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We investigate the behavior of waves in a periodic medium containing small
soft inclusions or cavities of arbitrary shape, such that the homogeneous
Dirichlet conditions are satisfied at the boundary. The leading terms of Bloch
waves, their dispersion relations, and cutoff frequencies are rigorously
derived. Our approach reveals the existence of exceptional wave vectors for
which Bloch waves are comprised of clusters of perturbed plane waves that
propagate in different directions. We demonstrate that for these exceptional
wave vectors, no Bloch waves propagate in any one specific direction.
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We construct ergodic discrete probability measure preserving equivalence
relations $\cR$ that has no proper ergodic normal subequivalence relations and
no proper ergodic finite-index subequivalence relations. We show that every
treeable equivalence relation satisfying a mild ergodicity condition and cost
$>1$ surjects onto every countable group with ergodic kernel. Lastly, we
provide a simple characterization of normality for subequivalence relations and
an algebraic description of the quotient.
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We show that for convex domains in Euclidean space, Cheeger's isoperimetric
inequality, spectral gap of the Neumann Laplacian, exponential concentration of
Lipschitz functions, and the a-priori weakest requirement that Lipschitz
functions have \emph{arbitrarily slow} uniform tail-decay, are all
quantitatively equivalent (to within universal constants, independent of the
dimension). This substantially extends previous results of Maz'ya, Cheeger,
Gromov--Milman, Buser and Ledoux. As an application, we conclude a sharp
quantitative stability result for the spectral gap of convex domains under
convex perturbations which preserve volume (up to constants) and under maps
which are ``on-average'' Lipschitz. We also provide a new characterization (up
to constants) of the spectral gap of a convex domain, as one over the square of
the average distance from the ``worst'' subset having half the measure of the
domain. In addition, we easily recover and extend many previously known lower
bounds on the spectral gap of convex domains, due to Payne--Weinberger,
Li--Yau, Kannan--Lov\'asz--Simonovits, Bobkov and Sodin. The proof involves
estimates on the diffusion semi-group following Bakry--Ledoux and a result from
Riemannian Geometry on the concavity of the isoperimetric profile. Our results
extend to the more general setting of Riemannian manifolds with density which
satisfy the $CD(0,\infty)$ curvature-dimension condition of Bakry-\'Emery.
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Source-sink systems are metapopulations of habitat patches with different,
and possibly temporally varying, habitat qualities, which are commonly used in
ecology to study the fate of spatially extended natural populations. We propose
new techniques that allow to disentangle the respective contributions of
demography and dispersal to the dynamics and fate of a single species in a
source-sink metapopulation. Our approach is valid for a general class of
stochastic, individual-based, stepping-stone models, with density-independent
demography and dispersal, provided the metapopulation is finite or else enjoys
some transitivity property. We provide 1) a simple criterion of persistence, by
studying the motion of a single random disperser until it returns to its
initial position; 2) a joint characterization of the long-term growth rate and
of the asymptotic occupancy frequencies of the ancestral lineage of a random
survivor, by using large deviations theory. Both techniques yield formulae
decoupling demography and dispersal, and can be adapted to the case of periodic
or random environments, where habitat qualities are autocorrelated in space and
possibly in time. In this last case, we display examples of coupled
time-averaged sinks allowing survival, as was previously known in the absence
of demographic stochasticity for fully mixing (Jansen and Yoshimura, 1998) and
even partially mixing (Evans et al., 2012; Schreiber, 2010) metapopulations.
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We investigate some aspects of N=2 twisted theories with matter
hypermultiplets in the fundamental representation of the gauge group. A
consistent formulation of these theories on a general four-manifold requires
turning on a particular magnetic flux, which we write down explicitly in the
case of SU(2k). We obtain the blowup formula and show that the blowup function
is given by a hyperelliptic sigma-function with singular characteristic. We
compute the contact terms and find, as a corollary, interesting identities
between hyperelliptic Theta functions.
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The relatively low Tc of Bi2Sr2CuO6+D allows to study normal-state down to
low temperatures and the non-substituted compound is intrinsically strongly
overdoped. Hole concentration can be adjusted trough oxygen excess, but few
data exist in the literature about the quantitative control of D. The
synthesis, achieved in air by solid-state reaction, needs long-time annealing
to obtain pure phase with stoichiometric cationic ratios. Thermogravimetric
techniques were used to explore oxygen non-stoichiometry. Absolute oxygen
content was determined by reduction with hydrogen, while the oxygen exchange
was studied between 300 C and 670 C with different PO2. Oxygen excess varies
between 0.14 and 0.18, with possibly two regimes of oxygen intercalation. These
results are compared to Bi-2212.
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Internet of Things (IoT) refers to the interconnection of physical objects
via the Internet. It utilises complex back-end systems which need different
capabilities depending on the requirements of the system. IoT has already been
used in various applications, such as agriculture, smart home, health,
automobiles, and smart grids. There are many IoT platforms, each of them
capable of providing specific services for such applications. Finding the best
match between application and platform is, however, a hard task as it can
difficult to understand the implications of small differences between
platforms. This paper builds on previous work that has identified twenty-one
important factors of an IoT platform, which were verified by Delphi method. We
demonstrate here how these factors can be used to discriminate between five
well known IoT platforms, which are arbitrarily chosen based on their market
share. These results illustrate how the proposed approach provides an objective
methodology that can be used to select the most suitable IoT platform for
different business applications based on their particular requirements.
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In sampling theory, stratification corresponds to a technique used in
surveys, which allows segmenting a population into homogeneous subpopulations
(strata) to produce statistics with a higher level of precision. In particular,
this article proposes a heuristic to solve the univariate stratification
problem - widely studied in the literature. One of its versions sets the number
of strata and the precision level and seeks to determine the limits that define
such strata to minimize the sample size allocated to the strata. A
heuristic-based on a stochastic optimization method and an exact optimization
method was developed to achieve this goal. The performance of this heuristic
was evaluated through computational experiments, considering its application in
various populations used in other works in the literature, based on 20
scenarios that combine different numbers of strata and levels of precision.
From the analysis of the obtained results, it is possible to verify that the
heuristic had a performance superior to four algorithms in the literature in
more than 94% of the cases, particularly concerning the known algorithms of
Kozak and Lavallee-Hidiroglou.
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Current and future weak lensing surveys will rely on photometrically
estimated redshifts of very large numbers of galaxies. In this paper, we
address several different aspects of the demanding photo-z performance that
will be required for future experiments, such as the proposed ESA Euclid
mission. It is first shown that the proposed all-sky near-infrared photometry
from Euclid, in combination with anticipated ground-based photometry (e.g.
PanStarrs-2 or DES) should yield the required precision in individual photo-z
of sigma(z) < 0.05(1+z) at I_AB < 24.5. Simple a priori rejection schemes based
on the photometry alone can be tuned to recognise objects with wildly
discrepant photo-z and to reduce the outlier fraction to < 0.25% with only
modest loss of otherwise usable objects. Turning to the more challenging
problem of determining the mean redshift <z> of a set of galaxies to a
precision of 0.002(1+z) we argue that, for many different reasons, this is best
accomplished by relying on the photo-z themselves rather than on the direct
measurement of <z> from spectroscopic redshifts of a representative subset of
the galaxies. A simple adaptive scheme based on the statistical properties of
the photo-z likelihood functions is shown to meet this stringent systematic
requirement. We also examine the effect of an imprecise correction for Galactic
extinction and the effects of contamination by fainter over-lapping objects in
photo-z determination. The overall conclusion of this work is that the
acquisition of photometrically estimated redshifts with the precision required
for Euclid, or other similar experiments, will be challenging but possible.
(abridged)
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Identification of string junction states of pure SU(2) Seiberg-Witten theory
as B-branes wrapped on a Calabi-Yau manifold in the geometric engineering limit
is discussed. The wrapped branes are known to correspond to objects in the
bounded derived category of coherent sheaves on the projective line $\cp{1}$ in
this limit. We identify the pronged strings with triangles in the underlying
triangulated category using Pi-stability. The spiral strings in the weak
coupling region are interpreted as certain projective resolutions of the
invertible sheaves. We discuss transitions between the spiral strings and
junctions using the grade introduced for Pi-stability through the central
charges of the corresponding objects.
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Using the production of a Higgs boson in association with a $W$ boson as a
test case, we assess the impact of dimension-8 operators within the context of
the Standard Model Effective Field Theory. Dimension-8--SM-interference and
dimension-6-squared terms appear at the same order in an expansion in
$1/\Lambda$, hence dimension-8 effects can be treated as a systematic
uncertainty on the new physics inferred from analyses using dimension-6
operators alone. To study the phenomenological consequences of dimension-8
operators, one must first determine the complete set of operators that can
contribute to a given process. We accomplish this through a combination of
Hilbert series methods, which yield the number of invariants and their field
content, and a step-by-step recipe to convert the Hilbert series output into a
phenomenologically useful format. The recipe we provide is general and applies
to any other process within the dimension $\le 8$ Standard Model Effective
Theory. We quantify the effects of dimension-8 by turning on one dimension-6
operator at a time and setting all dimension-8 operator coefficients to the
same magnitude. Under this procedure and given the current accuracy on
$\sigma(pp \to h\,W^+)$, we find the effect of dimension-8 operators on the
inferred new physics scale to be small, $\mathcal O(\text{few}\,\%)$, with some
variation depending on the relative signs of the dimension-8 coefficients and
on which dimension-6 operator is considered. The impact of the dimension-8
terms grows as $\sigma(pp \to h\,W^+)$ is measured more accurately or (more
significantly) in high-mass kinematic regions. We provide a FeynRules
implementation of our operator set to be used for further more detailed
analyses.
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An ordinary differential operator of the fourth order with coefficients
converging at infinity sufficiently rapidly to constant limits is considered.
Scattering theory for this operator is developed in terms of special solutions
of the corresponding differential equation. In contrast to equations of second
order "scattering" solutions contain exponentially decaying terms. A relation
between the scattering matrix and a matrix of coefficients at exponentially
decaying modes is found. In the second part of the paper the operator $D^4$ on
the half-axis with different boundary conditions at the point zero is studied.
Explicit formulas for basic objects of the scattering theory are found. In
particular, a classification of different types of zero-energy resonances is
given.
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Extensive muon spin relaxation measurements have been performed to determine
the magnetic field penetration depth in high-Tc cuprate superconductors with
simple hole doping, Zn-doping, overdoping, and formation of static SDW nano
islands. System dependence of $n_{s}/m^{*}$ (superconducting carrier density /
effective mass) reveals universal correlations between Tc and $n_{s}/m^{*}$ in
all these cases with / without perturbation. Evidence for spontaneous and
microscopic phase separation was obtained in the cases with strong
perturbation, i.e., Zn-doping. overdoping and SDW nano-islands. The length
scale of this heterogeneity is shown to be comparable to the in-plance
coherence length. We discuss implications of these results on condensation
mechanisms of HTSC systems, resorting to an analogy with He films, on regular
and porous media, reminding essential features of Bose-Einstein, BCS and
Kosterlitz-Thouless condensation/transition in 2-d and 3-d systems, and
comparing models of BE-BCS crossover and phase fluctuations. We propose a new
phase diagram for HTSC systems based on distinction between pair formation and
superconducting phase fluctuations in the pseudogap region and spontaneous
phase separation in the overdoped region. We also remind anomaly in BEDT and
A3C60 systems similar to that in overdoped cuprates, seen in the evolution from
superconducting to metallic ground state.
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By performing molecular dynamics simulations with up to 132 million
coarse-grained particles in half-micron sized boxes, we show that hydrodynamics
quantitatively explains the finite-size effects on diffusion of lipids,
proteins, and carbon nanotubes in membranes. The resulting Oseen correction
allows us to extract infinite-system diffusion coefficients and membrane
surface viscosities from membrane simulations despite the logarithmic
divergence of apparent diffusivities with increasing box width. The
hydrodynamic theory of diffusion applies also to membranes with asymmetric
leaflets and embedded proteins, and to a complex plasma-membrane mimetic.
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Transverse momentum dependent (TMD) parton distribution functions (PDFs),
TMDs for short, are defined as the Fourier transform of matrix elements of
nonlocal combinations of quark and gluon fields. The nonlocality is bridged by
gauge links, which for TMDs have characteristic paths (future or past
pointing), giving rise to a process dependence that breaks universality. It is
possible, however, to construct sets of universal TMDs of which in a given
process particular combinations are needed with calculable, process-dependent,
coefficients. This occurs for both T-odd and T-even TMDs, including also the
{\it unpolarized} quark and gluon TMDs. This extends the by now well-known
example of T-odd TMDs that appear with opposite sign in single-spin azimuthal
asymmetries in semi-inclusive deep inelastic scattering or in the Drell-Yan
process. In this paper we analyze the cases where TMDs enter multiplied by
products of two transverse momenta, which includes besides the $p_T$-broadening
observable, also instances with rank two structures. To experimentally
demonstrate the process dependence of the latter cases requires measurements of
second harmonic azimuthal asymmetries, while the $p_T$-broadening will require
measurements of processes beyond semi-inclusive deep inelastic scattering or
the Drell-Yan process. Furthermore, we propose specific quantities that will
allow for theoretical studies of the process dependence of TMDs using lattice
QCD calculations.
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We study the FeH Wing-Ford band at 9850 - 10200 Angstrons by means of the fit
of synthetic spectra to the observations of M stars, employing recent model
atmospheres. On the basis of the spectrum synthesis, we analyze the dependence
of the band upon atmospheric parameters. FeH lines are a very sensitive surface
gravity indicator, being stronger in dwarfs. They are also sensitive to
metallicity (Allard & Hauschildt 1995). The blending with CN lines, which are
stronger in giants, does not affect the response of the Wing-Ford band to
surface gravity at low resolution (or high velocity dispersions) because CN
lines, which are spread all along the spectrum, are smeared out at convolutions
of FWHM $\simgreat$ 3 Angstrons. We conclude that the Wing-Ford band is a
suitable dwarf/giant indicator for the study of composite stellar populations.
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We show that state-of-the-art services for creating trusted timestamps in
blockchain-based networks do not adequately allow for timestamping of web
pages. They accept data by value (e.g., images and text), but not by reference
(e.g., URIs of web pages). Also, we discuss difficulties in repeatedly
generating the same cryptographic hash value of an archived web page. We then
introduce several requirements to be fulfilled in order to produce repeatable
hash values for archived web pages.
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In a quasi-one-dimensional system the particles remain ordered from left to
right allowing the association of a volume element to the particle which on
average resides there. Thus the properties of that single particle can give the
local densities in the volume element. With reservoirs of different
temperatures connected to each end of the system a steady heat current with an
anomalous thermal conductivity results. A local configurational entropy density
is calculated from two-particle correlation functions which varies locally
within the nonequilibrium steady state. This local configurational entropy is
proposed as the configurational component of the local entropy of the
nonequilibrium steady state.
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We analyze the possibility that the cosmic ray knee appears at an energy
threshold where the proton-dark matter cross section becomes large due to new
TeV physics. It has been shown that such interactions could break the proton
and produce a diffuse gamma ray flux consistent with MILAGRO observations. We
argue that this hypothesis implies knees that scale with the atomic mass for
the different nuclei, as KASKADE data seem to indicate. We find that to explain
the change in the spectral index in the flux from E^{-2.7} to E^{-3.1} the
cross section must grow like E^{0.4+\beta} above the knee, where \beta=0.3-0.6
parametrizes the energy dependence of the age (\tau \propto E^{-\beta}) of the
cosmic rays reaching the Earth. The hypothesis also requires mbarn cross
sections (that could be modelled with TeV gravity) and large densities of dark
matter (that could be clumped around the sources of cosmic rays). We argue that
neutrinos would also exhibit a threshold at E=(m_\chi/m_p)E_{knee}\approx 10^8
GeV where their interaction with a nucleon becomes strong. Therefore, the
observation at ICECUBE or ANITA of standard neutrino events above this
threshold would disprove the scenario.
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Recently there has been a great deal of interest in tabletop experiments
intended to exhibit the quantum nature of gravity by demonstrating that it can
induce entanglement. We argue that these experiments also provide new
information about the interpretation of quantum mechanics: under appropriate
assumptions, $\psi$-complete interpretations will generally predict that these
experiments will have a positive result, $\psi$-nonphysical interpretations
predict that these experiments will not have a positive result, and for
$\psi$-supplemented models there may be arguments for either outcome. We
suggest that a positive outcome to these experimenst would rule out a class of
quantum gravity models that we refer to as $\psi$-incomplete quantum gravity
(PIQG) - i.e. models of the interaction between quantum mechanics and gravity
in which gravity is coupled to non-quantum beables rather than quantum beables.
We review some existing PIQG models and consider what more needs to be done to
make these sorts of approaches more appealing, and finally we discuss a
cosmological phenomenon which could be regarded as providing evidence for PIQG
models.
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Dispersive shock waves and solitons are fundamental nonlinear excitations in
dispersive media, but dispersive shock wave studies to date have been severely
constrained. Here we report on a novel dispersive hydrodynamics testbed: the
effectively frictionless dynamics of interfacial waves between two high
contrast, miscible, low Reynolds' number Stokes fluids. This scenario is
realized by injecting from below a lighter, viscous fluid into a column filled
with high viscosity fluid. The injected fluid forms a deformable pipe whose
diameter is proportional to the injection rate, enabling precise control over
the generation of symmetric interfacial waves. Buoyancy drives nonlinear
interfacial self-steepening while normal stresses give rise to dispersion of
interfacial waves. Extremely slow mass diffusion and mass conservation imply
that the interfacial waves are effectively dissipationless. This enables high
fidelity observations of large amplitude dispersive shock waves in this
spatially extended system, found to agree quantitatively with a nonlinear wave
averaging theory. Furthermore, several highly coherent phenomena are
investigated including dispersive shock wave backflow, the refraction or
absorption of solitons by dispersive shock waves, and the multi-phase merging
of two dispersive shock waves. The complex, coherent, nonlinear mixing of
dispersive shock waves and solitons observed here are universal features of
dissipationless, dispersive hydrodynamic flows.
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We propose a general method to study the solutions to nonlinear QCD evolution
equations, based on a deep analogy with the physics of traveling waves. In
particular, we show that the transition to the saturation regime of high energy
QCD is identical to the formation of the front of a traveling wave. Within this
physical picture, we provide the expressions for the saturation scale and the
gluon density profile as a function of the total rapidity and the transverse
momentum. The application to the Balitsky-Kovchegov equation for both fixed and
running coupling constants confirms the effectiveness of this method.
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We propose a combined computational approach based on the multi-phase-field
and the lattice Boltzmann method for the motion of solid particles under the
action of capillary forces. The accuracy of the method is analyzed by
comparison with the analytic solutions for the motion of two parallel plates of
finite extension connected by a capillary bridge. The method is then used to
investigate the dynamics of multiple spherical solid bodies connected via
capillary bridges. The amount of liquid connecting the spheres is varied, and
the influence of the resulting liquid-morphology on their dynamics is
investigated. It is shown that the method is suitable for a study of
liquid-phase sintering which includes both phase transformation and capillary
driven rigid body motion.
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The collective Raman cooling of a trapped two-component Fermi gas is
analyzed. We develop the quantum master equation that describes the collisions
and the laser cooling, in the festina lente regime, where the heating due to
photon reabsorption can be neglected. The numerical results based on Monte
Carlo simulations show, that three-dimensional temperatures of the order of
0.008 T_F can be achieved. We analyze the heating related to the background
losses, and conclude that our laser-cooling scheme can maintain the temperature
of the gas without significant additional losses. Finally we derive an analytic
expression for the temperature of a trapped Fermi gas heated by background
collisions, that agrees very well with the data obtained from the numerical
simulation.
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We present results of 2D and 3D PIC simulations of magnetic turbulence
production by isotropic cosmic-ray ions drifting upstream of SNR shocks. The
studies aim at testing recent predictions of a strong amplification of short
wavelength magnetic field and at studying the evolution of the magnetic
turbulence and its backreaction on cosmic rays. We observe that an oblique
filamentary mode grows more rapidly than the non-resonant parallel modes found
in analytical theory, and the growth rate of the field perturbations is much
slower than is estimated for the parallel plane-wave mode, possibly because in
our simulations we cannot maintain omega << Omega_i, the ion gyrofrequency, to
the degree required for the plane-wave mode to emerge. The evolved oblique
filamentary mode was also observed in MHD simulations to dominate in the
nonlinear phase. We thus confirm the generation of the turbulent magnetic field
due to the drift of cosmic-ray ions in the upstream plasma, but as our main
result find that the amplitude of the turbulence saturates at about dB/B~1. The
backreaction of the turbulence on the particles leads to an alignment of the
bulk-flow velocities of the cosmic rays and the background medium, which is an
essential characteristic of cosmic-ray modified shocks. It accounts for the
saturation of the instability at moderate field amplitudes. Previously
published MHD simulations have assumed a constant cosmic-ray current and no
energy or momentum flux in the cosmic rays, which excludes a backreaction of
the generated magnetic field on cosmic rays, and thus the saturation of the
field amplitude is artificially suppressed. This may explain the continued
growth of the magnetic field in the MHD simulations. A strong magnetic field
amplification to amplitudes dB >> B0 has not been demonstrated yet.
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The paper is devoted to constructing a random exponential attractor for some
classes of stochastic PDE's. We first prove the existence of an exponential
attractor for abstract random dynamical systems and study its dependence on a
parameter and then apply these results to a nonlinear reaction-diffusion system
with a random perturbation. We show, in particular, that the attractors can be
constructed in such a way that the symmetric distance between the attractors
for stochastic and deterministic problems goes to zero with the amplitude of
the random perturbation.
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The pseudo-polar Fourier transform is a specialized non-equally spaced
Fourier transform, which evaluates the Fourier transform on a near-polar grid,
known as the pseudo-polar grid. The advantage of the pseudo-polar grid over
other non-uniform sampling geometries is that the transformation, which samples
the Fourier transform on the pseudo-polar grid, can be inverted using a fast
and stable algorithm. For other sampling geometries, even if the non-equally
spaced Fourier transform can be inverted, the only known algorithms are
iterative. The convergence speed of these algorithms as well as their accuracy
are difficult to control, as they depend both on the sampling geometry as well
as on the unknown reconstructed object. In this paper, we present a direct
inversion algorithm for the three-dimensional pseudo-polar Fourier transform.
The algorithm is based only on one-dimensional resampling operations, and is
shown to be significantly faster than existing iterative inversion algorithms.
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A short overview is provided of the recent PHYSTAT$\nu$ meeting at CERN,
which dealt with statistical issues relevant for neutrino experiments.
|
The aim of this article is to study expansions of solutions to an extremal
metric type equation on the blow-up of constant scalar curvature K\"ahler
surfaces. This is related to finding constant scalar curvature K\"ahler (cscK)
metrics on K-stable blow-ups of extremal K\"ahler surfaces
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We reconsider the Mott transition problem in the presence of long range
Coulomb interactions. Using an extended DMFT, that sums an important class of
diagrams absent in ordinary DMFT, we show that in the presence of Coulomb the
Mott transition in two and three dimensions is discontinuous as envisioned by
Mott.
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We review tools that have been developed in recent years to maximize our
ability to discover and characterize new physics appearing in LHC events with
missing transverse momentum.
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Motivated by the Beauville decomposition of an abelian scheme and the
"Perverse = Chern" phenomenon for a compactified Jacobian fibration, we study
in this paper splittings of the perverse filtration for compactified Jacobian
fibrations.
On the one hand, we prove for the Beauville-Mukai system associated with an
irreducible curve class on a K3 surface the existence of a Fourier-stable
multiplicative splitting of the perverse filtration, which extends the
Beauville decomposition for the nonsingular fibers. Our approach is to
construct a Lefschetz decomposition associated with a Fourier-conjugate
$\mathfrak{sl}_2$-triple, which relies heavily on recent work concerning the
interaction between derived equivalences and LLV algebras for hyper-K\"ahler
varieties. Motivic lifting and connections to the Beauville-Voisin conjectures
are also discussed.
On the other hand, we construct for any $g\geq 2$ a compactified Jacobian
fibration of genus g curves such that each curve is integral with at worst
simple nodes and the (multiplicative) perverse filtration does not admit a
multiplicative splitting. This shows that in general an extension of the
Beauville decomposition cannot exist for compactified Jacobian fibrations even
when the simplest singular point appears.
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Supersymmetric Twin Higgs models ameliorate the fine-tuning of the
electroweak scale originating from the heavy scalar top partners required by
the non-discovery of them at the Large Hadron Collider. If the Lightest
Supersymmetric Particle resides in the twin sector, it may play the role of
dark matter even if it is charged under twin gauge interactions. We show that
the twin stau is a viable candidate for charged dark matter, even if the twin
electromagnetic gauge symmetry is unbroken, with thermal relic abundance that
naturally matches the observed dark matter abundance. A wide parameter space
satisfies all the experimental constraints including those on dark matter
self-interactions. Twin stau dark matter can be observed in future direct
detection experiments such as LUX-ZEPLIN. The stau has a mass in the range of
300-500 GeV, and in the minimal scenario, has a decay length long enough to be
observed as a disappearing track or a long-lived particle at the Large Hadron
Collider.
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We derive an equilibrium statistical theory for the macroscopic description
of a ferromagnetic material at positive finite temperatures. Our formulation
describes the most-probable equilibrium macrostates that yield a coherent
deterministic large-scale picture varying at the size of the domain, as well as
it captures the effect of random spin fluctuations caused by the thermal noise.
We discuss connections of the proposed formulation to the Landau-Lifschitz
theory and to the studies of domain formation based on Monte Carlo lattice
simulations.
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Recent observations support the hypothesis that a large fraction of
"short-hard" gamma-ray bursts (SHBs) are associated with compact binary
inspiral. Since gravitational-wave (GW) measurements of well-localized
inspiraling binaries can measure absolute source distances, simultaneous
observation of a binary's GWs and SHB would allow us to independently determine
both its luminosity distance and redshift. Such a "standard siren" (the GW
analog of a standard candle) would provide an excellent probe of the relatively
nearby universe's expansion, complementing other standard candles. In this
paper, we examine binary measurement using a Markov Chain Monte Carlo technique
to build the probability distributions describing measured parameters. We
assume that each SHB observation gives both sky position and the time of
coalescence, and we take both binary neutron stars and black hole-neutron star
coalescences as plausible SHB progenitors. We examine how well parameters
particularly distance) can be measured from GW observations of SHBs by a range
of ground-based detector networks. We find that earlier estimates overstate how
well distances can be measured, even at fairly large signal-to-noise ratio. The
fundamental limitation to determining distance proves to be a degeneracy
between distance and source inclination. Overcoming this limitation requires
that we either break this degeneracy, or measure enough sources to broadly
sample the inclination distribution. (Abridged)
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We evaluate machine comprehension models' robustness to noise and adversarial
attacks by performing novel perturbations at the character, word, and sentence
level. We experiment with different amounts of perturbations to examine model
confidence and misclassification rate, and contrast model performance in
adversarial training with different embedding types on two benchmark datasets.
We demonstrate improving model performance with ensembling. Finally, we analyze
factors that effect model behavior under adversarial training and develop a
model to predict model errors during adversarial attacks.
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Motivated by juggling sequences and bubble sort, we examine permutations on
the set {1,2,...,n} with d descents and maximum drop size k. We give explicit
formulas for enumerating such permutations for given integers k and d. We also
derive the related generating functions and prove unimodality and symmetry of
the coefficients.
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Social-aware recommendation approaches have been recognized as an effective
way to solve the data sparsity issue of traditional recommender systems. The
assumption behind is that the knowledge in social user-user connections can be
shared and transferred to the domain of user-item interactions, whereby to help
learn user preferences. However, most existing approaches merely adopt the
first-order connections among users during transfer learning, ignoring those
connections in higher orders. We argue that better recommendation performance
can also benefit from high-order social relations. In this paper, we propose a
novel Propagation-aware Transfer Learning Network (PTLN) based on the
propagation of social relations. We aim to better mine the sharing knowledge
hidden in social networks and thus further improve recommendation performance.
Specifically, we explore social influence in two aspects: (a) higher-order
friends have been taken into consideration by order bias; (b) different friends
in the same order will have distinct importance for recommendation by an
attention mechanism. Besides, we design a novel regularization to bridge the
gap between social relations and user-item interactions. We conduct extensive
experiments on two real-world datasets and beat other counterparts in terms of
ranking accuracy, especially for the cold-start users with few historical
interactions.
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We use runtime verification (RV) to check various specifications in a smart
apartment. The specifications can be broken down into three types: behavioral
correctness of the apartment sensors, detection of specific user activities
(known as activities of daily living), and composition of specifications of the
previous types. The context of the smart apartment provides us with a complex
system with a large number of components with two different hierarchies to
group specifications and sensors: geographically within the same room, floor or
globally in the apartment, and logically following the different types of
specifications. We leverage a recent approach to decentralized RV of
decentralized specifications, where monitors have their own specifications and
communicate together to verify more general specifications. We leverage the
hierarchies, modularity and re-use afforded by decentralized specifications to:
(1) scale beyond existing centralized RV techniques, and (2) greatly reduce
computation and communication costs.
|
In this paper, one-dimensional (1D) nonlinear wave equations $u_{tt}
-u_{xx}+V(x)u =f(u)$, with periodic boundary conditions are considered; V is a
periodic smooth or analytic function and the nonlinearity f is an analytic
function vanishing together with its derivative at u=0. It is proved that for
``most'' potentials V(x), the above equation admits small-amplitude periodic or
quasi-periodic solutions corresponding to finite dimensional invariant tori for
an associated infinite dimensional dynamical system. The proof is based on an
infinite dimensional KAM theorem which allows for multiple normal frequencies.
|
We present two different search methods for electromagnetic counterparts to
gravitational-wave (GW) events from ground-based detectors using archival NASA
high-energy data from the Fermi-GBM and RXTE-ASM instruments. To demonstrate
the methods, we use a limited number of representative GW background noise
events produced by a search for binary neutron star coalescence over the last
two months of the LIGO-Virgo S6/VSR3 joint science run. Time and sky location
provided by the GW data trigger a targeted search in the high-energy photon
data. We use two custom pipelines: one to search for prompt gamma-ray
counterparts in GBM, and the other to search for a variety of X-ray afterglow
model signals in ASM. We measure the efficiency of the joint pipelines to weak
gamma-ray burst counterparts, and a family of model X-ray afterglows. By
requiring a detectable signal in either electromagnetic instrument coincident
with a GW event, we are able to reject a large majority of GW candidates. This
reduces the signal-to-noise of the loudest surviving GW background event by
around 15-20%.
|
Mode II fatigue crack growth under reversed shear and static biaxial
compression was investigated in two bearing steels. Many aborted branches,
quasi-orthogonal to the main crack, were observed along the crack face. The
compressive stress parallel to the main crack hindered the growth of these
branches and favored coplanar mode II crack growth. The crack face sliding
displacement profiles measured by DIC were used to derive $\Delta_{\rm
KII,eff}$, at the main crack tip, using elastic-plastic FE simulations with
crack face friction, by an inverse method. Friction corrected crack growth
kinetics were obtained for mode II crack growth in both steels.
|
We explore the technical details and historical evolution of Charles Peirce's
articulation of a truth table in 1893, against the background of his
investigation into the truth-functional analysis of propositions involving
implication. In 1997, John Shosky discovered, on the verso of a page of the
typed transcript of Bertrand Russell's 1912 lecture on "The Philosophy of
Logical Atomism" truth table matrices. The matrix for negation is Russell's,
alongside of which is the matrix for material implication in the hand of Ludwig
Wittgenstein. It is shown that an unpublished manuscript identified as composed
by Peirce in 1893 includes a truth table matrix that is equivalent to the
matrix for material implication discovered by John Shosky. An unpublished
manuscript by Peirce identified as having been composed in 1883-84 in
connection with the composition of Peirce's "On the Algebra of Logic: A
Contribution to the Philosophy of Notation" that appeared in the American
Journal of Mathematics in 1885 includes an example of an indirect truth table
for the conditional.
|
In a universe with a cosmological constant, the large-scale gravitational
potential varies in time and this is, in principle, observable. Using an N-body
simulation of a $\Lambda$CDM universe, we show that linear theory is not
sufficiently accurate to predict the power spectrum of the time derivative,
$\dot{\Phi}$, needed to compute the imprint of large-scale structure on the
cosmic microwave background (CMB). The linear part of the $\dot{\Phi}$ power
spectrum (the integrated Sachs-Wolfe effect or ISW) drops quickly as the
relative importance of $\Omega_{\Lambda}$ diminishes at high redshift, while
the non-linear part (the Rees-Sciama effect or RS) evolves more slowly with
redshift. Therefore, the deviation of the total power spectrum from linear
theory occurs at larger scales at higher redshifts. The deviation occurs at
$k\sim 0.1 $ $h$ Mpc$^{-1}$ at $z=0$. The cross-correlation power spectrum of
the density $\delta$ with $\dot{\Phi}$ behaves differently to the power
spectrum of $\dot{\Phi}$. Firstly, the deviation from linear theory occurs at
smaller scales ($k\sim 1 $ $h$ Mpc$^{-1}$ at $z=0$). Secondly, the correlation
becomes negative when the non-linear effect dominates. For the
cross-correlation power spectrum of galaxy samples with the CMB, the non-linear
effect becomes significant at $l\sim 500$ and rapidly makes the cross power
spectrum negative. For high redshift samples, the cross-correlation is expected
to be suppressed by $5-10%$ on arcminute scales. The RS effect makes a
negligible contribution to the large-scale ISW cross-correlation measurement.
However, on arc-minute scales it will contaminate the expected
cross-correlation signal induced by the Sunyaev-Zel'dovich effect.
|
We present a simple analytical method to solve master equations for finite
temperatures and any initial conditions, which consists in the expansion of the
density operator into normal modes. These modes and the expansion coefficients
are obtained algebraically by using ladder superoperators. This algebraic
technique is successful in cases in which the Liouville superoperator is
quadratic in the creation and annihilation operators.
|
We establish a bijection between torsion pairs in the category of
finite-dimensional modules over a finite-dimensional algebra A and pairs (Z, I)
formed by a closed rigid set Z in the Ziegler spectrum of A and a set I of
indecomposable injective A-modules. This can be regarded as an extension of a
result from $\tau$-tilting theory which parametrises the functorially finite
torsion pairs over A. We also obtain a one-one-correspondence between
finite-dimensional bricks and certain (possibly infinite-dimensional)
indecomposable modules satisfying a rigidity condition. Our results also hold
when A is an artinian ring.
|
We analyse the Baryon Acoustic Oscillation (BAO) signal of the final Baryon
Oscillation Spectroscopic Survey (BOSS) data release (DR12). Our analysis is
performed in Fourier-space, using the power spectrum monopole and quadrupole.
The dataset includes $1\,198\,006$ galaxies over the redshift range $0.2 < z <
0.75$. We divide this dataset into three (overlapping) redshift bins with the
effective redshifts $\zeff = 0.38$, $0.51$ and $0.61$. We demonstrate the
reliability of our analysis pipeline using N-body simulations as well as $\sim
1000$ MultiDark-Patchy mock catalogues, which mimic the BOSS-DR12 target
selection. We apply density field reconstruction to enhance the BAO
signal-to-noise ratio. By including the power spectrum quadrupole we can
separate the line-of-sight and angular modes, which allows us to constrain the
angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$ separately.
We obtain two independent $1.6\%$ and $1.5\%$ constraints on $D_A(z)$ and
$2.9\%$ and $2.3\%$ constraints on $H(z)$ for the low ($\zeff=0.38$) and high
($\zeff=0.61$) redshift bin, respectively. We obtain two independent $1\%$ and
$0.9\%$ constraints on the angular averaged distance $D_V(z)$, when ignoring
the Alcock-Paczynski effect. The detection significance of the BAO signal is of
the order of $8\sigma$ (post-reconstruction) for each of the three redshift
bins. Our results are in good agreement with the Planck prediction within
$\Lambda$CDM. This paper is part of a set that analyses the final galaxy
clustering dataset from BOSS. The measurements and likelihoods presented here
are combined with others in~\citet{Alam2016} to produce the final cosmological
constraints from BOSS.
|
We reexamine critically the chiral expansion for the baryon magnetic moments
including the contributions from loops which involve intermediate octet and
decuplet baryons. We find that, contrary to some claims, the nonanalytic loop
contributions of orders $m_s^{1/2}$ and $m_s ln m_s$ are of the same general
size because of large coupling factors for the latter, and that the decuplet
contributions are as large as the octet contributions and must be included in a
consistent calculation. There is no clear evidence of the convergence of the
chiral series. The adequacy of the theory will not be established until
dynamical models are able to calculate the contributions from the counterterms
that largely hide the loop effects in fits to the data.
|
We show that the Pauli-Villars regularized action for a scalar field in a
gravitational background in 1+1 dimensions has, for any value of the cutoff M,
a symmetry which involves non-local transformations of the regulator field plus
(local) Weyl transformations of the metric tensor. These transformations, an
extension to the regularized action of the usual Weyl symmetry transformations
of the classical action, lead to a new interpretation of the conformal anomaly
in terms of the (non-anomalous) Jacobian for this symmetry. Moreover, the
Jacobian is automatically regularized, and yields the correct result when the
masses of the regulators tend to infinity. In this limit the transformations,
which are non-local in a scale of 1/M, become the usual Weyl transformation of
the metric. We also present the example of the chiral anomaly in 1+1
dimensions.
|
We derive the lower bound of uncertainty relations of two unitary operators
for a class of states based on the geometric-arithmetic inequality and
Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty
relations for three unitary operators. Compared to the known bound introduced
in Phys.Rev.A.100,022116(2019), the unitary uncertainty relations bound with
our method is tighter, to a certain extent. Meanwhile, some examples are given
in the paper to illustrate our conclusions.
|
It is known that the normalized volume of standard hypersimplices (defined as
some slices of the unit hypercube) are the Eulerian numbers. More generally, a
recent conjecture of Stanley relates the Ehrhart series of hypersimplices with
descents and excedences in permutations. This conjecture was proved by Nan Li,
who also gave a generalization to colored permutations. In this article, we
give another generalization to colored permutations, using the flag statistics
introduced by Foata and Han. We obtain in particular a new proof of Stanley's
conjecture, and some combinatorial identities relating pairs of Eulerian
statistics on colored permutations.
|
This paper presents a contact-implicit model predictive control (MPC)
framework for the real-time discovery of multi-contact motions, without
predefined contact mode sequences or foothold positions. This approach utilizes
the contact-implicit differential dynamic programming (DDP) framework, merging
the hard contact model with a linear complementarity constraint. We propose the
analytical gradient of the contact impulse based on relaxed complementarity
constraints to further the exploration of a variety of contact modes. By
leveraging a hard contact model-based simulation and computation of search
direction through a smooth gradient, our methodology identifies dynamically
feasible state trajectories, control inputs, and contact forces while
simultaneously unveiling new contact mode sequences. However, the broadened
scope of contact modes does not always ensure real-world applicability.
Recognizing this, we implemented differentiable cost terms to guide foot
trajectories and make gait patterns. Furthermore, to address the challenge of
unstable initial roll-outs in an MPC setting, we employ the multiple shooting
variant of DDP. The efficacy of the proposed framework is validated through
simulations and real-world demonstrations using a 45 kg HOUND quadruped robot,
performing various tasks in simulation and showcasing actual experiments
involving a forward trot and a front-leg rearing motion.
|
Data reduction rules are an established method in the algorithmic toolbox for
tackling computationally challenging problems. A data reduction rule is a
polynomial-time algorithm that, given a problem instance as input, outputs an
equivalent, typically smaller instance of the same problem. The application of
data reduction rules during the preprocessing of problem instances allows in
many cases to considerably shrink their size, or even solve them directly.
Commonly, these data reduction rules are applied exhaustively and in some fixed
order to obtain irreducible instances. It was often observed that by changing
the order of the rules, different irreducible instances can be obtained. We
propose to "undo" data reduction rules on irreducible instances, by which they
become larger, and then subsequently apply data reduction rules again to shrink
them. We show that this somewhat counter-intuitive approach can lead to
significantly smaller irreducible instances. The process of undoing data
reduction rules is not limited to "rolling back" data reduction rules applied
to the instance during preprocessing. Instead, we formulate so-called backward
rules, which essentially undo a data reduction rule, but without using any
information about which data reduction rules were applied to it previously. In
particular, based on the example of Vertex Cover we propose two methods
applying backward rules to shrink the instances further. In our experiments we
show that this way smaller irreducible instances consisting of real-world
graphs from the SNAP and DIMACS datasets can be computed.
|
More than 90% of the Galactic gas-related gamma-ray emissivity above 1 GeV is
attributed to the decay of neutral pions formed in collisions between cosmic
rays and interstellar matter, with lepton-induced processes becoming
increasingly important below 1 GeV. Given the high-quality measurements of the
gamma-ray emissivity of local interstellar gas between ~50 MeV and ~4 GeV
obtained with the Large Area Telescope on board the Fermi space observatory, it
is timely to re-investigate this topic in detail, including the hadronic
production mechanisms. The emissivity spectrum will allow the interstellar
cosmic-ray spectrum to be determined reliably, providing a reference for origin
and propagation studies as well as input to solar modulation models. A method
for such an analysis and illustrative results are presented.
|
The use of pre-shared entanglement in entanglement-assisted communication
offers a superior alternative to classical communication, especially in the
photon-starved regime and highly noisy environments. In this paper, we analyze
the performance of several low-complexity receivers that use optical parametric
amplifiers. The simulations demonstrate that receivers employing an
entanglement-assisted scheme with phase-shift-keying modulation can outperform
classical capacities. We present a 2x2 optical hybrid receiver for
entanglement-assisted communication and show that it has a roughly 10% lower
error probability compared to previously proposed optical parametric
amplifier-based receivers for more than 10 modes. However, the capacity of the
optical parametric amplifier-based receiver exceeds the Holevo capacity and the
capacities of the optical phase conjugate receiver and 2x2 optical hybrid
receiver in the case of a single mode. The numerical findings indicate that
surpassing the Holevo and Homodyne capacities does not require a large number
of signal-idler modes. Furthermore, we find that using unequal priors for BPSK
provides roughly three times the information rate advantage over equal priors.
|
We calculate accretion mass of interstellar objects (ISOs) like `Oumuamua
onto low-mass population III stars (Pop.~III survivors), and estimate surface
pollution of Pop.~III survivors. An ISO number density estimated from the
discovery of `Oumuamua is so high ($\sim 0.2$~au$^{-3}$) that Pop.~III
survivors have chances at colliding with ISOs $\gtrsim 10^5$ times per $1$~Gyr.
`Oumuamua itself would be sublimated near Pop.~III survivors, since it has
small size, $\sim 100$~m. However, ISOs with size $\gtrsim 3$~km would reach
the Pop.~III survivor surfaces. Supposing an ISO cumulative number density with
size larger than $D$ is $n \propto D^{-\alpha}$, Pop.~III survivors can accrete
ISO mass $\gtrsim 10^{-16}M_\odot$, or ISO iron mass $\gtrsim 10^{-17}M_\odot$,
if $\alpha < 4$. This iron mass is larger than the accretion mass of
interstellar medium (ISM) by several orders of magnitude. Taking into account
material mixing in a convection zone of Pop.~III survivors, we obtain their
surface pollution is typically [Fe/H] $\lesssim -8$ in most cases, however the
surface pollution of Pop.~III survivors with $0.8M_\odot$ can be [Fe/H]
$\gtrsim -6$ because of the very shallow convective layer. If we apply to
Pop.III survivors located at the Galactocentric distance of 8 kpc, the
dependence of the metal pollustion is as follows. If $\alpha > 4$, Pop.~III
survivors have no chance at colliding with ISOs with $D \gtrsim 3$~km, and keep
metal-free. If $3 < \alpha < 4$, Pop.~III survivors would be most polluted by
ISOs up to [Fe/H] $\sim -7$. If $\alpha < 3$ up to $D \sim 10$~km, Pop.~III
survivors could hide in metal-poor stars so far discovered. Pop.~III survivors
would be more polluted with decreasing the Galactocentric distance. Although
the metal pollution depends on $\alpha$ and the Galactocentric distance, we
first show the importance of ISOs for the metal pollution of Pop.~III
survivors.
|
The non-relativistic limit of the linear wave equation for zero and unity
spin bosons of mass $m$ in the Duffin-Kemmer-Petiau representation is
investigated by means of a unitary transformation, analogous to the
Foldy-Wouthuysen canonical transformation for a relativistic electron. The
interacting case is also analyzed, by considering a power series expansion of
the transformed Hamiltonian, thus demonstrating that all features of particle
dynamics can be recovered if corrections of order $1/m^{2}$ are taken into
account through a recursive iteration procedure.
|
We study the existence/nonexistence of positive solution to the problem of
the type: \begin{equation}\tag{$P_{\lambda}$} \begin{cases} \Delta^2u-\mu
a(x)u=f(u)+\lambda b(x)\quad\textrm{in $\Omega$,}\\ u>0 \quad\textrm{in
$\Omega$,}\\ u=0=\Delta u \quad\textrm{on $\partial\Omega$,} \end{cases}
\end{equation} where $\Omega$ is a smooth bounded domain in $\mathbb R^N$,
$N\geq 5$, $a, b, f$ are nonnegaive functions satisfying certain hypothesis
which we will specify later. $\mu,\lambda$ are positive constants. Under some
suitable conditions on functions $a, b, f$ and the constant $\mu$, we show that
there exists $\lambda^*>0$ such that when $0<\lambda<\lambda^*$,
($P_{\lambda}$) admits a solution in $W^{2,2}(\Omega)\cap W^{1,2}_0(\Omega)$
and for $\lambda>\lambda^*$, it does not have any solution in
$W^{2,2}(\Omega)\cap W^{1,2}_0(\Omega)$. Moreover as
$\lambda\uparrow\lambda^*$, minimal positive solution of ($P_{\lambda}$)
converges in $W^{2,2}(\Omega)\cap W^{1,2}_0(\Omega)$ to a solution of
($P_{\lambda^*}$). We also prove that there exists $\tilde{\lambda}^*<\infty$
such that $\lambda^*\leq\tilde{\lambda}^*$ and for $\lambda>\tilde{\lambda}^*$,
the above problem ($P_{\lambda}$) does not have any solution even in the
distributional sense/very weak sense and there is complete {\it blow-up}. Under
an additional integrability condition on $b$, we establish the uniqueness of
positive solution of ($P_{\lambda^*}$) in $W^{2,2}(\Omega)\cap
W^{1,2}_0(\Omega)$.
|
We show that when parameterized by triples of angles, the set of similarity
classes of labeled, oriented, possibly degenerate triangles has the natural
structure of the Clifford torus $\sf{T}$, a compact abelian Lie group. On this
torus the main triangle types form distinguished algebraic structures:
subgroups and cosets. The construction relies on a natural definition of
similarity for degenerate triangles.
We analyze the set of (unrestricted) similarity classes using a uniform
probability measure on $\sf{T}$ and compute the relative measures of the
different triangle types.
Our computations are compatible with the spherically symmetric probability
distribution analyzed in [Por94] and [ES15], which are based on vertices/side
lengths instead of angles.
|
Recent experimental results and developments in the theoretical treatment of
neutrino-nucleus interactions in the energy range of 1-10 GeV are discussed.
Difficulties in extracting neutrino-nucleon cross sections from
neutrino-nucleus scattering data are explained and significance of
understanding nuclear effects for neutrino oscillation experiments is stressed.
Detailed discussions of the status of two-body current contribution in the
kinematic region dominated by quasi-elastic scattering and specific features of
partonic nuclear effects in weak DIS scattering are presented.
|
Unruh deWitt detectors are important constructs in studying the dynamics of
quantum fields in any geometric background. Curvature also plays an important
role in setting up the correlations of a quantum field in a given spacetime.
For instance, massless fields are known to have large correlations in de Sitter
space as well as in certain class of Friedmann-Robertson-Walker (FRW)
universes. However, some of the correlations are secular in nature while some
are dynamic and spacetime dependent. An Unruh deWitt detector responds to such
divergences differently in different spacetimes. In this work, we study the
response rate of Unruh deWitt detectors which interact with quantum fields in
FRW spacetimes. We consider both conventionally as well as derivatively coupled
Unruh deWitt detectors. Particularly, we consider their interaction with
massless scalar fields in FRW spacetimes and nearly massless scalar fields in
de Sitter spacetime. We discuss how the term which gives rise to the infrared
divergence in the massless limit in de Sitter spacetime manifests itself at the
level of the response rate of these Unruh deWitt detectors in a wide class of
Friedmann spacetimes. To carry out this study, we use an equivalence between
massless scalar fields in FRW spacetimes with massive scalar fields in de
Sitter spacetime. Further, we show that while the derivative coupling regulates
the divergence appearing in de Sitter spacetime, it does not completely remove
them in matter dominated universe. This gives rise to large transitions in the
detector which can be used as a probe of setting up of large correlations in
late time era of the universe as well. We show that the coupling of hydrogen
atoms with gravitational waves takes a form that is similar to derivatively
coupled UdW detectors and hence has significant observational implications as a
probe of late time revival of quantum correlators.
|
In this paper, we establish a new scheme for identification and
classification of high intensity events generated by the propagation of light
through a photorefractive SBN crystal. Among these events, which are the
inevitable consequence of the development of modulation instability, are
speckling and soliton-like patterns. The usual classifiers developed on
statistical measures, such as the significant intensity, often provide only a
partial characterization of these events. Here, we try to overcome this
deficiency by implementing the convolution neural network method to relate
experimental data of light intensity distribution and corresponding numerical
outputs with different high intensity regimes. The train and test sets are
formed of experimentally obtained intensity profiles at the crystal output
facet and corresponding numerical profiles. The accuracy of detection of
speckles reaches maximum value of 100%, while the accuracy of solitons and
caustic detection is above 97%. These performances are promising for the
creation of neural network based routines for prediction of extreme events in
wave media.
|
Personalized medicine has received increasing attention among statisticians,
computer scientists, and clinical practitioners. A major component of
personalized medicine is the estimation of individualized treatment rules
(ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL)
to construct ITRs that directly optimize the clinical outcome. Although OWL
opens the door to introducing machine learning techniques to optimal treatment
regimes, it still has some problems in performance. In this article, we propose
a general framework, called Residual Weighted Learning (RWL), to improve finite
sample performance. Unlike OWL which weights misclassification errors by
clinical outcomes, RWL weights these errors by residuals of the outcome from a
regression fit on clinical covariates excluding treatment assignment. We
utilize the smoothed ramp loss function in RWL, and provide a difference of
convex (d.c.) algorithm to solve the corresponding non-convex optimization
problem. By estimating residuals with linear models or generalized linear
models, RWL can effectively deal with different types of outcomes, such as
continuous, binary and count outcomes. We also propose variable selection
methods for linear and nonlinear rules, respectively, to further improve the
performance. We show that the resulting estimator of the treatment rule is
consistent. We further obtain a rate of convergence for the difference between
the expected outcome using the estimated ITR and that of the optimal treatment
rule. The performance of the proposed RWL methods is illustrated in simulation
studies and in an analysis of cystic fibrosis clinical trial data.
|
Using numerical methods we present the first full nonlinear study of phantom
scalar field accreted into a black hole. We study different initial
configurations and find that the accretion of the field into the black hole can
reduce its area down to 50 percent within time scales of the order of few
masses of the initial horizon. The analysis includes the cases where the total
energy of the space-time is positive or negative. The confirmation of this
effect in full nonlinear general relativity implies that the accretion of
exotic matter could be considered an evaporation process. We speculate that if
this sort of exotic matter has some cosmological significance, this black hole
area reduction process might have played a crucial role in black hole formation
and population.
|
We construct an entangled photon polarimeter capable of monitoring a
two-qubit quantum state in real time. Using this polarimeter, we record a nine
frames-per-second video of a two-photon state's transition from separability to
entanglement.
|
The partition function of a factor graph and the partition function of the
dual factor graph are related to each other by the normal factor graph duality
theorem. We apply this result to the classical problem of computing the
partition function of the Ising model. In the one-dimensional case, we thus
obtain an alternative derivation of the (well-known) analytical solution. In
the two-dimensional case, we find that Monte Carlo methods are much more
efficient on the dual graph than on the original graph, especially at low
temperature.
|
Gapped periodic quantum systems exhibit an interesting Localization
Dichotomy, which emerges when one looks at the localization of the optimally
localized Wannier functions associated to the Bloch bands below the gap. As
recently proved, either these Wannier functions are exponentially localized, as
it happens whenever the Hamiltonian operator is time-reversal symmetric, or
they are delocalized in the sense that the expectation value of
$|\mathbf{x}|^2$ diverges. Intermediate regimes are forbidden.
Following the lesson of our Maestro, to whom this contribution is gratefully
dedicated, we find useful to explain this subtle mathematical phenomenon in the
simplest possible model, namely the discrete model proposed by Haldane (Phys.
Rev. Lett. 61, 2017 (1988)). We include a pedagogical introduction to the model
and we explain its Localization Dichotomy by explicit analytical arguments. We
then introduce the reader to the more general, model-independent version of the
dichotomy proved in (Commun. Math. Phys. 359, 61-100 (2018)), and finally we
announce further generalizations to non-periodic models.
|
By studying the example of smooth structures on CP^2#3(-CP^2) we illustrate
how surgery on a single embedded nullhomologous torus can be utilized to change
the symplectic structure, the Seiberg-Witten invariant, and hence the smooth
structure on a 4-manifold.
|
In this policy paper, we implement the epidemiological SIR to estimate the
basic reproduction number $\mathcal{R}_0$ at national and state level. We also
developed the statistical machine learning model to predict the cases ahead of
time. Our analysis indicates that the situation of Punjab
($\mathcal{R}_0\approx 16$) is not good. It requires immediate aggressive
attention. We see the $\mathcal{R}_0$ for Madhya Pradesh (3.37) , Maharastra
(3.25) and Tamil Nadu (3.09) are more than 3. The $\mathcal{R}_0$ of Andhra
Pradesh (2.96), Delhi (2.82) and West Bengal (2.77) is more than the India's
$\mathcal{R}_0=2.75$, as of 04 March, 2020. India's $\mathcal{R}_0=2.75$ (as of
04 March, 2020) is very much comparable to Hubei/China at the early disease
progression stage. Our analysis indicates that the early disease progression of
India is that of similar to China. Therefore, with lockdown in place, India
should expect as many as cases if not more like China. If lockdown works, we
should expect less than 66,224 cases by May 01,2020. All data and \texttt{R}
code for this paper is available from
\url{https://github.com/sourish-cmi/Covid19}
|
Collective-density variables have proved to be a useful tool in the
prediction and manipulation of how spatial patterns form in the classical
many-body problem. Previous work has employed properties of collective-density
variables along with a robust numerical optimization technique to find the
classical ground states of many-particle systems subject to radial pair
potentials in one, two and three dimensions. That work led to the
identification of ordered and disordered classical ground states. In this
paper, we extend these collective-coordinate studies by investigating the
ground states of directional pair potentials in two dimensions. Our study
focuses on directional potentials whose Fourier representations are non-zero on
compact sets that are symmetric with respect to the origin and zero everywhere
else. We choose to focus on one representative set which has exotic
ground-state properties: two circles whose centers are separated by some fixed
distance. We obtain ground states for this "two-circle" potential that display
large void regions in the disordered regime. As more degrees of freedom are
constrained the ground states exhibit a collapse of dimensionality
characterized by the emergence of filamentary structures and linear chains.
This collapse of dimensionality has not been observed before in related
studies.
|
A symmetrically doped double layer electron system with total filling
fraction $\nu=1/m$ decouples into two even denominator ($\nu=1/2 m$) composite
fermion `metals' when the layer spacing is large. Out-of-phase fluctuations of
the statistical gauge fields in this system mediate a singular attractive
pairing interaction between composite fermions in different layers. A
strong-coupling analysis shows that for any layer spacing $d$ this pairing
interaction leads to the formation of a paired quantum Hall state with a
zero-temperature gap $\Delta(0) \propto 1/d^2$. The less singular in-phase
gauge fluctuations suppress the size of the zero-temperature gap, $\Delta(0)
\propto 1/\left({d^2}{(\ln d)^6}\right)$, but do not eliminate the instability.
|
The magnetic field of a cuboidal cluster of eight magnetic spheres is
measured. It decays with the inverse seventh power of the distance. This
corresponds formally to a hitherto unheard-of multipole, namely a
dotriacontapole. This strong decay is explained on the basis of dipole-dipole
interaction and the symmetry of the ensuing ground state of the cuboidal
cluster. A method to build such dotriacontapoles is provided.
|
Evolutionary algorithms offer great promise for the automatic design of robot
bodies, tailoring them to specific environments or tasks. Most research is done
on simplified models or virtual robots in physics simulators, which do not
capture the natural noise and richness of the real world. Very few of these
virtual robots are built as physical robots, and the few that are will rarely
be further improved in the actual environment they operate in, limiting the
effectiveness of the automatic design process. We utilize our shape-shifting
quadruped robot, which allows us to optimize the design in its real-world
environment. The robot is able to change the length of its legs during
operation, and is robust enough for complex experiments and tasks. We have
co-evolved control and morphology in several different scenarios, and have seen
that the algorithm is able to exploit the dynamic morphology solely through
real-world experiments.
|
Higher-order topological insulators host gapless states on hinges or corners
of three-dimensional crystals. Recent studies suggested that even topologically
trivial insulators may exhibit fractionally quantized charges localized at
hinges or corners. Although most of the previous studies focused on
two-dimensional systems, in this work, we take the initial step toward the
systematic understanding of hinge and corner charges in three-dimensional
insulators. We consider five crystal shapes of vertex-transitive polyhedra with
the cubic symmetry such as a cube, an octahedron and a cuboctahedron. We derive
real-space formulas for the hinge and corner charges in terms of the electric
charges associated with bulk Wyckoff positions. We find that both the hinge and
corner charges can be predicted from the bulk perspective only modulo certain
fractions depending on the crystal shape, because the relaxation near
boundaries of the crystal may affect the fractional parts. In particular, we
show that a fractionally quantized charge $1/24$ mod $1/12$ in the unit of
elementary charge can appear in a crystal with a shape of a truncated cube or a
truncated octahedron. We also investigate momentum-space formulas for the hinge
and corner charges. It turns out that the irreducible representations of filled
bands at high-symmetry momenta are not sufficient to determine the corner
charge. We introduce an additional Wilson-loop invariant to resolve this issue.
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Current trends suggest that significant gender disparities exist within
Science, Technology, Engineering, and Mathematics (STEM) education at
university, with female students being underrepresented in physics, but more
equally represented in life sciences (e.g., biology, medicine). To understand
these trends, it is important to consider the context in which students make
decisions about which university courses to enrol in. The current study seeks
to investigate gender differences in STEM through a unique approach that
combines network analysis of student enrolment data with an interpretive lens
based on the sociological theory of Pierre Bourdieu. We generate a network of
courses taken by around 9000 undergraduate physics students (from 2009 to 2014)
to quantify Bourdieu's concept of field. We explore the properties of this
network to investigate gender differences in transverse movements (between
different academic fields) and vertical movements (changes in students'
achievement rankings within a field). Our findings indicate that female
students are more likely to make transverse movements into life science fields.
We also find that university physics does a poor job in attracting high
achieving students, and especially high achieving female students. Of the
students who do choose to study physics, low achieving female students are less
likely to continue than their male counterparts. The results and implications
are discussed in the context of Bourdieu's theory, and previous research. We
argue that in order to remove constraints on female student's study choices,
the field of physics needs to provide a culture in which all students feel like
they belong.
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We consider the effect of microwave radiation on the Hall resistivity in
two-dimension electron systems. It is shown that the photon-assisted impurity
scattering of electrons can result in oscillatory dependences of both
dissipative and Hall components of the conductivity and resistivity tensors on
the ratio of radiation frequency to cyclotron frequency. The Hall resistivity
can include a component induced by microwave radiation which is an even
function of the magnetic field. The phase of the dissipative resistivity
oscillations and the polarization dependence of their amplitude are compared
with those of the Hall resistivity oscillations. The developed model can
clarify the results of recent experimental observations of the radiation
induced Hall effect.
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Hypergraph states are multiqubit states whose combinatorial description and
entanglement properties generalize the well-studied class of graph states.
Graph states are important in applications such as measurement-based quantum
computation and quantum error correction. The study of hypergraph states, with
their richer multipartite entanglement and other nonlocal properties, has a
promising outlook for new insight into multipartite entanglement. We present
results analyzing local unitary symmetries of hypergraph states, including both
continuous and discrete families of symmetries. In particular, we show how
entanglement types can be detected and distinguished by certain configurations
in the hypergraphs from which hypergraph states are constructed.
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Despite being neighbouring countries and sharing the language of Bahasa
Melayu (ISO 639-3:ZSM), cultural and language education policy differences
between Singapore and Malaysia led to differences in the translation of the
"annoying" perceived affective quality (PAQ) attribute from English (ISO
639-3:ENG) to ZSM. This study expands upon the translation of the PAQ
attributes from eng to ZSM in Stage 1 of the Soundscapes Attributes Translation
Project (SATP) initiative, and presents the findings of Stage 2 listening tests
that investigated ethnonational differences in the translated ZSM PAQ
attributes and explored their circumplexity. A cross-cultural listening test
was conducted with 100 ZSM speakers from Malaysia and Singapore using the
common SATP protocol. The analysis revealed that Malaysian participants from
non-native ethnicities (my:o) showed PAQ perceptions more similar to Singapore
(sg) participants than native ethnic Malays (MY:M) in Malaysia. Differences
between Singapore and Malaysian groups were primarily observed in stimuli
related to water features, reflecting cultural and geographical variations.
Besides variations in water source-dominant stimuli perception, disparities
between MY:M and SG could be mainly attributed to vibrant scores. The findings
also suggest that the adoption of region-specific translations, such as
membingitkan in Singapore and menjengkelkan in Malaysia, adequately addressed
differences in the annoying attribute, as significant differences were observed
in one or fewer stimuli across ethnonational groups The circumplexity analysis
indicated that the quasi-circumplex model better fit the data compared to the
assumed equal angle quasi-circumplex model in ISO/TS 12913-3, although
deviations were observed possibly due to respondents' unfamiliarity with the
United Kingdom-centric context of the stimulus dataset...
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We construct a quasi-sure version (in the sense of Malliavin) of geometric
rough paths associated with a Gaussian process with long-time memory. As an
application we establish a large deviation principle (LDP) for capacities for
such Gaussian rough paths. Together with Lyons' universal limit theorem, our
results yield immediately the corresponding results for pathwise solutions to
stochastic differential equations driven by such Gaussian process in the sense
of rough paths. Moreover, our LDP result implies the result of Yoshida on the
LDP for capacities over the abstract Wiener space associated with such Gaussian
process.
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In this paper we study the small time asymptotic behavior of the spectral
heat content $\widetilde{Q}_D^{(\alpha)}(t)$ of an arbitrary bounded $C^{1,1}$
domain $D$ with respect to the \textit{subordinate killed Brownian motion} in
$D$ via an $(\alpha/2)$-stable subordinator. For all $\alpha\in (0,2)$, we
establish a two-term small time expansion for $\widetilde{Q}_D^{(\alpha)}(t)$
in all dimensions. When $\alpha\in (1,2)$ and $d\geq 2$, we establish a
three-term small time expansion for $\widetilde{Q}_D^{(\alpha)}(t)$.
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Spatial-Spectral Total Variation (SSTV) can quantify local smoothness of
image structures, so it is widely used in hyperspectral image (HSI) processing
tasks. Essentially, SSTV assumes a sparse structure of gradient maps calculated
along the spatial and spectral directions. In fact, these gradient tensors are
not only sparse, but also (approximately) low-rank under FFT, which we have
verified by numerical tests and theoretical analysis. Based on this fact, we
propose a novel TV regularization to simultaneously characterize the sparsity
and low-rank priors of the gradient map (LRSTV). The new regularization not
only imposes sparsity on the gradient map itself, but also penalize the rank on
the gradient map after Fourier transform along the spectral dimension. It
naturally encodes the sparsity and lowrank priors of the gradient map, and thus
is expected to reflect the inherent structure of the original image more
faithfully. Further, we use LRSTV to replace conventional SSTV and embed it in
the HSI processing model to improve its performance. Experimental results on
multiple public data-sets with heavy mixed noise show that the proposed model
can get 1.5dB improvement of PSNR.
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We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at
supersingular primes to include the case $a_p \neq 0$, where $a_p$ is the trace
of Frobenius. To do this, we algebraically construct $p$-adic $L$-functions
$L_p^{\sharp}$ and $L_p^{\flat}$ with the good growth properties of the
classical Pollack $p$-adic $L$-functions that in fact match them exactly when
$a_p=0$ and $p$ is odd. We then generalize Kobayashi's methods to define two
Selmer groups $\Sel^{\sharp}$ and $\Sel^{\flat}$ and formulate a main
conjecture, stating that each characteristic ideal of the duals of these Selmer
groups is generated by our $p$-adic $L$-functions $L_p^{\sharp}$ and
$L_p^{\flat}$. We then use results by Kato to prove a divisibility statement.
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Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ is a unique member of cuprate
superconductors where many studies suggest that CuO double chains are
responsible for superconductivity. One characteristic and non-trivial feature
of its electronic structure is a relatively large electron hopping $t$ between
nearest neighbor Cu sites with a Cu-O-Cu angle of around 90 degrees. In this
study, we have theoretically pinned down the origin of a large $|t|$ in the
double-chain structure of Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ using
first-principles calculation and tight-binding-model analysis. We have found
that, in the nearest neighbor hopping $t$, $d$-$d$ and $d$-$p$-$p$-$d$
contributions roughly cancel each other out and the $d$-$p$-$d$ hopping path
enhanced by the local distortion of the double chain is a key to get the large
$|t|$. Double-well band dispersion arising from the relatively large $|t/t'|$
allows the enhancement of spin-fluctuation-mediated superconductivity by the
incipient-band mechanism, where the one band bottom plays a role of the
incipient valley. Our study provides the important knowledge to understand the
unique superconductivity in Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$.
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In this short note, we describe some recent results on the pointwise
existence of the Lyapunov exponent for certain quasi-periodic cocyles.
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Let $D^{III}_n$ and $\mathscr{S}_n$ be the Cartan domains of type III that
consist of the symmetric $n \times n$ complex matrices $Z$ that satisfy
$Z\overline{Z} < I_n$ and $\mathrm{Im}(Z) > 0$, respectively. For these
domains, we study weighted Bergman spaces and Toeplitz operators acting on
them. We consider the Abelian groups $\mathbb{T}$, $\mathbb{R}_+$ and
$\mathrm{Symm}(n,\mathbb{R})$ (symmetric $n \times n$ real matrices), and their
actions on the Cartan domains of type III. We call the corresponding actions
Abelian Elliptic, Abelian Hyperbolic and Parabolic. The moment maps of these
three actions are computed and functions of them (moment map symbols) are used
to construct commutative $C^*$-algebras generated by Toeplitz operators. This
leads to a natural generalization of known results for the unit disk. We also
compute spectral integral formulas for the Toeplitz operators corresponding to
the Abelian Elliptic and Parabolic cases.
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The Sh2-294 HII region ionized by a single B0V star features several infrared
excess sources, a photodissociation region, and also a group of reddened stars
at its border. The star formation scenario in the region seems to be quite
complex. In this paper, we present follow-up results of Sh2-294 HII region at
3.6, 4.5, 5.8, and 8.0 microns observed with the Spitzer Space Telescope
Infrared Array Camera (IRAC), coupled with H2 (2.12 microns) observation, to
characterize the young population of the region and to understand its star
formation history. We identified 36 young stellar object (YSO, Class I, Class
II and Class I/II) candidates using IRAC color-color diagrams. It is found that
Class I sources are preferentially located at the outskirts of the HII region
and associated with enhanced H2 emission; none of them are located near the
central cluster. Combining the optical to mid-infrared (MIR) photometry of the
YSO candidates and using the spectral energy distribution fitting models, we
constrained stellar parameters and the evolutionary status of 33 YSO
candidates. Most of them are interpreted by the model as low-mass (< 4 solar
masses) YSOs; however, we also detected a massive YSO (~9 solar masses) of
Class I nature, embedded in a cloud of visual extinction of ~24 mag. Present
analysis suggests that the Class I sources are indeed younger population of the
region relative to Class II sources (age ~ 4.5 x 10^6 yr). We suggest that the
majority of the Class I sources, including the massive YSOs, are
second-generation stars of the region whose formation is possibly induced by
the expansion of the HII region powered by a ~ 4 x 10^6 yr B0 main-sequence
star.
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We study the Bose polaron problem in a nonequilibrium setting, by considering
an impurity embedded in a quantum fluid of light realized by exciton-polaritons
in a microcavity, subject to a coherent drive and dissipation on account of
pump and cavity losses. We obtain the polaron effective mass, the drag force
acting on the impurity, and determine polaron trajectories at a semiclassical
level. We find different dynamical regimes, originating from the unique
features of the excitation spectrum of driven-dissipative polariton fluids, in
particular a non-trivial regime of acceleration against the flow. Our work
promotes the study of impurity dynamics as an alternative testbed for probing
superfluidity in quantum fluids of light.
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We present results for the large-$N$ limit of the chiral condensate computed
from twisted reduced models. We followed a two-fold strategy, one constiting in
extracting the condensate from the quark-mass dependence of the pion mass, the
other consisting in extracting the condensate from the mode number of the Dirac
operator.
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We build, using group-theoretic methods, a general framework for approaching
multi-particle entanglement. As far as entanglement is concerned, two states of
n spin-1/2 particles are equivalent if they are on the same orbit of the group
of local rotations (U(2)^n). We give a method for finding the number of
parameters needed to describe inequivalent n spin-1/2 particles states. We also
describe how entanglement of states on a given orbit may be characterized by
the stability group of the action of the group of local rotations on any point
on the orbit.
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I review the state of the art of the theoretical calculations for decays
mediated by $b\to s \ell^+ \ell^-$ transitions, for $\ell=e,\mu$. I focus on
the predictions of observables in $B\to K \mu^+\mu^-$, $B\to K^* \mu^+\mu^-$,
and $B_s\to \phi \mu^+\mu^-$ decays, as many of these predictions are in
tension with the corresponding experimental measurements. I also briefly
discuss the $\Lambda_b\to \Lambda \mu^+\mu^-$ decay and present a new
calculation for this channel. Special emphasis is placed on the non-local
contributions, as they are the largest systematic uncertainties in these
decays. The current theoretical calculations for $b\to s \mu^+ \mu^-$ decays
are not able to explain the tensions with the experimental measurements.
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We perform a tomographic cross-correlation analysis of archival FIRAS data
and the BOSS galaxy redshift survey to constrain the amplitude of [CII]
$^2P_{3/2}\rightarrow$ $^2P_{1/2}$ fine structure emission. Our analysis
employs spherical harmonic tomography (SHT), which is based on the angular
cross-power spectrum between FIRAS maps and BOSS galaxy over-densities at each
pair of redshift bins, over a redshift range of $0.24<z<0.69$. We develop the
SHT approach for intensity mapping, where it has several advantages over
existing power spectral estimators. Our analysis constrains the product of the
[CII] bias and [CII] specific intensity, $b_{[CII]}I_{[CII]i}$, to be $<0.31$
MJy/sr at $z {\approx} 0.35$ and $<0.28$ MJy/sr at $z {\approx} 0.57$ at $95\%$
confidence. These limits are consistent with most current models of the [CII]
signal, as well as with higher-redshift [CII] cross-power spectrum measurements
from the Planck satellite and BOSS quasars. We also show that our analysis, if
applied to data from a more sensitive instrument such as the proposed PIXIE
satellite, can detect pessimistic [CII] models at high significance.
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Magnetic skyrmions are particle-like spin-swirling objects ubiquitously
realized in magnets. They are topologically stable chiral kinks composed of
multiple modulation waves of spiral spin structures, where the helicity of each
spiral is usually selected by antisymmetric exchange interactions in
noncentrosymmetric crystals. We report an experimental observation of a
distorted triangular lattice of skyrmions in the polar tetragonal magnet
EuNiGe$_3$, reflecting a strong coupling with the lattice. Moreover, through
resonant x-ray diffraction, we find that the magnetic helicity of the original
spiral at zero field is reversed when the skyrmion lattice is formed in a
magnetic field. This means that the energy gain provided by the skyrmion
lattice formation is larger than the antisymmetric exchange interaction. Our
findings will lead us to a further understanding of emergent magnetic states.
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This article deals with approximating steady-state particle-resolved fluid
flow around a fixed particle of interest under the influence of randomly
distributed stationary particles in a dispersed multiphase setup using
Convolutional Neural Network (CNN). The considered problem involves rotational
symmetry about the mean velocity (streamwise) direction. Thus, this work
enforces this symmetry using $\mathbf{\textbf{SE(3)-equivariant}}$, special
Euclidean group of dimension 3, CNN architecture, which is translation and
three-dimensional rotation equivariant. This study mainly explores the
generalization capabilities and benefits of SE(3)-equivariant network. Accurate
synthetic flow fields for Reynolds number and particle volume fraction
combinations spanning over a range of [86.22, 172.96] and [0.11, 0.45]
respectively are produced with careful application of symmetry-aware
data-driven approach.
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We construct non-constructible simplicial $d$-spheres with $d+10$ vertices
and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices
for $d\geq 3$.
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Optical coherence tomography angiography (OCTA) is a novel and clinically
promising imaging modality to image retinal and sub-retinal vasculature. Based
on repeated optical coherence tomography (OCT) scans, intensity changes are
observed over time and used to compute OCTA image data. OCTA data are prone to
noise and artifacts caused by variations in flow speed and patient movement. We
propose a novel iterative maximum a posteriori signal recovery algorithm in
order to generate OCTA volumes with reduced noise and increased image quality.
This algorithm is based on previous work on probabilistic OCTA signal models
and maximum likelihood estimates. Reconstruction results using total variation
minimization and wavelet shrinkage for regularization were compared against an
OCTA ground truth volume, merged from six co-registered single OCTA volumes.
The results show a significant improvement in peak signal-to-noise ratio and
structural similarity. The presented algorithm brings together OCTA image
generation and Bayesian statistics and can be developed into new OCTA image
generation and denoising algorithms.
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Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n,
\{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional
Banach space $\mathcal{X}$. Let $M,N\subseteq \{1, \dots, n\}$ be such that
\begin{align*}
o(M)^\frac{1}{q}o(N)^\frac{1}{p}< \frac{1}{\displaystyle \max_{1\leq j,k\leq
n}|g_k(\tau_j) |}, \end{align*} where $q$ is the conjugate index of $p$. Then
for all $x \in \mathcal{X}$, we show that \begin{align}\label{FGJU} (1) \quad
\quad \quad \quad \|x\|\leq
\left(1+\frac{1}{1-o(M)^\frac{1}{q}o(N)^\frac{1}{p}\displaystyle\max_{1\leq
j,k\leq n}|g_k(\tau_j)|}\right)\left[\left(\sum_{j\in
M^c}|f_j(x)|^p\right)^\frac{1}{p}+\left(\sum_{k\in N^c}|g_k(x)
|^p\right)^\frac{1}{p}\right]. \end{align}
We call Inequality (1) as \textbf{Functional Ghobber-Jaming Uncertainty
Principle}. Inequality (1) improves the uncertainty principle obtained by
Ghobber and Jaming \textit{[Linear Algebra Appl., 2011]}.
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We consider L^p-cohomology of reflexive Banach spaces and give a spectral
condition implying the vanishing of 1-cohomology with coefficients in uniformly
bounded representations on a Hilbert space.
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Recently there has been an interest in the potential of learning generative
models from a single image, as opposed to from a large dataset. This task is of
practical significance, as it means that generative models can be used in
domains where collecting a large dataset is not feasible. However, training a
model capable of generating realistic images from only a single sample is a
difficult problem. In this work, we conduct a number of experiments to
understand the challenges of training these methods and propose some best
practices that we found allowed us to generate improved results over previous
work in this space. One key piece is that unlike prior single image generation
methods, we concurrently train several stages in a sequential multi-stage
manner, allowing us to learn models with fewer stages of increasing image
resolution. Compared to a recent state of the art baseline, our model is up to
six times faster to train, has fewer parameters, and can better capture the
global structure of images.
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We use ab initio simulations to investigate the incorporation of pyridine
molecules (C$_5$H$_5$N) in the van der Waals gaps of Bi$_2$Se$_3$. The
intercalated pyridine molecules increase the separation distance between the
Bi$_2$Se$_3$ quintuple layers (QLs), suppressing the parity inversion of the
electronic states at the $\Gamma$-point. We find that the intercalated region
becomes a trivial insulator. By combining the pristine Bi$_2$Se$_3$ region with
the one intercalated by the molecules, we have a non-trivial/trivial
heterojunction characterized by the presence of (topologically protected)
metallic states at the interfacial region. Next we apply an external
compressive pressure to the system, and the results are (i) a decrease on the
separation distance between the QLs intercalated by pyridine molecules, and
(ii) the metallic states are shifted toward the bulk region, turning the system
back to insulator. That is, through a suitable tuning of the external pressure
in Bi$_2$Se$_3$, intercalated by pyridine molecules, we can control its
topological properties; turning-on and -off the topologically protected
metallic states lying at the non-trivial/trivial interface.
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Verstraelen et al. (J. Chem. Theory Comput. 12 (2016) 3894-3912) recently
introduced a new method for partitioning the electron density of a material
into constituent atoms. Their approach falls within the class of atomic
population analysis methods called stockholder charge partitioning methods in
which a material electron distribution is divided into overlapping atoms. The
Minimal Basis Iterative Stockholder (MBIS) method proposed by Verstraelen et
al. composes the pro-atom density as a sum of exponential functions, where the
number of exponential functions equals that element's row in the Periodic
Table. Specifically, one exponential function is used for H and He, two for Li
through Ne, three for Na through Ar, etc. In the MBIS method, the exponential
functions parameters defining the pro-atom density are optimized in a
self-consistent iterative procedure. Close examination reveals some important
anomalies in the article by Verstaelen et al. The purpose of this comment
article is to bring these important issues to readers' attention and to start a
discussion of them.
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