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We consider a relativistic particle model in an enlarged relativistic phase
space M^{18} = (X_\mu, P_\mu, \eta_\alpha, \oeta_\dalpha, \sigma_\alpha,
\osigma_\dalpha, e, \phi), which is derived from the free two-twistor dynamics.
The spin sector variables (\eta_\alpha, \oeta_\dalpha, \sigma_\alpha,\
osigma_\dalpha) satisfy two second class constraints and account for the
relativistic spin structure, and the pair (e,\phi) describes the electric
charge sector. After introducing the Liouville one-form on M^{18}, derived by a
non-linear transformation of the canonical Liouville one-form on the
two-twistor space, we analyze the dynamics described by the first and second
class constraints. We use a composite orthogonal basis in four-momentum space
to obtain the scalars defining the invariant spin projections. The
first-quantized theory provides a consistent set of wave equations, determining
the mass, spin, invariant spin projection and electric charge of the
relativistic particle. The wavefunction provides a generating functional for
free, massive higher spin fields.
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The high efficiency of converting kinetic energy into gamma-rays estimated
with late-time afterglows in Gamma-Ray Burst (GRB) phenomenon challenges the
commonly accepted internal-shock model. However, the efficiency is still highly
uncertain because it is sensitive to many effects. In this Letter we study the
sideways expansion effect of jets on estimating the efficiency. We find that
this effect is considerable, reducing the efficiency by a factor of $\sim0.5$
for typical parameters, when the afterglow data $\sim 10$ hr after the GRB
trigger are used to derive the kinetic energy. For a more dense circumburst
medium, this effect is more significant. As samples, taking this effect into
account, we specifically calculate the efficiency of two bursts whose
parameters were well constrained. Almost the same results are derived. This
suggests that the sideways expansion effect should be considered when the GRB
efficiency is estimated with the late afterglow data.
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We classify the trace anomaly for parity-invariant non-relativistic
Schr\"odinger theories in 2+1 dimensions coupled to background Newton-Cartan
gravity. The general anomaly structure looks very different from the one in the
z=2 Lifshitz theories. The type A content of the anomaly is remarkably
identical to that of the relativistic 3+1 dimensional case, suggesting the
conjecture that an a-theorem should exist also in the Newton-Cartan context.
Erratum: due to an overcounting of the number of linearly-independent terms
in the basis, the type A anomaly disappears if Frobenius condition is imposed.
See appended erratum for details. This crucial mistake was pointed out to us in
arXiv:1601.06795.
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We develop an online learning method for prediction, which is important in
problems with large and/or streaming data sets. We formulate the learning
approach using a covariance-fitting methodology, and show that the resulting
predictor has desirable computational and distribution-free properties: It is
implemented online with a runtime that scales linearly in the number of
samples; has a constant memory requirement; avoids local minima problems; and
prunes away redundant feature dimensions without relying on restrictive
assumptions on the data distribution. In conjunction with the split conformal
approach, it also produces distribution-free prediction confidence intervals in
a computationally efficient manner. The method is demonstrated on both real and
synthetic datasets.
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In this talk, I will concentrate on $Q^2$-dependence of deep inelastic sum
rules. I will first give a modern definition of deep-inelastic sum rules and
then discuss physical origins of their scaling violation at finite $Q^2$.
Following this, I discuss a few well-known examples, in particular, the Bjorken
sum rule, which is at the center of interest of this symposium. Finally, I
consider the $Q^2 \to 0$ limit of sum rules using low-energy theorems. I think
this can motivate some interesting CEBAF physics.
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We study the pi N -> pi pi N reaction around the N(1440) mass-shell energy.
Considering the total cross sections and invariant mass distributions, we
discuss the role of N(1440) and its decay processes. The calculation is
performed by extending our previous approach [Phys. Rev. C 69, 025206 (2004)]
to this reaction, in which only the nucleon and Delta(1232) were considered as
intermediate baryon states. The characteristics observed in the recent data for
the pi- p -> pi0 pi0 n reaction obtained by Crystal Ball Collaboration (CBC),
can be understood as a strong interference between the two decay processes:
N(1440) -> pi Delta(1232) and N(1440) -> N(pi pi)_S. It is also found that the
scalar-isoscalar pi pi rescattering effect in the NN*(pi pi)_S vertex, which
corresponds to the propagation of sigma meson, seems to be necessary for
explain ing the several observables of the pi N -> pi pi N reaction: the large
asymmetric shape in the pi0-pi0 invariant mass distributions of the pi- p ->
pi0 pi0 n reaction and the pi+ p -> pi+ pi+ n total cross section.
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Let $A/\overline{\mathbb{F}}\_p$ and $A'/\overline{\mathbb{F}}\_p$ be
supersingular principally polarized abelian varieties of dimension $g>1$. For
any prime $\ell \ne p$, we give an algorithm that finds a path $\phi \colon A
\rightarrow A'$ in the $(\ell, \dots , \ell)$-isogeny graph in
$\widetilde{O}(p^{g-1})$ group operations on a classical computer, and
$\widetilde{O}(\sqrt{p^{g-1}})$ calls to the Grover oracle on a quantum
computer. The idea is to find paths from $A$ and $A'$ to nodes that correspond
to products of lower dimensional abelian varieties, and to recurse down in
dimension until an elliptic path-finding algorithm (such as Delfs--Galbraith)
can be invoked to connect the paths in dimension $g=1$. In the general case
where $A$ and $A'$ are any two nodes in the graph, this algorithm presents an
asymptotic improvement over all of the algorithms in the current literature. In
the special case where $A$ and $A'$ are a known and relatively small number of
steps away from each other (as is the case in higher dimensional analogues of
SIDH), it gives an asymptotic improvement over the quantum claw finding
algorithms and an asymptotic improvement over the classical van
Oorschot--Wiener algorithm.
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We consider the estimation of a signal from the knowledge of its noisy linear
random Gaussian projections, a problem relevant in compressed sensing, sparse
superposition codes or code division multiple access just to cite few. There
has been a number of works considering the mutual information for this problem
using the heuristic replica method from statistical physics. Here we put these
considerations on a firm rigorous basis. First, we show, using a Guerra-type
interpolation, that the replica formula yields an upper bound to the exact
mutual information. Secondly, for many relevant practical cases, we present a
converse lower bound via a method that uses spatial coupling, state evolution
analysis and the I-MMSE theorem. This yields, in particular, a single letter
formula for the mutual information and the minimal-mean-square error for random
Gaussian linear estimation of all discrete bounded signals.
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Brains have evolved a diverse set of neurons with varying morphologies,
physiological properties and rich dynamics that impact their processing of
temporal information. By contrast, most neural network models include a
homogeneous set of units that only vary in terms of their spatial parameters
(weights and biases). To investigate the importance of temporal parameters to
neural function, we trained spiking neural networks on tasks of varying
temporal complexity, with different subsets of parameters held constant. We
find that in a tightly resource constrained setting, adapting conduction delays
is essential to solve all test conditions, and indeed that it is possible to
solve these tasks using only temporal parameters (delays and time constants)
with weights held constant. In the most complex spatio-temporal task we
studied, we found that an adaptable bursting parameter was essential. More
generally, allowing for adaptation of both temporal and spatial parameters
increases network robustness to noise, an important feature for both biological
brains and neuromorphic computing systems. In summary, our findings highlight
how rich and adaptable dynamics are key to solving temporally structured tasks
at a low neural resource cost, which may be part of the reason why biological
neurons vary so dramatically in their physiological properties.
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Floquet engineering is a convenient strategy to induce nonequilibrium
phenomena in molecular and solid-state systems, or to dramatically alter the
physicochemical properties of matter, bypassing costly and time-consuming
synthetic modifications. In this article, we investigate theoretically some
interesting consequences of the fact that an originally achiral molecular
system can exhibit nonzero circular dichroism (CD) when it is driven with
elliptically polarized light. More specifically, we consider an isotropic
ensemble of small cyclic molecular aggregates in solution whose local
low-frequency vibrational modes are driven by an elliptically polarized
continuous-wave infrared pump. We attribute the origin of a nonzero CD signal
to time-reversal symmetry breaking due to an excitonic Aharonov-Bohm (AB) phase
arising from a time-varying laser electric field, together with coherent
interchromophoric exciton hopping. The obtained Floquet engineered excitonic AB
phases are far more tunable than analogous magnetically-induced electronic AB
phases in nanoscale rings, highlighting a virtually unexplored potential that
Floquet engineered AB phases have in the coherent control of molecular
processes and simultaneously introducing new analogues of magneto-optical
effects in molecular systems which bypass the use of strong magnetic fields.
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We observed the HH 211 jet in the submillimeter continuum and the CO(3-2) and
SiO(8-7) transitions with the Submillimeter Array. The continuum source
detected at the center of the outflow shows an elongated morphology,
perpendicular to the direction of the outflow axis. The high-velocity emission
of both molecules shows a knotty and highly collimated structure. The SiO(8-7)
emission at the base of the outflow, close to the driving source, spans a wide
range of velocities, from -20 up to 40 km s^{-1}. This suggests that a
wide-angle wind may be the driving mechanism of the HH 211 outflow. For
distances greater than 5" (1500 AU) from the driving source, emission from both
transitions follows a Hubble-law behavior, with SiO(8-7) reaching higher
velocities than CO(3-2), and being located upstream of the CO(3-2) knots. This
indicates that the SiO(8-7) emission is likely tracing entrained gas very close
to the primary jet, while the CO(3-2) is tracing less dense entrained gas. From
the SiO(5-4) data of Hirano et al. we find that the SiO(8-7)/SiO(5-4)
brightness temperature ratio along the jet decreases for knots far from the
driving source. This is consistent with the density decreasing along the jet,
from (3-10)x10^6 cm^{-3} at 500 AU to (0.8-4)x10^6 cm^{-3} at 5000 AU from the
driving source.
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The barrel time-of-flight (TOF) detector for the PANDA experiment at FAIR in
Darmstadt is planned as a scintillator tile hodoscope (SciTil) using 8000 small
scintillator tiles. It will provide fast event timing for a software trigger in
the otherwise trigger-less data acquisition scheme of PANDA, relative timing in
a multiple track event topology as well as additional particle identification
in the low momentum region. The goal is to achieve a time resolution of sigma ~
100 ps. We have conducted measurements using organic scintillators coupled to
Silicon Photomultipliers (SiPM). The results are encouraging such that we are
confident to reach the required time resolution.
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Graphene has raised high expectations as a low-loss plasmonic material in
which the plasmon properties can be controlled via electrostatic doping. Here,
we analyze realistic configurations, which produce inhomogeneous doping, in
contrast to what has been so far assumed in the study of plasmons in
nanostructured graphene. Specifically, we investigate backgated ribbons,
co-planar ribbon pairs placed at opposite potentials, and individual ribbons
subject to a uniform electric field. Plasmons in backgated ribbons and ribbon
pairs are similar to those of uniformly doped ribbons, provided the Fermi
energy is appropriately scaled to compensate for finite-size effects such as
the divergence of the carrier density at the edges. In contrast, the plasmons
of a ribbon exposed to a uniform field exhibit distinct dispersion and spatial
profiles that considerably differ from uniformly doped ribbons. Our results
provide a road map to understand graphene plasmons under realistic
electrostatic doping conditions.
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Model predictive control (MPC) anticipates future events to take appropriate
control actions. Nonlinear MPC (NMPC) deals with nonlinear models and/or
constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in
2004, uses the GMRES iterative algorithm to solve a forward difference
approximation $Ax=b$ of the original NMPC equations on every time step. We have
previously proposed accelerating the GMRES and MINRES convergence by
preconditioning the coefficient matrix $A$. We now suggest simplifying the
construction of the preconditioner, by approximately solving a forward
recursion for the state and a backward recursion for the costate, or simply
reusing previously computed solutions.
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Alloys of Bi$_2$Te$_3$ and Sb$_2$Te$_3$ ((Bi$_{1-x}$Sb$_x$)$_2$Te$_3$) have
played an essential role in the exploration of topological surface states,
allowing us to study phenomena that would otherwise be obscured by bulk
contributions to conductivity. Thin films of these alloys have been
particularly important for tuning the energy of the Fermi level, a key step in
observing spin-polarized surface currents and the quantum anomalous Hall
effect. Previous studies reported the chemical tuning of the Fermi level to the
Dirac point by controlling the Sb:Bi composition ratio, but the optimum ratio
varies widely across various studies with no consensus. In this work, we use
scanning tunneling microscopy and Landau level spectroscopy, in combination
with X-ray photoemission spectroscopy to isolate the effects of growth factors
such as temperature and composition, and to provide a microscopic picture of
the role that disorder and composition play in determining the carrier density
of epitaxially grown (Bi,Sb)$_2$Te$_3$ thin films. Using Landau level
spectroscopy, we determine that the ideal Sb concentration to place the Fermi
energy to within a few meV of the Dirac point is $x\sim 0.7$. However, we find
that the post- growth annealing temperature can have a drastic impact on
microscopic structure as well as carrier density. In particular, we find that
when films are post-growth annealed at high temperature, better crystallinity
and surface roughness are achieved; but this also produces a larger Te defect
density, adding n-type carriers. This work provides key information necessary
for optimizing thin film quality in this fundamentally and technologically
important class of materials.
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We investigate the behavior of an $N$-component quantum rotor coupled to a
bosonic dissipative bath having a sub-Ohmic spectral density $J(\omega) \propto
\omega^s$ with $s<1$. With increasing dissipation strength, this system
undergoes a quantum phase transition from a delocalized phase to a localized
phase. We determine the exact critical behavior of this transition in the
large-$N$ limit. For $1>s>1/2$, we find nontrivial critical behavior
corresponding to an interacting renormalization group fixed point while we find
mean-field behavior for $s<1/2$. The results agree with those of the
corresponding long-range interacting classical model. The quantum-to-classical
mapping is therefore valid for the sub-Ohmic rotor model.
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Nanoscale photothermal sources find important applications in theranostics,
imaging, and catalysis. In this context, graphene offers a unique suite of
optical, electrical, and thermal properties, which we exploit to show
self-consistent active photothermal modulation of its nanoscale response. In
particular, we predict the existence of plasmons confined to the optical
landscape tailored by continuous-wave external-light pumping of homogeneous
graphene. This result relies on the high electron temperatures achievable in
optically pumped clean graphene while its lattice remains near ambient
temperature. Our study opens a new avenue toward the active optical control of
the nanophotonic response in graphene with potential application in
photothermal devices.
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Molecular D/H ratios are frequently used to probe the chemical past of Solar
System volatiles. Yet it is unclear which parts of the Solar Nebula hosted an
active deuterium fractionation chemistry. To address this question, we present
0".2-0".4 ALMA observations of DCO+ and DCN 2-1, 3-2 and 4-3 towards the nearby
protoplanetary disk around TW Hya, taken as part of the TW Hya Rosetta Stone
project, augmented with archival data. DCO+ is characterized by an excitation
temperature of ~40 K across the 70 au radius pebble disk, indicative of
emission from a warm, elevated molecular layer. Tentatively, DCN is present at
even higher temperatures. Both DCO+ and DCN present substantial emission
cavities in the inner disk, while in the outer disk the DCO+ and DCN
morphologies diverge: most DCN emission originates from a narrow ring peaking
around 30~au, with some additional diffuse DCN emission present at larger
radii, while DCO+ is present in a broad structured ring that extends past the
pebble disk. Based on parametric disk abundance models, these emission patterns
can be explained by a near-constant DCN abundance exterior to the cavity, and
an increasing DCO+ abundance with radius. There appears to be an active
deuterium fractionation chemistry in multiple disk regions around TW Hya, but
not in the cold planetesimal-forming midplane and in the inner disk. More
observations are needed to explore whether deuterium fractionation is actually
absent in these latter regions, and if its absence is a common feature, or
something peculiar to the old TW Hya disk.
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A non-perturbative lattice regularization of chiral fermions and bosons with
anomaly-free symmetry $G$ in 1+1D spacetime is proposed. More precisely, we ask
"whether there is a local short-range quantum Hamiltonian with a finite Hilbert
space for a finite system realizing onsite symmetry $G$ defined on a 1D spatial
lattice, such that its low energy physics produces a 1+1D anomaly-free chiral
matter theory of symmetry $G$?" In particular, we propose that the
3$_L$-5$_R$-4$_L$-0$_R$ U(1) chiral fermion theory, with two left-moving
fermions of charge-3 and 4, and two right-moving fermions of charge-5 and 0 at
low energy, can be put on a 1D spatial lattice where the U(1) symmetry is
realized as an onsite symmetry, if we include properly designed multi-fermion
interactions with intermediate strength. In general, we propose that any 1+1D
U(1)-anomaly-free chiral matter theory can be defined as a finite system on a
1D lattice with onsite symmetry by using a quantum Hamiltonian with continuous
time, but without suffering from Nielsen-Ninomiya theorem's fermion-doubling,
if we include properly-designed interactions between matter fields. We propose
how to design such interactions by looking for extra symmetries via
bosonization/fermionization. We comment on the new ingredients and the
differences of ours compared to Ginsparg-Wilson fermion, Eichten-Preskill, and
Chen-Giedt-Poppitz (CGP) models, and suggest modifying CGP model to have
successful mirror-decoupling. We show a topological non-perturbative proof of
the equivalence between $G$-symmetric 't Hooft anomaly cancellation conditions
and $G$-symmetric gapping rules (e.g. Haldane's stability conditions for
Luttinger liquid) for multi-U(1) symmetry. We expect our result holds
universally regardless of spatial Hamiltonian or Lagrangian/spacetime path
integral formulation. Numerical tests are demanding tasks but highly desirable
for future work.
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In this paper, we bring forth a novel approach of video text detection using
Fourier-Laplacian filtering in the frequency domain that includes a
verification technique using Hidden Markov Model (HMM). The proposed approach
deals with the text region appearing not only in horizontal or vertical
directions, but also in any other oblique or curved orientation in the image.
Until now only a few methods have been proposed that look into curved text
detection in video frames, wherein lies our novelty. In our approach, we first
apply Fourier-Laplacian transform on the image followed by an ideal
Laplacian-Gaussian filtering. Thereafter K-means clustering is employed to
obtain the asserted text areas depending on a maximum difference map. Next, the
obtained connected components (CC) are skeletonized to distinguish various text
strings. Complex components are disintegrated into simpler ones according to a
junction removal algorithm followed by a concatenation performed on possible
combination of the disjoint skeletons to obtain the corresponding text area.
Finally these text hypotheses are verified using HMM-based text/non-text
classification system. False positives are thus eliminated giving us a robust
text detection performance. We have tested our framework in multi-oriented text
lines in four scripts, namely, English, Chinese, Devanagari and Bengali, in
video frames and scene texts. The results obtained show that proposed approach
surpasses existing methods on text detection.
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Magnetic resonance spectroscopy (MRS) is an important technique in biomedical
research and it has the unique capability to give a non-invasive access to the
biochemical content (metabolites) of scanned organs. In the literature, the
quantification (the extraction of the potential biomarkers from the MRS
signals) involves the resolution of an inverse problem based on a parametric
model of the metabolite signal. However, poor signal-to-noise ratio (SNR),
presence of the macromolecule signal or high correlation between metabolite
spectral patterns can cause high uncertainties for most of the metabolites,
which is one of the main reasons that prevents use of MRS in clinical routine.
In this paper, quantification of metabolites in MR Spectroscopic imaging using
deep learning is proposed. A regression framework based on the Convolutional
Neural Networks (CNN) is introduced for an accurate estimation of spectral
parameters. The proposed model learns the spectral features from a large-scale
simulated data set with different variations of human brain spectra and SNRs.
Experimental results demonstrate the accuracy of the proposed method, compared
to state of the art standard quantification method (QUEST), on concentration of
20 metabolites and the macromolecule.
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In the limit of extremely rapid mass transfer, the response of a donor star
in an interacting binary becomes asymptotically one of adiabatic expansion. We
survey here adiabatic mass loss from Population I stars of mass 0.10 Msun to
100 Msun from the zero age main sequence to the base of the giant branch, or to
central hydrogen exhaustion for lower main sequence stars. For intermediate-
and high-mass stars, dynamical mass transfer is preceded by an extended phase
of thermal time scale mass transfer as the star is stripped of most of its
envelope mass. The critical mass ratio qad above which this delayed dynamical
instability occurs increases with advancing evolutionary age of the donor star,
by ever-increasing factors for more massive donors. Most intermediate- or
high-mass binaries with nondegenerate accretors probably evolve into contact
before manifesting this instability. As they approach the base of the giant
branch, however, and begin developing a convective envelope, qad plummets
dramatically among intermediate-mass stars, to values of order unity, and a
prompt dynamical instability occurs. Among low-mass stars, the prompt
instability prevails throughout main sequence evolution, with q_ad declining
with decreasing mass. Our calculated qad agree well with the behavior of
timedependent models by Chen & Han (2003) of intermediate-mass stars initiating
mass transfer in the Hertzsprung gap. Application of our results to cataclysmic
variables, as systems which must be stable against rapid mass transfer, nicely
circumscribes the range in qad as a function of orbital period in which they
are found. These results are intended to advance the verisimilitude of
population synthesis models of close binary evolution.
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Visual data in autonomous driving perception, such as camera image and LiDAR
point cloud, can be interpreted as a mixture of two aspects: semantic feature
and geometric structure. Semantics come from the appearance and context of
objects to the sensor, while geometric structure is the actual 3D shape of
point clouds. Most detectors on LiDAR point clouds focus only on analyzing the
geometric structure of objects in real 3D space. Unlike previous works, we
propose to learn both semantic feature and geometric structure via a unified
multi-view framework. Our method exploits the nature of LiDAR scans -- 2D range
images, and applies well-studied 2D convolutions to extract semantic features.
By fusing semantic and geometric features, our method outperforms
state-of-the-art approaches in all categories by a large margin. The
methodology of combining semantic and geometric features provides a unique
perspective of looking at the problems in real-world 3D point cloud detection.
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Previous results reported in the robotics literature show the relationship
between time-delay control (TDC) and proportional-integral-derivative control
(PID). In this paper, we show that incremental nonlinear dynamic inversion
(INDI) - more familiar in the aerospace community - are in fact equivalent to
TDC. This leads to a meaningful and systematic method for PI(D)-control tuning
of robust nonlinear flight control systems via INDI. We considered a
reformulation of the plant dynamics inversion which removes effector blending
models from the resulting control law, resulting in robust model-free control
laws like PI(D)-control.
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We study the collapse of a spherically symmetric dust distribution in
$d$-dimensional AdS spacetime. We investigate the role of dimensionality, and
the presence of a negative cosmological constant, in determining the formation
of trapped surfaces and the end state of gravitational collapse. We obtain the
self-similar solution for the case of zero cosmological constant, and show that
one cannot construct a self-similar solution when a cosmological constant is
included.
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Structured recursion schemes such as folds and unfolds have been widely used
for structuring both functional programs and program semantics. In this
context, it has been customary to implement denotational semantics as folds
over an inductive data type to ensure termination and compositionality.
Separately, operational models can be given by unfolds, and naturally not all
operational models coincide with a given denotational semantics in a meaningful
way. To ensure these semantics are coherent it is important to consider the
property of full abstraction which relates the denotational and the operational
model. In this paper, we show how to engineer a compositional semantics such
that full abstraction comes for free. We do this by using distributive laws
from which we generate both the operational and the denotational model. The
distributive laws ensure the semantics are fully abstract at the type level,
thus relieving the programmer from the burden of the proofs.
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We delve into pseudo-labeling for semi-supervised monocular 3D object
detection (SSM3OD) and discover two primary issues: a misalignment between the
prediction quality of 3D and 2D attributes and the tendency of depth
supervision derived from pseudo-labels to be noisy, leading to significant
optimization conflicts with other reliable forms of supervision. We introduce a
novel decoupled pseudo-labeling (DPL) approach for SSM3OD. Our approach
features a Decoupled Pseudo-label Generation (DPG) module, designed to
efficiently generate pseudo-labels by separately processing 2D and 3D
attributes. This module incorporates a unique homography-based method for
identifying dependable pseudo-labels in BEV space, specifically for 3D
attributes. Additionally, we present a DepthGradient Projection (DGP) module to
mitigate optimization conflicts caused by noisy depth supervision of
pseudo-labels, effectively decoupling the depth gradient and removing
conflicting gradients. This dual decoupling strategy-at both the pseudo-label
generation and gradient levels-significantly improves the utilization of
pseudo-labels in SSM3OD. Our comprehensive experiments on the KITTI benchmark
demonstrate the superiority of our method over existing approaches.
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For a simple model of chaotic dynamical systems with a large number of
degrees of freedom, we find that there is an ensemble of unstable periodic
orbits (UPOs) with the special property that the expectation values of
macroscopic quantities can be calculated using only one UPO sampled from the
ensemble. Evidence to support this conclusion is obtained by generating the
ensemble by Monte Carlo calculation for a statistical mechanical model
described by a space-time Hamiltonian that is expressed in terms of Floquet
exponents of UPOs. This result allows us to interpret the recent interesting
discovery that statistical properties of turbulence can be obtained from only
one UPO [G. Kawahara and S. Kida, J. Fluid Mech. {\bf 449}, 291 (2001); S. Kato
and M. Yamada, Phys. Rev. E {\bf 68}, 025302(R)(2003)].
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Satellite and shipboard data reveal the intermittent vertical information
transport mechanism of turbulence and internal waves that mixes the ocean,
atmosphere, planets and stars.
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We report evidence of Re and Mo segregation (up to 2.6 at.% and 1 at.%) along
with Cr and Co to the dislocations inside of {\gamma}' precipitates in a second
generation Ni-based single crystal superalloy, after creep deformation at
750{\deg}C under an applied stress of 800 MPa. The observed segregation effects
can be rationalized through bridging the solute partitioning behavior across
the {\gamma}/{\gamma}' interface and the pipe diffusion mechanism along the
core of the dislocation line. This understanding can provide new insights
enabling improved alloy design.
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The dynamics of amorphous granular matter with frictional interactions cannot
be derived in general from a Hamiltonian and therefore displays oscillatory
instabilities stemming from the onset of complex eigenvalues in the stability
matrix. These instabilities were discovered in the context of one and two
dimensional systems, while the three dimensional case was never studied in
detail. Here we fill this gap by deriving and demonstrating the presence of
oscillatory instabilities in a three dimensional granular packing. We study
binary assemblies of spheres of two sizes interacting via classical Hertz and
Mindlin force laws for the longitudinal and tangent interactions, respectively.
We formulate analytically the stability matrix in 3D and observe that a couple
of complex eigenvalues emerges at the onset of the instability as in the case
of frictional disks in two-dimensions. The dynamics then shows oscillatory
exponential growth in the Mean-Square-Displacement, followed by a catastrophic
event. The generality of these results for any choice of forces that break the
symplectic Hamiltonian symmetry is discussed.
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Estimating 3D articulated shapes like animal bodies from monocular images is
inherently challenging due to the ambiguities of camera viewpoint, pose,
texture, lighting, etc. We propose ARTIC3D, a self-supervised framework to
reconstruct per-instance 3D shapes from a sparse image collection in-the-wild.
Specifically, ARTIC3D is built upon a skeleton-based surface representation and
is further guided by 2D diffusion priors from Stable Diffusion. First, we
enhance the input images with occlusions/truncation via 2D diffusion to obtain
cleaner mask estimates and semantic features. Second, we perform
diffusion-guided 3D optimization to estimate shape and texture that are of
high-fidelity and faithful to input images. We also propose a novel technique
to calculate more stable image-level gradients via diffusion models compared to
existing alternatives. Finally, we produce realistic animations by fine-tuning
the rendered shape and texture under rigid part transformations. Extensive
evaluations on multiple existing datasets as well as newly introduced noisy web
image collections with occlusions and truncation demonstrate that ARTIC3D
outputs are more robust to noisy images, higher quality in terms of shape and
texture details, and more realistic when animated. Project page:
https://chhankyao.github.io/artic3d/
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Despite the popularisation of machine learning models, more often than not,
they still operate as black boxes with no insight into what is happening inside
the model. There exist a few methods that allow to visualise and explain why a
model has made a certain prediction. Those methods, however, allow
visualisation of the link between the input and output of the model without
presenting how the model learns to represent the data used to train the model
as whole. In this paper, a method that addresses that issue is proposed, with a
focus on visualising multi-dimensional time-series data. Experiments on a
high-frequency stock market dataset show that the method provides fast and
discernible visualisations. Large datasets can be visualised quickly and on one
plot, which makes it easy for a user to compare the learned representations of
the data. The developed method successfully combines known techniques to
provide an insight into the inner workings of time-series classification
models.
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An experimental technique for the light lambda-hypernuclei structure studies
by using (negative kaon, neutral pion) reaction and Neutral Meson Spectrometer
(NMS) developed at the BNL has been described. Position dependence calibration
of the BGO conversion planes of the NMS was invented as the solution to the
crucial constraint of the high resolution in single-lambda spectroscopy.
Position parameters of the BGO crystal rods were fitted out from the
out-of-kaon beam measured data as obtained by the original small highly
collimated Co-60 source method, based on the coincidences between top and
bottom signals of each BGO rod.
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A study of the reinforcement effect of a soft polymer matrix by hard
nanometric filler particles is presented. In the main part of this article, the
structure of the silica filler in the matrix is studied by Small Angle Neutron
Scattering (SANS), and stress-strain isotherms are measured to characterize the
rheological properties of the composites. Our analysis allows us to quantify
the degree of aggregation of the silica in the matrix, which is studied as a
function of pH (4-10), silica volume fraction (3-15%) and silica bead size
(average radius 78 A and 96 A). Rheological properties of the samples are
represented in terms of the strain-dependent reinforcement factor, which
highlights the contribution of the filler. Combining the structural information
with a quantitative analysis of the reinforcement factor, the aggregate size
and compacity (10%-40%) as a function of volume fraction and pH can be deduced.
In a second, more explorative study, the grafting of polymer chains on
nanosilica beads for future reinforcement applications is followed by SANS. The
structure of the silica and the polymer are measured separately by contrast
variation, using deuterated material. The aggregation of the silica beads in
solution is found to decrease during polymerization, reaching a rather low
final aggregation number (less than ten).
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Decision making is the cognitive process of selecting a course of action
among multiple alternatives. As the decision maker belongs to a complex
microenvironment (which contains multiple decision makers), has to make a
decision where multiple options are present which often leads to a phenomenon
known as the "paradox of choices". The latter refers to the case where too many
options can lead to negative outcomes, such as increased uncertainty, decision
paralysis, and frustration. Here, we employ an entropy driven mechanism within
a statistical physics framework to explain the premises of the paradox. In
turn, we focus on the emergence of a collective "paradox of choice", in the
case of interacting decision-making agents, quantified as the decision
synchronization time. Our findings reveal a trade-off between synchronization
time and the sensing radius, indicating the optimal conditions for information
transfer among group members, which significantly depends the individual
sensitivity parameters. Interestingly, when agents sense their microenvironment
in a biased way or their decisions are influenced by their past choices, then
the collective "paradox of choice" does not occur. In a nutshell, our theory
offers a low-dimensional and unified statistical explanation of the "paradox of
choice" at the individual and at the collective level.
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Many AI synthesis problems such as planning or scheduling may be modelized as
constraint satisfaction problems (CSP). A CSP is typically defined as the
problem of finding any consistent labeling for a fixed set of variables
satisfying all given constraints between these variables. However, for many
real tasks such as job-shop scheduling, time-table scheduling, design?, all
these constraints have not the same significance and have not to be necessarily
satisfied. A first distinction can be made between hard constraints, which
every solution should satisfy and soft constraints, whose satisfaction has not
to be certain. In this paper, we formalize the notion of possibilistic
constraint satisfaction problems that allows the modeling of uncertainly
satisfied constraints. We use a possibility distribution over labelings to
represent respective possibilities of each labeling. Necessity-valued
constraints allow a simple expression of the respective certainty degrees of
each constraint. The main advantage of our approach is its integration in the
CSP technical framework. Most classical techniques, such as Backtracking (BT),
arcconsistency enforcing (AC) or Forward Checking have been extended to handle
possibilistics CSP and are effectively implemented. The utility of our approach
is demonstrated on a simple design problem.
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We consider the problem of intelligent and efficient task allocation
mechanism in large-scale mobile edge computing (MEC), which can reduce delay
and energy consumption in a parallel and distributed optimization. In this
paper, we study the joint optimization model to consider cooperative task
management mechanism among mobile terminals (MT), macro cell base station
(MBS), and multiple small cell base station (SBS) for large-scale MEC
applications. We propose a parallel multi-block Alternating Direction Method of
Multipliers (ADMM) based method to model both requirements of low delay and low
energy consumption in the MEC system which formulates the task allocation under
those requirements as a nonlinear 0-1 integer programming problem. To solve the
optimization problem, we develop an efficient combination of conjugate
gradient, Newton and linear search techniques based algorithm with Logarithmic
Smoothing (for global variables updating) and the Cyclic Block coordinate
Gradient Projection (CBGP, for local variables updating) methods, which can
guarantee convergence and reduce computational complexity with a good
scalability. Numerical results demonstrate the effectiveness of the proposed
mechanism and it can effectively reduce delay and energy consumption for a
large-scale MEC system.
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Being able to predict stock prices might be the unspoken wish of stock
investors. Although stock prices are complicated to predict, there are many
theories about what affects their movements, including interest rates, news and
social media. With the help of Machine Learning, complex patterns in data can
be identified beyond the human intellect. In this thesis, a Machine Learning
model for time series forecasting is created and tested to predict stock
prices. The model is based on a neural network with several layers of LSTM and
fully connected layers. It is trained with historical stock values, technical
indicators and Twitter attribute information retrieved, extracted and
calculated from posts on the social media platform Twitter. These attributes
are sentiment score, favourites, followers, retweets and if an account is
verified. To collect data from Twitter, Twitter's API is used. Sentiment
analysis is conducted with VADER. The results show that by adding more Twitter
attributes, the MSE between the predicted prices and the actual prices improved
by 3%. With technical analysis taken into account, MSE decreases from 0.1617 to
0.1437, which is an improvement of around 11%. The restrictions of this study
include that the selected stock has to be publicly listed on the stock market
and popular on Twitter and among individual investors. Besides, the stock
markets' opening hours differ from Twitter, which constantly available. It may
therefore introduce noises in the model.
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Clifford's geometric algebra has enjoyed phenomenal development over the last
60 years by mathematicians, theoretical physicists, engineers and computer
scientists in robotics, artificial intelligence and data analysis, introducing
a myriad of different and often confusing notations. The geometric algebra of
Euclidean 3-space, the natural generalization of both the well-known
Gibbs-Heaviside vector algebra, and Hamilton's quaternions, is used here to
study spheroidal domains, spheroidal-graphic projections, the Laplace equation
and its Lie algebra of symmetries. The Cauchy-Kovalevska extension and the
Cauchy kernel function are treated in a unified way. The concept of a
quasi-monogenic family of functions is introduced and studied.
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Let $p$ be a prime number, and $G$ a compact $p$-adic Lie group. We recall
that the Iwasawa algebra $\Lambda(G)$ is defined to be the completed group ring
of $G$ over the ring of $p$-adic integers. Interesting examples of finitely
generated modules over $\Lambda(G),$ in which $G$ is the image of Galois in the
automorphism group of a $p$-adic Galois representation, abound in arithmetic
geometry. The study of such $\Lambda(G)$-modules arising from arithmetic
geometry can be thought of as a natural generalization of Iwasawa theory. One
of the cornerstones of classical Iwasawa theory is the fact that, when $G$ is
the additive group of $p$-adic integers, a good structure theory for finitely
generated $\Lambda(G)$-modules is known, up to pseudo-isomorphism. The aim of
the present paper is to extend as much as possible of this commutative
structure theory to the non-commuta tive case.
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In this article we formulate several conjectures concerning the lowest
eigenvalue of a Dirac operator with an external electrostatic potential. The
latter describes a relativistic quantum electron moving in the field of some
(pointwise or extended) nuclei. The main question we ask is whether the
eigenvalue is minimal when the nuclear charge is concentrated at one single
point. This well-known property in nonrelativistic quantum mechanics has
escaped all attempts of proof in the relativistic case.
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We study the response to perturbation of non-Poisson dichotomous fluctuations
that generate super-diffusion. We adopt the Liouville perspective and with it a
quantum-like approach based on splitting the density distribution into a
symmetric and an anti-symmetric component. To accomodate the equilibrium
condition behind the stationary correlation function, we study the time
evolution of the anti-symmetric component, while keeping the symmetric
component at equilibrium. For any realistic form of the perturbed distribution
density we expect a breakdown of the Onsager principle, namely, of the property
that the subsequent regression of the perturbation to equilibrium is identical
to the corresponding equilibrium correlation function. We find the directions
to follow for the calculation of higher-order correlation functions, an
unsettled problem, which has been addressed in the past by means of
approximations yielding quite different physical effects.
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The Burnside Problem asks whether a finitely generated group of exponent n is
finite.
We present a solution for 2-generator groups of prime power exponent. Results
of P. Hall and G. Higman extends the finiteness conclusion to groups having
composite exponents. Our main result, called the Generalized Burnside Theorem,
is a solvability theorem that applies to a family of groups called GB
(Generalized Burnside) groups that contain infinite as well as finite groups.
The final section discusses the extension to k-generator groups although
details are left for another time.
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We develop Bayesian models for density regression with emphasis on discrete
outcomes. The problem of density regression is approached by considering
methods for multivariate density estimation of mixed scale variables, and
obtaining conditional densities from the multivariate ones. The approach to
multivariate mixed scale outcome density estimation that we describe represents
discrete variables, either responses or covariates, as discretised versions of
continuous latent variables. We present and compare several models for
obtaining these thresholds in the challenging context of count data analysis
where the response may be over- and/or under-dispersed in some of the regions
of the covariate space. We utilise a nonparametric mixture of multivariate
Gaussians to model the directly observed and the latent continuous variables.
The paper presents a Markov chain Monte Carlo algorithm for posterior sampling,
sufficient conditions for weak consistency, and illustrations on density, mean
and quantile regression utilizing simulated and real datasets.
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We introduce and formalize a notion of "a priori knowledge" about a quantum
system, and show some properties about this form of knowledge. Finally, we show
that the Kochen-Specker theorem follows directly from this study. This version
is a draft version, the bibliography in particular is extremely scarce.
Comments welcome.
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Asymmetric features in exoplanet transit light curves are often interpreted
as a gravity darkening effect especially if there is spectroscopic evidence of
a spin-orbit misalignment. Since other processes can also lead to light curve
asymmetries this may lead to inaccurate gravity darkening parameters. Here we
investigate the case of non-radial pulsations as possible sources of asymmetry
and likely source of misinterpreted parameters through simulations. We obtained
a series of simulated transit light curves of a hypothetical exoplanet-star
system: a host star with no gravity darkening exhibiting small amplitude
pulsations, and a typical hot Jupiter in a circular, edge-on orbit. A number of
scenarios of pulsations of various amplitudes were considered, and a proper
account of the obscuring effect of transits on all the surface intensity
components was made. The magnitude of amplitude and phase modulations of
nonradial pulsations during transits was also also investigated. We then fitted
both a non-gravity-darkened, and a gravity-darkened, free spin-orbit axis model
on the data. The Akaike and Bayesian Information Criteria were used for an
objective selection of the most plausible model. We then explored the
dependence of the parameter deviations on the pulsation properties, in order to
identify configurations that can lead to falsely misaligned solutions.
Low-amplitude pulsations in general do not affect the determination of the
system parameters beyond their noise nature. However, frequencies close to
multiples of the orbital frequency are found to cause distortions leading to
solutions with a side tilted stellar rotational axis, they are therefore
preferable to clean beforehand for the sake of a correct analysis.
Additionally, for cases with higher-amplitude pulsations, it is recommended to
pre-process and clean the pulsations before analysis.
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Detection of hydroacoustic transmissions is a key enabling technology in
applications such as depth measurements, detection of objects, and undersea
mapping. To cope with the long channel delay spread and the low signal-to-noise
ratio, hydroacoustic signals are constructed with a large time-bandwidth
product, $N$. A promising detector for hydroacoustic signals is the normalized
matched filter (NMF). For the NMF, the detection threshold depends only on $N$,
thereby obviating the need to estimate the characteristics of the sea ambient
noise which are time-varying and hard to estimate. While previous works
analyzed the characteristics of the normalized matched filter (NMF), for
hydroacoustic signals with large $N$ values the expressions available are
computationally complicated to evaluate. Specifically for hydroacoustic signals
of large $N$ values, this paper presents approximations for the probability
distribution of the NMF. These approximations are found extremely accurate in
numerical simulations. We also outline a computationally efficient method to
calculate the receiver operating characteristic (ROC) which is required to
determine the detection threshold. Results from an experiment conducted in the
Mediterranean sea at depth of 900~m agree with the analysis.
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A linearized tensor renormalization group (LTRG) algorithm is proposed to
calculate the thermodynamic properties of one-dimensional quantum lattice
models, that is incorporated with the infinite time-evolving block decimation
technique, and allows for treating directly the two-dimensional transfer-matrix
tensor network. To illustrate its feasibility, the thermodynamic quantities of
the quantum XY spin chain are calculated accurately by the LTRG, and the
precision is shown to be comparable with (even better than) the transfer matrix
renormalization group (TMRG) method. Unlike the TMRG scheme that can only deal
with the infinite chains, the present LTRG algorithm could treat both finite
and infinite systems, and may be readily extended to boson and fermion quantum
lattice models.
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We observed the Crab pulsar in October 2008 at the Copernico Telescope in
Asiago - Cima Ekar with the optical photon counter Aqueye (the Asiago Quantum
Eye) which has the best temporal resolution and accuracy ever achieved in the
optical domain (hundreds of picoseconds). Our goal was to perform a detailed
analysis of the optical period and phase drift of the main peak of the Crab
pulsar and compare it with the Jodrell Bank ephemerides. We determined the
position of the main peak using the steepest zero of the cross-correlation
function between the pulsar signal and an accurate optical template. The pulsar
rotational period and period derivative have been measured with great accuracy
using observations covering only a 2 day time interval. The error on the period
is 1.7 ps, limited only by the statistical uncertainty. Both the rotational
frequency and its first derivative are in agreement with those from the Jodrell
Bank radio ephemerides archive. We also found evidence of the optical peak
leading the radio one by ~230 microseconds. The distribution of phase-residuals
of the whole dataset is slightly wider than that of a synthetic signal
generated as a sequence of pulses distributed in time with the probability
proportional to the pulse shape, such as the average count rate and background
level are those of the Crab pulsar observed with Aqueye. The counting
statistics and quality of the data allowed us to determine the pulsar period
and period derivative with great accuracy in 2 days only. The time of arrival
of the optical peak of the Crab pulsar leads the radio one in agreement with
what recently reported in the literature. The distribution of the phase
residuals can be approximated with a Gaussian and is consistent with being
completely caused by photon noise (for the best data sets).
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We use an analytical forward model based on perturbation theory to predict
the neutral hydrogen (HI) overdensity maps at low redshifts. We investigate its
performance by comparing it directly at the field level to the simulated HI
from the IllustrisTNG simulation TNG300-1 ($L=205\ h^{-1}$ Mpc), in both real
and redshift space. We demonstrate that HI is a biased tracer of the underlying
matter field and find that the cubic bias model describes the simulated HI
power spectrum to within 1% up to $k=0.4 \;(0.3) \,h\,{\rm Mpc}^{-1}$ in real
(redshift) space at redshifts $z=0,1$. Looking at counts in cells, we find an
excellent agreement between the theory and simulations for cells as small as 5
$h^{-1}$ Mpc. These results are in line with expectations from perturbation
theory and they imply that a perturbative description of the HI field is
sufficiently accurate given the characteristics of upcoming 21cm intensity
mapping surveys. Additionally, we study the statistical properties of the model
error - the difference between the truth and the model. We show that on large
scales this error is nearly Gaussian and that it has a flat power spectrum,
with amplitude significantly lower than the standard noise inferred from the HI
power spectrum. We explain the origin of this discrepancy, discuss its
implications for the HI power spectrum Fisher matrix forecasts and argue that
it motivates the HI field-level cosmological inference. On small scales in
redshift space we use the difference between the model and the truth as a proxy
for the Fingers-of-God effect. This allows us to estimate the nonlinear
velocity dispersion of HI and show that it is smaller than for the typical
spectroscopic galaxy samples at the same redshift. Finally, we provide a simple
prescription based on the perturbative forward model which can be used to
efficiently generate accurate HI mock data, in real and redshift space.
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We revisit the Hall effect and magnetoresistivity by incorporating the
anisotropic scattering caused by apical oxygen vacancies in overdoped La-based
cuprates. The theoretical calculations within the Fermi liquid picture agree
well with a handful of anomalous magneto-transport data, better than the
results using an isotropic scattering rate alone. In particular, we obtain the
upturn of Hall coefficient $R_H$ with decreasing temperature $T$, the initial
drop of $R_H$ in magnetic field $B$ in all overdoped regimes, the linear
resistivity $\rho$ versus $B$ near the van Hove doping level, the temperature
dependence of the magnetoresistivity ratio, and the violation of Kohler's law.
These results suggest that many of the anomalous transport behaviors in
overdoped La$_{2-x}$Sr$_x$CuO$_4$ could actually be understood within the Fermi
liquid picture.
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Let $H$ be a subgroup of $\pi_{1}(X,x_{0})$. In this paper, we extend the
concept of $X$ being SLT space to $H$-SLT space at $x_0$. First, we show that
the fibers of the endpoint projection $p_{H}:\tilde{X}_{H}\rightarrow X$ are
topological group when $X$ is $H$-SLT space at $x_0$ and $H$ is a normal
subgroup. Also, we show that under these conditions the concepts of
homotopically path Hausdorff relative to $H$ and homotopically Hausdorff
relative to $H$ coincide. Moreover, among other things, we show that the
endpoint projection map $p_{H}$ has the unique path lifting property if and
only if $H$ is a closed normal subgroup of $\pi_{1}^{qtop}(X,x_{0})$ when $X$
is SLT at $x_{0}$. Second, we present conditions under which the whisker
topology is agree with the quotient of compact-open topology on
$\tilde{X}_{H}$. Also, we study the relationship between open subsets of
$\pi_{1}^{wh}(X,x_{0})$ and $\pi_{1}^{qtop}(X,x_{0})$.
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The non-classical, nonmonotonic inference relation associated with the answer
set semantics for logic programs gives rise to a relationship of 'strong
equivalence' between logical programs that can be verified in 3-valued Goedel
logic, G3, the strongest non-classical intermediate propositional logic
(Lifschitz, Pearce and Valverde, 2001). In this paper we will show that KC (the
logic obtained by adding axiom ~A v ~~A to intuitionistic logic), is the
weakest intermediate logic for which strongly equivalent logic programs, in a
language allowing negations, are logically equivalent.
|
We describe symmetries of the braid monodromy decomposition for a class of
plane curves defined over reals including the real curves with no real points
and proving new divisibility relations for Alexander invariants of such curves.
|
We study feedback control over erasure channels with packet-dropouts. To
achieve robustness with respect to packet-dropouts, the controller transmits
data packets containing plant input predictions, which minimize a finite
horizon cost function. To reduce the data size of packets, we propose to adopt
sparsity-promoting optimizations, namely, ell-1-ell-2 and ell-2-constrained
ell-0 optimizations, for which efficient algorithms exist. We derive sufficient
conditions on design parameters, which guarantee (practical) stability of the
resulting feedback control systems when the number of consecutive
packet-dropouts is bounded.
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Suppose a finite dimensional semisimple Lie algebra $\mathfrak g$ acts by
derivations on a finite dimensional associative or Lie algebra $A$ over a field
of characteristic $0$. We prove the $\mathfrak g$-invariant analogs of
Wedderburn - Mal'cev and Levi theorems, and the analog of Amitsur's conjecture
on asymptotic behavior for codimensions of polynomial identities with
derivations of $A$. It turns out that for associative algebras the differential
PI-exponent coincides with the ordinary one. Also we prove the analog of
Amitsur's conjecture for finite dimensional associative algebras with an action
of a reductive affine algebraic group by automorphisms and anti-automorphisms
or graded by an arbitrary Abelian group. In addition, we provide criteria for
$G$-, $H$- and graded simplicity in terms of codimensions.
|
This is the third part in a series of papers in which we introduce and
develop a natural, general tensor category theory for suitable module
categories for a vertex (operator) algebra. In this paper (Part III), we
introduce and study intertwining maps and tensor product bifunctors.
|
In a recent work arXiv:2008.08601, Halverson, Maiti and Stoner proposed a
description of neural networks in terms of a Wilsonian effective field theory.
The infinite-width limit is mapped to a free field theory, while finite $N$
corrections are taken into account by interactions (non-Gaussian terms in the
action). In this paper, we study two related aspects of this correspondence.
First, we comment on the concepts of locality and power-counting in this
context. Indeed, these usual space-time notions may not hold for neural
networks (since inputs can be arbitrary), however, the renormalization group
provides natural notions of locality and scaling. Moreover, we comment on
several subtleties, for example, that data components may not have a
permutation symmetry: in that case, we argue that random tensor field theories
could provide a natural generalization. Second, we improve the perturbative
Wilsonian renormalization from arXiv:2008.08601 by providing an analysis in
terms of the nonperturbative renormalization group using the Wetterich-Morris
equation. An important difference with usual nonperturbative RG analysis is
that only the effective (IR) 2-point function is known, which requires setting
the problem with care. Our aim is to provide a useful formalism to investigate
neural networks behavior beyond the large-width limit (i.e.~far from Gaussian
limit) in a nonperturbative fashion. A major result of our analysis is that
changing the standard deviation of the neural network weight distribution can
be interpreted as a renormalization flow in the space of networks. We focus on
translations invariant kernels and provide preliminary numerical results.
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In this work, we report a lattice calculation of $x$-dependent valence pion
generalized parton distributions (GPDs) at zero skewness with multiple values
of the momentum transfer $-t$. The calculations are based on an $N_f=2+1$ gauge
ensemble of highly improved staggered quarks with Wilson-Clover valence
fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to
be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD
matrix elements for both symmetric and asymmetric momenta transfers with
similar values and show the equivalence of both frames. Then, focusing on the
asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD
matrix elements obtained from the lattice calculations. After the Fourier
transforms, the quasi-GPDs are then matched to the light-cone GPDs within the
framework of large momentum effective theory with improved matching, including
the next-to-next-to-leading order perturbative corrections, and leading
renormalon and renormalization group resummations. We also present the
3-dimensional image of the pion in impact-parameter space through the Fourier
transform of the momentum transfer $-t$.
|
We show a detailed investigation of the split Kondo effect in a carbon
nanotube quantum dot with multiple gate electrodes. It is found that the
splitting decreases for increasing magnetic field, to result in a recovered
zero-bias Kondo resonance at finite magnetic field. Surprisingly, in the same
charge state, but under different gate-configurations, the splitting does not
disappear for any value of the magnetic field, but we observe an avoided
crossing of two high-conductance lines. We think that our observations can be
understood in terms of a two-impurity Kondo effect with two spins coupled
antiferromagnetically. The exchange coupling between the two spins can be
influenced by a local gate, and the non-recovery of the Kondo resonance for
certain gate configurations is explained by the existence of a small
antisymmetric contribution to the exchange interaction between the two spins.
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The world is going through a challenging phase due to the disastrous effect
caused by the COVID-19 pandemic on the healthcare system and the economy. The
rate of spreading, post-COVID-19 symptoms, and the occurrence of new strands of
COVID-19 have put the healthcare systems in disruption across the globe. Due to
this, the task of accurately screening COVID-19 cases has become of utmost
priority. Since the virus infects the respiratory system, Chest X-Ray is an
imaging modality that is adopted extensively for the initial screening. We have
performed a comprehensive study that uses CXR images to identify COVID-19 cases
and realized the necessity of having a more generalizable model. We utilize
MobileNetV2 architecture as the feature extractor and integrate it into Capsule
Networks to construct a fully automated and lightweight model termed as
MobileCaps. MobileCaps is trained and evaluated on the publicly available
dataset with the model ensembling and Bayesian optimization strategies to
efficiently classify CXR images of patients with COVID-19 from non-COVID-19
pneumonia and healthy cases. The proposed model is further evaluated on two
additional RT-PCR confirmed datasets to demonstrate the generalizability. We
also introduce MobileCaps-S and leverage it for performing severity assessment
of CXR images of COVID-19 based on the Radiographic Assessment of Lung Edema
(RALE) scoring technique. Our classification model achieved an overall recall
of 91.60, 94.60, 92.20, and a precision of 98.50, 88.21, 92.62 for COVID-19,
non-COVID-19 pneumonia, and healthy cases, respectively. Further, the severity
assessment model attained an R$^2$ coefficient of 70.51. Owing to the fact that
the proposed models have fewer trainable parameters than the state-of-the-art
models reported in the literature, we believe our models will go a long way in
aiding healthcare systems in the battle against the pandemic.
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Virtual sensing techniques have gained traction in applications to the
structural health monitoring of monopile-based offshore wind turbines, as the
strain response below the mudline, which is a primary indicator of fatigue
damage accumulation, is impractical to measure directly with physical
instrumentation. The Gaussian process latent force model (GPFLM) is a
generalized Bayesian virtual sensing technique which combines a physics-driven
model of the structure with a data-driven model of latent variables of the
system to extrapolate unmeasured strain states. In the GPLFM, modeling of
unknown sources of excitation as a Gaussian process (GP) serves to facilitate
strain estimation by providing a complete stochastic characterization of the
covariance relationship between input forces and states, using properties of
the GP covariance kernel as well as correlation information supplied by the
mechanical model. It is shown that posterior inference of the latent inputs and
states is performed by Gaussian process regression of measured accelerations,
computed efficiently using Kalman filtering and Rauch-Tung-Striebel smoothing
in an augmented state-space model. While the GPLFM has been previously
demonstrated in numerical studies to improve upon other virtual sensing
techniques in terms of accuracy, robustness, and numerical stability, this work
provides one of the first cases of in-situ validation of the GPLFM. The
predicted strain response by the GPLFM is compared to subsoil strain data
collected from an operating offshore wind turbine in the Westermeerwind Park in
the Netherlands.
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We discuss a simple model for D-brane transport in non-abelian GLSMs. The
model is the elliptic curve version of a non-abelian GLSM introduced by Hori
and Tong and has gauge group U(2). It has two geometric phases, both of which
describe the same elliptic curve, once realised as a codimension five complete
intersection in G(2,5) and once as a determinantal variety. The determinantal
phase is strongly coupled with unbroken SU(2). There are two singular points in
the moduli space where the theory has a Coulomb branch. Using grade restriction
rules, we show how to transport B-branes between the two phases along paths
avoiding the singular points. With the help of the GLSM hemisphere partition
function we compute analytic continuation matrices and monodromy matrices,
confirming results obtained by different methods.
|
We classify all one-class genera of admissible lattice chains of length at
least 2 in hermitian spaces over number fields.
|
The ongoing integration of renewable generation and distributed energy
resources introduces new challenges to distribution network operation. Due to
the increasing volatility and uncertainty, distribution system operators (DSOs)
are seeking concepts to enable more active management and control. Flexibility
markets (FMs) offer a platform for economically efficient trading of
electricity flexibility between DSOs and other participants. The integration of
cyber, physical and market domains of multiple participants makes FMs a system
of cyber-physical systems (CPSs). While cross-domain integration sets the
foundation for efficient deployment of flexibility, it introduces new physical
and cyber vulnerabilities to participants. This work systematically formulates
threat scenarios for the CPSs of FMs, revealing several remaining security
challenges across all domains. Based on the threat scenarios, unresolved
monitoring requirements for secure participation of DSOs in FMs are identified,
providing the basis for future works that address these gaps with new technical
concepts.
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Subsequent to our recent report of SDW type transition at 190 K and
antiferromagnetic order below 20 K in EuFe2As2, we have studied the effect of
K-doping on the SDW transition at high temperature and AF order at low
temperature. 50% K doping suppresses the SDW transition and in turn gives rise
to high-temperature superconductivity below T_c = 32 K, as observed in the
electrical resistivity, AC susceptibility as well as magnetization. A well
defined anomaly in the specific heat provides additional evidence for bulk
superconductivity.
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This paper is a continuation of the work on unbounded Toeplitz-like operators
$T_\Om$ with rational matrix symbol $\Om$ initiated in Groenewald et. al
(Complex Anal. Oper. Theory 15, 1(2021)), where a Wiener-Hopf type
factorization of $\Om$ is obtained and used to determine when $T_\Om$ is
Fredholm and compute the Fredholm index in case $T_\Om$ is Fredholm. Due to the
high level of non-uniqueness and complicated form of the Wiener-Hopf type
factorization, it does not appear useful in determining when $T_\Om$ is
invertible. In the present paper we use state space methods to characterize
invertibility of $T_\Om$ in terms of the existence of a stabilizing solution of
an associated nonsymmetric discrete algebraic Riccati equation, which in turn
leads to a pseudo-canonical factorization of $\Om$ and concrete formulas of
$T_\Om^{-1}$.
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The role of disorder on physical systems has been widely studied in the
macroscopic and microscopic world. While static disorder is well understood in
many cases, the impact of time-dependent disorder on quantum gases is still
poorly investigated. In our experimental setup, we introduce and characterize a
method capable of producing time-controlled optical-speckle disorder.
Experimentally, coherent light illuminates a combination of a static and a
rotating diffuser, thereby collecting a spatially varying phase due to the
diffusers' structure and a temporally variable phase due to the relative
rotation. Controlling the rotation of the diffuser allows changing the speckle
realization or, for future work, the characteristic time scale of the change of
the speckle pattern, i.e. the correlation time, matching typical time scales of
the quantum gases investigated. We characterize the speckle pattern ex-situ by
measuring its intensity distribution cross-correlating different intensity
patterns. In-situ, we observe its impact on a molecular Bose-Einstein
condensate (BEC) and cross-correlate the density distributions of BECs probed
in different speckle realizations. As one diffuser rotates relative to the
other around the common optical axis, we trace the optical speckle's intensity
cross-correlations and the quantum gas' density cross-correlations. Our results
show comparable outcomes for both measurement methods. The setup allows us to
tune the disorder potential adapted to the characteristics of the quantum gas.
These studies pave the way for investigating nonequilibrium physics in
interacting quantum gases using controlled dynamical-disorder potentials.
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Emerging storage systems with new flash exhibit ultra-low latency (ULL) that
can address performance disparities between DRAM and conventional solid state
drives (SSDs) in the memory hierarchy. Considering the advanced low-latency
characteristics, different types of I/O completion methods (polling/hybrid) and
storage stack architecture (SPDK) are proposed. While these new techniques are
expected to take costly software interventions off the critical path in
ULL-applied systems, unfortunately no study exists to quantitatively analyze
system-level characteristics and challenges of combining such newly-introduced
techniques with real ULL SSDs. In this work, we comprehensively perform
empirical evaluations with 800GB ULL SSD prototypes and characterize ULL
behaviors by considering a wide range of I/O path parameters, such as different
queues and access patterns. We then analyze the efficiencies and challenges of
the polled-mode and hybrid polling I/O completion methods (added into Linux
kernels 4.4 and 4.10, respectively) and compare them with the efficiencies of a
conventional interrupt-based I/O path. In addition, we revisit the common
expectations of SPDK by examining all the system resources and parameters.
Finally, we demonstrate the challenges of ULL SSDs in a real SPDK-enabled
server-client system. Based on the performance behaviors that this study
uncovers, we also discuss several system implications, which are required to
take a full advantage of ULL SSD in the future.
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We compute the scattering amplitudes of four massless states for chiral
(closed) bosonic and type II superstrings using the Kawai-Lewellen-Tye ($KLT$)
factorization method. The amplitude in the chiral bosonic case is identical to
a field theory amplitude corresponding to the spin-$2$ tachyon, massless
gravitational sector and massive spin-2 tardyon states of the spectrum. Chiral
type II superstrings amplitude only possess poles associated with the massless
gravitational sector. We briefly discuss the extension of the calculation to
heterotic superstrings.
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Given a graph $G$, a total labeling on $G$ is called edge-antimagic total
(respectively, vertex-antimagic total) if all edge-weights (respectively,
vertex-weights) are pairwise distinct. If a labeling on $G$ is simultaneously
edge-antimagic total and vertex-antimagic total, it is called a totally
antimagic total labeling. A graph that admits totally antimagic total labeling
is called a totally antimagic total graph. In this paper, we prove that
ladders, prisms and generalised Pertersen graphs are totally antimagic total
graphs. We also show that the chain graph of totally antimagic total graphs is
a totally antimagic total graph.
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This paper outlines a comprehensive model to increase system efficiency,
preserve network bandwidth, monitor incoming and outgoing packets, ensure the
security of confidential files and reduce power wastage in an organization.
This model illustrates the use and potential application of a Network Analysis
Tool (NAT) in a multi-computer set-up of any scale. The model is designed to
run in the background and not hamper any currently executing applications,
while using minimum system resources. It was developed as open source software,
using VB. Net, with a view to overcoming limitations of legacy systems and
financial restrictions in small-to mid-level organizations like businesses and
educational institutes. It is fully-customizable and serves as a simple and
open-source alternative to existing software. The NAT relies on simple
client-server architecture and uses remote access to monitor and maintain the
computers on a network, for example logging off a user or shutting down a
computer after a certain "idle" time, enabling and disabling applications,
troubleshooting and so on. The NAT was tested in a laboratory and resultant
data is presented, along with the results of a survey that was conducted among
users.
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In this paper we study the behavior of the solution to the dbar-Neumann
problem for (0,1)-forms on a bi-disc in C^2. We show singularities which arise
at the distinguished boundary are of logarithmic and arctangent type.
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An impact parameter dependent unintegrated gluon distribution is constructed
as a solution of a nonlinear evolution equation with realistic Glauber--Gribov
input. Photon--jet correlations in the proton fragmentation region of pA
collisions are proposed as a direct probe of the nuclear unintegrated glue.
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This paper is about alerting acoustic event detection and sound source
localisation in an urban scenario. Specifically, we are interested in spotting
the presence of horns, and sirens of emergency vehicles. In order to obtain a
reliable system able to operate robustly despite the presence of traffic noise,
which can be copious, unstructured and unpredictable, we propose to treat the
spectrograms of incoming stereo signals as images, and apply semantic
segmentation, based on a Unet architecture, to extract the target sound from
the background noise. In a multi-task learning scheme, together with signal
denoising, we perform acoustic event classification to identify the nature of
the alerting sound. Lastly, we use the denoised signals to localise the
acoustic source on the horizon plane, by regressing the direction of arrival of
the sound through a CNN architecture. Our experimental evaluation shows an
average classification rate of 94%, and a median absolute error on the
localisation of 7.5{\deg} when operating on audio frames of 0.5s, and of
2.5{\deg} when operating on frames of 2.5s. The system offers excellent
performance in particularly challenging scenarios, where the noise level is
remarkably high.
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Humans frequently make decisions with the aid of artificially intelligent
(AI) systems. A common pattern is for the AI to recommend an action to the
human who retains control over the final decision. Researchers have identified
ensuring that a human has appropriate reliance on an AI as a critical component
of achieving complementary performance. We argue that the current definition of
appropriate reliance used in such research lacks formal statistical grounding
and can lead to contradictions. We propose a formal definition of reliance,
based on statistical decision theory, which separates the concepts of reliance
as the probability the decision-maker follows the AI's recommendation from
challenges a human may face in differentiating the signals and forming accurate
beliefs about the situation. Our definition gives rise to a framework that can
be used to guide the design and interpretation of studies on human-AI
complementarity and reliance. Using recent AI-advised decision making studies
from literature, we demonstrate how our framework can be used to separate the
loss due to mis-reliance from the loss due to not accurately differentiating
the signals. We evaluate these losses by comparing to a baseline and a
benchmark for complementary performance defined by the expected payoff achieved
by a rational decision-maker facing the same decision task as the behavioral
decision-makers.
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In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and
investigate their properties.
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In Part V of this study, we presented an original Lagrangian approach for
computing the dynamic characteristics along stationary rays, by solving the
linear, second-order Jacobi differential equation, considering four sets of
initial conditions as the basic solutions. We then focused on the computation
of the geometric spreading and identification of caustics, where only the two
point-source basic solutions with their corresponding initial conditions are
required. Solutions of the Jacobi equation represent the normal shift vectors
of the paraxial rays and define the geometry of the ray tube with respect to
the stationary central ray. Rather than the Lagrangian approach, the dynamic
characteristics are traditionally computed with the Hamiltonian approach,
formulated normally in terms of two first-order differential equations, where
the solution variables are the paraxial shifts and paraxial slowness changes
along the ray. In this part (Part VI), we compare and relate the two
approaches. We first combine the two first-order Hamiltonian dynamic equations,
eliminating the paraxial variations of the slowness vector. This leads to a
second-order differential equation in terms of the Hamiltonian shift alone,
whose ray-normal counterpart coincides with the normal shift of the
corresponding Lagrangian solution, while the ray-tangent component does not
affect the Jacobian and the geometric spreading. Comparing the proposed
Lagrangian approach to the dynamic ray tracing with the "classical" Hamiltonian
approach, we demonstrate that they are fully compatible for general anisotropy.
We then derive the two-way relationships between the Hamiltonian's and
Lagrangian's Hessians, which are the core computational elements of dynamic ray
theory. Finally, we demonstrate the relationships between these two types of
the Hessians numerically, for a general triclinic medium.
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We discuss (i) the evaluation of the expectation values of four-quark
operators assuming that the heavy quark expansion for $b$ sector converges at
the third order in $1/m_Q$, and (ii) the estimation of the duality breaking
short distance nonperturbative corrections to the parton decay rate. We finally
point out the implications of the result obtained for the assumption of
quark-hadron duality in heavy quark expansion.
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Composite Higgs models with a fermionic UV completion can contain additional
colored states beside the usual top-partners. We focus here on a model which
contains in addition SU(3) color octet top partners as well as color singlet
ones. The latter can in principle serve as a dark matter candidate. We consider
a particular composite Higgs model which contains SU(3) color octet top
partners besides the usually considered triplet representations. Moreover,
color singlet top partners are present as well which can in principle serve as
dark matter candidates. We investigate the LHC phenomenology of these unusual
top partners. Some of these states could at first glance be confused with
gluinos predicted in supersymmetric models.
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We investigate whether sophisticated volatility estimation improves the
out-of-sample performance of mean-variance portfolio strategies relative to the
naive 1/N strategy. The portfolio strategies rely solely upon second moments.
Using a diverse group of econometric and portfolio models across multiple
datasets, most models achieve higher Sharpe ratios and lower portfolio
volatility that are statistically and economically significant relative to the
naive rule, even after controlling for turnover costs. Our results suggest
benefits to employing more sophisticated econometric models than the sample
covariance matrix, and that mean-variance strategies often outperform the naive
portfolio across multiple datasets and assessment criteria.
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The nonperturbative approach to soft high-energy hadron-hadron scattering,
based on the analytic continuation of Euclidean Wilson-loop correlation
functions, makes possible the investigation of the problem of the asymptotic
energy dependence of hadron-hadron total cross sections by means of lattice
calculations. In this contribution we compare the lattice numerical results to
analytic results obtained with various nonperturbative techniques. We also
discuss the possibility to obtain indications of the rise of hadron-hadron
total cross sections with energy directly from the lattice data.
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Understanding the similarity of the numerous released large language models
(LLMs) has many uses, e.g., simplifying model selection, detecting illegal
model reuse, and advancing our understanding of what makes LLMs perform well.
In this work, we measure the similarity of representations of a set of LLMs
with 7B parameters. Our results suggest that some LLMs are substantially
different from others. We identify challenges of using representational
similarity measures that suggest the need of careful study of similarity scores
to avoid false conclusions.
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In this paper, we consider the transmit design for multi-input multi-output
(MIMO) wiretap channel including a malicious jammer. We first transform the
system model into the traditional three-node wiretap channel by whitening the
interference at the legitimate user. Additionally, the eavesdropper channel
state information (ECSI) may be fully or statistically known, even unknown to
the transmitter. Hence, some strategies are proposed in terms of different
levels of ECSI available to the transmitter in our paper. For the case of
unknown ECSI, a target rate for the legitimate user is first specified. And
then an inverse water-filling algorithm is put forward to find the optimal
power allocation for each information symbol, with a stepwise search being used
to adjust the spatial dimension allocated to artificial noise (AN) such that
the target rate is achievable. As for the case of statistical ECSI, several
simulated channels are randomly generated according to the distribution of
ECSI. We show that the ergodic secrecy capacity can be approximated as the
average secrecy capacity of these simulated channels. Through maximizing this
average secrecy capacity, we can obtain a feasible power and spatial dimension
allocation scheme by using one dimension search. Finally, numerical results
reveal the effectiveness and computational efficiency of our algorithms.
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In this paper, we study the embedded feature selection problem in linear
Support Vector Machines (SVMs), in which a cardinality constraint is employed,
leading to a fully explainable selection model. The problem is NP-hard due to
the presence of the cardinality constraint, even though the original linear SVM
amounts to a problem solvable in polynomial time. To handle the hard problem,
we first introduce two mixed-integer formulations for which novel SDP
relaxations are proposed. Exploiting the sparsity pattern of the relaxations,
we decompose the problems and obtain equivalent relaxations in a much smaller
cone, making the conic approaches scalable. To make the best usage of the
decomposed relaxations, we propose heuristics using the information of its
optimal solution. Moreover, an exact procedure is proposed by solving a
sequence of mixed-integer decomposed SDPs. Numerical results on classical
benchmarking datasets are reported, showing the efficiency and effectiveness of
our approach.
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Social influence cannot be identified from purely observational data on
social networks, because such influence is generically confounded with latent
homophily, i.e., with a node's network partners being informative about the
node's attributes and therefore its behavior. If the network grows according to
either a latent community (stochastic block) model, or a continuous latent
space model, then latent homophilous attributes can be consistently estimated
from the global pattern of social ties. We show that, for common versions of
those two network models, these estimates are so informative that controlling
for estimated attributes allows for asymptotically unbiased and consistent
estimation of social-influence effects in linear models. In particular, the
bias shrinks at a rate which directly reflects how much information the network
provides about the latent attributes. These are the first results on the
consistent non-experimental estimation of social-influence effects in the
presence of latent homophily, and we discuss the prospects for generalizing
them.
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With the rise of Deep Learning (DL), our world braces for AI in every edge
device, creating an urgent need for edge-AI SoCs. This SoC hardware needs to
support high throughput, reliable and secure AI processing at Ultra Low Power
(ULP), with a very short time to market. With its strong legacy in edge
solutions and open processing platforms, the EU is well-positioned to become a
leader in this SoC market. However, this requires AI edge processing to become
at least 100 times more energy-efficient, while offering sufficient flexibility
and scalability to deal with AI as a fast-moving target. Since the design space
of these complex SoCs is huge, advanced tooling is needed to make their design
tractable. The CONVOLVE project (currently in Inital stage) addresses these
roadblocks. It takes a holistic approach with innovations at all levels of the
design hierarchy. Starting with an overview of SOTA DL processing support and
our project methodology, this paper presents 8 important design choices largely
impacting the energy efficiency and flexibility of DL hardware. Finding good
solutions is key to making smart-edge computing a reality.
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The abundance of H2 in molecular clouds, relative to the commonly used tracer
CO, has only been measured toward a few embedded stars, which may be surrounded
by atypical gas. We present observations of near-infrared absorption by H2, CO,
and dust toward stars behind molecular clouds, providing a representative
sample of these molecules in cold molecular gas, primarily in the Taurus
Molecular Cloud. We find N_H2/A_V ~ 1.0x10^21 cm^-2, N_CO/A_V ~ 1.5x10^17 cm^-2
(1.8x10^17 including solid CO), and N_H2/N_CO ~ 6000. The measured N_H2/N_CO
ratio is consistent with that toward embedded stars in various molecular
clouds, but both are less than that derived from mm-wave observations of CO and
star counts. The difference apparently results from the higher directly
measured N_CO/A_V ratio.
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We consider homogeneous STIT tessellations Y in the \ell-dimensional
Euclidean space and show the triviality of the tail \sigma-algebra. This is a
sharpening of the mixing result by Lachi\`eze-Rey.
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We study projections in the bidual of a $C^*$-algebra $B$ that are null with
respect to a subalgebra $A$, that is projections $p\in B^{**}$ satisfying
$|\phi|(p)=0$ for every $\phi\in B^*$ annihilating $A$. In the separable case,
$A$-null projections are precisely the peak projections in the bidual of $A$ at
which the subalgebra $A$ interpolates the entire $C^*$-algebra $B$. These are
analogues of null sets in classical function theory, on which several profound
results rely. This motivates the development of a noncommutative variant, which
we use to find appropriate `quantized' versions of some of these classical
facts. Through a delicate generalization of a theorem of Varopoulos, we show
that, roughly speaking, sufficiently regular interpolation projections are null
precisely when their atomic parts are. As an application, we give alternative
proofs and sharpenings of some recent peak-interpolation results of Davidson
and Hartz for algebras on Hilbert function spaces, also illuminating thereby
how earlier noncommutative peak-interpolation theory may be applied. In another
direction, given a convex subset of the state space of $B$, we characterize
when the associated Riesz projection is null. This is then applied to various
important topics in noncommutative function theory, such as the F.& M. Riesz
property, the existence of Lebesgue decompositions, the description of Henkin
functionals, and Arveson's noncommutative Hardy spaces (maximal subdiagonal
algebras).
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The distribution of transversely polarized quarks inside a transversely
polarized nucleon, known as transversity, encodes a basic piece of information
on the nucleon structure, sharing the same status with the more familiar
unpolarized and helicity distributions. I will review its properties and
discuss different ways to access it, with highlights and limitations. Recent
phenomenological extractions and perspectives are also presented.
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Analog and digital quantum simulators can efficiently simulate quantum
many-body systems that appear in natural phenomena. However, experimental
limitations of near-term devices still make it challenging to perform the
entire process of quantum simulation. The purification-based quantum simulation
methods can alleviate the limitations in experiments such as the cooling
temperature and noise from the environment, while this method has the drawback
that it requires global entangled measurement with a prohibitively large number
of measurements that scales exponentially with the system size. In this Letter,
we propose that we can overcome these problems by restricting the entangled
measurements to the vicinity of the local observables to be measured, when the
locality of the system can be exploited. We provide theoretical guarantees that
the global purification operation can be replaced with local operations under
some conditions, in particular for the task of cooling and error mitigation. We
furthermore give a numerical verification that the localized purification is
valid even when conditions are not satisfied. Our method bridges the
fundamental concept of locality with quantum simulators, and therefore expected
to open a path to unexplored quantum many-body phenomena.
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With the advances in customized hardware for quantum annealing and
digital/CMOS Annealing, Quadratic Unconstrained Binary Optimization (QUBO)
models have received growing attention in the optimization literature.
Motivated by an existing general-purpose approach that derives QUBO models from
binary linear programs (BLP), we propose a novel Multilevel Constraint
Transformation Scheme (MLCTS) that derives QUBO models with fewer ancillary
binary variables. We formulate sufficient conditions for the existence of a
compact QUBO formulation (i.e., in the original BLP decision space) in terms of
constraint levelness and demonstrate the flexibility and applicability of MLCTS
on synthetic examples and several well-known combinatorial optimization
problems, i.e., the Maximum 2-Satisfiability Problem, the Linear Ordering
Problem, the Community Detection Problem, and the Maximum Independence Set
Problem. For a proof-of-concept, we compare the performance of two QUBO models
for the latter problem on both a general-purpose software-based solver and a
hardware-based QUBO solver. The MLCTS-derived models demonstrate significantly
better performance for both solvers, in particular, solving up to seven times
more instances with the hardware-based approach.
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We measure the rest-frame B-band luminosity function of red-sequence galaxies
(RSLF) of five intermediate-redshift (0.5 < z < 0.9), high-mass (sigma > 950
km/s) clusters. Cluster galaxies are identified through photometric redshifts
based on imaging in seven bands (five broad, and two narrow) using the WIYN
3.5m telescope. The luminosity functions are well-fit down to M_B^*+3 for all
of the clusters out to a radius of R_200. For comparison, the luminosity
functions for a sample of 59 low redshift clusters selected from the SDSS are
measured as well. There is a brightening trend (M_B^* increases by 0.7 mags by
z=0.75) with redshift comparable to what is seen in the field for similarly
defined galaxies, although there is a hint that the cluster red-sequence
brightening is more rapid in the past (z>0.5), and relatively shallow at more
recent times. Contrary to other claims, we find little evidence for evolution
of the faint end slope. Previous indications of evolution may be due to
limitations in measurement technique, bias in the sample selection, and cluster
to cluster variation. As seen in both the low and high redshift sample, a
significant amount of variation in luminosity functions parameters alpha and
M^* exists between individual clusters.
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For the innovation of spintronic technologies, Dirac materials, in which the
low-energy excitation is described as relativistic Dirac fermions, are one of
the most promising systems, because of the fascinating magnetotransport
associated with the extremely high mobility. To incorporate Dirac fermions into
spintronic applications, their quantum transport phenomena are desired to be
manipulated to a large extent by magnetic order in a solid. We here report a
bulk half-integer quantum Hall effect in a layered antiferromagnet EuMnBi$_2$,
in which field-controllable Eu magnetic order significantly suppresses the
interlayer coupling between the Bi layers with Dirac fermions. In addition to
the high mobility more than 10,000 cm$^2$/Vs, Landau level splittings
presumably due to the lifting of spin and valley degeneracy are noticeable even
in a bulk magnet. These results will pave a route to the engineering of
magnetically functionalized Dirac materials.
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This paper presents a framework that supports the implementation of parallel
solutions for the widespread parametric maximum flow computational routines
used in image segmentation algorithms. The framework is based on supergraphs, a
special construction combining several image graphs into a larger one, and
works on various architectures (multi-core or GPU), either locally or remotely
in a cluster of computing nodes. The framework can also be used for performance
evaluation of parallel implementations of maximum flow algorithms. We present
the case study of a state-of-the-art image segmentation algorithm based on
graph cuts, Constrained Parametric Min-Cut (CPMC), that uses the parallel
framework to solve parametric maximum flow problems, based on a GPU
implementation of the well-known push-relabel algorithm. Our results indicate
that real-time implementations based on the proposed techniques are possible.
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We present a method of generation of exact and explicit forms of one-sided,
heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x <
\infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a
distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2,
3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta <
1, we obtain g_{\alpha \beta}(x). The method is based on the construction of
the integral operator, called Levy transform, which implements the above
operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this
manner many of the recently obtained exact results for g_{l/k}(x). This
approach can be also recast as an application of the Efros theorem for
generalized Laplace convolutions. It relies solely on efficient definite
integration.
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A theorem of Graber, Harris, and Starr states that a rationally connected
fibration over a curve has a section. We study an analogous question in
symplectic geometry. Namely, given a rationally connected fibration over a
curve, can one find a section which gives a non-zero Gromov-Witten invariant?
We observe that for any fibration, the existence of a section which gives a
non-zero Gromov-Witten invariant only depends on the generic fiber, i.e. a
variety defined over the function field of a curve. Some examples of rationally
connected fibrations with this property are given, including all rational
surface fibrations. We also prove some results, which says that in certain
cases we can "lift" Gromov-Witten invariants of the base to the total space of
a rationally connected fibration.
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We investigate hybrid structures based on a bilayer quantum spin Hall system
in proximity to an s-wave superconductor as a platform to mimic time-reversal
symmetric topological superconductors. In this bilayer setup, the induced
pairing can be of intra- or inter-layer type, and domain walls of those
different types of pairing potentials host Kramers partners (time-reversal
conjugate pairs) of Majorana bound states. Interestingly, we discover that such
topological interfaces providing Majorana bound states can also be achieved in
an otherwise homogeneous system by a spatially dependent inter-layer gate
voltage. This gate voltage causes the relative electron densities of the two
layers to vary accordingly which suppresses the inter-layer pairing in regions
with strong gate voltage. We identify particular transport signatures
(zero-bias anomalies) in a five-terminal setup that are uniquely related to the
presence of Kramers pairs of Majorana bound states.
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