of two Gaussian distributions: smaller
estimation errors are achieved when the two Gaussian distributions are farther
apart. This phenomenon is also validated empirically through extensive
simulations. In the end, we apply this discriminative estimation method to rank
fidelity of synthetic image data using the MNIST dataset.
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The aim of this paper is to show that if an order preserving bijective
transformation of the Hilbert space effect algebra also preserves the
probability with respect to a fixed pair of mixed states, then it is an
ortho-order automorphism. A similar result for the orthomodular lattice of all
sharp effects (i.e., projections) is also presented.
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We show theoretically that finite two-dimensional (2D) photonic crystals in
thin semiconductor membranes strongly modify the spontaneous emission rate of
embedded dipole emitters. Three-dimensional Finite-Difference Time-Domain
calculations show over 7 times inhibition and 15 times enhancement of the
emission rate compared to the vacuum emission rate for judiciously oriented and
positioned dipoles. The vertical index confinement in membranes strongly
enhances modifications of the emission rate as compared to vertically
unconfined 2D photonic crystals. The emission rate modifications inside the
membrane mimic the local electric field mode density in a simple 2D model. The
inhibition of emission saturates exponentially as the crystal size around the
source is increased, with a $1/e$ length that is inversely proportional to the
bandwidth of the emission gap. We obtain inhibition of emission only close to
the slab center. However, enhancement of emission persists even outside the
membrane, with a distance dependence which dependence can be understood by
analyzing the contributions to the spontaneous emission rate of the different
vertically guided modes of the membrane. Finally we show that the emission
changes can even be observed in experiments with ensembles of randomly oriented
dipoles, despite the contribution of dipoles for which no gap exists.
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We show that the late-decaying particle scenario may be realized in the
supersymmetric singlet majoron model with the majoron scale $10-200$ TeV. The
smajoron decaying into two neutrinos is the late-decaying particle with the
mass $0.1-1$ TeV and the life-time $2\times10^3-8\times10^4$ seconds. The lower
limit of the majorino mass is $4-40$ TeV in order to avoid the overclosure of
the universe due to the decay-produced LSP. The muon neutrino and the tau
neutrino can be used to explain the atmospheric and the solar neutrino deficit.
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Through the hysteresis loop and magnetization spatial distribution we study
and compare two models for surface anisotropy in nanomagnets: a model with
transverse anisotropy axes and N\'eel's model. While surface anisotropy in the
transverse model induces several jumps in the hysteresis loop because of the
cluster-wise switching of spins, in the N\'eel model the jumps correspond to
successive {\it coherent partial rotations} of the whole bunch of spins. These
calculations together with experimental results suggest that N\'eel's model for
surface anisotropy is more appropriate.
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It is shown that at collider energies experimental multiplicity distributions
are well parameterized by a sum of Gupta-Sarma distributions. This extends
earlier description of the lower energy data by the two parameter sum of
Poissonians. Implications of the proposed parametrization for LHC are
discussed.
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Conversation requires a substantial amount of coordination between dialogue
participants, from managing turn taking to negotiating mutual understanding.
Part of this coordination effort surfaces as the reuse of linguistic behaviour
across speakers, a process often referred to as alignment. While the presence
of linguistic alignment is well documented in the literature, several questions
remain open, including the extent to which patterns of reuse across speakers
have an impact on the emergence of labelling conventions for novel referents.
In this study, we put forward a methodology for automatically detecting shared
lemmatised constructions -- expressions with a common lexical core used by both
speakers within a dialogue -- and apply it to a referential communication
corpus where participants aim to identify novel objects for which no
established labels exist. Our analyses uncover the usage patterns of shared
constructions in interaction and reveal that features such as their frequency
and the amount of different constructions used for a referent are associated
with the degree of object labelling convergence the participants exhibit after
social interaction. More generally, the present study shows that automatically
detected shared constructions offer a useful level of analysis to investigate
the dynamics of reference negotiation in dialogue.
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Using the Minimal Model Program, any degeneration of K-trivial varieties can
be arranged to be in a Kulikov type form, i.e. with trivial relative canonical
divisor and mild singularities. In the hyper-K\"ahler setting, we can then
deduce a finiteness statement for monodromy acting on $H^2$, once one knows
that one component of the central fiber is not uniruled. Independently of this,
using deep results from the geometry of hyper-K\"ahler manifolds, we prove that
a finite monodromy projective degeneration of hyper-K\"ahler manifolds has a
smooth filling (after base change and birational modifications). As a
consequence of these two results, we prove a generalization of Huybrechts'
theorem about birational versus deformation equivalence, allowing singular
central fibers. As an application, we give simple proofs for the deformation
type of certain geometric constructions of hyper-K\"ahler manifolds (e.g.
Debarre--Voisin or Laza--Sacc\`a--Voisin). In a slightly different direction,
we establish some basic properties (dimension and rational homology type) for
the dual complex of a Kulikov type degeneration of hyper-K\"ahler manifolds.
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We study the problem of phase transitions from 3D topological to normal
insulators without inversion symmetry. In contrast with the conclusions of some
previous work, we show that a Weyl semimetal always exists as an intermediate
phase regardless of any constriant from lattice symmetries, although the
interval of the critical region is sensitive to the choice of path in the
parameter space and can be very narrow. We demonstrate this behavior by
carrying out first-principles calculations on the noncentrosymmetric
topological insulators LaBiTe$_3$ and LuBiTe$_3$ and the trivial insulator
BiTeI. We find that a robust Weyl-semimetal phase exists in the solid solutions
LaBi$_{1-x}$Sb$_x$Te$_3$ and LuBi$_{1-x}$Sb$_x$Te$_3$ for
$x\!\approx\!38.5-41.9$\% and $x\!\approx\!40.5-45.1$\% respectively. A
low-energy effective model is also constructed to describe the critical
behavior in these two materials. In BiTeI, a Weyl semimetal also appears with
applied pressure, but only within a very small pressure range, which may
explain why it has not been experimentally observed.
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We consider the hard-core model with Metropolis transition probabilities on
finite grid graphs and investigate the asymptotic behavior of the first hitting
time between its two maximum-occupancy configurations in the low-temperature
regime. In particular, we show how the order-of-magnitude of this first hitting
time depends on the grid sizes and on the boundary conditions by means of a
novel combinatorial method. Our analysis also proves the asymptotic
exponentiality of the scaled hitting time and yields the mixing time of the
process in the low-temperature limit as side-result. In order to derive these
results, we extended the model-independent framework in [27] for first hitting
times to allow for a more general initial state and target subset.
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We introduce the quasi-partition algebra $QP_k(n)$ as a centralizer algebra
of the symmetric group. This algebra is a subalgebra of the partition algebra
and inherits many similar combinatorial properties. We construct a basis for
$QP_k(n)$, give a formula for its dimension in terms of the Bell numbers, and
describe a set of generators for $QP_k(n)$ as a complex algebra. In addition,
we give the dimensions and indexing set of its irreducible representations. We
also provide the Bratteli diagram for the tower of quasi-partition algebras
(constructed by letting $k$ range over the positive integers).
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The Dirac equation plays an essential role in the relativistic quantum
systems, which is reduced to a form similar to Schrodinger equation when a
certain potential's type is selected as the Cornell potential. By choosing the
generalized fractional derivative, the fractional Nikiforov-Uvarov method is
applied as a good efficient tool. The energy eigenvalues and corresponding wave
functions are obtained in the sense of fractional forms by solving Dirac
equation analytically. The special case is obtained, which is compatible with
the classical model. Solving the fractional Dirac equation will open a new path
to solve and improve results in the classical relativistic quantum systems.
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We study stochastic particle systems that conserve the particle density and
exhibit a condensation transition due to particle interactions. We restrict our
analysis to spatially homogeneous systems on finite lattices with stationary
product measures, which includes previously studied zero-range or misanthrope
processes. All known examples of such condensing processes are non-monotone,
i.e. the dynamics do not preserve a partial ordering of the state space and the
canonical measures (with a fixed number of particles) are not monotonically
ordered. For our main result we prove that condensing homogeneous particle
systems with finite critical density are necessarily non-monotone. On finite
lattices condensation can occur even when the critical density is infinite, in
this case we give an example of a condensing process that numerical evidence
suggests is monotone, and give a partial proof of its monotonicity.
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Residential Demand Response has emerged as a viable tool to alleviate supply
and demand imbalances of electricity, particularly during times when the
electric grid is strained due a shortage of supply. Demand Response providers
bid reduction capacity into the wholesale electricity market by asking their
customers under contract to temporarily reduce their consumption in exchange
for a monetary incentive. To contribute to the analysis of consumer behavior in
response to such incentives, this paper formulates Demand Response as a
Mechanism Design problem, where a Demand Response Provider elicits private
information of its rational, profit-maximizing customers who derive positive
expected utility by participating in reduction events. By designing an
incentive compatible and individually rational mechanism to collect users'
price elasticities of demand, the Demand Response provider can target the most
susceptible users to incentives. We measure reductions by comparing the
materialized consumption to the projected consumption, which we model as the
"10-in-10"-baseline, the regulatory standard set by the California Independent
System Operator. Due to the suboptimal performance of this baseline, we show,
using consumption data of residential customers in California, that Demand
Response Providers receive payments for "virtual reductions", which exist due
to the inaccuracies of the baseline rather than actual reductions. Improving
the accuracy of the baseline diminishes the contribution of these virtual
reductions.
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We expose a functional integration method for the averaging of continuous
products $\hat{P}_t$ of $N\times N$ random matrices. As an application, we
compute exactly the statistics of the Lyapunov spectrum of $\hat{P}_t$. This
problem is relevant to the study of the statistical properties of various
disordered physical systems, and specifically to the computation of the
multipoint correlators of a passive scalar advected by a random velocity field.
Apart from these applications, our method provides a general setting for
computing statistical properties of linear evolutionary systems subjected to a
white noise force field.
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We present a novel divide-and-conquer method for the neural summarization of
long documents. Our method exploits the discourse structure of the document and
uses sentence similarity to split the problem into an ensemble of smaller
summarization problems. In particular, we break a long document and its summary
into multiple source-target pairs, which are used for training a model that
learns to summarize each part of the document separately. These partial
summaries are then combined in order to produce a final complete summary. With
this approach we can decompose the problem of long document summarization into
smaller and simpler problems, reducing computational complexity and creating
more training examples, which at the same time contain less noise in the target
summaries compared to the standard approach. We demonstrate that this approach
paired with different summarization models, including sequence-to-sequence RNNs
and Transformers, can lead to improved summarization performance. Our best
models achieve results that are on par with the state-of-the-art in two two
publicly available datasets of academic articles.
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We study the dynamics of a single control atom and an atomic sample
interacting with a nonresonant cavity mode. The control atom is driven by an
auxiliary classical field. Under certain conditions, the coherent energy
exchange between the control atom and the atomic sample induced by the cavity
mode is described by the Jaynes-Cummings model. The idea provides a possibility
for quantum-state engineering and reconstruction for collective atomic modes.
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We define a contravariant functor K from the category of finite graphs and
graph morphisms to the category of finitely generated graded abelian groups and
homomorphisms. For a graph X, an abelian group B, and a nonnegative integer j,
an element of Hom(K^j(X),B) is a coherent family of B-valued flows on the set
of all graphs obtained by contracting some (j-1)-set of edges of X; in
particular, Hom(K^1(X),R) is the familiar (real) ``cycle-space'' of X. We show
that K(X) is torsion-free and that its Poincare polynomial is the
specialization t^{n-k}T_X(1/t,1+t) of the Tutte polynomial of X (here X has n
vertices and k components). Functoriality of K induces a functorial coalgebra
structure on K(X); dualizing, for any ring B we obtain a functorial B-algebra
structure on Hom(K(X),B). When B is commutative we present this algebra as a
quotient of a divided power algebra, leading to some interesting inequalities
on the coefficients of the above Poincare polynomial. We also provide a formula
for the theta function of the lattice of integer-valued flows in X, and
conclude with ten open problems.
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Subsets and Splits