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We develop a method to estimate the spin-spin interactions in the Hamiltonian
from the observed magnetization curve by machine learning based on Bayesian
inference. In our method, plausible spin-spin interactions are determined by
maximizing the posterior distribution, which is the conditional probability of
the spin-spin interactions in the Hamiltonian for a given magnetization curve
with observation noise. The conditional probability is obtained by the
Markov-chain Monte Carlo simulations combined with an exchange Monte Carlo
method. The efficiency of our method is tested using synthetic magnetization
curve data, and the results show that spin-spin interactions are estimated with
a high accuracy. In particular, the relevant terms of the spin-spin
interactions are successfully selected from the redundant interaction
candidates by the $l_1$ regularization in the prior distribution.
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We introduce the concept of hyperreflection groups, which are a
generalization of Coxeter groups. We prove the Deletion and Exchange Conditions
for hyperreflection groups, and we discuss special subgroups and fundamental
sectors of hyperreflection groups. In the second half of the paper, we prove
that Coxeter groups and graph products of groups are examples of
hyperreflection groups.
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Recently S.Galam and A.Mauger [Phys.Rev.E 56, 322 (1997); cond-mat/9706304 ]
proposed an approximant which relates the bond and the site percolation
threshold for a particular lattice. Their formula is based on a fit to exact
and simulation results obtained earlier for different periodic and aperiodic
lattices. However, the numerical result for an aperiodic dodecagonal lattice
does not agree well with the proposed formula. I present here new and more
precise data for this and other aperiodic lattices. The previously published
value for the dodecagonal lattice is confirmed. The reason for the deviation
from the Galam and Mauger approximant is discussed.
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In this paper, we first characterize the finiteness of fractal interpolation
functions (FIFs) on post critical finite self-similar sets. Then we study the
Laplacian of FIFs with uniform vertical scaling factors on Sierpinski gasket
(SG). As an application, we prove that the solution of the following Dirichlet
problem on SG is an FIF with uniform vertical scaling factor $\frac{1}{5}$:
$\Delta u=0$ on $SG\setminus \{q_1,q_2,q_3\}$, and $u(q_i)=a_i$, $i=1,2,3$,
where $q_i$, $i=1,2,3$, are boundary points of SG.
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The performance of an iterative reconstruction algorithm for X-ray tomography
is strongly determined by the features of the used forward and backprojector.
For this reason, a large number of studies has focused on the to design of
projectors with increasingly higher accuracy and speed. To what extent the
accuracy of an iterative algorithm is affected by the mathematical affinity and
the similarity between the actual implementation of the forward and
backprojection, referred here as "coupling projector-backprojector", has been
an overlooked aspect so far. The experimental study presented here shows that
the reconstruction quality and the convergence of an iterative algorithm
greatly rely on a good matching between the implementation of the tomographic
operators. In comparison, other aspects like the accuracy of the standalone
operators, the usage of physical constraints or the choice of stopping criteria
may even play a less relevant role.
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We show that new BRST charges in RNS superstring theory with nonstandard
ghost numbers, constructed in our recent work, can be mapped to deformed pure
spinor (PS) superstring theories, with the nilpotent pure spinor BRST charge
$Q_{PS}=\oint{\lambda^\alpha}d_\alpha$ still retaining its form but with
singular operator products between commuting spinor variables $\lambda^\alpha$.
Despite the OPE singularities, the pure spinor condition
$\lambda\gamma^m\lambda=0$ is still fulfilled in a weak sense, explained in the
paper. The operator product singularities correspond to introducing
interactions between the pure spinors. We conjecture that the leading
singularity orders of the OPE between two interacting pure spinors is related
to the ghost number of the corresponding BRST operator in RNS formalism.
Namely, it is conjectured that the BRST operators of minimal superconformal
ghost numbers $n=1,2,3...$ can be mapped to nilpotent BRST operators in the
deformed pure spinor formalism with the OPE of two commuting spinors having a
leading singularity order $\lambda(z)\lambda(w)\sim{O}(z-w)^{-2(n^2+6n+1)}$.
The conjecture is checked explicitly for the first non-trivial case $n=1$.
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Several comments are given to previous proofs of the generalised second law
of thermodynamics: black hole entropy plus ordinary matter entropy never
decreases for a thermally closed system. Arguments in favour of its truism are
given in the spirit of conventional thermodynamics.
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We present a completed, publicly available corpus of annotated semantic
relations of adpositions and case markers in Hindi. We used the multilingual
SNACS annotation scheme, which has been applied to a variety of typologically
diverse languages. Building on past work examining linguistic problems in SNACS
annotation, we use language models to attempt automatic labelling of SNACS
supersenses in Hindi and achieve results competitive with past work on English.
We look towards upstream applications in semantic role labelling and extension
to related languages such as Gujarati.
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In this paper we consider time dependent Schr\"odinger equations on the
one-dimensional torus $\T := \R /(2 \pi \Z)$ of the form $\partial_t u = \ii
{\cal V}(t)[u]$ where ${\cal V}(t)$ is a time dependent, self-adjoint
pseudo-differential operator of the form ${\cal V}(t) = V(t, x) |D|^M + {\cal
W}(t)$, $M > 1$, $|D| := \sqrt{- \partial_{xx}}$, $V$ is a smooth function
uniformly bounded from below and ${\cal W}$ is a time-dependent
pseudo-differential operator of order strictly smaller than $M$. We prove that
the solutions of the Schr\"odinger equation $\partial_t u = \ii {\cal V}(t)[u]$
grow at most as $t^\e$, $t \to + \infty$ for any $\e > 0$. The proof is based
on a reduction to constant coefficients up to smoothing remainders of the
vector field $\ii {\cal V}(t)$ which uses Egorov type theorems and
pseudo-differential calculus.
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This paper proposes a novel model, named Continuity-Discrimination
Convolutional Neural Network (CD-CNN), for visual object tracking. Existing
state-of-the-art tracking methods do not deal with temporal relationship in
video sequences, which leads to imperfect feature representations. To address
this problem, CD-CNN models temporal appearance continuity based on the idea of
temporal slowness. Mathematically, we prove that, by introducing temporal
appearance continuity into tracking, the upper bound of target appearance
representation error can be sufficiently small with high probability. Further,
in order to alleviate inaccurate target localization and drifting, we propose a
novel notion, object-centroid, to characterize not only objectness but also the
relative position of the target within a given patch. Both temporal appearance
continuity and object-centroid are jointly learned during offline training and
then transferred for online tracking. We evaluate our tracker through extensive
experiments on two challenging benchmarks and show its competitive tracking
performance compared with state-of-the-art trackers.
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We have explored the multi-component structure of electrical conductivity of
relativistic Fermionic and Bosonic fluid in presence of magnetic field by using
Kubo approach. This is done by explicitly evaluating the thermo-magnetic vector
current spectral functions using the real time formalism of finite temperature
field theory and the Schwinger proper time formalism. In absence of magnetic
field, the one-loop diagramatic representation of Kubo expression of any
transport coefficients is exactly same with relaxation time approximation (RTA)
based expression, but this equality does not hold for finite magnetic field
picture due to lacking of proper implementation of quantum effect in latter
approach. We have shown this discrepancy for particular transport coefficient -
electrical conductivity, whose starting point in Kubo approach will be
electromagnetic current-current correlator and its one-loop skeleton diagram
carrying two scalar/Dirac propagators for scalar/Dirac fluid. Through a
numerical comparison between RTA and Kubo expressions of conductivity
components (parallel and perpendicular), we have attempted to interpret detail
quantum field theoretical effect, contained by Kubo expression but not by RTA
expression. In classical RTA expression we get magnetic field independent
parallel conductivity due to zero Lorentz force but in field theoretical Kubo
expression, it decreases and increases with the magnetic field for scalar and
Dirac medium respectively due to Landau quantization effect. This parallel
component of conductivity can be interpreted as zero momentum limit of quantum
fluctuation with same Landau level internal lines. While for perpendicular
component of conductivity, fluctuation with Landau level differences $\pm 1$
are noticed, which might be a new realization of transportation in field
theoretical sector.
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We describe a realistic model for a focused high-intensity laser pulse in
three dimensions. Relativistic dynamics of an electron submitted to such pulse
is described by equations of motion with ponderomotive potential depending on a
single free parameter in the problem, which we refer to as the "asymmetry
parameter". It is shown that the asymmetry parameter can be chosen to provide
quantitative agreement of the developed theory with experimental results of
Malka et al. [Phys. Rev. Lett. 78, 3314 (1997)] who detected angular asymmetry
in the spatial pattern of electrons accelerated in vacuum by a high-intensity
laser pulse.
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Polarimetry is about to become a powerful tool for determining the
atmospheric properties of exoplanets. To provide the basis for the
interpretation of observational results and for predictive studies to guide
future observations, sophisticated analysis tools are required. Our goal is to
develop a radiative transfer tool that contains all the relevant continuum
polarization mechanisms for the comprehensive analysis of the polarized flux
resulting from the scattering in the atmosphere of, on the surface of, and in
the local planetary environment (e.g., planetary rings, exomoons) of
extra-solar planets. Furthermore, our goal is to avoid common simplifications
such as locally plane-parallel planetary atmospheres, the missing cross-talk
between latitudinal and longitudinal regions, or the assumption of either a
point-like star or plane-parallel illumination. As a platform for the newly
developed numerical algorithms, we use the 3D Monte Carlo radiative transfer
code POLARIS. The code is extended and optimized for the radiative transfer in
exoplanetary atmospheres. We investigate the reflected flux and its degree of
polarization for different phase angles for a homogeneous cloud-free atmosphere
and an inhomogeneous cloudy atmosphere. To take advantage of the 3D radiative
transfer and to demonstrate the potential of the code, the impact of an
additional circumplanetary ring on the reflected polarized flux is studied. The
presence of a circumplanetary ring consisting of small water-ice particles has
a noticeable impact on the reflected polarized radiation. In particular, the
reflected flux strongly increases at larger phase angles if the planetary orbit
is seen edge-on because the considered particles tend to scatter forwards. In
contrast, the degree of polarization decreases at these phase angles.
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We develop an approach where the quantum system states and quantum
observables are described as in classical statistical mechanics -- the states
are identified with probability distributions and observables, with random
variables. An example of the spin-1/2 state is considered. We show that the
triada of Malevich's squares can be used to illustrate the qubit state. We
formulate the superposition principle of quantum states in terms of
probabilities determining the quantum states. New formulas for nonlinear
addition rules of probabilities providing the probabilities associated with the
interference of quantum states are obtained. The evolution equation for quantum
states is given in the form of a kinetic equation for the probability
distribution identified with the state.
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Magnetic reconnection is essential to release the flux rope during its
ejection. The question remains: how does the magnetic reconnection change the
flux rope structure? Following the original study of \citet{Qiu2007}, we
compare properties of ICME/MC flux ropes measured at 1 AU and properties of
associated solar progenitors including flares, filaments, and CMEs. In
particular, the magnetic field-line twist distribution within interplanetary
magnetic flux ropes is systematically derived and examined. Our analysis shows
that for most of these events, the amount of twisted flux per AU in MCs is
comparable with the total reconnection flux on the Sun, and the sign of the MC
helicity is consistent with the sign of helicity of the solar source region
judged from the geometry of post-flare loops. Remarkably, we find that about
one half of the 18 magnetic flux ropes, most of them being associated with
erupting filaments, have a nearly uniform and relatively low twist distribution
from the axis to the edge, and the majority of the other flux ropes exhibit
very high twist near the axis, of up to $\gtrsim 5$ turns per AU, which
decreases toward the edge. The flux ropes are therefore not linear force free.
We also conduct detailed case studies showing the contrast of two events with
distinct twist distribution in MCs as well as different flare and dimming
characteristics in solar source regions, and discuss how reconnection geometry
reflected in flare morphology may be related to the structure of the flux rope
formed on the Sun.
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A well-known precursor of an imminent solar eruption is the appearance of a
hot S-shaped loop, also known as sigmoid, in an active region (AR).
Classically, the formation of such an S-shaped loop is envisaged to be
implemented by magnetic reconnection of two oppositely oriented J-shaped loops.
However, the details of reconnection are elusive due to weak emission and
subtle evolution during the pre-eruptive phase. In this paper, we investigate
how a single J-shaped loop transforms into an S-shaped one through the slippage
of one of its footpoints in NOAA AR 11719 on 2013 April 11. During an interval
of about 16 min, the J-shaped loop slips through a low-corona region of strong
electric current density in a bursty fashion, reaching a peak apparent speed as
fast as over 1000 km s$^{-1}$, at the slipping footpoint. The enhancement of
electric current density, as suggested by non-linear force-free field modeling,
indicates that the "non-idealness" of coronal plasma becomes locally important,
which may facilitate magnetic reconnection. The loop segment undergoing
slipping motions is heated; meanwhile, above the fixed footpoint coronal
emission dims due to a combination effect of the lengthening and heating of the
loop, the latter of which is manifested in the temporal variation of dimming
slope and of emission measure. These features together support an asymmetric
scenario of sigmoid formation through slipping reconnection of a single
J-shaped loop, which differs from the standard tether-cutting scenario
involving a double J-shaped loop system.
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We study the problem of computing robust controllable sets for discrete-time
linear systems with additive uncertainty. We propose a tractable and scalable
approach to inner- and outer-approximate robust controllable sets using
constrained zonotopes, when the additive uncertainty set is a symmetric,
convex, and compact set. Our least-squares-based approach uses novel
closed-form approximations of the Pontryagin difference between a constrained
zonotopic minuend and a symmetric, convex, and compact subtrahend. Unlike
existing approaches, our approach does not rely on convex optimization solvers,
and is projection-free for ellipsoidal and zonotopic uncertainty sets. We also
propose a least-squares-based approach to compute a convex, polyhedral
outer-approximation to constrained zonotopes, and characterize sufficient
conditions under which all these approximations are exact. We demonstrate the
computational efficiency and scalability of our approach in several case
studies, including the design of abort-safe rendezvous trajectories for a
spacecraft in near-rectilinear halo orbit under uncertainty. Our approach can
inner-approximate a 20-step robust controllable set for a 100-dimensional
linear system in under 15 seconds on a standard computer.
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Energy consumption is a major limitation of low power and mobile devices.
Efficient transmission protocols are required to minimize an energy consumption
of the mobile devices for ubiquitous connectivity in the next generation
wireless networks. Opportunistic schemes select a single relay using the
criteria of the best channel and achieve a near-optimal diversity performance
in a cooperative wireless system. In this paper, we study the energy efficiency
of the opportunistic schemes for device-to-device communication. In the
opportunistic approach, an energy consumed by devices is minimized by selecting
a single neighboring device as a relay using the criteria of minimum consumed
energy in each transmission in the uplink of a wireless network. We derive
analytical bounds and scaling laws on the expected energy consumption when the
devices experience log-normal shadowing with respect to a base station
considering both the transmission as well as circuit energy consumptions. We
show that the protocol improves the energy efficiency of the network comparing
to the direct transmission even if only a few devices are considered for
relaying. We also demonstrate the effectiveness of the protocol by means of
simulations in realistic scenarios of the wireless network.
|
Holomorphic vector bundles on $\mathbb C\times M$, $M$ a complex manifold,
with meromorphic connections with poles of Poincar\'e rank 1 along $\{0\}\times
M$ arise naturally in algebraic geometry. They are called $(TE)$-structures
here. This paper takes an abstract point of view. It gives a complete
classification of all $(TE)$-structures of rank 2 over germs $\big(M,t^0\big)$
of manifolds. In the case of $M$ a point, they separate into four types. Those
of three types have universal unfoldings, those of the fourth type (the
logarithmic type) not. The classification of unfoldings of $(TE)$-structures of
the fourth type is rich and interesting. The paper finds and lists also all
$(TE)$-structures which are basic in the following sense: Together they induce
all rank $2$ $(TE)$-structures, and each of them is not induced by any other
$(TE)$-structure in the list. Their base spaces $M$ turn out to be
2-dimensional $F$-manifolds with Euler fields. The paper gives also for each
such $F$-manifold a classification of all rank 2 $(TE)$-structures over it.
Also this classification is surprisingly rich. The backbone of the paper are
normal forms. Though also the monodromy and the geometry of the induced Higgs
fields and of the bases spaces are important and are considered.
|
This article investigates an extension of General Relativity based upon a
class of lifted metrics on the cotangent bundle of space-time. The dynamics of
the theory is determined by a fixed section of the cotangent bundle,
representing the momentum of a fluid flow, and Einstein's equations for the
fluid applied to the induced space-time metric on the submanifold of the
cotangent bundle defined by the image of the section. This construction is
formally analogous to the extension of Galilean Relativity by Special
Relativity, and is shown to reduce to General Relativity as the gravitational
constant approaches zero. By examining the consequences of the model for
homogeneous cosmologies, it is demonstrated that this construction globalizes
the equivalence principle, in that, the perfect fluid model of Special
Relativity is sufficient to predict both the inflationary and the current era.
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We develop a large-scale regularity theory of higher order for
divergence-form elliptic equations with heterogeneous coefficient fields $a$ in
the context of stochastic homogenization. The large-scale regularity of
$a$-harmonic functions is encoded by Liouville principles: The space of
$a$-harmonic functions that grow at most like a polynomial of degree $k$ has
the same dimension as in the constant-coefficient case. This result can be seen
as the qualitative side of a large-scale $C^{k,\alpha}$-regularity theory,
which in the present work is developed in the form of a corresponding
$C^{k,\alpha}$-"excess decay" estimate: For a given $a$-harmonic function $u$
on a ball $B_R$, its energy distance on some ball $B_r$ to the above space of
$a$-harmonic functions that grow at most like a polynomial of degree $k$ has
the natural decay in the radius $r$ above some minimal radius $r_0$.
Though motivated by stochastic homogenization, the contribution of this paper
is of purely deterministic nature: We work under the assumption that for the
given realization $a$ of the coefficient field, the couple $(\phi,\sigma)$ of
scalar and vector potentials of the harmonic coordinates, where $\phi$ is the
usual corrector, grows sublinearly in a mildly quantified way. We then
construct "$k$th-order correctors" and thereby the space of $a$-harmonic
functions that grow at most like a polynomial of degree $k$, establish the
above excess decay and then the corresponding Liouville principle.
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We present the All-Seeing Project V2: a new model and dataset designed for
understanding object relations in images. Specifically, we propose the
All-Seeing Model V2 (ASMv2) that integrates the formulation of text generation,
object localization, and relation comprehension into a relation conversation
(ReC) task. Leveraging this unified task, our model excels not only in
perceiving and recognizing all objects within the image but also in grasping
the intricate relation graph between them, diminishing the relation
hallucination often encountered by Multi-modal Large Language Models (MLLMs).
To facilitate training and evaluation of MLLMs in relation understanding, we
created the first high-quality ReC dataset ({AS-V2) which is aligned with the
format of standard instruction tuning data. In addition, we design a new
benchmark, termed Circular-based Relation Probing Evaluation (CRPE) for
comprehensively evaluating the relation comprehension capabilities of MLLMs.
Notably, our ASMv2 achieves an overall accuracy of 52.04 on this relation-aware
benchmark, surpassing the 43.14 of LLaVA-1.5 by a large margin. We hope that
our work can inspire more future research and contribute to the evolution
towards artificial general intelligence. Our project is released at
https://github.com/OpenGVLab/all-seeing.
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Array-intensive programs are often amenable to parallelization across many
cores on a single machine as well as scaling across multiple machines and hence
are well explored, especially in the domain of high-performance computing.
These programs typically undergo loop transformations and arithmetic
transformations in addition to parallelizing transformations. Although a lot of
effort has been invested in improving parallelizing compilers, experienced
programmers still resort to hand-optimized transformations which is typically
followed by careful tuning of the transformed program to finally obtain the
optimized program. Therefore, it is critical to verify that the functional
correctness of an original sequential program is not sacrificed during the
process of optimization. In this paper, we cover important literature on
functional verification of array-intensive programs which we believe can be a
good starting point for one interested in this field.
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In this paper, the polarization modes of gravitational waves in Horndeski
gravity are studied under the Palatini formalism. After obtaining the
linearized equation of perturbations in Minkowski background, we find that the
polarization modes of gravitational waves depend on the selection of the
theoretical parameters. The polarization modes can be divided into quite rich
cases by parameters. In all cases of parameter selection, there are $+$ and
$\times$ modes propagating at the speed of light but no vector modes. The only
difference from general relativity is scalar modes, especially the scalar
degrees of freedom can be 0, 1 or 2 in different cases. The appropriate
parameter cases can be expected to be selected in the detection of
gravitational wave polarization modes by Lisa, Taiji and TianQin in the future.
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The prevailing net-centric environment demands and enables modeling and
simulation to combine efforts from numerous disciplines. Software techniques
and methodology, in particular service-oriented architecture, provide such an
opportunity. Service-oriented simulation has been an emerging paradigm
following on from object- and process-oriented methods. However, the ad-hoc
frameworks proposed so far generally focus on specific domains or systems and
each has its pros and cons. They are capable of addressing different issues
within service-oriented simulation from different viewpoints. It is
increasingly important to describe and evaluate the progress of numerous
frameworks. In this paper, we propose a novel three-dimensional reference model
for a service-oriented simulation paradigm. The model can be used as a
guideline or an analytic means to find the potential and possible future
directions of the current simulation frameworks. In particular, the model
inspects the crossover between the disciplines of modeling and simulation,
service-orientation, and software/systems engineering. Based on the model, we
present a comprehensive survey on several classical service-oriented simulation
frameworks, including formalism-based, model-driven, interoperability protocol
based, eXtensible Modeling and Simulation Framework (XMSF), and Open Grid
Services Architecture (OGSA) based frameworks etc. The comparison of these
frameworks is also performed. Finally the significance both in academia and
practice are presented and future directions are pointed out.
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We show that the equation in the title (with $\Phi_m$ the $m$th cyclotomic
polynomial) has no integer solution with $n\ge 1$ in the cases $(m,p)=(15,41),
(15,5581),(10,271)$. These equations arise in a recent group theoretical
investigation by Z. Akhlaghi, M. Khatami and B. Khosravi.
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Wolf-Rayet (WR) stars in the Magellanic Clouds (MCs) are ideal for studying
the production of X-ray emission by their strong fast stellar winds. We have
started a systematic survey for X-ray emission from WR stars in the MCs using
archival Chandra, ROSAT, and XMM-Newton observations. In Paper I, we reported
the detection of X-ray emission from 29 WR stars using Chandra ACIS
observations of 70 WR stars in the MCs. In this paper, we report the search and
analysis of archival ROSAT PSPC and HRI observations of WR stars. While useful
ROSAT observations are available for 117 WR stars in the MCs, X-ray emission is
detected from only 7 of them. The detection rate of X-ray emission from MCs WR
stars in the ROSAT survey is much smaller than in the Chandra ACIS survey,
illustrating the necessity of high angular resolution and sensitivity. LMC-WR
101-102 and 116 were detected by both ROSAT and Chandra, but no large long-term
variations are evident.
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Recent measurements, in particular those on $\Lambda$ polarization and spin
alignment of vector mesons in $e^+e^-$ annihilation at LEP, and those on the
azimuthal asymmetry at HERA, have attracted much attention on the spin effects
in high energy fragmentation processes. In this talk, we make a brief
introduction to the different topics studied in this connection and a short
summary of the available data. After that, we present a short summary of the
main theoretical results that we obtained in studying these different topics.
The talk was mainly based on the publications [5-9] which have been finished in
collaboration with C.Boros, Liu Chun-xiu and Xu Qing-hua.
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It is shown that generalized CDT, the two-dimensional theory of quantum
gravity, constructed as a scaling limit from so-called causal dynamical
triangulations, can be obtained from a cubic matrix model. It involves taking a
new scaling limit of matrix models, which is more natural from a classical
point of view.
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The possibilty of performing high-rate calorimetry with a slow scintillator
crystal is studied. In this experimental situation, to avoid pulse pile-up, it
can be necessary to base the energy measurement on only a fraction of the
emitted light, thus spoiling the energy resolution. This effect was
experimentally studied with a BGO crystal and a photomultiplier followed by an
integrator, by measuring the peak amplitude of the signals. The experimental
data show that the energy resolution is exclusively due to the statistical
fluctuations of the number of photoelectrons contributing to the peak
amplitude. When such number is small its fluctuations are even smaller than
those predicted by Poisson statistics. These results were confirmed by a Monte
Carlo simulation which allows to estimate, in a general case, the energy
resolution, given the total number of photoelectrons, the scintillation time
and the integration time.
|
We outline a brief description of non commutative geometry and present some
applications in string theory. We use the fuzzy torus as our guiding example.
|
We analyze zero modes of the Dirac operator for SU(2) lattice gauge theory.
We find that the zero modes are strongly localized in all 4 directions. The
position of these lumps depends on the boundary conditions we use for the Dirac
operator. We compare periodic boundary conditions and anti-periodic boundary
conditions and find that the position of the zero modes jumps for about one
third of the configurations.
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Image fusion produces a single fused image from a set of input images. A new
method for image fusion is proposed based on Weighted Average Merging Method
(WAMM) in the NonSubsampled Contourlet Transform (NSCT) domain. A performance
analysis on various statistical fusion rules are also analysed both in NSCT and
Wavelet domain. Analysis has been made on medical images, remote sensing images
and multi focus images. Experimental results shows that the proposed method,
WAMM obtained better results in NSCT domain than the wavelet domain as it
preserves more edges and keeps the visual quality intact in the fused image.
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A calculation of the thermal quark propagator is presented taking the gluon
condensate above the critical temperature into account. The quark dispersion
relation and the dilepton production following from this propagator are
derived.
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We study the band structure modulation and spin-Hall effect of a
two-dimensional heavy-hole system with $k^3$-Rashba spin-orbit coupling (RSOC),
irradiated by linearly polarized light. We find that the band structure becomes
anisotropic under the illumination by the light. Most remarkably, a pair of
additional spin-degeneracy points (apart from $\Gamma$ point) emerge in the
energy dispersion, the locations of which are solely determined by the strength
of the amplitude of the incident light. If this degeneracy occurs around the
Fermi level, the spin-Hall conductivity (SHC) exhibits a resonance. Away from
the degeneracy points, the light rotates the average spin polarization. The
possible effects of $k^3$-Dresselhaus spin-orbit coupling are also discussed.
|
Evidence is presented for the associated production of a single top quark and
W boson in pp collisions at sqrt(s) = 7 TeV with the CMS experiment at the LHC.
The analyzed data corresponds to an integrated luminosity of 4.9 inverse
femtobarns. The measurement is performed using events with two leptons and a
jet originated from a b quark. A multivariate analysis based on kinematic
properties is utilized to separate the t t-bar background from the signal. The
observed signal has a significance of 4.0 sigma and corresponds to a cross
section of 16 +5 -4 pb, in agreement with the standard model expectation of
15.6 +/-0.4 +1.0 -1.2 pb.
|
One of the ways to understand the genesis and evolution of the universe is to
know how galaxies have formed and evolved. In this regard, the study of star
formation history (SFH) plays an important role in the accurate understanding
of galaxies. In this paper, we used long-period variable stars (LPVs) to
estimate the SFH in the Andromeda galaxy (M31). These cool stars reach their
peak luminosity in the final stage of their evolution; their birth mass is
directly related to their luminosity. Therefore, we construct the mass function
and the star formation history using stellar evolution models.
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Photoplethysmographic Imaging (PPGI) allows the determination of pulse rate
variability from sequential beat-to-beat intervals (BBI) and pulse wave
velocity from spatially resolved recorded pulse waves. In either case,
sufficient temporal accuracy is essential.
The presented work investigates the temporal accuracy of BBI estimation from
photoplethysmographic signals. Within comprehensive numerical simulation, we
systematically assess the impact of sampling rate, signal-to-noise ratio (SNR),
and beat-to-beat shape variations on the root mean square error (RMSE) between
real and estimated BBI.
Our results show that at sampling rates beyond 14 Hz only small errors exist
when interpolation is used. For example, the average RMSE is 3 ms for a
sampling rate of 14 Hz and an SNR of 18 dB. Further increasing the sampling
rate only results in marginal improvements, e.g. more than tripling the
sampling rate to 50 Hz reduces the error by approx. 14%. The most important
finding relates to the SNR, which is shown to have a much stronger influence on
the error than the sampling rate. For example, increasing the SNR from 18 dB to
24 dB at 14 Hz sampling rate reduced the error by almost 50% to 1.5 ms. Subtle
beat-to-beat shape variations, moreover, increase the error decisively by up to
800%.
Our results are highly relevant in three regards: first, they partially
explain different results in the literature on minimum sampling rates. Second,
they emphasize the importance to consider SNR and possibly shape variation in
investigations on the minimal sampling rate. Third, they underline the
importance of appropriate processing techniques to increase SNR. Importantly,
though our motivation is PPGI, the presented work immediately applies to
contact PPG and PPG in other settings such as wearables. To enable further
investigations, we make the scripts used in modelling and simulation freely
available.
|
Charge noise is the main hurdle preventing high-fidelity operation, in
particular that of two-qubit gates, of semiconductor-quantum-dot-based spin
qubits. While certain sweet spots where charge noise is substantially
suppressed have been demonstrated in several types of spin qubits, the
existence of one for coupled singlet-triplet qubits is unclear. We
theoretically demonstrate, using full configuration-interaction calculations,
that a range of nearly sweet spots appear in the coupled singlet-triplet qubit
system when a strong enough magnetic field is applied externally. We further
demonstrate that ramping to and from the judiciously chosen nearly sweet spot
using sequences based on the shortcut to adiabaticity offers maximal gate
fidelities under charge noise and phonon-induced decoherence. These results
should facilitate realization of high-fidelity two-qubit gates in
singlet-triplet qubit systems.
|
Driven lattice gases serve as canonical models for investigating collective
transport phenomena and properties of non-equilibrium steady states (NESS).
Here we study one-dimensional transport with nearest-neighbor interactions both
in closed bulk systems and in open channels coupled to two particle reservoirs
at the ends of the channel. For the widely employed Glauber rates we derive an
exact current-density relation in the bulk for unidirectional hopping. An
approach based on time-dependent density functional theory provides a good
description of the kinetics. For open systems, the system-reservoir couplings
are shown to have a striking influence on boundary-induced phase diagrams. The
role of particle-hole symmetry is discussed and its consequence on the topology
of the phase diagrams. It is furthermore demonstrated that systems with weak
bias can be mapped onto systems with unidirectional hopping.
|
Recent work in cross-lingual contextual word embedding learning cannot handle
multi-sense words well. In this work, we explore the characteristics of
contextual word embeddings and show the link between contextual word embeddings
and word senses. We propose two improving solutions by considering contextual
multi-sense word embeddings as noise (removal) and by generating cluster level
average anchor embeddings for contextual multi-sense word embeddings
(replacement). Experiments show that our solutions can improve the supervised
contextual word embeddings alignment for multi-sense words in a microscopic
perspective without hurting the macroscopic performance on the bilingual
lexicon induction task. For unsupervised alignment, our methods significantly
improve the performance on the bilingual lexicon induction task for more than
10 points.
|
The equilibrium structure, energy bands, phonon dispersions, and s- and
d-channel electron-phonon interactions (EPIs) are calculated for the
infinite-layer superconductor CaCuO2 doped with 0.24 holes per CuO2. The LDA
and the linear-response full-potential LMTO method were used. In the
equilibrium structure, oxygen is found to buckle slightly out of the plane and,
as a result, the characters of the energy bands near EF are found to be similar
to those of other optimally doped HTSCs. For the EPI we find lambda(s)=0.4, in
accord with previous LDA calculations for YBa2Cu3O7. This supports the common
belief that the EPI mechanism alone is insufficient to explain HTSC.
Lambda(x^2-y^2) is found to be positive and nearly as large as lambda(s). This
is surprising and indicates that the EPI could enhance some other d-wave
pairing mechanism. Like in YBa2Cu3O7, the buckling modes contribute
significantly to the EPI, although these contributions are proportional to the
static buckling and would vanish for flat planes. These numerical results can
be understood from a generic tight-binding model originally derived from the
LDA bands of YBa2Cu3O7. In the future, the role of anharmonicity of the
buckling-modes and the influence of the spin-fluctuations should be
investigated.
|
Large facial variations are the main challenge in face recognition. To this
end, previous variation-specific methods make full use of task-related prior to
design special network losses, which are typically not general among different
tasks and scenarios. In contrast, the existing generic methods focus on
improving the feature discriminability to minimize the intra-class distance
while maximizing the interclass distance, which perform well on easy samples
but fail on hard samples. To improve the performance on those hard samples for
general tasks, we propose a novel Distribution Distillation Loss to narrow the
performance gap between easy and hard samples, which is a simple, effective and
generic for various types of facial variations. Specifically, we first adopt
state-of-the-art classifiers such as ArcFace to construct two similarity
distributions: teacher distribution from easy samples and student distribution
from hard samples. Then, we propose a novel distribution-driven loss to
constrain the student distribution to approximate the teacher distribution,
which thus leads to smaller overlap between the positive and negative pairs in
the student distribution. We have conducted extensive experiments on both
generic large-scale face benchmarks and benchmarks with diverse variations on
race, resolution and pose. The quantitative results demonstrate the superiority
of our method over strong baselines, e.g., Arcface and Cosface.
|
We study experimentally and theoretically the probability density functions
of the injected and dissipated energy in a system of a colloidal particle
trapped in a double well potential periodically modulated by an external
perturbation. The work done by the external force and the dissipated energy are
measured close to the stochastic resonance where the injected power is maximum.
We show a good agreement between the probability density functions exactly
computed from a Langevin dynamics and the measured ones. The probability
density function of the work done on the particle satisfies the fluctuation
theorem.
|
This study corrects the hypsometric equation by restoring the nontraditional
terms to relax the hydrostatic approximation. The nontraditional terms include
one Coriolis term and two metric terms in the vertical momentum equation. The
hypsometric equations with and without the nontraditional correction are used
to calculate the geopotential height of pressure levels using more than 300,000
selected tropical rawinsonde profiles. With westerlies between two pressure
levels, the thickness of the layer increases, which reduces the upward pressure
gradient forces to balance the upward nontraditional Coriolis forces; the
opposite is true for easterlies. Hence, zonal winds are negatively correlated
with traditional geopotential height biases aloft. At 500 hPa, for example,
traditional geopotential height error in the tropical troposphere is on the
order of at least 0.5 m, which is considerable with respect to geopotential
height variability in tropical large-scale flow, on the order of 10 m to 15 m.
|
A single four-level atom interacting with two-mode cavities is investigated.
Under large detuning condition, we obtain the effective Hamiltonian which is
unitary squeezing operator of two-mode fields. Employing the input-output
theory, we find that the entanglement and squeezing of the output fields can be
achieved. By analyzing the squeezing spectrum, we show that asymmetric detuning
and asymmetric atomic initial state split the squeezing spectrum from one
valley into two minimum values, and appropriate leakage of the cavity is needed
for obtaining output entangled fields.
|
We consider a general (beyond $T\bar T$) deformation of the 2D $O(N+1)$
$\sigma$-model by the irrelevant dimension-four operators. The theory deformed
in this most general way is not integrable, and the $S$-matrix loses its
factorization properties. We perform the all-order summation of the leading
infrared logs for the $2 \to 2$ scattering amplitude and provide the exact
result for the $2 \to 2$ $S$-matrix in the leading logarithmic approximation.
These results can provide us with new insights into the properties of the
theories deformed by irrelevant operators more general than the $T\bar T$
deformation.
|
The expressions of momentum and energy of a particle in special relativity
are often derived in a quite unconvincing manner in elementary text, by
resorting either to electrodynamic or quantum considerations, or via the
introduction of the less-than-elementary concept of a four-vector. It is
instead possible, by exploiting considerations introduced by P. Epstein and A.
Einstein and exploited later by Feynman, to obtain a fully elementary
derivation of these expressions and of the $E=mc^2$ formula exploiting only
Lorentz transformations and the postulate of the conservation of quantities
defined for point-like particles which reduce to the Newtonian expressions of
momentum and energy in the classical limit.
|
Dietary intake estimation plays a crucial role in understanding the
nutritional habits of individuals and populations, aiding in the prevention and
management of diet-related health issues. Accurate estimation requires
comprehensive datasets of food scenes, including images, segmentation masks,
and accompanying dietary intake metadata. In this paper, we introduce
NutritionVerse-Real, an open access manually collected 2D food scene dataset
for dietary intake estimation with 889 images of 251 distinct dishes and 45
unique food types. The NutritionVerse-Real dataset was created by manually
collecting images of food scenes in real life, measuring the weight of every
ingredient and computing the associated dietary content of each dish using the
ingredient weights and nutritional information from the food packaging or the
Canada Nutrient File. Segmentation masks were then generated through human
labelling of the images. We provide further analysis on the data diversity to
highlight potential biases when using this data to develop models for dietary
intake estimation. NutritionVerse-Real is publicly available at
https://www.kaggle.com/datasets/nutritionverse/nutritionverse-real as part of
an open initiative to accelerate machine learning for dietary sensing.
|
In gravitational thermodynamics, the entropy of a black hole with distinct
surface gravities can be evaluated in a microcanonical ensemble. At the $WKB$
level, the entropy becomes the negative of the Euclidean action of the
constrained instanton, which is the seed for the black hole creation in the
no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite
universal formula in Euclidean quantum gravity that the entropy of a
nonrotating black hole is one quarter the sum of the products of the Euler
characteristics and the areas of the horizons. For Lovelock gravity, the
entropy and quantum creation of a black hole are also studied.
|
The formation of periodic wrinkles in soft layered materials due to
mechanical instabilities is prevalent in nature and has been proposed for use
in multiple applications. However, such phenomena have been explored
predominantly in quasi-static settings. In this work, we measure the dynamics
of soft elastomeric blocks with stiff surface films subjected to high-speed
impact, and observe wrinkles forming along with, and riding upon, waves
propagating through the system. We analyze our measurements with
large-deformation, nonlinear visco-hyperelastic Finite Element simulations
coupled to an analytical wrinkling model. The comparison between the measured
and simulated dynamics shows good agreement, and suggests that inertia and
viscoelasticity play an important role. This work encourages future studies of
the dynamics of surface instabilities in soft materials, including
large-deformation, highly nonlinear morphologies, and may have applications to
areas including impact mitigation, soft electronics, and the dynamics of soft
sandwich composites.
|
Let $A$ be a uniform algebra, $\theta:A\to M_n(\mathbb{C})$ be a continuous
homomorphism and $\alpha:A\to A$ be an antilinear contraction such that \[
\|\theta(f)+\theta(\alpha(f))^*\|\le 2\|f\| \quad(f\in A). \] We show that
$\|\theta\|\le 1+\sqrt{2}$, and that $1+\sqrt2$ is sharp. We conjecture that,
if further $\alpha(1)=1$, then we may conclude that $\|\theta\|\le2$. This
would yield a positive solution to the Crouzeix conjecture on numerical ranges.
In support of our conjecture, we prove that it is true in two special cases. We
also discuss a completely bounded version of our conjecture that brings into
play ideas from dilation theory.
|
In this paper we proof that there exists a function f(x) belongs to L^1[0,1]
such that a greedy algorithm with regard to generalized Walsh system does not
converge to f(x) in L^1[0,1] norm, i.e. the generalized Walsh system is not a
quasi-greedy basis in its linear span L^1[0,1].
|
We propose a gauged $B-L$ extension of the standard model (SM) where light
neutrinos are of Dirac type by virtue of tiny Yukawa couplings with the SM
Higgs. To achieve leptogenesis, we include additional heavy Majorana fermions
without introducing any $B-L$ violation by two units. An additional scalar
doublet with appropriate $B-L$ charge can allow heavy fermion coupling with the
SM leptons so that out of equilibrium decay of the former can lead to
generation of lepton asymmetry. Due to the $B-L$ gauge interactions of the
decaying fermion, the criteria of successful Dirac leptogenesis can also
constrain the gauge sector couplings so as to keep the corresponding washout
processes under control. The same $B-L$ gauge sector parameter space can also
be constrained from dark matter requirements if the latter is assumed to be a
SM singlet particle with non-zero $B-L$ charge. The same $B-L$ gauge
interactions also lead to additional thermalised relativistic degrees of
freedom $\Delta N_{\rm eff}$ from light Dirac neutrinos which are tightly
constrained by Planck 2018 data. While there exists parameter space from the
criteria of successful low scale Dirac leptogenesis, dark matter and $\Delta
N_{\rm eff}$ even after incorporating the latest collider bounds, all the
currently allowed parameters can be probed by future measurements of $\Delta
N_{\rm eff}$.
|
In this paper, a study of topological and algebraic properties of two
families of functions from the unit interval $I$ into the plane $\mathbb{R}^2$
is performed. The first family is the collection of all Peano curves, that is,
of those continuous mappings onto the unit square. The second one is the bigger
set of all space-filling curves, i.e. of those continuous functions $I \to
\mathbb{R}^2$ whose images have positive Jordan content. Emphasis is put on the
size of these families, in both topological and algebraic senses, when endowed
with natural structures.
|
An important challenge in several disciplines is to understand how sudden
changes can propagate among coupled systems. Examples include the
synchronization of business cycles, population collapse in patchy ecosystems,
markets shifting to a new technology platform, collapses in prices and in
confidence in financial markets, and protests erupting in multiple countries. A
number of mathematical models of these phenomena have multiple equilibria
separated by saddle-node bifurcations. We study this behavior in its normal
form as fast--slow ordinary differential equations. In our model, a system
consists of multiple subsystems, such as countries in the global economy or
patches of an ecosystem. Each subsystem is described by a scalar quantity, such
as economic output or population, that undergoes sudden changes via saddle-node
bifurcations. The subsystems are coupled via their scalar quantity (e.g., trade
couples economic output; diffusion couples populations); that coupling moves
the locations of their bifurcations. The model demonstrates two ways in which
sudden changes can propagate: they can cascade (one causing the next), or they
can hop over subsystems. The latter is absent from classic models of cascades.
For an application, we study the Arab Spring protests. After connecting the
model to sociological theories that have bistability, we use socioeconomic data
to estimate relative proximities to tipping points and Facebook data to
estimate couplings among countries. We find that although protests tend to
spread locally, they also seem to "hop" over countries, like in the stylized
model; this result highlights a new class of temporal motifs in longitudinal
network datasets.
|
Neural networks are universal approximators that traditionally have been used
to learn a map between function inputs and outputs. However, recent research
has demonstrated that deep neural networks can be used to approximate
operators, learning function-to-function mappings. Creating surrogate models to
supplement computationally expensive hypersonic aerothermodynamic models in
characterizing the response of flow fields at different angles of attack (AoA)
is an ideal application of neural operators. We investigate the use of neural
operators to infer flow fields (volume and surface quantities) around a
geometry based on a 3D waverider model based on experimental data measured at
the Arnold Engineering Development Center (AEDC) Hypervelocity Wind Tunnel
Number 9. We use a DeepONet neural operator which consists of two neural
networks, commonly called a branch and a trunk network. The final output is the
inner product of the output of the branch network and the output of the trunk
net. Because the flow field contains shocks across the entire volume, we
conduct a two-step training approach of the DeepONet that facilitates accurate
approximation of solutions even in the presence of discontinuities. We train
various DeepONet models to understand and predict pressure $(p)$, density
$(\rho)$, velocity $(u)$, heat flux $(Q_w)$, and total shear stress
$(\tau_{w})$ for the AEDC waverider geometry at Ma=7.36 across AoA that range
from $-10^{\circ}$ to $10^{\circ}$ for surface quantities and from
$-14^{\circ}$ to $14^{\circ}$ for volume quantities.
|
We prove from suitable large cardinal hypotheses that the least weakly
compact cardinal can be unfoldable, weakly measurable and even nearly
$\theta$-supercompact, for any desired $\theta$. In addition, we prove several
global results showing how the entire class of weakly compact cardinals, a
proper class, can be made to coincide with the class of unfoldable cardinals,
with the class of weakly measurable cardinals or with the class of nearly
$\theta_\kappa$-supercompact cardinals $\kappa$, for nearly any desired
function $\kappa\mapsto\theta_\kappa$. These results answer several questions
that had been open in the literature and extend to these large cardinals the
identity-crises phenomenon, first identified by Magidor with the strongly
compact cardinals.
|
We develop a systematic approach to contact and Jacobi structures on graded
supermanifolds. In this framework, contact structures are interpreted as
symplectic principal GL(1,R)-bundles. Gradings compatible with the
GL(1,R)-action lead to the concept of a graded contact manifold, in particular
a linear (more generally, n-linear) contact structure. Linear contact
structures are proven to be exactly the canonical contact structures on first
jets of line bundles. They provide linear Kirillov (or Jacobi) brackets and
give rise to the concept of a Kirillov algebroid, an analog of a Lie algebroid,
for which the corresponding cohomology operator is represented not by a vector
field (de Rham derivative) but a first-order differential operator. It is shown
that one can view Kirillov or Jacobi brackets as homological Hamiltonians on
linear contact manifolds. Contact manifolds of degree 2 are studied, as well as
contact analogs of Courant algebroids. We define lifting procedures that
provide us with constructions of canonical examples of the structures in
question.
|
It has been suggested that the 170 day period in the light curve of the low
mass X-ray binary 4U 1820-30 arises from the presence of a third body with a
large inclination to the binary orbit. We show that this long period motion
arises if the system is librating around the stable fixed point in a Kozai
resonance. We demonstrate that mass transfer drives the system toward this
fixed point, and calculate, both analytically and via numerical integrations,
that the period of libration is of order 170 days when the mutual inclination
is near the Kozai critical value. The non-zero eccentricity of the binary,
combined with tidal dissipation, implies that the rate of change of the binary
period would be slower than, or even of opposite sign to, that implied by
standard mass transfer models. If the 170 day period results from libration,
then, contrary to appearances, the orbital period of the inner binary is
increasing with time; in that case, (e/0.009)^2Q/k_2 > 2.5 x 10^9, where k_2 =
0.01 is the tidal Love number and e = 0.009 is the fiducial eccentricity of the
inner binary. It appears unlikely that the observed negative period derivative
results from the smaller than expected (but positive) value of \dot P combined
with the previously suggested acceleration of the system in the gravitational
field of the host globular cluster NGC 6624. The discrepancy between the
observed and expected period derivative requires further investigation.
|
We study the Higgs boson effects on third-generation squark-pair production
in proton-proton collision at the CERN Large Hadron Collider (LHC), including
$\Stop \Stop^*$, $\Stop\Sbot^*$, and $\Sbot \Sbot^*$. We found that substantial
enhancement can be obtained through s-channel exchanges of Higgs bosons at
large $\tan\beta$, at which the enhancement mainly comes from $b\bar b$, $b\bar
c$, and $c\bar b$ initial states. We compute the complete set of electroweak
(EW) contributions to all production channels. This completes previous
computations in the literature. We found that the EW contributions can be
significant and can reach up to 25% in more general scenarios and at the
resonance of the heavy Higgs boson. The size of Higgs enhancement is comparable
or even higher than the PDF uncertainties and so must be included in any
reliable analysis. A full analytical computation of all the EW contributions is
presented.
|
We study chaotic dynamics in nonholonomic model of Celtic stone. We show
that, for certain values of parameters characterizing geometrical and physical
properties of the stone, a strange Lorenz-like attractor is observed in the
model. We study also bifurcation scenarios for appearance and break-down of
this attractor.
|
We theoretically predict and experimentally demonstrate inhibition of linear
absorption for phase and group velocity mismatched second and third harmonic
generation in strongly absorbing materials, GaAs in particular, at frequencies
above the absorption edge. A 100-fs pump pulse tuned to 1300nm generates 650nm
and 435nm second and third harmonic pulses that propagate across a 450
micron-thick GaAs substrate without being absorbed. We attribute this to a
phase-locking mechanism that causes the pump to trap the harmonics and to
impress them with its dispersive properties.
|
Subwavelength resonators are small scaled objects that exhibit contrasting
medium properties (eigher in intensity or sign) while compared to the ones of a
uniform background. Such contrasts allow them to resonate at specific
frequencies. There are two ways to mathematically define these resonances.
First, as the frequencies for which the related system of integral equations is
not injective. Second, as the frequencies for which the related resolvent
operator of the natural Hamiltonian has a pole. In this work, we consider, as
the subwavelength resonator, the Minneart bubble. We show that these two
mentioned definitions are equivalent. Most importantly,
1. we derive the related resolvent estimates which are uniform in terms of
the size/contrast of the resonators. As a by product, we show that the
resolvent operators have no resonances in the upper half complex plane while
they exhibit two resonances in the lower half plane which converge to the real
axis, as the size of the bubble tends to zero. These resonances are related to
the Minnaert frequency (which constitutes their dominating real part).
2. we derive the asymptotic estimates of the generated scattered fields which
are uniform in terms of the incident frequency and which are valid everywhere
in space (i.e. inside or outside the bubble).
\end{enumerate} The dominating parts, for both the resolvent operator and the
scattered fields, are given by the ones of the point-scatterer supported at the
location of the bubble. In particular, these dominant parts are non trivial
(not the same as those of the background medium) if and only if the used
incident frequency identifies with the Minnaert one.
|
We analyze fermion mixing in the framework of field quantization in curved
spacetime. We compute the expectation value of the energy momentum tensor of
mixed fermions on the flavor vacuum. We consider spatially flat
Friedmann-Lemaitre-Robertson-Walker metrics, and we show that the energy
momentum tensor of the flavor vacuum is diagonal and conserved. Therefore it
can be interpreted as the effective energy momentum tensor of a perfect fluid.
In particular, assuming a fixed De Sitter background, the equation of state of
the fluid is consistent with that of dust and cold dark matter. Our results
establish a new link between quantum effects and classical fluids, and indicate
that the flavor vacuum of mixed fermions may represent a new component of dark
matter.
|
In an atomic, cancellative, commutative monoid, the \omega-value measures how
far an element is from being prime. In numerical monoids, we show that this
invariant exhibits eventual quasilinearity (i.e., periodic linearity). We apply
this result to describe the asymptotic behavior of the \omega-function for a
general numerical monoid and give an explicit formula when the monoid has
embedding dimension 2.
|
In this short note we prove a sector counting lemma for a class of Fermi
surface on the plane which are $C^2$-differentiable and strictly convex. This
result generalizes the one proved in \cite{FKT} for the class of
$C^{2+r}$-differentiable, $r\ge3$, strictly convex and strongly asymmetric
Fermi surfaces, and the one proved in \cite{FMRT} and \cite{BGM1}, for the
class of $C^2$-differentiable, strictly convex and central symmetric Fermi
surfaces. This new sector counting lemma can be used to construct interacting
many-fermion models for the doped graphene, in which the Fermi surface is
extended and quasi-symmetric.
|
In this paper the Randall-Sundrum model with brane-localized curvature terms
is considered. Within some range of parameters a compact extra dimension in
this model can be astronomically large. In this case the model predicts small
deviation from Newton's law at astronomical scales, caused by the massive
modes. The existence of this deviation can result in a slight affection on the
planetary motion trajectories.
|
The level densities and $\gamma$-ray strength functions of
$^{105,106,111,112}$Cd have been extracted from particle-$\gamma$ coincidence
data using the Oslo method. The level densities are in very good agreement with
known levels at low excitation energy. The $\gamma$-ray strength functions
display no strong enhancement for low $\gamma$ energies. However, more
low-energy strength is apparent for $^{105,106}$Cd than for $^{111,112}$Cd. For
$\gamma$ energies above $\approx$ 4 MeV, there is evidence for some extra
strength, similar to what has been previously observed for the Sn isotopes. The
origin of this extra strength is unclear; it might be due to $E1$ and $M1$
transitions originating from neutron skin oscillations or the spin-flip
resonance, respectively.
|
It is shown that for any choice of four different vertices x_1,...,x_4 in a
2-block G of order p>3, there is a hamiltonian cycle in G^2 containing four
different edges x_iy_i of E(G) for certain vertices y_i, i=1,2,3,4. This result
is best possible.
|
An experiment is described that tests theoretical predictions on how C-lines
incident obliquely on a surface behave on reflection. C-lines in a polarised
wave are the analogues of the optical vortices carried by a complex scalar
wave, which is the usual model for describing light and other electromagnetic
waves. The centre of a laser beam that carries a (degenerate) C-line is shifted
on reflection by the well-known Goos-H\"anchen and Imbert-Fedorov effects, but
the C-line itself splits into two, both of which are shifted longitudinally and
laterally; their shifts are different from that of the beam centre. To maximise
the effect to be measured, internal reflection in a glass prism close to the
critical angle was used. In a simple situation like this two recently published
independent theories of C-line reflection overlap and it is shown that their
predictions are identical. The measured differences in the lateral shifts of
the two reflected C-lines are compared with theoretical expectations over a
range of incidence angles.
|
We study the forces and torques experienced by pill-shaped Janus particles of
different aspect ratios where half of the surface obeys the no-slip boundary
condition and the other half obeys the Navier slip condition of varying slip
lengths. Using a recently developed boundary integral formulation whereby the
traditional singular behaviour of this approach is removed analytically, we
quantify the strength of the forces and torques experienced by such particles
in a uniform flow field in the Stokes regime. Depending on the aspect ratio and
the slip length, the force transverse to the flow direction can change sign.
This is a novel property unique to the Janus nature of the particles.
|
The neutral current e+/-p cross section has been measured up to values of
Bjorken x of approximately 1 with the ZEUS detector at HERA using an integrated
luminosity of 187 inv. pb of e-p and 142 inv. pb of e+p collisions at sqrt(s) =
318GeV. Differential cross sections in x and Q2, the exchanged boson
virtuality, are presented for Q2 geq 725GeV2. An improved reconstruction method
and greatly increased amount of data allows a finer binning in the high-x
region of the neutral current cross section and leads to a measurement with
much improved precision compared to a similar earlier analysis. The
measurements are compared to Standard Model expectations based on a variety of
recent parton distribution functions.
|
In this paper we describe a version of London Langevin molecular dynamics
simulations that allows for investigations of the vortex lattice melting
transition in the highly anisotropic high-temperature superconductor material
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We include the full electromagnetic
interaction as well as the Josephson interaction among pancake vortices. We
also implement periodic boundary conditions in all directions, including the
z-axis along which the magnetic field is applied. We show how to implement flux
cutting and reconnection as an analog to permutations in the multilevel Monte
Carlo scheme and demonstrate that this process leads to flux entanglement that
proliferates in the vortex liquid phase. The first-order melting transition of
the vortex lattice is observed to be in excellent agreement with previous
multilevel Monte Carlo simulations.
|
Recent advance on linear support vector machine with the 0-1 soft margin loss
($L_{0/1}$-SVM) shows that the 0-1 loss problem can be solved directly.
However, its theoretical and algorithmic requirements restrict us extending the
linear solving framework to its nonlinear kernel form directly, the absence of
explicit expression of Lagrangian dual function of $L_{0/1}$-SVM is one big
deficiency among of them. In this paper, by applying the nonparametric
representation theorem, we propose a nonlinear model for support vector machine
with 0-1 soft margin loss, called $L_{0/1}$-KSVM, which cunningly involves the
kernel technique into it and more importantly, follows the success on
systematically solving its linear task. Its optimal condition is explored
theoretically and a working set selection alternating direction method of
multipliers (ADMM) algorithm is introduced to acquire its numerical solution.
Moreover, we firstly present a closed-form definition to the support vector
(SV) of $L_{0/1}$-KSVM. Theoretically, we prove that all SVs of $L_{0/1}$-KSVM
are only located on the parallel decision surfaces. The experiment part also
shows that $L_{0/1}$-KSVM has much fewer SVs, simultaneously with a decent
predicting accuracy, when comparing to its linear peer $L_{0/1}$-SVM and the
other six nonlinear benchmark SVM classifiers.
|
We establish the monotonicity property for the mass of non-pluripolar
products on compact Kahler manifolds, and we initiate the study of complex
Monge-Ampere type equations with prescribed singularity type. Using the
variational method of Berman-Boucksom-Guedj-Zeriahi we prove existence and
uniqueness of solutions with small unbounded locus. We give applications to
Kahler-Einstein metrics with prescribed singularity, and we show that the
log-concavity property holds for non-pluripolar products with small unbounded
locus.
|
Recent studies have shown that velocity differences of very wide binary
stars, measured to high precision with GAIA, can provide an interesting test
for modified-gravity theories which emulate dark matter; in essence, MOND-like
theories (with external field effect included) predict that wide binaries
(wider than ~ 7 kAU) should orbit ~ 15% faster than Newtonian for similar
orbits; such a shift is readily detectable in principle in the sample of 9,000
candidate systems selected from GAIA EDR3 by Pittordis and Sutherland (2022;
PS22). However, the main obstacle at present is the observed "fat tail" of
candidate wide-binary systems with velocity differences at ~1.5 - 6x circular
velocity; this tail cannot be bound pure binary systems, but a possible
explanation of the tail is triple or quadruple systems with unresolved or
undetected additional star(s). While this tail can be modelled and
statistically subtracted, obtaining an accurate model for the triple population
is crucial for a robust test for modified gravity. In this paper we explore
prospects for observationally constraining the triple population: we simulate a
population of hierarchical triple systems "observed" as in PS22 at random
epochs and viewing angles; for each simulated system we evaluate various
possible methods for detecting the third star, including GAIA astrometry,
radial velocity drift, and several imaging methods from direct Rubin images,
speckle imaging and coronagraphic imaging. Results are generally encouraging,
in that typically 90% of the triple systems in the key regions of parameter
space are detectable; there is a moderate "dead zone" of cool brown-dwarf
companions at ~ 25-100 AU separation which are not detectable with any of our
baseline methods. A large but feasible observing campaign can greatly clarify
the effect of the triple/quadruple population and make the gravity test
decisive.
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About half of all known stellar systems with Sun-like stars consist of two or
more stars, significantly affecting the orbital stability of any planet in
these systems. This observational evidence has prompted a large array of
theoretical research, including the derivation of mathematically stringent
criteria for the orbital stability of planets in stellar binary systems, valid
for the "coplanar circular restricted three-body problem". In the following, we
use these criteria to explore the validity of results from previous theoretical
studies.
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A new approach to special relativity is presented which introduces coordinate
systems with imaginary time axes, observation systems, and coordinate bases.
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We discuss the approximation of the eigensolutions associated with the
Maxwell eigenvalues problem in the framework of least-squares finite elements.
We write the Maxwell curl curl equation as a system of two first order equation
and design a novel least-squares formulation whose minimum is attained at the
solution of the system. The eigensolution are then approximated by considering
the eigenmodes of the underlying solution operator. We study the convergence of
the finite element approximation and we show several numerical tests confirming
the good behavior of the method. It turns out that nodal elements can be
successfully employed for the approximation of our problem also in presence of
singular solutions.
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We consider the phenomenological implications of a class of compactified
string theories which naturally reproduces the flavour multiplet structure of
the Standard Model. The implications for gauge unification depends on which of
three possibilities is realised for obtaining light Higgs multiplets. The more
conventional one leads to predictions for the gauge couplings close to that of
the MSSM but with an increased value of the unification scale. The other two
cases offer a mechanism for bringing the prediction for the strong coupling
into agreement with the measured value while still increasing the unification
scale. The various possibilities lead to different expectations for the
structure of the quark masses.
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Reinforcement learning (RL) has been successful in training agents in various
learning environments, including video-games. However, such work modifies and
shrinks the action space from the game's original. This is to avoid trying
"pointless" actions and to ease the implementation. Currently, this is mostly
done based on intuition, with little systematic research supporting the design
decisions. In this work, we aim to gain insight on these action space
modifications by conducting extensive experiments in video-game environments.
Our results show how domain-specific removal of actions and discretization of
continuous actions can be crucial for successful learning. With these insights,
we hope to ease the use of RL in new environments, by clarifying what
action-spaces are easy to learn.
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Affinity maturation is crucial for improving the binding affinity of
antibodies to antigens. This process is mainly driven by point substitutions
caused by somatic hypermutations of the immunoglobulin gene. It also includes
deletions and insertions of genomic material known as indels. While the
landscape of point substitutions has been extensively studied, a detailed
statistical description of indels is still lacking. Here we present a
probabilistic inference tool to learn the statistics of indels from repertoire
sequencing data, which overcomes the pitfalls and biases of standard annotation
methods. The model includes antibody-specific maturation ages to account for
variable mutational loads in the repertoire. After validation on synthetic
data, we applied our tool to a large dataset of human immunoglobulin heavy
chains. The inferred model allows us to identify universal statistical features
of indels in heavy chains. We report distinct insertion and deletion hotspots,
and show that the distribution of lengths of indels follows a geometric
distribution, which puts constraints on future mechanistic models of the
hypermutation process.
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In extreme value statistics, the peaks-over-threshold method is widely used.
The method is based on the generalized Pareto distribution characterizing
probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We
present a generalization of this concept in the space of continuous functions.
We call this the generalized Pareto process. Differently from earlier papers,
our definition is not based on a distribution function but on functional
properties, and does not need a reference to a related max-stable process. As
an application, we use the theory to simulate wind fields connected to
disastrous storms on the basis of observed extreme but not disastrous storms.
We also establish the peaks-over-threshold approach in function space.
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Songs can be well arranged by professional music curators to form a riveting
playlist that creates engaging listening experiences. However, it is
time-consuming for curators to timely rearrange these playlists for fitting
trends in future. By exploiting the techniques of deep learning and
reinforcement learning, in this paper, we consider music playlist generation as
a language modeling problem and solve it by the proposed attention language
model with policy gradient. We develop a systematic and interactive approach so
that the resulting playlists can be tuned flexibly according to user
preferences. Considering a playlist as a sequence of words, we first train our
attention RNN language model on baseline recommended playlists. By optimizing
suitable imposed reward functions, the model is thus refined for corresponding
preferences. The experimental results demonstrate that our approach not only
generates coherent playlists automatically but is also able to flexibly
recommend personalized playlists for diversity, novelty and freshness.
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In this paper we evaluate the topological index of periodic solutions otained
via the Malkin-Loud bifurcation result. Incidentally, we do not assume that the
perturbation is differentiale.
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Large Multimodal Model (LMM) GPT-4V(ision) endows GPT-4 with visual grounding
capabilities, making it possible to handle certain tasks through the Visual
Question Answering (VQA) paradigm. This paper explores the potential of
VQA-oriented GPT-4V in the recently popular visual Anomaly Detection (AD) and
is the first to conduct qualitative and quantitative evaluations on the popular
MVTec AD and VisA datasets. Considering that this task requires both
image-/pixel-level evaluations, the proposed GPT-4V-AD framework contains three
components: \textbf{\textit{1)}} Granular Region Division, \textbf{\textit{2)}}
Prompt Designing, \textbf{\textit{3)}} Text2Segmentation for easy quantitative
evaluation, and have made some different attempts for comparative analysis. The
results show that GPT-4V can achieve certain results in the zero-shot AD task
through a VQA paradigm, such as achieving image-level 77.1/88.0 and pixel-level
68.0/76.6 AU-ROCs on MVTec AD and VisA datasets, respectively. However, its
performance still has a certain gap compared to the state-of-the-art zero-shot
method, \eg, WinCLIP and CLIP-AD, and further researches are needed. This study
provides a baseline reference for the research of VQA-oriented LMM in the
zero-shot AD task, and we also post several possible future works. Code is
available at \url{https://github.com/zhangzjn/GPT-4V-AD}.
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We present a novel and effective technique for performing text coherence
tasks while facilitating deeper insights into the data. Despite obtaining
ever-increasing task performance, modern deep-learning approaches to NLP tasks
often only provide users with the final network decision and no additional
understanding of the data. In this work, we show that a new type of sentence
embedding learned through self-supervision can be applied effectively to text
coherence tasks while serving as a window through which deeper understanding of
the data can be obtained. To produce these sentence embeddings, we train a
recurrent neural network to take individual sentences and predict their
location in a document in the form of a distribution over locations. We
demonstrate that these embeddings, combined with simple visual heuristics, can
be used to achieve performance competitive with state-of-the-art on multiple
text coherence tasks, outperforming more complex and specialized approaches.
Additionally, we demonstrate that these embeddings can provide insights useful
to writers for improving writing quality and informing document structuring,
and assisting readers in summarizing and locating information.
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This paper is devoted, first of all, to give a complete unified proof of the
Characterization Theorem for compact generalized $p-$K\"ahler manifolds
(Theorem 3.2). The proof is based on the classical duality between "closed"
positive forms and "exact" positive currents. In the last part of the paper we
approach the general case of non compact complex manifolds, where "exact"
positive forms seem to play a more significant role than "closed" forms. In
this setting, we state the appropriate characterization theorems and give some
interesting applications.
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We construct some AdS/QCD models by the systematic procedure of GKN. These
models reflect three rather different asymptotics the gauge theory beta
functions approach at the infrared region, $\beta\propto-\lambda^2, -\lambda^3$
and $\beta\propto-\lambda$, where $\lambda$ is the 't Hooft coupling constant.
We then calculate the heavy quark potentials in these models by holographic
methods and find that they can more consistently fit the lattice data relative
to the usual models which do not include the renormalization group improving
effects. But only use the lattice QCD heavy quark potentials as constrains, we
cannot distinguish which kind of infrared asymptotics is the better one.
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This thesis investigates the quantum properties of T-duality invariant
formalisms of String Theory. We introduce and review duality invariant
formalisms of String Theory including the Doubled Formalism. We calculate the
background field equations for the Doubled Formalism of Abelian T-duality and
show how they are consistent with those of a conventional String Theory
description of a toroidal compactification. We generalise these considerations
to the case of Poisson--Lie T-duality and show that the system of
renormalisation group equations obtained from the duality invariant parent
theory are equivalent to those of either of the T-dual pair of sigma-models. In
duality invariant formalisms it is quite common to loose manifest Lorentz
invariance at the level of the Lagrangian. The lack of manifest invariance
means that at the quantum level one might anticipate Lorentz anomalies and we
show that such anomalies cancel non-trivially. These represent important and
non-trivial consistency checks of the duality invariant approach to String
Theory.
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We find formulas for the macroscopic Minkowski and Hausdorff dimensions of
the range of an arbitrary transient walk in Z^d. This endeavor solves a problem
of Barlow and Taylor (1991).
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Recently the authors presented a matrix representation approach to real
Appell polynomials essentially determined by a nilpotent matrix with natural
number entries. It allows to consider a set of real Appell polynomials as
solution of a suitable first order initial value problem. The paper aims to
confirm that the unifying character of this approach can also be applied to the
construction of homogeneous Appell polynomials that are solutions of a
generalized Cauchy-Riemann system in Euclidean spaces of arbitrary dimension.
The result contributes to the development of techniques for polynomial
approximation and interpolation in non-commutative Hypercomplex Function
Theories with Clifford algebras.
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We present a study of the controllable nonlinear dynamics of a
micromechanical beam coupled to a dc-SQUID (superconducting quantum
interference device). The coupling between these systems places the modes of
the beam in a highly nonlinear potential, whose shape can be altered by varying
the control parameters of the SQUID. We detect the position of the beam by
placing it in an optical cavity, which frees the SQUID to be used solely for
actuation. This enables us to probe the previously unexplored full parameter
space of this device. We measure the frequency response of the beam and find
that it displays a periodic dependence on applied magnetic flux. To account for
this, we develop a model based on the standard theory for SQUID dynamics. In
addition, with the aim of understanding if the device can reach nonlinearity at
the single phonon level, we use this model to show that the responsivity of the
current circulating in the SQUID to the position of the beam can become
divergent, with its magnitude limited only by noise. This suggests a direction
for the generation of macroscopically distinguishable superposition states of
the beam.
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In the framework of the thermodynamic approach Landau-Ginzburg-Devonshire
(LGD) combined with the equations of electrostatics, we investigated the effect
of polarization surface screening on finite size effects of the phase diagrams,
polar and dielectric properties of ferroelectric nanoparticles of different
shapes. We obtained and analyzed the analytical results for the dependences of
the ferroelectric phase transition temperature, critical size, spontaneous
polarization and thermodynamic coercive field on the shape and size of
nanoparticles. The pronounced size effect of these characteristics on the
scaling parameter, the ratio of the particle characteristic size to the length
of the surface screening, was revealed. Also our modeling predicts a
significant impact of the flexo-chemical effect (that is a joint action of
flexoelectric effect and chemical pressure) on the temperature of phase
transition, polar and dielectric properties of nanoparticles when their
chemical composition deviates from the stoichiometric one. We showed on the
example of the stoichiometric nanosized and fine SrBi2Ta2O9 particles that
except the vicinity of the critical size, where the system splitting into
domains has an important role, results of analytical calculation of the
spontaneous polarization have little difference from the numerical ones. We
revealed a strong impact of the flexo-chemical effect on the phase transition
temperature, polar and dielectric properties of SryBi2+xTa2O9 nanoparticles
when the ratio Sr/Bi deviates from the stoichiometric value of 0.5 from 0.35 to
0.65. From the analysis of experimental data we derived the parameters of the
theory, namely coefficients of expansion of the LGD functional, contribution of
flexo-chemical effect and the length of the surface screening.
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Consider a reductive $p$-adic group $G$, its (complex-valued) Hecke algebra
$H(G)$ and the Harish-Chandra--Schwartz algebra $S(G)$. We compute the
Hochschild homology groups of $H(G)$ and of $S(G)$, and we describe the
outcomes in several ways.
Our main tools are algebraic families of smooth $G$-representations. With
those we construct maps from $HH_n (H(G))$ and $HH_n (S(G))$ to modules of
differential $n$-forms on affine varieties. For $n = 0$ this provides a
description of the cocentres of these algebras in terms of nice linear
functions on the Grothendieck group of finite length (tempered)
$G$-representations.
It is known from earlier work that every Bernstein ideal $H(G)^s$ of $H(G)$
is closely related to a crossed product algebra of the from $O(T) \rtimes W$.
Here $O(T)$ denotes the regular functions on the variety $T$ of unramified
characters of a Levi subgroup $L$ of $G$, and $W$ is a finite group acting on
$T$. We make this relation even stronger by establishing an isomorphism between
$HH_* (H(G)^s)$ and $HH_* (O(T) \rtimes W)$, although we have to say that in
some cases it is necessary to twist $C[W]$ by a 2-cocycle.
Similarly we prove that the Hochschild homology of the two-sided ideal
$S(G)^s$ of $S(G)$ is isomorphic to $HH_* (C^\infty (T_u) \rtimes W)$, where
$T_u$ denotes the Lie group of unitary unramified characters of $L$. In these
pictures of $HH_* (H(G))$ and $HH_* (S(G))$ we also show how the Bernstein
centre of $H(G)$ acts.
Finally, we derive similar expressions for the (periodic) cyclic homology
groups of $H(G)$ and of $S(G)$ and we relate that to topological K-theory.
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In addition to producing a strong gravitational signal, a short gamma-ray
burst (GRB), and a compact remnant, neutron star mergers eject significant
masses at significant kinetic energies. This mass ejection takes place via
dynamical mass ejection and a GRB jet but other processes have also been
suggested: a shock-breakout material, a cocoon resulting from the interaction
of the jet with other ejecta, and viscous and neutrino driven winds from the
central remnant or the accretion disk. The different components of the ejected
masses include up to a few percent of a solar mass, some of which is ejected at
relativistic velocities. The interaction of these ejecta with the surrounding
interstellar medium will produce a long lasting radio flare, in a similar way
to GRB afterglows or to radio supernovae. The relative strength of the
different signals depends strongly on the viewing angle. An observer along the
jet axis or close to it will detect a strong signal at a few dozen days from
the radio afterglow (or the orphan radio afterglow) produced by the highly
relativistic GRB jet. For a generic observer at larger viewing angles, the
dynamical ejecta, whose contribution peaks a year or so after the event, will
generally dominate. Depending on the observed frequency and the external
density, other components may also give rise to a significant contribution. We
also compare these estimates with the radio signature of the short GRB 130603B.
The radio flare from the dynamical ejecta might be detectable with the EVLA and
the LOFAR for the higher range of external densities $n\gtrsim 0.5{\rm
cm^{-3}}$.
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LLM agents have become increasingly sophisticated, especially in the realm of
cybersecurity. Researchers have shown that LLM agents can exploit real-world
vulnerabilities when given a description of the vulnerability and toy
capture-the-flag problems. However, these agents still perform poorly on
real-world vulnerabilities that are unknown to the agent ahead of time
(zero-day vulnerabilities).
In this work, we show that teams of LLM agents can exploit real-world,
zero-day vulnerabilities. Prior agents struggle with exploring many different
vulnerabilities and long-range planning when used alone. To resolve this, we
introduce HPTSA, a system of agents with a planning agent that can launch
subagents. The planning agent explores the system and determines which
subagents to call, resolving long-term planning issues when trying different
vulnerabilities. We construct a benchmark of 15 real-world vulnerabilities and
show that our team of agents improve over prior work by up to 4.5$\times$.
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We describe how the spin coherence time of a localized electron spin in
solids, i.e. a solid state spin qubit, can be prolonged by applying designed
electron spin resonance pulse sequences. In particular, the spin echo decay due
to the spectral diffusion of the electron spin resonance frequency induced by
the non-Markovian temporal fluctuations of the nuclear spin flip-flop dynamics
can be strongly suppressed using multiple-pulse sequences akin to the
Carr-Purcell-Meiboom-Gill pulse sequence in nuclear magnetic resonance. Spin
coherence time can be enhanced by factors of 4-10 in GaAs quantum dot and Si:P
quantum computer architectures using composite sequences with an even number of
pulses.
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Unsupervised learning methods for feature extraction are becoming more and
more popular. We combine the popular contrastive learning method (prototypical
contrastive learning) and the classic representation learning method
(autoencoder) to design an unsupervised feature learning network for
hyperspectral classification. Experiments have proved that our two proposed
autoencoder networks have good feature learning capabilities by themselves, and
the contrastive learning network we designed can better combine the features of
the two to learn more representative features. As a result, our method
surpasses other comparison methods in the hyperspectral classification
experiments, including some supervised methods. Moreover, our method maintains
a fast feature extraction speed than baseline methods. In addition, our method
reduces the requirements for huge computing resources, separates feature
extraction and contrastive learning, and allows more researchers to conduct
research and experiments on unsupervised contrastive learning.
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