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This paper presents some parallel developments in Quiver/Dimer Models,
Hypergeometric Systems and Dessins d'Enfants. The setting in which Gelfand,
Kapranov and Zelevinsky have formulated the theory of hypergeometric systems,
provides also a natural setting for dimer models. The Fast Inverse Algorithm,
the untwisting procedure and the Kasteleyn matrix for dimer models are recasted
in this setting. There is a relation between triangulations in GKZ theory and
some perfect matchings in the dimer models, so that the secondary polygon
coincides with the Newton polygon of the Kasteleyn determinant. Finally it is
observed in examples and conjectured to hold in general, that the determinant
of the Kasteleyn matrix with suitable weights becomes after a simple
transformation equal to the principal A-determinant in GKZ theory.
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We have measured Lick index equivalent widths to derive luminosity weighted
stellar ages and metallicities for thin and thick disk dominated regions of 9
edge-on disk galaxies with the ARC 3.5 meter telescope at Apache Point
Observatory. In all cases, the thick disks are confirmed to be old stellar
populations, with typical ages between 4 and 10 Gyr. The thin disks are
uniformly younger than the thick disks, and show strong radial age gradients,
with the outer regions of the disks being younger than 1 Gyr. We do not detect
any significant metallicity differences or alpha-element enhancement in the
thick disk stars compared to the thin disk, due to the insensitivity of the
Lick indices to these differences at low metallicity. We compare these results
to thick disks measured in other systems and to predictions from thick disk
formation models.
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We prove that Klein quartic maximizes the multiplicity of the first positive
eigenvalue of the Laplacian among all closed hyperbolic surfaces of genus $3$,
with multiplicity equal to $8$. We also obtain partial results in genus $2$,
where we find that the maximum multiplicity is between $3$ and $6$. Along the
way, we show that for every $g\geq 2$, there exists some $\delta_g>0$ such that
the multiplicity of any eigenvalue of the Laplacian on a closed hyperbolic
surface of genus $g$ in the interval $[0,1/4+\delta_g]$ is at most $2g-1$
despite the fact that this interval can contain arbitrarily many eigenvalues.
This extends a result of Otal to a larger interval but with a weaker bound,
which nevertheless improves upon the general upper bound of S\'evennec.
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We report a combined neutron scattering and magnetization study on the
multiferroic DyFeO3 which shows a very strong magnetoelectric effect. Applying
magnetic field along the c-axis, the weak ferromagnetic order of the Fe ions is
quickly recovered from a spin reorientation transition, and the long-range
antiferromagnetic order of Dy becomes a short-range one. We found that the
short-range order concurs with the multiferroic phase and is responsible for
its sizable hysteresis. Our H-T phase diagram suggests that the strong
magnetoelectric effect in DyFeO3 has to be understood with not only the weak
ferromagnetism of Fe but also the short-range antiferromagnetic order of Dy.
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High temperature superconductivity in cuprates arises from an electronic
state that remains poorly understood. We report the observation of a related
electronic state in a non-cuprate material Sr2IrO4 in which the unique cuprate
Fermiology is largely reproduced. Upon surface electron doping through in situ
deposition of alkali-metal atoms, angle-resolved photoemission spectra of
Sr2IrO4 display disconnected segments of zero-energy states, known as Fermi
arcs, and a gap as large as 80 meV. Its evolution toward a normal metal phase
with a closed Fermi surface as a function of doping and temperature parallels
that in the cuprates. Our result suggests that Sr2IrO4 is a useful model system
for comparison to the cuprates.
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The optical spectra of objects classified as QSOs in the SDSS DR6 are
analyzed with the aim of determining the value of the fine structure constant
in the past and then check for possible changes in the constant over
cosmological timescales. The analysis is done by measuring the position of the
fine structure lines of the [OIII] doublet (4959 and 5008) in QSO nebular
emission. From the sample of QSOs at redshifts z < 0.8 a subsample was selected
on the basis of the amplitude and width of the [OIII] lines. Two different
method were used to determine the position of the lines of the [OIII] doublet,
both giving similar results. Using a clean sample containing 1568 of such
spectra, a value of Delta alpha /alpha=(+2.4 +-2.5) x 10^{-5} (in the range of
redshifts 0-0.8) was determined. The use of a larger number of spectra allows a
factor ~5 improvement on previous constraints based on the same method. On the
whole, we find no evidence of changes in alpha on such cosmological timescales.
The mean variation compatible with our results is 1/ <t> Delta
alpha/alpha=(+0.7 +- 0.7) x 10^{-14} yr^{-1}. The analysis was extended to the
[NeIII] and [SII] doublets, although their usefulness is limited due to the
fact that all these doublets in QSOs tend to be fainter than [OIII], and that
some of them are affected by systematics.
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In this paper, we obtain optimal time-decay rates in $L^r(\mathbb R^3_+)$ for
$r\ge 1$ of global strong solutions to the nematic liquid crystal flows in
$\mathbb R^3_+$, provided the initial data has small $L^3(\mathbb R^3_+)$-norm.
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Systematic uncertainties in accelerator oscillation neutrino experiments
arise mostly from nuclear models describing neutrino-nucleus interactions. To
mitigate these uncertainties, we can study neutrino-nuclei interactions with
detectors possessing enhanced hadron detection capabilities at energies below
the nuclear Fermi level. Gaseous detectors not only lower the particle
detection threshold but also enable the investigation of nuclear effects on
various nuclei by allowing for changes in the gas composition. This approach
provides valuable insights into the modelling of neutrino-nucleus interactions
and significantly reduces associated uncertainties. Here, we discuss the design
and first operation of a gaseous argon time projection chamber optically read.
The detector operates at atmospheric pressure and features a single stage of
electron amplification based on a thick GEM. Here, photons are produced with
wavelengths in the vacuum ultraviolet regime. In an optical detector the
primary constraint is the light yield. This study explores the possibility of
increasing the light yield by applying a low electric field downstream of the
ThGEM. In this region, called the electroluminescence gap, electrons propagate
and excite the argon atoms, leading to the subsequent emission of photons. This
process occurs without any further electron amplification, and it is
demonstrated that the total light yield increases up to three times by applying
moderate electric fields of the order of 3~kV/cm. Finally, an indirect method
is discussed for determining the photon yield per charge gain of a ThGEM,
giving a value of 18.3 photons detected per secondary electron.
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We have studied the dephasing of a superconducting flux-qubit coupled to a
DC-SQUID based oscillator. By varying the bias conditions of both circuits we
were able to tune their effective coupling strength. This allowed us to measure
the effect of such a controllable and well-characterized environment on the
qubit coherence. We can quantitatively account for our data with a simple model
in which thermal fluctuations of the photon number in the oscillator are the
limiting factor. In particular, we observe a strong reduction of the dephasing
rate whenever the coupling is tuned to zero. At the optimal point we find a
large spin-echo decay time of $4 \mu s$.
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Using a single-scattering theory, we derive the expression of the degree of
polarization of the light scattered from a layer exhibiting both surface and
volume scattering. The expression puts forward the intimate connection between
the degree of polarization and the statistical correlation between surface and
volume disorders. It also permits a quantitative analysis of depolarization for
uncorrelated, partially correlated and perfectly correlated disorders. We show
that measuring the degree of polarization could allow one to assess the
surface-volume correlation function, and that, reciprocally, the degree of
polarization could be engineered by an appropriate design of the correlation
function.
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An algebra A not encountered in either the usual algebraic varieties or
supervarieties is introduced. A is a graded and deformed version of the
quaternions, with structure similar to that of a Jordan-Lie superalgebra as
defined by Okubo and Kamiya, but it is shown to be neither that of a purely
associative Lie superalgebra, nor that of a purely antiassociative Jordan-Lie
superalgebra. Rather, it exhibits a novel kind of associativity, here called
`ordered graded associativity', that is somewhat `in between' pure
associativity and pure antiassociativity. In addition to graded associativity,
the generators of A obey graded commutation relations encountered in both the
usual Lie superalgebras and in graded Jordan-Lie algebras. They also satisfy
new graded Jacobi identities that combine characteristics of the Jacobis obeyed
by the generators of ungraded Lie, graded Lie and graded Jordan-Lie algebras.
Mainly due to these three features, A is called a `mixed' Jordan-Lie
superalgebra. The present paper defines A and compares it with the Jordan-Lie
superalgebra defined by Okubo and Kamiya.
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Most research on the simulation of deformation and failure of metals has been
and continues to be performed using the finite element method. However, the
issues of mesh entanglement under large deformation, considerable complexity in
handling contact, and difficulties encountered while solving large deformation
fluid-structure interaction problems have led to the exploration of alternative
approaches. The material point method uses Lagrangian solid particles embedded
in an Eulerian grid. Particles interact via the grid with other particles in
the same body, with other solid bodies, and with fluids. Thus, the three issues
mentioned in the context of finite element analysis are circumvented.
In this paper, we present simulations of cylinders which fragment due to
explosively expanding gases generated by reactions in a high energy material
contained inside. The material point method is the numerical method chosen for
these simulations discussed in this paper. The plastic deformation of metals is
simulated using a hypoelastic-plastic stress update with radial return that
assumes an additive decomposition of the rate of deformation tensor. Various
plastic strain, plastic strain rate, and temperature dependent flow rules and
yield conditions are investigated. Failure at individual material points is
determined using porosity, damage and bifurcation conditions. Our models are
validated using data from high strain rate impact experiments. It is concluded
that the material point method possesses great potential for simulating high
strain-rate, large deformation fluid-structure interaction problems.
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We discuss the perturbative expansion of SU(N) Yang-Mills theories defined on
a d-dimensional torus of linear size l with twisted boundary conditions,
generalizing previous results in the literature. For a specific class of twist
tensors depending on a single integer flux value k, we show that perturbative
results to all orders depend on the combination lN^(2/d) and a flux-dependent
angle theta. This implies a new kind of volume independence that holds at
finite N and for fixed values of theta. Our results also provide interesting
information about the possible occurrence of tachyonic instabilities at
one-loop order. We support the prescription that instabilities are avoided, if
the large N limit is taken keeping theta > theta_c, and appropriately scaling
the magnetic flux k with N. Numerical results in 2+1 dimensions provide a test
of how these ideas extend into the non-perturbative regime.
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Here we show that the phenomenon of arbitrarily long-lived quasinormal modes
(called quasiresonances) of a massive scalar field in the vicinity of a black
hole is not an artifact of the test field approximation, but takes place also
when the (derivative) coupling of a scalar field with the Einstein tensor is
taken into consideration. We observe that at large coupling and high multipole
numbers, the growing modes appear in the spectrum, which are responsible for
the eikonal instability of the field. For small coupling, when the
configuration is stable, there appear the purely imaginary quasinormal modes
which are nonperturbative in the coupling constant. At the sufficiently small
coupling the nonminimal scalar field is stable and the asymptotic late-time
tails are not affected by the coupling term. The accurate calculations of
quasinormal frequencies for a massive scalar field with the derivative coupling
in the Reissner-Nordstr\"om black-hole background are performed with the help
of Frobenius method, time-domain integration and WKB expansion.
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The open-ended nature of language generation makes the evaluation of
autoregressive large language models (LLMs) challenging. One common evaluation
approach uses multiple-choice questions (MCQ) to limit the response space. The
model is then evaluated by ranking the candidate answers by the log probability
of the first token prediction. However, first-tokens may not consistently
reflect the final response output, due to model's diverse response styles such
as starting with "Sure" or refusing to answer. Consequently, MCQ evaluation is
not indicative of model behaviour when interacting with users. But by how much?
We evaluate how aligned first-token evaluation is with the text output along
several dimensions, namely final option choice, refusal rate, choice
distribution and robustness under prompt perturbation. Our results show that
the two approaches are severely misaligned on all dimensions, reaching mismatch
rates over 60%. Models heavily fine-tuned on conversational or safety data are
especially impacted. Crucially, models remain misaligned even when we
increasingly constrain prompts, i.e., force them to start with an option letter
or example template. Our findings i) underscore the importance of inspecting
the text output as well and ii) caution against relying solely on first-token
evaluation.
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Given a pair of fusion categories $C$ and $D$, we may form the free product
$C * D$ and the tensor product $C \boxtimes D$. It is natural to think of the
tensor product as a quotient of the free product. What other quotients are
possible?
When $C=D=A_2$, there is an infinite family of quotients interpolating
between the free product and the tensor product (closely related to the
$A_{2n-1}^{(1)}$ and $D_{n+2}^{(1)}$ subfactors at index 4). Bisch and Haagerup
discovered one example of such an intermediate quotient when $C=A_2$ and
$D=T_2$, and suggested that there might be another family here. We show that
such quotients are characterized by parameters $n \geq 1$ and $\omega$ with
$\omega^{2n}=1$. For $n=1,2,3$, we show $\omega$ must be 1, and construct the
corresponding quotient ($n=1$ is the tensor product, $n=2$ is the example
discovered by Bisch and Haagerup, and $n=3$ is new). We further show that there
are no such quotients for $4 \leq n \leq 10$. Our methods also apply to the
case when $C=D=T_2$, and we prove similar results there.
During the preparation of this manuscript we learnt of an independent result
of Liu's on subfactors. With the translation between the subfactor and fusion
category settings provided here, it follows there are no such quotients for any
$n \geq 4$.
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We give an exposition of a formula of Daskalopoulos, Hamilton and Sesum for
solutions to the Ricci flow on the 2-sphere. This is one of several estimates
used by them to classify ancient solutions on the 2-sphere.
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At high baryon chemical potential $\mu_B$, the equation of state of QCD
allows a weak-coupling expansion in the QCD coupling $\alpha_s$. The result is
currently known up to and including the full next-to-next-to-leading order
(NNLO) $\alpha_s^2$. Starting at this order, the computations are complicated
by the modification of particle propagation in a dense medium, which
necessitates non-perturbative treatment of the scale $\alpha_s^{1/2} \mu_B$. In
this work, we apply a Hard-Thermal-Loop scheme for capturing the contributions
of this scale to the weak-coupling expansion, and use it to determine the
leading-logarithm contribution to NNNLO: $\alpha_s^3 \ln^2 \alpha_s$. This
result is the first improvement to the equation of state of massless cold quark
matter in 40 years. The new term is negligibly small, and thus significantly
increases our confidence in the applicability of the weak-coupling expansion.
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The integral with respect to a multidimensional stochastic measure, for which
we assume only $\sigma$-additivity in probability, is studied. The continuity
and differentiability of its realizations are established.
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Quantum entanglement in multipartite systems cannot be shared freely. In
order to illuminate basic rules of entanglement sharing between qubits we
introduce a concept of an entangled structure (graph) such that each qubit of a
multipartite system is associated with a point (vertex) while a bi-partite
entanglement between two specific qubits is represented by a connection (edge)
between these points. We prove that any such entangled structure can be
associated with a pure state of a multi-qubit system. Moreover, we show that a
pure state corresponding to a given entangled structure is a superposition of
vectors from a subspace of the $2^N$-dimensional Hilbert space, whose dimension
grows linearly with the number of entangled pairs.
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Cloud droplet mobility is referred to here as a measure of the droplets
ability to move with ambient air. We claim that an important part of the
aerosol effect on convective clouds is driven by changes in droplet mobility.
We show that the mass-weighted average droplet terminal velocity, defined here
as the effective terminal velocity (eta) and its spread (sigma_eta) serve as
direct measures of this effect. Moreover, we develop analytical estimations for
eta and sigma_eta to show that changes in the relative dispersion of eta
(epsilon_eta = sigma_eta/eta) can serve as a sensitive predictor of the onset
of droplet-collection processes.
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We study the performance of Long Short-Term Memory networks for keystroke
biometric authentication at large scale in free-text scenarios. For this we
explore the performance of Long Short-Term Memory (LSTMs) networks trained with
a moderate number of keystrokes per identity and evaluated under different
scenarios including: i) three learning approaches depending on the loss
function (softmax, contrastive, and triplet loss); ii) different number of
training samples and lengths of keystroke sequences; iii) four databases based
on two device types (physical vs touchscreen keyboard); and iv) comparison with
existing approaches based on both traditional statistical methods and deep
learning architectures. Our approach called TypeNet achieves state-of-the-art
keystroke biometric authentication performance with an Equal Error Rate of 2.2%
and 9.2% for physical and touchscreen keyboards, respectively, significantly
outperforming previous approaches. Our experiments demonstrate a moderate
increase in error with up to 100,000 subjects, demonstrating the potential of
TypeNet to operate at an Internet scale. To the best of our knowledge, the
databases used in this work are the largest existing free-text keystroke
databases available for research with more than 136 million keystrokes from
168,000 subjects in physical keyboards, and 60,000 subjects with more than 63
million keystrokes acquired on mobile touchscreens.
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Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over
$\mathbb{C}$. In the 1950s Chevalley showed that $\mathfrak{g}$ admits
particular bases, now called ``Chevalley bases'', for which the corresponding
structure constants are integers. Such bases are not unique but, using
Lusztig's theory of canonical bases, one can single out a ``canonical''
Chevalley basis which is unique up to a global sign. In this paper, we give
explicit formulae for the structure constants with respect to such a basis.
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We report on an optical photometric and polarimetric campaign on the
accreting millisecond X-ray pulsar (AMXP) SAX J1808.4-3658 during its 2019
outburst. The emergence of a low-frequency excess in the spectral energy
distribution in the form of a red excess above the disc spectrum (seen most
prominently in z, i and R-bands) is observed as the outburst evolves. This is
indicative of optically thin synchrotron emission due to a jet, as seen
previously in this source and in other AMXPs during outburst. At the end of the
outburst decay, the source entered a reflaring state. The low-frequency excess
is still observed during the reflares. Our optical (BVRI) polarimetric campaign
shows variable linear polarization (LP) throughout the outburst. We show that
this is intrinsic to the source, with low-level but significant detections
(0.2-2%) in all bands. The LP spectrum is red during both the main outburst and
the reflaring state, favoring a jet origin for this variable polarization over
other interpretations, such as Thomson scattering with free electrons from the
disc or the propelled matter. During the reflaring state, a few episodes with
stronger LP level (1-2 %) are observed. The low-level, variable LP is
suggestive of strongly tangled magnetic fields near the base of the jet. These
results clearly demonstrate how polarimetry is a powerful tool for probing the
magnetic field structure in X-ray binary jets, similar to AGN jets.
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In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we
develop field-theoretical models of quantum nonequilibrium systems which could
exist today as relics from the very early universe. We consider relic excited
states generated by inflaton decay, as well as relic vacuum modes, for particle
species that decoupled close to the Planck temperature. Simple estimates
suggest that, at least in principle, quantum nonequilibrium could survive to
the present day for some relic systems. The main focus of this paper is to
describe the behaviour of such systems in terms of field theory, with the aim
of understanding how relic quantum nonequilibrium might manifest
experimentally. We show by explicit calculation that simple perturbative
couplings will transfer quantum nonequilibrium from one field to another (for
example from the inflaton field to its decay products). We also show that
fields in a state of quantum nonequilibrium will generate anomalous spectra for
standard energy measurements. Possible connections to current astrophysical
observations are briefly addressed.
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We give a generalization of the Penrose transform on Hermitian manifolds with
metrics locally conformally equivalent to Bochner-K\"ahler metrics. We also
give an explicit formula for the inverse transform. This paper is a
generalization of "The Twistor correspondence of the Dolbeault complex over
$\C^n$" (dg-ga/9501004) and intended to supersede it.
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The `extended Aharonov-Bohm (AB) period' recently proposed by Kusakabe and
Aoki [J. Phys. Soc. Jpn (65), 2772 (1996)] is extensively studied numerically
for finite size systems of strongly correlated electrons. While the extended AB
period is the system length times the flux quantum for noninteracting systems,
we have found the existence of the boundary across which the period is halved
or another boundary into an even shorter period on the phase diagram for these
models. If we compare this result with the phase diagram predicted from the
Tomonaga-Luttinger theory, devised for low-energy physics, the halved period
(or shorter periods) has a one-to-one correspondence to the existence of the
pairing (phase separation or metal-insulator transition) in these models. We
have also found for the t-J model that the extended AB period does not change
across the integrable-nonintegrable boundary despite the totally different
level statistics.
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We extend previous proofs that violations of the null energy condition (NEC)
are a generic and universal feature of traversable wormholes to completely
non-symmetric time-dependent wormholes. We show that the analysis can be
phrased purely in terms of local geometry at and near the wormhole throat, and
do not have to make any technical assumptions about asymptotic flatness or
other global properties. A key aspect of the analysis is the demonstration that
time-dependent wormholes have two throats, one for each direction through the
wormhole, and that the two throats coalesce only for the case of a static
wormhole.
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We present the analysis of four M dwarf stars -plus one M giant that seeped
past our selection criteria- observed in Cycle 3 of Kepler Guest Observer
program (GO3) in a search for intrinsic pulsations. Stellar oscillations in M
dwarfs were theoretically predicted by Rodr\'iguez-L\'opez et al. (2012) to be
in the range ~20-40 min and ~4-8 h, depending on the age and the excitation
mechanism. We requested Kepler short cadence observations to have an adequate
sampling of the oscillations. The targets were chosen on the basis of
detectable rotation in the initial Kepler results, biasing towards youth.The
analysis reveals no oscillations attributable to pulsations at a detection
limit of several parts per million, showing that either the driving mechanisms
are not efficient in developing the oscillations to observable amplitudes, or
that if pulsations are driven, the amplitudes are very low. The size of the
sample, and the possibility that the instability strip is not pure, allowing
the coexistence of pulsators and non-pulsators, prevent us from deriving
definite conclusions. Inmediate plans include more M dwarfs photometric
observations of similar precision with Kepler K2 mission and spectroscopic
searches already underway within the Cool Tiny Beats Project (Anglada-Escud\'e
et al. 2014, Berdi\~nas et al. 2014) with the high-resolution spectrographs
HARPS and HARPS-N.
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Above-threshold ionization (ATI) results from strong field laser-matter
interaction and it is one of the fundamental processes that may be used to
extract electron structural and dynamical information about the atomic or
molecular target. Moreover, it can also be used to characterize the laser field
itself. Here, we develop an analytical description of ATI, which extends the
theoretical Strong Field Approximation (SFA), for both the direct and
re-scattering transition amplitudes in atoms. From a non-local, but separable
potential, the bound-free dipole and the re-scattering transition matrix
elements are analytically computed. In comparison with the standard approaches
to the ATI process, our analytical derivation of the re-scattering matrix
elements allows us to study directly how the re-scattering process depends on
the atomic target and laser pulse features -we can turn on and off
contributions having different physical origins or corresponding to different
physical mechanisms. We compare SFA results with the full numerical solutions
of the time-dependent Schroedinger equation (TDSE) within the few-cycle pulse
regime. Good agreement between our SFA and TDSE model is found for the ATI
spectrum. Our model captures also the strong dependence of the photoelectron
spectra on the carrier envelope phase of the laser field.
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5G is envisioned to improve major key performance indicators (KPIs), such as
peak data rate, spectral efficiency, power consumption, complexity, connection
density, latency, and mobility. This chapter aims to provide a complete picture
of the ongoing 5G waveform discussions and overviews the major candidates. It
provides a brief description of the waveform and reveals the 5G use cases and
waveform design requirements. The chapter presents the main features of cyclic
prefix-orthogonal frequency-division multiplexing (CP-OFDM) that is deployed in
4G LTE systems. CP-OFDM is the baseline of the 5G waveform discussions since
the performance of a new waveform is usually compared with it. The chapter
examines the essential characteristics of the major waveform candidates along
with the related advantages and disadvantages. It summarizes and compares the
key features of different waveforms.
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We use state-of-the-art, three-dimensional non-local thermodynamic
equilibrium (non-LTE) radiative magnetohydrodynamic simulations of the quiet
solar atmosphere to carry out detailed tests of chromospheric magnetic field
diagnostics from free-free radiation at millimeter and submillimeter
wavelengths (mm/submm). The vertical component of the magnetic field was
deduced from the mm/submm brightness spectra and the degree of circular
polarization synthesized at millimeter frequencies. We used the frequency bands
observed by the Atacama Large Millimeter/Submillimeter Array (ALMA) as a
convenient reference. The magnetic field maps obtained describe the
longitudinal magnetic field at the effective formation heights of the relevant
wavelengths in the solar chromosphere. The comparison of the deduced and model
chromospheric magnetic fields at the spatial resolution of both the model and
current observations demonstrates a good correlation, but has a tendency to
underestimate the model field. The systematic discrepancy of about 10 percent
is probably due to averaging of the restored field over the heights
contributing to the radiation, weighted by the strength of the contribution. On
the whole, the method of probing the longitudinal component of the magnetic
field with free-free emission at mm/submm wavelengths is found to be applicable
to measurements of the weak quiet-Sun magnetic fields. However, successful
exploitation of this technique requires very accurate measurements of the
polarization properties (primary beam and receiver polarization response) of
the antennas, which will be the principal factor that determines the level to
which chromospheric magnetic fields can be measured. Consequently,
high-resolution and high-precision observations of circularly polarized
radiation at millimeter wavelengths can be a powerful tool for producing
chromospheric longitudinal magnetograms.
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Acquisition and tracking systems form an important component of free-space
optical communications due to directional nature of the optical signal.
Acquisition subsystems are needed in order to search and locate the receiver
terminal in an uncertainty/search region with very narrow laser beams. In this
paper, we have proposed and analyzed two adaptive search schemes for
acquisition systems that perform better---for the low probability of
detection---than the spiral scanning approach. The first of these schemes, the
adaptive spiral search, provides a better acquisition time performance by
dividing the search region into a number of smaller subregions, and
prioritizing search in regions of higher probability mass. The second
technique---the shotgun approach---searches the region in a random manner by
sampling the search region according to a Gaussian distribution. The adaptive
spiral scheme outperforms the shotgun approach in terms of acquisition time,
especially if the number of search subregions is large enough. However, a
higher pointing accuracy is required by the adaptive spiral search in order to
search the region precisely. On the other hand, the shotgun scanning approach
does not require such stringent pointing accuracy.
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In this paper, the modified entropic force law is studied by using a new kind
of generalized uncertainty principle which contains a minimal length, a minimal
momentum and a maximal momentum. Firstly, the quantum corrections to the
thermodynamics of a black hole is investigated. Then, according to Verlinde's
theory, the generalized uncertainty principle (GUP) corrected entropic force is
obtained. The result shows that the GUP corrected entropic force is related not
only to the properties of the black holes, but also to the Planck length and
the dimensionless constants $\alpha _{\rm{0}}$ and $\beta _{\rm{0}}$. Moreover,
based on the GUP corrected entropic force, we also derive the modified
Einstein's field equation (EFE) and the modified Friedmann equation.
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We propose a new type of superradiant laser based on a hot atomic beam
traversing an optical cavity. We show that the theoretical minimum linewidth
and maximum power are competitive with the best ultracoherent clock lasers.
Also, our system operates naturally in continuous wave mode, which has been
elusive for superradiant lasers so far. Unlike existing ultracoherent lasers,
our design is simple and rugged. This makes it a candidate for the first widely
accessible ultracoherent laser, as well as the first to realize sought-after
applications of ultracoherent lasers in challenging environments.
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In the past two-dimensional models of QFT have served as theoretical
laboratories for testing new concepts under mathematically controllable
condition. In more recent times low-dimensional models (e.g. chiral models,
factorizing models) often have been treated by special recipes in a way which
sometimes led to a loss of unity of QFT. In the present work I try to
counteract this apartheid tendency by reviewing past results within the setting
of the general principles of QFT. To this I add two new ideas: (1) a modular
interpretation of the chiral model Diff(S)-covariance with a close connection
to the recently formulated local covariance principle for QFT in curved
spacetime and (2) a derivation of the chiral model temperature duality from a
suitable operator formulation of the angular Wick rotation (in analogy to the
Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational
chiral theories. The SL(2,Z) modular Verlinde relation is a special case of
this thermal duality and (within the family of rational models) the matrix S
appearing in the thermal duality relation becomes identified with the
statistics character matrix S. The relevant angular Euclideanization'' is done
in the setting of the Tomita-Takesaki modular formalism of operator algebras.
I find it appropriate to dedicate this work to the memory of J. A. Swieca
with whom I shared the interest in two-dimensional models as a testing ground
for QFT for more than one decade.
This is a significantly extended version of an ``Encyclopedia of Mathematical
Physics'' contribution hep-th/0502125.
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This paper reports application of neuro- fuzzy inference system (NFIS) and
self organizing feature map neural networks (SOM) on detection of contact state
in a block system. In this manner, on a simple system, the evolution of contact
states, by parallelization of DDA, has been investigated. So, a comparison
between NFIS and SOM results has been presented. The results show applicability
of the proposed methods, by different accuracy, on detection of contact's
distribution.
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Planning under motion and observation uncertainties requires solution of a
stochastic control problem in the space of feedback policies. In this paper, we
reduce the general (n^2+n)-dimensional belief space planning problem to an
(n)-dimensional problem by obtaining a Linear Quadratic Gaussian (LQG) design
with the best nominal performance. Then, by taking the underlying trajectory of
the LQG controller as the decision variable, we pose a coupled design of
trajectory, estimator, and controller design through a Non-Linear Program (NLP)
that can be solved by a general NLP solver. We prove that under a first-order
approximation and a careful usage of the separation principle, our
approximations are valid. We give an analysis on the existing major belief
space planning methods and show that our algorithm has the lowest computational
burden. Finally, we extend our solution to contain general state and control
constraints. Our simulation results support our design.
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The thermal conductivity of Zn-doped YBCO crystals was studied at low
temperature (0.15 < T < 0.8 K) for different concentrations of Zn impurities. A
small amount of Zn induces a dramatic decrease in the non-linear component of
the low-temperature thermal conductivity. Moreover, the magnitude of the linear
component (obtained by extrapolating the data to T=0) is found to depend on Zn
concentration. After an initial decrease, this linear term, associated with the
electronic contribution to the conductivity, increases with increasing Zn
dopage. Such an increase is consistent with the introduction of low-energy
excitations by Zn impurities as expected for a $d_{x^2-y^2}$ superconducting
state in contrast to an anisotropic s-wave gap. The results are compared to
quantitative predictions of available theoretical models.
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In this paper we describe our search for galaxy protocluster candidates at
$4.5< z < 10$ and explore the environmental and physical properties of their
member galaxies identified through JWST wide-field surveys within the CEERS,
JADES, and PEARLS NEP-TDF fields. Combining with HST data, we identify 2948
robust $z>4.5$ candidates within an area of 185.4 arcmin$^2$. We determine
nearest neighbour statistics and galaxy environments. We find that high-$z$
galaxies in overdense environments exhibit higher star formation activity
compared to those in underdense regions. Galaxies in dense environments have a
slightly increased SFR at a given mass compared with galaxies in the lower
density environments. At the high mass end we also find a gradual flattening of
the $M_{\star}$-SFR slope. We find that galaxies in high-density regions often
have redder UV slopes than those in low-density regions, suggesting more dust
extinction, weaker Lyman-alpha emission and / or a higher damped Lyman-alpha
absorption. We also find that the mass-size relation remains consistent and
statistically similar across all environments. Furthermore, we quantitatively
assess the probability of a galaxy belonging to a protocluster candidate. In
total, we identified 26 overdensities at $z=5-7$ and estimate their dark matter
halo masses. We find that all protocluster candidates could evolve into
clusters with $M_{\rm halo} > 10^{14}M_{\odot}$ at $z = 0$, thereby supporting
the theoretical and simulation predictions of cluster formation. Notably, this
marks an early search for protocluster candidates in JWST wide field based on
photometric data, providing valuable candidates to study cosmic structure
formation at the early stages.
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When developing a (web) interface for a deductive database, functionality
required by the client is provided by means of HTTP handlers that wrap the
logical data access predicates. These handlers are responsible for converting
between client and server data representations and typically include options
for paginating results. Designing the web accessible API is difficult because
it is hard to predict the exact requirements of clients. Pengines changes this
picture. The client provides a Prolog program that selects the required data by
accessing the logical API of the server. The pengine infrastructure provides
general mechanisms for converting Prolog data and handling Prolog
non-determinism. The Pengines library is small (2000 lines Prolog, 150 lines
JavaScript). It greatly simplifies defining an AJAX based client for a Prolog
program and provides non-deterministic RPC between Prolog processes as well as
interaction with Prolog engines similar to Paul Tarau's engines. Pengines are
available as a standard package for SWI-Prolog 7.
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We provide conditions for stable equilibrium in Cournot duopoly models with
tax evasion and time delay. We prove that our conditions actually imply
asymptotically stable equilibrium and delay independence. Conditions include
the same marginal cost and equal probability for evading taxes. We give
examples of cost and inverse demand functions satisfying the proposed
conditions. Some economic interpretations of our results are also included.
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This paper proposes a dynamic primal-dual type algorithm to solve the optimal
scheduling problem in wireless networks subject to uncertain parameters, which
are generated by stochastic network processes such as random packet arrivals,
channel fading, and node mobilities. The algorithm is a generalization of the
well-known max-weight scheduling algorithm proposed by Tassiulas et al., where
only queue length information is used for computing the schedules when the
arrival rates are uncertain. Using the technique of fluid limits, sample path
convergence of the algorithm to an arbitrarily close to optimal solution is
proved, under the assumption that the Strong Law of Large Numbers (SLLN)
applies to the random processes which generate the uncertain parameters. The
performance of the algorithm is further verified by simulation results. The
method may potentially be applied to other applications where dynamic
algorithms for convex problems with uncertain parameters are needed.
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With the development of human space exploration, the space environment is
gradually filled with abandoned satellite debris and unknown micrometeorites,
which will seriously affect capture motion of space robot. Hence, a novel fast
collision-avoidance trajectory planning strategy for a dual-arm free-floating
space robot (FFSR) with predefined-time pose feedback will be mainly studied to
achieve micron-level tracking accuracy of end-effector in this paper. However,
similar to control, the exponential feedback results in larger initial joint
angular velocity relative to proportional feedback. Firstly, a pose-error-based
kinematic model of the FFSR will be derived from a control perspective. Then, a
cumulative dangerous field (CDF) collision-avoidance algorithm is applied in
predefined-time trajectory planning to achieve micron-level collision-avoidance
trajectory tracking precision. In the end, a GA-based optimization algorithm is
used to optimize the predefined-time parameter to obtain a motion trajectory of
low joint angular velocity of robotic arms. The simulation results verify our
conjecture and conclusion.
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In this paper, we develop a new scaling method to study spectral and Bergman
kernels for the k-th tensor power of a line bundle over a complex manifold
under local spectral gap condition. In particular, we establish a simple proof
of the pointwise asymptotics of spectral and Bergman kernels. As a new result,
in the function case, we obtain the leading term of Bergman kernel under
spectral gap with exponential decay. Moreover, in the general cases of
(0,q)-forms, the asymptotics remain valid while the curvature of the line
bundle is degenerate.
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In this article we give a simple, almost uniform proof that the lattice of
noncrossing partitions associated with a well-generated complex reflection
group is lexicographically shellable. So far a uniform proof is available only
for Coxeter groups. In particular we show that, for any complex reflection
group $W$ and any element $x\in W$, every $x$-compatible reflection order is a
recursive atom order of the corresponding interval in absolute order. Since any
Coxeter element $\gamma$ in any well-generated complex reflection group admits
a $\gamma$-compatible reflection order, the lexicographic shellability follows
from a well-known result due to Bj\"orner and Wachs.
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We describe an efficient quantum algorithm for the quantum Schur transform.
The Schur transform is an operation on a quantum computer that maps the
standard computational basis to a basis composed of irreducible representations
of the unitary and symmetric groups. We simplify and extend the algorithm of
Bacon, Chuang, and Harrow, and provide a new practical construction as well as
sharp theoretical and practical analyses. Our algorithm decomposes the Schur
transform on $n$ qubits into
$O\left(n^4\log\left(\frac{n}{\epsilon}\right)\right)$ operators in the
Clifford+T fault-tolerant gate set and uses exactly
$2\lfloor\log_2(n)\rfloor-1$ ancillary qubits. We extend our qubit algorithm to
decompose the Schur transform on $n$ qudits of dimension $d$ into
$O\left(d^{1+p}n^{3d}\log^p\left(\frac{d n}{\epsilon}\right)\right)$ primitive
operators from any universal gate set, for $p\approx3.97$.
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In this work, we describe, analyze, and implement a pseudospectral quadrature
method for a global computer modeling of the incompressible surface
Navier-Stokes equations on the rotating unit sphere. Our spectrally accurate
numerical error analysis is based on the Gevrey regularity of the solutions of
the Navier-Stokes equations on the sphere. The scheme is designed for
convenient application of fast evaluation techniques such as the fast Fourier
transform (FFT), and the implementation is based on a stable adaptive time
discretization.
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1T-TaS$_2$ is a charge-density-wave (CDW) compound with a Mott-insulating
ground state. The metallic state obtained by doping, substitution or pulsed
charge injection is characterized by an emergent CDW domain wall network, while
single domain walls can be found in the pristine Mott state. Here we study
whether and how the single walls become metallic. Tunneling spectroscopy
reveals partial suppression of the Mott gap and the presence of in-gap states
strongly localized at the domain-wall sites. Using the real-space dynamical
mean field theory description of the strongly correlated quantum-paramagnet
ground state we show that the local gap suppression follows from the increased
hopping along the connected zig-zag chain of lattice sites forming the domain
wall, and that full metallisation is preempted by the splitting of the
quasiparticle band into bonding and antibonding sub-bands due to the structural
dimerization of the wall, explaining the presence of the in-gap states and the
low density of states at the Fermi level.
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Neural networks are known to be vulnerable to adversarial examples. In this
note, we evaluate the two white-box defenses that appeared at CVPR 2018 and
find they are ineffective: when applying existing techniques, we can reduce the
accuracy of the defended models to 0%.
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We develop a new technique to construct mutually unbiased tripartite
absolutely maximally entangled bases. We first explore the tripartite
absolutely maximally entangled bases and mutually unbiased bases in
$\mathbb{C}^{d} \otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ based on
mutually orthogonal Latin squares. Then we generalize the approach to the case
of $\mathbb{C}^{d_{1}} \otimes \mathbb{C}^{d_{2}} \otimes
\mathbb{C}^{d_{1}d_{2}}$ by mutually weak orthogonal Latin squares. The concise
direct constructions of mutually unbiased tripartite absolutely maximally
entangled bases are remarkably presented with generality. Detailed examples in
$\mathbb{C}^{3} \otimes \mathbb{C}^{3} \otimes \mathbb{C}^{3},$ $\mathbb{C}^{2}
\otimes \mathbb{C}^{2} \otimes \mathbb{C}^{4}$ and $\mathbb{C}^{2} \otimes
\mathbb{C}^{5} \otimes \mathbb{C}^{10}$ are provided to illustrate the
advantages of our approach.
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A combination of synchrotron X-ray, neutron powder diffraction,
magnetization, heat capacity and electrical resistivity measurements reveals
that NdMnAsO is an antiferromagnetic semiconductor with large Neel temperature
(TN = 359(2) K). At room temperature the magnetic propagation vector k = 0 and
the Mn moments are directed along the crystallographic c-axis (mMn = 2.41(6)
BM). Upon cooling a spin reorientation (SR) transition of the Mn moments into
the ab-plane occurs (TSR = 23 K). This coincides with the long range ordering
of the Nd moments, which are restricted to the basal plane. The magnetic
propagation vector remains k = 0. At base temperature (1.6 K) the fitted
moments are mab,Mn = 3.72(1) BM and mab,Nd = 1.94(1) BM. The electrical
resistivity is characterized by a broad maximum at 250 K, below which it has a
metallic temperature dependence but semiconducting magnitude (rho250K = 50 Ohm
cm, residual resistivity ratio = 2), and a slight upturn at the SR transition.
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We present the two-loop corrected operator matrix elements contributing to
the scale evolution of the longitudinal spin structure function $g_1(x,Q^2)$
calculated up to finite terms which survive in the limit $\epsilon = N - 4 \to
0$. These terms are needed to renormalize the local operators up to third order
in the strong coupling constant $\alpha_s$. Further the expressions for the
two-loop corrected operator matrix elements can be inserted into one loop
graphs to obtain a part of the third order contributions to these matrix
elements. This work is a first step in obtaining the third order anomalous
dimensions so that a complete next-to-next-to-leading order (NNLO) analysis of
the above mentioned structure function can be carried out. In our calculation
particular attention is paid to the renormalization constant which is needed to
restore the Ward-identities violated by the HVBM prescription for the
$\gamma_5$-matrix in $N$-dimensional regularization.
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Using Lorentz covariant spinor helicity formalism we reorganize the unitary
scalar superfield light-cone path integral for the N=4 supersymmetric
Yang-Mills theory. In new variables in the chiral Fourier superspace the
quadratic and cubic parts of the classical action have manifest Lorentz,
kinematical and dynamical supersymmetry, with the exception of terms which
contribute only to the contact terms in the supergraphs with propagators
shrinking to a point. These terms have the same structure as supergraphs with
quartic light-cone vertices, which break dynamical supersymmetry. We present
evidence that all complicated terms breaking dynamical supersymmetry have to
cancel and therefore can be omitted. It is plausible that the new form of the
path integral leads to a set of relatively simple unitarity based rules with
manifest N=4 supersymmetry.
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Embedded planets are potentially the cause of substructures like gaps and
cavities observed in several protoplanetary disks. Thus, the substructures
observed in the continuum and in line emission encode information about the
presence of planets in the system and how they interact with the natal disk.
The pre-transitional disk around the star PDS 70 is the first case of two young
planets imaged within a dust depleted gap that was likely carved by themselves.
We aim to determine the spatial distribution of the gas and dust components in
the PDS 70 disk. The axisymmetric substructures observed in the resulting
profiles are interpreted in the context of planet-disk interactions. We develop
a thermo-chemical forward model for an axisymmetric disk to explain a subset of
the Atacama Large Millimeter/Submillimeter Array (ALMA) band 6 observations of
three CO isotopologues plus the continuum towards PDS 70. Combining the
inferred gas and dust distributions, the model results in a variable
gas-to-dust ratio profile throughout the disk that spans two orders of
magnitude within the first $130$ au and shows a step gradient towards the outer
disk, which is consistent with the presence of a pressure maxima driven by
planet-disk interactions. We find a gas density drop factor of ${\sim} 19$ at
the location of the planet PDS 70 c with respect to the peak gas density at
$75$ au. Combining this value with literature results on the hydrodynamics of
planet-disk interactions, we find this gas gap depth to be consistent with
independent planet mass estimates from infrared observations. Our findings
point towards gas stirring processes taking place in the common gap due to the
gravitational perturbation of both planets.
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Self-modifying code has many intriguing applications in a broad range of
fields including software security, artificial general intelligence, and
open-ended evolution. Having control over self-modifying code, however, is
still an open challenge since it is a balancing act between providing as much
freedom as possible so as not to limit possible solutions, while at the same
time imposing restriction to avoid security issues and invalid code or
solutions. In the present study, I provide a prototype implementation of how
one might curb self-modifying code by introducing control mechanisms for code
modifications within specific regions and for specific transitions between code
and data. I show that this is possible to achieve with the so-called allagmatic
method - a framework to formalise, model, implement, and interpret complex
systems inspired by Gilbert Simondon's philosophy of individuation and Alfred
North Whitehead's philosophy of organism. Thereby, the allagmatic method serves
as guidance for self-modification based on concepts defined in a metaphysical
framework. I conclude that the allagmatic method seems to be a suitable
framework for control mechanisms in self-modifying code and that there are
intriguing analogies between the presented control mechanisms and gene
regulation.
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We investigate a model of evolving random network, introduced by us
previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a
generalization of the Bak-Sneppen model of biological evolution, with the
modification that the underlying network can evolve by adding and removing
sites. The behavior and the averaged properties of the network depend on the
parameter $p$, the probability to establish link to the newly introduced site.
For $p=1$ the system is self-organized critical, with two distinct power-law
regimes with forward-avalanche exponents $\tau=1.98\pm 0.04$ and $\tau^\prime =
1.65\pm 0.05$. The average size of the network diverge as power-law when $p\to
1$. We study various geometrical properties of the network: probability
distribution of sizes and connectivities, size and number of disconnected
clusters and the dependence of mean distance between two sites on the cluster
size. The connection with models of growing networks with preferential
attachment is discussed.
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Hashing has been recognized as an efficient representation learning method to
effectively handle big data due to its low computational complexity and memory
cost. Most of the existing hashing methods focus on learning the
low-dimensional vectorized binary features based on the high-dimensional raw
vectorized features. However, studies on how to obtain preferable binary codes
from the original 2D image features for retrieval is very limited. This paper
proposes a bilinear supervised discrete hashing (BSDH) method based on 2D image
features which utilizes bilinear projections to binarize the image matrix
features such that the intrinsic characteristics in the 2D image space are
preserved in the learned binary codes. Meanwhile, the bilinear projection
approximation and vectorization binary codes regression are seamlessly
integrated together to formulate the final robust learning framework.
Furthermore, a discrete optimization strategy is developed to alternatively
update each variable for obtaining the high-quality binary codes. In addition,
two 2D image features, traditional SURF-based FVLAD feature and CNN-based
AlexConv5 feature are designed for further improving the performance of the
proposed BSDH method. Results of extensive experiments conducted on four
benchmark datasets show that the proposed BSDH method almost outperforms all
competing hashing methods with different input features by different evaluation
protocols.
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We report on observations of black hole Swift J1357.2-0933, a member of the
modest population of very faint X-ray transients. This source has previously
shown intense dips in the optical lightcurve, a phenomena that has been linked
to the existence of a "unique toroidal structure" in the inner region of the
disc, seen at a high inclination. Our observations, carried out by the Neil
Gehrels Swift and NuSTAR X-ray observatories, do not show the presence of
intense dips in the optical light curves. We find that the X-ray light curves
do not show any features that would straightforwardly support an edge-on
configuration or high inclination configuration of the orbit. This is similar
to what was seen in the X-ray observations of the source during its 2011
outburst. Moreover, the broadband spectra were well described with an absorbed
power-law model without any signatures of the cut-off at energies above 10 keV,
or any reflection from the disc or the putative torus. Thus, the X-ray data do
not support the unique obscuring torus scenario proposed for J1357. We also
performed a multi-wavelength study using the data of X-ray telescope and
Ultraviolet/Optical Telescope aboard Swift, taken during the 4.5 months
duration of the 2017 outburst. This is consistent with what was previously
inferred for this source. We found a correlation between the simultaneous X-ray
and ultraviolet/optical data and our study suggests that most of the
reprocessed flux must be coming out in the ultraviolet.
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We introduce the Red-Blue Separation problem on graphs, where we are given a
graph $G=(V,E)$ whose vertices are colored either red or blue, and we want to
select a (small) subset $S \subseteq V$, called red-blue separating set, such
that for every red-blue pair of vertices, there is a vertex $s \in S$ whose
closed neighborhood contains exactly one of the two vertices of the pair. We
study the computational complexity of Red-Blue Separation, in which one asks
whether a given red-blue colored graph has a red-blue separating set of size at
most a given integer. We prove that the problem is NP-complete even for
restricted graph classes. We also show that it is always approximable in
polynomial time within a factor of $2\ln n$, where $n$ is the input graph's
order. In contrast, for triangle-free graphs and for graphs of bounded maximum
degree, we show that Red-Blue Separation is solvable in polynomial time when
the size of the smaller color class is bounded by a constant. However, on
general graphs, we show that the problem is $W[2]$-hard even when parameterized
by the solution size plus the size of the smaller color class. We also consider
the problem Max Red-Blue Separation where the coloring is not part of the
input. Here, given an input graph $G$, we want to determine the smallest
integer $k$ such that, for every possible red-blue coloring of $G$, there is a
red-blue separating set of size at most $k$. We derive tight bounds on the
cardinality of an optimal solution of Max Red-Blue Separation, showing that it
can range from logarithmic in the graph order, up to the order minus one. We
also give bounds with respect to related parameters. For trees however we prove
an upper bound of two-thirds the order. We then show that Max Red-Blue
Separation is NP-hard, even for graphs of bounded maximum degree, but can be
approximated in polynomial time within a factor of $O(\ln^2 n)$.
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These are the notes for the lecture given by the author at the "Current
Events" Special Session of the AMS meeting in Baltimore on January 17, 2003.
Topics reviewed include the Langlands correspondence for GL(n) in the function
field case and its proof by V.Drinfeld and L.Lafforgue, the geometric Langlands
correspondence for GL(n) and its proof by D.Gaitsgory, K.Vilonen and the
author, and the work of A.Beilinson and V.Drinfled on the quantization of the
Hitchin system and the Langlands correspondence for an arbitrary semisimple
algebraic group.
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We present an $O(n^{1.5})$-space distance oracle for directed planar graphs
that answers distance queries in $O(\log n)$ time. Our oracle both
significantly simplifies and significantly improves the recent oracle of
Cohen-Addad, Dahlgaard and Wulff-Nilsen [FOCS 2017], which uses
$O(n^{5/3})$-space and answers queries in $O(\log n)$ time. We achieve this by
designing an elegant and efficient point location data structure for Voronoi
diagrams on planar graphs.
We further show a smooth tradeoff between space and query-time. For any $S\in
[n,n^2]$, we show an oracle of size $S$ that answers queries in $\tilde
O(\max\{1,n^{1.5}/S\})$ time. This new tradeoff is currently the best (up to
polylogarithmic factors) for the entire range of $S$ and improves by polynomial
factors over all the previously known tradeoffs for the range $S \in
[n,n^{5/3}]$.
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Asymptotic behavior of the three-dimensional stochastic Navier-Stokes
equations with Markov switching in additive noises is studied for
incompressible fluid flow in a bounded domain in the three-dimensional space.
To study such a system, we introduce a family of regularized equations and
investigate the asymptotic behavior of the regularized equations first. The
existence an ergodic measure for the regularized system is established via the
Krylov-Bogolyubov method. Then the existence of an stationary measure to the
original system is obtained by extracting a limit from the ergodic measures of
the family of the regularized system.
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Because cosmic rays are charged particles scrambled by magnetic fields,
combining direct measurements with other observations is crucial to
understanding their origin and propagation. As energetic particles traverse
matter and electromagnetic fields, they leave marks in the form of neutral
interaction products. Among those, gamma rays trace interactions of nuclei that
inelastically collide with interstellar gas, as well as of leptons that undergo
Bremsstrahlung and inverse-Compton scattering. Data collected by the Fermi
Large Area Telescope (LAT) are therefore telling us the story of cosmic rays
along their journey from sources through their home galaxies. Supernova
remnants emerge as a notable gamma-ray source population, and older remnants
interacting with interstellar matter finally show strong evidence of the
presence of accelerated nuclei. Yet the maximum energy attained by shock
accelerators is poorly constrained. Cygnus X, a massive star-forming region
established by the LAT as housing cosmic-ray sources, provides a test case to
study the impact of wind-driven turbulence on the early propagation.
Interstellar emission resulting from the large-scale propagation of cosmic rays
in the Milky Way is revealed in unprecedented detail that challenges some of
the simple assumptions used for the modeling. Moreover, the cosmic-ray induced
gamma-ray luminosities of galaxies scale quasi-linearly with their massive-
star formation rates, and suggests that for most systems a substantial fraction
of energy in cosmic rays escapes into the intergalactic medium. The nuclear
production models and the distribution of target gas and radiation fields, not
determined precisely enough yet, are key to exploiting the full potential of
gamma-ray data. Nevertheless, data being collected by Fermi and complementary
observations are bringing us ever closer to solving the cosmic-ray mystery.
(abridged)
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Named-entity recognition (NER) aims at identifying entities of interest in a
text. Artificial neural networks (ANNs) have recently been shown to outperform
existing NER systems. However, ANNs remain challenging to use for non-expert
users. In this paper, we present NeuroNER, an easy-to-use named-entity
recognition tool based on ANNs. Users can annotate entities using a graphical
web-based user interface (BRAT): the annotations are then used to train an ANN,
which in turn predict entities' locations and categories in new texts. NeuroNER
makes this annotation-training-prediction flow smooth and accessible to anyone.
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The presence of a surface at the inner boundary, such as in a neutron star or
a white dwarf, allows the existence of a standing shock in steady spherical
accretion.The standing shock can become unstable in 2D or 3D; this is called
the {\em standing accretion shock instability} (SASI).Two mechanisms --
advective-acoustic and purely acoustic -- have been proposed to explain SASI.
Using axisymmetric hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations,
we find that the advective-acoustic mechanism better matches the observed
oscillation timescales in our simulations. The global shock oscillations
present in the accretion flow can explain many observed high frequency
($\gtrsim 100$ Hz) quasi-periodic oscillations (QPOs) in X-ray binaries (XRBs).
The presence of a moderately strong magnetic field adds more features to the
shock oscillation pattern, giving rise to low frequency modulation in the
computed light curve. This low frequency modulation can be responsible for
$\sim 100$ Hz QPOs (known as hHz QPOs). We propose that the appearance of hHz
QPO determines the separation of twin peak QPOs of higher frequencies.
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Hirschfeld classified split del Pezzo surfaces of degree at least three whose
points are all contained on the lines in the surface. We continue his work and
begin the classification of split degree two del Pezzo surfaces over finite
fields whose points are all on the fifty-six exceptional curves of the
surfaces.
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We present a first-principle study of geometrical and electronic structure of
hexagonal single-walled silicon nanotubes with a monovacancy or a
substitutional defect. The C, Al or P atoms are chosen as substitutional
impurities. It is found that the defect such as a monovacancy or a
substitutional impurity results in deformation of the hexagonal single-walled
silicon nanotube. In both cases, a relatively localized unoccupied state near
the Fermi level occurs due to this local deformation. The difference in
geometrical and electronic properties of different substitutional impurities is
discussed.
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Whereas the total energy in zero-point fluctuations of the particle physics
vacuum gives rise to the cosmological constant problem, differences in the
vacuum give rise to real physical phenomena, such as the Casimir effect. Hence
we consider the zero-point energy bound between two parallel conducting plates
-- proxy for a solid slice of cosmological constant -- as a convenient
laboratory in which to investigate the gravitation and inertia of vacuum
energy. We calculate the Casimir effect in a weak gravitational field,
obtaining corrections to the vacuum stress-energy and attractive force on the
plates due to the curvature of spacetime. These results suggest that if the
cosmological constant is due to zero-point energy then it is susceptible to
fluctuations induced by gravitational sources.
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This paper is a short introduction to orthogonal polynomials, both the
general theory and some special classes. It ends with some remarks about the
usage of computer algebra for this theory.
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Micropillar compression experiments probing size effects in confined
plasticity of metal thin films, including the indirect imposition of
'canonical' simple shearing boundary conditions, show dramatically different
responses in compression and shear of the film. The Mesoscale Field Dislocation
Mechanics (MFDM) model is confronted with this set of experimental observations
and shown to be capable of modeling such behavior, without any ad-hoc
modification to the basic structure of the theory (including boundary
conditions), or the use of extra fitting parameters. This is a required
theoretical advance in the current state-of-the art of strain gradient
plasticity models. It is also shown that significantly different inhomogeneous
fields can display qualitatively similar size effect trends in overall
agreement with the experimental results. The (plastic) Swift and (elastic)
Poynting finite deformation effects are also demonstrated.
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Pedestrian trajectory prediction is an important technique of autonomous
driving, which has become a research hot-spot in recent years. Previous methods
mainly rely on the position relationship of pedestrians to model social
interaction, which is obviously not enough to represent the complex cases in
real situations. In addition, most of existing work usually introduce the scene
interaction module as an independent branch and embed the social interaction
features in the process of trajectory generation, rather than simultaneously
carrying out the social interaction and scene interaction, which may undermine
the rationality of trajectory prediction. In this paper, we propose one new
prediction model named Social Soft Attention Graph Convolution Network (SSAGCN)
which aims to simultaneously handle social interactions among pedestrians and
scene interactions between pedestrians and environments. In detail, when
modeling social interaction, we propose a new \emph{social soft attention
function}, which fully considers various interaction factors among pedestrians.
And it can distinguish the influence of pedestrians around the agent based on
different factors under various situations. For the physical interaction, we
propose one new \emph{sequential scene sharing mechanism}. The influence of the
scene on one agent at each moment can be shared with other neighbors through
social soft attention, therefore the influence of the scene is expanded both in
spatial and temporal dimension. With the help of these improvements, we
successfully obtain socially and physically acceptable predicted trajectories.
The experiments on public available datasets prove the effectiveness of SSAGCN
and have achieved state-of-the-art results.
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Tool flank wear monitoring can minimize machining downtime costs while
increasing productivity and product quality. In some industrial applications,
only a limited level of tool wear is allowed to attain necessary tolerances. It
may become challenging to monitor a limited level of tool wear in the data
collected from the machine due to the other components, such as the flexible
vibrations of the machine, dominating the measurement signals. In this study, a
tool wear monitoring technique to predict limited levels of tool wear from the
spindle motor current and dynamometer measurements is presented. High-frequency
spindle motor current data is collected with an industrial edge device while
the cutting forces and torque are measured with a rotary dynamometer in
drilling tests for a selected number of holes. Feature engineering is conducted
to identify the statistical features of the measurement signals that are most
sensitive to small changes in tool wear. A neural network based on the long
short-term memory (LSTM) architecture is developed to predict tool flank wear
from the measured spindle motor current and dynamometer signals. It is
demonstrated that the proposed technique predicts tool flank wear with good
accuracy and high computational efficiency. The proposed technique can easily
be implemented in an industrial edge device as a real-time predictive
maintenance application to minimize the costs due to manufacturing downtime and
tool underuse or overuse.
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In recent years, Multi-Agent Reinforcement Learning (MARL) has found
application in numerous areas of science and industry, such as autonomous
driving, telecommunications, and global health. Nevertheless, MARL suffers
from, for instance, an exponential growth of dimensions. Inherent properties of
quantum mechanics help to overcome these limitations, e.g., by significantly
reducing the number of trainable parameters. Previous studies have developed an
approach that uses gradient-free quantum Reinforcement Learning and
evolutionary optimization for variational quantum circuits (VQCs) to reduce the
trainable parameters and avoid barren plateaus as well as vanishing gradients.
This leads to a significantly better performance of VQCs compared to classical
neural networks with a similar number of trainable parameters and a reduction
in the number of parameters by more than 97 \% compared to similarly good
neural networks. We extend an approach of K\"olle et al. by proposing a
Gate-Based, a Layer-Based, and a Prototype-Based concept to mutate and
recombine VQCs. Our results show the best performance for mutation-only
strategies and the Gate-Based approach. In particular, we observe a
significantly better score, higher total and own collected coins, as well as a
superior own coin rate for the best agent when evaluated in the Coin Game
environment.
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For a knot diagram we introduce an operation which does not increase the
genus of the diagram and does not change its representing knot type. We also
describe a condition for this operation to certainly decrease the genus. The
proof involves the study of a relation between the genus of a virtual knot
diagram and the genus of a knotoid diagram, the former of which has been
introduced by Stoimenow, Tchernov and Vdovina, and the latter by Turaev
recently. Our operation has a simple interpretation in terms of Gauss codes and
hence can easily be computer-implemented.
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Using Wilson renormalization group, we show that if no integrated vector
operator of scaling dimension $-1$ exists, then scale invariance implies
conformal invariance. By using the Lebowitz inequalities, we prove that this
necessary condition is fulfilled in all dimensions for the Ising universality
class. This shows, in particular, that scale invariance implies conformal
invariance for the three-dimensional Ising model.
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This paper describes a prototype system that integrates social media analysis
into the European Flood Awareness System (EFAS). This integration allows the
collection of social media data to be automatically triggered by flood risk
warnings determined by a hydro-meteorological model. Then, we adopt a
multi-lingual approach to find flood-related messages by employing two
state-of-the-art methodologies: language-agnostic word embeddings and
language-aligned word embeddings. Both approaches can be used to bootstrap a
classifier of social media messages for a new language with little or no
labeled data. Finally, we describe a method for selecting relevant and
representative messages and displaying them back in the interface of EFAS.
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We consider multi-path routing of entanglement in quantum networks, where a
pre-prepared multipartite entangled 2D cluster state serves as a resource to
perform different tasks on demand. We show how to achieve parallel connections
between multiple, freely chosen groups of parties by performing appropriate
local measurements among diagonal paths, which preserves the entanglement
structure of the remaining state. We demonstrate how to route multiple
Bell-states along parallel lines via crossings, turns and fade-in/-outs,
analogously to a data bus. The results apply to networks at any scale.
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The gossip problem (telephone problem) is an information dissemination
problem in which each of $n$ nodes of a communication network has a unique
piece of information that must be transmitted to all the other nodes using
two-way communications (telephone calls) between the pairs of nodes. During a
call between the given two nodes, they exchange the whole information known to
them at that moment. In this paper we investigate the $k$-fault-tolerant gossip
problem, which is a generalization of the gossip problem, where at most $k$
arbitrary faults of calls are allowed. The problem is to find the minimal
number of calls $\tau(n,k)$ needed to guarantee the $k$-fault-tolerance. We
construct two classes of $k$-fault-tolerant gossip schemes (sequences of calls)
and found two upper bounds of $\tau(n,k)$, which improve the previously known
results. The first upper bound for general even $n$ is $\tau(n,k) \leq 1/2 n
\lceil\log_2 n\rceil + 1/2 n k$. This result is used to obtain the upper bound
for general odd $n$. From the expressions for the second upper bound it follows
that $\tau(n,k) \leq 2/3 n k + O(n)$ for large $n$. Assuming that the calls can
take place simultaneously, it is also of interest to find $k$-fault-tolerant
gossip schemes, which can spread the full information in minimal time. For even
$n$ we showed that the minimal time is $T(n,k)=\lceil\log_2 n\rceil + k$.
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In this paper we discuss decays of the Higgs boson to quarkonia in
association with a photon. We identify a new mechanism for producing such final
states in Higgs decays that leads to predictions for the decay rates that
differ by an order of magnitude from previous estimates. Although the branching
ratios for these processes are still small, the processes are experimentally
clean, and the H \to J/\psi+gamma decay should be observable at a 14 TeV LHC.
We point out that quantum interference between two different production
mechanisms makes the decay rates sensitive to the HQQbar couplings.
Consequently, measurements of the H \to J/\psi+gamma decay rate would allow one
to probe the Higgs-charm coupling directly at the LHC. We discuss the
experimental prospects for the observation of these decays and for the direct
measurement of the Hccbar coupling.
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We show that chemical modification of the trans-polyacetylene structure that
involves substitution of the backbone hydrogen atoms with conjugated side
groups, leads to reduction of the backbone bond alternation as well as
screening of the effective Coulomb interaction. Consequently the optical gap of
the substituted material is smaller than the parent polyene with the same
backbone length, and the excited state ordering is conducive to efficient
photoluminescence. The design of organic polymeric infrared lasers, in the
ideal long chain limit, thereby becomes possible.
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Galaxy-scale outflows, which are thought to provide the link connecting the
central black hole to its host galaxy, are now starting to be observed.
However, the physical origin of the mechanism driving the observed outflows,
whether due to energy-driving or radiation-driving, is still debated; and in
some cases, it is not clear whether the central source is an active galactic
nucleus (AGN) or a nuclear starburst. Here we study the role of radiation
pressure on dust in driving galactic-scale AGN outflows, and analyse the
dynamics of the outflowing shell as a function of the underlying physical
parameters. We show that high-velocity outflows ($\gtrsim$1000 km/s) with large
momentum flux ($\gtrsim 10 L/c$) can be obtained, by taking into account the
effects of radiation trapping. In particular, the high observed values of the
momentum boosts can be reproduced, provided that the shell is initially
optically thick to the reprocessed infrared radiation. Alternatively, the
inferred measurements of the momentum flux may be significantly biased by AGN
variability. In this context, the observations of powerful outflows on
kiloparsec scales, with no or weak signs of ongoing nuclear activity at the
present time, could be re-interpreted as relics of past AGN episodes.
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We study transmission power budget minimization of battery-powered nodes in a
remote state estimation problem over multi-hop wireless networks. Communication
links between nodes are subject to fading, thereby generating random dropouts.
Relay nodes help to transmit measurements from distributed sensors to an
estimator node. Hopping through each relay node introduces a unit delay.
Motivated by the need for estimators with low computational and implementation
cost, we propose a jump estimator whose modes depend on a Markovian parameter
that describes measurement transmission outcomes over a finite interval. It is
well known that transmission power helps to increase the reliability of
measurement transmissions, at the expense of reducing the life-time of the
nodes' battery. Motivated by this, we derive a tractable iterative procedure,
based on semi-definite programming, to design a finite set of filter gains, and
associated power control laws to minimize the energy budget while guaranteeing
an estimation performance level. This procedure allows us to tradeoff the
complexity of the filter implementation with performance and energy use.
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Syndromic surveillance systems continuously monitor multiple pre-diagnostic
daily streams of indicators from different regions with the aim of early
detection of disease outbreaks. The main objective of these systems is to
detect outbreaks hours or days before the clinical and laboratory confirmation.
The type of data that is being generated via these systems is usually
multivariate and seasonal with spatial and temporal dimensions. The algorithm
What's Strange About Recent Events (WSARE) is the state-of-the-art method for
such problems. It exhaustively searches for contrast sets in the multivariate
data and signals an alarm when find statistically significant rules. This
bottom-up approach presents a much lower detection delay comparing the existing
top-down approaches. However, WSARE is very sensitive to the small-scale
changes and subsequently comes with a relatively high rate of false alarms. We
propose a new approach called EigenEvent that is neither fully top-down nor
bottom-up. In this method, we instead of top-down or bottom-up search, track
changes in data correlation structure via eigenspace techniques. This new
methodology enables us to detect both overall changes (via eigenvalue) and
dimension-level changes (via eigenvectors). Experimental results on hundred
sets of benchmark data reveals that EigenEvent presents a better overall
performance comparing state-of-the-art, in particular in terms of the false
alarm rate.
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Phase noise (PN) is a major disturbance in MIMO systems, where the
contribution of different oscillators at the transmitter and the receiver side
may degrade the overall performance and offset the gains offered by MIMO
techniques. This is even more crucial in the case of massive MIMO, since the
number of PN sources may increase considerably. In this work, we propose an
iterative receiver based on the application of the expectation-maximization
algorithm. We consider a massive MIMO framework with a general association of
oscillators to antennas, and include other channel disturbances like imperfect
channel state information and Rician block fading. At each receiver iteration,
given the information on the transmitted symbols, steepest descent is used to
estimate the PN samples, with an optimized adaptive step size and a
threshold-based stopping rule. The results obtained for several test cases show
how the bit error rate and mean square error can benefit from the proposed
phase-detection algorithm, even to the point of reaching the same performance
as in the case where no PN is present, offering better results than a
state-of-the-art alternative. Further analysis of the results allow to draw
some useful trade-offs respecting final performance and consumption of
resources.
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Goldstone Apple Valley Radio Telescope (GAVRT) is a science education
partnership among NASA, the Jet Propulsion Laboratory (JPL), and the Lewis
Center for Educational Research (LCER), offering unique opportunities for K -12
students and their teachers. As part of a long-term Jupiter synchrotron
radiation (JSR) flux density monitoring program, LCER has been carrying out
Jupiter observations with some student participation. In this paper we present
the results of processed data sets observed between March 6, 2015 and April 6
2018. The data are divided into 5 epochs, grouped by time. We derive JSR
beaming curves at different epochs and Earth declinations. We present a
comparison of the observed beaming curves with those derived from most recent
models for the radiation belts. Our results show an increasing trend of the JSR
flux density which seem consistent with the models for the magnetospheric solar
wind interactions.
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Magnetic platelets with a vortex configuration are attracting considerable
attention. The discovery that excitation with small in-plane magnetic fields or
spin polarised currents can switch the polarisation of the vortex core did not
only open the possibility of using such systems in magnetic memories, but also
initiated the fundamental investigation of the core switching mechanism itself.
Micromagnetic models predict that the switching is mediated by a
vortex-antivortex pair, nucleated in a dynamically induced vortex core
deformation. In the same theoretical framework, a critical core velocity is
predicted, above which switching occurs. Although these models are extensively
studied and generally accepted, experimental support has been lacking until
now. In this work, we have used high-resolution time-resolved X-ray microscopy
to study the detailed dynamics in vortex structures. We could reveal the
dynamic vortex core deformation preceding the core switching. Also, the
threshold velocity could be measured, giving quantitative comparison with
micromagnetic models.
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Deepfakes have raised significant concerns due to their potential to spread
false information and compromise digital media integrity. In this work, we
propose a Generative Convolutional Vision Transformer (GenConViT) for deepfake
video detection. Our model combines ConvNeXt and Swin Transformer models for
feature extraction, and it utilizes Autoencoder and Variational Autoencoder to
learn from the latent data distribution. By learning from the visual artifacts
and latent data distribution, GenConViT achieves improved performance in
detecting a wide range of deepfake videos. The model is trained and evaluated
on DFDC, FF++, DeepfakeTIMIT, and Celeb-DF v2 datasets, achieving high
classification accuracy, F1 scores, and AUC values. The proposed GenConViT
model demonstrates robust performance in deepfake video detection, with an
average accuracy of 95.8% and an AUC value of 99.3% across the tested datasets.
Our proposed model addresses the challenge of generalizability in deepfake
detection by leveraging visual and latent features and providing an effective
solution for identifying a wide range of fake videos while preserving media
integrity. The code for GenConViT is available at
https://github.com/erprogs/GenConViT.
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(Sub) mm VLBI observations are strongly hindered by limited sensitivity, with
the fast tropospheric fluctuations being the dominant culprit. We predict great
benefits from applying next-generation frequency phase transfer calibration
techniques for the next generation Event Horizon Telescope, using simultaneous
multi-frequency observations. We present comparative simulation studies to
characterise its performance, the optimum configurations, and highlight the
benefits of including observations at 85\,GHz along with the 230 and 340\,GHz
bands. The results show a transformational impact on the ngEHT array
capabilities, with orders of magnitude improved sensitivity, observations
routinely possible over the whole year, and ability to carry out
micro-arcsecond astrometry measurements at the highest frequencies, amongst
others. This will enable the addressing of a host of innovative open scientific
questions in astrophysics. We present a solution for highly scatter-broadened
sources such as SgrA*, a prime ngEHT target. We conclude that adding the
85\,GHz band provides a pathway to an optimum and robust performance for ngEHT
in sub-millimeter VLBI, and strongly recommmend its inclusion in the
simultaneous multi-frequency receiver design.
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We present cavity QED experiments with an Er:YSO crystal magnetically coupled
to a 3D cylindrical sapphire loaded copper resonator. Such waveguide cavities
are promising for the realization of a superconducting quantum processor. Here,
we demonstrate the coherent integration of a rare-earth spin ensemble with the
3D architecture. The collective coupling strength of the Er$^{3+}$ spins to the
3D cavity is 21 MHz. The cylindrical sapphire loaded resonator allowed us to
explore the anisotropic collective coupling between the rare-earth doped
crystal and the cavity. This work shows the potential of spin doped solids in
3D quantum circuits for application as microwave quantum memories as well as
for prospective microwave to optical interfaces.
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For all $n > k \ge 1$, we give formulas for the nullity $N(n,k)$ of the $n
\times n$ skew-symmetric Toeplitz band matrix whose first $k$ superdiagonals
have all entries $1$ and whose remaining superdiagonals have all entries $0$.
This is accomplished by counting the number of cycles in certain directed
graphs. As an application, for each fixed integer $z\ge 0$ and large fixed $k$,
we give an asymptotic formula for the percentage of $n > k$ satisfying
$N(n,k)=z$. For the purpose of rapid computation, an algorithm is devised that
quickly computes $N(n,k)$ even for extremely large values of $n$ and $k$.
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Single-image deraining is rather challenging due to the unknown rain model.
Existing methods often make specific assumptions of the rain model, which can
hardly cover many diverse circumstances in the real world, making them have to
employ complex optimization or progressive refinement. This, however,
significantly affects these methods' efficiency and effectiveness for many
efficiency-critical applications. To fill this gap, in this paper, we regard
the single-image deraining as a general image-enhancing problem and originally
propose a model-free deraining method, i.e., EfficientDeRain, which is able to
process a rainy image within 10~ms (i.e., around 6~ms on average), over 80
times faster than the state-of-the-art method (i.e., RCDNet), while achieving
similar de-rain effects. We first propose the novel pixel-wise dilation
filtering. In particular, a rainy image is filtered with the pixel-wise kernels
estimated from a kernel prediction network, by which suitable multi-scale
kernels for each pixel can be efficiently predicted. Then, to eliminate the gap
between synthetic and real data, we further propose an effective data
augmentation method (i.e., RainMix) that helps to train network for real rainy
image handling.We perform comprehensive evaluation on both synthetic and
real-world rainy datasets to demonstrate the effectiveness and efficiency of
our method. We release the model and code in
https://github.com/tsingqguo/efficientderain.git.
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In this talk we review our theoretical understanding of spin glasses paying a
particular attention to the basic physical ideas. We introduce the replica
method and we describe its probabilistic consequences (we stress the recently
discovered importance of stochastic stability). We show that the replica method
is not restricted to systems with quenched disorder. We present the
consequences on the dynamics of the system when it slows approaches equilibrium
are presented: they are confirmed by large scale simulations, while we are
still awaiting for a direct experimental verification.
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Closed orbit feedback (COFB) systems used for the global orbit correction
rely on the pseudo-inversion of the orbit response matrix (ORM). A mismatch
between the model ORM used in the controller and the actual machine ORM can
affect the performance of the feedback system. In this paper, the typical
sources of such model mismatch such as acceleration ramp ORM variation,
intensity-dependent tune shift and beta beating are considered in simulation
studies. Their effect on the performance and the stability margins are
investigated for both the slow and fast regimes of a COFB system operation. The
spectral radius stability condition is utilized instead of the small gain
theorem to arrive at the theoretical limits of COFB stability and comparisons
with simulations for SIS18 of GSI and experiments at the Cooler synchrotron
(COSY) in the Forschungzentrum J\"ulich (FZJ) are also presented.
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We construct clusters of bound particles for a quantum integrable derivative
delta-function Bose gas in one dimension. It is found that clusters of bound
particles can be constructed for this Bose gas for some special values of the
coupling constant, by taking the quasi-momenta associated with the
corresponding Bethe state to be equidistant points on a single circle in the
complex momentum plane. Interestingly, there exists a connection between the
above mentioned special values of the coupling constant and some fractions
belonging to the Farey sequences in number theory. This connection leads to a
classification of the clusters of bound particles for the derivative
delta-function Bose gas and the determination of various properties of these
clusters like their size and their stability under a variation of the coupling
constant.
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Conjugations in space $L^2$ of the unit circle commuting with multiplication
by $z$ or intertwining multiplications by $z$ and $\bar z$ are characterized.
We also study their behaviour with respect to the Hardy space, subspaces
invariant for the unilateral shift and model spaces.
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Let $k$ be a field. In this paper we will show that any factorial
$\mathbb{A}^1$-form $A$ over any $k$-algebra $R$ is trivial, if $A$ has a
retraction to $R$.
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The $O(N)$ model with scalar quartic interactions at its ultraviolet fixed
point, and the $O(N)$ model with scalar cubic interactions at its infra-red
fixed point are conjectured to be equivalent. This has been checked by
comparing various features of the two models at their respective fixed points.
Recently, the scaling dimensions of a family of operators of fixed charge $Q$
have been shown to match at the FPs up to $\cal{O}\left(\frac{1}{N^2}\right)$at
leading order (LO) and next-to-leading order (NLO) in $Q$ using a semiclassical
computation which is valid to all orders in the coupling. Here we perform a
complementary but overlapping comparison using a perturbative calculation in
six dimensions, up to three-loop order in the coupling, to compare these
critical scaling dimensions beyond NLO in $Q$, in fact to all relevant orders
in $Q$. We also obtain the corresponding results at
$\cal{O}\left(\frac{1}{N^3}\right)$ for the cubic theory.
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Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological
group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem:
A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is
a.p. for $H\curvearrowright X$. Moreover, if $T\curvearrowright X$ is minimal
with $H\lhd T$, then $\mathscr{O}_H\colon X\rightarrow2^X$,
${x\mapsto\overline{Hx}}$ is a continuous mapping, and, $T\curvearrowright X/H$
is an a.p. nontrivial factor of $T\curvearrowright X$ iff $T\curvearrowright
X\times T/H$ is not minimal.
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Let $R$ be a noetherian ring and $M$ a finite $R$-module. With a linear form
$\chi$ on $M$ one associates the Koszul complex $K(\chi)$. If $M$ is a free
module, then the homology of $K(\chi)$ is well-understood, and in particular it
is grade sensitive with respect to $\Im\chi$.
In this note we investigate the case of a module $M$ of projective dimension
1 (more precisely, $M$ has a free resolution of length 1) for which the first
non-vanishing Fitting ideal $\I_M$ has the maximally possible grade $r+1$,
$r=\rank M$. Then $h=\grade \Im\chi\le r+1$ for all linear forms $\chi$ on $M$,
and it turns out that $H_{r-i}(K(\chi))=0$ for all even $i<h$ and
$H_{r-i}(K(\chi))\iso \SS^{(i-1)/2}(C)$ for all odd $i<h$ where $\SS$ denotes
symmetric power and $C=\Ext_R^1(M,R)$, in other words, $C=\Cok\psi^*$ for a
presentation $$ 0\to F\stackrel{\psi}{\to} G \to M\to 0. $$ Moreover, if $h\le
r$, then $H_{r-h}(K(\chi))$ is neither 0 nor isomorphic to a symmetric power of
$C$, so that it is justified to say that $K(\chi)$ is grade sensitive for the
modules $M$ under consideration.
We furthermore show that the maximally possible value $\grade \Im\chi=r+1$
can only occur in two extreme cases: (i) $r=1$ or (ii) $\rank F=1$ and $r$ is
odd.
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Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.