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Minimisation of discrete energies defined over factors is an important
problem in computer vision, and a vast number of MAP inference algorithms have
been proposed. Different inference algorithms perform better on factor graph
models (GMs) from different underlying problem classes, and in general it is
difficult to know which algorithm will yield the lowest energy for a given GM.
To mitigate this difficulty, survey papers advise the practitioner on what
algorithms perform well on what classes of models. We take the next step
forward, and present a technique to automatically select the best inference
algorithm for an input GM. We validate our method experimentally on an extended
version of the OpenGM2 benchmark, containing a diverse set of vision problems.
On average, our method selects an inference algorithm yielding labellings with
96% of variables the same as the best available algorithm.
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In this paper we consider the problem of maximizing the Area under the ROC
curve (AUC) which is a widely used performance metric in imbalanced
classification and anomaly detection. Due to the pairwise nonlinearity of the
objective function, classical SGD algorithms do not apply to the task of AUC
maximization. We propose a novel stochastic proximal algorithm for AUC
maximization which is scalable to large scale streaming data. Our algorithm can
accommodate general penalty terms and is easy to implement with favorable
$O(d)$ space and per-iteration time complexities. We establish a
high-probability convergence rate $O(1/\sqrt{T})$ for the general convex
setting, and improve it to a fast convergence rate $O(1/T)$ for the cases of
strongly convex regularizers and no regularization term (without strong
convexity). Our proof does not need the uniform boundedness assumption on the
loss function or the iterates which is more fidelity to the practice. Finally,
we perform extensive experiments over various benchmark data sets from
real-world application domains which show the superior performance of our
algorithm over the existing AUC maximization algorithms.
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In this note, we study a special case of the $4$-pt non-vacuum classical
block associated with the $\mathcal{W}_3$ algebra. We formulate the monodromy
problem for the block and derive monodromy equations within the heavy-light
approximation. Fixing the remaining functional arbitrariness using parameters
of the $4$-pt vacuum $\mathcal{W}_3$ block, we compute the $4$-pt non-vacuum
$\mathcal{W}_3$ block function.
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We study low--temperature non Gaussian thermal fluctuations of a system of
classical particles around a (hypothetical) crystalline ground state. These
thermal fluctuations are described by the behaviour of a system of long range
interacting charged dipoles at high--temperature and high--density. For the
case of uniformly bounded fluctuations, the low--temperature linked cluster
expansion describing the contribution to the free energy is derived and
analysed. Finally some nonpertubative results on the existence and independence
of boundary conditions of the Gibbs states for the associated dipole systems
are obtained.
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The availability of large-scale facial databases, together with the
remarkable progresses of deep learning technologies, in particular Generative
Adversarial Networks (GANs), have led to the generation of extremely realistic
fake facial content, raising obvious concerns about the potential for misuse.
Such concerns have fostered the research on manipulation detection methods
that, contrary to humans, have already achieved astonishing results in various
scenarios. In this study, we focus on the synthesis of entire facial images,
which is a specific type of facial manipulation. The main contributions of this
study are four-fold: i) a novel strategy to remove GAN "fingerprints" from
synthetic fake images based on autoencoders is described, in order to spoof
facial manipulation detection systems while keeping the visual quality of the
resulting images; ii) an in-depth analysis of the recent literature in facial
manipulation detection; iii) a complete experimental assessment of this type of
facial manipulation, considering the state-of-the-art fake detection systems
(based on holistic deep networks, steganalysis, and local artifacts), remarking
how challenging is this task in unconstrained scenarios; and finally iv) we
announce a novel public database, named iFakeFaceDB, yielding from the
application of our proposed GAN-fingerprint Removal approach (GANprintR) to
already very realistic synthetic fake images.
The results obtained in our empirical evaluation show that additional efforts
are required to develop robust facial manipulation detection systems against
unseen conditions and spoof techniques, such as the one proposed in this study.
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Photonic entangled states lie at the heart of quantum science for the
demonstrations of quantum mechanics foundations and supply as a key resource
for approaching various quantum technologies. An integrated realization of such
states will certainly guarantee a high-degree of entanglement and improve the
performance like portability, stability and miniaturization, hence becomes an
inevitable tendency towards the integrated quantum optics. Here, we report the
compact realization of steerable photonic path-entangled states from a
monolithic quadratic nonlinear photonic crystal. The crystal acts as an
inherent beam splitter to distribute photons into coherent spatial modes,
producing the heralded single-photon even appealing beamlike two-photon
path-entanglement, wherein the entanglement is characterized by quantum spatial
beatings. Such multifunctional entangled source can be further extended to
high-dimensional fashion and multi-photon level as well as involved with other
degrees of freedom, which paves a desirable way to engineer miniaturized
quantum light source.
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Metaverse, a burgeoning technological trend that combines virtual and
augmented reality, provides users with a fully digital environment where they
can assume a virtual identity through a digital avatar and interact with others
as they were in the real world. Its applications span diverse domains such as
economy (with its entry into the cryptocurrency field), finance, social life,
working environment, healthcare, real estate, and education. During the
COVID-19 and post-COVID-19 era, universities have rapidly adopted e-learning
technologies to provide students with online access to learning content and
platforms, rendering previous considerations on integrating such technologies
or preparing institutional infrastructures virtually obsolete. In light of this
context, the present study proposes a framework for analyzing university
students' acceptance and intention to use metaverse technologies in education,
drawing upon the Technology Acceptance Model (TAM). The study aims to
investigate the relationship between students' intention to use metaverse
technologies in education, hereafter referred to as MetaEducation, and selected
TAM constructs, including Attitude, Perceived Usefulness, Perceived Ease of
Use, Self-efficacy of metaverse technologies in education, and Subjective Norm.
Notably, Self-efficacy and Subjective Norm have a positive influence on
Attitude and Perceived Usefulness, whereas Perceived Ease of Use does not
exhibit a strong correlation with Attitude or Perceived Usefulness. The authors
postulate that the weak associations between the study's constructs may be
attributed to limited knowledge regarding MetaEducation and its potential
benefits. Further investigation and analysis of the study's proposed model are
warranted to comprehensively understand the complex dynamics involved in the
acceptance and utilization of MetaEducation technologies in the realm of higher
education
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We have studied the body-centered cubic (bcc), face-centered cubic (fcc) and
hexagonal close-packed (hcp) phases of Fe alloyed with 25 at. % of Ni at
Earth's core conditions using an ab initio local density approximation +
dynamical mean-field theory (LDA+DMFT) approach. The alloys have been modeled
by ordered crystal structures based on the bcc, fcc, and hcp unit cells with
minimum possible cell size allowing for the proper composition. Our
calculations demonstrate that the strength of electronic correlations on the Fe
3d shell is highly sensitive to the phase and local environment. In the bcc
phase the 3d electrons at the Fe site with Fe only nearest neighbors remain
rather strongly correlated even at extreme pressure-temperature conditions,
with the local and uniform magnetic susceptibility exhibiting a
Curie-Weiss-like temperature evolution and the quasi-particle lifetime {\Gamma}
featuring a non-Fermi-liquid temperature dependence. In contrast, for the
corresponding Fe site in the hcp phase we predict a weakly-correlated
Fermi-liquid state with a temperature-independent local susceptibility and a
quadratic temperature dependence of {\Gamma}. The iron sites with nickel atoms
in the local environment exhibit behavior in the range between those two
extreme cases, with the strength of correlations gradually increasing along the
hcp-fcc-bcc sequence. Further, the inter-site magnetic interactions in the bcc
and hcp phases are also strongly affected by the presence of Ni nearest
neighbors. The sensitivity to the local environment is related to modifications
of the Fe partial density of states due to mixing with Ni 3d-states.
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We show that (i) any constrained polynomial optimization problem (POP) has an
equivalent formulation on a variety contained in an Euclidean sphere and (ii)
the resulting semidefinite relaxations in the moment-SOS hierarchy have the
constant trace property (CTP) for the involved matrices. We then exploit the
CTP to avoid solving the semidefinite relaxations via interior-point methods
and rather use ad-hoc spectral methods that minimize the largest eigenvalue of
a matrix pencil. Convergence to the optimal value of the semidefinite
relaxation is guaranteed. As a result we obtain a hierarchy of nonsmooth
"spectral relaxations" of the initial POP. Efficiency and robustness of this
spectral hierarchy is tested against several equality constrained POPs on a
sphere as well as on a sample of randomly generated quadratically constrained
quadratic problems (QCQPs).
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We develop the embedded gradient vector field method, introduced in [8] and
[9], for the case of the special unitary group $\mathcal{SU}(N)$ regarded as a
constraint submanifold of the unitary group $\mathcal{U}(N)$. The optimization
problem associated to the trace fidelity cost function defined on
$\mathcal{SU}(N)$ that appears in the context of $\mathcal{SU}(N)$ quantum
control landscapes is completely solved using the embedded gradient vector
field method. We prove that for $N\geq 5$, the landscape is not
$\mathcal{SU}(N)$-trap free, there are always kinematic local extrema that are
not global extrema.
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We prove a Lieb-Thirring type inequality for a complex perturbation of a
d-dimensional massive Dirac operator $D_m, m\geq 0$ whose spectrum is $]-\infty
, -m]\cup[m , +\infty[$. The difficulty of the study is that the unperturbed
operator is not bounded from below in this case, and, to overcome it, we use
the methods of complex function theory. The methods of the article also give
similar results for complex perturbations of the Klein-Gordon operator.
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In this study, we forecast the population of the Philippines using a discrete
age-structured compartmental model. We estimated the future population
structure of the Philippines if the government imposes an n-child policy on top
of the declining current birth and death rate trend of the country.
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A set of locally finite perimeter $E \subset \mathbb{R}^{n}$ is called an
anisotropic minimal surface in an open set $A$ if $\Phi(E;A) \le \Phi(F;A)$ for
some surface energy $\Phi(E;A) = \int_{\partial^{*}E \cap A} \| \nu_{E}\| d
\mathcal{H}^{n-1}$ and all sets of locally finite perimeter $F$ such that $E
\Delta F \subset \subset A$.
In this short note we provide the details of a geometric proof verifying that
all anisotropic surface minimizers in $\mathbb{R}^{2}$ whose corresponding
integrand $\| \cdot \|$ is strictly convex are locally disjoint unions of line
segments. This demonstrates that, in the plane, strict convexity of $\| \cdot
\|$ is both necessary and sufficient for regularity. The corresponding
Bernstein theorem is also proven: global anisotropic minimizers $E \subset
\mathbb{R}^{2}$ are half-spaces.
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In this article, we are proposing a thorough analysis of the cross, and the
in-plane thermal conductivity of thin-film materials based on the 3$\omega$
method. The analysis accommodates a 2D mathematical heat transfer model of a
semi-infinite body and the details of the sample preparation followed by the
measurement process. The presented mathematical model for the system considers
a two-dimensional space for its solution. It enables the calculation of the
cross-plane thermal conductivity with a single frequency measurement, the
derived equation opens new opportunities for frequency-based and
penetration-depth dependent thermal conductivity analysis. The derived equation
for the in-plane thermal conductivity is dependent on the cross-plane thermal
conductivity. Both in and cross-plane thermal conductivities enable the
measurements in two steps of measurements, the resistance-temperature slope
measurement and another set of measures that extracts the third harmonic of the
voltage signal. We evaluated the methodology in two sets of samples, silicon
nitride and boron nitride, both on silicon wafers. We observed anisotropic
thermal conductivity in the cross and the in-plane direction, despite the
isotropic nature of the thin films, which we relate to the total anisotropy of
the thin film-substrate system. The technique is conducive to the thermal
analysis of next-generation nanoelectronic devices.
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Composite Higgs models predict the existence of resonances. We study in
detail the collider phenomenology of both the vector and fermionic resonances,
including the possibility of both of them being light and within the reach of
the LHC. We present current constraints from di-boson, di-lepton resonance
searches and top partner pair searches on a set of simplified benchmark models
based on the minimal coset $SO(5)/SO(4)$, and make projections for the reach of
the HL-LHC. We find that the cascade decay channels for the vector resonances
into top partners, or vice versa, can play an important role in the
phenomenology of the models. We present a conservative estimate for their reach
by using the same-sign di-lepton final states. As a simple extrapolation of our
work, we also present the projected reach at the 27 TeV HE-LHC and a 100 TeV
$pp$ collider.
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A new mechanism of bi-linear magnetoresistance (BMR) is studied theoretically
within the minimal model describing surface electronic states in topological
insulators (TIs). The BMR appears as a consequence of the second-order response
to electric field, and depends linearly on both electric field (current) and
magnetic field. The mechanism is based on the interplay of current-induced spin
polarization and scattering processes due to peculiar spin-orbit defects. The
proposed mechanism is compared to that based on a Fermi surface warping, and is
shown to be dominant at lower Fermi energies. We provide a consistent
theoretical approach based on the Green function formalism and show that the
magnetic field dependent relaxation processes in the presence of
non-equilibrium current-induced spin polarization give rise to the BMR.
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We study the intermediate statistics of the spectrum of quasi-energies and of
the eigenfunctions in the kicked rotator, in the case when the corresponding
system is fully chaotic while quantally localized. As for the eigenphases, we
find clear evidence that the spectral statistics is well described by the Brody
distribution, notably better than by the Izrailev's one, which has been
proposed and used broadly to describe such cases. We also studied the
eigenfunctions of the Floquet operator and their localization. We show the
existence of a scaling law between the repulsion parameter with relative
localization length, but only as a first order approximation, since another
parameter plays a role. We believe and have evidence that a similar analysis
applies in time-independent Hamilton systems.
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In this paper, we study a wireless networked control system (WNCS) with $N
\ge 2$ sub-systems sharing a common wireless channel. Each sub-system consists
of a plant and a controller and the control message must be delivered from the
controller to the plant through the shared wireless channel. The wireless
channel is unreliable due to interference and fading. As a result, a packet can
be successfully delivered in a slot with a certain probability. A network
scheduling policy determines how to transmit those control messages generated
by such $N$ sub-systems and directly influences the transmission delay of
control messages. We first consider the case that all sub-systems have the same
sampling period. We characterize the stability condition of such a WNCS under
the joint design of the control policy and the network scheduling policy by
means of $2^N$ linear inequalities. We further simplify the stability condition
into only one linear inequality for two special cases: the perfect-channel case
where the wireless channel can successfully deliver a control message with
certainty in each slot, and the symmetric-structure case where all sub-systems
have identical system parameters. We then consider the case that different
sub-systems can have different sampling periods, where we characterize a
sufficient condition for stability.
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Static spherically symmetric solutions of the Einstein-Maxwell gravity with
the dilaton field are described. The solutions correspond to black holes and
are generalizations of the previously known dilaton black hole solution. In
addition to mass and electric charge these solutions are labeled by a new
parameter, the dilaton charge of the black hole. Different effects of the
dilaton charge on the geometry of space-time of such black holes are studied.
It is shown that in most cases the scalar curvature is divergent at the
horizons. Another feature of the dilaton black hole is that there is a finite
interval of values of electric charge for which no black hole can exist.
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We present a method to compute the number of particles occupying spherical
single-particle (SSP) levels within the energy density functional (EDF)
framework. These SSP levels are defined for each nucleus by performing
self-consistent mean-field calculations. The nuclear many-body states, in which
the occupation numbers are evaluated, are obtained with a symmetry conserving
configuration mixing (SCCM) method based on the Gogny EDF. The method allows a
closer comparison between EDF and shell model with configuration mixing in
large valence spaces (SM-CI) results, and can serve as a guidance to define
physically sound valence spaces for SM-CI calculations. As a first application
of the method, we analyze the onset of deformation in neutron-rich $N=40$
isotones and the role of the SSP levels around this harmonic oscillator magic
number, with particular emphasis in the structure of $^{64}$Cr.
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Using Monte Carlo dynamics and the Monte Carlo Histogram Method, the simple
three-dimensional 27 monomer lattice copolymer is examined in depth. The
thermodynamic properties of various sequences are examined contrasting the
behavior of good and poor folding sequences. The good (fast folding) sequences
have sharp well-defined thermodynamic transitions while the slow folding
sequences have broad ones. We find two independent transitions: a collapse
transition to compact states and a folding transition from compact states to
the native state. The collapse transition is second order-like, while folding
is first order. The system is also studied as a function of the energy
parameters. In particular, as the average energetic drive toward compactness is
reduced, the two transitions approach each other. At zero average drive,
collapse and folding occur almost simultaneously; i.e., the chain collapses
directly into the native state. At a specific value of this energy drive the
folding temperature falls below the glass point, indicating that the chain is
now trapped in local minimum. By varying one parameter in this simple model, we
obtain a diverse array of behaviors which may be useful in understanding the
different folding properties of various proteins.
|
Long Short-Term Memory (LSTM) infers the long term dependency through a cell
state maintained by the input and the forget gate structures, which models a
gate output as a value in [0,1] through a sigmoid function. However, due to the
graduality of the sigmoid function, the sigmoid gate is not flexible in
representing multi-modality or skewness. Besides, the previous models lack
modeling on the correlation between the gates, which would be a new method to
adopt inductive bias for a relationship between previous and current input.
This paper proposes a new gate structure with the bivariate Beta distribution.
The proposed gate structure enables probabilistic modeling on the gates within
the LSTM cell so that the modelers can customize the cell state flow with
priors and distributions. Moreover, we theoretically show the higher upper
bound of the gradient compared to the sigmoid function, and we empirically
observed that the bivariate Beta distribution gate structure provides higher
gradient values in training. We demonstrate the effectiveness of bivariate Beta
gate structure on the sentence classification, image classification, polyphonic
music modeling, and image caption generation.
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Two-species condensing zero range processes (ZRPs) are interacting particle
systems with two species of particles and zero range interaction exhibiting
phase separation outside a domain of sub-critical densities. We prove the
hydrodynamic limit of nearest neighbour mean zero two-species condensing zero
range processes with bounded local jump rate for sub-critical initial profiles,
i.e., for initial profiles whose image is contained in the region of
sub-critical densities. The proof is based on H. T. Yau's relative entropy
method, which relies on the existence of sufficiently regular solutions to the
hydrodynamic equation. In the particular case of the species-blind ZRP, we
prove that the solutions of the hydrodynamic equation exist globally in time
and thus the hydrodynamic limit is valid for all times.
|
Large-volume optical coherence tomography (OCT)-setups employ scanning
mirrors and suffer from non-linear geometric distortion artifacts in which the
degree of distortion is determined by the maximum angles over which the mirrors
rotate. In this chapter, we describe a straightforward approach to correct for
these distortion artifacts, creating an alternative to previously reported
ray-tracing schemes that are unable to apply these corrections in real-time. By
implementing the proposed 3D recalibration algorithm on the graphics card of a
standard computer, this feature can be applied in real-time. We validate the
accuracy of the technique using OCT measurements of a highly curved object
within a large imaging volume of 12.35 x 10.13 x 2.36 mm^3. The resulting 3D
object shape measurements are compared against high-resolution and
aberration-free optical profilometry measurements. Maintaining an optical
resolution of <10 micron within the sample, both axially and transversally, we
realized a real-time, high-resolution, large-volume OCT imaging system, capable
of producing distortion corrected wide-field OCT data with a geometric surface
shape accuracy of <15 micron.
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We report on the recent development of a versatile analog front-end
compatible with a negative-ion $\mu$-TPC for a directional dark matter search
as well as a dual-phase, next-generation $\mathcal{O}$(10~kt) liquid argon TPC
to study neutrino oscillations, nucleon decay, and astrophysical neutrinos.
Although the operating conditions for negative-ion and liquid argon TPCs are
quite different (room temperature \textit{vs.} $\sim$88~K operation,
respectively), the readout electronics requirements are similar. Both require a
wide-dynamic range up to 1600 fC, and less than 2000--5000 e$^-$ noise for a
typical signal of 80 fC with a detector capacitance of $C_{\rm det} \approx
300$~pF. In order to fulfill such challenging requirements, a prototype ASIC
was newly designed using 180-nm CMOS technology. Here, we report on the
performance of this ASIC, including measurements of shaping time, dynamic
range, and equivalent noise charge (ENC). We also demonstrate the first
operation of this ASIC on a low-pressure negative-ion $\mu$-TPC.
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The nature of the interface in lateral heterostructures of 2D monolayer
semiconductors including its composition, size, and heterogeneity critically
impacts the functionalities it engenders on the 2D system for next-generation
optoelectronics. Here, we use tip-enhanced Raman scattering (TERS) to
characterize the interface in a single-layer MoS2/WS2 lateral heterostructure
with a spatial resolution of 50 nm. Resonant and non-resonant TERS
spectroscopies reveal that the interface is alloyed with a size that varies
over an order of magnitude-from 50-600 nm-within a single crystallite.
Nanoscale imaging of the continuous interfacial evolution of the resonant and
non-resonant Raman spectra enables the deconvolution of defect-activation,
resonant enhancement, and material composition for several vibrational modes in
single-layer MoS2, MoxW1-xS2, and WS2. The results demonstrate the capabilities
of nanoscale TERS spectroscopy to elucidate macroscopic structure-property
relationships in 2D materials and to characterize lateral interfaces of 2D
systems on length scales that are imperative for devices.
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The presumed Wolf-Rayet star progenitors of Type Ib/c supernovae have fast,
low density winds and the shock waves generated by the supernova interaction
with the wind are not expected to be radiative at typical times of observation.
The injected energy spectrum of radio emitting electrons typically has an
observed index p=3, which is suggestive of acceleration in cosmic ray dominated
shocks. The early, absorbed part of the radio light curves can be attributed to
synchrotron self-absorption, which leads to constraints on the magnetic field
in the emitting region and on the circumstellar density. The range of
circumstellar densities inferred from the radio emission is somewhat broader
than that for Galactic Wolf-Rayet stars, if similar efficiencies of synchrotron
emission are assumed in the extragalactic supernovae. For the observed and
expected ranges of circumstellar densities to roughly overlap, a high
efficiency of magnetic field production in the shocked region is required
(epsilon_B ~ 0.1). For the expected densities around a Wolf-Rayet star, a
nonthermal mechanism is generally required to explain the observed X-ray
luminosities of Type Ib/c supernovae. Although the inverse Compton mechanism
can explain the observed X-ray emission from SN 2002ap if the wind parameters
are taken from the radio model, the mechanism is not promising for other
supernovae unless the postshock magnetic energy density is much smaller than
the electron energy density. In some cases another mechanism is definitely
needed and we suggest that it is X-ray synchrotron emission in a case where the
shock wave is cosmic ray dominated so that the electron energy spectrum
flattens at high energy. More comprehensive X-ray observations of a Type Ib/c
supernova are needed to determine whether this suggestion is correct.
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Discovering successful coordinated behaviors is a central challenge in
Multi-Agent Reinforcement Learning (MARL) since it requires exploring a joint
action space that grows exponentially with the number of agents. In this paper,
we propose a mechanism for achieving sufficient exploration and coordination in
a team of agents. Specifically, agents are rewarded for contributing to a more
diversified team behavior by employing proper intrinsic motivation functions.
To learn meaningful coordination protocols, we structure agents' interactions
by introducing a novel framework, where at each timestep, an agent simulates
counterfactual rollouts of its policy and, through a sequence of computations,
assesses the gap between other agents' current behaviors and their targets.
Actions that minimize the gap are considered highly influential and are
rewarded. We evaluate our approach on a set of challenging tasks with sparse
rewards and partial observability that require learning complex cooperative
strategies under a proper exploration scheme, such as the StarCraft Multi-Agent
Challenge. Our methods show significantly improved performances over different
baselines across all tasks.
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We study the Polonyi problem in the framework of no-scale type supergravity
models. We show that the lightest superparticle (LSP) produced in the decay of
the Polonyi field may contribute too much to the present density of the
universe. By requiring that LSP should not overclose the universe, we obtain a
stringent constraint on the reheating temperature after the decay of the
Polonyi field. We calculate the LSP density with physical parameters obtained
by solving renormalization group equations in the minimal supersymmetric SU(5)
model and find that the reheating temperature should be greater than about
100MeV which corresponds to $O$(100)TeV of the Polonyi mass.
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Time-series data is being increasingly collected and stud- ied in several
areas such as neuroscience, climate science, transportation, and social media.
Discovery of complex patterns of relationships between individual time-series,
using data-driven approaches can improve our understanding of real-world
systems. While traditional approaches typically study relationships between two
entire time series, many interesting relationships in real-world applications
exist in small sub-intervals of time while remaining absent or feeble during
other sub-intervals. In this paper, we define the notion of a sub-interval
relationship (SIR) to capture inter- actions between two time series that are
prominent only in certain sub-intervals of time. We propose a novel and
efficient approach to find most interesting SIR in a pair of time series. We
evaluate our proposed approach on two real-world datasets from climate science
and neuroscience domain and demonstrated the scalability and computational
efficiency of our proposed approach. We further evaluated our discovered SIRs
based on a randomization based procedure. Our results indicated the existence
of several such relationships that are statistically significant, some of which
were also found to have physical interpretation.
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We apply the method of asymptotic homogenization to metamaterials with
microscopically bianisotropic inclusions to calculate a full set of
constitutive parameters in the long wavelength limit. Two different
implementations of electromagnetic asymptotic homogenization are presented. We
test the homogenization procedure on two different metamaterial examples.
Finally, the analytical solution for long wavelength homogenization of a one
dimensional metamaterial with microscopically bi-isotropic inclusions is
derived.
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We present spatially resolved maps of six individually-detected Lyman alpha
haloes (LAHs) as well as a first statistical analysis of the Lyman alpha (Lya)
spectral signature in the circum-galactic medium of high-redshift star-forming
galaxies using MUSE. Our resolved spectroscopic analysis of the LAHs reveals
significant intrahalo variations of the Lya line profile. Using a
three-dimensional two-component model for the Lya emission, we measure the full
width at half maximum (FWHM), the peak velocity shift and the asymmetry of the
Lya line in the core and in the halo of 19 galaxies. We find that the Lya line
shape is statistically different in the halo compared to the core for ~40% of
our galaxies. Similarly to object-by-object based studies and a recent resolved
study using lensing, we find a correlation between the peak velocity shift and
the width of the Lya line both at the interstellar and circum-galactic scales.
While there is a lack of correlation between the spectral properties and the
spatial scale lengths of our LAHs, we find a correlation between the width of
the line in the LAH and the halo flux fraction. Interestingly, UV bright
galaxies show broader, more redshifted and less asymmetric Lya lines in their
haloes. The most significant correlation found is for the FWHM of the line and
the UV continuum slope of the galaxy, suggesting that the redder galaxies have
broader Lya lines. The generally broad and red line shapes found in the halo
component suggests that the Lya haloes are powered either by scattering
processes through an outflowing medium, fluorescent emission from outflowing
cold clumps of gas, or a mix of both. Considering the large diversity of the
Lya line profiles observed in our sample and the lack of strong correlation,
the interpretation of our results is still broadly open and underlines the need
for realistic spatially resolved models of the LAHs.
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We present a practical method for evaluating the scattering amplitude
$f_s(\theta,\phi)$ that arises in the context of the scattering of scalar,
electromagnetic and gravitational planar waves by a rotating black hole. The
partial-wave representation of $f_s$ is a divergent series, but $f_s$ itself
diverges only at a single point on the sphere. Here we show that $f_s$ can be
expressed as the product of a reduced series and a pre-factor that diverges
only at this point. The coefficients of the reduced series are found
iteratively as linear combinations of those in the original series, and the
reduced series is shown to have amenable convergence properties. This
series-reduction method has its origins in an approach originally used in
electron scattering calculations in the 1950s, which we have extended to the
axisymmetric context for all bosonic fields.
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We study the NMSSM with universal Susy breaking terms (besides the Higgs
sector) at the GUT scale. Within this constrained parameter space, it is not
difficult to find a Higgs boson with a mass of about 125 GeV and an enhanced
cross section in the diphoton channel. An additional lighter Higgs boson with
reduced couplings and a mass <123 GeV is potentially observable at the LHC. The
NMSSM-specific Yukawa couplings lambda and kappa are relatively large and
tan(beta) is small, such that lambda, kappa and the top Yukawa coupling are of
order 1 at the GUT scale. The lightest stop can be as light as 105 GeV, and the
fine-tuning is modest. WMAP constraints can be satisfied by a dominantly
higgsino-like LSP with substantial bino, wino and singlino admixtures and a
mass of ~60-90 GeV, which would potentially be detectable by XENON100.
|
Game theory is an established branch of mathematics that offers a rich set of
mathematical tools for multi-person strategic decision making that can be used
to model the interactions of decision makers in security problems who compete
for limited and shared resources. This article presents a review of the
literature in the area of game theoretical modelling of network/cybersecurity.
|
We present results of the first systematic search for submillimetre continuum
emission from z=2, radio-quiet, optically-luminous quasars, using the
SCUBA/JCMT. We have observed a homogeneous sample of 57 quasars in the redshift
range 1.5<z<3.0- the epoch during which the comoving density of luminous AGN
peaks- to make a systematic comparison with an equivalent sample at high (z>4)
redshift. The target sensitivity of the survey (3sigma=10mJy at 850um) was
chosen to enable efficient identification of bright submm sources, suitable for
detailed follow-up. 9 targets are detected, with fluxes in the range 7-17mJy.
Although there is a suggestion of variation of submm detectability between z=2
and z=4, this is consistent with the K-correction of a characteristic
far-infrared spectrum. Additionally, the weighted mean fluxes of non-detections
at z=2 and z>4 are comparable.
|
Substantial changes in the generation portfolio take place due to the fast
growth of renewable energy generation, of which the major types such as wind
and solar power have significant forecast uncertainty. Reducing the impacts of
uncertainty requires the cooperation of system participants, which are
supported by proper market rules and incentives. In this paper, we propose a
bilateral reserve market for variable generation (VG) producers and capacity
resource providers. In this market, VG producers purchase bilateral reserve
services (BRSs) to reduce potential imbalance penalties, and BRS providers earn
profits on their available capacity for re-dispatch. We show in this paper that
by introducing this product, the VG producers' overall imbalance costs are
linked to both their forecast quality and the available system capacity, which
follows the cost-causation principle. Case studies demonstrate how the proposed
BRS mechanism works and its effectiveness.
|
Examining limitations is a crucial step in the scholarly research reviewing
process, revealing aspects where a study might lack decisiveness or require
enhancement. This aids readers in considering broader implications for further
research. In this article, we present a novel and challenging task of
Suggestive Limitation Generation (SLG) for research papers. We compile a
dataset called \textbf{\textit{LimGen}}, encompassing 4068 research papers and
their associated limitations from the ACL anthology. We investigate several
approaches to harness large language models (LLMs) for producing suggestive
limitations, by thoroughly examining the related challenges, practical
insights, and potential opportunities. Our LimGen dataset and code can be
accessed at \url{https://github.com/arbmf/LimGen}.
|
Offline reinforcement learning is important in many settings with available
observational data but the inability to deploy new policies online due to
safety, cost, and other concerns. Many recent advances in causal inference and
machine learning target estimation of causal contrast functions such as CATE,
which is sufficient for optimizing decisions and can adapt to potentially
smoother structure. We develop a dynamic generalization of the R-learner (Nie
and Wager 2021, Lewis and Syrgkanis 2021) for estimating and optimizing the
difference of $Q^\pi$-functions, $Q^\pi(s,1)-Q^\pi(s,0)$ (which can be used to
optimize multiple-valued actions). We leverage orthogonal estimation to improve
convergence rates in the presence of slower nuisance estimation rates and prove
consistency of policy optimization under a margin condition. The method can
leverage black-box nuisance estimators of the $Q$-function and behavior policy
to target estimation of a more structured $Q$-function contrast.
|
We propose a new framework, Translation between Augmented Natural Languages
(TANL), to solve many structured prediction language tasks including joint
entity and relation extraction, nested named entity recognition, relation
classification, semantic role labeling, event extraction, coreference
resolution, and dialogue state tracking. Instead of tackling the problem by
training task-specific discriminative classifiers, we frame it as a translation
task between augmented natural languages, from which the task-relevant
information can be easily extracted. Our approach can match or outperform
task-specific models on all tasks, and in particular, achieves new
state-of-the-art results on joint entity and relation extraction (CoNLL04, ADE,
NYT, and ACE2005 datasets), relation classification (FewRel and TACRED), and
semantic role labeling (CoNLL-2005 and CoNLL-2012). We accomplish this while
using the same architecture and hyperparameters for all tasks and even when
training a single model to solve all tasks at the same time (multi-task
learning). Finally, we show that our framework can also significantly improve
the performance in a low-resource regime, thanks to better use of label
semantics.
|
The fully heavy axial-vector diquark-antidiquark structures $bb\overline{c}
\overline{c}$ are explored by means of the QCD sum rule method. They are
modeled as four-quark mesons $T_{\mathrm{1}}$ and $T_{\mathrm{2}}$ composed of
$b^{T}C\sigma _{\mu \nu }\gamma _{5}b$, $\overline{c}\gamma ^{\nu }C
\overline{c}^{T}$ and $b^{T}C\gamma _{\mu }\gamma _{5}b$, $\overline{c}C
\overline{c}^{T}$ diquarks, respectively. The spectroscopic parameters of the
tetraquarks $T_{\mathrm{1}}$ and $T_{\mathrm{2}}$ are determined in the context
of the QCD two-point sum rule method. Results obtained for masses of these
states $m_{1} =(12715\pm 86)~\mathrm{MeV}$ and $m_{2}=(13383\pm 92)~
\mathrm{MeV}$ are used to fix their strong decay channels. The full width $
\Gamma (T_{\mathrm{1}})$ of the diquark-antidiquark state $T_{\mathrm{1}}$ is
estimated by considering the processes $T_{\mathrm{1}} \to B_{c}^{-}B_{c}^{\ast
-}$ and $T_{\mathrm{1}} \to B_{c}^{\ast -}B_{c}^{\ast -} $. The decays to
mesons $B_{c}^{-}B_{c}^{\ast -}$, $B_{c}^{-}(2S)B_{c}^{ \ast -}$ and
$B_{c}^{\ast -}B_{c}^{\ast -}$ are employed to evaluate $\Gamma
(T_{\mathrm{2}})$. Results obtained for the widths $\Gamma (T_{\mathrm{1}
})=(44.3\pm 8.8)~\mathrm{MeV}$ and $\Gamma (T_{\mathrm{2}})=(82.5\pm 13.7)~
\mathrm{MeV}$ of these tetraquarks in conjunction with their masses are useful
for future experimental studies of fully heavy resonances.
|
We give a complete analytic and geometric description of the horofunction
boundary for polygonal sub-Finsler metrics---that is, those that arise as
asymptotic cones of word metrics---on the Heisenberg group. We develop theory
for the more general case of horofunction boundaries in homogeneous groups by
connecting horofunctions to Pansu derivatives of the distance function.
|
The article is devoted to the simulation of viscous incompressible turbulent
fluid flow based on solving the Reynolds averaged Navier-Stokes (RANS)
equations with different k-omega models. The isogeometrical approach is used
for the discretization based on the Galerkin method. Primary goal of using
isogeometric analysis is to be always geometrically exact, independent of the
discretization, and to avoid a time-consuming generation of meshes of
computational domains. For higher Reynolds numbers, we use stabilization SUPG
technique in equations for k and omega. The solutions are compared with the
standard benchmark example of turbulent flow over a backward facing step.
|
Concept-based interpretations of black-box models are often more intuitive
for humans to understand. The most widely adopted approach for concept-based
interpretation is Concept Activation Vector (CAV). CAV relies on learning a
linear relation between some latent representation of a given model and
concepts. The linear separability is usually implicitly assumed but does not
hold true in general. In this work, we started from the original intent of
concept-based interpretation and proposed Concept Gradient (CG), extending
concept-based interpretation beyond linear concept functions. We showed that
for a general (potentially non-linear) concept, we can mathematically evaluate
how a small change of concept affecting the model's prediction, which leads to
an extension of gradient-based interpretation to the concept space. We
demonstrated empirically that CG outperforms CAV in both toy examples and real
world datasets.
|
Quantum chaotic systems are conjectured to display a spectrum whose
fine-grained features (gaps and correlations) are well described by Random
Matrix Theory (RMT). We propose and develop a complementary version of this
conjecture: quantum chaotic systems display a Lanczos spectrum whose local
means and covariances are well described by RMT. To support this proposal, we
first demonstrate its validity in examples of chaotic and integrable systems.
We then show that for Haar-random initial states in RMTs the mean and
covariance of the Lanczos spectrum suffices to produce the full long time
behavior of general survival probabilities including the spectral form factor,
as well as the spread complexity. In addition, for initial states with
continuous overlap with energy eigenstates, we analytically find the long time
averages of the probabilities of Krylov basis elements in terms of the mean
Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the
statistics of which differentiate integrable systems and classes of quantum
chaos. Finally, we clarify the relation between spread complexity and the
universality classes of RMT by exploring various values of the Dyson index and
Poisson distributed spectra.
|
Massive black holes (MBHs) in galactic nuclei are believed to be surrounded
by a high density stellar cluster, whose mass is mostly in hard-to-detect faint
stars and compact remnants. Such dark cusps dominate the dynamics near the MBH:
a dark cusp in the Galactic center (GC) of the Milky Way would strongly affect
orbital tests of General Relativity there; on cosmic scales, dark cusps set the
rates of gravitational wave emission events from compact remnants that spiral
into MBHs, and they modify the rates of tidal disruption events, to list only
some implications. A recently discovered long-period massive young binary (P_12
<~ 1 yr, M_12 ~ O(100 M_sun), T_12 ~ 6x10^6 yr), only ~0.1 pc from the Galactic
MBH (Pfuhl et al 2013), sets a lower bound on the 2-body relaxation timescale
there, min t_rlx ~ (P_12/M_12)^(2/3)T_12 ~ 10^7 yr, and correspondingly, an
upper bound on the stellar number density, max n ~ few x 10^8/<M_star^2>
1/pc^3, based on the binary's survival against evaporation by the dark cusp.
However, a conservative dynamical estimate, the drain limit, implies t_rlx >
O(10^8) yr. Such massive binaries are thus too short-lived and tightly bound to
constrain a dense relaxed dark cusp. We explore here in detail the use of
longer-period, less massive and longer-lived binaries (P_12 ~ few yr, M_12 ~
2-4 M_sun, T_12 ~ 10^8-10^10 yr), presently just below the detection threshold,
for probing the dark cusp, and develop the framework for translating their
future detections among the giants in the GC into dynamical constraints.
|
We introduce a one-parameter family of random infinite quadrangulations of
the half-plane, which we call the uniform infinite half-planar quadrangulations
with skewness (UIHPQ$_p$ for short, with $p\in[0,1/2]$ measuring the skewness).
They interpolate between Kesten's tree corresponding to $p=0$ and the usual
UIHPQ with a general boundary corresponding to $p=1/2$. As we make precise,
these models arise as local limits of uniform quadrangulations with a boundary
when their volume and perimeter grow in a properly fine-tuned way, and they
represent all local limits of (sub)critical Boltzmann quadrangulations whose
perimeter tend to infinity. Our main result shows that the family
(UIHPQ$_p$)$_p$ approximates the Brownian half-planes BHP$_\theta$, $\theta\geq
0$, recently introduced in Baur, Miermont, and Ray (2016). For $p<1/2$, we give
a description of the UIHPQ$_p$ in terms of a looptree associated to a critical
two-type Galton-Watson tree conditioned to survive.
|
Maximal arcs in small projective Hjelmslev geometries are classified up to
isomorphism, and the parameters of the associated codes are determined.
|
Machine learning (ML) models can underperform on certain population groups
due to choices made during model development and bias inherent in the data. We
categorize sources of discrimination in the ML pipeline into two classes:
aleatoric discrimination, which is inherent in the data distribution, and
epistemic discrimination, which is due to decisions made during model
development. We quantify aleatoric discrimination by determining the
performance limits of a model under fairness constraints, assuming perfect
knowledge of the data distribution. We demonstrate how to characterize
aleatoric discrimination by applying Blackwell's results on comparing
statistical experiments. We then quantify epistemic discrimination as the gap
between a model's accuracy when fairness constraints are applied and the limit
posed by aleatoric discrimination. We apply this approach to benchmark existing
fairness interventions and investigate fairness risks in data with missing
values. Our results indicate that state-of-the-art fairness interventions are
effective at removing epistemic discrimination on standard (overused) tabular
datasets. However, when data has missing values, there is still significant
room for improvement in handling aleatoric discrimination.
|
For a continuous complex-valued function g on the real line without zeros,
several notions of a mean winding number are introduced. We give necessary
conditions for a Toeplitz operator with matrix-valued symbol G to be
semi-Fredholm in terms of mean winding numbers of det G. The matrix function G
is assumed to be continuous on the real line, and no other apriori assumptions
on it are made.
|
An additional spheroidal integral of motion and a group of dynamic symmetry
in a model quantum-mechanical problem of two centres eZ_{1}Z_{2}omega with
Coulomb and oscillator interactions is obtained, the group properties of its
solutions being studied. P(3) \otimes P(2,1), P(5,1) and P(4,2) groups are
considered as the dynamic symmetry groups of the problem, among them P(3)
\otimes P(2,1) group possessing the smallest number of parameters. The obtained
results may appear useful at the calcuations of QQq-baryons and QQg-mesons
energy spectra.
|
We demonstrate radio-frequency tuning of the energy of individual CdTe/ZnTe
quantum dots (QDs) by Surface Acoustic Waves (SAWs). Despite the very weak
piezoelectric coefficient of ZnTe, SAW in the GHz range can be launched on a
ZnTe surface using interdigitated transducers deposited on a c-axis oriented
ZnO layer grown on ZnTe containing CdTe QDs. The photoluminescence (PL) of
individual QDs is used as a nanometer-scale sensor of the acoustic strain
field. The energy of QDs is modulated by SAW in the GHz range and leads to
characteristic broadening of time-integrated PL spectra. The dynamic modulation
of the QD PL energy can also be detected in the time domain using phase-locked
time domain spectroscopy. This technique is in particular used for monitoring
complex local acoustic fields resulting from the superposition of two or more
SAW pulses in a cavity. Under magnetic field, the dynamic spectral tuning of a
single QD by SAW can be used to generate single photons with alternating
circular polarization controlled in the GHz range.
|
Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's
theorem and point out a loophole in it. We also demonstrate on this example
that quantum mechanics is a local realistic theory.
|
In this article, we consider a class of bi-stable reaction-diffusion
equations in two components on the real line. We assume that the system is
singularly perturbed, i.e. that the ratio of the diffusion coefficients is
(asymptotically) small. This class admits front solutions that are
asymptotically close to the (stable) front solution of the `trivial' scalar
bi-stable limit system $u_t = u_{xx} + u(1-u^2)$. However, in the system these
fronts can become unstable by varying parameters. This destabilization is
either caused by the essential spectrum associated to the linearized stability
problem, or by an eigenvalue that exists near the essential spectrum. We use
the Evans function to study the various bifurcation mechanisms and establish an
explicit connection between the character of the destabilization and the
possible appearance of saddle-node bifurcations of heteroclinic orbits in the
existence problem.
|
Given a user's historical interaction sequence, online novel recommendation
suggests the next novel the user may be interested in. Online novel
recommendation is important but underexplored. In this paper, we concentrate on
recommending online novels to new users of an online novel reading platform,
whose first visits to the platform occurred in the last seven days. We have two
observations about online novel recommendation for new users. First, repeat
novel consumption of new users is a common phenomenon. Second, interactions
between users and novels are informative. To accurately predict whether a user
will reconsume a novel, it is crucial to characterize each interaction at a
fine-grained level. Based on these two observations, we propose a neural
network for online novel recommendation, called NovelNet. NovelNet can
recommend the next novel from both the user's consumed novels and new novels
simultaneously. Specifically, an interaction encoder is used to obtain accurate
interaction representation considering fine-grained attributes of interaction,
and a pointer network with a pointwise loss is incorporated into NovelNet to
recommend previously-consumed novels. Moreover, an online novel recommendation
dataset is built from a well-known online novel reading platform and is
released for public use as a benchmark. Experimental results on the dataset
demonstrate the effectiveness of NovelNet.
|
We have built a CsI(Tl) gamma-ray detector array for the NPDGamma experiment
to search for a small parity-violating directional asymmetry in the angular
distribution of 2.2 MeV gamma-rays from the capture of polarized cold neutrons
by protons with a sensitivity of several ppb. The weak pion-nucleon coupling
constant can be determined from this asymmetry. The small size of the asymmetry
requires a high cold neutron flux, control of systematic errors at the ppb
level, and the use of current mode gamma-ray detection with vacuum photo diodes
and low-noise solid-state preamplifiers. The average detector photoelectron
yield was determined to be 1300 photoelectrons per MeV. The RMS width seen in
the measurement is therefore dominated by the fluctuations in the number of
gamma rays absorbed in the detector (counting statistics) rather than the
intrinsic detector noise. The detectors were tested for noise performance,
sensitivity to magnetic fields, pedestal stability and cosmic background. False
asymmetries due to gain changes and electronic pickup in the detector system
were measured to be consistent with zero to an accuracy of $10^{-9}$ in a few
hours. We report on the design, operating criteria, and the results of
measurements performed to test the detector array.
|
We study the inflow-outflow boundary value problem on an interval, the analog
of the 1D shock tube problem for gas dynamics, for general systems of
hyperbolic-parabolic conservation laws. In a first set of investigations, we
study existence, uniqueness, and stability, showing in particular local
existence, uniqueness, and stability of small amplitude solutions for general
symmetrizable systems. In a second set of investigations, we investigate
structure and behavior in the small- and large-viscosity limits. A phenomenon
of particular interest is the generic appearance of characteristic boundary
layers in the inviscid limit, arising from noncharacteristic data for the
viscous problem, even of arbitrarily small amplitude. This induces an
interesting new type of \transcharacteristic" hyperbolic boundary condition
governing the formal inviscid limit.
|
In this note we prove the Weinstein conjecture for a class of symplectic
manifolds including the uniruled manifolds based on Liu-Tian's result.
|
Molecular absorption lines measured along the line of sight of distant
quasars are important probes of the gas evolution in galaxies as a function of
redshift.
A review is made of the handful of molecular absorbing systems studied so
far, with the present sensitivity of mm instruments. They produce information
on the chemistry of the ISM at z \sim 1, the physical state of the gas, in
terms of clumpiness, density and temperature. The CMB temperature can be
derived as a function of z, and also any possible variations of fundamental
constants can be constrained. With the sensitivity of ALMA, many more absorbing
systems can be studied, for which some predictions and perspectives are
described.
|
Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most
recognized method in sufficient dimension reduction. While promising progress
has been made in theory and methods of high-dimensional SIR, two remaining
challenges are still nagging high-dimensional multivariate applications. First,
choosing the number of slices in SIR is a difficult problem, and it depends on
the sample size, the distribution of variables, and other practical
considerations. Second, the extension of SIR from univariate response to
multivariate is not trivial. Targeting at the same dimension reduction subspace
as SIR, we propose a new slicing-free method that provides a unified solution
to sufficient dimension reduction with high-dimensional covariates and
univariate or multivariate response. We achieve this by adopting the recently
developed martingale difference divergence matrix (MDDM, Lee & Shao 2018) and
penalized eigen-decomposition algorithms. To establish the consistency of our
method with a high-dimensional predictor and a multivariate response, we
develop a new concentration inequality for sample MDDM around its population
counterpart using theories for U-statistics, which may be of independent
interest. Simulations and real data analysis demonstrate the favorable finite
sample performance of the proposed method.
|
We propose the action for the nonrelativistic string invariant under general
coordinate transformations on the string worldsheet. The Hamiltonian
formulation for the nonrelativistic string is given. Particular solutions of
the Euler-Lagrange equations are found in the time gauge.
|
We propose a new dark-state cooling method of trapped ion systems in the
Lamb-Dicke limit. With application of microwave dressing the ion, we can obtain
two electromagnetically induced transparency structures. The heating effects
caused by the carrier and the blue sideband transition vanish due to the EIT
effects and the final mean phonon numbers can be much less than the recoil
limit. Our scheme is robust to fluctuations of microwave power and laser
intensities which provides a broad cooling bandwidth to cool motional modes of
a linear ion chain. Moreover, it is more suitable to cool four-level ions on a
large-scale ion chip.
|
We propose that the Matrix Profile data structure, conventionally applied to
large scale time-series data mining, is applicable to the analysis and
suppression of cyclical error in electromechanical systems, paving the way for
an intelligent family of adaptable control systems which respond to
environmental error at a computational cost low enough to be practical in
embedded applications. We construct and evaluate the efficacy of a control
algorithm utilizing the Matrix Profile, which we call Cyclical
Electromechanical Error Denial System (CEEDS).
|
Inspired by the works of L. Carlitz and Z.-W. Sun on cyclotomic matrices, in
this paper, we investigate certain cyclotomic matrices involving Gauss sums
over finite fields, which can be viewed as finite field analogues of certain
matrices related to the Gamma function.
For example, let $q=p^n$ be an odd prime power with $p$ prime and
$n\in\mathbb{Z}^+$. Let $\zeta_p=e^{2\pi{\bf i}/p}$ and let $\chi$ be a
generator of the group of all mutiplicative characters of the finite field
$\mathbb{F}_q$. For the Gauss sum
$$G_q(\chi^{r})=\sum_{x\in\mathbb{F}_q}\chi^{r}(x)\zeta_p^{{\rm
Tr}_{\mathbb{F}_q/\mathbb{F}_p}(x)},$$
we prove that
$$\det \left[G_q(\chi^{2i+2j})\right]_{0\le i,j\le
(q-3)/2}=(-1)^{\alpha_p}\left(\frac{q-1}{2}\right)^{\frac{q-1}{2}}2^{\frac{p^{n-1}-1}{2}},$$
where
$$\alpha_p=
\begin{cases}
1 & \mbox{if}\ n\equiv 1\pmod 2,
(p^2+7)/8 & \mbox{if}\ n\equiv 0\pmod 2.
\end{cases}$$
|
Let $\Sigma$ be a surface with a symplectic form, let $\phi$ be a
symplectomorphism of $\Sigma$, and let $Y$ be the mapping torus of $\phi$. We
show that the dimensions of moduli spaces of embedded pseudoholomorphic curves
in $\R\times Y$, with cylindrical ends asymptotic to periodic orbits of $\phi$
or multiple covers thereof, are bounded from above by an additive relative
index. We deduce some compactness results for these moduli spaces.
This paper establishes some of the foundations for a program with Michael
Thaddeus, to understand the Seiberg-Witten Floer homology of $Y$ in terms of
such pseudoholomorphic curves. Analogues of our results should also hold in
three dimensional contact homology.
|
In this analytical study, we have presented a new type of solving procedure
with aim to obtain the coordinates of small mass m, which moves around primary
M_Sun, referred to non-inertial frame of restricted two-body problem (R2BP)
with modified potential function (taking into account the components of
variable velocity of central body M_Sun motion) instead of classical potential
function for Kepler formulation of R2BP. Meanwhile, system of equations of
motion has been successfully explored with respect to the existence of
analytical way for presentation of the solution in polar coordinates with
radial distance r = r(t). We have obtained analytical formula for function t =
t(r) via appropriate elliptic integral. Having obtained the inversed dependence
r = r(t), we can obtain the time-dependence for the polar angle as well. Also,
we have pointed out how to express components of solution (including initial
conditions) from cartesian to polar coordinates.
|
The microscopic modeling of spin-orbit entangled $j=1/2$ Mott insulators such
as the layered hexagonal Iridates Na$_2$IrO$_3$ and Li$_2$IrO$_3$ has spurred
an interest in the physics of Heisenberg-Kitaev models. Here we explore the
effect of lattice distortions on the formation of the collective spin-orbital
states which include not only conventionally ordered phases but also gapped and
gapless spin-orbital liquids. In particular, we demonstrate that in the
presence of spatial anisotropies of the exchange couplings conventionally
ordered states are formed through an order-by-disorder selection which is not
only sensitive to the type of exchange anisotropy but also to the relative
strength of the Heisenberg and Kitaev couplings. The spin-orbital liquid phases
of the Kitaev limit -- a gapless phase in the vicinity of spatially isotropic
couplings and a gapped Z$_2$ phase for a dominant spatial anisotropy of the
exchange couplings -- show vastly different sensitivities to the inclusion of a
Heisenberg exchange. While the gapless phase is remarkably stable, the gapped
Z$_2$ phase quickly breaks down in what might be a rather unconventional phase
transition driven by the simultaneous condensation of its elementary
excitations.
|
Scores of on-going microlensing events are now announced yearly by the
microlensing discovery teams OGLE, MACHO and EROS. These early warning systems
have allowed other international microlensing networks to focus considerable
resources on intense photometric - and occasionally spectroscopic - monitoring
of microlensing events. Early results include: metallicity measurements of main
sequence Galactic bulge stars; limb darkening determinations for stars in the
Bulge and Small Magellanic Cloud; proper motion measurements that constrain
microlens identity; and constraints on Jovian-mass planets orbiting (presumably
stellar) lenses. These results and auxiliary science such as variable star
studies and optical identification of gamma ray bursts are reviewed.
|
We statistically analyse a recent sample of data points measuring the
fine-structure constant alpha (relative to the terrestrial value) in quasar
absorption systems. Using different statistical techniques, we find general
agreement with previous authors that a dipole model is a well-justified fit to
the data. We determine the significance of the dipole fit relative to that of a
simple monopole fit, discuss the consistency of the interpretation, and test
alternate models for potential variation of alpha against the data. Using a
simple analysis we find that the monopole term (the constant offset in (delta
alpha)/alpha) may be caused by non-terrestrial magnesium isotope abundances in
the absorbers. Finally we test the domain-wall model against the data.
|
In Goal-oriented Reinforcement learning, relabeling the raw goals in past
experience to provide agents with hindsight ability is a major solution to the
reward sparsity problem. In this paper, to enhance the diversity of relabeled
goals, we develop FGI (Foresight Goal Inference), a new relabeling strategy
that relabels the goals by looking into the future with a learned dynamics
model. Besides, to improve sample efficiency, we propose to use the dynamics
model to generate simulated trajectories for policy training. By integrating
these two improvements, we introduce the MapGo framework (Model-Assisted Policy
Optimization for Goal-oriented tasks). In our experiments, we first show the
effectiveness of the FGI strategy compared with the hindsight one, and then
show that the MapGo framework achieves higher sample efficiency when compared
to model-free baselines on a set of complicated tasks.
|
We study heterogeneity in the effect of a mindset intervention on
student-level performance through an observational dataset from the National
Study of Learning Mindsets (NSLM). Our analysis uses machine learning (ML) to
address the following associated problems: assessing treatment group overlap
and covariate balance, imputing conditional average treatment effects, and
interpreting imputed effects. By comparing several different model families we
illustrate the flexibility of both off-the-shelf and purpose-built estimators.
We find that the mindset intervention has a positive average effect of 0.26,
95%-CI [0.22, 0.30], and that heterogeneity in the range of [0.1, 0.4] is
moderated by school-level achievement level, poverty concentration, urbanicity,
and student prior expectations.
|
In recent years, deep neural networks (DNNs) based approaches have achieved
the start-of-the-art performance for music source separation (MSS). Although
previous methods have addressed the large receptive field modeling using
various methods, the temporal and frequency correlations of the music
spectrogram with repeated patterns have not been explicitly explored for the
MSS task. In this paper, a temporal-frequency attention module is proposed to
model the spectrogram correlations along both temporal and frequency
dimensions. Moreover, a multi-scale attention is proposed to effectively
capture the correlations for music signal. The experimental results on MUSDB18
dataset show that the proposed method outperforms the existing state-of-the-art
systems with 9.51 dB signal-to-distortion ratio (SDR) on separating the vocal
stems, which is the primary practical application of MSS.
|
Many panel studies collect refreshment samples---new, randomly sampled
respondents who complete the questionnaire at the same time as a subsequent
wave of the panel. With appropriate modeling, these samples can be leveraged to
correct inferences for biases caused by non-ignorable attrition. We present
such a model when the panel includes many categorical survey variables. The
model relies on a Bayesian latent pattern mixture model, in which an indicator
for attrition and the survey variables are modeled jointly via a latent class
model. We allow the multinomial probabilities within classes to depend on the
attrition indicator, which offers additional flexibility over standard
applications of latent class models. We present results of simulation studies
that illustrate the benefits of this flexibility. We apply the model to correct
attrition bias in an analysis of data from the 2007-2008 Associated Press/Yahoo
News election panel study.
|
The Einstein equations are solved algebraically to model a hybrid
astrophysical compact object consisting of a preon gas core, a mantle of
electrically charged hot quark-gluon plasma, and an outer envelope of charged
hadronic matter which is matched to an exterior Reissner-Nordstrom vacuum. The
piecewise-continuous metric and the pressure and density functions consist of
polynomials that are everywhere well-behaved. Boundary conditions at each
interface yield estimates for physical parameters applicable to each layer, and
to the star as a whole.
|
In this paper, we study the local exact controllability to special
trajectories of the micropolar fluid systems in dimension d = 2 and d = 3. We
show that controllability is possible acting only on one velocity.
|
In this paper, an analytical method that solves the forward displacement
problem of several common spherical parallel manipulators (SPMs) is presented.
The method uses the the quaternion algebra to restate the problem as a system
of four quadrics in four variables and uses an algebraic geometry result by
Dixon from 1908 to solve. In addition, a case study is presented for a specific
SPM.
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The study of Galactic Cosmic-ray electrons (CREs) saw important developments
in recent years, with the assumption of positron production only in interaction
of hadronic Cosmic-rays with interstellar matter challenged by new measurements
of CRE spectrum and related quantities. Indeed, all recent experiments seem to
confirm an hardening in the positrons, a feature that is totally in contrast
with the all-secondaries hypothesis, even if significant disagreements are
present about the CRE spectral behavior and the possible presence of spectral
features. Together with insufficient precision of current measurements, these
disagreements prevent the identification of the primary positron source, with
models involving Dark matter or astrophysical sources like Super Nova Remnants
and Pulsar Wind Nebula all able to explain current data.
The fermi-LAT contribution to the CRE study was fundamental, with the 2009
measurement of the positron + electron spectrum extended to the 7 MeV - 1TeV
range with a statistics already exceeding previous results by many order of
magnitude; since then, the last statistic has largely increased, while the LAT
event reconstruction was significantly improved.
In this article the reader will find an extensive and historical review of
the CRE science, a summary of the history of gamma astronomy before fermi, an
accurate description of the LAT and of its data analysis, a review of the
present knowledge about CRE spectrum and on the theories that try to explain
it, and finally a description of the changes and improvements introduced in the
LAT event reconstruction process at the beginning of 2015.
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We discuss possible non-standard contributions to the top-quark width,
particularly the virtual effects on the standard decay $t\rightarrow W^+\,b$
within the context of the MSSM. We also place a renewed emphasis on the
unconventional mode $t\rightarrow H^+\,b$ in the light of recent analyses of
$Z$-boson observables. It turns out that in the region of parameter space
highlighted by $Z$-boson physics, the charged Higgs mode should exhibite an
appreciable branching fraction as compared to the standard decay of the top
quark. Remarkably enough, the corresponding quantum effects in this region are
also rather large, slowly decoupling, and most likely resolvable in the next
generation of experiments at Tevatron and at LHC.
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Contemporary quantum devices are reaching new limits in size and complexity,
allowing for the experimental exploration of emergent quantum modes. However,
this increased complexity introduces significant challenges in device tuning
and control. Here, we demonstrate autonomous tuning of emergent Majorana zero
modes in a minimal realization of a Kitaev chain. We achieve this task using
cross-platform transfer learning. First, we train a tuning model on a theory
model. Next, we retrain it using a Kitaev chain realization in a
two-dimensional electron gas. Finally, we apply this model to tune a Kitaev
chain realized in quantum dots coupled through a semiconductor-superconductor
section in a one-dimensional nanowire. Utilizing a convolutional neural
network, we predict the tunneling and Cooper pair splitting rates from
differential conductance measurements, employing these predictions to adjust
the electrochemical potential to a Majorana sweet spot. The algorithm
successfully converges to the immediate vicinity of a sweet spot (within 1.5 mV
in 67.6% of attempts and within 4.5 mV in 80.9% of cases), typically finding a
sweet spot in 45 minutes or less. This advancement is a stepping stone towards
autonomous tuning of emergent modes in interacting systems, and towards
foundational tuning machine learning models that can be deployed across a range
of experimental platforms.
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A nitrogen gas Raman cell system has been constructed to shift a 70 J 527 nm
laser beam to 600 nm with 20 J of energy. The 600 nm probe and a 200J, 527 nm
pump beam were optically mixed in a laser produced (gas jet) plasma. The
beating of the two laser beams formed a ponderomotive force that can drive
Kinetic Electrostatic Electron Nonlinear (KEEN) waves discovered in
Vlasov-Poisson simulations by Afeyan et al [1,2]. KEEN waves were detected in
these experiments where traditional plasma theory would declare there to be a
spectral gap (ie no linear waves possible). The detection was done using
Thomson scattering with probe wavelengths of both 351 nm and 263.5 nm.
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Regular incidence complexes are combinatorial incidence structures
generalizing regular convex polytopes, regular complex polytopes, various types
of incidence geometries, and many other highly symmetric objects. The special
case of abstract regular polytopes has been well-studied. The paper describes
the combinatorial structure of a regular incidence complex in terms of a system
of distinguished generating subgroups of its automorphism group or a
flag-transitive subgroup. Then the groups admitting a flag-transitive action on
an incidence complex are characterized as generalized string C-groups. Further,
extensions of regular incidence complexes are studied, and certain incidence
complexes particularly close to abstract polytopes, called abstract polytope
complexes, are investigated.
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In estimating the causal effect of a continuous exposure or treatment, it is
important to control for all confounding factors. However, most existing
methods require parametric specification for how control variables influence
the outcome or generalized propensity score, and inference on treatment effects
is usually sensitive to this choice. Additionally, it is often the goal to
estimate how the treatment effect varies across observed units. To address this
gap, we propose a semiparametric model using Bayesian tree ensembles for
estimating the causal effect of a continuous treatment of exposure which (i)
does not require a priori parametric specification of the influence of control
variables, and (ii) allows for identification of effect modification by
pre-specified moderators. The main parametric assumption we make is that the
effect of the exposure on the outcome is linear, with the steepness of this
relationship determined by a nonparametric function of the moderators, and we
provide heuristics to diagnose the validity of this assumption. We apply our
methods to revisit a 2001 study of how abortion rates affect incidence of
crime.
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We report tentative evidence for a cold stellar stream in the ultra-diffuse
galaxy NGC1052-DF2. If confirmed, this stream (which we refer to as "The Maybe
Stream") would be the first cold stellar stream detected outside of the Local
Group. The candidate stream is very narrow and has an unusual and highly curved
shape.
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Contrary to a previously published claim it is found that the spheroidal
galaxies NGC 147 and NGC 185 probably form a stable binary system. Distance
estimates place this pair on the near side of the Andromeda subgroup of the
Local Group. The fact that this system has probably remained stable over a
Hubble time suggests that it does not have a plunging orbit that brings it very
close to M 31. It is noted that the only two Local Group galaxy pairs, in which
the components have comparable masses, also have similar morphological types.
NGC 147 and NGC 185 are both spheroidals, while the LMC and SMC are both
irregulars. This suggests that protogalaxies of similar mass that are spawned
in similar environments evolve into objects having similar morphologies.
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In this paper we construct massive supermultiplets out of appropriate set of
massless ones in the same way as massive spin s particle could be constructed
out of massless spin s,s-1,... ones leading to gauge invariant description of
massive particle. Mainly we consider massive spin 3/2 supermultiplets in a flat
d=4 Minkowski space both without central charge for N=1,2,3 as well as with
central charge for N=2,4. Besides, we give two examples of massive N=1
supermultiplets with spin 3/2 and 2 in AdS_4 space.
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The FIND algorithm (also called Quickselect) is a fundamental algorithm to
select ranks or quantiles within a set of data. It was shown by Gr\"ubel and
R\"osler that the number of key comparisons required by Find as a process of
the quantiles $\alpha\in[0,1]$ in a natural probabilistic model converges after
normalization in distribution within the c\`adl\`ag space $D[0,1]$ endowed with
the Skorokhod metric. We show that the process of the residuals in the latter
convergence after normalization converges in distribution to a mixture of
Gaussian processes in $D[0,1]$ and identify the limit's conditional covariance
functions. A similar result holds for the related algorithm QuickVal. Our
method extends to other cost measures such as the number of swaps (key
exchanges) required by Find or cost measures which are based on key comparisons
but take into account that the cost of a comparison between two keys may depend
on their values, an example being the number of bit comparisons needed to
compare keys given by their bit expansions.
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Graph-based clustering plays an important role in the clustering area. Recent
studies about graph convolution neural networks have achieved impressive
success on graph type data. However, in general clustering tasks, the graph
structure of data does not exist such that the strategy to construct a graph is
crucial for performance. Therefore, how to extend graph convolution networks
into general clustering tasks is an attractive problem. In this paper, we
propose a graph auto-encoder for general data clustering, which constructs the
graph adaptively according to the generative perspective of graphs. The
adaptive process is designed to induce the model to exploit the high-level
information behind data and utilize the non-Euclidean structure sufficiently.
We further design a novel mechanism with rigorous analysis to avoid the
collapse caused by the adaptive construction. Via combining the generative
model for network embedding and graph-based clustering, a graph auto-encoder
with a novel decoder is developed such that it performs well in weighted graph
used scenarios. Extensive experiments prove the superiority of our model.
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Utilization of multiple trajectories of a dynamical system model provides us
with several benefits in approximation of time series. For short term
predictions a high accuracy can be achieved via switches to new trajectory at
any time. Different long term trends (tendency to different stationary points)
of the phase portrait characterize various scenarios of the process realization
influenced by externalities. The dynamical system's phase portrait analysis
helps to see if the equations properly describe the reality. We also extend the
dynamical systems approach (discussed in \cite{R5}) to the dynamical systems
with external control.
We illustrate these ideas with the help of new examples of the rental
properties HOMES.mil platform data. We also compare the qualitative properties
of HOMES.mil and Wikipedia.org platforms' phase portraits and the corresponding
differences of the two platforms' users. In our last example with COVID-19 data
we discuss the high accuracy of the short term prediction of confirmed
infection cases, recovery cases and death cases in various countries.
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Assuming an effective quadratic Hamiltonian, we derive an approximate, linear
stochastic equation of motion for the density-fluctuations in liquids, composed
of overdamped Brownian particles. From this approach, time dependent two point
correlation functions (such as the intermediate scattering function) are
derived. We show that this correlation function is exact at short times, for
any interaction and, in particular, for arbitrary external potentials so that
it applies to confined systems. Furthermore, we discuss the relation of this
approach to previous ones, such as dynamical density functional theory as well
as the formally exact treatment. This approach, inspired by the well known
Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of
motion, may be seen as its microscopic version, containing information about
the details on the particle level.
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Electromagnetic metasurfaces have attracted significant interest recently due
to their low profile and advantageous applications. Practically, many
metasurface designs start with a set of constraints for the radiated far-field,
such as main-beam direction(s) and side lobe levels, and end with a non-uniform
physical structure for the surface. This problem is quite challenging, since
the required tangential field transformations are not completely known when
only constraints are placed on the scattered fields. Hence, the required
surface properties cannot be solved for analytically. Moreover, the translation
of the desired surface properties to the physical unit cells can be
time-consuming and difficult, as it is often a one-to-many mapping in a large
solution space. Here, we divide the inverse design process into two steps: a
macroscopic and microscopic design step. In the former, we use an iterative
optimization process to find the surface properties that radiate a far-field
pattern that complies with specified constraints. This iterative process
exploits non-radiating currents to ensure a passive and lossless design. In the
microscopic step, these optimized surface properties are realized with physical
unit cells using machine learning surrogate models. The effectiveness of this
end-to-end synthesis process is demonstrated through measurement results of a
beam-splitting prototype.
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For a symplectic isotopy on the two-dimensional disc we show that the
classical spectral invariants of Viterbo [20] can be extended in a meaningful
way to {\it non-compactly} supported Hamiltonians. We establish some basic
properties of these extended invariants and as an application we show that
Hutchings' inequality in [8] between the Calabi invariant and the mean action
spectrum holds without any assumptions on the isotopy; in [8] it is assumed
that the Calabi invariant is less than the rotation number (or action) on the
boundary.
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Recent spectropolarimetric surveys (MiMeS, BOB) have revealed that
approximately 7% of massive stars host stable, surface dipolar magnetic fields
with strengths on the order of kG. These fields channel the dense radiatively
driven stellar wind into a circumstellar magnetosphere. Wind-sensitive UV
spectral lines can probe the density and velocity structure of massive star
magnetospheres, providing insight into wind-field interactions. To date,
large-scale magnetohydrodynamic modeling of this phenomenon has been limited by
the associated computational cost. Our analysis, using the Analytic Dynamical
Magnetosphere model, solves this problem by applying a simple analytic
prescription to efficiently calculate synthetic UV spectral lines. It can
therefore be applied in the context of a larger parameter study to derive the
wind properties for the population of known magnetic O stars. We also present
the latest UV spectra of the magnetic O star NGC 1624-2 obtained with HST/COS,
which test the limits of our models and suggest a particularly complex
magnetospheric structure for this archetypal object.
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Motivated to measure the QED birefringence and to detect pseudoscalar-photon
interaction, we started to build up the Q & A experiment (QED [Quantum
Electrodynamics] and Axion experiment) in 1994. In this talk, we first review
our 3.5 m Fabry-Perot interferometer together with our results of measuring
Cotton-Mouton effects of gases. We are uprading our interferometer to 7 m
armlength with a new 1.8 m 2.3 T permanent magnet capable of rotation up to 13
cycles per second. We will use 532 nm Nd:YAG laser as light source with cavity
finesse around 100,000, and aim at 10 nrad/Hz^{1/2} optical sensitivity. With
all these achieved and the upgrading of vacuum, QED birefringence would be
measured to 28% in about 50 days. Along the way, we should be able to improve
on the dichroism detection significantly.
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We prove a necessary condition for a dynamic integro-differential equation to
be an Euler-Lagrange equation. New and interesting results for the discrete and
quantum calculus are obtained as particular cases. An example of a second order
dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time
scale, is given.
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Following the success of the so-called algebraic approach to the study of
decision constraint satisfaction problems (CSPs), exact optimization of valued
CSPs, and most recently promise CSPs, we propose an algebraic framework for
valued promise CSPs.
To every valued promise CSP we associate an algebraic object, its so-called
valued minion. Our main result shows that the existence of a homomorphism
between the associated valued minions implies a polynomial-time reduction
between the original CSPs. We also show that this general reduction theorem
includes important inapproximability results, for instance, the
inapproximability of almost solvable systems of linear equations beyond the
random assignment threshold.
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Message-passing methods provide a powerful approach for calculating the
expected size of cascades either on random networks (e.g., drawn from a
configuration-model ensemble or its generalizations) asymptotically as the
number $N$ of nodes becomes infinite or on specific finite-size networks. We
review the message-passing approach and show how to derive it for
configuration-model networks using the methods of (Dhar et al., 1997) and
(Gleeson, 2008). Using this approach, we explain for such networks how to
determine an analytical expression for a "cascade condition", which determines
whether a global cascade will occur. We extend this approach to the
message-passing methods for specific finite-size networks (Shrestha and Moore,
2014; Lokhov et al., 2015), and we derive a generalized cascade condition.
Throughout this chapter, we illustrate these ideas using the Watts threshold
model.
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Attributed network embedding has attracted plenty of interest in recent
years. It aims to learn task-independent, low-dimensional, and continuous
vectors for nodes preserving both topology and attribute information. Most of
the existing methods, such as random-walk based methods and GCNs, mainly focus
on the local information, i.e., the attributes of the neighbours. Thus, they
have been well studied for assortative networks (i.e., networks with
communities) but ignored disassortative networks (i.e., networks with
multipartite, hubs, and hybrid structures), which are common in the real world.
To enable model both assortative and disassortative networks, we propose a
block-based generative model for attributed network embedding from a
probability perspective. Specifically, the nodes are assigned to several blocks
wherein the nodes in the same block share the similar linkage patterns. These
patterns can define assortative networks containing communities or
disassortative networks with the multipartite, hub, or any hybrid structures.
To preserve the attribute information, we assume that each node has a hidden
embedding related to its assigned block. We use a neural network to
characterize the nonlinearity between node embeddings and node attributes. We
perform extensive experiments on real-world and synthetic attributed networks.
The results show that our proposed method consistently outperforms
state-of-the-art embedding methods for both clustering and classification
tasks, especially on disassortative networks.
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During the shock-wave propagation in a core-collapse supernova (SN), matter
turbulence may affect neutrino flavor conversion probabilities. Such effects
have been usually studied by adding parametrized small-scale random
fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric
matter density profiles. Recently, however, two-dimensional (2D) SN models have
reached a space resolution high enough to directly trace anisotropic density
profiles, down to scales smaller than the typical neutrino oscillation length.
In this context, we analyze the statistical properties of a large set of SN
matter density profiles obtained in a high-resolution 2D simulation, focusing
on a post-bounce time (2 s) suited to study shock-wave effects on neutrino
propagation on scales as small as O(100) km and possibly below. We clearly find
the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as
generically expected in 2D turbulence spectra. We then compute the flavor
evolution of SN neutrinos along representative realizations of the turbulent
matter density profiles, and observe no or modest damping of the neutrino
crossing probabilities on their way through the shock wave. In order to check
the effect of possibly unresolved fluctuations at scales below O(100) km, we
also apply a randomization procedure anchored to the power spectrum calculated
from the simulation, and find consistent results within \pm 1 sigma
fluctuations. These results show the importance of anchoring turbulence effects
on SN neutrinos to realistic, fine-grained SN models.
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We are concerned with spherically symmetric solutions of the Euler equations
for multidimensional compressible fluids, which are motivated by many important
physical situations. Various evidences indicate that spherically symmetric
solutions of the compressible Euler equations may blow up near the origin at
certain time under some circumstance. The central feature is the strengthening
of waves as they move radially inward. A longstanding open, fundamental
question is whether concentration could form at the origin. In this paper, we
develop a method of vanishing viscosity and related estimate techniques for
viscosity approximate solutions, and establish the convergence of the
approximate solutions to a global finite-energy entropy solution of the
compressible Euler equations with spherical symmetry and large initial data.
This indicates that concentration does not form in the vanishing viscosity
limit, even though the density may blow up at certain time. To achieve this, we
first construct global smooth solutions of appropriate initial-boundary value
problems for the Euler equations with designed viscosity terms, an approximate
pressure function, and boundary conditions, and then we establish the strong
convergence of the viscosity approximate solutions to a finite-energy entropy
solutions of the Euler equations.
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Multistate Markov models are a canonical parametric approach for data
modeling of observed or latent stochastic processes supported on a finite state
space. Continuous-time Markov processes describe data that are observed
irregularly over time, as is often the case in longitudinal medical data, for
example. Assuming that a continuous-time Markov process is time-homogeneous, a
closed-form likelihood function can be derived from the Kolmogorov forward
equations -- a system of differential equations with a well-known
matrix-exponential solution. Unfortunately, however, the forward equations do
not admit an analytical solution for continuous-time, time-inhomogeneous Markov
processes, and so researchers and practitioners often make the simplifying
assumption that the process is piecewise time-homogeneous. In this paper, we
provide intuitions and illustrations of the potential biases for parameter
estimation that may ensue in the more realistic scenario that the
piecewise-homogeneous assumption is violated, and we advocate for a solution
for likelihood computation in a truly time-inhomogeneous fashion. Particular
focus is afforded to the context of multistate Markov models that allow for
state label misclassifications, which applies more broadly to hidden Markov
models (HMMs), and Bayesian computations bypass the necessity for
computationally demanding numerical gradient approximations for obtaining
maximum likelihood estimates (MLEs). Supplemental materials are available
online.
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