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We analyze numerically ensembles of tight-binding Hamiltonians describing
highly-symmetric graphene nanoflakes with weak diagonal disorder induced by
random electrostatic potential landscapes. When increasing the disorder
strength, statistical distribution of energy levels evolves from Poissonian to
Wigner, indicating the transition to quantum chaos. Power laws with the
universal exponent map the disorder strength in nanoflakes of different sizes,
boundaries, and microscopic disorder types onto a single parameter in additive
random-matrix model.
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Invariant conditions for conformable fractional problems of the calculus of
variations under the presence of external forces in the dynamics are studied.
Depending on the type of transformations considered, different necessary
conditions of invariance are obtained. As particular cases, we prove fractional
versions of Noether's symmetry theorem. Invariant conditions for fractional
optimal control problems, using the Hamiltonian formalism, are also
investigated. As an example of potential application in Physics, we show that
with conformable derivatives it is possible to formulate an Action Principle
for particles under frictional forces that is far simpler than the one obtained
with classical fractional derivatives.
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We study the BPS domain walls of supersymmetric Yang-Mills for arbitrary
gauge group. We describe the degeneracies of domain walls interpolating between
arbitrary pairs of vacua. A recently proposed large N duality sheds light on
various aspects of such domain walls. In particular, for the case of G = SU(N)
the domain walls correspond to wrapped D-branes giving rise to a 2+1
dimensional U(k) gauge theory on the domain wall with a Chern-Simons term of
level N. This leads to a counting of BPS degeneracies of domain walls in
agreement with expected results.
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We present a review of theories of states of quantum matter without
quasiparticle excitations. Solvable examples of such states are provided
through a holographic duality with gravitational theories in an emergent
spatial dimension. We review the duality between gravitational backgrounds and
the various states of quantum matter which live on the boundary. We then
describe quantum matter at a fixed commensurate density (often described by
conformal field theories), and also compressible quantum matter with variable
density, providing an extensive discussion of transport in both cases. We
present a unified discussion of the holographic theory of transport with memory
matrix and hydrodynamic methods, allowing a direct connection to experimentally
realized quantum matter. We also explore other important challenges in
non-quasiparticle physics, including symmetry broken phases such as
superconductors and non-equilibrium dynamics.
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We consider an exponentially stable closed loop interconnection of a
continuous linear plant and a continuous linear controller, and we study the
problem of interconnecting the plant output to the controller input through a
digital channel. We propose a family of "transmission-lazy" sensors whose goal
is to transmit the measured plant output information as little as possible
while preserving closed-loop stability. In particular, we propose two
transmission policies, providing conditions on the transmission parameters.
These guarantee global asymptotic stability when the plant state is available
or when an estimate of the state is available (provided by a classical
continuous linear observer). Moreover, under a specific condition, they
guarantee global exponential stability
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We use the perturbation method to calculate the masses and widths for 27-plet
baryons with spin 3/2 from chiral soliton models. According to the masses and
quantum numbers, we find all the candidates for non-exotic members of 27-plet.
The calculation of the widths shows that these candidates manifest an
approximate symmetry of the 27 representation of the SU(3) group, and the
quantum numbers of $\Xi(1950)$ seem to be $I(J^P)={1/2}({3/2}^+)$. Up to
leading order of the strange quark mass, we find that the exotic members have
widths much larger than those of the anti-decuplet members.
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In recent years, a variety of gradient-based first-order methods have been
developed to solve bi-level optimization problems for learning applications.
However, theoretical guarantees of these existing approaches heavily rely on
the simplification that for each fixed upper-level variable, the lower-level
solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this
work, we first design a counter-example to illustrate the invalidation of such
LLS condition. Then by formulating BLPs from the view point of optimistic
bi-level and aggregating hierarchical objective information, we establish
Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic
framework for generic bi-level optimization. Theoretically, we derive a new
methodology to prove the convergence of BDA without the LLS condition. Our
investigations also demonstrate that BDA is indeed compatible to a verify of
particular first-order computation modules. Additionally, as an interesting
byproduct, we also improve these conventional first-order bi-level schemes
(under the LLS simplification). Particularly, we establish their convergences
with weaker assumptions. Extensive experiments justify our theoretical results
and demonstrate the superiority of the proposed BDA for different tasks,
including hyper-parameter optimization and meta learning.
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Generative networks implicitly approximate complex densities from their
sampling with impressive accuracy. However, because of the enormous scale of
modern datasets, this training process is often computationally expensive. We
cast generative network training into the recent framework of compressive
learning: we reduce the computational burden of large-scale datasets by first
harshly compressing them in a single pass as a single sketch vector. We then
propose a cost function, which approximates the Maximum Mean Discrepancy
metric, but requires only this sketch, which makes it time- and
memory-efficient to optimize.
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This is a survey of the book arXiv:0810.5645 with Yinan Song. Let X be a
Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers
DT^a(t) which count stable sheaves with Chern character a on X, with respect to
a Gieseker stability condition t. They are defined only for Chern characters a
for which there are no strictly semistable sheaves on X. They have the good
property that they are unchanged under deformations of X. Their behaviour under
change of stability condition t was not understood until now.
We discuss "generalized Donaldson-Thomas invariants" \bar{DT}^a(t). These are
rational numbers, defined for all Chern characters a, and are equal to DT^a(t)
if there are no strictly semistable sheaves in class a. They are
deformation-invariant, and have a known transformation law under change of
stability condition. We conjecture they can be written in terms of integral
"BPS invariants" \hat{DT}^a(t) when the stability condition t is "generic".
We extend the theory to abelian categories of representations of a quiver
with relations coming from a superpotential, and connect our ideas with
Szendroi's "noncommutative Donaldson-Thomas invariants" and work by Reineke and
others. There is significant overlap between arXiv:0810.5645 and the
independent paper arXiv:0811.2435 by Kontsevich and Soibelman.
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We consider pairs of commuting isometries that are annihilated by a
polynomial. We show that the polynomial must be inner toral, which is a
geometric condition on its zero set. We show that cyclic pairs of commuting
isometries are nearly unitarily equivalent if they are annihilated by the same
minimal polynomial.
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Structured codes based on lattices were shown to provide enlarged capacity
for multi-user communication networks. In this paper, we study
capacity-approaching irregular repeat accumulate (IRA) codes over integer rings
$\mathbb{Z}_{2^{m}}$ for $2^m$-PAM signaling, $m=1,2,\cdots$. Such codes
feature the property that the integer sum of $K$ codewords belongs to the
extended codebook (or lattice) w.r.t. the base code. With it, \emph{%
structured binning} can be utilized and the gains promised in lattice based
network information theory can be materialized in practice. In designing IRA
ring codes, we first analyze the effect of zero-divisors of integer ring on the
iterative belief-propagation (BP) decoding, and show the invalidity of
symmetric Gaussian approximation. Then we propose a doubly IRA (D-IRA) ring
code structure, consisting of \emph{irregular multiplier distribution} and
\emph{irregular node-degree distribution}, that can restore the symmetry and
optimize the BP decoding threshold. For point-to-point AWGN channel with $% 2^m
$-PAM inputs, D-IRA ring codes perform as low as 0.29 dB to the capacity
limits, outperforming existing bit-interleaved coded-modulation (BICM) and IRA
modulation codes over GF($2^m$). We then proceed to design D-IRA ring codes for
two important multi-user communication setups, namely compute-forward (CF) and
dirty paper coding (DPC), with $2^m$-PAM signaling. With it, a physical-layer
network coding scheme yields a gap to the CF limit by 0.24 dB, and a simple
linear DPC scheme exhibits a gap to the capacity by 0.91 dB.
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This article describes a set of methods for quickly computing the solution to
the regularized optimal transport problem. It generalizes and improves upon the
widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp
algorithm). We first propose to rely on regularized nonlinear acceleration
schemes. In practice, such approaches lead to fast algorithms, but their global
convergence is not ensured. Hence, we next propose a new algorithm with
convergence guarantees. The idea is to overrelax the Bregman projection
operators, allowing for faster convergence. We propose a simple method for
establishing global convergence by ensuring the decrease of a Lyapunov function
at each step. An adaptive choice of overrelaxation parameter based on the
Lyapunov function is constructed. We also suggest a heuristic to choose a
suitable asymptotic overrelaxation parameter, based on a local convergence
analysis. Our numerical experiments show a gain in convergence speed by an
order of magnitude in certain regimes.
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We present the result for the invariant B_K factor of K0-anti-K0 mixing in
the chiral limit and to next-to-leading order in the 1/Nc expansion. We
explicitly demonstrate the cancellation of the renormalization scale and scheme
dependences between short- and long-distance contributions in the final
expression. Numerical estimates are then given, by taking into account
increasingly refined short- and long-distance constraints of the underlying QCD
Green's function which governs the B_K factor.
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Violation of Lorentz symmetry can result in two distinct effects in the
propagation of the gravitational waves (GWs). One is a modified dispersion
relation and another is a frequency-dependent damping of GWs. While the former
has been extensively studied in the literature, in this paper we concentrate on
the frequency-dependent damping effect that arises from several specific
Lorentz-violating theories, such as spatial covariant gravities,
Ho\v{r}ava-Lifshitz gravities, etc. This Lorentz-violating damping effect
changes the damping rate of GWs at different frequencies and leads to an
amplitude correction to the GW waveform of compact binary inspiral systems.
With this modified waveform, we then use the Fisher information matrix to
investigate the prospects of constraining the Lorentz-violating damping effect
with GW observations. We consider both ground-based and space-based GW
detectors, including the advanced LIGO, Einstein Telescope, Cosmic Explorer
(CE), Taiji, TianQin, and LISA. Our results indicate that the ground-based
detectors in general give tighter constraints than those from the space-based
detectors. Among the considered three ground-based detectors, CE can give the
tightest constraints on the Lorentz-violating damping effect, which improves
the current constraint from LIGO-Virgo-KAGRA events by about 8 times.
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The purpose of this article is to study the strict convexity of the Mabuchi
functional along a $C^{1,1}$-geodesic, with the aid of the
$\epsilon$-geodesics. We proved the $L^2$-convergence of the fiberwise volume
element of the $\epsilon$-geodesic. Moreover, the geodesic is proved to be
uniformly fiberwise non-degenerate if the Mabuchi functional is
$\epsilon$-affine.
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We present a three-dimensional (3D) study of common envelope events (CEEs) to
provide a foundation for future one-dimensional (1D) methods to model the
self-regulated phase of a CEE. The considered CEEs with a low-mass red giant
end with one of three different outcomes -- merger, slow spiral-in, or prompt
formation of a binary. To understand which physical processes determine
different outcomes, and to evaluate how well 1D simulations model the
self-regulated phase of a CEE, we introduce tools that map our 3D models to 1D
profiles. We discuss the differences in the angular momentum and energy
redistribution in 1D and 3D codes. We identified four types of ejection
processes: the pre-plunge-in ejection, the outflow during the plunge-in, the
outflow driven by recombination, and the ejection triggered by a contraction of
the circumbinary envelope. Significant mass is lost in all cases, including the
mergers. Therefore a self-regulated spiral-in can start only with a strongly
reduced envelope mass. We derive the condition to start a recombination
outflow, which can proceed either as a runaway or a stationary outflow. We show
that the way the energy of the inspiraling companion is added to the envelope
in 1D studies intensifies the envelope's entropy increase, alters the start of
the recombination outflow, and leads to different outcomes in 1D and 3D
studies. The steady recombination outflow may dispel most of the envelope in
all slow spiral-in cases, making the existence of a long-term self-regulated
phase debatable, at least for low-mass giant donors.
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Given a group $G$ and a class of manifolds $\CC$ (e.g. symplectic, contact,
K\"ahler etc), it is an old problem to find a manifold $M_G \in \CC$ whose
fundamental group is $G$. This article refines it: for a group $G$ and a
positive integer $r$ find $M_G \in \CC$ such that $\pi_1(M_G)=G$ and
$\pi_i(M_G)=0$ for $1<i<r$. We thus provide a unified point of view
systematizing known and new results in this direction for various different
classes of manifolds. The largest $r$ for which such an $M_G \in \CC$ can be
found is called the homotopical height $ht_\CC(G)$. Homotopical height provides
a dimensional obstruction to finding a $K(G,1)$ space within the given class
$\CC$, leading to a hierarchy of these classes in terms of "softness" or
"hardness" \`a la Gromov. We show that the classes of closed contact, CR, and
almost complex manifolds as well as the class of (open) Stein manifolds are
soft.
The classes $\SP$ and $\CA$ of closed symplectic and complex manifolds
exhibit intermediate "softness" in the sense that every finitely presented
group $G$ can be realized as the fundamental group of a manifold in $\SP$ and a
manifold in $\CA$. For these classes, $ht_\CC(G)$ provides a numerical
invariant for finitely presented groups. We give explicit computations of these
invariants for some standard finitely presented groups.
We use the notion of homotopical height within the "hard" category of
K\"ahler groups to obtain partial answers to questions of Toledo regarding
second cohomology and second group cohomology of K\"ahler groups. We also
modify and generalize a construction due to Dimca, Papadima and Suciu to give a
potentially large class of projective groups violating property FP.
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We investigate the influence of dissipation on one- and two-qubit rotations
in coupled semiconductor quantum dots, using a (pseudo) spin-boson model with
adiabatically varying parameters. For weak dissipation, we solve a master
equation, compare with direct perturbation theory, and derive an expression for
the `fidelity loss' during a simple operation that adiabatically moves an
electron between two coupled dots. We discuss the possibility of visualizing
coherent quantum oscillations in electron `pump' currents, combining quantum
adiabaticity and Coulomb blockade. In two-qubit spin-swap operations where the
role of intermediate charge states has been discussed recently, we apply our
formalism to calculate the fidelity loss due to charge tunneling between two
dots.
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In this contribution, we consider the problem of blind source separation in a
Bayesian estimation framework. The wavelet representation allows us to assign
an adequate prior distribution to the wavelet coefficients of the sources. MCMC
algorithms are implemented to test the validity of the proposed approach, and
the non linear approximation of the wavelet transform is exploited to aleviate
the algorithm.
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Building Energy Rating (BER) stands as a pivotal metric, enabling building
owners, policymakers, and urban planners to understand the energy-saving
potential through improving building energy efficiency. As such, enhancing
buildings' BER levels is expected to directly contribute to the reduction of
carbon emissions and promote climate improvement. Nonetheless, the BER
assessment process is vulnerable to missing and inaccurate measurements. In
this study, we introduce \texttt{CLEAR}, a data-driven approach designed to
scrutinize the inconsistencies in BER assessments through self-supervised
contrastive learning. We validated the effectiveness of \texttt{CLEAR} using a
dataset representing Irish building stocks. Our experiments uncovered evidence
of inconsistent BER assessments, highlighting measurement data corruption
within this real-world dataset.
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This article provides a quantitative analysis of privacy-compromising
mechanisms on 1 million popular websites. Findings indicate that nearly 9 in 10
websites leak user data to parties of which the user is likely unaware; more
than 6 in 10 websites spawn third- party cookies; and more than 8 in 10
websites load Javascript code from external parties onto users' computers.
Sites that leak user data contact an average of nine external domains,
indicating that users may be tracked by multiple entities in tandem. By tracing
the unintended disclosure of personal browsing histories on the Web, it is
revealed that a handful of U.S. companies receive the vast bulk of user data.
Finally, roughly 1 in 5 websites are potentially vulnerable to known National
Security Agency spying techniques at the time of analysis.
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When sharing data among researchers or releasing data for public use, there
is a risk of exposing sensitive information of individuals in the data set.
Data synthesis (DS) is a statistical disclosure limitation technique for
releasing synthetic data sets with pseudo individual records. Traditional DS
techniques often rely on strong assumptions of a data intruder's behaviors and
background knowledge to assess disclosure risk. Differential privacy (DP)
formulates a theoretical approach for a strong and robust privacy guarantee in
data release without having to model intruders' behaviors. Efforts have been
made aiming to incorporate the DP concept in the DS process. In this paper, we
examine current DIfferentially Private Data Synthesis (DIPS) techniques for
releasing individual-level surrogate data for the original data, compare the
techniques conceptually, and evaluate the statistical utility and inferential
properties of the synthetic data via each DIPS technique through extensive
simulation studies. Our work sheds light on the practical feasibility and
utility of the various DIPS approaches, and suggests future research directions
for DIPS.
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In the framework of finite temperature conformal scalar field theory on de
Sitter space-time the linearized Einstein equations for the renormalized stress
tensor are exactly solved. In this theory quantum field fluctuations are
concentrated near two spheres of the de Sitter radius, propagating as light
wave fronts. Related cosmological aspects are shortly discussed. The analysis,
performed for flat expanding universe, shows exponential damping of the
back-reaction effects far from these spherical objects. The obtained solutions
for the semiclassical Einstein equations in de Sitter background can be
straightforwardly extended also to the anti-de Sitter geometry.
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We present radio observations and optical spectroscopy of the giant low
surface brightness (LSB) galaxy PGC 045080 (or 1300+0144). PGC 045080 is a
moderately distant galaxy having a highly inclined optical disk and massive HI
gas content. Radio continuum observations of the galaxy were carried out at 320
MHz, 610 MHz and 1.4 GHz. Continuum emission was detected and mapped in the
galaxy. The emission appears extended over the inner disk at all three
frequencies. At 1.4 GHz and 610 MHz it appears to have two distinct lobes. We
also did optical spectroscopy of the galaxy nucleus; the spectrum did not show
any strong emission lines associated with AGN activity but the presence of a
weak AGN cannot be ruled out. Furthermore, comparison of the H$\alpha$ flux and
radio continuum at 1.4 GHz suggests that a significant fraction of the emission
is non-thermal in nature. Hence we conclude that a weak or hidden AGN may be
present in PGC 045080. The extended radio emission represents lobes/jets from
the AGN. These observations show that although LSB galaxies are metal poor and
have very little star formation, their centers can host significant AGN
activity. We also mapped the HI gas disk and velocity field in PGC 045080. The
HI disk extends well beyond the optical disk and appears warped. In the HI
intensity maps, the disk appears distinctly lopsided. The velocity field is
disturbed on the lopsided side of the disk but is fairly uniform in the other
half. We derived the HI rotation curve for the galaxy from the velocity field.
The rotation curve has a flat rotation speed of ~ 190 km/s.
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Determination of fundamental parameters of stars impacts all fields of
astrophysics, from galaxy evolution to constraining the internal structure of
exoplanets. This paper presents a detailed spectroscopic analysis of Barnard's
star that compares an exceptionally high-quality (an average signal-to-noise
ratio of $\sim$1000 in the entire domain), high-resolution NIR spectrum taken
with CFHT/SPIRou to PHOENIX-ACES stellar atmosphere models. The observed
spectrum shows thousands of lines not identified in the models with a similar
large number of lines present in the model but not in the observed data. We
also identify several other caveats such as continuum mismatch, unresolved
contamination and spectral lines significantly shifted from their expected
wavelengths, all of these can be a source of bias for abundance determination.
Out of $>10^4$ observed lines in the NIR that could be used for chemical
spectroscopy, we identify a short list of a few hundred lines that are
reliable. We present a novel method for determining the effective temperature
and overall metallicity of slowly-rotating M dwarfs that uses several groups of
lines as opposed to bulk spectral fitting methods. With this method, we infer
$T_{eff}$ = 3231 $\pm$ 21 K for Barnard's star, consistent with the value of
3238 $\pm$ 11 K inferred from the interferometric method. We also provide
abundance measurements of 15 different elements for Barnard's star, including
the abundances of four elements (K, O, Y, Th) never reported before for this
star. This work emphasizes the need to improve current atmosphere models to
fully exploit the NIR domain for chemical spectroscopy analysis.
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The semiconductor industry is one of the most technology-evolving and
capital-intensive market sectors. Effective inspection and metrology are
necessary to improve product yield, increase product quality and reduce costs.
In recent years, many semiconductor manufacturing equipments are equipped with
sensors to facilitate real-time monitoring of the production process. These
production-state and equipment-state sensor data provide an opportunity to
practice machine-learning technologies in various domains, such as
anomaly/fault detection, maintenance scheduling, quality prediction, etc. In
this work, we focus on the task of soft sensing regression, which uses sensor
data to predict impending inspection measurements that used to be measured in
wafer inspection and metrology systems. We proposed an LSTM-based regressor and
designed two loss functions for model training. Although engineers may look at
our prediction errors in a subjective manner, a new piece-wise evaluation
metric was proposed for assessing model accuracy in a mathematical way. The
experimental results demonstrated that the proposed model can achieve accurate
and early prediction of various types of inspections in complicated
manufacturing processes.
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The discrete variable representation (DVR) basis is nearly optimal for
numerically representing wave functions in nuclear physics: Suitable problems
enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that
one can often use smaller basis sets than with the traditional harmonic
oscillator basis, and still benefit from the simple analytic properties of the
DVR bases which requires no overlap integrals, simply permit using various
Jacobi coordinates, and admit straightforward analyses of the ultraviolet and
infrared convergence properties.
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The top quark flavor changing neutral current (FCNC) process is an excellent
probe to search for new physics in top sector since the Standard Model
expectation is extremely suppressed. We explore Higgs-mediated top quark FCNC,
focusing on $H$-$t$-$c$ Yukawa coupling $\lambda_{ct}$ within the general two
Higgs doublet model. After electroweak symmetry breaking the top quark FCNC
couplings are included in the charged Higgs Yukawa sector so that they
contribute to various processes in flavor physics. To probe $\lambda_{ct}$, we
study anomalous single top production and the same sign top pair production at
the LHC in association with flavor physics from the tree-level processes $B\to
D^{(*)}\tau\nu$, $B\to \tau \nu$ as well as from the loop-level processes $B_d
\to X_s \gamma$, $B_{d,s}-{\overline B}_{d,s}$ mixing. We perform combined
analysis of all the constraints regarding the fine-tuning argument to fit the
data and discuss future prospect. The recently updated measurements on $B\to
D^{(*)}\tau\nu$ still prefer large $\lambda_{ct}$, but we show that the current
bound on the same sign top pair production at the LHC gives the most
significant upper bound on $\lambda_{ct}$ to be less than $10\sim30$ depending
on neutral heavy Higgs masses. We also find that for the given upper bound on
$\lambda_{ct}$, $B\to D^{(*)}\tau\nu$ put significant lower bound on
$H$-$\tau$-$\tau$ Yukawa coupling, and the bound is proportional to the charged
Higgs mass.
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The COVID-19 pandemic continues to severely undermine the prosperity of the
global health system. To combat this pandemic, effective screening techniques
for infected patients are indispensable. There is no doubt that the use of
chest X-ray images for radiological assessment is one of the essential
screening techniques. Some of the early studies revealed that the patient's
chest X-ray images showed abnormalities, which is natural for patients infected
with COVID-19. In this paper, we proposed a parallel-dilated convolutional
neural network (CNN) based COVID-19 detection system from chest x-ray images,
named as Parallel-Dilated COVIDNet (PDCOVIDNet). First, the publicly available
chest X-ray collection fully preloaded and enhanced, and then classified by the
proposed method. Differing convolution dilation rate in a parallel form
demonstrates the proof-of-principle for using PDCOVIDNet to extract
radiological features for COVID-19 detection. Accordingly, we have assisted our
method with two visualization methods, which are specifically designed to
increase understanding of the key components associated with COVID-19
infection. Both visualization methods compute gradients for a given image
category related to feature maps of the last convolutional layer to create a
class-discriminative region. In our experiment, we used a total of 2,905 chest
X-ray images, comprising three cases (such as COVID-19, normal, and viral
pneumonia), and empirical evaluations revealed that the proposed method
extracted more significant features expeditiously related to the suspected
disease. The experimental results demonstrate that our proposed method
significantly improves performance metrics: accuracy, precision, recall, and F1
scores reach 96.58%, 96.58%, 96.59%, and 96.58%, respectively, which is
comparable or enhanced compared with the state-of-the-art methods.
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We give an overview of some applications of a general variational principle.
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Heisenberg's uncertainty principle, exemplified by the gamma ray thought
experiment, suggests that any finite precision measurement disturbs any
observables noncommuting with the measured observable. Here, it is shown that
this statement contradicts the limit of the accuracy of measurements under
conservation laws originally found by Wigner in 1950s, and should be modified
to correctly derive the unavoidable noise caused by the conservation law
induced decoherence. The obtained accuracy limit leads to an interesting
conclusion that a widely accepted, but rather naive, physical encoding of
qubits for quantum computing suffers significantly from the decoherence induced
by the angular momentum conservation law.
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Understanding the near-field electromagnetic interactions that produce
optical orbital angular momentum (OAM) is central to the integration of twisted
light into nanotechnology. Here, we examine the cathodoluminescence (CL) of
plasmonic vortices carrying OAM generated in spiral nanostructures through
scanning transmission electron microscopy (STEM). The nanospiral geometry
defines the photonic local density of states (LDOS) sampled by STEM-CL, which
provides access to the phase and amplitude of the plasmonic vortex with
nanometer spatial and meV spectral resolution. We map the full spectral
dispersion of the plasmonic vortex in the spiral structure and examine the
effects of increasing topological charge on the plasmon phase and amplitude in
the detected CL signal. The vortex is mapped in CL over a broad spectral range,
and deviations between the predicted and detected positions of near-field
optical signatures of as much as 5 per cent are observed. Finally, enhanced
luminescence is observed from concentric spirals of like handedness compared to
that from concentric spirals of opposite handedness, indicating the potential
to couple plasmonic vortices to chiral nanostructures for sensitive detection
and manipulation of optical OAM.
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We study 2d $\mathcal{N}=(2,2)$ quiver gauge theories without flavor nodes.
There is a special class of quivers whose gauge group ranks stay positive in
any duality frame. We illustrate this with the Abelian Kronecker quiver and the
Abelian Markov quiver as the simplest examples. In the geometric phase, they
engineer an infinite sequence of projective spaces and hypersurfaces in
Calabi-Yau spaces, respectively. We show that the Markov quiver provides an
Abelianization of SU(3) SQCD. Turning on the FI parameters and the $\theta$
angles for the Abelian quiver effectively deform SQCD by such parameters. For
an Abelian necklace quiver corresponding to SU($k$) SQCD, we find evidence for
singular loci supporting non-compact Coulomb branches in the K\"ahler moduli
space.
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In this paper we introduce a new logarithmic double phase type operator of
the form\begin{align*}\mathcal{G}u:=-\operatorname{div}\left(|\nabla
u|^{p(x)-2}\nabla u+\mu(x)\left[\log(e+|\nabla u|)+\frac{|\nabla
u|}{q(x)(e+|\nabla u|)}\right]|\nabla u|^{q(x)-2} \nabla u
\right),\end{align*}where $\Omega\subseteq\mathbb{R}^N$, $N\geq 2$, is a
bounded domain with Lipschitz boundary $\partial\Omega$, $p,q\in
C(\overline{\Omega})$ with $1<p(x)\leq q(x)$ for all $x\in\overline{\Omega}$
and $\mu\in L^1(\Omega)$. First, we prove that the logarithmic Musielak-Orlicz
Sobolev spaces $W^{1,\mathcal{H}_{\log}}(\Omega)$ and $W^{1,
\mathcal{H}_{\log}}_0(\Omega)$ with
$\mathcal{H}_{\log}(x,t)=t^{p(x)}+\mu(x)t^{q(x)}\log(e+t)$ for $(x,t)\in
\overline{\Omega}\times [0,\infty)$ are separable, reflexive Banach spaces and
$W^{1,\mathcal{H}_{\log}}_0(\Omega)$ can be equipped with an equivalent norm.
We also prove several embedding results for these spaces and the closedness of
these spaces under truncations. In addition we show the density of smooth
functions in $W^{1,\mathcal{H}_{\log}}(\Omega)$ even in the case of an
unbounded domain by supposing Nekvinda's decay condition on $p(\cdot)$. The
second part is devoted to the properties of the operator and it turns out that
it is bounded, continuous, strictly monotone, of type (S$_+$), coercive and a
homeomorphism. As a result of independent interest we also present a new
version of Young's inequality for the product of a power-law and a logarithm.
In the last part of this work we consider equations driven by our new operator
with superlinear right-hand sides. We prove multiplicity results for this type
of equation, in particular about sign-changing solutions, by making use of a
suitable variation of the corresponding Nehari manifold together with the
quantitative deformation lemma and the Poincar\'e-Miranda existence theorem.
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A graph $G$ is said to be $k$-$\gamma_{c}$-critical if the connected
domination number $\gamma_{c}(G) = k$ and $\gamma_{c}(G + uv) < k$ for every
$uv \in E(\overline{G})$. Let $\delta, \kappa$ and $\alpha$ be respectively the
minimum degree, the connectivity and the independence number. In this paper, we
show that a $3$-$\gamma_{c}$-critical graph $G$ satisfies $\alpha \leq \kappa +
2$. Moreover, if $\kappa \geq 3$, then $\alpha = \kappa + p$ if and only if
$\alpha = \delta + p$ for all $p \in \{1, 2\}$. We show that the condition
$\kappa + 1 \leq \alpha \leq \kappa + 2$ is best possible to prove that $\kappa
= \delta$. By these result, we conclude our paper with an open problem on
Hamiltonian connected of $3$-$\gamma_{c}$-critical graphs.
|
As the intensity of neutrino beams produced at accelerators increases,
important systematic errors due to poor knowledge of production cross sections
for pions and kaons arise. Among other goals, the NA61/SHINE (SHINE=SPS Heavy
Ion and Neutrino Experiment) detector at CERN SPS aims at precision
hadro-production measurements to characterise the neutrino beam of the T2K
experiment at J-PARC. These measurements are performed using a 30GeV proton
beam produced at the SPS with a thin carbon target and a full T2K replica
target. Preliminary spectra of $\pi^{+}$ and $\pi^{-}$ inclusive cross section
were obtained from pilot data collected in 2007 with a 2 cm thick target. After
a description of the SHINE detector and its particle identification
capabilities, results from three different analysis are discussed.
|
We analyze boundedly rational updating from aggregate statistics in a model
with binary actions and binary states. Agents each take an irreversible action
in sequence after observing the unordered set of previous actions. Each agent
first forms her prior based on the aggregate statistic, then incorporates her
signal with the prior based on Bayes rule, and finally applies a decision rule
that assigns a (mixed) action to each belief. If priors are formed according to
a discretized DeGroot rule, then actions converge to the state (in
probability), i.e., \emph{asymptotic learning}, in any informative information
structure if and only if the decision rule satisfies probability matching. This
result generalizes to unspecified information settings where information
structures differ across agents and agents know only the information structure
generating their own signal. Also, the main result extends to the case of $n$
states and $n$ actions.
|
The online semi-random graph process is a one-player game which starts with
the empty graph on $n$ vertices. At every round, a player (called Builder) is
presented with a vertex $v$ chosen uniformly at random and independently from
previous rounds, and constructs an edge of their choice that is incident to
$v$. Inspired by recent advances on the semi-random graph process, we define a
family of generalised online semi-random models.
We analyse a particular instance that shares similar features with the
original semi-random graph process and determine the hitting times of the
classical graph properties minimum degree $k$, $k$-connectivity, containment of
a perfect matching, a Hamiltonian cycle and an $H$-factor for a fixed graph $H$
possessing an additional tree-like property. Along the way, we derive a few
consequences of the famous Aldous-Broder algorithm that may be of independent
interest.
|
A search for the progenitor of SN~2010jl, an unusually luminous core-collapse
supernova of Type~IIn, using pre-explosion {\it Hubble}/WFPC2 and {\it
Spitzer}/IRAC images of the region, yielded upper limits on the UV and
near-infrared (IR) fluxes from any candidate star. These upper limits constrain
the luminosity and effective temperature of the progenitor, the mass of any
preexisting dust in its surrounding circumstellar medium (CSM), and dust
proximity to the star. A {\it lower} limit on the CSM dust mass is required to
hide a luminous progenitor from detection by {\it Hubble}. {\it Upper} limits
on the CSM dust mass and constraints on its proximity to the star are set by
requiring that the absorbed and reradiated IR emission not exceed the IRAC
upper limits. Using the combined extinction-IR emission constraints we present
viable $M_d-R_1$ combinations, where $M_d$ and $R_1$ are the CSM dust mass and
its inner radius. These depend on the CSM outer radius, dust composition and
grain size, and the properties of the progenitor. The results constrain the
pre-supernova evolution of the progenitor, and the nature and origin of the
observed post-explosion IR emission from SN~2010jl. In particular, an
$\eta$~Car-type progenitor will require at least 4~mag of visual extinction to
avoid detection by the {\it Hubble}. This can be achieved with dust masses
$\gtrsim 10^{-3}$~\msun\ (less than the estimated 0.2-0.5~\msun\ around
$\eta$~Car) which must be located at distances of $\gtrsim 10^{16}$~cm from the
star to avoid detection by {\it Spitzer}.
|
Globular clusters (GCs) formed when the Milky Way experienced a phase of
rapid assembly. We use the wealth of information contained in the Galactic GC
population to quantify the properties of the satellite galaxies from which the
Milky Way assembled. To achieve this, we train an artificial neural network on
the E-MOSAICS cosmological simulations of the co-formation and co-evolution of
GCs and their host galaxies. The network uses the ages, metallicities, and
orbital properties of GCs that formed in the same progenitor galaxies to
predict the stellar masses and accretion redshifts of these progenitors. We
apply the network to Galactic GCs associated with five progenitors: {\it
Gaia}-Enceladus, the Helmi streams, Sequoia, Sagittarius, and the recently
discovered, `low-energy' GCs, which provide an excellent match to the predicted
properties of the enigmatic galaxy `Kraken'. The five galaxies cover a narrow
stellar mass range [$M_\star=(0.6{-}4.6)\times10^8~{\rm M}_\odot$], but have
widely different accretion redshifts ($z_{\rm acc}=0.57{-}2.65$). All accretion
events represent minor mergers, but Kraken likely represents the most major
merger ever experienced by the Milky Way, with stellar and virial mass ratios
of $r_{M_\star}=1$:$31^{+34}_{-16}$ and $r_{M_{\rm h}}=1$:$7^{+4}_{-2}$,
respectively. The progenitors match the $z=0$ relation between GC number and
halo virial mass, but have elevated specific frequencies, suggesting an
evolution with redshift. Even though these progenitors likely were the Milky
Way's most massive accretion events, they contributed a total mass of only
$\log{(M_{\rm \star,tot}/{\rm M}_\odot)}=9.0\pm0.1$, similar to the stellar
halo. This implies that the Milky Way grew its stellar mass mostly by in-situ
star formation. We conclude by organising these accretion events into the most
detailed reconstruction to date of the Milky Way's merger tree.
|
Holmboe (1962) postulated that resonant interaction between two or more
progressive, linear interfacial waves produces exponentially growing
instabilities in idealized (broken-line profiles), homogeneous or density
stratified, inviscid shear layers. In this paper, we generalize Holmboe's
mechanistic picture of linear shear instabilities by (i) not initially
specifying the type of the waves, and (ii) by providing the option for
non-normal growth. We demonstrate the mechanism behind linear shear
instabilities by proposing a purely kinematic model consisting of two linear,
Doppler-shifted, progressive interfacial waves moving in opposite directions.
Moreover, we have found a necessary and sufficient (N&S) condition for the
existence of exponentially growing instabilities in idealized shear flows. The
two interfacial waves, starting from arbitrary initial conditions, eventually
phase-lock and resonate (grow exponentially), provided the N&S condition is
satisfied. The instability mechanism occurring prior to reaching steady state
is non-modal, favouring rapid transient growth. The theoretical underpinnings
of our wave interaction model is analogous to that of synchronization between
two coupled harmonic oscillators. Our proposed model is used to study three
well known types of shear instabilities - Rayleigh/Kelvin-Helmholtz, Holmboe
and Taylor-Caulfield. We show that the N&S condition provides a range of
unstable wavenumbers for each instability type, and this range matches the
predictions of the canonical normal-mode based linear stability theory.
|
Information centric networking (ICN) proposes to redesign the Internet by
replacing its host-centric design with information-centric design.
Communication among entities is established at the naming level, with the
receiver side (referred to as the Consumer) acting as the driving force behind
content delivery, by interacting with the network through Interest message
transmissions. One of the proposed advantages for ICN is its support for
mobility, by de-coupling applications from transport semantics. However, so
far, little research has been conducted to understand the interaction between
ICN and mobility of consuming and producing applications, in protocols purely
based on information-centric principles, particularly in the case of NDN. In
this paper, we present our findings on the mobility-based performance of Named
Data Networking (NDN) in wireless access networks. Through simulations, we show
that the current NDN architecture is not efficient in handling mobility and
architectural enhancements needs to be done to fully support mobility of
Consumers and Producers.
|
Let $d$ be a positive integer, and let $\mu$ be a finite measure on $\br^d$.
In this paper we ask when it is possible to find a subset $\Lambda$ in $\br^d$
such that the corresponding complex exponential functions $e_\lambda$ indexed
by $\Lambda$ are orthogonal and total in $L^2(\mu)$. If this happens, we say
that $(\mu, \Lambda)$ is a spectral pair. This is a Fourier duality, and the
$x$-variable for the $L^2(\mu)$-functions is one side in the duality, while the
points in $\Lambda$ is the other. Stated this way, the framework is too wide,
and we shall restrict attention to measures $\mu$ which come with an intrinsic
scaling symmetry built in and specified by a finite and prescribed system of
contractive affine mappings in $\br^d$; an affine iterated function system
(IFS). This setting allows us to generate candidates for spectral pairs in such
a way that the sets on both sides of the Fourier duality are generated by
suitably chosen affine IFSs. For a given affine setup, we spell out the
appropriate duality conditions that the two dual IFS-systems must have. Our
condition is stated in terms of certain complex Hadamard matrices. Our main
results give two ways of building higher dimensional spectral pairs from
combinatorial algebra and spectral theory applied to lower dimensional systems.
|
The present status of universality tests of the weak couplings for quarks and
leptons is reviewed, with updated information for the muon lifetime and for
first-row inputs in the CKM matrix. We discuss the impact of this
high-precision SM test in constraining new physics models. We also discuss a
precise lepton flavor-violation test from leptonic K decays and recent progress
in K-Kbar mixing.
|
Collective (elementary) excitations of quantum bosonic condensates, including
condensates of exciton polaritons in semiconductor microcavities, are a
sensitive probe of interparticle interactions. In anisotropic microcavities
with momentum-dependent TE-TM splitting of the optical modes, the excitations
dispersions are predicted to be strongly anisotropic, which is a consequence of
the synthetic magnetic gauge field of the cavity, as well as the interplay
between different interaction strengths for polaritons in the singlet and
triplet spin configurations. Here, by directly measuring the dispersion of the
collective excitations in a high-density optically trapped exciton-polariton
condensate, we observe excellent agreement with the theoretical predictions for
spinor polariton excitations. We extract the inter- and intra-spin polariton
interaction constants and map out the characteristic spin textures in an
interacting spinor condensate of exciton polaritons.
|
The measurement of light charged particles evaporated from the reaction
6,7Li+6Li has been carried out at extreme backward angle in the energy range 14
- 20 MeV. Calculations from the code ALICE91 show that the symmetry of the
target-projectile combination and the choice of level density parameter play
important roles in explaining the evaporation spectra for these light particle
systems. In above barrier energy region the fusion cross-section is not
suppressed for these loosely bound nuclei.
|
The metal-insulator transition of the Magneli phase Ti4O7 is studied by means
of augmented spherical wave (ASW) electronic structure calculations as based on
density functional theory and the local density approximation. The results show
that the metal-insulator transition arises from a complex interplay of charge
order, orbital order, and singlet formation of those Ti 3d states which mediate
metal-metal bonding inside the four-atom chains characteristic of the material.
Ti4O7 thus combines important aspects of Fe3O4 and VO2. While the charge
ordering closely resembles that observed at the Verwey transition, the orbital
order and singlet formation appear to be identical to the mechanisms driving
the metal-insulator transition of vanadium dioxide.
|
In this paper, we study the OOD generalization of neural algorithmic
reasoning tasks, where the goal is to learn an algorithm (e.g., sorting,
breadth-first search, and depth-first search) from input-output pairs using
deep neural networks. First, we argue that OOD generalization in this setting
is significantly different than common OOD settings. For example, some
phenomena in OOD generalization of image classifications such as \emph{accuracy
on the line} are not observed here, and techniques such as data augmentation
methods do not help as assumptions underlying many augmentation techniques are
often violated. Second, we analyze the main challenges (e.g., input
distribution shift, non-representative data generation, and uninformative
validation metrics) of the current leading benchmark, i.e., CLRS
\citep{deepmind2021clrs}, which contains 30 algorithmic reasoning tasks. We
propose several solutions, including a simple-yet-effective fix to the input
distribution shift and improved data generation. Finally, we propose an
attention-based 2WL-graph neural network (GNN) processor which complements
message-passing GNNs so their combination outperforms the state-of-the-art
model by a 3% margin averaged over all algorithms. Our code is available at:
\url{https://github.com/smahdavi4/clrs}.
|
We report some minimal surfaces that can be seen as copies of a triply
periodic minimal surface (TPMS) related by reflections in parallel mirrors. We
call them minimal twin surfaces for the resemblance with twin crystal. Brakke's
Surface Evolver is employed to construct twinnings of various classical TPMS,
including Schwarz' Primitive (P) and Diamond (D) surfaces, their rhombohedral
deformations (rPD), and Schoen's Gyroid (G) surface. Our numerical results
provide strong evidences for the mathematical existence of D twins and G twins,
which are recently observed in experiment by material scientists. For rPD
twins, we develop a good understanding, by noticing examples previously
constructed by Traizet (2008) and Fujimori and Weber (2009). Our knowledge on G
twins is, by contrast, very limited. Nevertheless, our experiments lead to new
cubic polyhedral models for the D and G surfaces, inspired by which we
speculate new TPMS deformations in the framework of Traizet.
|
The concept of reconfigurable fluid antennas (FA) is a potential and
promising solution to enhance the spectral efficiency of wireless communication
networks. Despite their many advantages, FA-enabled communications have
limitations as they require an enormous amount of spectral resources in order
to select the most desirable position of the radiating element from a large
number of prescribed locations. In this paper, we present an analytical
framework for the outage performance of large-scale FA-enabled communications,
where all user equipments (UEs) employ circular multi-FA array. In contrast to
existing studies, which assume perfect channel state information, the developed
framework accurately captures the channel estimation errors on the performance
of the considered network deployments. In particular, we focus on the limited
coherence interval scenario, where a novel sequential linear minimum
mean-squared error (LMMSE)-based channel estimation method is performed for
only a very small number of FA ports. Next, for the communication of each BS
with its associated UE, a low-complexity port-selection technique is employed,
where the port that provides the highest
signal-to-interference-plus-noise-ratio is selected among the ports that are
estimated to provide the strongest channel from each FA. By using stochastic
geometry tools, we derive both analytical and closed-form expressions for the
outage probability, highlighting the impact of channel estimation on the
performance of FA-based UEs. Our results reveal the trade-off imposed between
improving the network's performance and reducing the channel estimation
quality, indicating new insights for the design of FA-enabled communications.
|
We investigate local entropy theory, particularly the property of having
completely positive entropy (CPE), from a descriptive set-theoretic point of
view. We aim to determine descriptive complexity of different families of
dynamical systems with CPE.
For a large class of compact $X$, we show that the family of dynamical
systems on $X$ with CPE is complete coanalytic and hence not Borel. When we
restrict our attention to dynamical systems having special properties such as
the mixing property or the shadowing property, we obtain some contrasting
behavior. In particular, the notion of CPE and the notion of uniform positive
entropy, a Borel property, coincide for mixing maps on topological graphs. On
the other hand, the class of mixing map on the Cantor space is coanalytic and
not Borel.
For dynamical systems with the shadowing property, the notions CPE and
uniform positive entropy coincide regardless of the phase space.
|
One of the hallmarks of cancer cells is their exceptional ability to migrate
within the extracellular matrix (ECM) for gaining access to the circulatory
system, a critical step of cancer metastasis. RhoA, a small GTPase, is known to
be a key molecular switch that toggles between actomyosin contractility and
lamellipodial protrusion during cell migration. Current understanding of RhoA
activity in cell migration has been largely derived from studies of cells
plated on a two-dimensional (2D) substrate using a FRET biosensor. There has
been increasing evidence that cells behave differently in a more
physiologically relevant three-dimensional (3D) environment, however, studies
of RhoA activities in 3D have been hindered by low signal-to-noise ratio in
fluorescence imaging. In this paper, we present a machine learning-assisted
FRET technique to follow the spatiotemporal dynamics of RhoA activities of
single breast tumor cells (MDA-MB-231) migrating in a 3D as well as a 2D
environment using a RhoA biosensor. We found that RhoA activity is more
polarized along the long axis of the cell for single cells migrating on 2D
fibronectin-coated glass versus those embedded in 3D collagen matrices. In
particular, RhoA activities of cells in 2D exhibit a distinct front-to-back and
back-to-front movement during migration in contrast to those in 3D. Finally,
regardless of dimensionality, RhoA polarization is found to be correlated with
cell shape.
|
Empirical falsifiability of the predictions of physical theories is the
cornerstone of the scientific method. Physical theories attribute empirically
falsifiable operational properties to sets of physical preparations. A theory
is said to be empirically complete if such properties allow for a not
fine-tuned realist explanation, as properties of underlying probability
distributions over states of reality. Such theories satisfy a family of
equalities among fundamental operational properties, characterized exclusively
by the number of preparations. Quantum preparations deviate from these
equalities, and the maximal quantum deviation increases with the number of
preparations. These deviations not only signify the incompleteness of the
operational quantum formalism, but they simultaneously imply quantum over
classical advantage in suitably constrained one-way communication tasks,
highlighting the delicate interplay between the two.
|
We prove a sufficient condition under which a semigroup admits no finite
identity basis. As an application, it is shown that the identities of the
Kauffman monoid $\mathcal{K}_n$ are nonfinitely based for each $n\ge 3$. This
result holds also for the case when $\mathcal{K}_n$ is considered as an
involution semigroup under either of its natural involutions.
|
Using single-crystal X-ray diffraction we characterise the 235\,K
incommensurate phase transition in the hybrid molecular framework
tetraethylammonium silver(I) dicyanoargentate, [NEt$_4$]Ag$_3$(CN)$_4$. We
demonstrate the transition to involve spontaneous resolution of chiral
[NEt$_4$]$^+$ conformations, giving rise to a state in which molecular
chirality is incommensurately modulated throughout the crystal lattice. We
refer to this state as an incommensurate chirality density wave (XDW) phase,
which represents a fundamentally new type of chiral symmetry breaking in the
solid state. Drawing on parallels to the incommensurate ferroelectric
transition of NaNO$_2$ we suggest the XDW state arises through coupling between
acoustic (shear) and molecular rotoinversion modes. Such coupling is
symmetry-forbidden at the Brillouin zone centre but symmetry-allowed for small
but finite modulation vectors $\mathbf q=[0,0,q_z]^\ast$. The importance of
long-wavelength chirality modulations in the physics of this hybrid framework
may have implications for the generation of mesoscale chiral textures, as
required for advanced photonic materials.
|
The equations for Yang-Mills field in a medium are derived in a linear
approximation with respect to the gauge coupling parameter and the external
field. The obtained equations closely resemble the macroscopic Maxwell
equations. A canonical quantization is performed for a family of Fermi-like
gauges in the case of constant and diagonal (in the group indices) tensors of
electric permittivity and magnetic permeability. The physical subspace is
defined and the gauge field propagator is evaluated for a particular choice of
the gauge. The propagator is applied for evaluation of the cross-section of
ellastic quark scattering in the Born approximation. Possible applications to
Cherenkov-type gluon radiation are commented briefly.
|
Chest X-ray (CXR) is a low-cost medical imaging technique. It is a common
procedure for the identification of many respiratory diseases compared to MRI,
CT, and PET scans. This paper presents the use of generative adversarial
networks (GAN) to perform the task of lung segmentation on a given CXR. GANs
are popular to generate realistic data by learning the mapping from one domain
to another. In our work, the generator of the GAN is trained to generate a
segmented mask of a given input CXR. The discriminator distinguishes between a
ground truth and the generated mask, and updates the generator through the
adversarial loss measure. The objective is to generate masks for the input CXR,
which are as realistic as possible compared to the ground truth masks. The
model is trained and evaluated using four different discriminators referred to
as D1, D2, D3, and D4, respectively. Experimental results on three different
CXR datasets reveal that the proposed model is able to achieve a dice-score of
0.9740, and IOU score of 0.943, which are better than other reported
state-of-the art results.
|
The relic gravitational waves (gw) are the cleanest probe of the violent
times in the very early history of the Universe. They are expected to leave
signatures in the observed cosmic microwave background anisotropies. We
significantly improved our previous analysis [1] of the 5-year WMAP $TT$ and
$TE$ data at lower multipoles $\ell$. This more general analysis returned
essentially the same maximum likelihood (ML) result (unfortunately, surrounded
by large remaining uncertainties): the relic gw are present and they are
responsible for approximately 20% of the temperature quadrupole. We identify
and discuss the reasons by which the contribution of gw can be overlooked in a
data analysis. One of the reasons is a misleading reliance on data from very
high multipoles $\ell$, another - a too narrow understanding of the problem as
the search for $B$-modes of polarization, rather than the detection of relic gw
with the help of all correlation functions. Our analysis of WMAP5 data has led
to the identification of a whole family of models characterized by relatively
high values of the likelihood function. Using the Fisher matrix formalism we
formulated forecasts for {\it Planck} mission in the context of this family of
models. We explore in details various `optimistic', `pessimistic' and `dream
case' scenarios. We show that in some circumstances the $B$-mode detection may
be very inconclusive, at the level of signal-to-noise ratio $S/N =1.75$,
whereas a smarter data analysis can reveal the same gw signal at $S/N= 6.48$.
The final result is encouraging. Even under unfavourable conditions in terms of
instrumental noises and foregrounds, the relic gw, if they are characterized by
the ML parameters that we found from WMAP5 data, will be detected by {\it
Planck} at the level $S/N = 3.65$.
|
We present a new particle tracking software algorithm designed to accurately
track the motion of low-contrast particles against a background with large
variations in light levels. The method is based on a polynomial fit of the
intensity around each feature point, weighted by a Gaussian function of the
distance from the centre, and is especially suitable for tracking endogeneous
particles in the cell, imaged with bright field, phase contrast or fluorescence
optical microscopy. Furthermore, the method can simultaneously track particles
of all different sizes, and allows significant freedom in their shape. The
algorithm is evaluated using the quantitative measures of accuracy and
precision of previous authors, using simulated images at variable
signal-to-noise ratios. To these we add a new test of the error due to a
non-uniform background. Finally the tracking of particles in real cell images
is demonstrated. The method is made freely available for non-commencial use as
a software package with a graphical user-inferface, which can be run within the
Matlab programming environment.
|
We consider the general problem of recovering a high-dimensional signal from
noisy quantized measurements. Quantization, especially coarse quantization such
as 1-bit sign measurements, leads to severe information loss and thus a good
prior knowledge of the unknown signal is helpful for accurate recovery.
Motivated by the power of score-based generative models (SGM, also known as
diffusion models) in capturing the rich structure of natural signals beyond
simple sparsity, we propose an unsupervised data-driven approach called
quantized compressed sensing with SGM (QCS-SGM), where the prior distribution
is modeled by a pre-trained SGM. To perform posterior sampling, an annealed
pseudo-likelihood score called noise perturbed pseudo-likelihood score is
introduced and combined with the prior score of SGM. The proposed QCS-SGM
applies to an arbitrary number of quantization bits. Experiments on a variety
of baseline datasets demonstrate that the proposed QCS-SGM significantly
outperforms existing state-of-the-art algorithms by a large margin for both
in-distribution and out-of-distribution samples. Moreover, as a posterior
sampling method, QCS-SGM can be easily used to obtain confidence intervals or
uncertainty estimates of the reconstructed results. The code is available at
https://github.com/mengxiangming/QCS-SGM.
|
We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an
inhomogeneous magnetic field. We first consider entanglement teleportation, and
then focus on the teleportation fidelity under different conditions. The
effects of anisotropy and the magnetic field, both uniform and inhomogeneous,
are discussed. We also find that, though entanglement teleportation does
require an entangled quantum channel, a nonzero critical value of minimum
entanglement is not always necessary.
|
Cells count become a challenging problem when the cells move in a continuous
stream, and their boundaries are difficult for visual detection. To resolve
this problem we modified the training and decision making processes using
curriculum learning and multi-view predictions techniques, respectively.
|
The light curve of the microlensing event KMT-2021-BLG-1898 exhibits a
short-term central anomaly with double-bump features that cannot be explained
by the usual binary-lens or binary-source interpretations. With the aim of
interpreting the anomaly, we analyze the lensing light curve under various
sophisticated models. We find that the anomaly is explained by a model, in
which both the lens and source are binaries (2L2S model). For this
interpretation, the lens is a planetary system with a planet/host mass ratio of
$q\sim 1.5\times 10^{-3}$, and the source is a binary composed of a turn off or
a subgiant star and a mid K dwarf. The double-bump feature of the anomaly can
also be depicted by a triple-lens model (3L1S model), in which the lens is a
planetary system containing two planets. Among the two interpretations, the
2L2S model is favored over the 3L1S model not only because it yields a better
fit to the data, by $\Delta\chi^2=[14.3$--18.5], but also the Einstein radii
derived independently from the two stars of the binary source result in
consistent values. According to the 2L2S interpretation, KMT-2021-BLG-1898 is
the third planetary lensing event occurring on a binary stellar system,
following MOA-2010-BLG-117 and KMT-2018-BLG-1743. Under the 2L2S
interpretation, we identify two solutions resulting from the close-wide
degeneracy in determining the planet-host separation. From a Bayesian analysis,
we estimate that the planet has a mass of $\sim 0.7$--0.8~$M_{\rm J}$, and it
orbits an early M dwarf host with a mass of $\sim 0.5~M_\odot$. The projected
planet-host separation is $\sim 1.9$~AU and $\sim 3.0$~AU according to the
close and wide solutions, respectively.
|
The elliptical galaxy NGC 1550 at a redshift of $z=0.01239$, identified with
an extended X-ray source RX J0419+0225, was observed with {\it XMM-Newton} for
31 ks. From the X-ray data and archival near infra-red data of Two Micron All
Sky survay, we derive the profiles of components constituting the NGC 1550
system; the gas mass, total mass, metal mass, and galaxy luminosity. The metals
(oxygen, silicon, and iron) are extended to $\sim 200$ kpc from the center,
wherein $\sim$ 70% of the $K$-band luminosity is carried by NGC 1550 itself. As
first revealed with {\it ASCA}, the data reconfirms the presence of a dark
halo, of which the mass ($1.6 \times 10^{13} M_{\odot}$) is typical of a galaxy
group rather than of a single galaxy. Within 210 kpc, the $K$-band
mass-to-light ratio reaches $75 M_{\odot}/L_{\odot}$, which is comparable to
those of clusters of galaxies. The iron-mass-to-light ratio profile (silicon-
and oxygen mass-to-light ratio profiles as well) exhibits about two orders of
magnitude decrease toward the center. Further studies comparing mass densities
of metals with those of the other cluster components reveal that the iron (as
well as silicon) in the ICM traces very well the total gravitating mass,
whereas the stellar component is significantly more concentrated to within
several tens kpc of the NGC 1550 nucleus. Thus, in the central region, the
amount of metals is significantly depleted for the luminous galaxy light. Among
a few possible explanations of this effect, the most likely scenario is that
galaxies in this system were initially much more extended than today, and
gradually fell to the center and merged into NGC 1550.
|
Optical cavities find diverse uses in lasers, frequency combs, optomechanics,
and optical signal processors. Complete reconfigurability of the resonant
frequency as well as the loss enables development of generic field programmable
cavities for achieving the desired performance in these applications.
Conventional reconfigurable cavities are generally limited to specific material
platforms or specific optical tuning methods and require sophisticated
fabrication. Furthermore, the tuning of the loss is coupled to the
resonance-shift in the cavity. We propose and demonstrate a simple and generic
interferometer in a cavity structure that enables quasiperiodic modification of
the internal cavity loss and the cavity resonance to reconfigure the Q-factor,
transmission characteristics, and group delay of the hybrid cavity, with simple
tuning of the optical phase in the interferometer. We also demonstrate methods
to decouple the tuning of the loss from the resonance-shift, that enables
resonance-locked reconfigurability. This structure also enables resonance-shift
to both shorter and longer wavelengths using the same phase-tuning technique,
which is challenging to achieve in conventional reconfigurable cavities. These
devices can be implemented in any guided-wave platform (on-chip or fiber-optic)
with potential applications in programmable photonics and reconfigurable
optomechanics.
|
The DSM-1 was published in 1952, contains 128 diagnostic categories,
described in 132 pages. The DSM-5 appeared in 2013, contains 541 diagnostic
categories, described in 947 pages. The field of psychology is characterised by
a steady proliferation of diagnostic models and subcategories, that seems to be
inspired by the principle of "divide and inflate". This approach is in contrast
with experimental evidence, which suggests on one hand that traumas of various
kind are often present in the anamnesis of patients and, on the other, that the
gene variants implicated are shared across a wide range of diagnoses. In this
work I propose a holistic approach, built with tools borrowed from the field of
Artificial Intelligence. My model is based on two pillars. The first one is
trauma, which represents the attack to the mind, is psychological in nature and
has its origin in the environment. The second pillar is dissociation, which
represents the mind defence in both physiological and pathological conditions,
and incorporates all other defence mechanisms. Damages to dissociation can be
considered as another category of attacks, that are neurobiological in nature
and can be of genetic or environmental origin. They include, among other
factors, synaptic over-pruning, abuse of drugs and inflammation. These factors
concur to weaken the defence, represented by the neural networks that implement
the dissociation mechanism in the brain. The model is subsequently used to
interpret five mental conditions: PTSD, complex PTSD, dissociative identity
disorder, schizophrenia and bipolar disorder. Ideally, this is a first step
towards building a model that aims to explain a wider range of
psychopathological affections with a single theoretical framework. The last
part is dedicated to sketching a new psychotherapy for psychological trauma.
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In passive imaging, one attempts to reconstruct some coefficients in a wave
equation from correlations of observed randomly excited solutions to this wave
equation. Many methods proposed for this class of inverse problem so far are
only qualitative, e.g., trying to identify the support of a perturbation. Major
challenges are the increase in dimensionality when computing correlations from
primary data in a preprocessing step, and often very poor pointwise
signal-to-noise ratios. In this paper, we propose an approach that addresses
both of these challenges: It works only on the primary data while implicitly
using the full information contained in the correlation data, and it provides
quantitative estimates and convergence by iteration.
Our work is motivated by helioseismic holography, a well-established imaging
method to map heterogenities and flows in the solar interior. We show that the
back-propagation used in classical helioseismic holography can be interpreted
as the adjoint of the Fr\'echet derivative of the operator which maps the
properties of the solar interior to the correlation data on the solar surface.
The theoretical and numerical framework for passive imaging problems developed
in this paper extends helioseismic holography to nonlinear problems and allows
for quantitative reconstructions. We present a proof of concept in uniform
media.
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We define the notion of a minimal affinization of an irreducible
representation of $U_q(g)$. We prove that minimal affinizations exist and
establish their uniqueness in the rank 2 case.
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Most of the widely used quantum programming languages and libraries are not
designed for the tightly coupled nature of hybrid quantum-classical algorithms,
which run on quantum resources that are integrated on-premise with classical
HPC infrastructure. We propose a programming model using the API provided by
OpenMP to target quantum devices, which provides an easy-to-use and efficient
interface for HPC applications to utilize quantum compute resources. We have
implemented a variational quantum eigensolver using the programming model,
which has been tested using a classical simulator. We are in the process of
testing on the quantum resources hosted at the Leibniz Supercomputing Centre
(LRZ).
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We record a particularly simple construction on top of Lumsdaine's local
universes that allows for a Coquand-style universe of propositions with
propositional extensionality to be interpreted in a category with subobject
classifiers.
|
The response part of the exchange-correlation potential of Kohn-Sham density
functional theory plays a very important role, for example for the calculation
of accurate band gaps and excitation energies. Here we analyze this part of the
potential in the limit of infinite interaction in density functional theory,
showing that in the one-dimensional case it satisfies a very simple sum rule.
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We investigate the polarization state dynamics of single photon pulse for
optical fiber quantum communication channels. On the basis of a birefringence
vector model in which amplitude and direction are both stochastic variables,
Jones vector is obtained by solving the frequency domain wave equation. The
fidelity of output quantum state and degree of polarization of the pulse are
also obtained from the density operators. It is shown that the fidelity of
quantum state decreases quickly and tends to a stable value along optical
fiber, and increases for larger mean fluctuation magnitude of the stochastic
fiber birefringence. Degree of polarization is nearly constant for small mean
fluctuation magnitude of the birefringence. The fidelity and degree of
polarization vary in the same way for Gaussian and rectangular frequency
spectrum envelope, while the value of Lorentzian spectrum is smaller.
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In this paper, we study the black box optimization problem under the
Polyak--Lojasiewicz (PL) condition, assuming that the objective function is not
just smooth, but has higher smoothness. By using "kernel-based" approximation
instead of the exact gradient in Stochastic Gradient Descent method, we improve
the best known results of convergence in the class of gradient-free algorithms
solving problem under PL condition. We generalize our results to the case where
a zero-order oracle returns a function value at a point with some adversarial
noise. We verify our theoretical results on the example of solving a system of
nonlinear equations.
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We study the mean Uhlmann curvature in fermionic systems undergoing a
dissipative driven phase transition. We consider a paradigmatic class of
lattice fermion systems in non-equilibrium steady-state of an open system with
local reservoirs, which are characterised by a Gaussian fermionic steady state.
In the thermodynamical limit, in systems with translational invariance we show
that a singular behaviour of the Uhlmann curvature represents a sufficient
criterion for criticalities, in the sense of diverging correlation length, and
it is not otherwise sensitive to the closure of the Liouvillian dissipative
gap. In finite size systems, we show that the scaling behaviour of the mean
Uhlmann curvature maps faithfully the phase diagram, and a relation to the
dissipative gap is put forward. We argue that the mean Uhlmann phase can shade
light upon the nature of non equilibrium steady state criticality in particular
with regard to the role played by quantum vs classical fluctuations.
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Statistical pragmatism embraces all efficient methods in statistical
inference. Augmentation of the collected data is used herein to obtain
representative population information from a large class of non-representative
population's units. Parameter expansion of a probability model is shown to
reduce the upper bound on the sum of error probabilities for a test of simple
hypotheses, and a measure, R, is proposed for the effect of activating
additional component(s) in the sufficient statistic.
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In this paper we formulate two generalizations of Agoh's conjecture. We also
formulate conjectures involving congruence modulo primes about hyperbolic
secant, hyperbolic tangent, N\"orlund numbers, as well as about coefficients of
expansions in powers of other analytic functions. We formulate a thesis about
combinatorial objects that do not produce fake primes.
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We discuss the impact of chiral symmetry constraints on the quark-mass
dependence of meson resonance pole positions, which are encoded in
non-perturbative parametrizations of meson scattering amplitudes.
Model-independent conditions on such parametrizations are derived, which are
shown to guarantee the correct functional form of the leading quark-mass
corrections to the resonance pole positions. Some model amplitudes for $\pi\pi$
scattering, widely used for the determination of $\rho$ and $\sigma$ resonance
properties from results of lattice simulations, are tested explicitly with
respect to these conditions.
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In the founding paper on unbounded $KK$-theory it was established by Baaj and
Julg that the bounded transform, which associates a class in $KK$-theory to any
unbounded Kasparov module, is a surjective homomorphism (under a separability
assumption). In this paper, we provide an equivalence relation on unbounded
Kasparov modules and we thereby describe the kernel of the bounded transform.
This allows us to introduce a notion of topological unbounded $KK$-theory,
which becomes isomorphic to $KK$-theory via the bounded transform. The
equivalence relation is formulated entirely at the level of unbounded Kasparov
modules and consists of homotopies together with an extra degeneracy condition.
Our degenerate unbounded Kasparov modules are called spectrally decomposable
since they admit a decomposition into a part with positive spectrum and a part
with negative spectrum.
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For the evolutionary Stokes problem with dynamic boundary condition we show
maximal regularity of weak solutions in time. Due to the characteriation of
$R$-sectorial operators on Hilbert spaces, the proof reduces to finding the
correct functional analytic setting and proving that an operator is sectorial,
i.e. generates an analytic semigroup.
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We present a budget-free experimental setup and procedure for benchmarking
numericaloptimization algorithms in a black-box scenario. This procedure can be
applied with the COCO benchmarking platform. We describe initialization of and
input to the algorithm and touch upon therelevance of termination and restarts.
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To address the challenge of backpropagating the gradient through categorical
variables, we propose the augment-REINFORCE-swap-merge (ARSM) gradient
estimator that is unbiased and has low variance. ARSM first uses variable
augmentation, REINFORCE, and Rao-Blackwellization to re-express the gradient as
an expectation under the Dirichlet distribution, then uses variable swapping to
construct differently expressed but equivalent expectations, and finally shares
common random numbers between these expectations to achieve significant
variance reduction. Experimental results show ARSM closely resembles the
performance of the true gradient for optimization in univariate settings;
outperforms existing estimators by a large margin when applied to categorical
variational auto-encoders; and provides a "try-and-see self-critic" variance
reduction method for discrete-action policy gradient, which removes the need of
estimating baselines by generating a random number of pseudo actions and
estimating their action-value functions.
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Scattering problems with locally perturbed periodic surfaces have been
studied both theoretically and numerically in recent years. In this paper, we
will discuss the regularity results of the Bloch transform of the total fields.
The idea is inspired by Theorem a in \cite{Kirsc1993}, which considered how the
total field depends on the wave numbers and the incident angles, with a family
of plain incident fields and a smooth enough periodic surface. We will show
that when the incident field satisfies some certain conditions, the Bloch
transform of the total field depends analytically on the quasi-periodicities
one the straight line $\R$ except for a countable number of points, while near
such points, a square-root like singularity exists. We also give some examples
to show that the conditions are satisfied by a large number of commonly used
incident fields. This result also provides a probability to improve the
numerical solution of this kind of problems, which is expected to be discussed
in our future papers.
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In the present paper we combine an N-body code that simulates the dynamics of
young dense stellar systems with a massive star evolution handler that accounts
in a realistic way for the effects of stellar wind mass loss. We discuss two
topics:
1. The formation and the evolution of very massive stars (with a mass >120
Mo) is followed in detail. These very massive stars are formed in the cluster
core as a consequence of the successive (physical) collison of 10-20 most
massive stars of the cluster (the process is known as runaway merging). The
further evolution is governed by stellar wind mass loss during core hydrogen
burning and during core helium burning (the WR phase of very massive stars).
Our simulations reveal that as a consequence of runaway merging in clusters
with solar and supersolar values, massive black holes can be formed but with a
maximum mass of 70 Mo. In small metallicity clusters however, it cannot be
excluded that the runaway merging process is responsible for pair instability
supernovae or for the formation of intermediate mass black holes with a mass of
several 100 Mo.
2. Massive runaways can be formed via the supernova explosion of one of the
components in a binary (the Blaauw scenario) or via dynamical interaction of a
single star and a binary or between two binaries in a star cluster. We explore
the possibility that the most massive runaways (e.g., zeta Pup, lambda Cep,
BD+433654) are the product of the collision and merger of 2 or 3 massive stars.
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The "Seifert Conjecture" asks, "Does every non-singular vector field on the
3-sphere ${\mathbb S}^3$ have a periodic orbit?" In a celebrated work, Krystyna
Kuperberg gave a construction of a smooth aperiodic vector field on a plug,
which is then used to construct counter-examples to the Seifert Conjecture for
smooth flows on the $3$-sphere, and on compact 3-manifolds in general. The
dynamics of the flows in these plugs have been extensively studied, with more
precise results known in special "generic" cases of the construction. Moreover,
the dynamical properties of smooth perturbations of Kuperberg's construction
have been considered. In this work, we recall some of the results obtained to
date for the Kuperberg flows and their perturbations. Then the main point of
this work is to focus attention on how the known results for Kuperberg flows
depend on the assumptions imposed on the flows, and to discuss some of the many
interesting questions and problems that remain open about their dynamical and
ergodic properties.
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The demand of computational resources for the modeling process increases as
the scale of the datasets does, since traditional approaches for regression
involve inverting huge data matrices. The main problem relies on the large data
size, and so a standard approach is subsampling that aims at obtaining the most
informative portion of the big data. In the current paper, we explore an
existing approach based on leverage scores, proposed for subdata selection in
linear model discrimination. Our objective is to propose the aforementioned
approach for selecting the most informative data points to estimate unknown
parameters in both the first-order linear model and a model with interactions.
We conclude that the approach based on leverage scores improves existing
approaches, providing simulation experiments as well as a real data
application.
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Many intriguing properties of driven nonlinear resonators, including the
appearance of chaos, are very important for understanding the universal
features of nonlinear dynamical systems and can have great practical
significance. We consider a cylindrical cavity resonator driven by an
alternating voltage and filled with a nonlinear nondispersive medium. It is
assumed that the medium lacks a center of inversion and the dependence of the
electric displacement on the electric field can be approximated by an
exponential function. We show that the Maxwell equations are integrated exactly
in this case and the field components in the cavity are represented in terms of
implicit functions of special form. The driven electromagnetic oscillations in
the cavity are found to display very interesting temporal behavior and their
Fourier spectra contain singular continuous components. To the best of our
knowledge, this is the first demonstration of the existence of a singular
continuous (fractal) spectrum in an exactly integrable system.
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Recent studies have shown that Deep Neural Networks (DNNs) are vulnerable to
the backdoor attacks, which leads to malicious behaviors of DNNs when specific
triggers are attached to the input images. It was further demonstrated that the
infected DNNs possess a collection of channels, which are more sensitive to the
backdoor triggers compared with normal channels. Pruning these channels was
then shown to be effective in mitigating the backdoor behaviors. To locate
those channels, it is natural to consider their Lipschitzness, which measures
their sensitivity against worst-case perturbations on the inputs. In this work,
we introduce a novel concept called Channel Lipschitz Constant (CLC), which is
defined as the Lipschitz constant of the mapping from the input images to the
output of each channel. Then we provide empirical evidences to show the strong
correlation between an Upper bound of the CLC (UCLC) and the trigger-activated
change on the channel activation. Since UCLC can be directly calculated from
the weight matrices, we can detect the potential backdoor channels in a
data-free manner, and do simple pruning on the infected DNN to repair the
model. The proposed Channel Lipschitzness based Pruning (CLP) method is super
fast, simple, data-free and robust to the choice of the pruning threshold.
Extensive experiments are conducted to evaluate the efficiency and
effectiveness of CLP, which achieves state-of-the-art results among the
mainstream defense methods even without any data. Source codes are available at
https://github.com/rkteddy/channel-Lipschitzness-based-pruning.
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Mobile service robots are proving to be increasingly effective in a range of
applications, such as healthcare, monitoring Activities of Daily Living (ADL),
and facilitating Ambient Assisted Living (AAL). These robots heavily rely on
Human Action Recognition (HAR) to interpret human actions and intentions.
However, for HAR to function effectively on service robots, it requires prior
knowledge of human presence (human detection) and identification of individuals
to monitor (human tracking). In this work, we propose an end-to-end pipeline
that encompasses the entire process, starting from human detection and
tracking, leading to action recognition. The pipeline is designed to operate in
near real-time while ensuring all stages of processing are performed on the
edge, reducing the need for centralised computation. To identify the most
suitable models for our mobile robot, we conducted a series of experiments
comparing state-of-the-art solutions based on both their detection performance
and efficiency. To evaluate the effectiveness of our proposed pipeline, we
proposed a dataset comprising daily household activities. By presenting our
findings and analysing the results, we demonstrate the efficacy of our approach
in enabling mobile robots to understand and respond to human behaviour in
real-world scenarios relying mainly on the data from their RGB cameras.
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We investigate the properties of the metallic state obtained by photo-doping
carriers into a Mott insulator. In a strongly interacting system, these
carriers have a long life-time, so that they can dissipate their kinetic energy
to a phonon bath. In the relaxed state, the scattering rate saturates at a
non-zero temperature-independent value, and the momentum-resolved spectral
function features broad bands which differ from the well-defined quasi-particle
bands of a chemically doped system. Our results indicate that a photo-doped
Mott insulator behaves as a bad metal, in which strong scattering between
doublons and holes inhibits Fermi-liquid behavior down to low temperature.
|
A recently proposed extension of the interaction flow method is applied to
exemplary cases of selected physical and methodical parameters for the
two-dimensional Hubbard model away from half-filling and perfect nesting. In
this scheme, the self-energy is calculated on the real-frequency axis and its
feedback on the flow of interactions is included in a simple manner via a
momentum-dependent quasi-particle weight. Results for two different types of
self-energy feedback are compared to the case without feedback and to existing
results stemming from calculations for imaginary frequencies. Various physical
and non-physical aspects which influence the outcome qualitatively and
quantitatively are addressed. Some tentative directions for future developments
are suggested.
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The ground-state energy, the effective mass and the number of virtual phonons
of the optical large polaron confined strictly in one dimension have been
estimated by using the generalized Gaussian approximation. The leading-order
terms take care of all Gaussian fluctuations in the system and improve the
conventional variational estimates at finite coupling. Particularly, the lowest
upper bound to the polaron ground-state energy has been obtained. The
non-Gaussian contributions systematically correct the leading-order
approximations. We have obtained exact analytical solutions in the weak- and
strong-coupling limit and reasonable numerical data for intermediate coupling.
Our result for the number of excited phonons limits the validity region of the
few-phonon approximation methods.
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We introduce the notion of limiting theories, giving examples and providing a
sufficient condition under which the first order theory of a structure is the
limit of the first order theories of a collection of substructures. We also
give a new proof that theories like that of infinite sets are not finitely
axiomatizable.
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The bright submillimetre (sub-mm) galaxy MM 18423+5938 at redshift 3.9296 has
been predicted from mid-infrared and millimetre photometry to have an
exceptionally large total infrared (IR) luminosity. We present new radio
imaging at 1.4 GHz with the Westerbork Synthesis Radio Telescope that is used
to determine a radio-derived total IR luminosity for MM 18423+5938 via the well
established radio-far-infrared correlation. The flux density is found to be
S_1.4 GHz = 217 +/- 37 \mu Jy, which corresponds to a rest-frame luminosity
density of L_1.4 GHz = 2.32 +/- 0.40 x 10^25 / u W / Hz, where u is the
magnification from a probable gravitational lens. The radio-derived total IR
luminosity and star-formation rate are L_8-1000 \mu m = 5.6^+4.1_-2.4 x 10^13 /
u L_sol and SFR = 9.4^+7.4_-4.9 x 10^3 / u M_sol / yr, respectively, which are
~9 times smaller than those previously reported. These differences are
attributed to the IR spectral energy distribution of MM 18423+5938 being poorly
constrained by the limited number of reliable photometric data that are
currently available, and from a previous misidentification of the object at 70
\mu m. Using the radio derived total IR luminosity as a constraint, the
temperature of the cold dust component is found to be T ~ 24^+7_-5 K for a dust
emissivity of \beta = 1.5 +/- 0.5. The radio-derived properties of this galaxy
are still large given the low excitation temperature implied by the CO emission
lines and the temperature of the cold dust. Therefore, we conclude that MM
18423+5938 is probably gravitationally lensed.
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We say a unitary operator acting on a set of qubits has been compiled if it
has been expressed as a SEO (sequence of elementary operations, like CNOTs and
single-qubit operations). SEO's are often represented as quantum circuits.
arXiv:quant-ph/0702144 by Farhi-Goldstone-Gutmann has inspired a recent flurry
of papers, that propose quantum algorithms for evaluating NAND formulas via
quantum walks over tree graphs. These algorithms use two types of unitary
evolution: oracle and non-oracle. Non-oracle evolutions are independent of the
NAND formula input, whereas oracle evolutions depend on this input. In this
paper we compile (i.e., give explicit SEOs and their associated quantum
circuits for) the oracle and non-oracle evolution operators used in some of
these NAND formula evaluators. We consider here only the case of balanced
binary NAND trees. Our compilation methods are based on the CSD (Cosine Sine
Decomposition), a matrix decomposition from Linear Algebra. The CS
decomposition has been used very successfully in the past to compile
unstructured unitary matrices exactly.
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We show that when the speed of control is bounded, there is a widely
applicable minimal-time control problem for which a coherent feedback protocol
is optimal, and is faster than all measurement-based feedback protocols, where
the latter are defined in a strict sense. The superiority of the coherent
protocol is due to the fact that it can exploit a geodesic path in Hilbert
space, a path that measurement-based protocols cannot follow.
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It is possible that the scale of gravity, parameterized by the apparent
Planck mass, may obtain different values within different universes in an
encompassing multiverse. We investigate the range over which the Planck mass
may scan while still satisfying anthropic constraints. The window for
anthropically allowed values of the Planck mass may have important consequences
for landscape predictions. For example, if the likelihood to observe some value
of the Planck mass is weighted by the inflationary expansion factors of the
universes that contain that value, then it appears extremely unlikely to
observe the value of the Planck mass that is measured within our universe. This
is another example of the runaway inflation problem discussed in recent
literature. We also show that the window for the Planck mass significantly
weakens the anthropic constraint upon the cosmological constant when both are
allowed to vary over a landscape.
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We theoretically study the magnetoresistance of a CPP-GMR system with current
confined paths (CCP) in the framework of Valet-Fert theory. The continuity
equations for charge and spin currents are numerically solved with the
three-dimensional CCP geometry by use of finite element method. It is confirmed
that the MR ratio is enhanced by the CCP structure, which is consistent with
the experimental results. Moreover, we find that there exists a certain contact
width which maximize the MR ratio. We show that the contact width which
maximize the MR ratio is well described by the effective resistance matching.
|
We demonstrate a prototype of a Focused Ion Beam machine based on the
ionization of a laser-cooled cesium beam adapted for imaging and modifying
different surfaces in the few-tens nanometer range. Efficient atomic ionization
is obtained by laser promoting ground-state atoms into a target excited Rydberg
state, then field-ionizing them in an electric field gradient. The method
allows obtaining ion currents up to 130 pA. Comparison with the standard direct
photo-ionization of the atomic beam shows, in our conditions, a 40-times larger
ion yield. Preliminary imaging results at ion energies in the 1-5 keV range are
obtained with a resolution around 40 nm, in the present version of the
prototype. Our ion beam is expected to be extremely monochromatic, with an
energy spread of the order of 1 eV, offering great prospects for lithography,
imaging and surface analysis.
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In 1976 S. Hawking claimed that "Because part of the information about the
state of the system is lost down the hole, the final situation is represented
by a density matrix rather than a pure quantum state" (Verbatim from ref. 2).
This was the starting point of the popular "black hole (BH) information
paradox". In a series of papers, together with collaborators, we naturally
interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing
a model of excited BH somewhat similar to the historical semi-classical Bohr
model of the structure of a hydrogen atom. Here we explicitly write down, for
the same model, a time dependent Schr\"odinger equation for the system composed
by Hawking radiation and BH QNMs. The physical state and the correspondent wave
function are written in terms of an unitary evolution matrix instead of a
density matrix. Thus, the final state results to be a pure quantum state
instead of a mixed one. Hence, Hawking's claim is falsified because BHs result
to be well defined quantum mechanical systems, having ordered, discrete quantum
spectra, which respect 't Hooft's assumption that Schr\"oedinger equations can
be used universally for all dynamics in the universe. As a consequence,
information comes out in BH evaporation in terms of pure states in an unitary
time dependent evolution. In Section 4 of this paper we show that the present
approach permits also to solve the entanglement problem connected with the
information paradox.
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Using magnetic neutron scattering we characterize an unusual low temperature
phase in orthorhombic SrCuO2. The material contains zigzag spin ladders formed
by pairs of S=1/2 chains (J=180 meV) coupled through a weak frustrated
interaction |J'|<0.1J. At T<Tc1=5.0(4)K an elastic peak develops in a gapless
magnetic excitation spectrum indicating spin freezing on a time scale larger
than 200 picoseconds. While the frozen state has long range commensurate
antiferromagnetic order along the chains with the correlation length exceeding
200 lattice periods along the c-axis and a substantial correlation length of
60(25) spacings along the a-axis perpendicular to the zigzag plane, only 2
lattice units are correlated along the b-axis which is the direction of the
frustrated interactions. The frozen magnetic moment of each Cu ion is very
small, 0.033(7) Bohr magneton even at T=0.35K, and has unusual temperature
dependence with a cusp at Tc2=1.5K reminiscent of a phase transition. We argue
that slow dynamics of stripe-like cooperative magnetic defects in tetragonal
a-c planes yield this anisotropic frozen state.
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Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.