text
stringlengths 6
128k
|
|---|
We consider large-scale linear inverse problems in Bayesian settings. We
follow a recent line of work that applies the approximate message passing (AMP)
framework to multi-processor (MP) computational systems, where each processor
node stores and processes a subset of rows of the measurement matrix along with
corresponding measurements. In each MP-AMP iteration, nodes of the MP system
and its fusion center exchange lossily compressed messages pertaining to their
estimates of the input. In this setup, we derive the optimal per-iteration
coding rates using dynamic programming. We analyze the excess mean squared
error (EMSE) beyond the minimum mean squared error (MMSE), and prove that, in
the limit of low EMSE, the optimal coding rates increase approximately linearly
per iteration. Additionally, we obtain that the combined cost of computation
and communication scales with the desired estimation quality according to
$O(\log^2(1/\text{EMSE}))$. Finally, we study trade-offs between the physical
costs of the estimation process including computation time, communication
loads, and the estimation quality as a multi-objective optimization problem,
and characterize the properties of the Pareto optimal surfaces.
|
The Landau potential in the general Ginzburg-Landau theory with two order
parameters and all possible quadratic and quartic terms cannot be minimized
with the straightforward algebra. Here, a geometric approach is presented that
circumvents this computational difficulty and allows one to get insight into
many properties of the model in the mean-field approximation.
|
We investigate the lepton flavor violation (LFV) decays, $\tau\to l\gamma$
($l=\mu, e$) and $\mu\to e\gamma$, and the newly observed muon $g-2$ anomaly in
the framwork of a squential fourth generation model with a heavy fourth
neutrino, $\nu'$. By using the recent experimental bounds, we take the
constraints of the $4\times 4$ leptonic mixing matrix element factors,
$|V_{1\nu'} V_{2\nu'}|^2$, $|V_{1\nu'} V_{3\nu'}|^2 $ and $|V_{3\nu'}
V_{2\nu'}|^2$. We find that LFV decays and $g_\mu -2$ can exclude most of the
parameter space of the 4th generation neutrino mass $m_{\nu'}$ and give
stringent constraints on the existence of the fourth generation.
|
We study generalized Hermite polynomials with rectangular matrix arguments
arising in multivariate statistical analysis and the theory of zonal
polynomials. We show that these are well-suited for expressing the Wiener-Ito
chaos expansion of functionals of the spectral measure associated with Gaussian
matrices. In particular, we obtain the Wiener chaos expansion of Gaussian
determinants of the form $\det(XX^T)^{1/2}$ and prove that, in the setting
where the rows of $X$ are i.i.d. centred Gaussian vectors with a given
covariance matrix, its projection coefficients admit a geometric interpretation
in terms of intrinsic volumes of ellipsoids, thus extending the content of
Kabluchko and Zaporozhets (2012) to arbitrary chaotic projection coefficients.
Our proofs are based on a crucial relation between generalized Hermite
polynomials and generalized Laguerre polynomials. In a second part, we
introduce the matrix analog of the classical Mehler's formula for the
Ornstein-Uhlenbeck semigroup and prove that matrix-variate Hermite polynomials
are eigenfunctions of these operators. As a byproduct, we derive an
orthogonality relation for Hermite polynomials evaluated at correlated Gaussian
matrices. We apply our results to vectors of independent arithmetic random
waves on the three-torus, proving in particular a CLT in the high-energy regime
for a generalized notion of total variation on the full torus.
|
This paper describes the application of a laser diffraction technique to the
study of electroconvection in nematic liquid crystal cells. It allows a
real-time quantitative access to pattern wave lengths and amplitudes. The
diffraction profile of the spatial periodic pattern is calculated and compared
quantitatively to experimental intensity profiles. For small director tilt
amplitudes $\phi$, the phase grating generated in normally incident undeflected
light and the first order term correction from light deflection is derived
analytically. It yields an $I\propto\phi^4$ dependence of the diffracted
intensity $I$ on the amplitude of director deflections. For larger director
tilt amplitudes, phase and amplitude modulations of deflection of light in the
inhomogeneous director field are calculated numerically. We apply the
calculations to the determination of the director deflection and measure growth
and decay rates of the dissipative patterns under periodic excitation. Real
time analysis of pattern amplitudes under stochastic excitation is
demonstrated.
|
We present measurements of the galaxy luminosity and stellar mass function in
a 3.71 deg$^2$ (0.3 Mpc$^2$) area in the core of the Virgo cluster, based on
$ugriz$ data from the Next Generation Virgo Cluster Survey (NGVS). The galaxy
sample consists of 352 objects brighter than $M_g=-9.13$ mag, the 50%
completeness limit of the survey. Using a Bayesian analysis, we find a best-fit
faint end slope of $\alpha=-1.33 \pm 0.02$ for the g-band luminosity function;
consistent results are found for the stellar mass function as well as the
luminosity function in the other four NGVS bandpasses. We discuss the
implications for the faint-end slope of adding 92 ultra compact dwarfs galaxies
(UCDs) -- previously compiled by the NGVS in this region -- to the galaxy
sample, assuming that UCDs are the stripped remnants of nucleated dwarf
galaxies. Under this assumption, the slope of the luminosity function (down to
the UCD faint magnitude limit, $M_g = -9.6$ mag) increases dramatically, up to
$\alpha = -1.60 \pm 0.06$ when correcting for the expected number of disrupted
non-nucleated galaxies. We also calculate the total number of UCDs and globular
clusters that may have been deposited in the core of Virgo due to the
disruption of satellites, both nucleated and non-nucleated. We estimate that
~150 objects with $M_g\lesssim-9.6$ mag and that are currently classified as
globular clusters, might, in fact, be the nuclei of disrupted galaxies. We
further estimate that as many as 40% of the (mostly blue) globular clusters in
the core of Virgo might once have belonged to such satellites; these same
disrupted satellites might have contributed ~40% of the total luminosity in
galaxies observed in the core region today. Finally, we use an updated Local
Group galaxy catalog to provide a new measurement of the luminosity function of
Local Group satellites, $\alpha=-1.21\pm0.05$.
|
M dwarfs show the highest rocky planet occurrence among all spectral types,
in some instances within the Habitable Zone. Because some of them are very
active stars, they are often subject to frequent and powerful flaring, which
can be a double-edged sword in regard of exoplanet habitability. On one hand,
the increased flux during flare events can trigger the chemical reactions that
are necessary to build the basis of prebiotic chemistry. On the other hand,
sufficiently strong flares may erode exoplanets' atmospheres and reduce their
UV protection. Recent observations of flares have shown that the flaring flux
can be x100 times stronger in UV than in the optical. UV is also preferable to
constrain more accurately both the prebiotic abiogenesis and the atmospheric
erosion. For these reasons, we are developing a CubeSat payload concept to
complement current flare surveys operating in the optical. This CubeSat will
observe a high number of flaring M dwarfs, following an all-sky scanning law
coverage, both in the UV and the optical to better understand the different
effective temperatures as wavelengths and flaring status go. This will
complement the bright optical flares data acquired from the current
ground-based, high-cadence, wide FoV surveys. Another scientific planned goal
is to conduct few-minute after-the-flare follow-up optical ground-based
time-resolved spectroscopy, that will be triggered by the detection of UV
flares in space on board of the proposed CubeSat. Finally, the study of M
dwarfs stellar activity in the UV band will provide useful data for larger
forthcoming missions that will survey exoplanets, such as PLATO, ARIEL, HabEx
and LUVOIR.
|
In this paper we study two directions of extending the classical Erd\H
os-Ko-Rado theorem which states that any family of $k$-element subsets of the
set $[n] = \{1,\ldots,n\}$ in which any two sets intersect, has cardinality at
most ${n-1\choose k-1}$.
In the first part of the paper we study the families of $\{0,\pm
1\}$-vectors. Denote by $\mathcal L_k$ the family of all vectors $\mathbf v$
from $\{0,\pm 1\}^n$ such that $\langle\mathbf v,\mathbf v\rangle = k$. For any
$k$, most $l$ and sufficiently large $n$ we determine the maximal size of the
family $\mathcal V\subset \mathcal L_k$ such that for any $\mathbf v,\mathbf
w\in \mathcal V$ we have $\langle \mathbf v,\mathbf w\rangle\ge l$. We find
some exact values of this function for all $n$ for small values of $k$.
In the second part of the paper we study cross-intersecting pairs of
families. We say that two families are $\mathcal A, \mathcal B$ are
\textit{$s$-cross-intersecting}, if for any $A\in\mathcal A,B\in \mathcal B$ we
have $|A\cap B|\ge s$. We also say that a set family $\mathcal A$ is {\it
$t$-intersecting}, if for any $A_1,A_2\in \mathcal A$ we have $|A_1\cap A_2|\ge
t$. For a pair of nonempty $s$-cross-intersecting $t$-intersecting families
$\mathcal A,\mathcal B$ of $k$-sets, we determine the maximal value of
$|\mathcal A|+|\mathcal B|$ for $n$ sufficiently large.
|
We prove new upper bounds on the multicolour Ramsey numbers of paths and even
cycles. It is well known that $(k-1)n+o(n)\leq R_k(P_n)\leq R_k(C_n)\leq
kn+o(n)$. The upper bound was recently improved by S\'ark\"ozy who showed that
$R_k(C_n)\leq\left(k-\frac{k}{16k^3+1}\right)n+o(n)$. Here we show $R_k(C_n)
\leq (k-\frac14)n +o(n)$, obtaining the first improvement to the coefficient of
the linear term by an absolute constant.
|
Using molecular dynamics simulations we investigate the structure of a system
of particles interacting through a continuous core-softened interparticle
potential. We found for the translational order parameter, t, a local maximum
at a density $\rho_{t-max}$ and a local minimum at $\rho_{t-min} >
\rho_{t-max}$. Between $\rho_{t-max}$ and $\rho_{t-min}$, the $t$ parameter
anomalously decreases upon pressure. For the orientational order parameter,
$Q_6$, was observed a maximum at a density $\rho_{t-max}< \rho_{Qmax} <
\rho_{t-min}$. For densities between $\rho_{Qmax}$ and $\rho_{t-min}$, both the
translational (t) and orientational ($Q_6$) order parameters have anomalous
behavior. We know that this system also exhibits density and diffusion anomaly.
We found that the region in the pressure-temperature phase-diagram of the
structural anomaly englobes the region of the diffusion anomaly that is larger
than the region limited by the temperature of maximum density. This cascade of
anomalies (structural, dynamic and thermodynamic) for our model has the same
hierarchy of that one observed for the SPC/E water.
|
In this article, we present a one-field monolithic fictitious domain (FD)
method for simulation of general fluid-structure interactions (FSI). One-field
means only one velocity field is solved in the whole domain, based upon the use
of an appropriate L2 projection. Monolithic means the fluid and solid equations
are solved synchronously (rather than sequentially). We argue that the proposed
method has the same generality and robustness as FD methods with distributed
Lagrange multiplier (DLM) but is significantly more computationally efficient
(because of one-field) whilst being very straightforward to implement. The
method is described in detail, followed by the presentation of multiple
computational examples in order to validate it across a wide range of fluid and
solid parameters and interactions.
|
Inelastic neutron scattering is used to study the finite-temperature scaling
behavior of the local dynamic structure factor in the quasi-one-dimensional
quantum antiferromagnet NTENP
($\text{Ni(N,N'-bis(3-aminopropyl)propane-1,3-diamine)(}\mu\text{-NO}_2\text{)ClO}_4$),
at its field-induced Ising quantum critical point. The validity and the
limitations of the theoretically predicted scaling relations are tested.
|
We present analytical results (up to a numerical diagonalization of a real
symmetric matrix) for a set of time- and ensemble-average physical observables
in the non-Hookean Gaussian Network Model (GNM) - a generalization of the Rouse
model to elastic networks with links with a certain degree of extensional and
rotational stiffness. We focus on a set of coarse-grained observables that may
be of interest in the analysis of GNM in the context of internal motions in
proteins and mechanical frames in contact with a heat bath. A C++ computer code
is made available that implements all analytical results.
|
We present a new pseudospectral code, bamps, for numerical relativity written
with the evolution of collapsing gravitational waves in mind. We employ the
first order generalized harmonic gauge formulation. The relevant theory is
reviewed and the numerical method is critically examined and specialized for
the task at hand. In particular we investigate formulation parameters, gauge
and constraint preserving boundary conditions well-suited to non-vanishing
gauge source functions. Different types of axisymmetric twist-free moment of
time symmetry gravitational wave initial data are discussed. A treatment of the
axisymmetric apparent horizon condition is presented with careful attention to
regularity on axis. Our apparent horizon finder is then evaluated in a number
of test cases. Moving on to evolutions, we investigate modifications to the
generalized harmonic gauge constraint damping scheme to improve conservation in
the strong field regime. We demonstrate strong-scaling of our pseudospectral
penalty code. We employ the Cartoon method to efficiently evolve axisymmetric
data in our 3+1 dimensional code. We perform test evolutions of Schwarzschild
perturbed by gravitational waves and by gauge pulses, both to demonstrate the
use of our blackhole excision scheme and for comparison with earlier results.
Finally numerical evolutions of supercritical Brill waves are presented to
demonstrate durability of the excision scheme for the dynamical formation of a
blackhole.
|
This paper addresses the problem of distributed detection in multi-agent
networks. Agents receive private signals about an unknown state of the world.
The underlying state is globally identifiable, yet informative signals may be
dispersed throughout the network. Using an optimization-based framework, we
develop an iterative local strategy for updating individual beliefs. In
contrast to the existing literature which focuses on asymptotic learning, we
provide a finite-time analysis. Furthermore, we introduce a Kullback-Leibler
cost to compare the efficiency of the algorithm to its centralized counterpart.
Our bounds on the cost are expressed in terms of network size, spectral gap,
centrality of each agent and relative entropy of agents' signal structures. A
key observation is that distributing more informative signals to central agents
results in a faster learning rate. Furthermore, optimizing the weights, we can
speed up learning by improving the spectral gap. We also quantify the effect of
link failures on learning speed in symmetric networks. We finally provide
numerical simulations which verify our theoretical results.
|
We review the measurements of dark energy enabled by observations of the Deep
Drilling Fields and the optimization of survey design for cosmological
measurements. This white paper is the result of efforts by the LSST DESC
Observing Strategy Task Force (OSTF), which represents the entire
collaboration, and aims to make recommendations on observing strategy for the
DDFs that will benefit all cosmological analyses with LSST. It is accompanied
by the DESC-WFD white paper (Lochner et al.). We argue for altering the nominal
deep drilling plan to have $>6$ month seasons, interweaving $gri$ and $zy$
observations every 3 days with 2, 4, 8, 25, 4 visits in $grizy$, respectively.
These recommendations are guided by metrics optimizing constraints on dark
energy and mitigation of systematic uncertainties, including specific
requirements on total number of visits after Y1 and Y10 for photometric
redshifts (photo-$z$) and weak lensing systematics. We specify the precise
locations for the previously-chosen LSST deep fields (ELAIS-S1, XMM-LSS, CDF-S,
and COSMOS) and recommend Akari Deep Field South as the planned fifth deep
field in order to synergize with Euclid and WFIRST. Our recommended DDF
strategy uses $6.2\%$ of the LSST survey time. We briefly discuss synergy with
white papers from other collaborations, as well as additional mini-surveys and
Target-of-Opportunity programs that lead to better measurements of dark energy.
|
The magnetic field (B-field) of the starless dark cloud L1544 has been
studied using near-infrared (NIR) background starlight polarimetry (BSP) and
archival data in order to characterize the properties of the plane-of-sky
B-field. NIR linear polarization measurements of over 1,700 stars were obtained
in the H-band and 201 of these were also measured in the K-band. The NIR BSP
properties are correlated with reddening, as traced using the RJCE (H-M)
method, and with thermal dust emission from the L1544 cloud and envelope seen
in Herschel maps. The NIR polarization position angles change at the location
of the cloud and exhibit their lowest dispersion of position angles there,
offering strong evidence that NIR polarization traces the plane-of-sky B-field
of L1544. In this paper, the uniformity of the plane-of-sky B-field in the
envelope region of L1544 is quantitatively assessed. This allowed evaluating
the approach of assuming uniform field geometry when measuring relative
mass-to-flux ratios in the cloud envelope and core based on averaging of the
envelope radio Zeeman observations, as in Crutcher et al. (2009). In L1544, the
NIR BSP shows the envelope B-field to be significantly non-uniform and likely
not suitable for averaging Zeeman properties without treating intrinsic
variations. Deeper analyses of the NIR BSP and related data sets, including
estimates of the B-field strength and testing how it varies with position and
gas density, are the subjects of later papers in this series.
|
We present a new parallel PM N-body code named PMFAST that is freely
available to the public. PMFAST is based on a two-level mesh gravity solver
where the gravitational forces are separated into long and short range
components. The decomposition scheme minimizes communication costs and allows
tolerance for slow networks. The code approaches optimality in several
dimensions. The force computations are local and exploit highly optimized
vendor FFT libraries. It features minimal memory overhead, with the particle
positions and velocities being the main cost. The code features support for
distributed and shared memory parallelization through the use of MPI and
OpenMP, respectively.
The current release version uses two grid levels on a slab decomposition,
with periodic boundary conditions for cosmological applications. Open boundary
conditions could be added with little computational overhead. We present timing
information and results from a recent cosmological production run of the code
using a 3712^3 mesh with 6.4 x 10^9 particles. PMFAST is cost-effective,
memory-efficient, and is publicly available.
|
Parametric X-ray radiation (PXR) from relativistic electrons moving in a
crystal along the crystal-vacuum interface is considered. In this geometry the
emission of photons is happening in the regime of extremely asymmetric
diffraction (EAD). In the EAD case the whole crystal length contributes to the
formation of X-ray radiation opposed to Laue and Bragg geometries, where the
emission intensity is defined by the X-ray absorption length. We demonstrate
that this phenomenon should be described within the dynamical theory of
diffraction and predict a radical increase of the PXR intensity. In particular,
under realistic electron-beam parameters, an increase of two orders of
magnitude in PXR-EAD intensity can be obtained in comparison with conventional
experimental geometries of PXR. In addition we discuss in details the
experimental feasibility of the detection of PXR-EAD.
|
A quantum deformation of the Virasoro algebra is defined. The Kac
determinants at arbitrary levels are conjectured. We construct a bosonic
realization of the quantum deformed Virasoro algebra. Singular vectors are
expressed by the Macdonald symmetric functions. This is proved by constructing
screening currents acting on the bosonic Fock space.
|
To study emotions at the macroscopic level, affective scientists have made
extensive use of sentiment analysis on social media text. However, this
approach can suffer from a series of methodological issues with respect to
sampling biases and measurement error. To date, it has not been validated if
social media sentiment can measure the day to day temporal dynamics of emotions
aggregated at the macro level of a whole online community. We ran a large-scale
survey at an online newspaper to gather daily self-reports of affective states
from its users and compare these with aggregated results of sentiment analysis
of user discussions on the same online platform. Additionally, we preregistered
a replication of our study using Twitter text as a macroscope of emotions for
the same community. For both platforms, we find strong correlations between
text analysis results and levels of self-reported emotions, as well as between
inter-day changes of both measurements. We further show that a combination of
supervised and unsupervised text analysis methods is the most accurate approach
to measure emotion aggregates. We illustrate the application of such social
media macroscopes when studying the association between the number of new
COVID-19 cases and emotions, showing that the strength of associations is
comparable when using survey data as when using social media data. Our findings
indicate that macro level dynamics of affective states of users of an online
platform can be tracked with social media text, complementing surveys when
self-reported data is not available or difficult to gather.
|
We survey graph reachability indexing techniques for efficient processing of
graph reachability queries in two types of popular graph models: plain graphs
and edge-labeled graphs. Reachability queries are fundamental in graph
processing, and reachability indexes are specialized data structures tailored
for speeding up such queries. Work on this topic goes back four decades -- we
include 33 of the proposed techniques. Plain graphs contain only vertices and
edges, with reachability queries checking path existence between a source and
target vertex. Edge-labeled graphs, in contrast, augment plain graphs by adding
edge labels. Reachability queries in edge-labeled graphs incorporate path
constraints based on edge labels, assessing both path existence and compliance
with constraints.
We categorize techniques in both plain and edge-labeled graphs and discuss
the approaches according to this classification, using existing techniques as
exemplars. We discuss the main challenges within each class and how these might
be addressed in other approaches. We conclude with a discussion of the open
research challenges and future research directions, along the lines of
integrating reachability indexes into graph data management systems. This
survey serves as a comprehensive resource for researchers and practitioners
interested in the advancements, techniques, and challenges on reachability
indexing in graph analytics.
|
Using N-body simulations we study the structures induced on a galactic disc
by repeated flybys of a companion in decaying eccentric orbit around the disc.
Our system is composed by a stellar disc, bulge and live dark matter halo, and
we study the system's dynamical response to a sequence of a companion's flybys,
when we vary i) the disc's temperature (parameterized by Toomre's Q-parameter)
and ii) the companion's mass and initial orbit. We use a new 3D Cartesian grid
code: MAIN (Mesh-adaptive Approximate Inverse N-body solver). The main features
of MAIN are reviewed, with emphasis on the use of a new Symmetric Factored
Approximate Sparse Inverse (SFASI) matrix in conjunction with the multigrid
method that allows the efficient solution of Poisson's equation in three space
variables. We find that: i) companions need to be assigned initial masses in a
rather narrow window of values in order to produce significant and more
long-standing non-axisymmetric structures (bars and spirals) in the main
galaxy's disc by the repeated flyby mechanism. ii) a crucial phenomenon is the
antagonism between companion-excited and self-excited modes on the disc. Values
of $Q >1.5$ are needed in order to allow for the growth of the
companion-excited modes to prevail over the the growth of the disc's
self-excited modes. iii) We give evidence that the companion-induced spiral
structure is best represented by a density wave with pattern speed nearly
constant in a region extending from the ILR to a radius close to, but inside,
corotation.
|
Numerical reasoning skills are essential for complex question answering (CQA)
over text. It requires opertaions including counting, comparison, addition and
subtraction. A successful approach to CQA on text, Neural Module Networks
(NMNs), follows the programmer-interpreter paradigm and leverages specialised
modules to perform compositional reasoning. However, the NMNs framework does
not consider the relationship between numbers and entities in both questions
and paragraphs. We propose effective techniques to improve NMNs' numerical
reasoning capabilities by making the interpreter question-aware and capturing
the relationship between entities and numbers. On the same subset of the DROP
dataset for CQA on text, experimental results show that our additions
outperform the original NMNs by 3.0 points for the overall F1 score.
|
Using the concept of finite-size scaling, Monte Carlo calculations of various
models have become a very useful tool for the study of critical phenomena, with
the system linear dimension as a variable. As an example, several recent
studies of Ising models are discussed, as well as the extension to models of
polymer mixtures and solutions. It is shown that using appropriate cluster
algorithms, even the scaling functions describing the crossover from the Ising
universality class to the mean-field behavior with increasing interaction range
can be described. Additionally, the issue of finite-size scaling in Ising
models above the marginal dimension (d*=4) is discussed.
|
Various modern and highly popular applications make use of user data traces
in order to offer specific services, often for the purpose of improving the
user's experience while using such applications. However, even when user data
is privatized by employing privacy-preserving mechanisms (PPM), users' privacy
may still be compromised by an external party who leverages statistical
matching methods to match users' traces with their previous activities. In this
paper, we obtain the theoretical bounds on user privacy for situations in which
user traces are matchable to sequences of prior behavior, despite anonymization
of data time series. We provide both achievability and converse results for the
case where the data trace of each user consists of independent and identically
distributed (i.i.d.) random samples drawn from a multinomial distribution, as
well as the case that the users' data points are dependent over time and the
data trace of each user is governed by a Markov chain model.
|
We classify the extensions of the Standard Model (SM) according to the
structure of local operators in the weak effective Hamiltonian and the presence
or absence of new flavour and CP-violating interactions beyond those
represented by the CKM matrix. In particular we review characteristic
properties of models with minimal flavour violation (MFV), models with
significant contributions from Higgs penguins and models with enhanced Z^0
penguins carrying a large new CP-violating phase. Within the latter models, the
anomalous behaviour of certain B\to\pi K observables implies large departures
from the SM predictions for rare and CP-violating K and B decays. Most
spectacular is the enhancement of Br(K_L->pi^0 nu nubar) by one order of
magnitude and a strong violation of the MFV relation
(\sin2\beta)_{\pi\nu\bar\nu}=(\sin2\beta)_{\psi K_S}. On the other hand our
prediction for (\sin2\beta)_{\phi K_S}\approx 0.9 differs from the Belle result
by the sign but is consistent with the BaBar value. We give a personal shopping
list for the coming years.
|
Multi-wavelength analysis of the young massive cluster VVV CL077 is presented
for the first time. Our Chandra survey of this region enabled the detection of
three X-ray emitting stellar members of the cluster, as well as a possible
diffuse X-ray component that extends a few arcseconds from the cluster core
with an intrinsic flux of (9+/-3)x10^-14 erg cm^-2 s^-1 in the 0.5-10 keV band.
Infrared spectra we obtained for two of these X-ray point sources show
absorption lines typical of the atmospheres of massive O stars. The X-ray
spectrum from the visible extent of VVV CL077 i.e., a 15"-radius around the
cluster, can be modeled with an absorbed power law with nH = (6+/-4)x10^22
cm^-2 and gamma = 2+/-1. In addition, the X-ray core of VVV CL077 coincides
with diffuse emission seen in the infrared band and with a local maximum in the
radio continuum map. A possible association with a neighboring H II region
would place VVV CL077 at a distance of around 11 kpc; on the far side of the
Norma Arm. At this distance, the cluster is 0.8 pc wide with a mass density of
(1-4)x10^3 Msol pc^-3.
|
In this paper we derive a two-component system of nonlinear equations which
model two-dimensional shallow water waves with constant vorticity. Then we
prove well-posedness of this equation using a geometrical framework which
allows us to recast this equation as a geodesic flow on an infinite dimensional
manifold. Finally, we provide a criteria for global existence.
|
Interstellar molecular clouds are gamma ray sources through the interactions
with cosmic ray protons followed by production of neutral pions which decay
into gamma rays. We present new NANTEN2 observations of the TeV gamma ray SNR
RXJ1713.7-3946 and the W28 region in the 12CO J=2-1, 4-3 and 7-6 emission
lines. In RXJ1713.7-3946 we confirm that the local molecular gas having
velocities around -10 km/s shows remarkably good spatial correlations with the
SNR. We show that the X ray peaks are well correlated with the molecular gas
over the whole SNR and suggest that the interactions between the SNR and the
molecular gas play an important role in cosmic ray acceleration via several
ways including magnetic field compression. The CO J=4-3 distribution towards
peak C shows a compact and dense cloud core having a size of about 1 pc as well
as a broad wing. The core shows a notable anti-correlation with the Suzaku X
ray image and is also associated with hard gamma rays as observed with HESS.
Based on these findings, we present a picture that peak C is a molecular clump
survived against the impact of the SN blast waves and is surrounded by high
energy electrons emitting the X ray. The TeV gamma ray distribution is, on the
other hand, more extended into the molecular gas, supporting the hadronic
origin of gamma ray production. W28 is one of the most outstanding star forming
regions exhibiting TeV gamma rays as identified through a comparison between
the NANTEN CO dataset and HESS gamma ray sources. In the W28 region, we show
the CO J=2-1 distribution over the whole region as well as the detailed image
of the two TeV gamma ray peaks. One of them show strong CO J=7-6 emission,
suggesting high excitation conditions in this high mass star forming core. A
pursuit for the detailed mechanism to produce gamma rays is in progress.
|
We investigate the effect of school closure and subsequent reopening on the
transmission of COVID-19, by considering Denmark, Norway, Sweden, and German
states as case studies. By comparing the growth rates in daily hospitalisations
or confirmed cases under different interventions, we provide evidence that the
effect of school closure is visible as a reduction in the growth rate
approximately 9 days after implementation. Limited school attendance, such as
older students sitting exams or the partial return of younger year groups, does
not appear to significantly affect community transmission. A large-scale
reopening of schools while controlling or suppressing the epidemic appears
feasible in countries such as Denmark or Norway, where community transmission
is generally low. However, school reopening can contribute to significant
increases in the growth rate in countries like Germany, where community
transmission is relatively high. Our findings underscore the need for a
cautious evaluation of reopening strategies that ensure low classroom occupancy
and a solid infrastructure to quickly identify and isolate new infections.
|
For a graph $G = (V, E)$, a Roman dominating function $f : V \rightarrow \{0,
1, 2\}$ has the property that every vertex $v \in V $with $f (v) = 0$ has a
neighbor $u$ with $f (u) = 2$. The weight of a Roman dominating function $f$ is
the sum $f (V) = \cup_{v\in V} f (v)$, and the minimum weight of a Roman
dominating function on $G$ is the Roman domination number $\gamma_R(G)$ of $G$.
The Roman bondage number $b_R(G)$ of $G$ is the minimum cardinality of all sets
$F \subseteq E$ for which $\gamma_R(G - F) > \gamma_R(G)$. A graph $G$ is in
the class $\mathcal{R}_{UVR}$ if the Roman domination number remains unchanged
when a vertex is deleted. In this paper we obtain tight upper bounds for
$\gamma_R(G)$ and $b_R(G)$ provided a graph $G$ is in $\mathcal{R}_{UVR}$. We
present necessary and sufficient conditions for a tree to be in the class
$\mathcal{R}_{UV R}$. We give a constructive characterization of
$\mathcal{R}_{UVR}$-trees using labellings.
|
We review the recent progress made in understanding instantons at finite
temperature (calorons) with non-trivial holonomy, and their monopole
constituents as relevant degrees of freedom for the confined phase.
|
Deep neural networks are vulnerable to adversarial attacks. White-box
adversarial attacks can fool neural networks with small adversarial
perturbations, especially for large size images. However, keeping successful
adversarial perturbations imperceptible is especially challenging for
transfer-based black-box adversarial attacks. Often such adversarial examples
can be easily spotted due to their unpleasantly poor visual qualities, which
compromises the threat of adversarial attacks in practice. In this study, to
improve the image quality of black-box adversarial examples perceptually, we
propose structure-aware adversarial attacks by generating adversarial images
based on psychological perceptual models. Specifically, we allow higher
perturbations on perceptually insignificant regions, while assigning lower or
no perturbation on visually sensitive regions. In addition to the proposed
spatial-constrained adversarial perturbations, we also propose a novel
structure-aware frequency adversarial attack method in the discrete cosine
transform (DCT) domain. Since the proposed attacks are independent of the
gradient estimation, they can be directly incorporated with existing
gradient-based attacks. Experimental results show that, with the comparable
attack success rate (ASR), the proposed methods can produce adversarial
examples with considerably improved visual quality for free. With the
comparable perceptual quality, the proposed approaches achieve higher attack
success rates: particularly for the frequency structure-aware attacks, the
average ASR improves more than 10% over the baseline attacks.
|
We present the driven response at T=30mK of 6 GHz superconducting resonators
constructed from capacitively-shunted three dimensional (3D) aluminum
nanobridge superconducting quantum interference devices (nanoSQUIDs). We
observe flux modulation of the resonant frequency in quantitative agreement
with numerical calculation and characteristic of near-ideal short weak link
junctions. Under strong microwave excitation, we observe stable bifurcation in
devices with coupled quality factor (Q) ranging from ~30-3500. Near this bias
point, parametric amplification with > 20dB gain, 40 MHz bandwidth, and near
quantum-limited noise performance is observed. Our results indicate that 3D
nanobridge junctions are attractive circuit elements to realize quantum bits.
|
The stunning qualitative improvement of recent text-to-image models has led
to their widespread attention and adoption. However, we lack a comprehensive
quantitative understanding of their capabilities and risks. To fill this gap,
we introduce a new benchmark, Holistic Evaluation of Text-to-Image Models
(HEIM). Whereas previous evaluations focus mostly on text-image alignment and
image quality, we identify 12 aspects, including text-image alignment, image
quality, aesthetics, originality, reasoning, knowledge, bias, toxicity,
fairness, robustness, multilinguality, and efficiency. We curate 62 scenarios
encompassing these aspects and evaluate 26 state-of-the-art text-to-image
models on this benchmark. Our results reveal that no single model excels in all
aspects, with different models demonstrating different strengths. We release
the generated images and human evaluation results for full transparency at
https://crfm.stanford.edu/heim/v1.1.0 and the code at
https://github.com/stanford-crfm/helm, which is integrated with the HELM
codebase.
|
We study long-range correlation functions of the rectangular Ising lattice
with cyclic boundary conditions. Specifically, we consider the situation in
which two spins are on the same column, and at least one spin is on or near
free boundaries. The low-temperature series expansions of the correlation
functions are presented when the spin-spin couplings are the same in both
directions. The exact correlation functions can be obtained by D log Pade for
the cases with simple algebraic resultant expressions. The present results show
that as the two spins are infinitely far from each other, the correlation
function is equal to the product of the row magnetizations of the corresponding
spins as expected. In terms of low-temperature series expansions, the approach
of this m-th row correlation function to the bulk correlation function for
increasing m can be understood from the observation that the dominant terms of
their series expansions are the same successively in the above two correlation
functions. The number of these dominant terms increases monotonically as m
increases.
|
Teaching an anthropomorphic robot from human example offers the opportunity
to impart humanlike qualities on its movement. In this work we present a
reinforcement learning based method for teaching a real world bipedal robot to
perform movements directly from human motion capture data. Our method
seamlessly transitions from training in a simulation environment to executing
on a physical robot without requiring any real world training iterations or
offline steps. To overcome the disparity in joint configurations between the
robot and the motion capture actor, our method incorporates motion re-targeting
into the training process. Domain randomization techniques are used to
compensate for the differences between the simulated and physical systems. We
demonstrate our method on an internally developed humanoid robot with movements
ranging from a dynamic walk cycle to complex balancing and waving. Our
controller preserves the style imparted by the motion capture data and exhibits
graceful failure modes resulting in safe operation for the robot. This work was
performed for research purposes only.
|
We study the electric and thermoelectric transport properties of correlated
quantum dots coupled to two ferromagnetic leads and one superconducting
electrode. Transport through such hybrid devices depends on the interplay of
ferromagnetic-contact induced exchange field, superconducting proximity effect
and correlations leading to the Kondo effect. We consider the limit of large
superconducting gap. The system can be then modeled by an effective Hamiltonian
with a particle-non-conserving term describing the creation and annihilation of
Cooper pairs. By means of the full density-matrix numerical renormalization
group method, we analyze the behavior of electrical and thermal conductances,
as well as the Seebeck coefficient as a function of temperature, dot level
position and the strength of the coupling to the superconductor. We show that
the exchange field may be considerably affected by the superconducting
proximity effect and is generally a function of Andreev bound state energies.
Increasing the coupling to the superconductor may raise the Kondo temperature
and partially restore the exchange-field-split Kondo resonance. The competition
between ferromagnetic and superconducting proximity effects is reflected in the
corresponding temperature and dot level dependence of both the linear
conductance and the (spin) thermopower.
|
Stellar population studies of globular clusters have suggested that the
brightest clusters in the Galaxy might actually be the remnant nuclei of dwarf
spheroidal galaxies. If the present Galactic globular clusters formed within
larger stellar systems, they are likely surrounded by extra-tidal halos and/or
tails made up of stars that were tidally stripped from their parent systems.
The stellar surroundings around globular clusters are therefore one of the best
places to look for the remnants of an ancient dwarf galaxy. Here an attempt is
made to search for tidal debris around the supernovae enriched globular
clusters M22 and NGC 1851 as well as the kinematically unique cluster NGC 3201.
The stellar parameters from the Radial Velocity Experiment (RAVE) are used to
identify stars with RAVE metallicities, radial velocities and
elemental-abundances consistent with the abundance patterns and properties of
the stars in M22, NGC 1851 and NGC 3201. The discovery of RAVE stars that may
be associated with M22 and NGC 1851 are reported, some of which are at
projected distances of ~10 degrees away from the core of these clusters.
Numerous RAVE stars associated with NGC 3201 suggest that either the tidal
radius of this cluster is underestimated, or that there are some unbound stars
extending a few arc minutes from the edge of the cluster's radius. No further
extra-tidal stars associated with NGC 3201 could be identified. The bright
magnitudes of the RAVE stars make them easy targets for high resolution
follow-up observations, allowing an eventual further chemical tagging to
solidify (or exclude) stars outside the tidal radius of the cluster as tidal
debris. In both our radial velocity histograms of the regions surrounding NGC
1851 and NGC 3201, a peak of stars at 230 km/s is seen, consistent with
extended tidal debris from omega Centauri.
|
In this note, we will explain the connection between the Seven Circles
Theorem and hyperbolic geometry, then prove a stronger result about hyperbolic
geometry hexagons which implies the Seven Circles Theorem as a special case.
|
We consider the meta-equilibrium state of a composite system made up of
independent subsystems satisfying the additive form of external constraints, as
recently discussed by Abe [Phys. Rev. E {\bf 63}, 061105 (2001)]. We derive the
additive entropy $S$ underlying a composable entropy $\tilde{S}$ by identifying
the common intensive variable. The simplest form of composable entropy
satisfies Tsallis-type nonadditivity and the most general composable form is
interpreted as a monotonically increasing funtion $H$ of this simplest form.
This is consistent with the observation that the meta-equilibrium can be
equivalently described by the maximum of either $H[\tilde{S}]$ or $\tilde{S}$
and the intensive variable is same in both cases.
|
We introduce a new training algorithm for variety of deep neural networks
that utilize random complex exponential activation functions. Our approach
employs a Markov Chain Monte Carlo sampling procedure to iteratively train
network layers, avoiding global and gradient-based optimization while
maintaining error control. It consistently attains the theoretical
approximation rate for residual networks with complex exponential activation
functions, determined by network complexity. Additionally, it enables efficient
learning of multiscale and high-frequency features, producing interpretable
parameter distributions. Despite using sinusoidal basis functions, we do not
observe Gibbs phenomena in approximating discontinuous target functions.
|
Sufficient conditions are established for sampled-data feedback global
asymptotic stabilization for nonlinear autonomous systems. One of our main
results is an extension of the well known Artstein-Sontag theorem on feedback
stabilization concerning affine in the control systems. A second aim of the
present work is to provide sufficient conditions for sampled-data feedback
asymptotic stabilization for two interconnected nonlinear systems. Lie
algebraic sufficient conditions are derived for the case of affine in the
control interconnected systems without drift terms.
|
We study some natural linear systems carried by polarized Nikulin surfaces of
genus g. We determine their positivity and establish their Brill-Noether
theory. As an application, we compute the class of some natural effective
divisors associated to these linear systems on the moduli space of Nikulin
surfaces, relying upon recent work of Farkas and Rim\'{a}nyi.
|
In cooperative localization, communicating mobile agents use inter-agent
relative measurements to improve their dead-reckoning-based global
localization. Measurement scheduling enables an agent to decide which subset of
available inter-agent relative measurements it should process when its
computational resources are limited. Optimal measurement scheduling is an
NP-hard combinatorial optimization problem. The so-called sequential greedy
(SG) algorithm is a popular suboptimal polynomial-time solution for this
problem. However, the merit function evaluation for the SG algorithms requires
access to the state estimate vector and error covariance matrix of all the
landmark agents (teammates that an agent can take measurements from). This
paper proposes a measurement scheduling for CL that follows the SG approach but
reduces the communication and computation cost by using a neural network-based
surrogate model as a proxy for the SG algorithm's merit function. The
significance of this model is that it is driven by local information and only a
scalar metadata from the landmark agents. This solution addresses the time and
memory complexity issues of running the SG algorithm in three ways: (a)
reducing the inter-agent communication message size, (b) decreasing the
complexity of function evaluations by using a simpler surrogate (proxy)
function, (c) reducing the required memory size.Simulations demonstrate our
results.
|
We show that the recently measured asymmetry in helicity-angle spectra of the
Lambda-hyperons produced in the reaction pp -> K^+Lambda p reaction and the
energy dependence of the total pp -> K^+Lambda p cross section can be explained
consistently by the same Lambda p final-state interaction. Assuming that there
is no final-state interaction in the Sigma^0 p channel, as suggested by the
available data, we can also reproduce the energy dependence of the
Lambda/Sigma^0 production ratio and, in particular, the rather large ratio
observed near the reaction thresholds. The nominal ratio of the Lambda and
Sigma^0 production amplitudes squared, i.e. when disregarding the final-state
interaction, turns out to be about 3, which is in line with hyperon production
data from proton and nuclear targets available at high energies.
|
The Carrell-Chapuy recurrence formulas dramatically improve the efficiency of
counting orientable rooted maps by genus, either by number of edges alone or by
number of edges and vertices. This paper presents an implementation of these
formulas with three applications: the computation of an explicit rational
expression for the ordinary generating functions of rooted map numbers with a
given positive genus, the construction of large tables of rooted map numbers,
and the use of these tables, together with the method of A. Mednykh and R.
Nedela, to count unrooted maps by genus and number of edges and vertices.
|
We present the thermopower S(T) and the resistivity rho(T) of
Lu(1-x)Yb(x)Rh2Si2 in the temperature range 3 K < T < 300 K. S(T) is found to
change from two minima for dilute systems (x < 0.5) to a single large minimum
in pure YbRh2Si2. A similar behavior has also been found for the magnetic
contribution to the resistivity rho_mag(T). The appearance of the low-T extrema
in S(T) and rho_mag(T) is attributed to the lowering of the Kondo scale with
decreasing x. The evolution of the characteristic energy scales for both the
Kondo effect and the crystal electric field splitting are deduced. An
extrapolation allows to estimate the Kondo temperature of YbRh2Si2 to 29 K.
|
The modifications induced in the calculation of the cross section of the
diffractive process gamma gamma -> J/Psi J/Psi when the gluon propagator is
changed are analyzed. Instead of the usual perturbative gluon propagator,
alternative forms obtained using non-perturbative methods like Dyson-Schwinger
equations are used to consider in a more consistent way the contributions of
the infrared region. The result shows a reduction in the differential
cross-section for low momentum transfer once compared with the perturbative
result, to be confirmed with future experimental results from TESLA.
|
Magnetic bubbles are remarkable spin structures that developed in uniaxial
magnets with strong magnetocrystalline anisotropy. Several contradictory
reports have been published concerning the magnetic bubble structure in a
metallic magnet MnNiGa: Biskyrmions or type-II bubbles. Lorentz microscopy in
polycrystalline MnNiGa was used to explain the magnetic bubble structure.
Depending on the connection between the magnetic easy axis and the observation
plane, two types of magnetic bubbles were formed. Magnetic bubbles with
180{\deg} domains were formed if the easy axis was away from the direction
perpendicular to the observation plane. The contrast of biskyrmion is
reproduced by this form of a magnetic bubble. When the easy axis was
approximately perpendicular to the observing plane, type-II bubbles were
observed in the same specimen. The findings will fill a knowledge gap between
prior reports on magnetic bubbles in MnNiGa.
|
We derive the thermal conductivities of one-dimensional harmonic and
anharmonic lattices with self-consistent heat baths (BRV lattice) from the
Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we
obtain the same result as previous works. However, our approach is heuristic
and reveals phonon picture explicitly within the heat transport process. The
results for harmonic and anharmonic lattices are compared with numerical
calculations from Green-Kubo formula. The consistency between derivation and
simulation strongly supports that effective (renormalized) phonons are energy
carriers in anharmonic lattices although there exist some other excitations
such as solitons and breathers.
|
We describe a method to upper bound the quantum query complexity of Boolean
formula evaluation problems, using fundamental theorems about the general
adversary bound. This nonconstructive method can give an upper bound on query
complexity without producing an algorithm. For example, we describe an oracle
problem which we prove (non-constructively) can be solved in $O(1)$ queries,
where the previous best quantum algorithm uses a polylogarithmic number of
queries. We then give an explicit $O(1)$-query algorithm for this problem based
on span programs.
|
Grid space partitioning is a technique to speed up queries to graphics
databases. We present a parallel grid construction algorithm which can
efficiently construct a structured grid on GPU hardware. Our approach is
substantially faster than existing uniform grid construction algorithms,
especially on non-homogeneous scenes. Indeed, it can populate a grid in
real-time (at rates over 25 Hz), for architectural scenes with 10 million
triangles.
|
The significant progress on Generative Adversarial Networks (GANs) have made
it possible to generate surprisingly realistic images for single object based
on natural language descriptions. However, controlled generation of images for
multiple entities with explicit interactions is still difficult to achieve due
to the scene layout generation heavily suffer from the diversity object scaling
and spatial locations. In this paper, we proposed a novel framework for
generating realistic image layout from textual scene graphs. In our framework,
a spatial constraint module is designed to fit reasonable scaling and spatial
layout of object pairs with considering relationship between them. Moreover, a
contextual fusion module is introduced for fusing pair-wise spatial information
in terms of object dependency in scene graph. By using these two modules, our
proposed framework tends to generate more commonsense layout which is helpful
for realistic image generation. Experimental results including quantitative
results, qualitative results and user studies on two different scene graph
datasets demonstrate our proposed framework's ability to generate complex and
logical layout with multiple objects from scene graph.
|
Generative diffusion processes are an emerging and effective tool for image
and speech generation. In the existing methods, the underline noise
distribution of the diffusion process is Gaussian noise. However, fitting
distributions with more degrees of freedom, could help the performance of such
generative models. In this work, we investigate other types of noise
distribution for the diffusion process. Specifically, we show that noise from
Gamma distribution provides improved results for image and speech generation.
Moreover, we show that using a mixture of Gaussian noise variables in the
diffusion process improves the performance over a diffusion process that is
based on a single distribution. Our approach preserves the ability to
efficiently sample state in the training diffusion process while using Gamma
noise and a mixture of noise.
|
As an emerging antenna technology, a fluid antenna system (FAS) enhances
spatial diversity to improve both sensing and communication performance by
shifting the active antennas among available ports. In this letter, we study
the potential of shifting the integrated sensing and communication (ISAC)
trade-off with FAS. We propose the model for FAS-enabled ISAC and jointly
optimize the transmit beamforming and port selection of FAS. In particular, we
aim to minimize the transmit power, while satisfying both communication and
sensing requirements. An efficient iterative algorithm based on sparse
optimization, convex approximation, and a penalty approach is developed. The
simulation results show that the proposed scheme can attain 33% reductions in
transmit power with guaranteed sensing and communication performance, showing
the great potential of the fluid antenna for striking a flexible tradeoff
between sensing and communication in ISAC systems.
|
We study the dynamics of a collection of nonlinearly coupled limit cycle
oscillators, relevant to systems ranging from neuronal populations to
electrical circuits, under coupling topologies varying from a regular ring to a
random network. We find that the trajectories of this system escape to infinity
under regular coupling, for sufficiently strong coupling strengths. However,
when some fraction of the regular connections are dynamically randomized, the
unbounded growth is suppressed and the system always remains bounded. Further
we determine the critical fraction of random links necessary for successful
prevention of explosive behaviour, for different network rewiring time-scales.
These results suggest a mechanism by which blow-ups may be controlled in
extended oscillator systems.
|
Recently a new approach in constructing the conserved charges in cosmological
Einstein's gravity was given. In this new formulation, instead of using the
explicit form of the field equations a covariantly conserved rank four tensor
was used. In the resulting charge expression, instead of the first derivative
of the metric perturbation, the linearized Riemann tensor appears along with
the derivative of the background Killing vector fields. Here we give a detailed
analysis of the first order and the second order perturbation theory in a
gauge-invariant form in cosmological Einstein's gravity. The linearized
Einstein tensor is gauge-invariant at the first order but it is not so at the
second order, which complicates the discussion. This method depends on the
assumption that the first order metric perturbation can be decomposed into
gauge-variant and gauge-invariant parts and the gauge-variant parts do not
contribute to physical quantities.
|
Audio-visual active speaker detection (AV-ASD) aims to identify which visible
face is speaking in a scene with one or more persons. Most existing AV-ASD
methods prioritize capturing speech-lip correspondence. However, there is a
noticeable gap in addressing the challenges from real-world AV-ASD scenarios.
Due to the presence of low-quality noisy videos in such cases, AV-ASD systems
without a selective listening ability are short of effectively filtering out
disruptive voice components from mixed audio inputs. In this paper, we propose
a Multi-modal Speaker Extraction-to-Detection framework named `MuSED', which is
pre-trained with audio-visual target speaker extraction to learn the denoising
ability, then it is fine-tuned with the AV-ASD task. Meanwhile, to better
capture the multi-modal information and deal with real-world problems such as
missing modality, MuSED is modelled on the time domain directly and integrates
the multi-modal plus-and-minus augmentation strategy. Our experiments
demonstrate that MuSED substantially outperforms the state-of-the-art AV-ASD
methods and achieves 95.6% mAP on the AVA-ActiveSpeaker dataset, 98.3% AP on
the ASW dataset, and 97.9% F1 on the Columbia AV-ASD dataset, respectively. We
will publicly release the code in due course.
|
We study the fractal dimension of the spectrum of a quasiperiodical
Schrodinger operator associated to a sturmian potential. We consider potential
defined with irrationnal number verifying a generic diophantine condition. We
recall how shape and box dimension of the spectrum is linked to the irrational
number properties. In the first place, we give general lower bound of the box
dimension of the spectrum, true for all irrational numbers. In the second
place, we improve this lower bound for almost all irrational numbers. We
finally recall dynamical implication of the first bound.
|
Many real-life contractual relations differ completely from the clean, static
model at the heart of principal-agent theory. Typically, they involve repeated
strategic interactions of the principal and agent, taking place under
uncertainty and over time. While appealing in theory, players seldom use
complex dynamic strategies in practice, often preferring to circumvent
complexity and approach uncertainty through learning. We initiate the study of
repeated contracts with a learning agent, focusing on agents who achieve
no-regret outcomes.
Optimizing against a no-regret agent is a known open problem in general
games; we achieve an optimal solution to this problem for a canonical contract
setting, in which the agent's choice among multiple actions leads to
success/failure. The solution has a surprisingly simple structure: for some
$\alpha > 0$, initially offer the agent a linear contract with scalar $\alpha$,
then switch to offering a linear contract with scalar $0$. This switch causes
the agent to ``free-fall'' through their action space and during this time
provides the principal with non-zero reward at zero cost. Despite apparent
exploitation of the agent, this dynamic contract can leave \emph{both} players
better off compared to the best static contract. Our results generalize beyond
success/failure, to arbitrary non-linear contracts which the principal rescales
dynamically.
Finally, we quantify the dependence of our results on knowledge of the time
horizon, and are the first to address this consideration in the study of
strategizing against learning agents.
|
Most neuroimaging experiments are under-powered, limited by the number of
subjects and cognitive processes that an individual study can investigate.
Nonetheless, over decades of research, neuroscience has accumulated an
extensive wealth of results. It remains a challenge to digest this growing
knowledge base and obtain new insights since existing meta-analytic tools are
limited to keyword queries. In this work, we propose Text2Brain, a neural
network approach for coordinate-based meta-analysis of neuroimaging studies to
synthesize brain activation maps from open-ended text queries. Combining a
transformer-based text encoder and a 3D image generator, Text2Brain was trained
on variable-length text snippets and their corresponding activation maps
sampled from 13,000 published neuroimaging studies. We demonstrate that
Text2Brain can synthesize anatomically-plausible neural activation patterns
from free-form textual descriptions of cognitive concepts. Text2Brain is
available at https://braininterpreter.com as a web-based tool for retrieving
established priors and generating new hypotheses for neuroscience research.
|
Matching the rail cross-section profiles measured on site with the designed
profile is a must to evaluate the wear of the rail, which is very important for
track maintenance and rail safety. So far, the measured rail profiles to be
matched usually have four features, that is, large amount of data, diverse
section shapes, hardware made errors, and human experience needs to be
introduced to solve the complex situation on site during matching process.
However, traditional matching methods based on feature points or feature lines
could no longer meet the requirements. To this end, we first establish the rail
profiles matching dataset composed of 46386 pairs of professional manual
matched data, then propose a general high-precision method for rail profiles
matching using pre-trained convolutional neural network (CNN). This new method
based on deep learning is promising to be the dominant approach for this issue.
Source code is at
https://github.com/Kunqi1994/Deep-learning-on-rail-profile-matching.
|
We apply a spherical harmonic analysis to the Point Source Redshift Survey
(PSCz), to compute the real-space galaxy power spectrum and the degree of
redshift distortion caused by peculiar velocities. We employ new parameter
eigenvector and hierarchical data compression techniques, allowing a much
larger number of harmonic modes to be included, and correspondingly smaller
error bars. Using 4644 harmonic modes, compressed to 2278, we find that the
IRAS redshift-space distortion parameter is $\beta = 0.39 \pm 0.12$ and the
amplitude of galaxy clustering on a scale of $k=0.1 \Mpch$ is $\Delta_{\rm
gal}(0.1)=0.42 \pm 0.02$. Combining these we find the amplitude of mass
perturbations is $\Delta_m(0.1)=(0.16\pm0.04) \Omega_m^{-0.6}$. A preliminary
model fitting analysis combining the PSCz amplitudes with the CMB and abundance
of clusters yields the cosmological matter density parameter $\Omega_m=0.16\pm
0.03$, the amplitude of primordial perturbations $Q=(8.4\pm 3.8) \times
10^{-5}$, and the IRAS bias parameter $b=0.84\pm 0.28$.
|
Tackling climate change is at the top of many agendas. In this context,
emission trading schemes are considered as promising tools. The regulatory
framework for an emission trading scheme introduces a market for emission
allowances and creates a need for risk management by appropriate financial
contracts. In this work, we address logical principles underlying their
valuation.
|
In ecology, foraging requires animals to expend energy in order to obtain
resources. The cost of foraging can be reduced through kleptoparasitism, the
theft of a resource that another individual has expended effort to acquire.
Thus, kleptoparasitism is one of the most significant feeding techniques in
ecology. In this study, we investigate a two predator one prey paradigm in
which one predator acts as a kleptoparasite and the other as a host. This
research considers the post-kleptoparasitism scenario, which has received
little attention in the literature. Parametric requirements for the existence
as well as local and global stability of biologically viable equilibria have
been proposed. The occurrences of various one parametric bifurcations, such as
saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation, as
well as two parametric bifurcations, such as Bautin bifurcation, are explored
in depth. Relatively low growth rate of first predator induces a subcritical
Hopf bifurcation although a supercritical Hopf bifurcation occurs at relatively
high growth rate of first predator making coexistence of all three species
possible. Some numerical simulations have been provided for the purpose of
verifying our theoretical conclusions.
|
We present a device for specifying and reasoning about syntax for datatypes,
programming languages, and logic calculi. More precisely, we study a notion of
"signature" for specifying syntactic constructions.
In the spirit of Initial Semantics, we define the "syntax generated by a
signature" to be the initial object -- if it exists -- in a suitable category
of models. In our framework, the existence of an associated syntax to a
signature is not automatically guaranteed. We identify, via the notion of
presentation of a signature, a large class of signatures that do generate a
syntax.
Our (presentable) signatures subsume classical algebraic signatures (i.e.,
signatures for languages with variable binding, such as the pure lambda
calculus) and extend them to include several other significant examples of
syntactic constructions.
One key feature of our notions of signature, syntax, and presentation is that
they are highly compositional, in the sense that complex examples can be
obtained by gluing simpler ones. Moreover, through the Initial Semantics
approach, our framework provides, beyond the desired algebra of terms, a
well-behaved substitution and the induction and recursion principles associated
to the syntax.
This paper builds upon ideas from a previous attempt by Hirschowitz-Maggesi,
which, in turn, was directly inspired by some earlier work of
Ghani-Uustalu-Hamana and Matthes-Uustalu.
The main results presented in the paper are computer-checked within the
UniMath system.
|
We continue the study of root-theoretic Young diagrams (RYDs) from
[Searles-Yong '13]. We provide an RYD formula for the $GL_n$ Belkale-Kumar
product, after [Knutson-Purbhoo '11], and we give a translation of the indexing
set of [Buch-Kresch-Tamvakis '09] for Schubert varieties of non-maximal
isotropic Grassmannians into RYDs. We then use this translation to prove that
the RYD formulas of [Searles-Yong '13] for Schubert calculus of the classical
(co)adjoint varieties agree with the Pieri rules of [Buch-Kresch-Tamvakis '09],
which were needed in the proofs of the (co)adjoint formulas.
|
Machine and deep learning survival models demonstrate similar or even
improved time-to-event prediction capabilities compared to classical
statistical learning methods yet are too complex to be interpreted by humans.
Several model-agnostic explanations are available to overcome this issue;
however, none directly explain the survival function prediction. In this paper,
we introduce SurvSHAP(t), the first time-dependent explanation that allows for
interpreting survival black-box models. It is based on SHapley Additive
exPlanations with solid theoretical foundations and a broad adoption among
machine learning practitioners. The proposed methods aim to enhance precision
diagnostics and support domain experts in making decisions. Experiments on
synthetic and medical data confirm that SurvSHAP(t) can detect variables with a
time-dependent effect, and its aggregation is a better determinant of the
importance of variables for a prediction than SurvLIME. SurvSHAP(t) is
model-agnostic and can be applied to all models with functional output. We
provide an accessible implementation of time-dependent explanations in Python
at http://github.com/MI2DataLab/survshap.
|
Motivated by the study of systems of higher order boundary value problems
with functional boundary conditions, we discuss, by topological methods, the
solvability of a fairly general class of systems of perturbed Hammerstein
integral equations, where the nonlinearities and the functionals involved
depend on some derivatives. We improve and complement earlier results in the
literature. We also provide some examples in order to illustrate the
applicability of the theoretical results.
|
We present the results of a Chandra soft X-ray observation of the spectacular
ionization cone in the nearby Seyfert 2 galaxy NGC 5252. As almost invariably
observed in obscured AGN, the soft X-ray emission exhibits a remarkable
morphological concidence with the cone ionized gas as traced by HST O[III]
images. Energy-resolved images and high-resolution spectroscopy suggest that
the X-ray emitting gas is photoionized by the AGN, at least on scales as large
as the innermost gas and stellar ring (<3 kpc). Assuming that the whole cone is
photoionized by the AGN, we reconstruct the history of the active nucles in the
last 100000 years.
|
Moments when a time series changes its behaviour are called change points.
Detection of such points is a well-known problem, which can be found in many
applications: quality monitoring of industrial processes, failure detection in
complex systems, health monitoring, speech recognition and video analysis.
Occurrence of change point implies that the state of the system is altered and
its timely detection might help to prevent unwanted consequences. In this
paper, we present two online change-point detection approaches based on neural
networks. These algorithms demonstrate linear computational complexity and are
suitable for change-point detection in large time series. We compare them with
the best known algorithms on various synthetic and real world data sets.
Experiments show that the proposed methods outperform known approaches.
|
We study maximum selection and sorting of $n$ numbers using pairwise
comparators that output the larger of their two inputs if the inputs are more
than a given threshold apart, and output an adversarially-chosen input
otherwise. We consider two adversarial models. A non-adaptive adversary that
decides on the outcomes in advance based solely on the inputs, and an adaptive
adversary that can decide on the outcome of each query depending on previous
queries and outcomes.
Against the non-adaptive adversary, we derive a maximum-selection algorithm
that uses at most $2n$ comparisons in expectation, and a sorting algorithm that
uses at most $2n \ln n$ comparisons in expectation. These numbers are within
small constant factors from the best possible. Against the adaptive adversary,
we propose a maximum-selection algorithm that uses $\Theta(n\log
(1/{\epsilon}))$ comparisons to output a correct answer with probability at
least $1-\epsilon$. The existence of this algorithm affirmatively resolves an
open problem of Ajtai, Feldman, Hassadim, and Nelson.
Our study was motivated by a density-estimation problem where, given samples
from an unknown underlying distribution, we would like to find a distribution
in a known class of $n$ candidate distributions that is close to underlying
distribution in $\ell_1$ distance. Scheffe's algorithm outputs a distribution
at an $\ell_1$ distance at most 9 times the minimum and runs in time
$\Theta(n^2\log n)$. Using maximum selection, we propose an algorithm with the
same approximation guarantee but run time of $\Theta(n\log n)$.
|
The long-standing problem of whether the cosmological constant affects
directly the deflection of light caused by a gravitational lens is
reconsidered. We use a new approach based on the Hawking quasilocal mass of a
sphere grazed by light rays and on its splitting into local and cosmological
parts. Previous literature restricted to the cosmological constant is extended
to any form of dark energy accelerating the universe in which the gravitational
lens is embedded.
|
In segmentation problems, inference on change-point position and model
selection are two difficult issues due to the discrete nature of change-points.
In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable
formulae for the posterior distribution of variables such as the number of
change-points or their positions. We also derive a new selection criterion that
accounts for the reliability of the results. All these results are based on an
efficient strategy to explore the whole segmentation space, which is very
large. We illustrate our methodology on both simulated data and a comparative
genomic hybridisation profile.
|
We consider the coupled Einstein-Maxwell-Boltzmann system with cosmological
constant in presence of a massive scalar field. The background metric is that
of Friedman-Lema\^itre-Robertson-Walker space time in the spatially homogeneous
case where the unknown functions only depend on time and not on the space
variables $(x^i)$, $i=1,2,3$. By combining the energy estimates method with
that of characteristics we derive under suitable conditions on the chock kernel
(see Eq. 2.20), a local (in time) solution of the coupled system. Further,
under the hypotheses that the data are small in some appropriate norms and that
the cosmological constant satisfies $\Lambda > -4\pi m^2\Phi_0^2$, we derive a
unique global (in time) solution (Theorem 6.1).
|
We show that, when a spatially localised electric pulse is applied at the
edge of a quantum spin Hall system, electron wavepackets of the helical states
can be photoexcited by purely intra-branch electrical transitions, without
invoking the bulk states or the magnetic Zeeman coupling. In particular, as
long as the electric pulse remains applied, the photoexcited densities lose
their character of right- and left-movers, whereas after the ending of the
pulse they propagate in opposite directions without dispersion, i.e.
maintaining their space profile unaltered. Notably we find that, while the
momentum distribution of the photoexcited wave packets depends on the
temperature $T$ and the chemical potential $\mu$ of the initial equilibrium
state and displays a non-linear behavior on the amplitude of the applied pulse,
in the mesoscopic regime the space profile of the wave packets is independent
of $T$ and $\mu$. Instead, it depends purely on the applied electric pulse, in
a linear manner, as a signature of the chiral anomaly characterising massless
Dirac electrons. We also discuss how the photoexcited wave packets can be
tailored with the electric pulse parameters, for both low and finite
frequencies.
|
In this thesis, we study the diffusive and ballistic behaviors of random walk
in random environment (RWRE) in an integer lattice with dimension at least 2.
Our contributions are in three directions: a conditional law of large numbers
and regeneration structures for RWRE in Gibbsian environments, quenched
invariance principles for balanced elliptic (but non uniformly elliptic)
environments, and a proof of the Einstein relation for balanced iid uniformly
elliptic environments.
|
Biological studies on in vitro cell cultures are of fundamental importance to
investigate cells response to external stimuli, such as new drugs for treatment
of specific pathologies, or to study communication between electrogenic cells.
Although three-dimensional (3D) nanostructures brought tremendous improvements
on biosensors used for various biological in vitro studies, including drug
delivery and electrical recording, there is still a lack of multifunctional
capabilities that could help gaining deeper insights in several bio-related
research fields. In this work, the electrical recording of large cell ensembles
and the intracellular delivery of few selected cells are combined on the same
device by integrating microfluidics channels on the bottom of a multi-electrode
array decorated with 3D hollow nanostructures. The novel platform allows to
record intracellular-like action potentials from large ensembles of
cardiomyocytes derived from human Induced Pluripotent Stem Cells (hiPSC) and
from the HL-1 line, while different molecules are selectively delivered into
single/few targeted cells. The proposed approach shows high potential for
enabling new comprehensive studies that can relate drug effects to network
level cell communication processes.
|
We aim to understand how actions are performed and identify subtle
differences, such as 'fold firmly' vs. 'fold gently'. To this end, we propose a
method which recognizes adverbs across different actions. However, such
fine-grained annotations are difficult to obtain and their long-tailed nature
makes it challenging to recognize adverbs in rare action-adverb compositions.
Our approach therefore uses semi-supervised learning with multiple adverb
pseudo-labels to leverage videos with only action labels. Combined with
adaptive thresholding of these pseudo-adverbs we are able to make efficient use
of the available data while tackling the long-tailed distribution.
Additionally, we gather adverb annotations for three existing video retrieval
datasets, which allows us to introduce the new tasks of recognizing adverbs in
unseen action-adverb compositions and unseen domains. Experiments demonstrate
the effectiveness of our method, which outperforms prior work in recognizing
adverbs and semi-supervised works adapted for adverb recognition. We also show
how adverbs can relate fine-grained actions.
|
Instrumental variables (IVs) are widely used for estimating causal effects in
the presence of unmeasured confounding. Under the standard IV model, however,
the average treatment effect (ATE) is only partially identifiable. To address
this, we propose novel assumptions that allow for identification of the ATE.
Our identification assumptions are clearly separated from model assumptions
needed for estimation, so that researchers are not required to commit to a
specific observed data model in establishing identification. We then construct
multiple estimators that are consistent under three different observed data
models, and multiply robust estimators that are consistent in the union of
these observed data models. We pay special attention to the case of binary
outcomes, for which we obtain bounded estimators of the ATE that are guaranteed
to lie between -1 and 1. Our approaches are illustrated with simulations and a
data analysis evaluating the causal effect of education on earnings.
|
Boolean calculus has been studied extensively in the past in the context of
switching circuits, error-correcting codes etc. This work generalizes several
approaches to defining a differential calculus for Boolean functions. A unified
theory of Boolean calculus, complete with k-forms and integration, is presented
through the use of Zhegalkin algebras (i.e., algebraic normal forms),
culminating in a Stokes-like theorem for Boolean functions.
|
We propose a method for unsupervised domain adaptation that trains a shared
embedding to align the joint distributions of inputs (domain) and outputs
(classes), making any classifier agnostic to the domain. Joint alignment
ensures that not only the marginal distributions of the domain are aligned, but
the labels as well. We propose a novel objective function that encourages the
class-conditional distributions to have disjoint support in feature space. We
further exploit adversarial regularization to improve the performance of the
classifier on the domain for which no annotated data is available.
|
The interrelation between the generation of large-scale electric fields and
that of large-scale magnetic fields due to the breaking of the conformal
invariance of the electromagnetic field in inflationary cosmology is studied.
It is shown that if large-scale magnetic fields with a sufficiently large
amplitude are generated during inflation, the generation of large-scale
electric fields is suppressed, and vice versa. Furthermore, a physical
interpretation of the result and its cosmological significance are considered.
|
Throughout their history, homo sapiens have used technologies to better
satisfy their needs. The relation between needs and technology is so
fundamental that the US National Research Council defined the distinguishing
characteristic of technology as its goal "to make modifications in the world to
meet human needs". Artificial intelligence (AI) is one of the most promising
emerging technologies of our time. Similar to other technologies, AI is
expected "to meet [human] needs". In this article, we reflect on the
relationship between needs and AI, and call for the realisation of needs-aware
AI systems. We argue that re-thinking needs for, through, and by AI can be a
very useful means towards the development of realistic approaches for
Sustainable, Human-centric, Accountable, Lawful, and Ethical (HALE) AI systems.
We discuss some of the most critical gaps, barriers, enablers, and drivers of
co-creating future AI-based socio-technical systems in which [human] needs are
well considered and met. Finally, we provide an overview of potential threats
and HALE considerations that should be carefully taken into account, and call
for joint, immediate, and interdisciplinary efforts and collaborations.
|
We present a method how to estimate from experimental data of a turbulent
velocity field the drift and the diffusion coefficient of a Fokker-Planck
equation. It is shown that solutions of this Fokker-Planck equation reproduce
with high accuracy the statistics of velocity increments in the inertial range.
Using solutions with different initial conditions at large scales we show that
they converge. This can be interpreted as a signature of the universality of
small scale turbulence in the limit of large inertial ranges.
|
Heisenberg and Schr{\"o}dinger uncertainty principles give lower bounds for
the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$, in a state $\rho$,
if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$
is not zero.
In this paper we prove an uncertainty principle in Schr{\"o}dinger form where
the bound for the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$
depends on the area spanned by the commutators $[\rho,A]$ and $[\rho,B]$ with
respect to an arbitrary quantum version of the Fisher information.
|
In data science and machine learning, hierarchical parametric models, such as
mixture models, are often used. They contain two kinds of variables: observable
variables, which represent the parts of the data that can be directly measured,
and latent variables, which represent the underlying processes that generate
the data. Although there has been an increase in research on the estimation
accuracy for observable variables, the theoretical analysis of estimating
latent variables has not been thoroughly investigated. In a previous study, we
determined the accuracy of a Bayes estimation for the joint probability of the
latent variables in a dataset, and we proved that the Bayes method is
asymptotically more accurate than the maximum-likelihood method. However, the
accuracy of the Bayes estimation for a single latent variable remains unknown.
In the present paper, we derive the asymptotic expansions of the error
functions, which are defined by the Kullback-Leibler divergence, for two types
of single-variable estimations when the statistical regularity is satisfied.
Our results indicate that the accuracies of the Bayes and maximum-likelihood
methods are asymptotically equivalent and clarify that the Bayes method is only
advantageous for multivariable estimations.
|
This paper proposes a post-disaster cyber-physical interdependent restoration
scheduling (CPIRS) framework for active distribution networks (ADN) where the
simultaneous damages on cyber and physical networks are considered. The ad hoc
wireless device-to-device (D2D) communication is leveraged, for the first time,
to establish cyber networks instantly after the disaster to support ADN
restoration. The repair and operation crew dispatching, the remote-controlled
network reconfiguration and the system operation with DERs can be effectively
coordinated under the cyber-physical interactions. The uncertain outputs of
renewable energy resources (RESs) are represented by budget-constrained
polyhedral uncertainty sets. Through implementing linearization techniques on
disjunctive expressions, a monolithic mixed-integer linear programming (MILP)
based two-stage robust optimization model is formulated and subsequently solved
by a customized column-and-constraint generation (C&CG) algorithm. Numerical
results on the IEEE 123-node distribution system demonstrate the effectiveness
and superiorities of the proposed CPIRS method for ADN.
|
Research focused on the conjunction between quantum computing and routing
problems has been very prolific in recent years. Most of the works revolve
around classical problems such as the Traveling Salesman Problem or the Vehicle
Routing Problem. The real-world applicability of these problems is dependent on
the objectives and constraints considered. Anyway, it is undeniable that it is
often difficult to translate complex requirements into these classical
formulations.The main objective of this research is to present a solving scheme
for dealing with realistic instances while maintaining all the characteristics
and restrictions of the original real-world problem. Thus, a quantum-classical
strategy has been developed, coined Q4RPD, that considers a set of real
constraints such as a heterogeneous fleet of vehicles, priority deliveries, and
capacities characterized by two values: weight and dimensions of the packages.
Q4RPD resorts to the Leap Constrained Quadratic Model Hybrid Solver of D-Wave.
To demonstrate the application of Q4RPD, an experimentation composed of six
different instances has been conducted, aiming to serve as illustrative
examples.
|
We consider a family of positive solutions to the system of $k$ components \[
-\Delta u_{i,\beta} = f(x, u_{i,\beta}) - \beta u_{i,\beta} \sum_{j \neq i}
a_{ij} u_{j,\beta}^2 \qquad \text{in $\Omega$}, \] where $\Omega \subset
\mathbb{R}^N$ with $N \ge 2$. It is known that uniform bounds in $L^\infty$ of
$\{\mathbf{u}_{\beta}\}$ imply convergence of the densities to a segregated
configuration, as the competition parameter $\beta$ diverges to $+\infty$. In
this paper %we study more closely the asymptotic property of the solutions of
the system in this singular limit: we establish sharp quantitative point-wise
estimates for the densities around the interface between different components,
and we characterize the asymptotic profile of $\mathbf{u}_\beta$ in terms of
entire solutions to the limit system \[
\Delta U_i = U_i \sum_{j\neq i} a_{ij} U_j^2. \] Moreover, we develop a
uniform-in-$\beta$ regularity theory for the interfaces.
|
The limits of previous methods promote us to design a new approach (named
PRESTAGE) to predict proton single event effect (SEE) cross-sections using
heavy-ion test data. To more realistically simulate the SEE mechanisms, we
adopt Geant4 and the location-dependent strategy to describe the physics
processes and the sensitivity of the device. Cross-sections predicted by
PRESTAGE for over twenty devices are compared with the measured data. Evidences
show that PRESTAGE can calculate not only single event upsets induced by proton
indirect ionization, but also direct ionization effects and single event
latch-ups. Most of the PRESTAGE calculated results agree with the experimental
data within a factor of 2-3.
|
Summary talk given at the International Workshop on Linear Colliders LCWS 99,
Sitges (Barcelona), April 28 - May 5, 1999
|
Using the language of algebroid stacks, we will show that Kashiwara's
quantization of a complex contact manifold is unique.
|
The light-quark non-strange scalar mesons a0(980), f0(980), f0(1370),
a0(1450), f0(1500) and f0(1710) are of great interest as there is no generally
accepted view of their structure which can encompass q-q-qbar-qbar, molecular,
q-qbar and glueball states in various combinations. It has been shown
previously that the radiative decays of the scalar mesons to rho and omega are
a good probe of their structure and provide good discrimination among models.
Scalar meson photoproduction is proposed as an alternative to measuring
radiative decays and it is shown that it is a feasible proposition.
|
Massive multiple-input multiple-output (MIMO) systems hold the potential to
be an enabling technology for 5G cellular. Uniform planar array (UPA) antenna
structures are a focus of much commercial discussion because of their ability
to enable a large number of antennas in a relatively small area. With UPA
antenna structures, the base station can control the beam direction in both the
horizontal and vertical domains simultaneously. However, channel conditions may
dictate that one dimension requires higher channel state information (CSI)
accuracy than the other. We propose the use of an additional one bit of
feedback information sent from the user to the base station to indicate the
preferred domain on top of the feedback overhead of CSI quantization in
frequency division duplexing (FDD) massive MIMO systems. Combined with
variable-rate CSI quantization schemes, the numerical studies show that the
additional one bit of feedback can increase the quality of CSI significantly
for UPA antenna structures.
|
We show that the base spaces of the semiuniversal unfoldings of some weighted
homogeneous singularities can be identified with moduli spaces of
$A_\infty$-structures on the trivial extension algebras of the endomorphism
algebras of the tilting objects. The same algebras also appear in the Fukaya
categories of their mirrors. Based on these identifications, we discuss
applications to homological mirror symmetry for Milnor fibers, and give a proof
of homological mirror symmetry for an $n$-dimensional affine hypersurface of
degree $n + 2$ and the double cover of the $n$-dimensional affine space
branched along a degree $2n + 2$ hypersurface. Along the way, we also give a
proof of a conjecture of Seidel from math/0206155 which may be of independent
interest.
|
Off-resonant interaction of fluctuating photons in a resonator with a qubit
increases the qubit dephasing rate. We use this effect to measure a small
average number of intracavity photons that are coherently or thermally driven.
For spectral resolution, we do this by subjecting the qubit to a
Carr-Purcell-Meiboom-Gill (CPMG) sequence and record the qubit dephasing rate
for various periods between qubit $\pi$-pulses. The recorded data is then
analyzed with formulas for the photon-induced dephasing rate that we have
derived for the non-Gaussian noise regime with an arbitrary ratio
$2\chi/\kappa$, where $2\chi$ is the qubit frequency shift due to a single
photon and $\kappa$ is the resonator decay rate. We show that the presented
CPMG dephasing rate formulas agree well with experimental results and
demonstrate measurement of thermal and coherent photon populations at the level
of a few $10^{-4}$.
|
In this paper we study the volume growth in the component of fibered twists
in Milnor fibers of Brieskorn polynomials. We obtain a uniform lower bound of
the volume growth for a class of Brieskorn polynomials using a Smith inequality
for involutions in wrapped Floer homology. To this end, we investigate a family
of real Lagrangians in those Milnor fibers whose topology can be systematically
described in terms of the join construction.
|
Subsets and Splits