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We study the attractive Hubbard model with mass imbalance to clarify low
temperature properties of the fermionic mixtures in the optical lattice. By
combining dynamical mean-field theory with the continuous-time quantum Monte
Carlo simulation, we discuss the competition between the superfluid and density
wave states at half filling. By calculating the energy and the order parameter
for each state, we clarify that the coexisting (supersolid) state, where the
density wave and superfluid states are degenerate, is realized in the system.
We then determine the phase diagram at finite temperatures.
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Problem definition: Mining for heterogeneous responses to an intervention is
a crucial step for data-driven operations, for instance to personalize
treatment or pricing. We investigate how to estimate price sensitivity from
transaction-level data. In causal inference terms, we estimate heterogeneous
treatment effects when (a) the response to treatment (here, whether a customer
buys a product) is binary, and (b) treatment assignments are partially observed
(here, full information is only available for purchased items).
Methodology/Results: We propose a recursive partitioning procedure to estimate
heterogeneous odds ratio, a widely used measure of treatment effect in medicine
and social sciences. We integrate an adversarial imputation step to allow for
robust estimation even in presence of partially observed treatment assignments.
We validate our methodology on synthetic data and apply it to three case
studies from political science, medicine, and revenue management. Managerial
Implications: Our robust heterogeneous odds ratio estimation method is a simple
and intuitive tool to quantify heterogeneity in patients or customers and
personalize interventions, while lifting a central limitation in many revenue
management data.
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The leading correction to scaling associated with departures of the initial
condition from the scaling morphology is determined for some soluble models of
phase-ordering kinetics. The result for the pair correlation function has the
form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a
characteristic length scale extracted from the energy. The
correction-to-scaling exponent \omega has the value \omega=4 for the d=1
Glauber model, the n-vector model with n=\infty, and the approximate theory of
Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega
has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for
d=3. The correction-to-scaling functions f_1(x) are also calculated.
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We present an isolated Milky Way-like simulation in GADGET2 N-body SPH code.
The Galactic disk star formation rate (SFR) surface densities and stellar mass
indicative of Solar neighbourhood are used as thresholds to model the
distribution of stellar mass in life friendly environments. SFR and stellar
component density are calculated averaging the GADGET2 particle properties on a
2D grid mapped on the Galactic plane. The peak values for possibly habitable
stellar mass surface density move from $10$ to $15$ kpc cylindrical
galactocentric distance in $10$ Gyr simulated time span. At $10$ Gyr the
simulation results imply the following. Stellar particles which have spent
almost all of their life time in habitable friendly conditions reside typically
at $\sim16$ kpc from Galactic centre and are $\sim 3$ Gyr old. Stellar
particles that have spent $\ge 90 \%$ of their $4-5$ Gyr long life time in
habitable friendly conditions, are also predominantly found in the outskirts of
the Galactic disk. Less then $1 \%$ of these particles can be found at a
typical Solar system galactocentric distance of $8-10$ kpc. Our results imply
that the evolution of an isolated spiral galaxy is likely to result in galactic
civilizations emerging at the outskirts of the galactic disk around stellar
hosts younger than the Sun.
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We present an anisotropic cosmological model based on a new exact solution of
Einstein equations. The matter content consists of an anisotropic scalar field
minimally coupled to gravity and of two isotropic perfect fluids that represent
dust matter and radiation. The spacetime is described by a spatially
homogeneous, Bianchi type III metric with a conformal expansion. The model
respects the evolution of the scale factor predicted by standard cosmology, as
well as the isotropy of the cosmic microwave background. Remarkably, the
introduction of the scalar field, apart from explaining the spacetime
anisotropy, gives rise to an energy density that is close to the critical
density. As a consequence, the model is quasiflat during the entire history of
the universe. Using these results, we are also able to construct approximate
solutions for shear-free cosmological models with rotation. We finally carry
out a quantitative discussion of the validity of such solutions, showing that
our approximations are acceptably good if the angular velocity of the universe
is within the observational bounds derived from rotation of galaxies.
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We describe our recent attempts to model substructure in dark matter halos
down to very small masses, using a semi-analytic model of halo formation. The
results suggest that numerical simulations of halo formation may still be
missing substructure in the central regions of halos due to purely numerical
effects. If confirmed, this central 'overmerging' problem will have important
consequences for the interpretation of lensing measurements of substructure. We
also show that the spatial distribution of subhalos relative to the satellite
companions of the Milky Way rules out at least one simple model of how dwarf
galaxies form in low-mass halos.
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Self-calibration of camera intrinsics and radial distortion has a long
history of research in the computer vision community. However, it remains rare
to see real applications of such techniques to modern Simultaneous Localization
And Mapping (SLAM) systems, especially in driving scenarios. In this paper, we
revisit the geometric approach to this problem, and provide a theoretical proof
that explicitly shows the ambiguity between radial distortion and scene depth
when two-view geometry is used to self-calibrate the radial distortion. In view
of such geometric degeneracy, we propose a learning approach that trains a
convolutional neural network (CNN) on a large amount of synthetic data. We
demonstrate the utility of our proposed method by applying it as a
checkerboard-free calibration tool for SLAM, achieving comparable or superior
performance to previous learning and hand-crafted methods.
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We explore the relationship between symmetrisation and entanglement through
measurements on few-particle systems in a multi-well potential. In particular,
considering two or three trapped atoms, we measure and distinguish correlations
arising from two different physical origins: antisymmetrisation of the
fermionic wavefunction and interaction between particles. We quantify this
through the entanglement negativity of states, and the introduction of an
antisymmetric negativity, which allows us to understand the role that
symmetrisation plays in the measured entanglement properties. We apply this
concept both to pure theoretical states and to experimentally reconstructed
density matrices of two or three mobile particles in an array of optical
tweezers.
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We study the effect of constant shifts on the zeros of rational harmomic
functions $f(z) = r(z) - \conj{z}$. In particular, we characterize how shifting
through the caustics of $f$ changes the number of zeros and their respective
orientations. This also yields insight into the nature of the singular zeros of
$f$. Our results have applications in gravitational lensing theory, where
certain such functions $f$ represent gravitational point-mass lenses, and a
constant shift can be interpreted as the position of the light source of the
lens.
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Soit $K$ un corps global et $G$ un $K$-groupe fini r\'esoluble. Sous
certaines hypoth\`eses sur une extension d\'eployant $G$, on d\'emontre que
l'espace homog\`ene $V:=G'/G$ avec $G'$ un $K$-groupe semi-simple simplement
connexe v\'erifie l'approximation faible. On utilise une version plus pr\'ecise
de ce r\'esultat pour d\'emontrer le principe de Hasse pour des espaces
homog\`enes $X$ sous un $K$-groupe $G'$ semi-simple simplement connexe \`a
stabilisateur g\'eom\'etrique $\bar G$ fini et r\'esoluble, sous certaines
hypoth\`eses sur le $K$-lien $(\bar G,\kappa)$ d\'efini par $X$.
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Let $K$ be a global field and $G$ a finite solvable $K$-group. Under certain
hypotheses concerning the extension splitting $G$, we show that the homogeneous
space $V=G'/G$ with $G'$ a semi-simple simply connected $K$-group has weak
approximation. We use a more precise version of this result to prove the Hasse
principle for homogeneous spaces $X$ under a semi-simple simply connected
$K$-group $G'$ with finite solvable geometric stabilizer $\bar G$, under
certain hypotheses concerning the $K$-kernel (or $K$-lien) $(\bar G,\kappa)$
defined by $X$.
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The propagation of excitons in TMD monolayers has been intensively studied
revealing interesting many-particle effects, such as halo formation and
non-classical diffusion. Initial studies have investigated how exciton
transport changes in twisted TMD bilayers, including Coulomb repulsion and
Hubbard-like exciton hopping. In this work, we investigate the
twist-angle-dependent transition of the hopping regime to the dispersive regime
of effectively free excitons. Based on a microscopic approach for excitons in
the presence of a moir\'e potential, we show that the hopping regime occurs up
to an angle of approximately 2{\deg} and is well described by the Hubbard
model. At large angles, however, the Hubbard model fails due to increasingly
delocalized exciton states. Here, the quantum mechanical dispersion of free
particles with an effective mass determines the propagation of excitons.
Overall, our work provides microscopic insights into the character of exciton
propagation in twisted van der Waals heterostructures.
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Ordinal cumulative probability models (CPMs) -- also known as cumulative link
models -- such as the proportional odds regression model are typically used for
discrete ordered outcomes, but can accommodate both continuous and mixed
discrete/continuous outcomes since these are also ordered. Recent papers
describe ordinal CPMs in this setting using non-parametric maximum likelihood
estimation. We formulate a Bayesian CPM for continuous or mixed outcome data.
Bayesian CPMs inherit many of the benefits of frequentist CPMs and have
advantages with regard to interpretation, flexibility, and exact inference
(within simulation error) for parameters and functions of parameters. We
explore characteristics of the Bayesian CPM through simulations and a case
study using HIV biomarker data. In addition, we provide the package 'bayesCPM'
which implements Bayesian CPM models using the R interface to the Stan
probabilistic programing language. The Bayesian CPM for continuous outcomes can
be implemented with only minor modifications to the prior specification and,
despite some limitations, has generally good statistical performance with
moderate or large sample sizes.
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The demand and use of mobile phones, PDAs and smart phones are constantly on
the rise as such, manufacturers of these devices are improving the technology
and usability of these devices constantly. Due to the handy shape and size
these devices come in, their processing capabilities and functionalities, they
are preferred by many over the conventional desktop or laptop computers. Mobile
devices are being used today to perform most tasks that a desktop or laptop
computer could be used for. On this premise, mobile devices are also used to
connect to the resources of cloud computing hence, mobile cloud computing
(MCC). The seemingly ubiquitous and pervasive nature of most mobile devices has
made it acceptable and adequate to match the ubiquitous and pervasive nature of
cloud computing. Mobile cloud computing is said to have increased the
challenges known to cloud computing due to the security loop holes that most
mobile devices have.
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We give separability criteria for general multi-qubit states in terms of
diagonal and anti-diagonal entries. We define two numbers which are obtained
from diagonal and anti-diagonal entries, respectively, and compare them to get
criteria. They give rise to characterizations of separability when all the
entries are zero except for diagonal and anti-diagonal, like
Greenberger-Horne-Zeilinger diagonal states. The criteria is strong enough to
get nonzero volume of entanglement with positive partial transposes.
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We consider the statistical mechanics of a classical particle in a
one-dimensional box subjected to a random potential which constitutes a Wiener
process on the coordinate axis. The distribution of the free energy and all
correlation functions of the Gibbs states may be calculated exactly as a
function of the box length and temperature. This allows for a detailed test of
results obtained by the replica variational approximation scheme. We show that
this scheme provides a reasonable estimate of the averaged free energy.
Furthermore our results shed more light on the validity of the concept of
approximate ultrametricity which is a central assumption of the replica
variational method.
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In this paper we consider utilizing a residual neural network (ResNet) to
solve ordinary differential equations. Stochastic gradient descent method is
applied to obtain the optimal parameter set of weights and biases of the
network. We apply forward Euler, Runge-Kutta2 and Runge-Kutta4 finite
difference methods to generate three sets of targets training the ResNet and
carry out the target study. The well trained ResNet behaves just as its
counterpart of the corresponding one-step finite difference method. In
particular, we carry out (1) the architecture study in terms of number of
hidden layers and neurons per layer to find the optimal ResNet structure; (2)
the target study to verify the ResNet solver behaves as accurate as its finite
difference method counterpart; (3) solution trajectory simulation. Even the
ResNet solver looks like and is implemented in a way similar to forward Euler
scheme, its accuracy can be as high as any one step method. A sequence of
numerical examples are presented to demonstrate the performance of the ResNet
solver.
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We propose a new static approach to Role-Based Access Control (RBAC) policy
enforcement. The static approach we advocate includes a new design methodology,
for applications involving RBAC, which integrates the security requirements
into the system's architecture. We apply this new approach to policies
restricting calls to methods in Java applications. We present a language to
express RBAC policies on calls to methods in Java, a set of design patterns
which Java programs must adhere to for the policy to be enforced statically,
and a description of the checks made by our static verifier for static
enforcement.
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The width measure \emph{treedepth}, also known as vertex ranking, centered
coloring and elimination tree height, is a well-established notion which has
recently seen a resurgence of interest. We present an algorithm which---given
as input an $n$-vertex graph, a tree decomposition of the graph of width $w$,
and an integer $t$---decides Treedepth, i.e. whether the treedepth of the graph
is at most $t$, in time $2^{O(wt)} \cdot n$. If necessary, a witness structure
for the treedepth can be constructed in the same running time. In conjunction
with previous results we provide a simple algorithm and a fast algorithm which
decide treedepth in time $2^{2^{O(t)}} \cdot n$ and $2^{O(t^2)} \cdot n$,
respectively, which do not require a tree decomposition as part of their input.
The former answers an open question posed by Ossona de Mendez and Nesetril as
to whether deciding Treedepth admits an algorithm with a linear running time
(for every fixed $t$) that does not rely on Courcelle's Theorem or other heavy
machinery. For chordal graphs we can prove a running time of $2^{O(t \log
t)}\cdot n$ for the same algorithm.
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Robotic assistance has significantly improved the outcomes of open
microsurgery and rigid endoscopic surgery, however is yet to make an impact in
flexible endoscopic neurosurgery. Some of the most common intracranial
procedures for treatment of hydrocephalus and tumors stand to benefit from
increased dexterity and reduced invasiveness offered by robotic systems that
can navigate in the deep ventricular system of the brain. We review a spectrum
of flexible robotic devices, from the traditional highly actuated approach, to
more novel and bio-inspired mechanisms for safe navigation. For each
technology, we identify the operating principle and are able to evaluate the
potential for minimally invasive surgical applications. Overall, rigid-type
continuum robots have seen the most development, however, approaches combining
rigid and soft robotic principles into innovative devices, are ideally situated
to address safety and complexity limitations after future design evolution. We
also observe a number of related challenges in the field, from surgeon-robot
interfaces to robot evaluation procedures. Fundamentally, the challenges
revolve around a guarantee of safety in robotic devices with the prerequisites
to assist and improve upon surgical tasks. With innovative designs, materials
and evaluation techniques emerging, we see potential impacts in the next 5--10
years.
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We study the time evolution of a state of a relativistic quantum field theory
restricted to a spatial subregion $\Omega$. More precisely, we use the
Feynman-Vernon influence functional formalism to describe the dynamics of the
field theory in the interior of $\Omega$ arising after integrating out the
degrees of freedom in the exterior. We show how the influence of the
environment gets encoded in a boundary term. Furthermore, we derive a
stochastic equation of motion for the field expectation value in the interior.
We find that the boundary conditions obtained in this way are energy
non-conserving and non-local in space and time. Our results find applications
in understanding the emergence of local thermalization in relativistic quantum
field theories and the relationship between quantum field theory and
relativistic fluid dynamics.
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A continuous complex rotation of time $t\mapsto t\EXP{-i\theta}$ is shown to
smooth out the huge fluctuations that characterise chaotic tunnelling. This is
illustrated in the kicked rotor model (quantum standard map) where the period
of the map is complexified: the associated chaotic classical dynamics, if
significant for $\theta=0$, is blurred out long before the Wick rotation is
completed ($\theta=\pi/2$). The influence of resonances on tunnelling rates
weakens exponentially as $\theta$ increases from zero, all the more rapidly the
sharper the fluctuations. The long range fluctuations can therefore be
identified in a deterministic way without ambiguity. When the last ones have
been washed out, tunnelling recovers the (quasi-)integrable exponential
behaviour governed by the action of a regular instanton.
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This paper introduces OptimizedDP, a high-performance software library that
solves time-dependent Hamilton-Jacobi partial differential equation (PDE),
computes backward reachable sets with application in robotics, and contains
value iterations algorithm implementation for continuous action-state space
Markov Decision Process (MDP) while leveraging user-friendliness of Python for
different problem specifications without sacrificing efficiency of the core
computation. These algorithms are all based on dynamic programming, and hence
can both be challenging to implement and have bad execution runtime due to the
large high-dimensional tabular arrays. Although there are existing toolboxes
for level set methods that are used to solve the HJ PDE, our toolbox makes
solving the PDE at higher dimensions possible as well as having an order of
magnitude improvement in execution times compared to other toolboxes while
keeping the interface easy to specify different dynamical systems description.
Our toolbox is available online at https://github.com/SFU-MARS/optimized_dp.
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We present a dust-column--dependent extinction curve parameters for
ultraviolet wavelengths at high Galactic latitudes. This extinction function
diverges from previous work in that it takes into account the results of Peek &
Schiminovich 2013 (Paper I), which demonstrated that there is more reddening in
the GALEX bands than would be otherwise expected for E(B-V) < 0.2. We also test
the biases in the Planck and SFD extinction maps, and find that the SFD
extinction maps are significantly biased at E(B-V) < 0.2. We find that while an
extinction function that that takes into account a varying R_FUV with E(B-V)
dramatically improves our estimation of FUV-NUV colors, a fit that also
includes HI column density dependence is superior. The ultraviolet extinction
function we present here follows the model of Fitzpatrick 1999, varying only
the amplitude of the FUV rise parameter to be consistent with the data.
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We present a unified duality approach to Bayesian persuasion. The optimal
dual variable, interpreted as a price function on the state space, is shown to
be a supergradient of the concave closure of the objective function at the
prior belief. Strong duality holds when the objective function is Lipschitz
continuous.
When the objective depends on the posterior belief through a set of moments,
the price function induces prices for posterior moments that solve the
corresponding dual problem. Thus, our general approach unifies known results
for one-dimensional moment persuasion, while yielding new results for the
multi-dimensional case. In particular, we provide a necessary and sufficient
condition for the optimality of convex-partitional signals, derive structural
properties of solutions, and characterize the optimal persuasion scheme in the
case when the state is two-dimensional and the objective is quadratic.
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Solar photosphere and chromosphere are composed of weakly ionized plasma for
which collisional coupling decreases with height. This implies a breakdown of
some hypotheses underlying magnetohydrodynamics at low altitudes and gives rise
to non-ideal MHD effects such as ambipolar diffusion, Hall effect, etc.
Recently, there has been progress in understanding the role of these effects
for the dynamics and energetics of the solar atmosphere. There are evidences
that such phenomena as wave propagation and damping, magnetic reconnection,
formation of stable magnetic field concentrations, magnetic flux emergence,
etc. can be affected. This paper reviews the current state-of-the-art of
multi-fluid MHD modeling of the coupled solar atmosphere.
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Variational Auto-Encoders (VAEs) have been widely applied for learning
compact, low-dimensional latent representations of high-dimensional data. When
the correlation structure among data points is available, previous work
proposed Correlated Variational Auto-Encoders (CVAEs), which employ a
structured mixture model as prior and a structured variational posterior for
each mixture component to enforce that the learned latent representations
follow the same correlation structure. However, as we demonstrate in this work,
such a choice cannot guarantee that CVAEs capture all the correlations.
Furthermore, it prevents us from obtaining a tractable joint and marginal
variational distribution. To address these issues, we propose Adaptive
Correlated Variational Auto-Encoders (ACVAEs), which apply an adaptive prior
distribution that can be adjusted during training and can learn a tractable
joint variational distribution. Its tractable form also enables further
refinement with belief propagation. Experimental results on link prediction and
hierarchical clustering show that ACVAEs significantly outperform CVAEs among
other benchmarks.
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We investigate at a high angular resolution the spatial and kinematic
structure of the S255IR high mass star-forming region, which demonstrated
recently the first disk-mediated accretion burst in the massive young stellar
object. The observations were performed with ALMA in Band 7 at an angular
resolution $ \sim 0.1^{\prime\prime}$, which corresponds to $ \sim 180 $ AU.
The 0.9 mm continuum, C$^{34}$S(7-6) and CCH $N=4-3$ data show a presence of
very narrow ($ \sim 1000 $ AU), very dense ($n\sim 10^7$ cm$^{-3}$) and warm
filamentary structures in this area. At least some of them represent apparently
dense walls around the high velocity molecular outflow with a wide opening
angle from the S255IR-SMA1 core, which is associated with the NIRS3 YSO. This
wide-angle outflow surrounds a narrow jet. At the ends of the molecular outflow
there are shocks, traced in the SiO(8-7) emission. The SiO abundance there is
enhanced by at least 3 orders of magnitude. The CO(3-2) and SiO(8-7) data show
a collimated and extended high velocity outflow from another dense core in this
area, SMA2. The outflow is bent and consists of a chain of knots, which may
indicate periodic ejections possibly arising from a binary system consisting of
low or intermediate mass protostars. The C$^{34}$S emission shows evidence of
rotation of the parent core. Finally, we detected two new low mass compact
cores in this area (designated as SMM1 and SMM2), which may represent
prestellar objects.
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The Belle experiment, running at the KEKB e+e- asymmetric energy collider
during the first decade of the century, achieved its original objective of
measuring precisely differences between particles and anti-particles in the B
system. After collecting 1000 fb-1 of data at various Upsilon resonances, Belle
also obtained the many other physics results described in this article.
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In this paper, we study stable equivalence of exotically knotted surfaces in
4-manifolds, surfaces that are topologically isotopic but not smoothly
isotopic. We prove that any pair of embedded surfaces in the same homology
class become smoothly isotopic after stabilizing them by handle additions in
the ambient 4-manifold, which can moreover assumed to be attached in a standard
way (locally and unknottedly) in many favorable situations. In particular, any
exotically knotted pair of surfaces with cyclic fundamental group complements
become smoothly isotopic after a same number of standard stabilizations -
analogous to C.T.C. Wall's celebrated result on the stable equivalence of
simply-connected 4-manifolds. We moreover show that all constructions of exotic
knottings of surfaces we are aware of, which display a good variety of
techniques and ideas, produce surfaces that become smoothly isotopic after a
single stabilization.
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Predictions of localized Majorana modes, and ideas for manipulating these
degrees of freedom, are the two key ingredients in proposals for physical
platforms for Majorana quantum computation. Several proposals envisage a
scalable network of such Majorana modes coupled bilinearly to each other by
quantum-mechanical mixing amplitudes. Here, we develop a theoretical framework
for characterizing collective topologically protected zero-energy Majorana
fermion excitations of such networks of localized Majorana modes. A key
ingredient in our work is the Gallai-Edmonds decomposition of a general graph,
which we use to obtain an alternate ``local'' proof of a ``global'' result of
Lov{\'a}sz and Anderson on the dimension of the topologically protected null
space of {\em real skew-symmetric} (or pure-imaginary hermitean) adjacency
matrices of general graphs. Our approach to Lov{\'a}sz and Anderson's result
constructs a maximally-localized basis for the said null-space from the
Gallai-Edmonds decomposition of the graph. Applied to the graph of the Majorana
network in question, this gives a method for characterizing basis-independent
properties of these collective topologically protected Majorana fermion
excitations, and relating these properties to the correlation function of
monomers in the ensemble of maximum matchings (maximally-packed dimer covers)
of the corresponding network graph. Our approach can also be used to identify
signatures of zero-energy excitations in systems modeled by a free-fermion
Hamiltonian with a hopping matrix of this type; an interesting example is
provided by vacancy-induced Curie tails in generalizations (on non-bipartite
lattices) of Kitaev's honeycomb model.
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Current flight control validation is heavily based on linear analysis and
high fidelity, nonlinear simulations. Continuing developments of nonlinear
analysis tools for flight control has greatly enhanced the validation process.
Many analysis tools are reliant on assuming the analytical flight dynamics but
this paper proposes an approach using only simulation data. First, this paper
presents improvements to a method for estimating the region of attraction (ROA)
of nonlinear systems governed by ordinary differential equations (ODEs) based
only on trajectory measurements. Faster and more accurate convergence to the
true ROA results. These improvements make the proposed algorithm feasible in
higher-dimensional and more complex systems. Next, these tools are used to
analyze the four-state longitudinal dynamics of NASA's Generic Transport Model
(GTM) aircraft. A piecewise polynomial model of the GTM is used to simulate
trajectories and the developed analysis tools are used to estimate the ROA
around a trim condition based only on this trajectory data. Finally, the
algorithm presented is extended to estimate the ROA of finitely many
equilibrium point systems and of general equilibrium set (arbitrary equilibrium
points and limit cycles) systems.
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We analyze the characteristic series, the $KO$ series and the series
associated with the Witten genus, and their analytic forms as the $q$-analogs
of classical special functions (in particular $q$-analog of the beta integral
and the gamma function). $q$-series admit an analytic interpretation in terms
of the spectral Ruelle functions, and their relations to appropriate elliptic
modular forms can be described. We show that there is a deep correspondence
between the characteristic series of the Witten genus and $KO$ characteristic
series, on one side, and the denominator identities and characters of $N=2$
superconformal algebras, and the affine Lie (super)algebras on the other. We
represent the characteristic series in the form of double series using the
Hecke-Rogers modular identity.
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We calculate the angular two-point autocorrelation function (ACF) of the soft
X-ray background (SXRB) produced by the warm-hot intergalactic medium (WHIM)
associated with dark halos, motivated primarily by searching for missing
baryons and distinguishing different physical processes of the WHIM in dark
halos. We employ a purely analytic model for the halo population which is
completely determined by the universal density profile and the Press-Schechter
mass function. We then adopt a phenomenological approach to nongravitational
processes of the WHIM such as preheating and radiative cooling. It shows that
the power spectra of the SXRB predicted by three WHIM models, namely, the
self-similar model, preheating model and cooling model demonstrate remarkably
different signatures in both amplitude and shape, with the peak locations
moving from 4X10^4 for the self-similar model to a smaller value of (3-5)X10^3
when nongravitational processes are taken into account. The corresponding ACFs
for preheating and cooling models become shallower too as compared with the
prediction of the self-similar model. This may permit an effective probe of the
physical processes of the WHIM in massive halos in conjunction with the
observationally determined power spectrum or ACF of the SXRB from diffuse WHIM.
However, a direct comparison of our theoretical predictions with existing data
(e.g. the ACF determined from ROSAT observations) is still difficult because of
the dominant contribution of AGNs in the soft X-ray sky. We discuss briefly the
implication of our results for resolving the missing baryon problem in the
local universe.
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Based on the Isospin-dependent transport model Boltzmann-Uehling-Uhlenbeck
(IBUU), effects of the difference of the high momentum tails (HMTs) of nucleon
momentum distribution in colliding nuclei on some isospin-sensitive observables
are studied in the $^{197}\rm {Au}+^{197}\rm {Au}$ reactions at incident beam
energy of 400 MeV/nucleon. It is found that the nucleon transverse and elliptic
flows, the free neutron to proton ratio at low momenta are all less sensitive
to the specific form of the HMT, while the free neutron to proton ratio at high
momenta and the yields of $\pi^{-}$ and $\pi^{+}$ as well as the
$\pi^{-}/\pi^{+}$ ratio around the Coulomb peak are sensitive to the specific
form of the HMT. Combining the present studies with the experimental
measurements at rare-isotope reaction facilities worldwide, one may get more
insights into the nuclear short-range correlations in heavy nuclei or nuclear
matter.
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Let $\mathfrak g$ be a symmetrizable Kac-Moody Lie algebra, and let
$V_{\hat{\mathfrak g},\hbar}^\ell$, $L_{\hat{\mathfrak g},\hbar}^\ell$ be the
quantum affine vertex algebras constructed in [11]. For any complex numbers
$\ell$ and $\ell'$, we present an $\hbar$-adic quantum vertex algebra
homomorphism $\Delta$ from $V_{\hat{\mathfrak g},\hbar}^{\ell+\ell'}$ to the
twisted tensor product $\hbar$-adic quantum vertex algebra $V_{\hat{\mathfrak
g},\hbar}^\ell\widehat\otimes V_{\hat{\mathfrak g},\hbar}^{\ell'}$. In
addition, if both $\ell$ and $\ell'$ are positive integers, we show that
$\Delta$ induces an $\hbar$-adic quantum vertex algebra homomorphism from
$L_{\hat{\mathfrak g},\hbar}^{\ell+\ell'}$ to the twisted tensor product
$\hbar$-adic quantum vertex algebra $L_{\hat{\mathfrak
g},\hbar}^\ell\widehat\otimes L_{\hat{\mathfrak g},\hbar}^{\ell'}$. Moreover,
we prove the coassociativity of $\Delta$.
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We study the structure of domain walls in multiferroic magnets with the
conical spiral ordering. We formulate a simple spin model which has a conical
spiral ground state in absence of magnetic anisotropies. We find a transition
from the regime where ferromagnetic and ferroelectric domain walls are clamped
to the regime where they are decoupled and derive a continuum model describing
rotation of the spiral plane at the domain wall. The importance of these
results for the switching phenomena observed in CoCr2O4 is discussed.
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We study a recently proposed formulation of overlap fermions at finite
density. In particular we compute the energy density as a function of the
chemical potential and the temperature. It is shown that overlap fermions with
chemical potential reproduce the correct continuum behavior.
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We introduce models of generic rigidity percolation in two dimensions on
hierarchical networks, and solve them exactly by means of a renormalization
transformation. We then study how the possibility for the network to self
organize in order to avoid stressed bonds may change the phase diagram. In
contrast to what happens on random graphs and in some recent numerical studies
at zero temperature, we do not find a true intermediate phase separating the
usual rigid and floppy ones.
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Recent studies indicate that leveraging off-the-shelf or fine-tuned
retrievers, capable of retrieving relevant in-context examples tailored to the
input query, enhances few-shot in-context learning of English. However,
adapting these methods to other languages, especially low-resource ones, poses
challenges due to the scarcity of cross-lingual retrievers and annotated data.
Thus, we introduce XAMPLER: Cross-Lingual Example Retrieval, a method tailored
to tackle the challenge of cross-lingual in-context learning using only
annotated English data. XAMPLER first trains a retriever based on Glot500, a
multilingual small language model, using positive and negative English examples
constructed from the predictions of a multilingual large language model, i.e.,
MaLA500. Leveraging the cross-lingual capacity of the retriever, it can
directly retrieve English examples as few-shot examples for in-context learning
of target languages. Experiments on the multilingual text classification
benchmark SIB200 with 176 languages show that XAMPLER substantially improves
the in-context learning performance across languages. Our code is available at
\url{https://github.com/cisnlp/XAMPLER}.
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This article motivates, describes, and presents the PBSCR dataset for
studying composer recognition of classical piano music. Our goal was to design
a dataset that facilitates large-scale research on composer recognition that is
suitable for modern architectures and training practices. To achieve this goal,
we utilize the abundance of sheet music images and rich metadata on IMSLP, use
a previously proposed feature representation called a bootleg score to encode
the location of noteheads relative to staff lines, and present the data in an
extremely simple format (2D binary images) to encourage rapid exploration and
iteration. The dataset itself contains 40,000 62x64 bootleg score images for a
9-class recognition task, 100,000 62x64 bootleg score images for a 100-class
recognition task, and 29,310 unlabeled variable-length bootleg score images for
pretraining. The labeled data is presented in a form that mirrors MNIST images,
in order to make it extremely easy to visualize, manipulate, and train models
in an efficient manner. We include relevant information to connect each bootleg
score image with its underlying raw sheet music image, and we scrape, organize,
and compile metadata from IMSLP on all piano works to facilitate multimodal
research and allow for convenient linking to other datasets. We release
baseline results in a supervised and low-shot setting for future works to
compare against, and we discuss open research questions that the PBSCR data is
especially well suited to facilitate research on.
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A major concern of Machine Learning (ML) models is their opacity. They are
deployed in an increasing number of applications where they often operate as
black boxes that do not provide explanations for their predictions. Among
others, the potential harms associated with the lack of understanding of the
models' rationales include privacy violations, adversarial manipulations, and
unfair discrimination. As a result, the accountability and transparency of ML
models have been posed as critical desiderata by works in policy and law,
philosophy, and computer science.
In computer science, the decision-making process of ML models has been
studied by developing accountability and transparency methods. Accountability
methods, such as adversarial attacks and diagnostic datasets, expose
vulnerabilities of ML models that could lead to malicious manipulations or
systematic faults in their predictions. Transparency methods explain the
rationales behind models' predictions gaining the trust of relevant
stakeholders and potentially uncovering mistakes and unfairness in models'
decisions. To this end, transparency methods have to meet accountability
requirements as well, e.g., being robust and faithful to the underlying
rationales of a model.
This thesis presents my research that expands our collective knowledge in the
areas of accountability and transparency of ML models developed for complex
reasoning tasks over text.
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Biometric authentication is one of the promising alternatives to standard
password-based authentication offering better usability and security. In this
work, we revisit the biometric authentication based on "fuzzy signatures"
introduced by Takahashi et al. (ACNS'15, IJIS'19). These are special types of
digital signatures where the secret signing key can be a "fuzzy" data such as
user's biometrics. Compared to other cryptographically secure biometric
authentications as those relying on fuzzy extractors, the fuzzy signature-based
scheme provides a more attractive security guarantee. However, despite their
potential values, fuzzy signatures have not attracted much attention owing to
their theory-oriented presentations in all prior works. For instance, the
discussion on the practical feasibility of the assumptions (such as the entropy
of user biometrics), which the security of fuzzy signatures hinges on, is
completely missing.
In this work, we revisit fuzzy signatures and show that we can indeed
efficiently and securely implement them in practice. At a high level, our
contribution is threefold: (i) we provide a much simpler, more efficient, and
direct construction of fuzzy signature compared to prior works; (ii) we
establish novel statistical techniques to experimentally evaluate the
conditions on biometrics that are required to securely instantiate fuzzy
signatures; and (iii) we provide experimental results using a real-world
finger-vein dataset to show that finger-veins from a single hand are sufficient
to construct efficient and secure fuzzy signatures.
Our performance analysis shows that in a practical scenario with 112-bits of
security, the size of the signature is 1256 bytes, and the running time for
signing/verification is only a few milliseconds.
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Dynamical systems that are contracting on a subspace are said to be
semicontracting. Semicontraction theory is a useful tool in the study of
consensus algorithms and dynamical flow systems such as Markov chains. To
develop a comprehensive theory of semicontracting systems, we investigate
seminorms on vector spaces and define two canonical notions: projection and
distance semi-norms. We show that the well-known lp ergodic coefficients are
induced matrix seminorms and play a central role in stability problems. In
particular, we formulate a duality theorem that explains why the
Markov-Dobrushin coefficient is the rate of contraction for both averaging and
conservation flows in discrete time. Moreover, we obtain parallel results for
induced matrix log seminorms. Finally, we propose comprehensive theorems for
strong semicontractivity of linear and non-linear time-varying dynamical
systems with invariance and conservation properties both in discrete and
continuous time.
|
In the paper we propose general framework for Automatic Secret Generation and
Sharing (ASGS) that should be independent of underlying secret sharing scheme.
ASGS allows to prevent the dealer from knowing the secret or even to eliminate
him at all. Two situations are discussed. First concerns simultaneous
generation and sharing of the random, prior nonexistent secret. Such a secret
remains unknown until it is reconstructed. Next, we propose the framework for
automatic sharing of a known secret. In this case the dealer does not know the
secret and the secret owner does not know the shares. We present opportunities
for joining ASGS with other extended capabilities, with special emphasize on
PVSS and proactive secret sharing. Finally, we illustrate framework with
practical implementation.
Keywords: cryptography, secret sharing, data security, extended capabilities,
extended key verification protocol
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We derive an integro-differential equation for propagation of cosmological
gravitation waves in spatially closed cosmology whereas the traceless
transverse tensor part of the anisotropic stress tensor is free streaming
neutrinos (including antineutrinos), which have been traveling essentially
without collision since temperature dropped below about $ 10^{10} K$. We
studied the short wavelengths and long wavelengths of gravitational waves (GWs)
that enter the horizon in closed spacetime. The solution shows that the
anisotropic stress reduces the squared amplitude by 76% for wavelengths that
enter the horizon during radiation-dominated phase and this reduction is less
for the wavelength that enter the horizon at later times. At the end we compare
the results to the
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This is the second of a series of articles providing a foundation for the
theory of Drinfeld modular forms of arbitrary rank. In the present part, we
compare the analytic theory with the algebraic one that was begun in a paper of
the third author. For any arithmetic congruence subgroup and any integral
weight we establish an isomorphism between the space of analytic modular forms
with the space of algebraic modular forms defined in terms of the Satake
compactification. From this we deduce the important result that this space is
finite dimensional.
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With the increasingly available large-scale cancer genomics datasets, machine
learning approaches have played an important role in revealing novel insights
into cancer development. Existing methods have shown encouraging performance in
identifying genes that are predictive for cancer survival, but are still
limited in modeling the distribution over genes. Here, we proposed a novel
method that can simulate the gene expression distribution at any given time
point, including those that are out of the range of the observed time points.
In order to model the irregular time series where each patient is one
observation, we integrated a neural ordinary differential equation (neural ODE)
with cox regression into our framework. We evaluated our method on eight cancer
types on TCGA and observed a substantial improvement over existing approaches.
Our visualization results and further analysis indicate how our method can be
used to simulate expression at the early cancer stage, offering the possibility
for early cancer identification.
|
Accuracy certificates for convex minimization problems allow for online
verification of the accuracy of approximate solutions and provide a
theoretically valid online stopping criterion. When solving the Lagrange dual
problem, accuracy certificates produce a simple way to recover an approximate
primal solution and estimate its accuracy. In this paper, we generalize
accuracy certificates for the setting of inexact first-order oracle, including
the setting of primal and Lagrange dual pair of problems. We further propose an
explicit way to construct accuracy certificates for a large class of cutting
plane methods based on polytopes. As a by-product, we show that the considered
cutting plane methods can be efficiently used with a noisy oracle even thought
they were originally designed to be equipped with an exact oracle. Finally, we
illustrate the work of the proposed certificates in the numerical experiments
highlighting that our certificates provide a tight upper bound on the objective
residual.
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In this work, we study some models of scalar fields in 1+1 dimensions with
non-linear self-interactions. Here, we show how it is possible to extend the
solutions recently reported in the literature for some classes of nonlinear
equations like the nonlinear Klein-Gordon equation, the generalized
Camassa-Holm and the Benjamin-Bona-Mahony equations. It is shown that the
solutions obtained by Yomba [1], when using the so-called auxiliary equation
method, can be reached by mapping them into some known nonlinear equations.
This is achieved through a suitable sequence of translation and power-like
transformations. Particularly, the parent-like equations used here are the ones
for the $\lambda \phi^4$ model and the Weierstrass equation. This last one,
allow us to get oscillating solutions for the models under analysis. We also
systematize the approach in order to show how to get a larger class of
nonlinear equations which, as far as we know, were not taken into account in
the literature up to now.
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Pseudo-differential operators of type $(1,1)$ and order $m$ are continuous
from $F_p^{s+m,q}$ to $F_p^{s,q}$ if $s>d/\min{(1,p,q)}-d$ for $0<p<\infty$,
and from $B_p^{s+m,q}$ to $B_{p}^{s,q}$ if $s>d/\min{(1,p)}-d$ for
$0<p\leq\infty$. In this work we extend the $F$-boundedness result to
$p=\infty$. Additionally, we prove that the operators map $F_{\infty}^{m,1}$
into $bmo$ when $s=0$, and consider H\"ormander's twisted diagonal condition
for arbitrary $s\in\mathbb{R}$. We also prove that the restrictions on $s$ are
necessary conditions for the boundedness to hold.
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We study a generalisation of the family of non-(virtually pro-$p$)
hereditarily just infinite profinite groups introduced by J.\! S.\! Wilson in
2010. We prove that this family contains groups of finite lower rank. We also
show that many groups in this family are not topologically finitely
presentable.
|
The BL Lac S5 2007+777 was observed by us with Chandra, to find the X-ray
counterpart to its 18" radio jet, and study its structure. Indeed, a bright
X-ray jet was discovered in the 33 ks ACIS-S image of the source. We present
its properties and briefly discuss the implications.
|
As an example of the categorical apparatus of pseudo algebras over
2-theories, we show that pseudo algebras over the 2-theory of categories can be
viewed as pseudo double categories with folding or as appropriate 2-functors
into bicategories. Foldings are equivalent to connection pairs, and also to
thin structures if the vertical and horizontal morphisms coincide. In a sense,
the squares of a double category with folding are determined in a functorial
way by the 2-cells of the horizontal 2-category. As a special case, strict
2-algebras with one object and everything invertible are crossed modules under
a group.
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This paper aims at proposing a model representing individuals' welfare using
Sen's capability approach (CA). It is the first step of an attempt to measure
the negative impact caused by the damage at a Common on a given population's
welfare, and widely speaking, a first step into modelling collective threat.
The CA is a multidimensional representation of persons' well-beings which
account for human diversity. It has received substantial attention from
scholars from different disciplines such as philosophy, economics and social
scientist. Nevertheless, there is no empirical work that really fits the
theoretical framework. Our goal is to show that the capability approach can be
very useful for decision aiding, especially if we fill the gap between the
theory and the empirical work; thus we will propose a framework that is both
usable and a close representation of what capability is.
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Twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (h-BN)
substrate can exhibit an anomalous Hall effect at 3/4 filling due to the
spontaneous valley polarization in valley resolved moir\'e bands with opposite
Chern number [Science 367, 900 (2020), Science 365, 605 (2019)]. It was
observed that a small DC current is able to switch the valley polarization and
reverse the sign of the Hall conductance [Science 367, 900 (2020), Science 365,
605 (2019)]. Here, we discuss the mechanism of the current switching of valley
polarization near the transition temperature, where bulk dissipative transport
dominates. We show that for a sample with rotational symmetry breaking, a DC
current may generate an electron density difference between the two valleys
(valley density difference). The current induced valley density difference in
turn induces a first order transition in the valley polarization. We emphasize
that the inter-valley scattering plays a central role since it is the channel
for exchanging electrons between the two valleys. We further estimate the
valley density difference in the TBG/h-BN system with a microscopic model, and
find a significant enhancement of the effect in the magic angle regime.
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We investigate the Lawson genus $2$ surface by methods from integrable system
theory. We prove that the associated family of flat connections comes from a
family of flat connections on a $4-$punctured sphere. We describe the
symmetries of the holonomy and show that it is already determined by the
holonomy around one of the punctures. We show the existence of a meromorphic
DPW potential for the Lawson surface which is globally defined on the surface.
We determine this potential explicitly up to two unknown functions depending
only on the spectral parameter.
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We calculate neutrino-induced fission cross sections for selected nuclei with
Z=84-92. We show that these reactions populate the daughter nucleus at
excitation energies where shell effects are significantly washed out,
effectively reducing the fission barrier. If the r-process occurs in the
presence of a strong neutrino fluence, and electron neutrino average energies
are sufficiently high, perhaps as a result of matter-enhanced neutrino flavor
transformation, then neutrino-induced fission could lead to significant
alteration in the r-process flow in slow outflow scenarios.
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We construct analytic (3+1)-dimensional Skyrmions living at finite Baryon
density in the SU(N) Skyrme model that are not trivial embeddings of SU(2) into
SU(N). We used Euler angles decomposition for arbitrary N and the generalized
hedgehog Ansatz at finite Baryon density. The Skyrmions of high topological
charge that we find represent smooth Baryonic layers whose properties can be
computed explicitly. In particular, we determine the energy to Baryon charge
ratio for any N showing the smoothness of the large N limit. The closeness to
the BPS bound of these configurations can also be analyzed. The energy density
profiles of these finite density Skyrmions have \textit{lasagna-like} shape in
agreement with recent experimental findings. The shear modulus can be precisely
estimated as well and our analytical result is close to recent numerical
studies in the literature.
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We present a proof that the number of breakpoints in the arrival function
between two terminals in graphs of treewidth $w$ is $n^{O(\log^2 w)}$ when the
edge arrival functions are piecewise linear. This is an improvement on the
bound of $n^{\Theta(\log n)}$ by Foschini, Hershberger, and Suri for graphs
without any bound on treewidth. We provide an algorithm for calculating this
arrival function using star-mesh transformations, a generalization of the
wye-delta-wye transformations.
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We investigated the ferromagnetic resonance signals in a polycrystalline
permalloy thin strip under in-plane low static magnetic field. A series of DC
voltages, which contain ferromagnetic resonance or spin wave resonance signals,
were measured by inducing microwave frequencies greater than 10 gigahertz. The
resonant signals measured in low magnetic field show different properties from
those detected in high field condition. Based on the theory of DC effects in
ferromagnetic resonance and the experimental data of anisotropic
magnetoresistance, a quantitative model was proposed. We found that the shape
anisotropy significantly affects magnetization, and distorts the resonant
signals in low field condition.
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We present a unified three-dimensional model of the convection zone and upper
atmosphere of the Sun in spherical geometry. In this model, magnetic fields,
generated by a helically forced dynamo in the convection zone, emerge without
the assistance of magnetic buoyancy. We use an isothermal equation of state
with gravity and density stratification. Recurrent plasmoid ejections, which
rise through the outer atmosphere, is observed. In addition, the current
helicity of the small--scale field is transported outwards and form large
structures like magnetic clouds.
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Starting from the observation of an R^n-Gaussian vector of mean f and
covariance matrix \sigma^2 I_n (I_n is the identity matrix), we propose a
method for building a Euclidean confidence ball around f, with prescribed
probability of coverage. For each n, we describe its nonasymptotic property and
show its optimality with respect to some criteria.
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Magnetization dynamics and spin waves in ferromagnets are investigated using
the inertial Landau-Lifshitz-Gilbert equation. Taking inertial magnetization
dynamics into account, dispersion relations describing the propagation of
nutation spin waves in an arbitrary direction relative to the applied magnetic
field are derived via Maxwell's equations. It is found that the inertia of
magnetization causes the hybridization of electromagnetic waves and nutation
spin waves in ferromagnets, hybrid nutation spin waves emerge, and the redshift
of frequencies of precession spin waves is initiated, which transforms to
precession-nutation spin waves. These effects depend sharply on the direction
of wave propagation relative to the applied magnetic field. Moreover, the waves
propagating parallel to the applied field are circularly polarized, while the
waves propagating perpendicular to that field are elliptically polarized. The
characteristics of these spin nutation waves are also analyzed.
|
We investigate the fluctuations around the average density profile in the
weakly asymmetric exclusion process with open boundaries in the steady state.
We show that these fluctuations are given, in the macroscopic limit, by a
centered Gaussian field and we compute explicitly its covariance function. We
use two approaches. The first method is dynamical and based on fluctuations
around the hydrodynamic limit. We prove that the density fluctuations evolve
macroscopically according to an autonomous stochastic equation, and we search
for the stationary distribution of this evolution. The second approach, which
is based on a representation of the steady state as a sum over paths, allows
one to write the density fluctuations in the steady state as a sum over two
independent processes, one of which is the derivative of a Brownian motion, the
other one being related to a random path in a potential.
|
Kernel density estimation is a simple and effective method that lies at the
heart of many important machine learning applications. Unfortunately, kernel
methods scale poorly for large, high dimensional datasets. Approximate kernel
density estimation has a prohibitively high memory and computation cost,
especially in the streaming setting. Recent sampling algorithms for high
dimensional densities can reduce the computation cost but cannot operate
online, while streaming algorithms cannot handle high dimensional datasets due
to the curse of dimensionality. We propose RACE, an efficient sketching
algorithm for kernel density estimation on high-dimensional streaming data.
RACE compresses a set of N high dimensional vectors into a small array of
integer counters. This array is sufficient to estimate the kernel density for a
large class of kernels. Our sketch is practical to implement and comes with
strong theoretical guarantees. We evaluate our method on real-world
high-dimensional datasets and show that our sketch achieves 10x better
compression compared to competing methods.
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In this paper, we show that the homotopy category of N-complexes of
projective R-modules is triangle equivalent to the homotopy category of
projective T_{N-1}(R)- modules where T_{N-1}(R) is the ring of triangular
matrices of order N-1 with entries in R. We also define the notions of
N-singularity category and N-totally acyclic complexes. We show that the
category of N-totally acyclic complexes of finitely generated projective
R-modules embeds in the N-singularity category, which is a result analogous to
the case of ordinary chain complexes.
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The thermodynamics of stochastic non-Markovian systems is still widely
unexplored. We present an analytical approach for the net steady-state heat
flux in nonlinear overdamped systems subject to a continuous feedback force
with a discrete time delay. We show that the feedback inevitably leads to a
finite heat flow even for vanishingly small delay times. Application to an
exemplary (bistable) system reveals that the feedback induces heating as well
as cooling regimes and leads to a maximum of the medium entropy production at
coherence resonance conditions.
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It is well known that a random q-ary code of rate \Omega(\epsilon^2) is list
decodable up to radius (1 - 1/q - \epsilon) with list sizes on the order of
1/\epsilon^2, with probability 1 - o(1). However, until recently, a similar
statement about random linear codes has until remained elusive. In a recent
paper, Cheraghchi, Guruswami, and Velingker show a connection between list
decodability of random linear codes and the Restricted Isometry Property from
compressed sensing, and use this connection to prove that a random linear code
of rate \Omega(\epsilon^2 / log^3(1/\epsilon)) achieves the list decoding
properties above, with constant probability. We improve on their result to show
that in fact we may take the rate to be \Omega(\epsilon^2), which is optimal,
and further that the success probability is 1 - o(1), rather than constant. As
an added benefit, our proof is relatively simple. Finally, we extend our
methods to more general ensembles of linear codes. As an example, we show that
randomly punctured Reed-Muller codes have the same list decoding properties as
the original codes, even when the rate is improved to a constant.
|
We study Ptolemy constant and uniformity constant in various plane domains
including triangles, quadrilaterals and ellipses.
|
The ability to make educated predictions about their surroundings, and
associate them with certain confidence, is important for intelligent systems,
like autonomous vehicles and robots. It allows them to plan early and decide
accordingly. Motivated by this observation, in this paper we utilize
information from a video sequence with a narrow field-of-view to infer the
scene at a wider field-of-view. To this end, we propose a temporally consistent
field-of-view extrapolation framework, namely FoV-Net, that: (1) leverages 3D
information to propagate the observed scene parts from past frames; (2)
aggregates the propagated multi-frame information using an attention-based
feature aggregation module and a gated self-attention module, simultaneously
hallucinating any unobserved scene parts; and (3) assigns an interpretable
uncertainty value at each pixel. Extensive experiments show that FoV-Net does
not only extrapolate the temporally consistent wide field-of-view scene better
than existing alternatives, but also provides the associated uncertainty which
may benefit critical decision-making downstream applications. Project page is
at http://charliememory.github.io/RAL21_FoV.
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As a fundamental and extensively studied task in computer vision, image
segmentation aims to locate and identify different semantic concepts at the
pixel level. Recently, inspired by In-Context Learning (ICL), several
generalist segmentation frameworks have been proposed, providing a promising
paradigm for segmenting specific objects. However, existing works mostly ignore
the value of visual prompts or simply apply similarity sorting to select
contextual examples. In this paper, we focus on rethinking and improving the
example selection strategy. By comprehensive comparisons, we first demonstrate
that ICL-based segmentation models are sensitive to different contexts.
Furthermore, empirical evidence indicates that the diversity of contextual
prompts plays a crucial role in guiding segmentation. Based on the above
insights, we propose a new stepwise context search method. Different from
previous works, we construct a small yet rich candidate pool and adaptively
search the well-matched contexts. More importantly, this method effectively
reduces the annotation cost by compacting the search space. Extensive
experiments show that our method is an effective strategy for selecting
examples and enhancing segmentation performance.
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We prove a version the Penrose inequality for black hole space-times which
are perturbations of the Schwarzschild exterior in a slab around a null
hypersurface $\underline{\mathcal{N}}_0$. $\underline{\mathcal{N}}_0$
terminates at past null infinity $\mathcal{I}^-$ and
$\mathcal{S}_0:=\partial\underline{\mathcal{N}}_0$ is chosen to be a marginally
outer trapped sphere. We show that the area of $\mathcal{S}_0$ yields a lower
bound for the Bondi energy of sections of past null infinity, thus also for the
total ADM energy. Our argument is perturbative, and rests on suitably deforming
the initial null hypersurface $\underline{\mathcal{N}}_0$ to one for which the
natural "luminosity" foliation originally introduced by Hawking yields a
monotonically increasing Hawking mass, and for which the leaves of this
foliation become asymptotically round. It is to ensure the latter (essential)
property that we perform the deformation of the initial nullhypersurface
$\underline{\mathcal{N}}_0$.
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Recent results suggest that quantum computers possess the potential to speed
up nonconvex optimization problems. However, a crucial factor for the
implementation of quantum optimization algorithms is their robustness against
experimental and statistical noises. In this paper, we systematically study
quantum algorithms for finding an $\epsilon$-approximate second-order
stationary point ($\epsilon$-SOSP) of a $d$-dimensional nonconvex function, a
fundamental problem in nonconvex optimization, with noisy zeroth- or
first-order oracles as inputs. We first prove that, up to noise of
$O(\epsilon^{10}/d^5)$, accelerated perturbed gradient descent with quantum
gradient estimation takes $O(\log d/\epsilon^{1.75})$ quantum queries to find
an $\epsilon$-SOSP. We then prove that perturbed gradient descent is robust to
the noise of $O(\epsilon^6/d^4)$ and $O(\epsilon/d^{0.5+\zeta})$ for $\zeta>0$
on the zeroth- and first-order oracles, respectively, which provides a quantum
algorithm with poly-logarithmic query complexity. We then propose a stochastic
gradient descent algorithm using quantum mean estimation on the Gaussian
smoothing of noisy oracles, which is robust to $O(\epsilon^{1.5}/d)$ and
$O(\epsilon/\sqrt{d})$ noise on the zeroth- and first-order oracles,
respectively. The quantum algorithm takes $O(d^{2.5}/\epsilon^{3.5})$ and
$O(d^2/\epsilon^3)$ queries to the two oracles, giving a polynomial speedup
over the classical counterparts. Moreover, we characterize the domains where
quantum algorithms can find an $\epsilon$-SOSP with poly-logarithmic,
polynomial, or exponential number of queries in $d$, or the problem is
information-theoretically unsolvable even by an infinite number of queries. In
addition, we prove an $\Omega(\epsilon^{-12/7})$ lower bound in $\epsilon$ for
any randomized classical and quantum algorithm to find an $\epsilon$-SOSP using
either noisy zeroth- or first-order oracles.
|
We compare derived categories of the category of strict polynomial functors
over a finite field and the category of ordinary endofunctors on the category
of vector spaces. We introduce two intermediate categories: the category of
$\infty$--affine strict polynomial functors and the category of spectra of
strict polynomial functors. They provide a conceptual framework for
compuational theorems of Franjou--Friedlander--Scorichenko--Suslin and clarify
the role of inverting Frobenius morphism in comparing rational and discrete
cohomology.
|
We investigate the Lyth relationship between the tensor-scalar ratio, r, and
the variation of the inflaton field, Delta phi, over the course of inflation.
For inflationary models that produce at least 55 e-folds of inflation, there is
a correlation between r and Delta phi as anticipated by Lyth, but the scatter
around the relationship is huge. However, for inflationary models that satisfy
current observational constraints on the scalar spectral index and its first
derivative, the Lyth relationship is much tighter. In particular, any
inflationary model with r > 10^-3 must have Delta phi > m_pl. Large field
variations are therefore required if a tensor mode signal is to be detected in
any foreseeable cosmic microwave background (CMB) polarization experiment.
|
We present the three-pion spectrum with maximal isospin in a finite volume
determined from lattice QCD, including excited states in addition to the ground
states across various irreducible representations at zero and nonzero total
momentum. The required correlation functions, from which the spectrum is
extracted, are computed using a newly implemented algorithm which speeds up the
computation by more than an order of magnitude. On a subset of the data we
extract a nonzero value of the three-pion threshold scattering amplitude using
the $1/L$ expansion of the three-particle quantization condition, which
consistently describes all states at zero total momentum. The finite-volume
spectrum is publicly available to facilitate further explorations within the
available three-particle finite-volume approaches.
|
Beyond attaining domain generalization (DG), visual recognition models should
also be data-efficient during learning by leveraging limited labels. We study
the problem of Semi-Supervised Domain Generalization (SSDG) which is crucial
for real-world applications like automated healthcare. SSDG requires learning a
cross-domain generalizable model when the given training data is only partially
labelled. Empirical investigations reveal that the DG methods tend to
underperform in SSDG settings, likely because they are unable to exploit the
unlabelled data. Semi-supervised learning (SSL) shows improved but still
inferior results compared to fully-supervised learning. A key challenge, faced
by the best-performing SSL-based SSDG methods, is selecting accurate
pseudo-labels under multiple domain shifts and reducing overfitting to source
domains under limited labels. In this work, we propose new SSDG approach, which
utilizes a novel uncertainty-guided pseudo-labelling with model averaging
(UPLM). Our uncertainty-guided pseudo-labelling (UPL) uses model uncertainty to
improve pseudo-labelling selection, addressing poor model calibration under
multi-source unlabelled data. The UPL technique, enhanced by our novel model
averaging (MA) strategy, mitigates overfitting to source domains with limited
labels. Extensive experiments on key representative DG datasets suggest that
our method demonstrates effectiveness against existing methods. Our code and
chosen labelled data seeds are available on GitHub:
https://github.com/Adnan-Khan7/UPLM
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We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for
promoting l1-minimization in sparse and compressible vector recovery. We prove
its convergence and we estimate its local rate. We show how the algorithm can
be modified in order to promote lt-minimization for t<1, and how this
modification produces superlinear rates of convergence.
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The lowest Landau level of bilayer graphene has an octet of internal degrees
of freedom, composed from spin, valley and orbital two-level systems. Dominance
of $n=0$ orbitals over $n=1$ orbitals in low energy quantum fluctuations leads
to distinct fractional quantum Hall characteristics compared dominance of $n=1$
over $n=0$. The competition between $n=0$ and $n=1$ orbitals depends
sensitively on particle-hole asymmetry and on Lamb shifts due to exchange
interactions with the negative energy sea, which must be accounted for
simultaneously in assessing the orbital competition. We identify the
circumstances under which $n=1$, which supports strong even-denominator FQH
states with non-abelian quasiparticles, emerges robustly as the low-energy
Landau level.
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Knowledge of intrinsic shape and orientation of galaxy clusters is crucial to
understand their formation and evolution. We propose a novel model which uses
Bayesian inference to determine the intrinsic form of the hot intracluster
medium of galaxy clusters. The method exploits X-ray spectroscopic and
photometric data plus measurements of the Sunyaev-Zel'dovich effect (SZe). The
gas distribution is modelled with an ellipsoidal parametric profile who can fit
observed X-ray surface-brightness and temperature. Comparison with the SZ
amplitude fixes the elongation along the line of sight. Finally, Bayesian
inference allows us to deproject the measured elongation and the projected
ellipticity and constrain the intrinsic shape and orientation of the cluster.
We apply the method to the rich cluster Abell 1689, which was targeted by the
Chandra and XMM satellites as well as by several SZe observatories.
Observations cover in detail a region <~ 1 Mpc. Our analysis favours a mildly
triaxial cluster with a minor to major axis ratio of 0.70+-0.15, preferentially
elongated along the line of sight, as expected for massive lensing clusters.
The triaxial structure together with the orientation bias can reconcile X-ray
with lensing analyses and supports the view of A1689 as a just slightly
over-concentrated massive cluster not so far from hydrostatic equilibrium.
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We present a novel methodology for the numerical solution of problems of
diffraction by infinitely thin screens in three dimensional space. Our approach
relies on new integral formulations as well as associated high-order quadrature
rules. The new integral formulations involve weighted versions of the classical
integral operators associated with the thin-screen Dirichlet and Neumann
problems as well as a generalization to the open surface problem of the
classical Calderon formulae. The high-order quadrature rules we introduce for
these operators, in turn, resolve the multiple Green function and edge
singularities (which occur at arbitrarily close distances from each other, and
which include weakly singular as well as hypersingular kernels) and thus give
rise to super-algebraically fast convergence as the discretization sizes are
increased. When used in conjunction with Krylov-subspace linear algebra solvers
such as GMRES, the resulting solvers produce results of high accuracy in small
numbers of iterations for low and high frequencies alike. We demonstrate our
methodology with a variety of numerical results for screen and aperture
problems at high frequencies---including simulation of classical experiments
such as the diffraction by a circular disc (including observation of the famous
Poisson spot), interference fringes resulting from diffraction across two
nearby circular apertures, as well as more complex geometries consisting of
multiple scatterers and cavities.
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Medical image segmentation is crucial for clinical diagnosis. The
Segmentation Anything Model (SAM) serves as a powerful foundation model for
visual segmentation and can be adapted for medical image segmentation. However,
medical imaging data typically contain privacy-sensitive information, making it
challenging to train foundation models with centralized storage and sharing. To
date, there are few foundation models tailored for medical image deployment
within the federated learning framework, and the segmentation performance, as
well as the efficiency of communication and training, remain unexplored. In
response to these issues, we developed Federated Foundation models for Medical
image Segmentation (FedFMS), which includes the Federated SAM (FedSAM) and a
communication and training-efficient Federated SAM with Medical SAM Adapter
(FedMSA). Comprehensive experiments on diverse datasets are conducted to
investigate the performance disparities between centralized training and
federated learning across various configurations of FedFMS. The experiments
revealed that FedFMS could achieve performance comparable to models trained via
centralized training methods while maintaining privacy. Furthermore, FedMSA
demonstrated the potential to enhance communication and training efficiency.
Our model implementation codes are available at
https://github.com/LIU-YUXI/FedFMS.
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In this paper, we classify the solutions of the following critical Choquard
equation \[ (-\Delta)^{\frac{n}{2}} u(x) = \int_{\mathbb{R}^n}
\frac{e^{\frac{2n- \mu}{2}u(y)}}{|x-y|^{\mu}}dy e^{\frac{2n- \mu}{2}u(x)}, \
\text{in} \ \mathbb{R}^n, \] where $ 0<\mu < n$, $ n\ge 2$. Suppose $ u(x) =
o(|x|^2) \ \text{at} \ \infty $ for $ n \geq 3$ and satisfies \[
\int_{\mathbb{R}^n}e^{\frac{2n- \mu}{2}u(y)} dy < \infty, \
\int_{\mathbb{R}^n}\int_{\mathbb{R}^n}\frac{e^{\frac{2n-
\mu}{2}u(y)}}{|x-y|^{\mu}} e^{\frac{2n- \mu}{2}u(x)} dy dx < \infty. \] By
using the method of moving spheres, we show that the solutions have the
following form \[ u(x)= \ln \frac{C_1(\varepsilon)}{|x-x_0|^2 + \varepsilon^2}.
\]
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Optics of metamaterials is shown to provide interesting table top models of
many non-trivial space-time metrics. The range of possibilities is broader than
the one allowed in classical general relativity. For example, extraordinary
waves in indefinite metamaterials experience an effective metric, which is
formally equivalent to the "two times physics" model in 2+2 dimensions. An
optical analogue of a "big bang" event is presented during which a (2+1)
Minkowski space-time is created together with large number of particles
populating this space-time. Such metamaterial models enable experimental
exploration of the metric phase transitions to and from the Minkowski
space-time as a function of temperature and/or light frequency.
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In order to avoid the risk of information leakage during the information
mutual transmission between two authorized participants, i.e., Alice and Bob, a
quantum dialogue protocol based on the entanglement swapping between any two
Bell states and the shared secret Bell state is proposed. The proposed protocol
integrates the ideas of block transmission, two-step transmission and unitary
operation encoding together using the Bell states as the information carriers.
Besides the entanglement swapping between any two Bell states, a shared secret
Bell state is also used to overcome the information leakage problem, which not
only makes Bob aware of the prepared initial state but also is used for Bob's
encoding and entanglement swapping. Security analysis shows that the proposed
protocol can resist the general active attacks from an outside eavesdropper
Eve. Moreover, the relation between the maximal amount of information Eve can
gain and the detection probability is derived.
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We propose a model to estimate the fundamental frequency in monophonic audio,
often referred to as pitch estimation. We acknowledge the fact that obtaining
ground truth annotations at the required temporal and frequency resolution is a
particularly daunting task. Therefore, we propose to adopt a self-supervised
learning technique, which is able to estimate pitch without any form of
supervision. The key observation is that pitch shift maps to a simple
translation when the audio signal is analysed through the lens of the
constant-Q transform (CQT). We design a self-supervised task by feeding two
shifted slices of the CQT to the same convolutional encoder, and require that
the difference in the outputs is proportional to the corresponding difference
in pitch. In addition, we introduce a small model head on top of the encoder,
which is able to determine the confidence of the pitch estimate, so as to
distinguish between voiced and unvoiced audio. Our results show that the
proposed method is able to estimate pitch at a level of accuracy comparable to
fully supervised models, both on clean and noisy audio samples, although it
does not require access to large labeled datasets.
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We make an exhaustive investigation on the pentaquark states $qqqc\bar{c}$
($q=u, d$ and $s$) and discuss the effect of color structures in a multiquark
color flux-tube model. We exhibit a novel picture of the structure and
properties of the states $P_c$ and $P_{cs}$ observed by the LHCb Collaboration.
We can describe the states as the compact pentaquark states in the model. The
spin-parity of the group of $P_c(4312)^+$ and $P_c(4337)^+$ is $\frac{1}{2}^-$
while that of the group of $P_c(4380)^+$, $P_c(4440)^+$ and $P_c(4457)^+$ is
$\frac{3}{2}^-$. Their structures are pentagon, diquark, pentagon, diquark, and
octet, respectively. The members in each group can be analogically called QCD
isomers because of their the same spin-parity and quark content but different
color structures. The singlet $P_{cs}(4459)^0$ has pentagon structure and
spin-parity of $\frac{1}{2}^-$. In addition, we also predict the $P_{cs}$,
$P_{c ss}$ and $P_{csss}$ families in the model. The five-body confinement
potential based on the color flux-tube picture, which is a collective degree of
freedom and induces QCD isomer phenomenon, plays an important role in the
formation of the compact states.
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The superconductor UCoGe is analyzed with electronic structure calculations
using Linearized Augmented Plane Wave method based on Density Functional
Theory. Ferromagnetic and antiferromagnetic calculations with and without
correlations (via LDA+U) were done. In this compound the Fermi level is
situated in a region where the main contribution to DOS comes from the U-5f
orbital. The magnetic moment is mainly due to the Co-3d orbital with a small
contribution from the U-5f orbital. The possibility of fully non-collinear
magnetism in this compound seems to be ruled out. These results are compared
with the isostructural compound URhGe, in this case the magnetism comes mostly
from the U-5f orbital.
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Coherent radio bursts detected from M dwarfs have some analogy with solar
radio bursts, but reach orders of magnitude higher luminosities. These events
trace particle acceleration, powered by magnetic reconnection, shock fronts
(such as formed by coronal mass ejections, CMEs), and magnetospheric currents,
in some cases offering the only window into these processes in stellar
atmospheres. We conducted a 58-hour, ultra-wideband survey for coherent radio
bursts on 5 active M dwarfs. We used the Karl G. Jansky Very Large Array (VLA)
to observe simultaneously in three frequency bands covering a subset of 224-482
MHz and 1-6 GHz, achieving the widest fractional bandwidth to date for any
observations of stellar radio bursts. We detected 22 bursts across 13 epochs,
providing the first large sample of wideband dynamic spectra of stellar
coherent radio bursts. The observed bursts have diverse morphology, with
durations ranging from seconds to hours, but all share strong (40-100%)
circular polarization. No events resemble solar Type II bursts (often
associated with CMEs), but we cannot rule out the occurrence of radio-quiet
stellar CMEs. The hours-long bursts are all polarized in the sense of the
x-mode of the star's large-scale magnetic field, suggesting they are cyclotron
maser emission from electrons accelerated in the large-scale field, analogous
to auroral processes on ultracool dwarfs. The duty cycle of luminous coherent
bursts peaks at 25% at 1-1.4 GHz, declining at lower and higher frequencies,
indicating source regions in the low corona. At these frequencies, active M
dwarfs should be the most common galactic transient source.
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Optical tweezers have become essential tools to manipulate atoms or molecules
at a single particle level. However, using standard diffracted-limited optical
systems, the transverse size of the trap is lower bounded by the optical
wavelength, limiting the application range of optical tweezers. Here we report
trapping of single ultracold atom in an optical trap that can be continuously
tuned from a standard Airy focus to a subwavelength hotspot smaller than the
usual Abbe's diffraction limit. The hotspot was generated using the effect of
superoscillations, by the precise interference of multiple free-space coherent
waves. We argue that superoscillatory trapping and continuous potential tuning
offer not only a way to generate compact and tenable ensembles of trapped atoms
for quantum simulators but will also be useful in single molecule quantum
chemistry and the study of cooperative atom-photon interaction within
subwavelength arrays of quantum emitters.
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The Internet of Things (IoT) is considered as the key enabling technology for
smart services. Security and privacy are particularly open challenges for IoT
applications due to the widespread use of commodity devices. This work
introduces two hardware-based lightweight security mechanisms to ensure sensed
data trustworthiness (i.e., sensed data protection and sensor node protection)
and usage privacy of the sensors (i.e., privacy-aware reporting of the sensed
data) for centralized and decentralized IoT applications. Physically unclonable
functions (PUF) form the basis of both proposed mechanisms. To demonstrate the
feasibility of our PUF-based approach, we have implemented and evaluated PUFs
on three platforms (Atmel 8-bit MCU, ARM Cortex M4 32 bit MCU, and Zynq7010
SoC) with varying complexities. We have also implemented our trusted sensing
and privacy-aware reporting scheme (for centralized applications) and secure
node scheme (for decentralized applications) on a visual sensor node comprising
an OV5642 image sensor and a Zynq7010 SoC. Our experimental evaluation shows a
low overhead wrt.~latency, storage, hardware, and communication incurred by our
security mechanisms.
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The Belle experiment at the KEKB electron-positron collider is expected to
have collected close to one billion $\Upsilon$(4S) events by the time it comes
to an end in 2009. An upgrade to KEKB has been proposed. It is designed for an
order of magnitude higher luminosity than KEKB, following a three-year
construction period. The ultimate goal of $8 \times 10^{35}{\rm cm}^{-2}{\rm
s}^{-1}$ luminosity would be reached through further improvements over several
years. To exploit the physics accessible through this improved luminosity, an
upgrade of the Belle detector is also planned. A new international
collaboration, temporarily named sBelle, is in the process of being formed.
Super-KEKB and sBelle were officially placed on the KEK 5-year Roadmap in early
2008.
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Astronomical objects frequently exhibit structure over a wide range of scales
whereas many telescopes, especially interferometer arrays, only sample a
limited range of spatial scales. In order to properly image these objects,
images from a set of instruments covering the range of scales may be needed.
These images then must be combined in a manner to recover all spatial scales.
This paper describes the feathering technique for image combination in the
Fourier transform plane. Implementations in several packages are discussed and
example combinations of single dish and interferometric observations of both
simulated and celestial radio emission are given.
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We present new high-resolution chemical-abundance analyses for the well-known
high proper-motion subdwarfs G64-12 and G64-37, based on very high
signal-to-noise spectra (S/N ~ 700/1) with resolving power R ~ 95,000. These
high-quality data enable the first reliable determination of the carbon
abundances for these two stars; we classify them as carbon-enhanced metal-poor
(CEMP) stars based on their carbonicities, which both exceed [C/Fe] = +1.0.
They are sub-classified as CEMP- no Group-II stars, based on their location in
the Yoon-Beers diagram of absolute carbon abundance, A(C) vs. [Fe/H], as well
as on the conventional diagnostic [Ba/Fe]. The relatively low absolute carbon
abundances of CEMP-no stars, in combination with the high effective
temperatures of these two stars (Teff ~ 6500 K) weakens their CH molecular
features to the point that accurate carbon abundances can only be estimated
from spectra with very high S/N. A comparison of the observed abundance
patterns with the predicted yields from massive, metal-free supernova models
reduces the inferred progenitor masses by factors of ~ 2-3, and explosion
energies by factors of ~ 10-15, compared to those derived using previously
claimed carbon abundance estimates. There are certainly many more warm CEMP-no
stars near the halo main-sequence turnoff that have been overlooked in past
studies, directly impacting the derived frequencies of CEMP-no stars as a
function of metallicity, a probe that provides important constraints on
Galactic chemical evolution models, the initial mass function in the early
Universe, and first-star nucleosynthesis.
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In this paper, we give a full classification of the nonexistence of positive
weak solutions to the semilinear elliptic inequality involving the fractional
Hardy potential in punctured and in exterior domains. Our methods are
self-contained and new. The main ideas and key ingredients will be discussed in
the next section after Theorem 1.1 for punctured domains, and after Theorem 1.4
for exterior domains. We will also explain why all the previous methods and
techniques do not apply to our general setting. Let us give here a foretaste of
our line of attack: Based on the imbalance between the Hardy operator and the
nonlinearity, we can obtain an initial asymptotic behavior rate at the origin (
for punctured domains) or at infinity ( exterior domains).We then improve this
rate by using the interaction with the nonlinearity. By repeating this process
finite number of times, a contradiction will be deduced from the nonexistence
for the related non-homogeneous fractional Hardy problem. This process allows
us to obtain the nonexistence for the fractional Hardy problem with larger
ranges . Our study covers all possible ranges, and our results are optimal.
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We investigate several versions of the telescope conjecture on localized
categories of spectra, and implications between them. Generalizing the "finite
localization" construction, we show that on such categories, localizing away
from a set of strongly dualizable objects is smashing. We classify all smashing
localizations on the harmonic category, HFp-local category and I-local
category, where I is the Brown-Comenetz dual of the sphere spectrum; all are
localizations away from strongly dualizable objects, although these categories
have no nonzero compact objects. The Bousfield lattices of the harmonic,
E(n)-local, K(n)-local, HFp-local and I-local categories are described, along
with some lattice maps between them. One consequence is that in none of these
categories is there a nonzero object that squares to zero. Another is that the
HFp-local category has localizing subcategories that are not Bousfield classes.
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The rational homology of the IA-automorphism group $\operatorname{IA}_n$ of
the free group $F_n$ is still mysterious. We study the quotient of the rational
homology of $\operatorname{IA}_n$ that is obtained as the image of the map
induced by the abelianization map, which we call the Albanese homology of
$\operatorname{IA}_n$. We obtain a representation-stable
$\operatorname{GL}(n,\mathbb{Q})$-subquotient of the Albanese homology of
$\operatorname{IA}_n$, which conjecturally coincides with the entire Albanese
homology of $\operatorname{IA}_n$. In particular, we obtain a lower bound of
the dimension of the Albanese homology of $\operatorname{IA}_n$ for each
homological degree in a stable range. Moreover, we determine the entire third
Albanese homology of $\operatorname{IA}_n$ for $n\ge 9$. We also study the
Albanese homology of an analogue of $\operatorname{IA}_n$ to the outer
automorphism group of $F_n$ and the Albanese homology of the Torelli groups of
surfaces. Moreover, we study the relation between the Albanese homology of
$\operatorname{IA}_n$ and the cohomology of $\operatorname{Aut}(F_n)$ with
twisted coefficients.
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A small fraction of giants possess photospheric lithium(Li) abundance higher
than the value predicted by the standard stellar evolution models, and the
detailed mechanisms of Li enhancement are complicated and lack a definite
conclusion. In order to better understand the Li enhancement behaviors, a large
and homogeneous Li-rich giants sample is needed. In this study, we designed a
modified convolutional neural network model called Coord-DenseNet to determine
the A(Li) of Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)
low-resolution survey (LRS) giant spectra. The precision is good on the test
set: MAE=0.15 dex, and {\sigma}=0.21 dex. We used this model to predict the Li
abundance of more than 900,000 LAMOST DR8 LRS giant spectra and identified
7,768 Li-rich giants with Li abundances ranging from 2.0 to 5.4 dex, accounting
for about 1.02% of all giants. We compared the Li abundance estimated by our
work with those derived from high-resolution spectra. We found that the
consistency was good if the overall deviation of 0.27 dex between them was not
considered. The analysis shows that the difference is mainly due to the high
A(Li) from the medium-resolution spectra in the training set. This sample of
Li-rich giants dramatically expands the existing sample size of Li-rich giants
and provides us with more samples to further study the formation and evolution
of Li-rich giants.
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We study recombinations of D-brane systems intersecting at more than one
angle using super Yang-Mills theory. We find the condensation of an
off-diagonal tachyon mode relates to the recombination, as was clarified for
branes at one angle in hep-th/0303204. For branes at two angles, after the
tachyon mode between two D2-branes condensed, D2-brane charge is distributed in
the bulk near the intersection point. We also find that, when two intersection
angles are equal, the off-diagonal lowest mode is massless, and a new stable
non-abelian configuration, which is supersymmetric up to a quadratic order in
the fluctuations, is obtained by the deformation by this mode.
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Text classification is an important and classical problem in natural language
processing. There have been a number of studies that applied convolutional
neural networks (convolution on regular grid, e.g., sequence) to
classification. However, only a limited number of studies have explored the
more flexible graph convolutional neural networks (convolution on non-grid,
e.g., arbitrary graph) for the task. In this work, we propose to use graph
convolutional networks for text classification. We build a single text graph
for a corpus based on word co-occurrence and document word relations, then
learn a Text Graph Convolutional Network (Text GCN) for the corpus. Our Text
GCN is initialized with one-hot representation for word and document, it then
jointly learns the embeddings for both words and documents, as supervised by
the known class labels for documents. Our experimental results on multiple
benchmark datasets demonstrate that a vanilla Text GCN without any external
word embeddings or knowledge outperforms state-of-the-art methods for text
classification. On the other hand, Text GCN also learns predictive word and
document embeddings. In addition, experimental results show that the
improvement of Text GCN over state-of-the-art comparison methods become more
prominent as we lower the percentage of training data, suggesting the
robustness of Text GCN to less training data in text classification.
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