  With the rapid advances of autonomous driving, it becomes critical to equip
its sensing system with more holistic 3D perception. However, existing works
focus on parsing either the objects (e.g. cars and pedestrians) or scenes (e.g.
trees and buildings) from the LiDAR sensor. In this work, we address the task
of LiDAR-based panoptic segmentation, which aims to parse both objects and
scenes in a unified manner. As one of the first endeavors towards this new
challenging task, we propose the Dynamic Shifting Network (DS-Net), which
serves as an effective panoptic segmentation framework in the point cloud
realm. In particular, DS-Net has three appealing properties: 1) strong backbone
design. DS-Net adopts the cylinder convolution that is specifically designed
for LiDAR point clouds. The extracted features are shared by the semantic
branch and the instance branch which operates in a bottom-up clustering style.
2) Dynamic Shifting for complex point distributions. We observe that
commonly-used clustering algorithms like BFS or DBSCAN are incapable of
handling complex autonomous driving scenes with non-uniform point cloud
distributions and varying instance sizes. Thus, we present an efficient
learnable clustering module, dynamic shifting, which adapts kernel functions
on-the-fly for different instances. 3) Consensus-driven Fusion. Finally,
consensus-driven fusion is used to deal with the disagreement between semantic
and instance predictions. To comprehensively evaluate the performance of
LiDAR-based panoptic segmentation, we construct and curate benchmarks from two
large-scale autonomous driving LiDAR datasets, SemanticKITTI and nuScenes.
Extensive experiments demonstrate that our proposed DS-Net achieves superior
accuracies over current state-of-the-art methods. Notably, we achieve 1st place
on the public leaderboard of SemanticKITTI, outperforming 2nd place by 2.6% in
terms of the PQ metric.


  The Internet has emerged as perhaps the most important network in modern
computing, but rather miraculously, it was created through the individual
actions of a multitude of agents rather than by a central planning authority.
This motivates the game theoretic study of network formation, and our paper
considers one of the most-well studied models, originally proposed by Fabrikant
et al. In it, each of N agents corresponds to a vertex, which can create edges
to other vertices at a cost of alpha each, for some parameter alpha. Every edge
can be freely used by every vertex, regardless of who paid the creation cost.
To reflect the desire to be close to other vertices, each agent's cost function
is further augmented by the sum total of all (graph theoretic) distances to all
other vertices.
  Previous research proved that for many regimes of the (alpha, N) parameter
space, the total social cost (sum of all agents' costs) of every Nash
equilibrium is bounded by at most a constant multiple of the optimal social
cost. In algorithmic game theoretic nomenclature, this approximation ratio is
called the price of anarchy. In our paper, we significantly sharpen some of
those results, proving that for all constant non-integral alpha > 2, the price
of anarchy is in fact 1+o(1), i.e., not only is it bounded by a constant, but
it tends to 1 as N tends to infinity. For constant integral alpha >= 2, we show
that the price of anarchy is bounded away from 1. We provide quantitative
estimates on the rates of convergence for both results.


  In this paper we revisit the greatest common right divisor (GCRD) extraction
from a set of polynomial matrices $P_i(\lambda)\in \F[\la]^{m_i\times n}$,
$i=1,\ldots,k$ with coefficients in a generic field $\F$, and with common
column dimension $n$. We give necessary and sufficient conditions for a matrix
$G(\la)\in \F[\la]^{\ell\times n}$ to be a GCRD using the Smith normal form of
the $m \times n$ compound matrix $P(\lambda)$ obtained by concatenating
$P_i(\lambda)$ vertically, where $m=\sum_{i=1}^k m_i$. We also describe the
complete set of degrees of freedom for the solution $G(\la)$, and we link it to
the Smith form and Hermite form of $P(\la)$. We then give an algorithm for
constructing a particular minimum rank solution for this problem when $\F=\C$
or $\R$, using state-space techniques. This new method works directly on the
coefficient matrices of $P(\la)$, using orthogonal transformations only. The
method is based on the staircase algorithm, applied to a particular pencil
derived from a generalized state-space model of $P(\la)$.


  We study rings $R$ for which whenever non-zero polynomials $f(x)$ and $g(x)$
satisfy $f(x)g(x)f(x)=0$, it implies that there is a non-zero element $r\in R$
such that $f(x)rf(x)=0$. We call such rings inner McCoy rings. We explore some
examples of rings that are inner McCoy, determine relationships between the
class of inner McCoy rings and some known classes of rings. Furthermore, we
show that the maximal inner McCoy subring of a matrix ring is the triangular
matrix ring. Finally, we construct new inner McCoy rings from known ones.


  In-flight measurement of the antenna main beams of the Planck instruments is
a crucial input to the data analysis pipeline. We study the main beam
reconstruction achievable through external planets using a flight simulator to
model their observation. We restrict our analysis to the 30 GHz LFI channel but
the method can be easily extended to higher frequency channels. We show that it
is possible to fit the antenna response from Jupiter and Saturn to obtain an
accurate, robust, simple and fast reconstruction of the main beam properties
under very general conditions, independently of the calibration accuracy.
  In addition, we find that a bivariate Gaussian approximation of the main beam
shapes represents a significant improvement with respect to a symmetric
representation.
  We also show that it is possible to combine the detection of the planet's
transit and Planck's very accurate in-flight calibration to measure the
planet's temperature at millimetric wavelengths with an accuracy at the %
level.
  This work is based on Planck-LFI activities.


  In this paper, we establish some Harnack type inequalities satisfied by
positive solutions of nonlocal inhomogeneous equations arising in the
description of various phenomena ranging from population dynamics to
micro-magnetism. For regular domains, we also derive an inequality up to the
boundary. The main difficulty in such context lies in a precise control of the
solutions outside a compact set and the existence of local uniform estimates.
We overcome this problem by proving a contraction result which makes the $L^1$
norms of the solutions on two compact sets $\o_1\subset\subset\o_2$ equivalent.
We also construct the principal positive eigenfunctions associated to
particular nonlocal operators by using the corresponding Harnack type
inequalities.


  The destitution of image data and corresponding expert annotations limit the
training capacities of AI diagnostic models and potentially inhibit their
performance. To address such a problem of data and label scarcity, generative
models have been developed to augment the training datasets. Previously
proposed generative models usually require manually adjusted annotations (e.g.,
segmentation masks) or need pre-labeling. However, studies have found that
these pre-labeling based methods can induce hallucinating artifacts, which
might mislead the downstream clinical tasks, while manual adjustment could be
onerous and subjective. To avoid manual adjustment and pre-labeling, we propose
a novel controllable and simultaneous synthesizer (dubbed CS$^2$) in this study
to generate both realistic images and corresponding annotations at the same
time. Our CS$^2$ model is trained and validated using high resolution CT (HRCT)
data collected from COVID-19 patients to realize an efficient infections
segmentation with minimal human intervention. Our contributions include 1) a
conditional image synthesis network that receives both style information from
reference CT images and structural information from unsupervised segmentation
masks, and 2) a corresponding segmentation mask synthesis network to
automatically segment these synthesized images simultaneously. Our experimental
studies on HRCT scans collected from COVID-19 patients demonstrate that our
CS$^2$ model can lead to realistic synthesized datasets and promising
segmentation results of COVID infections compared to the state-of-the-art
nnUNet trained and fine-tuned in a fully supervised manner.


  We report nonlinear behavior in the motion of driven nanowire cantilevers.
The nonlinearity can be described by the Duffing equation and is used to
demonstrate mechanical mixing of two distinct excitation frequencies.
Furthermore, we demonstrate that the nonlinearity can be used to amplify a
signal at a frequency close to the mechanical resonance of the nanowire
oscillator. Up to 26 dB of amplitude gain are demonstrated in this way.


  Human Pose Estimation (HPE) plays a crucial role in computer vision
applications. However, it is difficult to deploy state-of-the-art models on
resouce-limited devices due to the high computational costs of the networks. In
this work, a binary human pose estimator named BiHRNet(Binary HRNet) is
proposed, whose weights and activations are expressed as $\pm$1. BiHRNet
retains the keypoint extraction ability of HRNet, while using fewer computing
resources by adapting binary neural network (BNN). In order to reduce the
accuracy drop caused by network binarization, two categories of techniques are
proposed in this work. For optimizing the training process for binary pose
estimator, we propose a new loss function combining KL divergence loss with
AWing loss, which makes the binary network obtain more comprehensive output
distribution from its real-valued counterpart to reduce information loss caused
by binarization. For designing more binarization-friendly structures, we
propose a new information reconstruction bottleneck called IR Bottleneck to
retain more information in the initial stage of the network. In addition, we
also propose a multi-scale basic block called MS-Block for information
retention. Our work has less computation cost with few precision drop.
Experimental results demonstrate that BiHRNet achieves a PCKh of 87.9 on the
MPII dataset, which outperforms all binary pose estimation networks. On the
challenging of COCO dataset, the proposed method enables the binary neural
network to achieve 70.8 mAP, which is better than most tested lightweight
full-precision networks.


  The variational Monte Carlo method is applied to investigate the ground state
energy of the lithium atom and its ions up to Z=10 in the presence of an
external magnetic field regime with {\gamma}=0 ~ 100 a.u. Our calculations are
based on using three forms of compact and accurate trial wave functions, which
were put forward in calculating energies in the absence of magnetic field. The
obtained results are in good agreement with the most recent accurate values and
also with the exact values.


  We consider a 5D SUSY $SU(3)_c\times SU(2)_L\times U(1)_Y\times {\cal U}(1)$
model compactified on an $S^{(1)}/Z_2$ orbifold. To cancel anomalies arising
from the presence of ${\cal U}(1)$, we employ a Chern-Simons term and also
chiral fields which could reside on the brane or in the bulk depending on the
model. The presence of ${\cal U}(1)$ symmetry leads to baryon number
conservation, gives rise to matter parity, and permits satisfactory neutrino
masses and mixings even for a low fundamental scale. The brane Fayet-Iliopoulos
D-terms naturally break ${\cal U}(1)$, leaving N=1 SUSY unbroken in 4
dimensions.


  Physical aging of glycerol following temperature jumps is studied by
dielectric spectroscopy at temperatures just below the glass transition
temperature. The data are analyzed using two single-parameter aging tests
developed by Hecksher et al. [J. Chem. Phys. 142, 241103 (2015)]. We generalize
these tests to include jumps ending at different temperatures. Moreover, four
times larger jumps than previously are studied. The single-parameter aging
tests are here for the first time applied to a hydrogen-bonded liquid. We
conclude that glycerol obeys single-parameter aging to a good approximation.


  An isolated horizon (IH) is a null hypersurface at which the geometry is held
fixed. This generalizes the notion of an event horizon so that the black hole
is an object that is in local equilibrium with its (possibly) dynamic
environment. The first law of IH mechanics that arises from the framework
relates quantities that are all defined at the horizon.
  IHs have been extensively studied in Einstein gravity with various matter
couplings and rotation, and in asymptotically flat and asymptotically anti-de
Sitter (ADS) spacetimes in all dimensions $D\geq3$. Motivated by the
nonuniqueness of black holes in higher dimensions and by the black-hole/string
correspondence principle, we devote this thesis to the extension of the
framework to include IHs in string-inspired gravity models, specifically to
Einstein-Maxwell-Chern-Simons (EMCS) theory and to Einstein-Gauss-Bonnet (EGB)
theory in higher dimensions.
  The focus is on determining the generic features of black holes that are
solutions to the field equations of the theories under consideration. We obtain
various results for non-extremal, extremal and supersymmetric IHs in EM-CS
theory, and for non-rotating IHs in EGB theory.
  (An extended abstract is given in the PDF file.)


  The Crystal Ball Collaboration has recently reported the differential cross
sections and $\Lambda$ polarization for the reaction $K^-p\rightarrow
\pi^0\Lambda$ using an incident $K^-$ beam with momenta between 514 and 750
MeV/$c$. We make a partial wave analysis for this process with an effective
Lagrangian approach and study the properties of some $\Sigma$ resonances around
this energy range. With the inclusion of the 4-star resonances $\Sigma(1189)$,
$\Sigma^*(1385)$, $\Sigma(1670){3\over 2}^-$, $\Sigma(1775){5\over 2}^-$, as
well as a $\Sigma(1635){1\over 2}^+$, which is compatible with the 3-star
$\Sigma(1660){1\over 2}^+$ in PDG, our results can well reproduce the
experimental data. The parameters on the $\Sigma$ resonances and related
couplings are studied.


  Stellar systems are broadly divided into collisional and non-collisional. The
latter are large-N systems with long relaxation timescales and can be simulated
disregarding two-body interactions, while either computationally expensive
direct N-body simulations or approximate schemes are required to properly model
the former. Large globular clusters and nuclear star clusters, with relaxation
timescales of the order of a Hubble time, are small enough to display some
collisional behaviour and big enough to be impossible to simulate with direct
$N$-body codes and current hardware. We introduce a new method to simulate
collisional stellar systems, and validate it by comparison with direct $N$-body
codes on small-$N$ simulations. The Multi-Particle collision for Dense stellar
systems Code (MPCDSS) is a new code for evolving stellar systems with the
Multi-Particle Collision method. Such method amounts to a stochastic collision
rule that allows to conserve exactly the energy and momentum over a cluster of
particles experiencing the collision. The code complexity scales with $N \log
N$ in the number of particles. Unlike Monte-Carlo codes, MPCDSS can easily
model asymmetric, non-homogeneous, unrelaxed and rotating systems, while
allowing us to follow the orbits of individual stars. We evolve small ($N = 3.2
\times 10^4$) star clusters with MPCDSS and with the direct-summation code
NBODY6, finding a similar evolution of key indicators. We then simulate
different initial conditions in the $10^4 - 10^6$ star range. MPCDSS bridges
the gap between small, collisional systems that can be simulated with direct
$N$-body codes and large noncollisional systems. MPCDSS in principle allows us
to simulate globular clusters such as Omega Cen and M54 and even the nuclear
star cluster, beyond the limits of current direct N-body codes in terms of the
number of particles.


  k-space undersampling is a standard technique to accelerate MR image
acquisitions. Reconstruction techniques including GeneRalized Autocalibrating
Partial Parallel Acquisition(GRAPPA) and its variants are utilized extensively
in clinical and research settings. A reconstruction model combining GRAPPA with
a conditional generative adversarial network (GAN) was developed and tested on
multi-coil human brain images from the fastMRI dataset. For various
acceleration rates, GAN and GRAPPA reconstructions were compared in terms of
peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). For an
acceleration rate of R=4, PSNR improved from 33.88 using regularized GRAPPA to
37.65 using GAN. GAN consistently outperformed GRAPPA for various acceleration
rates.


  Measurements of the scalar dissipation rate are performed in an impulsively
started gas jet, using planar laser induced fluorescence. The measurements are
well resolved spatially. The deteriorating effect of experimental noise on this
experiment is treated with a Wiener filter, which is shown to be applicable to
this large-scale inhomogeneous flow. The accuracy of the scalar dissipation
rate is within $20\%$, as determined from an explicit calculation of the
filtering errors. The residual fields that remain after the filtering are
analysed in detail and their statistical properties show that these resemble
white noise to a good approximation. The level of corrections is minimal for
the scalar field but it is of the order of $40\%$ for the scalar dissipation
rate. An examination of the filtering operation using modeled spectra and the
measured spatial resolution shows that the Wiener filter produces errors in the
estimate of the scalar dissipation rate $\sim30\%$, for Taylor-scale Reynolds
number up to 1000. The implications of this modelling are discussed with
respect to common experimental situations and point out the relative merits of
improving the spatial resolution as compared to improvements in the signal to
noise ratio.


  We consider hard three-loop corrections to hyperfine splitting in muonium and
positronium generated by the diagrams with closed electron loops. There are six
gauge-invariant sets of such diagrams that generate corrections of order
$m\alpha^7$. The contributions of these diagrams are calculated for an
arbitrary electron-muon mass ratio without expansion in the small mass ratio.
We obtain the formulae for contributions to hyperfine splitting that in the
case of small mass ratio describe corrections for muonium and in the case of
equal masses describe corrections for positronium. First few terms of the
expansion of hard corrections in the small mass ratio were earlier calculated
for muonium analytically. We check numerically that the new results coincide
with the sum of the known terms of the expansion in the case of small mass
ratio. In the case of equal masses we obtain hard nonlogarithmic corrections of
order $m\alpha^7$ to hyperfine splitting in positronium.


  Transferability estimation has been an essential tool in selecting a
pre-trained model and the layers in it for transfer learning, to transfer, so
as to maximize the performance on a target task and prevent negative transfer.
Existing estimation algorithms either require intensive training on target
tasks or have difficulties in evaluating the transferability between layers. To
this end, we propose a simple, efficient, and effective transferability measure
named TransRate. Through a single pass over examples of a target task,
TransRate measures the transferability as the mutual information between
features of target examples extracted by a pre-trained model and their labels.
We overcome the challenge of efficient mutual information estimation by
resorting to coding rate that serves as an effective alternative to entropy.
From the perspective of feature representation, the resulting TransRate
evaluates both completeness (whether features contain sufficient information of
a target task) and compactness (whether features of each class are compact
enough for good generalization) of pre-trained features. Theoretically, we have
analyzed the close connection of TransRate to the performance after transfer
learning. Despite its extraordinary simplicity in 10 lines of codes, TransRate
performs remarkably well in extensive evaluations on 32 pre-trained models and
16 downstream tasks.


  This article focuses on signal classification for deep-sea acoustic neutrino
detection. In the deep sea, the background of transient signals is very
diverse. Approaches like matched filtering are not sufficient to distinguish
between neutrino-like signals and other transient signals with similar
signature, which are forming the acoustic background for neutrino detection in
the deep-sea environment. A classification system based on machine learning
algorithms is analysed with the goal to find a robust and effective way to
perform this task. For a well-trained model, a testing error on the level of
one percent is achieved for strong classifiers like Random Forest and Boosting
Trees using the extracted features of the signal as input and utilising dense
clusters of sensors instead of single sensors.


  We present the SIBIA (Scalable Integrated Biophysics-based Image Analysis)
framework for joint image registration and biophysical inversion and we apply
it to analyse MR images of glioblastomas (primary brain tumors). In particular,
we consider the following problem. Given the segmentation of a normal brain MRI
and the segmentation of a cancer patient MRI, we wish to determine tumor growth
parameters and a registration map so that if we "grow a tumor" (using our tumor
model) in the normal segmented image and then register it to the patient
segmented image, then the registration mismatch is as small as possible. We
call this "the coupled problem" because it two-way couples the biophysical
inversion and registration problems. In the image registration step we solve a
large-deformation diffeomorphic registration problem parameterized by an
Eulerian velocity field. In the biophysical inversion step we estimate
parameters in a reaction-diffusion tumor growth model that is formulated as a
partial differential equation.
  In this paper, our contributions are the introduction of a PDE-constrained
optimization formulation of the coupled problem, the derivation of the
optimality conditions, and the derivation of a Picard iterative scheme for the
solution of the coupled problem. In addition, we perform several tests to
experimentally assess the performance of our method on synthetic and clinical
datasets. We demonstrate the convergence of the SIBIA optimization solver in
different usage scenarios. We demonstrate that we can accurately solve the
coupled problem in three dimensions ($256^3$ resolution) in a few minutes using
11 dual-x86 nodes. Also, we demonstrate that, with our coupled approach, we can
successfully register normal MRI to tumor-bearing MRI while obtaining Dice
coefficients that match those achieved when registering of normal-to-normal
MRI.


  Counterspeech, defined as a response to mitigate online hate speech, is
increasingly used as a non-censorial solution. Addressing hate speech
effectively involves dispelling the stereotypes, prejudices, and biases often
subtly implied in brief, single-sentence statements or abuses. These implicit
expressions challenge language models, especially in seq2seq tasks, as model
performance typically excels with longer contexts. Our study introduces CoARL,
a novel framework enhancing counterspeech generation by modeling the pragmatic
implications underlying social biases in hateful statements. CoARL's first two
phases involve sequential multi-instruction tuning, teaching the model to
understand intents, reactions, and harms of offensive statements, and then
learning task-specific low-rank adapter weights for generating
intent-conditioned counterspeech. The final phase uses reinforcement learning
to fine-tune outputs for effectiveness and non-toxicity. CoARL outperforms
existing benchmarks in intent-conditioned counterspeech generation, showing an
average improvement of 3 points in intent-conformity and 4 points in
argument-quality metrics. Extensive human evaluation supports CoARL's efficacy
in generating superior and more context-appropriate responses compared to
existing systems, including prominent LLMs like ChatGPT.


  Federated Edge Learning (FEEL) emerges as a pioneering distributed machine
learning paradigm for the 6G Hyper-Connectivity, harnessing data from the
Internet of Things (IoT) devices while upholding data privacy. However, current
FEEL algorithms struggle with non-independent and non-identically distributed
(non-IID) data, leading to elevated communication costs and compromised model
accuracy. To address these statistical imbalances within FEEL, we introduce a
clustered data sharing framework, mitigating data heterogeneity by selectively
sharing partial data from cluster heads to trusted associates through
sidelink-aided multicasting. The collective communication pattern is integral
to FEEL training, where both cluster formation and the efficiency of
communication and computation impact training latency and accuracy
simultaneously. To tackle the strictly coupled data sharing and resource
optimization, we decompose the overall optimization problem into the clients
clustering and effective data sharing subproblems. Specifically, a
distribution-based adaptive clustering algorithm (DACA) is devised basing on
three deductive cluster forming conditions, which ensures the maximum sharing
yield. Meanwhile, we design a stochastic optimization based joint computed
frequency and shared data volume optimization (JFVO) algorithm, determining the
optimal resource allocation with an uncertain objective function. The
experiments show that the proposed framework facilitates FEEL on non-IID
datasets with faster convergence rate and higher model accuracy in a limited
communication environment.


  The accurate computation of non-linear optical properties (NLOPs) in large
polymers requires accounting for electronic correlation effects with a
reasonable computational cost. The Random Phase Approximation (RPA) used in the
adiabatic connection fluctuation theorem is known to be a reliable and
cost-effective method to render electronic correlation effects when combined
with the density-fitting techniques and the integration over imaginary
frequencies. We explore the ability of the RPA energy expression to predict
NLOPs by evaluating RPA electronic energies in the presence of finite electric
fields to obtain (using the finite difference method) static polarizabilities
and hyper-polarizabilities. We show that RPA based on hybrid functional
self-consistent field calculations yields as accurate NLOPs as the best-tuned
double-hybrid functionals developed today, with the additional advantage that
RPA avoids any system-specific adjustment.


  Attenuation study of a province is considered as a basic quantity for seismic
hazard assessment, ground motion simulation process and source parameter
studies. It is already established that the study of two physical processes,
first, the seismic sources and second, propagation of the waves, is essential
for seismic-hazard mapping, attenuation being one of the properties paying
importance to the latter. Here, a computational tool entitled CodaQback is
presented. Based on back scattering model, this versatile software is equipped
with user friendly graphical user interface. It also allows quick picking of
phases for computing coda attenuation parameter. All outputs after each
execution step in CodaQback are efficiently exported stepwise into a separate
folder in excel and text formats. This CodaQback is checked in real data
analysis and there is found to be good matching of computed values with already
established ones. It is envisioned that this package will enable user to derive
quick and reliable estimation of coda attenuation parameter irrespective of
geological and geo-morphological units.


  We consider the reconstruction of the CMB lensing potential and its power
spectrum of the full sphere in presence of sky-cuts due to point sources and
Galactic contaminations. Those two effects are treated separately. Small
regions contaminated by point sources are filled in using Gaussian constrained
realizations. The Galactic plane is simply masked using an apodized mask before
lensing reconstruction. This algorithm recovers the power spectrum of the
lensing potential with no significant bias.


  A unific helical field as geometric structure in an internal space is
proposed which has the ability to serve attributes inherent to point particles.
Transition between our observational space and the warped infinitesimal space
is considered in an operational fashion. It is seen, that rotational eigenvalue
equation satisfied by the vector field equivalent to Gromeka-Beltrami flow
familiar to plasma astrophysics provides a spatio-unifier that sustains complex
orthogonal coupling between rotational, internal coordinate space and angular
momentum space. Self-consistent normalization of the rotational coordinate
owing to the unifier is compared to renormalization of quantum electrodynamics.
A numerical value comparable to the electromagnetic coupling constant in the
nonrelativistic limit is derived from theoretical analysis involving the
rotational eigenvalue that charged leptons should internally refer to. It is
found that chiral asymmetry of the helical eigenflows can be reflected in
electroweak symmetry breaking. This study might provide a key to settle
geometrical problem of preceding theories accommodated by extra-dimensions of
space.


  We explore an alternative way of finding the link between a PT non-Hermitian
Hamiltonian and a Hermitian one. Based on the analysis of the scattering
problem for an imaginary potential and its time reversal process, it is shown
that any real-energy eigenstate of a PT tight-binding lattice with on-site
imaginary potentials shares the same wave function with a resonant transmission
state of the corresponding Hermitian lattice embedded in a chain. It indicates
that the PT eigenstate of a PT non-Hermitian Hamiltonian has connection to the
resonance transmission state of the extended Hermitian Hamiltonian.


  We consider the calculation of scattering amplitudes in field theories dual
to Lifshitz spacetimes. These amplitudes provide an interesting probe of the IR
structure of the field theory; our aim is to use them to explore the observable
consequences of the singularity in the spacetime. We assume the amplitudes can
be related by T-duality to a Wilson loop, as in the AdS case, and determine the
bulk minimal surfaces for the simplest cusp Wilson loop. We use this to
determine the leading IR singularity in the amplitude. We find there is a
stronger IR singularity for z >1 than for z=1, with a coefficient which
vanishes as z goes to 1.


  In this paper we assess the relationship of the population of Active Galactic
Nuclei (AGN) selected by hard X-rays to the traditional population of AGN with
strong optical emission lines. First, we study the emission-line properties of
a new hard X-ray selected sample of 47 local AGN (classified optically as both
Type 1 and Type 2 AGN). We find that the hard X- ray (3-20 keV) and
[OIII]$\lambda$5007 optical emission-line luminosities are well-correlated over
a range of about four orders-of-magnitude in luminosity (mean luminosity ratio
2.15 dex with a standard deviation of $\sigma$ = 0.51 dex). Second, we study
the hard X-ray properties of a sample of 55 local AGN selected from the
literature on the basis of the flux in the [OIII] line. The correlation between
the hard X-ray (2-10 keV) and [OIII] luminosity for the Type 1 AGN is
consistent with what is seen in the hard X-ray selected sample. However, the
Type 2 AGN have a much larger range in the luminosity ratio, and many are very
weak in hard X-rays (as expected for heavily absorbed AGN). We then compare the
hard X-ray (3-20 keV) and [OIII] luminosity functions of AGN in the local
universe. These have similar faint-end slopes with a luminosity ratio of 1.60
dex (0.55 dex smaller than the mean value for individual hard X-ray selected
AGN). We conclude that at low redshift, selection by narrow optical emission-
lines will recover most AGN selected by hard X-rays (with the exception of BL
Lac objects). However, selection by hard X-rays misses a significant fraction
of the local AGN population with strong emission lines.


We discuss some basic properties of the Sibony functions and pseudometrics.


  Most client hosts are equipped with multiple network interfaces (e.g., WiFi
and cellular networks). Simultaneous access of multiple interfaces can
significantly improve the users' quality of experience (QoE) in video
streaming. An intuitive approach to achieve it is to use Multi-path TCP
(MPTCP). However, the deployment of MPTCP, especially with link preference,
requires OS kernel update at both the client and server side, and a vast amount
of commercial content providers do not support MPTCP. Thus, in this paper, we
realize a multi-path video streaming algorithm in the application layer
instead, by considering Scalable Video Coding (SVC), where each layer of every
chunk can be fetched from only one of the orthogonal paths. We formulate the
quality decisions of video chunks subject to the available bandwidth of the
different paths, chunk deadlines, and link preferences as an optimization
problem. The objective is to to optimize a QoE metric that maintains a tradeoff
between maximizing the playback rate of every chunk and ensuring fairness among
chunks. The QoE is a weighted some of the following metrics: skip/stall
duration, average playback rate, and quality switching rate. However, the
weights are chosen such that pushing more chunks to the same quality level is
more preferable over any other choice. Even though the formulation is a
non-convex discrete optimization, we show that the problem can be solved
optimally with a polynomial complexity in some special cases. We further
propose an online algorithm where several challenges including bandwidth
prediction errors, are addressed. Extensive emulated experiments in a real
testbed with real traces of public dataset reveal the robustness of our scheme
and demonstrate its significant performance improvement compared to other
multi-path algorithms.


  The MAJORANA DEMONSTRATOR is a neutrinoless double-beta decay
($0\nu\beta\beta$) experiment containing $\sim$30 kg of p-type point contact
germanium detectors enriched to 88% in 76Ge and $\sim$14 kg of natural
germanium detectors. The detectors are housed in two electroformed copper
cryostats and surrounded by a graded passive shield with active muon veto. An
extensive radioassay campaign was performed prior to installation to insure the
use of ultra-clean materials. The DEMONSTRATOR achieved one of the lowest
background rates in the region of the $0\nu\beta\beta$ Q-value, 15.7 $\pm$ 1.4
cts/(FWHM t y) from the low-background configuration spanning most of the 64.5
kg-yr active exposure. Nevertheless this background rate is a factor of five
higher than the projected background rate. This discrepancy arises from an
excess of events from the 232Th decay chain. Background model fits aim to
understand this deviation from assay-based projections, potentially determine
the source(s) of observed backgrounds, and allow a precision measurement of the
two-neutrino double-beta decay half-life. The fits agree with earlier
simulation studies, which indicate the origin of the 232Th excess is not from a
near-detector component and have informed design decisions for the
next-generation LEGEND experiment. Recent findings have narrowed the suspected
locations for the excess activity, motivating a final simulation and assay
campaign to complete the background model.


  Intrinsic dimensionality (ID) is one of the most fundamental characteristics
of multi-dimensional data point clouds. Knowing ID is crucial to choose the
appropriate machine learning approach as well as to understand its behavior and
validate it. ID can be computed globally for the whole data point distribution,
or computed locally in different regions of the data space. In this paper, we
introduce new local estimators of ID based on linear separability of
multi-dimensional data point clouds, which is one of the manifestations of
concentration of measure. We empirically study the properties of these
estimators and compare them with other recently introduced ID estimators
exploiting various effects of measure concentration. Observed differences
between estimators can be used to anticipate their behaviour in practical
applications.


  We show that provided $\log^{50} n/n \leq p \leq 1 - n^{-1/4}\log^9 n$ we can
with high probability find a collection of $\lfloor \delta(G)/2 \rfloor$
edge-disjoint Hamilton cycles in $G \sim G_{n, p}$, plus an additional
edge-disjoint matching of size $\lfloor n/2 \rfloor$ if $\delta(G)$ is odd.
This confirms, for the above range of $p$, a conjecture of Frieze and
Krivelevich.


  By using the sieve method of combinatorics, we study $k$-error linear
complexity distribution of $2^n$-periodic binary sequences based on Games-Chan
algorithm. For $k=4,5$, the complete counting functions on the $k$-error linear
complexity of $2^n$-periodic balanced binary sequences (with linear complexity
less than $2^n$) are presented. As a consequence of the result, the complete
counting functions on the 4-error linear complexity of $2^n$-periodic binary
sequences (with linear complexity $2^n$ or less than $2^n$) are obvious.
Generally, the complete counting functions on the $k$-error linear complexity
of $2^n$-periodic binary sequences can be obtained with a similar approach.


  Recent decades have witnessed online social media being a big-data window for
quantificationally testifying conventional social theories and exploring much
detailed human behavioral patterns. In this paper, by tracing the emoticon use
in Weibo, a group of hidden "ambivalent users" are disclosed for frequently
posting ambivalent tweets containing both positive and negative emotions.
Further investigation reveals that this ambivalent expression could be a novel
indicator of many unusual social behaviors. For instance, ambivalent users with
the female as the majority like to make a sound in midnights or at weekends.
They mention their close friends frequently in ambivalent tweets, which attract
more replies and thus serve as a more private communication way. Ambivalent
users also respond differently to public affairs from others and demonstrate
more interests in entertainment and sports events. Moreover, the sentiment
shift of words adopted in ambivalent tweets is more evident than usual and
exhibits a clear "negative to positive" pattern. The above observations, though
being promiscuous seemingly, actually point to the self regulation of negative
mood in Weibo, which could find its base from the emotion management theories
in sociology but makes an interesting extension to the online environment.
Finally, as an interesting corollary, ambivalent users are found connected with
compulsive buyers and turn out to be perfect targets for online marketing.


  The population of close-in exoplanets features a desert of hot Neptunes whose
origin is uncertain. These planets may have lost their atmosphere, eroding into
mini-Neptunes and super-Earths. Direct observations of evaporating atmospheres
are essential to derive mass-loss estimates and constrain this scenario. The
metastable 1083.3nm HeI triplet represents a powerful diagnostic of atmospheric
evaporation since it traces the hot gas in extended exoplanet atmospheres, is
observable from the ground, and is weakly affected by interstellar medium
absorption. We conducted a uniform HeI transmission spectroscopy survey,
focusing on 9 planets located at the edges of the Neptunian desert, aiming to
gain insights into the role of photo-evaporation in its formation. We observed
one transit per planet using the high-resolution, near-infrared spectrograph
GIANO-B on the Telescopio Nazionale Galileo. We focused our analysis on the HeI
triplet by computing high-resolution transmission spectra. We then employed the
p-winds model to interpret the observed transmission spectra. We found no sign
of planetary absorption in the HeI triplet in any of the investigated targets.
We thus provided 3sigma upper-limit estimations on the thermosphere absorption,
temperature, and mass loss, and combined them with past measurements to search
for correlations with parameters thought to be drivers in the formation of the
HeI triplet. Our results strengthen the importance of performing homogeneous
surveys and analyses to bring clarification in the HeI detection and hence in
the Neptunian desert origin. Our findings corroborate the literature
expectations that the HeI absorption signal correlates with the stellar mass
and the received XUV flux. However, these trends seem to disappear in terms of
mass-loss rates; further studies are essential to shed light on this aspect and
to understand better the photo-evaporation process.


  While 2D generative adversarial networks have enabled high-resolution image
synthesis, they largely lack an understanding of the 3D world and the image
formation process. Thus, they do not provide precise control over camera
viewpoint or object pose. To address this problem, several recent approaches
leverage intermediate voxel-based representations in combination with
differentiable rendering. However, existing methods either produce low image
resolution or fall short in disentangling camera and scene properties, e.g.,
the object identity may vary with the viewpoint. In this paper, we propose a
generative model for radiance fields which have recently proven successful for
novel view synthesis of a single scene. In contrast to voxel-based
representations, radiance fields are not confined to a coarse discretization of
the 3D space, yet allow for disentangling camera and scene properties while
degrading gracefully in the presence of reconstruction ambiguity. By
introducing a multi-scale patch-based discriminator, we demonstrate synthesis
of high-resolution images while training our model from unposed 2D images
alone. We systematically analyze our approach on several challenging synthetic
and real-world datasets. Our experiments reveal that radiance fields are a
powerful representation for generative image synthesis, leading to 3D
consistent models that render with high fidelity.


  The Brownian motion of a charged test particle caused by quantum
electromagnetic vacuum fluctuations between two perfectly conducting plates is
examined and the mean squared fluctuations in the velocity and position of the
test particle are calculated. Our results show that the Brownian motion in the
direction normal to the plates is reinforced in comparison to that in the
single-plate case. The effective temperature associated with this normal
Brownian motion could be three times as large as that in the single-plate case.
However, the negative dispersions for the velocity and position in the
longitudinal directions, which could be interpreted as reducing the quantum
uncertainties of the particle, acquire positive corrections due to the presence
of the second plate, and are thus weakened.


  We propose a method for broadband long-wavelength photodetection using the
nonlinear Hall effect in non-centrosymmetric quantum materials. The inherently
quadratic relation between transverse current and input voltage at zero
magnetic field is used to rectify the incident terahertz or infrared electric
field into a direct current, without invoking any diode. Our photodetector
operates at zero external bias with fast response speed and has zero threshold
voltage. Remarkably, the intrinsic current responsivity due to Berry curvature
mechanism is a material property independent of the incident frequency or the
scattering rate, which can be evaluated from first-principles electronic
structure calculations. We identify the Weyl semimetal NbP for terahertz
photodection with large current responsivity reaching $\sim 1$A/W without
external bias.


  In the field of spin-controlled semiconductor lasers, massive effort has been
focused upon materials with long spin relaxation times (~ns). In contrast, we
demonstrate room-temperature spin-polarized ultrafast pulsed lasing in InGaAs
quantum wells (~10 ps) embedded within a GaAs microcavity. The microcavity
studied here is similar to vertical-cavity surface-emitting lasers (VCSEL) used
in optical communication. Unlike a VCSEL, the present polariton laser has
nonlinear output and energy shifts owing to the mixing of the free-carrier
polarization and cavity light field. At room temperature, we observe features
resembling those in exciton-polariton condensates at cryogenic temperatures,
including the spontaneous build-up of spatial coherence, macroscopic
occupation, and spin polarization. Our results should stimulate activities to
exploit spin-orbit interaction and many-body effects for fundamental studies of
quantum light-matter fluids and developments of spin-dependent optoelectronic
devices.


  We investigate the problem of existence and uniqueness of ground states at
fixed mass for two families of focusing nonlinear Schr\"odinger equations on
the line.
  The first family consists of NLS with power nonlinearities concentrated at a
point. For such model, we prove existence and uniqueness of ground states at
every mass when the nonlinearity power is $L^2-$subcritical and at a threshold
value of the mass in the $L^2-$critical regime.
  The second family is obtained by adding a standard power nonlinearity to the
previous setting. In this case, we prove existence and uniqueness at every mass
in the doubly subcritical case, namely when both the powers related to the
pointwise and the standard nonlinearity are subcritical. If only one power is
critical, then existence and uniqueness hold only at masses lower than the
critical mass associated to the critical nonlinearity. Finally, in the doubly
critical case ground states exist only at critical mass, whose value results
from a non--trivial interplay between the two nonlinearities.


  Model-based eye tracking has been a dominant approach for eye gaze tracking
because of its ability to generalize to different subjects, without the need of
any training data and eye gaze annotations. Model-based eye tracking, however,
is susceptible to eye feature detection errors, in particular for eye tracking
in the wild. To address this issue, we propose a Bayesian framework for
model-based eye tracking. The proposed system consists of a cascade-Bayesian
Convolutional Neural Network (c-BCNN) to capture the probabilistic
relationships between eye appearance and its landmarks, and a geometric eye
model to estimate eye gaze from the eye landmarks. Given a testing eye image,
the Bayesian framework can generate, through Bayesian inference, the eye gaze
distribution without explicit landmark detection and model training, based on
which it not only estimates the most likely eye gaze but also its uncertainty.
Furthermore, with Bayesian inference instead of point-based inference, our
model can not only generalize better to different sub-jects, head poses, and
environments but also is robust to image noise and landmark detection errors.
Finally, with the estimated gaze uncertainty, we can construct a cascade
architecture that allows us to progressively improve gaze estimation accuracy.
Compared to state-of-the-art model-based and learning-based methods, the
proposed Bayesian framework demonstrates significant improvement in
generalization capability across several benchmark datasets and in accuracy and
robustness under challenging real-world conditions.


  The Harish-Chandra--Howe local character expansion expresses the characters
of reductive, $p$-adic groups in terms of Fourier transforms of nilpotent
orbital integrals on their Lie algebras, and Murnaghan--Kirillov theory
expresses many characters of reductive, $p$-adic groups in terms of Fourier
transforms of semisimple orbital integrals (also on their Lie algebras). In
many cases, the evaluation of these Fourier transforms seems intractable; but,
for $\operatorname{SL}_2$, the nilpotent orbital integrals have already been
computed. In this paper, we use a variant of Huntsinger's integral formula, and
the theory of $p$-adic special functions, to compute semisimple orbital
integrals.


  Systems based on bag-of-words models from image features collected at maxima
of sparse interest point operators have been used successfully for both
computer visual object and action recognition tasks. While the sparse,
interest-point based approach to recognition is not inconsistent with visual
processing in biological systems that operate in `saccade and fixate' regimes,
the methodology and emphasis in the human and the computer vision communities
remains sharply distinct. Here, we make three contributions aiming to bridge
this gap. First, we complement existing state-of-the art large scale dynamic
computer vision annotated datasets like Hollywood-2 and UCF Sports with human
eye movements collected under the ecological constraints of the visual action
recognition task. To our knowledge these are the first large human eye tracking
datasets to be collected and made publicly available for video,
vision.imar.ro/eyetracking (497,107 frames, each viewed by 16 subjects), unique
in terms of their (a) large scale and computer vision relevance, (b) dynamic,
video stimuli, (c) task control, as opposed to free-viewing. Second, we
introduce novel sequential consistency and alignment measures, which underline
the remarkable stability of patterns of visual search among subjects. Third, we
leverage the significant amount of collected data in order to pursue studies
and build automatic, end-to-end trainable computer vision systems based on
human eye movements. Our studies not only shed light on the differences between
computer vision spatio-temporal interest point image sampling strategies and
the human fixations, as well as their impact for visual recognition
performance, but also demonstrate that human fixations can be accurately
predicted, and when used in an end-to-end automatic system, leveraging some of
the advanced computer vision practice, can lead to state of the art results.


  X-shooter and ISIS WHT spectra of the starforming galaxy PHL 293B also known
as A2228-00 and SDSS J223036.79-000636.9 are presented in this paper.
  We find broad (FWHM = 1000km/s) and very broad (FWZI = 4000km/s) components
in the Balmer lines, narrow absorption components in the Balmer series
blueshifted by 800km/s, previously undetected FeII multiplet (42) absorptions
also blueshifted by 800km/s, IR CaII triplet stellar absorptions consistent
with [Fe/H] < -2.0 and no broad components or blushifted absorptions in the HeI
lines. Based on historical records, we found no optical variability at the 5
sigma level of 0.02 mag between 2005 and 2013 and no optical variability at the
level of 0.1mag for the past 24 years.
  The lack of variability rules out transient phenomena like luminous blue
variables or SN IIn as the origin of the blue shifted absorptions of HI and
FeII. The evidence points to either a young and dense expanding supershell or a
stationary cooling wind, in both cases driven by the young cluster wind.


  Vlahos et al., Ref. 1, NPJ Clean water. 4, 50 (2021) have reported the
presence of pesticide contamination above safe levels in a "single time-point
analysis" of well water in a region in Sri Lanka where chronic kidney disease
of unknown etiology (CKDu) is endemic. They conclude "that agrochemical use in
paddy and other agricultural practices ... of the Green Revolution in Sri Lanka
may now be contributing to ill health, rapid progression of disease, and
mortality". The authors also propose "reducing ... agrochemical contaminants in
Sri Lanka and other tropical countries to reduce ... CKDu". These conclusions,
based on what they call a "single time-point analysis", tantamount to an
identification of the etiology of CKDu are unsupported by the evidence
presented by Vlahos et al. They do not satisfy, say, even the simplest of
Bradford-Hill criteria for causation. In particular, (i) similar but
non-persistent pesticide excesses have been detected sporadically in most parts
of the country including where there is no CKDu; (ii) the pesticides reported
in (1) cause both hepatotoxicity and nephrotoxicity; the latter with glomerular
damage while CKDu is associated with tubulo-interstitial damage where no
hepatotoxic symptoms have been reported; (iii) the pesticides detected have
short half-lives and are used over short periods during farming; so the one
time-point analysis is inadequate and misleading; (iv) farming communities that
use pesticides in the same way but remain essentially without CKDu are found to
exist adjacent to communities with CKDu; (v) the CKDu prevalence seems to
correlate with local geomorphology but without correlation to agriculture which
is practiced in most parts of the country. .


  The aim of this paper is to show that between standard operator algebras
every bijective map with a certain multiplicativity property related to Jordan
triple isomorphisms of associative rings is automatically additive.


  Single crystal of YCoGa5 has been grown via Ga self-flux. In this paper, we
report the single crystal growth, crystallographic parameters, resistivity,
heat capacity, and band structure results of YCoGa5. YCoGa5 accommodates the
HoCoGa5 type structure (space group P4/mmm (No. 123), Z = 1, a = 4.2131(6) A, c
= 6.7929(13) A, which is isostructural to the extensively studied heavy fermion
superconductor system CeMIn5 (M = Co, Rh, Ir) and the unconventional
superconductor PuCoGa5 with Tc = 18.5 K. No superconductivity is observed down
to 1.75 K. Band structure calculation results show that its band at the Fermi
level is mainly composed of Co-3d and Ga-4p electrons states, which explains
its similarity of physical properties to YbCoGa5 and LuCoGa5.


  We study the functor $\operatorname{Def}_E^k$ of infinitesimal deformations
of a locally free sheaf $E$ of $\mathcal{O}_X$-modules on a smooth variety $X$,
such that at least $k$ independent sections lift to the deformed sheaf, where
$h^0(E) \geq k$. We deduce some information on the $k$-th Brill-Noether locus
of $E$, such as the description of the tangent cone at some singular points, of
the tangent space at some smooth ones and some links between the smoothness of
the functor $\operatorname{Def}_E^k$ and the smoothness of some well know
deformations functors and their associated moduli spaces. As a tool for the
investigation of $\operatorname{Def}_E^k$, we study infinitesimal deformations
of the pairs $(E,U)$, where $U$ is a linear subspace of sections of $E$. We
generalise to the case where $E$ has any rank and $X$ any dimension many
classical results concerning the moduli space of coherent systems, like the
description of its tangent space and the link between its smoothness and the
injectivity of the Petri map.


  Recent practical approaches for the use of current generation noisy quantum
devices in the simulation of quantum many-body problems have been dominated by
the use of a variational quantum eigensolver (VQE). These coupled
quantum-classical algorithms leverage the ability to perform many repeated
measurements to avoid the currently prohibitive gate depths often required for
exact quantum algorithms, with the restriction of a parameterized circuit to
describe the states of interest. In this work, we show how the calculation of
zero-temperature dynamic correlation functions defining the linear response
characteristics of quantum systems can also be recast into a modified VQE
algorithm, which can be incorporated into the current variational quantum
infrastructure. This allows for these important physical expectation values
describing the dynamics of the system to be directly converged on the frequency
axis, and they approach exactness over all frequencies as the flexibility of
the parameterization increases. The frequency resolution hence does not
explicitly scale with gate depth, which is approximately twice as deep as a
ground state VQE. We apply the method to compute the single-particle Green's
function of ab initio dihydrogen and lithium hydride molecules, and demonstrate
the use of a practical active space embedding approach to extend to larger
systems. While currently limited by the fidelity of two-qubit gates, whose
number is increased compared to the ground state algorithm on current devices,
we believe the approach shows potential for the extraction of frequency
dynamics of correlated systems on near-term quantum processors.


  In this paper we propose an enhanced soft cancellation (SCAN) decoder for
polar codes based on decoding stages permutation. The proposed soft
cancellation list (SCANL) decoder runs $L$ independent SCAN decoders, each one
relying on a different permuted factor graph. The estimated bits are selected
among the $L$ candidates through a dedicated metric provided by the decoders.
Furthermore, we introduce an early-termination scheme reducing decoding latency
without affecting error correction performance. We investigate the
error-correction performance of the proposed scheme under various combinations
of number of iterations used, permutation set and early-termination condition.
Simulation results show that the proposed SCANL provides similar results when
compared with belief propagation list, while having a smaller complexity.
Moreover, for large list sizes, SCANL outperforms non-CRC aided successive
cancellation list decoding.


  Weakly constrained double field theory, in the sense of Hull and Zwiebach,
captures the subsector of string theory on toroidal backgrounds that includes
gravity, $B$-field and dilaton together with all of their massive Kaluza-Klein
and winding modes, which are encoded in doubled coordinates subject to the
`weak constraint'. Due to the complications of the weak constraint, this theory
was only known to cubic order. Here we construct the quartic interactions for
the case that all dimensions are toroidal and doubled. Starting from the
kinematic $C_{\infty}$ algebra ${\cal K}$ of pure Yang-Mills theory and its
hidden Lie-type algebra, we construct the $L_{\infty}$ algebra of weakly
constrained double field theory on a subspace of the `double copied' tensor
product space ${\cal K}\otimes\bar{\cal K}$, by doing homotopy transfer to the
weakly constrained subspace and performing a non-local shift that is
well-defined on the torus. We test the resulting three-brackets, and establish
their uniqueness up to cohomologically trivial terms, by verifying the Jacobi
identities up to homotopy for the gauge sector.


  The asymptotic expansion of the massive scalar field propagator on a
n-dimensional lattice is derived. The method used is based on the evaluation of
the asymptotic expansion of the modified Bessel function $I_{\nu}(\nu^{2}
\beta)$ as the order $\nu$ grows to infinity.


  Artificial intelligence (AI) has seen a tremendous surge in capabilities
thanks to the use of foundation models trained on internet-scale data. On the
flip side, the uncurated nature of internet-scale data also poses significant
privacy and legal risks, as they often contain personal information or
copyrighted material that should not be trained on without permission. In this
work, we propose as a mitigation measure a recipe to train foundation vision
models with differential privacy (DP) guarantee. We identify masked
autoencoders as a suitable learning algorithm that aligns well with DP-SGD, and
train ViP -- a Vision transformer with differential Privacy -- under a strict
privacy budget of $\epsilon=8$ on the LAION400M dataset. We evaluate the
quality of representation learned by ViP using standard downstream vision
tasks; in particular, ViP achieves a (non-private) linear probing accuracy of
$55.7\%$ on ImageNet, comparable to that of end-to-end trained AlexNet (trained
and evaluated on ImageNet). Our result suggests that scaling to internet-scale
data can be practical for private learning. Code is available at
\url{https://github.com/facebookresearch/ViP-MAE}.


  The Fano resonance in quantum dots embedded in Aharonov-Bohm rings is
examined theoretically, using two models of non-interacting electrons. The
first model yields an analytical expression for the conductance G. G is written
in an extended Fano form with a complex parameter. The shape of the resonance
can be asymmetric or symmetric, depending on the magnetic flux enclosed in the
ring. The "phase" of the resonance is changed continuously with increasing the
flux in two-terminal situations. These are in accordance with recent
experimental results. In the second model, we consider the dephasing effect on
the Fano resonance by numerical calculations.


  We present a structured overview of adaptation algorithms for neural
network-based speech recognition, considering both hybrid hidden Markov model /
neural network systems and end-to-end neural network systems, with a focus on
speaker adaptation, domain adaptation, and accent adaptation. The overview
characterizes adaptation algorithms as based on embeddings, model parameter
adaptation, or data augmentation. We present a meta-analysis of the performance
of speech recognition adaptation algorithms, based on relative error rate
reductions as reported in the literature.


  75 years after the term "entanglement" was coined to a peculiar feature
inherent to quantum systems, the connection between quantum and classical
mechanics remains an open problem. Drawing on recent results obtained in
semiclassical systems, we discuss here the fate of entanglement in a closed
system as Planck's constant becomes vanishingly small. In that case the
generation of entanglement in a quantum system is perfectly reproduced by
properly defined correlations of the corresponding classical system. We
speculate on what these results could imply regarding the status of
entanglement and of the ensuing quantum correlations.


  The eigenvalues of the Dirac operator at finite volume encode whether or not
chiral symmetry is spontaneously broken in a massless theory. We apply this
framework in a particular BSM context, namely SU(3) gauge theory with N_f=2
massless flavors in the 2-index symmetric (sextet) representation. Our first
results are at a single lattice spacing. We find that both the density of
near-zero eigenvalues and the renormalization group invariant mode number
indicate spontaneous symmetry breaking. Quantitatively, there is a discrepancy
between the determination of the fermion condensate in the chiral limit via the
eigenvalue spectrum and the determinations from direct measurements of the
chiral condensate and the GMOR relation. We comment on possible explanations of
this discrepancy and further refinements of this study.


  Multilingual Pretrained Language Models (MPLMs) have shown their strong
multilinguality in recent empirical cross-lingual transfer studies. In this
paper, we propose the Prompts Augmented by Retrieval Crosslingually (PARC)
pipeline to improve the zero-shot performance on low-resource languages (LRLs)
by augmenting the context with semantically similar sentences retrieved from a
high-resource language (HRL) as prompts. PARC improves the zero-shot
performance on three downstream tasks (binary sentiment classification, topic
categorization and natural language inference) with multilingual parallel test
sets across 10 LRLs covering 6 language families in both unlabeled settings
(+5.1%) and labeled settings (+16.3%). PARC-labeled also outperforms the
finetuning baseline by 3.7%. We find a significant positive correlation between
cross-lingual transfer performance on one side, and the similarity between the
high- and low-resource languages as well as the amount of low-resource
pretraining data on the other side. A robustness analysis suggests that PARC
has the potential to achieve even stronger performance with more powerful
MPLMs.


  Compartmental epidemic models have been widely used for predicting the course
of epidemics, from estimating the basic reproduction number to guiding
intervention policies. Studies commonly acknowledge these models' assumptions
but less often justify their validity in the specific context in which they are
being used. Our purpose is not to argue for specific alternatives or
modifications to compartmental models, but rather to show how assumptions can
constrain model outcomes to a narrow portion of the wide landscape of potential
epidemic behaviors. This concrete examination of well-known models also serves
to illustrate general principles of modeling that can be applied in other
contexts.


  Respondent-driven sampling (RDS) is a link-tracing procedure for surveying
hidden or hard-to-reach populations in which subjects recruit other subjects
via their social network. There is significant research interest in detecting
clustering or dependence of epidemiological traits in networks, but researchers
disagree about whether data from RDS studies can reveal it. Two distinct
mechanisms account for dependence in traits of recruiters and recruitees in an
RDS study: homophily, the tendency for individuals to share social ties with
others exhibiting similar characteristics, and preferential recruitment, in
which recruiters do not recruit uniformly at random from their available
alters. The different effects of network homophily and preferential recruitment
in RDS studies have been a source of confusion in methodological research on
RDS, and in empirical studies of the social context of health risk in hidden
populations. In this paper, we give rigorous definitions of homophily and
preferential recruitment and show that neither can be measured precisely in
general RDS studies. We derive nonparametric identification regions for
homophily and preferential recruitment and show that these parameters are not
point identified unless the network takes a degenerate form. The results
indicate that claims of homophily or recruitment bias measured from empirical
RDS studies may not be credible. We apply our identification results to a study
involving both a network census and RDS on a population of injection drug users
in Hartford, CT.


  We present the differential rates for exclusive $\Bbar\to X \ell_1 \ell_2$,
where $\ell_1$ is a charged massless lepton and $\ell_2$ is a charged or
neutral massless lepton, and $X$ is a mesonic system up to spin 2. The cases of
interest are semileptonic (SL) $\Bbar\to \xcu\ellm \barnuell$ decays, and
$\Bbar \to X_s \ellm \ellp$ where the the di-lepton can be $c \bar{c}$
resonances or non-resonant electroweak penguins (EWP). We consider helicity
amplitudes having non-zero relative phases that can be potential new sources
for CP-violation. Our motivations for these additional phases include a complex
right-handed admixture in the hadronic weak charged current for the SL decays
and complex Wilson coefficients in the effective Hamiltonians for the EWP
decays. We demonstrate the efficacy of a novel technique of projecting out the
individual angular moments in the full rate expression in a model-independent
fashion. Our work is geared towards ongoing data analyses at $\babar$ and LHCb.


  The paper studies the Karoubi envelope of a one-dimensional topological
theory with defects and inner endpoints, defined over a field. It turns out
that the Karoubi envelope is determined by a symmetric Frobenius algebra K
associated to the theory. The Karoubi envelope is then equivalent to the
quotient of the Frobenius-Brauer category of K modulo the ideal of negligible
morphisms. Symmetric Frobenius algebras, such as K, describe two-dimensional
TQFTs for the category of thin flat surfaces, and elements of the algebra can
be turned into defects on the side boundaries of these surfaces. We also
explain how to couple K to the universal construction restricted to closed
surfaces to define a topological theory of open-closed two-dimensional
cobordisms which is usually not an open-closed 2D TQFT.


  Quantum teleportation is studied in noninertial frame, for fermionic case,
when Alice and Bob share a general nonclassical correlated state. In
noninertial frames two fidelities of teleportation are given. It is found that
the average fidelity of teleportation from a separable and nonclassical
correlated state is increasing with the amount of nonclassical correlation of
the state. However, for any particular nonclassical correlated state, the
fidelity of teleportation decreases by increasing the acceleration.


  Supersymmetric models with extended group structure beyond the standard model
are revisited in the framework of general gauge mediation. Sum rules for
sfermion masses are shown to depend genuinely on the group structure, which can
serve as important probes for specific models. The left-right model and models
with extra U(1) are worked out for illustrations. If the couplings of extra
gauge groups are small, supersymmetric hidden valleys of the scale 10-100 GeV
can be naturally constructed in companion of a TeV-scale supersymmetric visible
sector.


  GARR optical network is composed of two separate optical network domains at
the national level. With the aim to integrate them we implemented alien
wavelengths to deliver high-performance services improving the overall network
efficiency. This paper describes the path followed to deploy the alien
wavelengths in the GARR operational infrastructure from the planning phase to
the production network.


  Inflationary solutions are constructed in a specific five-dimensional model
with boundaries motivated by heterotic M-theory. We concentrate on the case
where the vacuum energy is provided by potentials on those boundaries. It is
pointed out that the presence of such potentials necessarily excites bulk
Kaluza-Klein modes. We distinguish a linear and a non-linear regime for those
modes. In the linear regime, inflation can be discussed in an effective
four-dimensional theory in the conventional way. We lift a four-dimensional
inflating solution up to five dimensions where it represents an inflating
domain wall pair. This shows explicitly the inhomogeneity in the fifth
dimension. We also demonstrate the existence of inflating solutions with
unconventional properties in the non-linear regime. Specifically, we find
solutions with and without an horizon between the two boundaries. These
solutions have certain problems associated with the stability of the additional
dimension and the persistence of initial excitations of the Kaluza-Klein modes.


  I present here a collection of formulas inspired from the Ramanujan
Notebooks. These formulas were found using an experimental method based on
three widely available symbolic computation programs: PARI-Gp, Maple and
Mathematica. A new formula is presented for Zeta(5).


  The mass matrices of the charged leptons and neutrinos, previously derived in
a minimal S_3-invariant extension of the Standard Model, were reparametrized in
terms of their eigenvalues. We obtained explicit, analytical expressions for
all entries in the neutrino mixing matrix, V_PMNS, the neutrino mixing angles
and the Majorana phases as functions of the masses of charged leptons and
neutrinos in excellent agreement with the latest experimental values. The
resulting V_PMNS matrix is very close to the tri-bimaximal form of the neutrino
mixing matrix. We also derived explicit analytical expressions for the matrices
of the Yukawa couplings and computed the branching ratios of some selected
flavour changing neutral current processes as functions of the masses of the
charged leptons and the neutral Higgs bosons. We find that the S_3 x Z_2
flavour symmetry and the strong mass hierarchy of the charged leptons strongly
suppress the FCNC processes in the leptonic sector well below the present
experimental upper bounds by many orders of magnitude.


  Mobile multi-robot teams deployed for monitoring or search-and-rescue
missions in urban disaster areas can greatly improve the quality of vital data
collected on-site. Analysis of such data can identify hazards and save lives.
Unfortunately, such real deployments at scale are cost prohibitive and robot
failures lead to data loss. Moreover, scaled-down deployments do not capture
significant levels of interaction and communication complexity. To tackle this
problem, we propose novel mobility and failure generation frameworks that allow
realistic simulations of mobile robot networks for large scale disaster
scenarios. Furthermore, since data replication techniques can improve the
survivability of data collected during the operation, we propose an adaptive,
scalable data replication technique that achieves high data survivability with
low overhead. Our technique considers the anticipated robot failures and robot
heterogeneity to decide how aggressively to replicate data. In addition, it
considers survivability priorities, with some data requiring more effort to be
saved than others. Using our novel simulation generation frameworks, we compare
our adaptive technique with flooding and broadcast-based replication techniques
and show that for failure rates of up to 60% it ensures better data
survivability with lower communication costs.


  In previous work we described when a single geometric representation, valued
in a linear algebraic group, of the Galois group of a number field lifts
through a central torus quotient to a geometric representation. In this paper
we prove a much sharper result for systems of l-adic representations, such as
the l-adic realizations of a motive, having common "good reduction" properties.
Namely, such systems admit geometric lifts with good reduction outside a common
finite set of primes. The method yields new proofs of theorems of Tate (the
original result on lifting projective representations over number fields) and
Wintenberger (an analogue of our main result in the setting of lifting through
a central isogeny).


  Bursting oscillations are commonly seen as a mechanism for information coding
in neuroscience and have also been observed in many physical, biochemical, and
chemical systems. This study focuses on the computational investigation of
mixed-mode bursting oscillations (MMBOs) generated by a simple two-dimensional
integrate-and-fire-or-burst (IFB) model. We demonstrate a new paradigm for the
generation of MMBOs, where birhythmicity and noise are the key components. In
the absence of noise, the proposed model exhibits birhythmicity of two
independent bursting patterns, bursts of two spikes and bursts of three spikes,
depending on the initial condition of the model. Noise induces the random
transitions between two bursting states which leads to MMBOs, and the
transition rate increases with the noise intensity. Our results provide a
systematic view of the roles of noise and initial condition: the bursting
dynamics produced by the proposed model heavily rely on the initial conditions
when noise is weak; while for intermediate and strong noise, the burst dynamics
are independent of the initial condition.


  In quantum theory its action is usually taken to be real, but we can consider
another theory whose action is complex. In addition, in the Feynman path
integral, the time integration is usually performed over the period between the
initial time $T_A$ and some specific time, say, the present time $t$. Besides
such a future-not-included theory, we can consider the future-included theory,
in which not only the past state $| A(T_A) \rangle$ at the initial time $T_A$
but also the future state $| B(T_B) \rangle$ at the final time $T_B$ is given
at first, and the time integration is performed over the whole period from the
past to the future. Thus quantum theory can be classified into four types,
according to whether its action is real or not, and whether the future is
included or not. We argue that, if a theory is described with a complex action,
then such a theory is suggested to be the future-included theory, rather than
the future-not-included theory. Otherwise persons living at different times
would see different histories of the universe.


  Despite its existing incentives for leecher cooperation, BitTorrent file
sharing fundamentally relies on the presence of seeder peers. Seeder peers
essentially operate outside the BitTorrent incentives, with two caveats: slow
downlinks lead to increased numbers of "temporary" seeders (who left their
console, but will terminate their seeder role when they return), and the
copyright liability boon that file segmentation offers for permanent seeders.
Using a simple epidemic model for a two-segment BitTorrent swarm, we focus on
the BitTorrent rule to disseminate the (locally) rarest segments first. With
our model, we show that the rarest-segment first rule minimizes transition time
to seeder (complete file acquisition) and equalizes the segment populations in
steady-state. We discuss how alternative dissemination rules may {\em
beneficially increase} file acquisition times causing leechers to remain in the
system longer (particularly as temporary seeders). The result is that leechers
are further enticed to cooperate. This eliminates the threat of extinction of
rare segments which is prevented by the needed presence of permanent seeders.
Our model allows us to study the corresponding trade-offs between performance
improvement, load on permanent seeders, and content availability, which we
leave for future work. Finally, interpreting the two-segment model as one
involving a rare segment and a "lumped" segment representing the rest, we study
a model that jointly considers control of rare segments and different uplinks
causing "choking," where high-uplink peers will not engage in certain
transactions with low-uplink peers.


  Graph representation learning has made major strides over the past decade.
However, in many relational domains, the input data are not suited for simple
graph representations as the relationships between entities go beyond pairwise
interactions. In such cases, the relationships in the data are better
represented as hyperedges (set of entities) of a non-uniform hypergraph. While
there have been works on principled methods for learning representations of
nodes of a hypergraph, these approaches are limited in their applicability to
tasks on non-uniform hypergraphs (hyperedges with different cardinalities). In
this work, we exploit the incidence structure to develop a hypergraph neural
network to learn provably expressive representations of variable sized
hyperedges which preserve local-isomorphism in the line graph of the
hypergraph, while also being invariant to permutations of its constituent
vertices. Specifically, for a given vertex set, we propose frameworks for (1)
hyperedge classification and (2) variable sized expansion of partially observed
hyperedges which captures the higher order interactions among vertices and
hyperedges. We evaluate performance on multiple real-world hypergraph datasets
and demonstrate consistent, significant improvement in accuracy, over
state-of-the-art models.


  We present shell model calculations of both the structure of 17F and the
reactions 16O(p,gamma)17F, 16O(p,p)16O. We use the ZBM interaction which
provides a good description of the properties of 16O and neighbouring nuclei
and, in particular it takes account for the complicated correlations in
coexisting low-lying states of 16O.


  A search is presented for massive long-lived particles, in the 20-60 GeV mass
range with lifetimes between 5 and 100 ps. The dataset used corresponds to 0.62
1\fb of proton-proton collision data collected by the LHCb detector at
sqrt(s)=7 TeV. The particles are assumed to be pair-produced by the decay of a
Higgs-like boson with mass between 80 and 140 GeV. No excess above the
background expectation is observed and limits are set on the production
cross-section as a function of the long-lived particle mass and lifetime and of
the Higgs-like boson mass.


  Elliptic partial differential equations must be solved numerically for many
problems in numerical relativity, such as initial data for every simulation of
merging black holes and neutron stars. Existing elliptic solvers can take
multiple days to solve these problems at high resolution and when matter is
involved, because they are either hard to parallelize or require a large amount
of computational resources. Here we present a new solver for linear and
nonlinear elliptic problems that is designed to scale with resolution and to
parallelize on computing clusters. To achieve this we employ a discontinuous
Galerkin discretization, an iterative multigrid-Schwarz preconditioned
Newton-Krylov algorithm, and a task-based parallelism paradigm. To accelerate
convergence of the elliptic solver we have developed novel
subdomain-preconditioning techniques. We find that our multigrid-Schwarz
preconditioned elliptic solves achieve iteration counts that are independent of
resolution, and our task-based parallel programs scale over 200 million degrees
of freedom to at least a few thousand cores. Our new code solves a classic
initial data problem for binary black holes faster than the spectral code SpEC
when distributed to only eight cores, and in a fraction of the time on more
cores. It is publicly accessible in the next-generation SpECTRE numerical
relativity code. Our results pave the way for highly parallel elliptic solves
in numerical relativity and beyond.


  We present long-slit spectroscopic observations of 40 Galaxy On Top Of
Quasars (GOTOQs) at ${0.37 \leqslant z \leqslant 1.01}$ using the South African
Large Telescope. Using this and available photometric data, we measure the
impact parameters of the foreground galaxies to be in the range of 3$-$16 kpc
with a median value of 8.6 kpc. This is the largest sample of galaxies
producing MgII absorption at such low impact parameters. These quasar-galaxy
pairs are ideal for probing the disk-halo interface. At such impact parameters,
we do not find any significant anti-correlation between rest equivalent width
(REW) of CaII, MnII, FeII, MgII, and MgI absorptions and impact parameters.
These sight lines are typically redder than those of strong MgII absorbers,
with the color excess, E(B$-$V) for our sample ranging from $-$0.191 to 0.422,
with a median value of 0.058. In the E(B$-$V) vs. W$_{3935}$ plane, GOTOQs
occupy the same region as CaII absorbers. For a given E(B$-$V), we find larger
W$_{3935}$ than what has been found in the Milky Way, probably due to a smaller
dust-to-gas ratio in GOTOQs. Galaxy parameters could be measured for twelve
cases, and their properties seem to follow the trends found for strong MgII
absorbers. Measuring the host galaxy properties for the full sample using HST
photometry or AO-assisted ground-based imaging is important to gain insights
into the relationship between the stellar mass of galaxies and the metal line
REW distributions at low impact parameters.


  We consider supersymmetric near-horizon geometries in heterotic supergravity
up to two loop order in sigma model perturbation theory. We identify the
conditions for the horizons to admit enhancement of supersymmetry. We show that
solutions which undergo supersymmetry enhancement exhibit an sl(2,R) symmetry,
and we describe the geometry of their horizon sections. We also prove a
modified Lichnerowicz type theorem, incorporating $\alpha'$ corrections, which
relates Killing spinors to zero modes of near-horizon Dirac operators.
Furthermore, we demonstrate that there are no AdS2 solutions in heterotic
supergravity up to second order in $\alpha'$ for which the fields are smooth
and the internal space is smooth and compact without boundary. We investigate a
class of nearly supersymmetric horizons, for which the gravitino Killing spinor
equation is satisfied on the spatial cross sections but not the dilatino one,
and present a description of their geometry.


  There has been significant attention to the research on dense video
captioning, which aims to automatically localize and caption all events within
untrimmed video. Several studies introduce methods by designing dense video
captioning as a multitasking problem of event localization and event captioning
to consider inter-task relations. However, addressing both tasks using only
visual input is challenging due to the lack of semantic content. In this study,
we address this by proposing a novel framework inspired by the cognitive
information processing of humans. Our model utilizes external memory to
incorporate prior knowledge. The memory retrieval method is proposed with
cross-modal video-to-text matching. To effectively incorporate retrieved text
features, the versatile encoder and the decoder with visual and textual
cross-attention modules are designed. Comparative experiments have been
conducted to show the effectiveness of the proposed method on ActivityNet
Captions and YouCook2 datasets. Experimental results show promising performance
of our model without extensive pretraining from a large video dataset.


  Schools with the highest average student performance are often the smallest
schools; localities with the highest rates of some cancers are frequently small
and the effects observed in clinical trials are likely to be largest for the
smallest numbers of subjects. Informal explanations of this "small-schools
phenomenon" point to the fact that the sample means of smaller samples have
higher variances. But this cannot be a complete explanation: If we draw two
samples from a diffuse distribution that is symmetric about some point, then
the chance that the smaller sample has larger mean is 50\%. A particular
consequence of results proved below is that if one draws three or more samples
of different sizes from the same normal distribution, then the sample mean of
the smallest sample is most likely to be highest, the sample mean of the second
smallest sample is second most likely to be highest, and so on; this is true
even though for any pair of samples, each one of the pair is equally likely to
have the larger sample mean.
  Our conclusions are relevant to certain stochastic choice models including
the following generalization of Thurstone's Law of Comparative Judgment. There
are $n$ items. Item $i$ is preferred to item $j$ if $Z_i < Z_j$, where $Z$ is a
random $n$-vector of preference scores. Suppose $\mathbb{P}\{Z_i = Z_j\} = 0$
for $i \ne j$, so there are no ties. Item $k$ is the favorite if $Z_k <
\min_{i\ne k} Z_i$. Let $p_i$ denote the chance that item $i$ is the favorite.
We characterize a large class of distributions for $Z$ for which $p_1 > p_2 >
\cdots > p_n$. Our results are most surprising when $\mathbb{P}\{Z_i < Z_j\} =
\mathbb{P}\{Z_i > Z_j\} = \frac{1}{2}$ for $i \ne j$, so neither of any two
items is likely to be preferred over the other in a pairwise comparison.


  We consider special classes of linear bounded operators in Banach spaces and
suggest certain operator variant of symbolic calculus. It permits to formulate
an index theorem and to describe Fredholm properties of elliptic
pseudo-differential operator on manifolds with non-smooth boundaries.


  We study weakly interacting mixtures of ultracold atoms composed of bosonic
and fermionic species in 2D and 1D. When interactions between particles are
appropriately tuned, self-bound quantum liquids can be formed. We show that
while formation of these droplets in 2D is due to the higher order correction
terms contributing to the total energy and originating in quantum fluctuations,
in 1D geometry the quantum fluctuations have a negligible role on formation of
the self-bound systems. The leading mean-field interactions are then sufficient
for droplet formation in 1D. We analyse stability conditions for 2D and 1D
systems and predict values of equilibrium densities of droplets.


  The North American Nanohertz Observatory for Gravitational Waves (NANOGrav)
has reported evidence for the presence of an isotropic nanohertz gravitational
wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by
a population of inspiraling supermassive black hole binary (SMBHB) systems,
then the background is predicted to be anisotropic, depending on the
distribution of these systems in the local Universe and the statistical
properties of the SMBHB population. In this work, we search for anisotropy in
the GWB using multiple methods and bases to describe the distribution of the
GWB power on the sky. We do not find significant evidence of anisotropy, and
place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such
that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the
anisotropy expected from a random distribution of SMBHB systems using
astrophysical simulations conditioned on the isotropic GWB inferred in the
15-yr dataset, and show that this dataset has sufficient sensitivity to probe a
large fraction of the predicted level of anisotropy. We end by highlighting the
opportunities and challenges in searching for anisotropy in pulsar timing array
data.


  Inferring graph structure from observations on the nodes is an important and
popular network science task. Departing from the more common inference of a
single graph and motivated by social and biological networks, we study the
problem of jointly inferring multiple graphs from the observation of signals at
their nodes (graph signals), which are assumed to be stationary in the sought
graphs. From a mathematical point of view, graph stationarity implies that the
mapping between the covariance of the signals and the sparse matrix
representing the underlying graph is given by a matrix polynomial. A prominent
example is that of Markov random fields, where the inverse of the covariance
yields the sparse matrix of interest. From a modeling perspective, stationary
graph signals can be used to model linear network processes evolving on a set
of (not necessarily known) networks. Leveraging that matrix polynomials
commute, a convex optimization method along with sufficient conditions that
guarantee the recovery of the true graphs are provided when perfect covariance
information is available. Particularly important from an empirical viewpoint,
we provide high-probability bounds on the recovery error as a function of the
number of signals observed and other key problem parameters. Numerical
experiments using synthetic and real-world data demonstrate the effectiveness
of the proposed method with perfect covariance information as well as its
robustness in the noisy regime.


  Message passing neural networks have become a method of choice for learning
on graphs, in particular the prediction of chemical properties and the
acceleration of molecular dynamics studies. While they readily scale to large
training data sets, previous approaches have proven to be less data efficient
than kernel methods. We identify limitations of invariant representations as a
major reason and extend the message passing formulation to rotationally
equivariant representations. On this basis, we propose the polarizable atom
interaction neural network (PaiNN) and improve on common molecule benchmarks
over previous networks, while reducing model size and inference time. We
leverage the equivariant atomwise representations obtained by PaiNN for the
prediction of tensorial properties. Finally, we apply this to the simulation of
molecular spectra, achieving speedups of 4-5 orders of magnitude compared to
the electronic structure reference.


  Typically, search engines provide query suggestions to assist users in the
search process. Query suggestions are very important for improving users search
experience. However, most query suggestions are based on the user's search
logs, and they can be influenced by infrequently searched queries. Depending on
the user's query, query suggestions can be ineffective in global search engines
but effective in a domestic search engine. Conversely, it can be effective in
global engines and weak in domestic engines. In addition, log-based query
suggestions require many search logs, which makes them difficult to construct
outside of a large search engine. Some search engines do not provide query
suggestions, making searches difficult for users. These query suggestion
vulnerabilities degrade the user's search experience. In this study, we develop
a meta-suggestion, a new query suggestion scheme. Similar to meta-searches,
meta-suggestions retrieves candidate queries of suggestions from other search
engines. Meta-suggestions generate suggestions by reranking the aggregated
candidate queries. We develop a meta-suggestion engine (MSE) browser extension
that generates meta-suggestions. It can provide query suggestions for any
webpage and does not require a search log. Comparing our meta-suggestions to
major search engines such as Google, showed a 17% performance improvement on
normalized discounted cumulative gain (NDCG) and a 31% improvement on
precision. If more detailed factors, such as user preferences are discovered
through continued research, it is expected that user searches will greatly
improve. An enhanced user search experience is possible if factors, such as
user preference, are examined in future work.


  For every $n\geq 3,$ we construct an $n$-dimensional Banach space which is
isometric to a subspace of $L_{1/2}$ but is not isometric to a subspace of
$L_1.$ The isomorphic version of this problem (posed by S. Kwapien in 1969) is
still open. Another example gives a Banach subspace of $L_{1/4}$ which does not
embed isometrically in $L_{1/2}.$ Note that, from the isomorphic point of view,
all the spaces $L_q$ with $q<1$ have the same Banach subspaces.


  In this study, we have identified certain fundamental limitations of a mixing
length parameterization used in a popular turbulent kinetic energy-based
subgrid-scale model. Replacing this parameterization with a more physically
realistic one significantly improves the overall quality of the large-eddy
simulations (LESs) of stable boundary layers. For the range of grid sizes
considered here (specifically, 1 m -- 12.5 m), the revision dramatically
reduces the grid-size sensitivity of the simulations. Most importantly, the
revised scheme allows us to reliably estimate the first- and second-order
statistics of a well-known LES intercomparison case, even with a coarse
grid-size of O(10 m).


  Motivated by synchronization problems in noisy environments, we study the
Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We
consider a specific form of the weights, where the strength (and the associated
cost) of a link is proportional to $(k_{i}k_{j})^{\beta}$ with $k_{i}$ and
$k_{j}$ being the degrees of the nodes connected by the link. Subject to the
constraint that the total network cost is fixed, we find that in the mean-field
approximation on uncorrelated scale-free graphs, synchronization is optimal at
$\beta^{*}$$=$-1. Numerical results, based on exact numerical diagonalization
of the corresponding network Laplacian, confirm the mean-field results, with
small corrections to the optimal value of $\beta^{*}$. Employing our recent
connections between the Edwards-Wilkinson process and resistor networks, and
some well-known connections between random walks and resistor networks, we also
pursue a naturally related problem of optimizing performance in queue-limited
communication networks utilizing local weighted routing schemes.


  In this research, we develop a trading strategy for the discrete-time optimal
liquidation problem of large order trading with different market
microstructures in an illiquid market. In this framework, the flow of orders
can be viewed as a point process with stochastic intensity. We model the price
impact as a linear function of a self-exciting dynamic process. We formulate
the liquidation problem as a discrete-time Markov Decision Processes, where the
state process is a Piecewise Deterministic Markov Process (PDMP). The numerical
results indicate that an optimal trading strategy is dependent on
characteristics of the market microstructure. When no orders above certain
value come the optimal solution takes offers in the lower levels of the limit
order book in order to prevent not filling of orders and facing final inventory
costs.


  We consider a non-convex constrained Lagrangian formulation of a fundamental
bi-criteria optimization problem for variable selection in statistical
learning; the two criteria are a smooth (possibly) nonconvex loss function,
measuring the fitness of the model to data, and the latter function is a
difference-of-convex (DC) regularization, employed to promote some extra
structure on the solution, like sparsity. This general class of nonconvex
problems arises in many big-data applications, from statistical machine
learning to physical sciences and engineering. We develop the first unified
distributed algorithmic framework for these problems and establish its
asymptotic convergence to d-stationary solutions. Two key features of the
method are: i) it can be implemented on arbitrary networks (digraphs) with
(possibly) time-varying connectivity; and ii) it does not require the
restrictive assumption that the (sub)gradient of the objective function is
bounded, which enlarges significantly the class of statistical learning
problems that can be solved with convergence guarantees.


  We investigate multiple variants of the game Cops and Robbers. Playing it on
an $n \times n$ toroidal chess graph, the game is varied by defining moves for
cops and robbers differently, always mimicking moves of certain chess pieces.
In these cases, the cop number is completely determined.


  For a given topological dynamical system $(X,T)$ over a compact set $X$ with
a metric $d$, the "variational principle" states that \begin{equation*}
\sup_{\mu}h_\mu(T) = h(T) = h_d(T), \end{equation*} where $h_\mu(T)$ is the
Kolmogorov-Sinai entropy, with the supremum taken over every $T$-invariant
probability measure, $h_d(T)$ is the Bowen entropy, and $h(T)$ is the
topological entropy as defined by Adler, Konheim and McAndrew. In [9], the
concept of topological entropy was adapted for the case where $T$ is a proper
map and $X$ is locally compact separable and metrizable, and the variational
principle was extended to \begin{equation*} \sup_{\mu}h_\mu(T) = h(T) = \min_d
h_d(T), \end{equation*} where the minimum is taken over every distance
compatible with the topology of $X$. In the present work, we dropped the
properness assumption, extending the above result for any continuous map $T$.
  We also apply our results to extend some previous formulas for the
topological entropy of continuous endomorphisms of connected Lie groups proved
in [4]. In particular, we prove that any linear transformation $T: V \to V$
over a finite dimensional vector space $V$ has null topological entropy.