  In this talk, we report on results about the width of the resonances for a
slowly varying perturbation of a periodic operator. The study takes place in
dimension one. The perturbation is assumed to be analytic and local in the
sense that it tends to a constant at $+\infty$ and at $-\infty$; these
constants may differ. Modulo an assumption on the relative position of the
range of the local perturbation with respect to the spectrum of the background
periodic operator, we show that the width of the resonances is essentially
given by a tunneling effect in a suitable phase space.


  Neural network compression has recently received much attention due to the
computational requirements of modern deep models. In this work, our objective
is to transfer knowledge from a deep and accurate model to a smaller one. Our
contributions are threefold: (i) we propose an adversarial network compression
approach to train the small student network to mimic the large teacher, without
the need for labels during training; (ii) we introduce a regularization scheme
to prevent a trivially-strong discriminator without reducing the network
capacity and (iii) our approach generalizes on different teacher-student
models.
  In an extensive evaluation on five standard datasets, we show that our
student has small accuracy drop, achieves better performance than other
knowledge transfer approaches and it surpasses the performance of the same
network trained with labels. In addition, we demonstrate state-of-the-art
results compared to other compression strategies.


  Medical image classification poses unique challenges due to the long-tailed
distribution of diseases, the co-occurrence of diagnostic findings, and the
multiple views available for each study or patient. This paper introduces our
solution to the ICCV CVAMD 2023 Shared Task on CXR-LT: Multi-Label Long-Tailed
Classification on Chest X-Rays. Our approach introduces CheXFusion, a
transformer-based fusion module incorporating multi-view images. The fusion
module, guided by self-attention and cross-attention mechanisms, efficiently
aggregates multi-view features while considering label co-occurrence.
Furthermore, we explore data balancing and self-training methods to optimize
the model's performance. Our solution achieves state-of-the-art results with
0.372 mAP in the MIMIC-CXR test set, securing 1st place in the competition. Our
success in the task underscores the significance of considering multi-view
settings, class imbalance, and label co-occurrence in medical image
classification. Public code is available at
https://github.com/dongkyuk/CXR-LT-public-solution


  We explore the classical communication over quantum channels with one sender
and two receivers, or with two senders and one receiver, First, for the quantum
broadcast channel (QBC) and the quantum multi-access channel (QMAC), we study
the classical communication assisted by non-signalling and
positive-partial-transpose-preserving codes, and obtain efficiently computable
one-shot bounds to assess the performance of classical communication. Second,
we consider the asymptotic communication capability of communication over the
QBC and QMAC. We derive an efficiently computable strong converse bound for the
capacity region, which behaves better than the previous semidefinite
programming strong converse bound for point-to-point channels. Third, we obtain
a converse bound on the one-shot capacity region based on the hypothesis
testing divergence between the given channel and a certain class of
subchannels. As applications, we analyze the communication performance for some
basic network channels, including the classical broadcast channels and a
specific class of quantum broadcast channels.


  We study completely reducible fibers of pencils of hypersurfaces on $\mathbb
P^n$ and associated codimension one foliations of $\mathbb P^n$.
  Using methods from theory of foliations we obtain certain upper bounds for
the number of these fibers as functions only of $n$.
  Equivalently this gives upper bounds for the dimensions of resonance
varieties of hyperplane arrangements.
  We obtain similar bounds for the dimensions of the characteristic varieties
of the arrangement complements.


  Nowadays, we are to find out solutions to huge computing problems very
rapidly. It brings the idea of parallel computing in which several machines or
processors work cooperatively for computational tasks. In the past decades,
there are a lot of variations in perceiving the importance of parallelism in
computing machines. And it is observed that the parallel computing is a
superior solution to many of the computing limitations like speed and density;
non-recurring and high cost; and power consumption and heat dissipation etc.
The commercial multiprocessors have emerged with lower prices than the
mainframe machines and supercomputers machines. In this article the high
performance computing (HPC) through parallel programming paradigms (PPPs) are
discussed with their constructs and design approaches.


  Microtearing modes have been widely reported as a tearing parity electron
temperature gradient driven plasma instability, which leads to fine scale
tearing of the magnetic flux surfaces thereby resulting in reconnection of
magnetic field lines and formation of magnetic islands. In slab geometry it has
previously been shown that the drive mechanism requires a finite collision
frequency. However, we find in linear gyrokinetic simulations that a
collisionless fine-scale tearing parity instability exists even at low and zero
collision frequency. Detailed studies reveal that these slab modes are also
driven by electron temperature gradient but are sensitive to electron finite
Larmor radius effects, and have a radial wavenumber much smaller than the
binormal wavenumber, which is comparable to the ion Larmor radius. Furthermore,
they exist even in the electrostatic limit and electromagnetic effects actually
have a stabilising influence on this collisionless tearing mode. An analytic
model shows that this collisionless small scale tearing mode is consistent with
a tearing parity slab electron temperature gradient (ETG) mode, which can be
more unstable than the twisting parity ETG mode that is often studied. This
small-scale tearing parity mode can lead to magnetic islands, which, in turn,
can influence turbulent transport in magnetised plasmas.


  Several recent all-speed time-explicit numerical methods for the Euler
equations on Cartesian grids are presented and their properties assessed
experimentally on a complex application. These methods are truly
multi-dimensional, i.e. the flux through an interface also depends on the
values in cells adjacent to the endpoints of the edges (corners).


  While the expectation is that the majority of gravitational wave events
observable by ground-based detectors will be emitted by compact binaries in
quasi-circular orbits, the growing number of detections suggests the
possibility of detecting waves from binaries with non-negligible orbital
eccentricity in the near future. Several gravitational wave models incorporate
the effects of small orbital eccentricities ($e \lesssim 0.2$), but these
models may not be sufficient to analyze waves from systems with moderate
eccentricity. We recently developed a gravitational wave model that faithfully
accounts for eccentric corrections in the moderate eccentricity regime ($e
\lesssim 0.8$ for certain source masses) at 3rd post-Newtonian order. Here we
consider the data analysis implications of this particular waveform model by
producing and analyzing posteriors via Markov Chain Monte Carlo methods. We
find that the accuracy to which eccentricity and source masses can be measured
can increase by 2 orders of magnitude with increasing eccentricity of the
signal. We also find that signals with low eccentricity can be confidently
identified as eccentric as soon as their eccentricity exceeds 0.008 (0.05) for
low (high) mass systems, suggesting eccentric detections are likely to come
first from low-mass systems. We complete our analysis by investigating the
systematic (mismodeling) error inherent in our post-Newtonian model, finding
that for signals with a signal-to-noise ratio of 15, the systematic error is
below the statistical error for eccentricities as high as 0.8 (0.5) for low
(high) mass systems. We also investigate the systematic error that arises from
using a model that neglects eccentricity when the signal is truly eccentric,
finding that the systematic error exceeds the statistical error in mass for
eccentricities as small as 0.02.


  It will be argued that among the known systems in three dimensions that have
string like excitations periodic U(1) pure gauge theories are the most likely
candidates to lead to a string representation of their universal properties.
Some recent work with F. David will also be reviewed.


  I discuss the analytic structure of thermodynamic quantities for complex
values of thermodynamic variables within Landau theory. In particular, the
singularities connected with phase transitions of second order, first order and
cross over types are examined. A conformal mapping is introduced, which may be
used to explore the thermodynamics of strongly interacting matter at finite
values of the baryon chemical potential $\mu$ starting from lattice QCD results
at $\mu^{2}\leq 0$. This method allows us to improve the convergence of a
Taylor expansion about $\mu=0$ and to enhance the sensitivity to physical
singularities in the complex $\mu$ plane. The technique is illustrated by an
application to a second-order transition in a chiral effective model.


  Credal sets are one of the most important models for describing probabilistic
uncertainty. They usually arise as convex sets of probabilistic models
compatible with judgments provided in terms of coherent lower previsions or
more specific models such as coherent lower probabilities or probability
intervals. In finite spaces, credal sets usually take the form of convex
polytopes. Many properties of convex polytopes can be derived from their normal
cones, which form polyhedral complexes called normal fans. We analyze the
properties of normal cones corresponding to credal sets of coherent lower
probabilities. For two important classes of coherent lower probabilities,
2-monotone lower probabilities and probability intervals, we provide a detailed
description of the normal fan structure. These structures are related to the
structure of the extreme points of the credal sets. To arrive at our main
results, we provide some general results on triangulated normal fans of convex
polyhedra and their adjacency structure.


  It is well understood that in ADAS applications, a good estimate of the pose
of the vehicle is required. This paper proposes a metaphorically named 2.5D
odometry, whereby the planar odometry derived from the yaw rate sensor and four
wheel speed sensors is augmented by a linear model of suspension. While the
core of the planar odometry is a yaw rate model that is already understood in
the literature, we augment this by fitting a quadratic to the incoming signals,
enabling interpolation, extrapolation, and a finer integration of the vehicle
position. We show, by experimental results with a DGPS/IMU reference, that this
model provides highly accurate odometry estimates, compared with existing
methods. Utilising sensors that return the change in height of vehicle
reference points with changing suspension configurations, we define a planar
model of the vehicle suspension, thus augmenting the odometry model. We present
an experimental framework and evaluations criteria by which the goodness of the
odometry is evaluated and compared with existing methods. This odometry model
has been designed to support low-speed surround-view camera systems that are
well-known. Thus, we present some application results that show a performance
boost for viewing and computer vision applications using the proposed odometry


  Consider a finite positive integer. If it is even, divide it by 2, and if it
is odd, multiply it by 3 and add 1. This will give you a new integer. Following
the procedure for the new integer, you will receive another integer. Repeat the
steps, and after a few repetitions, you will finally reach 1. Collatz
conjecture states that the final integer in the mentioned process will always
be 1, no matter what integer it starts with. Although the procedure of the
conjecture is easy to describe, its correctness has not yet been confirmed.
This article proves the conjecture by introducing a tree topology of it. Given
the proposed tree, we can prove that all integers are uniquely distributed on
the tree, and there is no cycle other than 1-2-1. We also see how every
trajectory ends in 1.


  In this work we numerically investigate the flow conditions inside uniform
and non-uniform street canyons well within the atmospheric boundary layer. The
numerical simulations use the steady RANS method with the near-wall modelling
approach to simulate wall roughness at the boundary. With the aim of
investigating both flow structure in broad terms, and pedestrian comfort in the
street canyon between parallel buildings, we test different canyon
configurations with varied street width, building width and building height.
Turbulent conditions are broadly expected to hold within the
physically-realistic range of Reynolds number of order $10^6$ considered here,
where we take the building height to be a characteristic length scale, and the
free stream velocity as the characteristic velocity. In addition to discussing
the features of the canyon and wake flow, we investigate the effects of canyon
geometry on pedestrian comfort by using the Extended Land Beaufort Scale for
this purpose. We present and compare pedestrian comfort maps for each of our
geometries.


  We consider the large-N Calogero model in the \h\ collective-field approach
based on the $1/N$ expansion. The Bogomol'nyi limit appears and the
corresponding equation for the semiclassical configuration gives the correct
ground-state energy. Using the method of the orthogonal polynomial we find the
excitation spectrum of density fluctuations around the semiclassical solution
for any value of the statistical parametar $\l$. The wave functions of the
excited states are explicitly constructed as a product of Hermite polynomials
in terms of the collective modes.The two-point correlation function is
calculated as a series expansion in $1/\rho$ for any intermediate statistics.


  We investigate the effects of temperature variance, grain size variation,
flow regimes, and the use of Support Vector Machines (SVMs) in avalanche
studies. The temperature variance experiments involved ice single crystals and
polycrystals, revealing that the scale-free pattern of avalanche sizes remains
consistent regardless of temperature. The dynamics of dislocations in
polycrystals were found to be independent of stress level and temperature. The
Material Point Method (MPM) was used to explore snow avalanche behavior and
identify flow regimes. The MPM accurately represented various flow patterns of
snow avalanches, although challenges remained in capturing powder clouds. SVMs
were employed for avalanche forecasting, using meteorological and snowpack
variables as input features. The selected features provided insights into
snowfall characteristics, snow accumulation, rain interaction, snowdrift
patterns, cloud dynamics, snowpack mechanics, and temperature distribution
within the snowpack. The findings contribute to a better understanding of
avalanche dynamics and offer potential improvements in avalanche trend
predictions.


  Using the method of quantum trajectories we study a quantum chaotic
dissipative ratchet appearing for particles in a pulsed asymmetric potential in
the presence of a dissipative environment. The system is characterized by
directed transport emerging from a quantum strange attractor. This model
exhibits, in the limit of small effective Planck constant, a transition from
quantum to classical behavior, in agreement with the correspondence principle.
We also discuss parameter values suitable for implementation of the quantum
ratchet effect with cold atoms in optical lattices.


  In this paper, we prove global in time Strichartz estimates for the
fractional Schr\"odinger operators, namely $e^{-it\Lambda_g^\sigma}$ with
$\sigma \in (0,\infty)\backslash \{1\}$ and $\Lambda_g:=\sqrt{-\Delta_g}$ where
$\Delta_g$ is the Laplace-Beltrami operator on asymptotically Euclidean
manifolds $(\mathbb{R}^d,g)$. Let $f_0\in C^\infty_0(\mathbb{R})$ be a smooth
cutoff equal 1 near zero. We firstly show that the high frequency part
$(1-f_0)(P)e^{-it\Lambda_g^\sigma}$ satisfies global in time Strichartz
estimates as on $\mathbb{R}^d$ of dimension $d\geq 2$ inside a compact set
under non-trapping condition. On the other hand, under the moderate trapping
assumption, the high frequency part also satisfies the global in time
Strichartz estimates outside a compact set. We next prove that the low
frequency part $f_0(P)e^{-it\Lambda_g^\sigma}$ satisfies global in time
Strichartz estimates as on $\mathbb{R}^d$ of dimension $d\geq 3$ without using
any geometric assumption on $g$. As a byproduct, we prove global in time
Strichartz estimates for the fractional Schr\"odinger and wave equations on
$(\mathbb{R}^d, g), d\geq 3$ under non-trapping condition.


  The HIgh-Resolution Mid-infrarEd Spectrometer (HIRMES) is the 3rd Generation
Instrument for the Stratospheric Observatory For Infrared Astronomy (SOFIA),
currently in development at the NASA Goddard Space Flight Center (GSFC), and
due for commissioning in 2019. By combining direct-detection Transition Edge
Sensor (TES) bolometer arrays, grating-dispersive spectroscopy, and a host of
Fabry-Perot tunable filters, HIRMES will provide the ability for High
Resolution (R~100,000), Mid-Resolution (R~10,000), and Low-Resolution (R~600)
slit-spectroscopy, and 2D Spectral Imaging (R~2000 at selected wavelengths)
over the 25 - 122 {\mu}m mid-far infrared waveband. The driving science
application is the evolution of proto-planetary systems via measurements of
water-vapor, water-ice, deuterated hydrogen (HD), and neutral oxygen lines.
However, HIRMES has been designed to be as flexible as possible to cover a wide
range of science cases that fall within its phase-space, all whilst reaching
sensitivities and observing powers not yet seen thus far on SOFIA, providing
unique observing capabilities which will remain unmatched for decades.


  We review and critically evaluate our proposal of a pulse amplification
scheme based on two Bose-Einstein condensates inside the resonator of a
mode-locked laser. Two condensates are used for compensating the group velocity
dispersion. Ultraslow light propagation through the condensate leads to a
considerable increase in the cavity round-trip delay time, lowers the effective
repetition rate of the laser, and hence scales up the output pulse energy. It
has been recently argued that atom-atom interactions would make our proposal
even more efficient. However, neither in our original proposal nor in the case
of interactions, limitations due to heating of the condensates by optical
energy absorption were taken into account. Our results show that there is a
critical time of operation, $~0.3$ ms, for the optimal amplification factor,
which is in the order of $\sim 10^2$ at effective condensate lengths in the
order of $\sim 50$ $\mu$m. The bandwidth limitation of the amplifier on the
minimum temporal width of the pulse that can be amplified with this technique
is also discussed.


  Let R be a local ring of dimension d. Buchweitz asks if the rank of the d-th
syzygy of a module of finite lengh is greater than or equal to the rank of the
d-th syzygy of the residue field, unless the module has finite projective
dimension. Assuming that R is Gorenstein, we prove that if the question is
affrmative, then R is a hypersurface. If moreover R has dimension two, then we
show that the converse also holds true.


  We use spectra observed with the integral-field spectrograph MUSE to reveal
the central kinematics of the Galactic globular cluster Messier 80 (M80, NGC
6093). Using observations obtained with the recently commissioned narrow-field
mode of MUSE, we are able to analyse 932 stars in the central 7.5 arcsec by 7.5
arcsec of the cluster for which no useful spectra previously existed. Mean
radial velocities of individual stars derived from the spectra are compared to
predictions from axisymmetric Jeans models, resulting in radial profiles of the
velocity dispersion, the rotation amplitude, and the mass-to-light ratio. The
new data allow us to search for an intermediate-mass black hole (IMBH) in the
centre of the cluster. Our Jeans model finds two similarly probable solutions
around different dynamical cluster centres. The first solution has a centre
close to the photometric estimates available in the literature and does not
need an IMBH to fit the observed kinematics. The second solution contains a
location of the cluster centre that is offset by about 2.4 arcsec from the
first one and it needs an IMBH mass of $4600^{+1700}_{-1400}$ solar masses.
N-body models support the existence of an IMBH in this cluster with a mass of
up to 6000 solar masses in this cluster, although models without an IMBH
provide a better fit to the observed surface brightness profile. They further
indicate that the cluster has lost nearly all stellar-mass black holes. We
further discuss the detection of two potential high-velocity stars with radial
velocities of 80 to 90 km/s relative to the cluster mean.


  We study the heat content asymptotics on a Riemannian manifold with smoooth
boundary defined by Dirichlet, Neumann, transmittal and transmission boundary
conditions.


  In this paper we treat some fractal and statistical features of the DNA
sequences. First, a fractal record model of DNA sequence is proposed by mapping
DNA sequences to integer sequences, followed by R/S analysis of the model and
computation of the Hurst exponents. Second, we consider transition between the
four kinds of bases within DNA. The transition matrix analysis of DNA sequences
shows that some measures of complexity based on transition proportion matrix
are of interest. We use some measures of complexity to distinguish exon and
intron. Regarding the evolution, we find that for species of higher grade, the
transition rate among the four kinds of bases goes further from the
equilibrium.


  The hippocampal formation is thought to learn spatial maps of environments,
and in many models this learning process consists of forming a sensory
association for each location in the environment. This is inefficient, akin to
learning a large lookup table for each environment. Spatial maps can be learned
much more efficiently if the maps instead consist of arrangements of sparse
environment parts. In this work, I approach spatial mapping as a problem of
learning graphs of environment parts. Each node in the learned graph,
represented by hippocampal engram cells, is associated with feature information
in lateral entorhinal cortex (LEC) and location information in medial
entorhinal cortex (MEC) using empirically observed neuron types. Each edge in
the graph represents the relation between two parts, and it is associated with
coarse displacement information. This core idea of associating arbitrary
information with nodes and edges is not inherently spatial, so this proposed
fast-relation-graph-learning algorithm can expand to incorporate many spatial
and non-spatial tasks.


  Issues with coreference resolution are one of the most frequently mentioned
challenges for information extraction from the biomedical literature. Thus, the
biomedical genre has long been the second most researched genre for coreference
resolution after the news domain, and the subject of a great deal of research
for NLP in general. In recent years this interest has grown enormously leading
to the development of a number of substantial datasets, of domain-specific
contextual language models, and of several architectures. In this paper we
review the state-of-the-art of coreference in the biomedical domain with a
particular attention on these most recent developments.


  Gamma-ray emission in active galaxies is likely produced within the inner
jet, or in the close vicinity of the supermassive black hole (SMBH) at
sub-parsec distances. Gamma rays have to pass through the surrounding massive
stellar cluster which luminous stars can accidentally appear close to the
observer's line of sight. In such a case, soft radiation of massive stars can
create enough target for transient absorption of the gamma rays in multi-GeV to
TeV energy range. We consider the effect of such stellar encounters on the
gamma-ray spectrum produced within the massive stellar cluster surrounding a
central SMBH. We predict characteristic, time-dependent effects on the
gamma-ray spectra due to the encounter with the single luminous star and also
stellar binary system. We conclude that during the encounter, the gamma-ray
spectrum of an active galaxy should steepen at tens of GeV and harden in the
range of hundreds of GeV. As an example, we consider such effects on the
spectra observed from a typical blazar, 1ES\ 1959+650 (in an active state) and
also in the case of a radio galaxy M87 (in a low state). It is shown that
observation of such transient characteristic features in the gamma-ray spectra,
observed from blazars and radio galaxies, lays within the sensitivity of the
future Cherenkov Telescope Array.


  Gibbs states (i.e., thermal states) can be used for several applications such
as quantum simulation, quantum machine learning, quantum optimization, and the
study of open quantum systems. Moreover, semi-definite programming,
combinatorial optimization problems, and training quantum Boltzmann machines
can all be addressed by sampling from well-prepared Gibbs states. With that,
however, comes the fact that preparing and sampling from Gibbs states on a
quantum computer are notoriously difficult tasks. Such tasks can require large
overhead in resources and/or calibration even in the simplest of cases, as well
as the fact that the implementation might be limited to only a specific set of
systems. We propose a method based on sampling from a quasi-distribution
consisting of tensor products of mixed states on local clusters, i.e.,
expanding the full Gibbs state into a sum of products of local "Gibbs-cumulant"
type states easier to implement and sample from on quantum hardware. We begin
with presenting results for 4-spin linear chains with XY spin interactions, for
which we obtain the $ZZ$ dynamical spin-spin correlation functions. We also
present the results of measuring the specific heat of the 8-spin chain Gibbs
state $\rho_8$.


  We investigate the age-chemical abundance structure of the outer Galactic
disc at a galactocentric distance of r > 10 kpc as recently revealed by the
SDSS/APOGEE survey. Two sequences are present in the [alpha/Fe]-[Fe/H] plane
with systematically different stellar ages. Surprisingly, the young sequence is
less metal-rich, suggesting a recent dilution process by additional gas
accretion. As the stars with the lowest iron abundance in the younger sequence
also show an enhancement in alpha-element abundance, the gas accretion event
must have involved a burst of star formation. In order to explain these
observations, we construct a chemical evolution model. In this model we include
a relatively short episode of gas accretion at late times on top of an
underlying secular accretion over long timescales. Our model is successful at
reproducing the observed distribution of stars in the three dimensional space
of [alpha/Fe]-[Fe/H]-Age in the outer disc. We find that a late-time accretion
with a delay of 8.2 Gyr and a timescale of 0.7 Gyr best fits the observed data,
in particular the presence of the young, metal-poor sequence. Our best-fit
model further implies that the amount of accreted gas in the late-time
accretion event needs to be about three times the local gas reservoir in the
outer disc at the time of accretion in order to sufficiently dilute the metal
abundance. Given this large fraction, we interpret the late-time accretion
event as a minor merger presumably with a gas-rich dwarf galaxy with a mass M_*
< 10^9 M_Sun and a gas fraction of ~ 75 per cent.


  Recurrent neural networks (RNNs) trained on low-dimensional tasks have been
widely used to model functional biological networks. However, the solutions
found by learning and the effect of initial connectivity are not well
understood. Here, we examine RNNs trained using gradient descent on different
tasks inspired by the neuroscience literature. We find that the changes in
recurrent connectivity can be described by low-rank matrices, despite the
unconstrained nature of the learning algorithm. To identify the origin of the
low-rank structure, we turn to an analytically tractable setting: training a
linear RNN on a simplified task. We show how the low-dimensional task structure
leads to low-rank changes to connectivity. This low-rank structure allows us to
explain and quantify the phenomenon of accelerated learning in the presence of
random initial connectivity. Altogether, our study opens a new perspective to
understanding trained RNNs in terms of both the learning process and the
resulting network structure.


  Dephasing induced by residual thermal photons in the readout resonator is a
leading factor limiting the coherence times of qubits in the circuit QED
architecture. This residual thermal population, of the order of
$10^{-1}$--$10^{-3}$, is suspected to arise from noise impinging on the
resonator from its input and output ports. To address this problem, we designed
and tested a new type of band-pass microwave attenuator that consists of a
dissipative cavity well thermalized to the mixing chamber stage of a dilution
refrigerator. By adding such a cavity attenuator inline with a 3D
superconducting cavity housing a transmon qubit, we have reproducibly measured
increased qubit coherence times. At base temperature, through Hahn echo
experiment, we measured $T_{2\mathrm{e}}/2T_1 = 1.0\,({+0.0}/{-0.1})$ for two
qubits over multiple cooldowns. Through noise-induced dephasing measurement, we
obtained an upper bound $2\times 10^{-4}$ on the residual photon population in
the fundamental mode of the readout cavity, which to our knowledge is the
lowest value reported so far. These results validate an effective method for
protecting qubits against photon noise, which can be developed into a standard
technology for quantum circuit experiments.


  Softmax-based losses have achieved state-of-the-art performances on various
tasks such as face recognition and re-identification. However, these methods
highly relied on clean datasets with global labels, which limits their usage in
many real-world applications. An important reason is that merging and
organizing datasets from various temporal and spatial scenarios is usually not
realistic, as noisy labels can be introduced and exponential-increasing
resources are required. To address this issue, we propose a novel
mining-during-training strategy called Basket-based Softmax (BBS) as well as
its parallel version to effectively train models on multiple datasets in an
end-to-end fashion. Specifically, for each training sample, we simultaneously
adopt similarity scores as the clue to mining negative classes from other
datasets, and dynamically add them to assist the learning of discriminative
features. Experimentally, we demonstrate the efficiency and superiority of the
BBS on the tasks of face recognition and re-identification, with both simulated
and real-world datasets.


  Angular distributions of elastic $^{140}$Ce($\alpha$,$\alpha$)$^{140}$Ce
scattering are analyzed in the framework of the optical model from low energies
around the Coulomb barrier up to about 40\,MeV. From the local fits the total
reaction cross section $\sigma_{\rm{reac}}$ is extracted. This procedure
requires experimental scattering data with small uncertainties. The results for
$\sigma_{\rm{reac}}$ are compared to predictions of different systematic global
potentials. It is found that the total reaction cross section
$\sigma_{\rm{reac}}$ is well predicted from all global potentials under study
although the reproduction of the angular distributions is not perfect in all
cases. In addition, the lower energy limit for the extraction of
$\sigma_{\rm{reac}}$ from elastic scattering angular distributions is analyzed.
Finally, the potentials under study are used to calculate the
$^{143}$Nd(n,$\alpha$)$^{140}$Ce cross section, and the predictions are
compared to experimental data.


  We study the event-by-event fluctuations of the charged particles and compare
the results of different Monte-Carlo Generators (MCG): VNIb, HIJING,
HIJING/B${\bar B}$ and RQMD. We find that the $D$-measure can be used to
distinguish between the different gluon populations that are present in the MCG
models. On the other hand, the value of the $D$-measure shows high sensitivity
to the rescattering effects in VNIb model, but lower sensitivity to the
rescattering effects in RQMD model. We also find that the $D$-measures from AA
are consistent with the $D$-measures from $pp$ for all generators except VNIb.
Therefore, any deviation among the values of $D$-measure for different impact
parameters and between
  $pp$ and $AA$ collisions may indicate that either the rescattering effects
play a key role in the interactions or there is new physics in $AA$ collisions.


  The ontogeny of osmoregulation was examined in the branchial cavity of
embryonic and early post-embryonic stages of the crayfish Astacus leptodactylus
maintained in freshwater, at the sub-cellular level through the detection of
the sodium-potassium adenosine triphosphatase (Na(+),K(+)-ATPase). The
embryonic rate of development was calculated according to the eye index (EI)
which was 430-450 microm at hatching. The distribution of the enzyme was
identified by immunofluorescence microscopy using a monoclonal antibody
IgGalpha5 raised against the avian alpha-subunit of the Na(+),K(+)-ATPase.
Immunoreactivity staining, indicating the presence of Na(+), K(+)-ATPase
appeared in the gills of late embryos (EI>/=400 microm), i.e. a few days before
hatching time, and steadily increased throughout the late embryonic and early
post-embryonic development. The appearance of the enzyme correlates with the
ability to osmoregulate which also occurs late in the embryonic development at
EI 410-420 microm and with tissue differentiation within the gill filaments.
These observations indicate that the physiological shift from osmoconforming
embryos to hyper-regulating late embryos and post-hatching stages in freshwater
must originate partly from the differentiation in the gill epithelia of
ionocytes which are the site of ion pumping, as suggested by the location of
Na(+),K(+)-ATPase. Only the gills were immunostained and a lack of specific
staining was noted in the lamina and the branchiostegites. Therefore,
osmoregulation through Na(+)active uptake is likely achieved in embryos at the
gill level; all the newly formed gills in embryos function in ion regulation;
other parts of the branchial chamber such as the branchiostegites and lamina do
not appear to be involved in osmoregulation.


  DP-coloring (also called correspondence coloring) is a generalization of list
coloring that has been widely studied in recent years after its introduction by
Dvo\v{r}\'{a}k and Postle in 2015. As the analogue of the chromatic polynomial
$P(G,m)$, the DP color function of a graph $G$, denoted $P_{DP}(G,m)$, counts
the minimum number of DP-colorings over all possible $m$-fold covers. It is
known that, unlike the list color function $P_{\ell}(G,m)$, for any $g \geq 3$
there exists a graph $G$ with girth $g$ such that $P_{DP}(G,m) < P(G,m)$ when
$m$ is sufficiently large. Thus, two fundamental open questions regarding the
DP color function are: (i) for which $G$ does there exist an $N \in \mathbb{N}$
such that $P_{DP}(G,m) = P(G,m)$ whenever $m \geq N$, (ii) Given a graph $G$
does there always exist an $N \in \mathbb{N}$ and a polynomial $p(m)$ such that
$P_{DP}(G,m) = p(m)$ whenever $m \geq N$?
  In this paper we give exact formulas for the DP color function of a Theta
graph based on the parity of its path lengths. This gives an explicit answer,
including the formulas for the polynomials that are not the chromatic
polynomial, to both the questions above for Theta graphs. We extend this result
to Generalized Theta graphs by characterizing the exact parity condition that
ensures the DP color function eventually equals the chromatic polynomial. To
answer the second question for Generalized Theta graphs, we confirm it for the
larger class of graphs with a feedback vertex set of size one.


  We study adaptive regret bounds in terms of the variation of the losses (the
so-called path-length bounds) for both multi-armed bandit and more generally
linear bandit. We first show that the seemingly suboptimal path-length bound of
(Wei and Luo, 2018) is in fact not improvable for adaptive adversary. Despite
this negative result, we then develop two new algorithms, one that strictly
improves over (Wei and Luo, 2018) with a smaller path-length measure, and the
other which improves over (Wei and Luo, 2018) for oblivious adversary when the
path-length is large. Our algorithms are based on the well-studied optimistic
mirror descent framework, but importantly with several novel techniques,
including new optimistic predictions, a slight bias towards recently selected
arms, and the use of a hybrid regularizer similar to that of (Bubeck et al.,
2018).
  Furthermore, we extend our results to linear bandit by showing a reduction to
obtaining dynamic regret for a full-information problem, followed by a further
reduction to convex body chasing. We propose a simple greedy chasing algorithm
for squared 2-norm, leading to new dynamic regret results and as a consequence
the first path-length regret for general linear bandit as well.


  The Fermi-Hubbard model is one of the key models of condensed matter physics,
which holds a potential for explaining the mystery of high-temperature
superconductivity. Recent progress in ultracold atoms in optical lattices has
paved the way to studying the model's phase diagram using the tools of quantum
simulation, which emerged as a promising alternative to the numerical
calculations plagued by the infamous sign problem. However, the temperatures
achieved using elaborate laser cooling protocols so far have been too high to
show the appearance of antiferromagnetic and superconducting quantum phases
directly. In this work, we demonstrate that using the machinery of dissipative
quantum state engineering, one can efficiently prepare antiferromagnetic order
in present-day experiments with ultracold fermions. The core of the approach is
to add incoherent laser scattering in such a way that the antiferromagnetic
state emerges as the dark state of the driven-dissipative dynamics. In order to
elucidate the development of the antiferromagnetic order we employ two
complementary techniques: Monte Carlo wave function simulations for small
systems and a recently proposed variational method for open quantum systems,
operating in the thermodynamic limit. The controlled dissipation channels
described in this work are straightforward to add to already existing
experimental setups.


  We compare the MOG and MOND predictions of the Tully-Fisher relationship to
observations using gas-rich galaxies for which the baryonic mass can be
estimated accurately. We find that both theories are in good agreement with the
data. Future observations of large, gas-rich galaxies may offer a means to
distinguish between these two theories.


  The outcomes of elections, product sales, and the structure of social
connections are all determined by the choices individuals make when presented
with a set of options, so understanding the factors that contribute to choice
is crucial. Of particular interest are context effects, which occur when the
set of available options influences a chooser's relative preferences, as they
violate traditional rationality assumptions yet are widespread in practice.
However, identifying these effects from observed choices is challenging, often
requiring foreknowledge of the effect to be measured. In contrast, we provide a
method for the automatic discovery of a broad class of context effects from
observed choice data. Our models are easier to train and more flexible than
existing models and also yield intuitive, interpretable, and statistically
testable context effects. Using our models, we identify new context effects in
widely used choice datasets and provide the first analysis of choice set
context effects in social network growth.


  The (Co,Ni)Al2O4 is an aluminum transition metals oxide which falls into the
category of aluminate spinels. The synthesis of nano-crystalline spinels has
been investigated extensively due to their potential applications such as a
high-density magnetic recording, microwave devices magnetic fluids, ceramic
pigment as well as a heterogeneous catalytic material. In the present study,
attempts have been made to synthesise the nano-crystalline (Co,Ni)Al2O4 spinel
powders by ball milling and subsequent annealing. An alloy of Al70 Ni15 Co15,
exhibiting the formation of a complex intermetallic compound known as decagonal
quasicrystals in the as-solidified condition, is selected as the starting
material for mechanical milling. It is interesting to note that this alloy is
close to the stoichiometry of aluminum and transition metal atoms required to
form of the aluminate spinel. The milling was carried out in an attritor mill
at 400 rpm for 40 hours with ball to powder ratio of 20:1 in hexane medium and
the annealing was performed for 10, 20 and 40 h at 600 0 C in air in side the
furnace in order to oxidize the decagonal phase and finally to form the spinel
structures. The X-ray diffraction (XRD) and transmission electron microscopy
(TEM) confirmed the formation of nano-sized decagonal phase after milling and
then (Co,Ni)Al2O4 spinel type structure from the nano-size decagonal phase
during annealing. The average crystallite size has been found to be ~40 nm by
XRD and TEM studies, the lattice strain is 0.6 %, and the lattice parameter is
8.0756 A . The ferromagnetic behaviour is also observed in the milled and the
annealed samples.


  The High-Altitude Water Cherenkov (HAWC) Observatory is used for detecting
TeV gamma rays. HAWC is operating at 4,100 meters above level sea on the slope
of the Sierra Negra Volcano in the State of Puebla, Mexico, and consists of an
array of 300 water Cherenkov detectors (WCDs) covering an area of 22,000 $m^2$.
Each WCD is equipped with four photomultiplier tubes (PMTs) to detect Cherenkov
emission in the water from secondary particles of extensive air-shower (EAS)
that are produced in the interactions of primary particles (gamma rays or
charged cosmic rays) in the atmosphere. HAWC is able to reconstruct the EAS in
the 0.5 to 100 TeV energy range. In order to improve the core determination for
events with high energy ($>10$ TeV) when the events arrive outside of the HAWC
array, the Outrigger upgrade project is adding 350 small WCDs around the main
array. These outrigger tanks each have one PMT in a 1.5 meter diameter
cylindrical polyethylene tank, covering a total area four times larger than
that of the HAWC array. In this work we present leak light testing to identify
the stability of the detector and an analysis of deposited charges to
understand the detector performance.


  There are many applications that benefit from computing the exact divergence
between 2 discrete probability measures, including machine learning.
Unfortunately, in the absence of any assumptions on the structure or
independencies within these distributions, computing the divergence between
them is an intractable problem in high dimensions. We show that we are able to
compute a wide family of functionals and divergences, such as the alpha-beta
divergence, between two decomposable models, i.e. chordal Markov networks, in
time exponential to the treewidth of these models. The alpha-beta divergence is
a family of divergences that include popular divergences such as the
Kullback-Leibler divergence, the Hellinger distance, and the chi-squared
divergence. Thus, we can accurately compute the exact values of any of this
broad class of divergences to the extent to which we can accurately model the
two distributions using decomposable models.


  We present mid-infrared spectra and images from the GEMINI-N (+Michelle)
observations of fragments SW3-[B] and SW3-[C] of the ecliptic (Jupiter Family)
comet 73P/Schwassmann-Wachmann 3 pre-perihelion. We observed fragment B soon
after an outburst event (between 2006 April 16 - 26 UT) and detected
crystalline silicates. The mineralogy of both fragments was dominated by
amorphous carbon and amorphous pyroxene. The grain size distribution (assuming
a Hanner modified power-law) for fragment SW3-[B] has a peak grain radius of
a_p ~ 0.5 micron, and for fragment SW3-[C], a_p ~ 0.3 micron; both values
larger than the peak grain radius of the size distribution for the dust ejected
from ecliptic comet 9P/Tempel 1 during the Deep Impact event (a_p = 0.2 micron.
The silicate-to-carbon ratio and the silicate crystalline mass fraction for the
submicron to micron-size portion of the grain size distribution on the nucleus
of fragment SW3-[B] was 1.341 +0.250 -0.253 and 0.335 +0.089 -0.112,
respectively, while on the nucleus of fragment SW3-[C] was 0.671 +0.076 -0.076
and 0.257 +0.039 -0.043, respectively. The similarity in mineralogy and grain
properties between the two fragments implies that 73P/Schwassmann-Wachmann 3 is
homogeneous in composition. The slight differences in grain size distribution
and silicate-to-carbon ratio between the two fragments likely arises because
SW3-[B] was actively fragmenting throughout its passage while the activity in
SW3-[C] was primarily driven by jets. The lack of diverse mineralogy in the
fragments SW3-[B] and SW3-[C] of 73P/Schwassmann-Wachmann 3 along with the
relatively larger peak in the coma grain size distribution suggests the parent
body of this comet may have formed in a region of the solar nebula with
different environmental properties than the natal sites where comet C/1995 O1
(Hale-Bopp) and 9P/Tempel 1 nuclei aggregated.


  Simple form scalar differential equation with delay and non-linear negative
periodic feedback is considered. The existence of slowly oscillating periodic
solutions with the same period as the feedback coefficient is shown numerically
within the admissible range for the periods.


  Learning from demonstrations is a popular tool for accelerating and reducing
the exploration requirements of reinforcement learning. When providing expert
demonstrations to human students, we know that the demonstrations must fall
within a particular range of difficulties called the "Zone of Proximal
Development (ZPD)". If they are too easy the student learns nothing, but if
they are too difficult the student is unable to follow along. This raises the
question: Given a set of potential demonstrators, which among them is best
suited for teaching any particular learner? Prior work, such as the popular
Deep Q-learning from Demonstrations (DQfD) algorithm has generally focused on
single demonstrators. In this work we consider the problem of choosing among
multiple demonstrators of varying skill levels. Our results align with
intuition from human learners: it is not always the best policy to draw
demonstrations from the best performing demonstrator (in terms of reward). We
show that careful selection of teaching strategies can result in sample
efficiency gains in the learner's environment across nine Atari games


  Results are presented for the time evolution of fermions initially in a
non-zero temperature normal phase, following the switch on of an attractive
interaction. The dynamics are studied in the disordered phase close to the
critical point, where the superfluid fluctuations are large. The analysis is
conducted within a two-particle irreducible, large $N$ approximation. The
system is considered from the perspective of critical quenches where it is
shown that the fluctuations follow universal model A dynamics. A signature of
this universality is found in a singular correction to the fermion lifetime,
given by a scaling form $t^{(3-d)/2}S_d(\varepsilon^2 t)$, where $d$ is the
spatial dimension, $t$ is the time since the quench, and $\varepsilon$ is the
fermion energy. The singular behavior of the spectral density is interpreted as
arising due to incoherent Andreev reflections off superfluid fluctuations.


  We present a footstep planning policy for quadrupedal locomotion that is able
to directly take into consideration a-priori safety information in its
decisions. At its core, a learning process analyzes terrain patches,
classifying each landing location by its kinematic feasibility, shin collision,
and terrain roughness. This information is then encoded into a small vector
representation and passed as an additional state to the footstep planning
policy, which furthermore proposes only safe footstep location by applying a
masked variant of the Proximal Policy Optimization algorithm. The performance
of the proposed approach is shown by comparative simulations and experiments on
an electric quadruped robot walking in different rough terrain scenarios. We
show that violations of the above safety conditions are greatly reduced both
during training and the successive deployment of the policy, resulting in an
inherently safer footstep planner. Furthermore, we show how, as a byproduct,
fewer reward terms are needed to shape the behavior of the policy, which in
return is able to achieve both better final performances and sample efficiency.


  Mobile Network Operators (MNOs) are evolving towards becoming data-driven,
while delivering capacity to collect and analyze data. This can help in
enhancing user experiences while empowering the operation workforce and
building new business models. Mobile traffic demands of users can give insights
to MNOs to plan, decide and act depending on network conditions. In this paper,
we investigate the behaviour of Istanbul residents using the cellular network
traffic activity over spatial and temporal dimensions via exploratory factor
analysis (EFA) using a major MNO's cellular network traffic data in Turkey. Our
results reveal various time and spatial patterns for Istanbul residents such as
morning and evening commuting factors, business and residential factors as well
as nightlife and weekend afternoon factors as the most prominent cultural
behaviour. The analysis results also demonstrate interesting findings such as
tunnels and transportation paths selected by Istanbul residents may differ
during morning rush work hour compared to evening rush after-work hour.


  As Moore's law comes to an end, neuromorphic approaches to computing are on
the rise. One of these, passive photonic reservoir computing, is a strong
candidate for computing at high bitrates (> 10 Gbps) and with low energy
consumption. Currently though, both benefits are limited by the necessity to
perform training and readout operations in the electrical domain. Thus, efforts
are currently underway in the photonic community to design an integrated
optical readout, which allows to perform all operations in the optical domain.
In addition to the technological challenge of designing such a readout, new
algorithms have to be designed in order to train it. Foremost, suitable
algorithms need to be able to deal with the fact that the actual on-chip
reservoir states are not directly observable. In this work, we investigate
several options for such a training algorithm and propose a solution in which
the complex states of the reservoir can be observed by appropriately setting
the readout weights, while iterating over a predefined input sequence. We
perform numerical simulations in order to compare our method with an ideal
baseline requiring full observability as well as with an established black-box
optimization approach (CMA-ES).


  We study a number of two-user interference networks with multiple-antenna
transmitters/receivers, transmitter side information in the form of linear
combinations (over finite-field) of the information messages, and two-hop
relaying. We start with a Cognitive Interference Channel (CIC) where one of the
transmitters (non-cognitive) has knowledge of a rank-1 linear combination of
the two information messages, while the other transmitter (cognitive) has
access to a rank-2 linear combination of the same messages. This is referred to
as the Network-Coded CIC, since such linear combination may be the result of
some random linear network coding scheme implemented in the backbone wired
network. For such channel we develop an achievable region based on a few novel
concepts: Precoded Compute and Forward (PCoF) with Channel Integer Alignment
(CIA), combined with standard Dirty-Paper Coding. We also develop a capacity
region outer bound and find the sum symmetric GDoF of the Network-Coded CIC.
Through the GDoF characterization, we show that knowing "mixed data" (linear
combinations of the information messages) provides an unbounded spectral
efficiency gain over the classical CIC counterpart, if the ratio of SNR to INR
is larger than certain threshold. Then, we consider a Gaussian relay network
having the two-user MIMO IC as the main building block. We use PCoF with CIA to
convert the MIMO IC into a deterministic finite-field IC. Then, we use a linear
precoding scheme over the finite-field to eliminate interference in the
finite-field domain. Using this unified approach, we characterize the symmetric
sum rate of the two-user MIMO IC with coordination, cognition, and two-hops. We
also provide finite-SNR results which show that the proposed coding schemes are
competitive against state of the art interference avoidance based on orthogonal
access, for Rayleigh fading channels.


  The $f$-$d$ magnetic exchange interaction is considered to be a key
ingredient for many exotic topological phases in pyrochlore iridates. Here, we
have investigated the evolution of structural, magnetic and electronic
properties in doped pyrochlore iridate, (Y$_{1-x}$Pr$_x$)$_2$Ir$_2$O$_7$. Apart
from geometrical frustration, pyrochlore iridates are well known for its active
spin-orbit coupling effect. The substitution of Pr$^{3+}$ (4$f^2$) for the
nonmagnetic Y$^{3+}$ (4$d^0$) acts as a magnetic doping, which provides an
ideal platform to study $f$-$d$ exchange interaction without altering the
Ir-sublattice. With Pr substitution, system retains its original cubic
structural symmetry but the local structural parameters show an evolution with
the doping concentration $x$. The robust magnetic-insulating state in
Y$_2$Ir$_2$O$_7$ is drastically weakened, while Pr$_2$Ir$_2$O$_7$ ($x$ = 1.0)
shows a paramagnetic-metallic behavior. A metal-insulator transition is
observed for $x$ = 0.8 sample. This evolution of magnetic and electronic
properties are believed to be induced by an exchange interaction between
localized Pr-4$f$ and itinerant Ir-5$d$ electrons as well as by an increased
hybridization between Ir-$t_{2g}$ and (basal) O-$p$ orbitals as observed in XAS
study. The resistivity in insulating materials follows a power-law behavior
with a decreasing exponent with $x$. A negative magnetoresistance is observed
for present series of samples at low temperature and where the
magnetoresistance shows a quadratic field dependence at higher fields.


  State-of-the-art methods for video action recognition commonly use an
ensemble of two networks: the spatial stream, which takes RGB frames as input,
and the temporal stream, which takes optical flow as input. In recent work,
both of these streams consist of 3D Convolutional Neural Networks, which apply
spatiotemporal filters to the video clip before performing classification.
Conceptually, the temporal filters should allow the spatial stream to learn
motion representations, making the temporal stream redundant. However, we still
see significant benefits in action recognition performance by including an
entirely separate temporal stream, indicating that the spatial stream is
"missing" some of the signal captured by the temporal stream. In this work, we
first investigate whether motion representations are indeed missing in the
spatial stream of 3D CNNs. Second, we demonstrate that these motion
representations can be improved by distillation, by tuning the spatial stream
to predict the outputs of the temporal stream, effectively combining both
models into a single stream. Finally, we show that our Distilled 3D Network
(D3D) achieves performance on par with two-stream approaches, using only a
single model and with no need to compute optical flow.


  iGraphMatch is an R package for finding corresponding vertices between two
graphs, also known as graph matching. The package implements three categories
of prevalent graph matching algorithms including relaxation-based,
percolation-based, and spectral-based, which are applicable to matching graphs
under general settings: weighted directed graphs of different order and graphs
of multiple layers. We provide versatile options to incorporate prior
information in the form of seeds with or without noise and similarity scores.
In addition, iGraphMatch provides functions to summarize the graph matching
results in terms of several evaluation measures and visualize the matching
performance. Finally, the package enables users to sample correlated random
graph pairs from classic random graph models to generate data for simulations.
This paper illustrates the practical applications of the package to the
analysis of graph matching by detailed examples using real data from
communication, neuron, and transportation networks.


  The distribution of offsets between the brightest cluster galaxies of galaxy
clusters and the centroid of their dark matter distributions is a promising
probe of the underlying dark matter physics. In particular, since this
distribution is sensitive to the shape of the potential in galaxy cluster
cores, it constitutes a test of dark matter self-interaction on the largest
mass scales in the universe. We examine these offsets in three suites of modern
cosmological simulations; IllustrisTNG, MillenniumTNG and BAHAMAS. For clusters
above $10^{14}\rm{M_\odot}$, we examine the dependence of the offset
distribution on gravitational softening length, the method used to identify
centroids, redshift, mass, baryonic physics, and establish the stability of our
results with respect to various nuisance parameter choices. We find that
offsets are overwhelmingly measured to be smaller than the minimum converged
length scale in each simulation, with a median offset of $\sim1\rm{kpc}$ in the
highest resolution simulation considered, TNG300-1, which uses a gravitational
softening length of $1.48\rm{kpc}$. We also find that centroids identified via
source extraction on smoothed dark matter and stellar particle data are
consistent with the potential minimum, but that observationally relevant
methods sensitive to cluster strong gravitational lensing scales, or those
using gas as a tracer for the potential can overestimate offsets by factors of
$\sim10$ and $\sim30$, respectively. This has the potential to reduce tensions
with existing offset measurements which have served as evidence for a nonzero
dark matter self-interaction cross section.


  We study global variational properties of the space of solutions to
$-\varepsilon^2\Delta u + W'(u)=0$ on any closed Riemannian manifold $M$. Our
techniques are inspired by recent advances in the variational theory of minimal
hypersurfaces and extend a well-known analogy with the theory of phase
transitions. First, we show that solutions at the lowest positive energy level
are either stable or obtained by min-max and have index 1. We show that if
$\varepsilon$ is not small enough, in terms of the Cheeger constant of $M$,
then there are no interesting solutions. However, we show that the number of
min-max solutions to the equation above goes to infinity as $\varepsilon\to 0$
and their energies have sublinear growth. This result is sharp in the sense
that for generic metrics the number of solutions is finite, for fixed
$\varepsilon$, as shown recently by G. Smith. We also show that the energy of
the min-max solutions accumulate, as $\varepsilon \to 0$, around
limit-interfaces which are smooth embedded minimal hypersurfaces whose area
with multiplicity grows sublinearly. For generic metrics with ${\rm Ric}_M>0$,
the limit-interface of the solutions at the lowest positive energy level is an
embedded minimal hypersurface of least area in the sense of Mazet-Rosenberg.
Finally, we prove that the min-max energy values are bounded from below by the
widths of the area functional as defined by Marques-Neves.


  Several recent works in scientific machine learning have revived interest in
the application of neural networks to partial differential equations (PDEs). A
popular approach is to aggregate the residual form of the governing PDE and its
boundary conditions as soft penalties into a composite objective/loss function
for training neural networks, which is commonly referred to as physics-informed
neural networks (PINNs). In the present study, we visualize the loss landscapes
and distributions of learned parameters and explain the ways this particular
formulation of the objective function may hinder or even prevent convergence
when dealing with challenging target solutions. We construct a purely
data-driven loss function composed of both the boundary loss and the domain
loss. Using this data-driven loss function and, separately, a physics-informed
loss function, we then train two neural network models with the same
architecture. We show that incomparable scales between boundary and domain loss
terms are the culprit behind the poor performance. Additionally, we assess the
performance of both approaches on two elliptic problems with increasingly
complex target solutions. Based on our analysis of their loss landscapes and
learned parameter distributions, we observe that a physics-informed neural
network with a composite objective function formulation produces highly
non-convex loss surfaces that are difficult to optimize and are more prone to
the problem of vanishing gradients.


  It is discussed to which extent the AdS-CFT correspondence is compatible with
fundamental requirements in quantum field theory.


  This paper introduces immersive humanitarian visualization as a promising
research area in information visualization. Humanitarian visualizations are
data visualizations designed to promote human welfare. This paper explains why
immersive display technologies taken broadly (e.g, virtual reality, augmented
reality, ambient displays and physical representations) open up a range of
opportunities for humanitarian visualization. In particular, immersive displays
offer ways to make remote and hidden human suffering more salient. They also
offer ways to communicate quantitative facts together with qualitative
information and visceral experiences, in order to provide a holistic
understanding of humanitarian issues that could support more informed
humanitarian decisions. But despite some promising preliminary work, immersive
humanitarian visualization has not taken off as a research topic yet. The goal
of this paper is to encourage, motivate, and inspire future research in this
area.


  This dissertation focuses on the development of novel scheduling and resource
allocation schemes, which take into account and regulate the energy constraints
imposed by the levels of harvested energy. To this direction, first, the
optimal energy, time, and bandwidth allocation problem for the downlink of
energy harvesting base stations (EHBSs) is investigated, with the main focus
being on autonomous EHBSs. The presented analysis considers the impact of the
energy constraint on users' preferences and the BS's revenue. In order to model
the competitive nature of the problem, game theory is used. The next two
chapters focus on wireless powered networks (WPNs) and simultaneous wireless
information and power transfer (SWIPT) using radio frequency (RF) technology.
One of the main contributions of these chapters is the introduction of both
uplink and downlink non-orthogonal multiple access (NOMA) for WPNs. Moreover,
the individual data rates and fairness are improved, while the formulated
problems are optimally and efficiently solved. It is shown that, compared to
orthogonal multiple access, NOMA offers a considerable improvement in
throughput, fairness, and energy efficiency. Rather than this, proportional
fairness is maximized and uplink/downlink of WPNs are jointly optimized, in
which cases, except for NOMA, time division multiple access (TDMA) is also
investigated. Furthermore, the role of interference is considered, which has
been recognized as one of the main reasons of the asymmetric overall
degradation of the users' performance, due to different path-loss values,
called from now on as cascaded near-far problem. Moreover, SWIPT is
investigated and efficiently optimized in the context of multicarrier
cooperative communication networks. Finally, simultaneous lightwave information
and power transfer (SLIPT) is introduced, while novel and fundamental
techniques are proposed.


  We present the program EvolFMC v.2 that solves the evolution equations in QCD
for the parton momentum distributions by means of the Monte Carlo technique
based on the Markovian process. The program solves the DGLAP-type evolution as
well as modified-DGLAP ones. In both cases the evolution can be performed in
the LO or NLO approximation. The quarks are treated as massless. The overall
technical precision of the code has been established at 0.05% precision level.
This way, for the first time ever, we demonstrate that with the Monte Carlo
method one can solve the evolution equations with precision comparable to the
other numerical methods.


  We partially describe equivariant Dirac and generalized complex structures on
a homogeneous space $G/K$ by giving equivalent data involving only the Lie
algebra. We consider real semisimple adjoint orbits in any semisimple Lie
algebra over $\mathbb R$ and real nilpotent orbits in $sl_n (\mathbb R)$. We
give a complete classification for Riemannian symmetric spaces and for a
compact group modulo a closed, connected subgroup containing a Cartan subgroup.


  The aim of this paper is to start the study of images of graded polynomials
on full matrix algebras. We work with the matrix algebra $M_n(K)$ over a field
$K$ endowed with its canonical $\mathbb{Z}_n$-grading (Vasilovsky's grading).
We explicitly determine the possibilities for the linear span of the image of a
multilinear graded polynomial over the field $\mathbb Q$ of rational numbers
and state an analogue of the L'vov-Kaplansky conjecture about images of
multilinear graded polynomials on $n\times n$ matrices, where $n$ is a prime
number. We confirm such conjecture for polynomials of degree 2 over $M_n(K)$
when $K$ is a quadratically closed field of characteristic zero or greater than
$n$ and for polynomials of arbitrary degree over matrices of order 2. We also
determine all the possible images of semi-homogeneous graded polynomials
evaluated on $M_2(K)$.


  We study a scenario in which the baryon asymmetry is created through Hawking
radiation from primordial black holes via a dynamically-generated chemical
potential. This mechanism can also be used to generate the observed dark matter
abundance, regardless of whether or not the black holes fully evaporate. In the
case that evaporation ceases, the observed dark matter abundance is generically
comprised of both relic black holes and an asymmetric dark matter component. We
show that this two-component dark matter scenario can simultaneously account
for the observed baryon asymmetry and the cosmological dark matter, a
possibility which evades constraints on either individual candidate.


  We report an experimental and numerical study of femtosecond multi-pulse
laser-induced densification in vitreous silica (v-SiO2) and its signature in
Raman spectra. We compare the experimental findings to recently developed
molecular dynamics (MD) approach accounting for bond-breaking due to laser
irradiation, together with a dynamical matrix approach and bond polarizability
model based on first-principle calculations for the estimation of Raman
spectra. We observe two stages of the laser-induced densification and Raman
spectrum evolution: growth during several hundreds of pulses followed by
further saturation. At the medium-range, the network connectivity change in
v-SiO2 is expressed in reduction of major ring fractions leading to more
compacted structure. With the help of Sen & Thorpe model, we also study the
short-range order transformation and derive the interbonding Si-O-Si angle
change from the Raman measurements. Experimental findings are in excellent
agreement with our MD simulations, and, hence, support bond-breaking mechanism
of laser-induced densification. Thus, our modeling explains well the
laser-induced changes both in the short-range order caused by the appearance of
Si-coordination defects and medium-range order connected to evolution of the
ring distribution. Finally, our findings disclose similarities between
sheared-, permanently-densified- and laser-induced-glass and suggest
interesting future experiment in order to clarify the impact of the
thermo-mechanical history on glasses under shear, cold- and hot-compression,
and laser-induced densification.


  Very recently, the LHCb Collaboration reported their new results about the
pentaquarks at charm energy region. Based on the new experimental results, we
recalculate the molecular states composed of a $\Sigma_c^{(*)}$ baryon and a
$\bar{D}^{(*)}$ meson in a quasipotential Bethe-Salpeter equation approach. The
two-peak structure around 4450 MeV can be interpreted as two $\Sigma_c
\bar{D}^*$ bound states with spin parities $1/2^-$ and $3/2^-$. The newly
observed pentaquark $P_c(4312)$ can be assigned as a $\Sigma_c\bar{D}$ bound
state with spin parity $1/2^-$. The experimental determination of spin parities
will be very helpful to understand the internal structure of these pentaquarks.


  Imitation learning (IL) can train computationally-efficient sensorimotor
policies from a resource-intensive Model Predictive Controller (MPC), but it
often requires many samples, leading to long training times or limited
robustness. To address these issues, we combine IL with a variant of robust MPC
that accounts for process and sensing uncertainties, and we design a data
augmentation (DA) strategy that enables efficient learning of vision-based
policies. The proposed DA method, named Tube-NeRF, leverages Neural Radiance
Fields (NeRFs) to generate novel synthetic images, and uses properties of the
robust MPC (the tube) to select relevant views and to efficiently compute the
corresponding actions. We tailor our approach to the task of localization and
trajectory tracking on a multirotor, by learning a visuomotor policy that
generates control actions using images from the onboard camera as only source
of horizontal position. Numerical evaluations show 80-fold increase in
demonstration efficiency and a 50% reduction in training time over current IL
methods. Additionally, our policies successfully transfer to a real multirotor,
achieving low tracking errors despite large disturbances, with an onboard
inference time of only 1.5 ms.
  Video: https://youtu.be/_W5z33ZK1m4


  The Fibonacci index of a graph is the number of its stable sets. This
parameter is widely studied and has applications in chemical graph theory. In
this paper, we establish tight upper bounds for the Fibonacci index in terms of
the stability number and the order of general graphs and connected graphs.
Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an
graphs and a connected variant of them are also extremal for these particular
problems.


  [Abridged and Edited] We investigate nuclear light profiles in 135 ATLAS3D
galaxies for which the Hubble Space Telescope (HST) imaging is available and
compare them to the large scale kinematics obtained with the SAURON
integral-field spectrograph. Specific angular momentum, lambda_R, correlates
with the shape of nuclear light profiles, where cores are typically found in
slow rotators and core-less galaxies are fast rotators. Cores are found only in
massive galaxies and only in systems with the stellar mass M>8x10^10 Msun.
Based on our sample, we, however, see no evidence for a bimodal distribution of
nuclear slopes. The best predictor for finding a core is based on the stellar
velocity dispersion within an effective radius, sigma_e, and specific angular
momentum, where cores are found for lambda_R<0.25 and sigma_e>160 km/s. We
estimate that only about 10% of nearby early-type galaxies contain cores.
Furthermore, we show that there is a genuine population of fast rotators with
cores. We also show that core fast rotators are morphologically, kinematically
and dynamically different from core slow rotators. The cores of fast rotators
could harbour black holes of similar masses to those in core slow rotators, but
typically more massive than those found in core-less fast rotators. Core-less
galaxies, and especially core-less fast rotators, are under-luminous in the
diffuse X-ray emission, but the presence of a core does not imply high X-ray
luminosities. We postulate a possible population of core-less galaxies among
slow rotators, which can not be explained as face-on discs, but comprise a
genuine sub-population of slow rotators. These galaxies are typically less
massive and flatter than core slow rotators, and show evidence for dynamical
cold structures and exponential photometric components. We discuss possible
processes for formation of cores and their subsequent preservation.


  We use quantum Monte-Carlo simulations to calculate the phase diagram and the
correlation functions for the quantum phase transitions in the two-dimensional
dissipative XY model with and without four-fold anisotropy. Without anisotropy,
the model describes the superconductor to insulator transition in
two-dimensional dirty superconductors. With anisotropy, the model represents
the loop-current order observed in the under-doped cuprates and its
fluctuations, as well as the fluctuations near the ordering vector in simple
models of itinerant antiferromagnets. These calculations test an analytic
solution of the model which re-expressed it in terms of topological excitations
- the vortices with interactions only in space but none in time, and warps with
leading interactions only in time but none in space, as well as sub-leading
interactions which are both space and time-dependent. For parameters for which
the proliferation of warps dominates the phase transition, the critical
fluctuations as a function of the deviation of the dissipation parameter
$\alpha$ from its critical value $\alpha_c$ are scale-invariant in imaginary
time $\tau$ as the correlation length in time $\xi_{\tau} = \tau_c
e^{|\alpha_c/(\alpha_c-\alpha)|^{1/2}}$ diverges. On the other hand, the
spatial correlations develop with a correlation length $\xi_x \approx \xi_0
\log{(\xi_{\tau})}$, with $\xi_0$ of the order of a lattice constant. The
dynamic correlation exponent $z$ is therefore $\infty$. These results are
consistent with the phenomenology proposed for the strange metal properties of
the cuprates. The Monte-Carlo calculations also directly show warps and
vortices. Their density and correlations across the various transitions in the
model are calculated and related to those of the order parameter in the
original model.


  An important task in health research is to characterize time-to-event
outcomes such as disease onset or mortality in terms of a potentially
high-dimensional set of risk factors. For example, prospective cohort studies
of Alzheimer's disease typically enroll older adults for observation over
several decades to assess the long-term impact of genetic and other factors on
cognitive decline and mortality. The accelerated failure time model is
particularly well-suited to such studies, structuring covariate effects as
`horizontal' changes to the survival quantiles that conceptually reflect shifts
in the outcome distribution due to lifelong exposures. However, this modeling
task is complicated by the enrollment of adults at differing ages, and
intermittent followup visits leading to interval censored outcome information.
Moreover, genetic and clinical risk factors are not only high-dimensional, but
characterized by underlying grouping structure, such as by function or gene
location. Such grouped high-dimensional covariates require shrinkage methods
that directly acknowledge this structure to facilitate variable selection and
estimation. In this paper, we address these considerations directly by
proposing a Bayesian accelerated failure time model with a group-structured
lasso penalty, designed for left-truncated and interval-censored time-to-event
data. We develop a custom Markov chain Monte Carlo sampler for efficient
estimation, and investigate the impact of various methods of penalty tuning and
thresholding for variable selection. We present a simulation study examining
the performance of this method relative to models with an ordinary lasso
penalty, and apply the proposed method to identify groups of predictive genetic
and clinical risk factors for Alzheimer's disease in the Religious Orders Study
and Memory and Aging Project (ROSMAP) prospective cohort studies of AD and
dementia.


  The technical merits of weak value amplification techniques are analyzed. We
consider models of several different types of technical noise in an optical
context and show that weak value amplification techniques (which only use a
small fraction of the photons) compare favorably with standard techniques
(which uses all of them). Using the Fisher information metric, we demonstrate
that weak value techniques can put all of the Fisher information about the
detected parameter into a small portion of the events and show how this fact
alone gives technical advantages. We go on to consider a time correlated noise
model, and find that a Fisher information analysis indicates that while the
standard method can have much larger information about the detected parameter
than the postselected technique. However, the estimator needed to gather the
information is technically difficult to implement, showing that the inefficient
(but practical) signal-to-noise estimation of the parameter is usually
superior. We also describe other technical advantages unique to imaginary weak
value amplification techniques, focusing on beam deflection measurements. In
this case, we discuss combined noise types (such as detector transverse jitter,
angular beam jitter before the interferometer and turbulence) for which the
interferometric weak value technique gives higher Fisher information over
conventional methods. We go on to calculate the Fisher information of the
recently proposed photon recycling scheme for beam deflection measurements, and
show it further boosts the Fisher information by the inverse postselection
probability relative to the standard measurement case.


  Active learning aims to identify the most informative data from an unlabeled
data pool that enables a model to reach the desired accuracy rapidly. This
benefits especially deep neural networks which generally require a huge number
of labeled samples to achieve high performance. Most existing active learning
methods have been evaluated in an ideal setting where only samples relevant to
the target task, i.e., in-distribution samples, exist in an unlabeled data
pool. A data pool gathered from the wild, however, is likely to include samples
that are irrelevant to the target task at all and/or too ambiguous to assign a
single class label even for the oracle. We argue that assuming an unlabeled
data pool consisting of samples from various distributions is more realistic.
In this work, we introduce new active learning benchmarks that include
ambiguous, task-irrelevant out-of-distribution as well as in-distribution
samples. We also propose an active learning method designed to acquire
informative in-distribution samples in priority. The proposed method leverages
both labeled and unlabeled data pools and selects samples from clusters on the
feature space constructed via contrastive learning. Experimental results
demonstrate that the proposed method requires a lower annotation budget than
existing active learning methods to reach the same level of accuracy.


  Feed-forward ReLU neural networks partition their input domain into finitely
many "affine regions" of constant neuron activation pattern and affine
behaviour. We analyze their mathematical structure and provide algorithmic
primitives for an efficient application of linear programming related
techniques for iterative minimization of such non-convex functions. In
particular, we propose an extension of the Simplex algorithm which is iterating
on induced vertices but, in addition, is able to change its feasible region
computationally efficiently to adjacent "affine regions". This way, we obtain
the Barrodale-Roberts algorithm for LAD regression as a special case, but also
are able to train the first layer of neural networks with L1 training loss
decreasing in every step.


  New invariants in the one-dimensional family of 3-periodic orbits in the
elliptic billiard were introduced by the authors in "Can the Elliptic Billiard
Still Surprise Us?" (2020), Math. Intelligencer, 42(1): 6--17, some of which
were generalized to $N>3$. Invariants mentioned there included ratios of radii
and/or areas, sum of angle cosines, and a special stationary circle. Here we
present some of the proofs omitted there as well as a few new related facts.


  In a previous article [math.CO/9712207], we derived the alternating-sign
matrix (ASM) theorem from the Izergin-Korepin determinant for a partition
function for square ice with domain wall boundary. Here we show that the same
argument enumerates three other symmetry classes of alternating-sign matrices:
VSASMs (vertically symmetric ASMs), even HTSASMs (half-turn-symmetric ASMs),
and even QTSASMs (quarter-turn-symmetric ASMs). The VSASM enumeration was
conjectured by Mills; the others by Robbins [math.CO/0008045]. We introduce
several new types of ASMs: UASMs (ASMs with a U-turn side), UUASMs (two U-turn
sides), OSASMs (off-diagonally symmetric ASMs), OOSASMs (off-diagonally,
off-antidiagonally symmetric), and UOSASMs (off-diagonally symmetric with
U-turn sides). UASMs generalize VSASMs, while UUASMs generalize VHSASMs
(vertically and horizontally symmetric ASMs) and another new class, VHPASMs
(vertically and horizontally perverse). OSASMs, OOSASMs, and UOSASMs are
related to the remaining symmetry classes of ASMs, namely DSASMs (diagonally
symmetric), DASASMs (diagonally, anti-diagonally symmetric), and TSASMs
(totally symmetric ASMs). We enumerate several of these new classes, and we
provide several 2-enumerations and 3-enumerations.
  Our main technical tool is a set of multi-parameter determinant and Pfaffian
formulas generalizing the Izergin-Korepin determinant for ASMs and the Tsuchiya
determinant for UASMs [solv-int/9804010]. We evaluate specializations of the
determinants and Pfaffians using the factor exhaustion method.


  he inhomogeneous structure of a fluid at a wall can be characterized in
several ways. Within a thermodynamic description the surface free energy
$\gamma$ and the excess adsorption $\Gamma$ are of central importance. For
theoretical studies closed expression of $\gamma$ and $\Gamma$ can be very
valuable; however, even for a well-studied model system such as a hard-sphere
fluid at a planar hard wall, the accuracy of existing expressions for $\gamma$
and $\Gamma$, compared to precise computer simulation data, can still be
improved. Here, we compare several known expressions for $\gamma$ and $\Gamma$
to the most precise computer simulation data. While good agreement is generally
found at low to intermediate fluid densities, the existing parameterizations
show significant deviation at high density. In this work, we propose new
parameterizations for $\gamma$ and $\Gamma$ that agree with the simulation data
within statistical error over the entire fluid density range.


  The present paper is devoted to an algebraic treatment of the joint spectral
theory within the framework of Noetherian modules over an algebra finite
extension of an algebraically closed field. We prove the spectral mapping
theorem and analyze the index of tuples in purely algebraic case. The index
function over tuples from the coordinate ring of a variety is naturally
extended up to a numerical Tor-polynomial. Based on Serre's multiplicity
formula, we deduce that Tor-polynomial is just the Samuel polynomial of the
local algebra.


  In the context of load balancing, Lu et al. introduced the distributed
Join-Idle-Queue algorithm, where a group of dispatchers distribute jobs to a
cluster of parallel servers. Each dispatcher maintains a queue of idle servers;
when a job arrives to a dispatcher, it sends it to a server on its queue, or to
a random server if the queue is empty. In turn, when a server has no jobs, it
requests to be placed on the idle queue of a randomly chosen dispatcher.
  Although this algorithm was shown to be quite effective, the original
asymptotic analysis makes simplifying assumptions that become increasingly
inaccurate as the system load increases. Further, the analysis does not
naturally generalize to interesting variations, such as having a server request
to be placed on the idle queue of a dispatcher before it has completed all
jobs, which can be beneficial under high loads.
  We provide a new asymptotic analysis of Join-Idle-Queue systems based on mean
field fluid limit methods, deriving families of differential equations that
describe these systems. Our analysis avoids previous simplifying assumptions,
is empirically more accurate, and generalizes naturally to the variation
described above, as well as other simple variations. Our theoretical and
empirical analyses shed further light on the performance of Join-Idle-Queue,
including potential performance pitfalls under high load.


  The capture of a compact object in a galactic nucleus by a massive black hole
(MBH) is the best way to map space and time around it. Compact objects such as
stellar black holes on a capture orbit with a very high eccentricity have been
wrongly assumed to be lost for the system after an intense burst of radiation,
which has been described as a "direct plunge". We prove that these very
eccentric capture orbits spend actually a similar number of cycles in a
LISA-like detector as those with lower eccentricities if the central MBH is
spinning. Although the rates are higher for high-eccentricity EMRIs, the spin
also enhances the rates of lower-eccentricity EMRIs. This last kind have
received more attention because of the fact that high-eccentricity EMRIs were
thought to be direct plunges and thus negligible. On the other hand, recent
work on stellar dynamics has demonstrated that there seems to be a complot in
phase space acting on these lower-eccentricity captures, since their rates
decrease significantly by the presence of a blockade in the rate at which
orbital angular momenta change takes place. This so-called "Schwarzschild
barrier" is a result of the impact of relativistic precession on to the stellar
potential torques, and thus it affects the enhancement on lower-eccentricity
EMRIs that one would expect from resonant relaxation. We confirm and quantify
the existence of this barrier using a statitical sample of 2,500
direct-summation N-body simulations using both a post-Newtonian but also, and
for the first time, a geodesic approximation for the relativistic orbits. The
existence of the barrier prevents "traditional EMRIs" from approaching the
central MBH, but if the central MBH is spinning the rate will be anyway
dominated by highly-eccentric extreme-mass ratio inspirals, which insolently
ignore the presence of the barrier, because they are driven by two-body
relaxation.


  Clustering is widely studied in statistics and machine learning, with
applications in a variety of fields. As opposed to classical algorithms which
return a single clustering solution, Bayesian nonparametric models provide a
posterior over the entire space of partitions, allowing one to assess
statistical properties, such as uncertainty on the number of clusters. However,
an important problem is how to summarize the posterior; the huge dimension of
partition space and difficulties in visualizing it add to this problem. In a
Bayesian analysis, the posterior of a real-valued parameter of interest is
often summarized by reporting a point estimate such as the posterior mean along
with 95% credible intervals to characterize uncertainty. In this paper, we
extend these ideas to develop appropriate point estimates and credible sets to
summarize the posterior of clustering structure based on decision and
information theoretic techniques.


  Although large language models (LLMs) have achieved great success in vast
real-world applications, their vulnerabilities towards noisy inputs have
significantly limited their uses, especially in high-stake environments. In
these contexts, it is crucial to ensure that every prediction made by large
language models is stable, i.e., LLM predictions should be consistent given
minor differences in the input. This largely falls into the study of certified
robust LLMs, i.e., all predictions of LLM are certified to be correct in a
local region around the input. Randomized smoothing has demonstrated great
potential in certifying the robustness and prediction stability of LLMs.
However, randomized smoothing requires adding noise to the input before model
prediction, and its certification performance depends largely on the model's
performance on corrupted data. As a result, its direct application to LLMs
remains challenging and often results in a small certification radius. To
address this issue, we take advantage of the multitasking nature of LLMs and
propose to denoise the corrupted inputs with LLMs in a self-denoising manner.
Different from previous works like denoised smoothing, which requires training
a separate model to robustify LLM, our method enjoys far better efficiency and
flexibility. Our experiment results show that our method outperforms the
existing certification methods under both certified robustness and empirical
robustness. The codes are available at
https://github.com/UCSB-NLP-Chang/SelfDenoise.


  Structured light 3D surface imaging is a school of techniques in which
structured light patterns are used for measuring the depth map of the object.
Among all the designed structured light patterns, phase pattern has become most
popular because of its high resolution and high accuracy. Accordingly, phase
measuring profolimetry (PMP) has become the mainstream of structured light
technology. In this letter, we introduce the concept of phase sampling
profilometry (PSP) that calculates the phase unambiguously in the
spatial-frequency domain with only one pattern image. Therefore, PSP is capable
of measuring the 3D shapes of the moving objects robustly with single-shot.


  Manually constructing a Wordnet is a difficult task, needing years of
experts' time. As a first step to automatically construct full Wordnets, we
propose approaches to generate Wordnet synsets for languages both resource-rich
and resource-poor, using publicly available Wordnets, a machine translator
and/or a single bilingual dictionary. Our algorithms translate synsets of
existing Wordnets to a target language T, then apply a ranking method on the
translation candidates to find best translations in T. Our approaches are
applicable to any language which has at least one existing bilingual dictionary
translating from English to it.


  A theory of intermittency differentiation is developed for a general class of
Gaussian Multiplicative Chaos measures including the measure of Bacry and Muzy
on the interval and circle as special cases. An exact, non-local functional
equation is derived for the derivative of a general functional of the total
mass of the measure with respect to intermittency. The formal solution is given
in the form of an intermittency expansion and proved to be a renormalized
expansion in the centered moments of the total mass of the measure. The full
intermittency expansion of the Mellin transform of the total mass is computed
in terms of the corresponding expansion of log-moments. The theory is shown to
extend to the dependence structure of the measure. For application, the
intermittency expansion of the Bacry-Muzy measure on the circle is computed
exactly, and the Morris integral probability distribution is shown to reproduce
the moments of the total mass and the intermittency expansion, resulting in the
conjecture that it is the distribution of the total mass. It is conjectured in
general that the intermittency expansion captures the distribution of the total
mass uniquely.


  In this study, a gait phase classification method based on SVM multiclass
classification is introduced, with a focus on the precise identification of the
stance and swing phases, which are further subdivided into seven phases. Data
from individual IMU sensors, such as Shank Acceleration X, Y, Z, Shank Gyro X,
and Knee Angles, are used as features in this classification model. The
suggested technique successfully classifies the various gait phases with a
significant accuracy of about 90.3%. Gait phase classification is crucial,
especially in the domains of exoskeletons and prosthetics, where accurate
identification of gait phases enables seamless integration with assistive
equipment, improving mobility, stability, and energy economy. This study
extends the study of gait and offers an effective method for correctly
identifying gait phases from Shank IMU sensor data, with potential applications
in biomechanical research, exoskeletons, rehabilitation, and prosthetics.


  This is Part II of a two-part paper series that studies the use of the
proportional fairness (PF) utility function as the basis for capacity
allocation and scheduling in multi-channel multi-rate wireless networks. The
contributions of Part II are twofold. (i) First, we extend the problem
formulation, theoretical results, and algorithms to the case of time-varying
channels, where opportunistic capacity allocation and scheduling can be
exploited to improve system performance. We lay down the theoretical foundation
for optimization that "couples" the time-varying characteristic of channels
with the requirements of the underlying applications into one consideration. In
particular, the extent to which opportunistic optimization is possible is not
just a function of how fast the channel characteristics vary, but also a
function of the elasticity of the underlying applications for delayed capacity
allocation. (ii) Second, building upon our theoretical framework and results,
we study subcarrier allocation and scheduling in orthogonal frequency division
multiplexing (OFDM) cellular wireless networks. We introduce the concept of a
W-normalized Doppler frequency to capture the extent to which opportunistic
scheduling can be exploited to achieve throughput-fairness performance gain. We
show that a "look-back PF" scheduling can strike a good balance between system
throughput and fairness while taking the underlying application requirements
into account.


  We investigate the multiplicity properties of 408 B-type stars observed in
the 30 Doradus region of the Large Magellanic Cloud with multi-epoch
spectroscopy from the VLT-FLAMES Tarantula Survey (VFTS). We use a
cross-correlation method to estimate relative radial velocities from the helium
and metal absorption lines for each of our targets. Objects with significant
radial-velocity variations (and with an amplitude larger than 16 km/s) are
classified as spectroscopic binaries. We find an observed spectroscopic binary
fraction (defined by periods of <10^3.5 d and mass ratios >0.1) for the B-type
stars, f_B(obs) = 0.25 +/- 0.02, which appears constant across the field of
view, except for the two older clusters (Hodge 301 and SL 639). These two
clusters have significantly lower fractions of 0.08 +/- 0.08 and 0.10 +/- 0.09,
respectively. Using synthetic populations and a model of our observed epochs
and their potential biases, we constrain the intrinsic multiplicity properties
of the dwarf and giant (i.e. relatively unevolved) B-type stars in 30 Dor. We
obtain a present-day binary fraction f_B(true) = 0.58 +/- 0.11, with a flat
period distribution. Within the uncertainties, the multiplicity properties of
the B-type stars agree with those for the O stars in 30 Dor from the VFTS.


  A longstanding problem attributed to I. Schur says that for a finite group
$G$, the exponent of the second homology group $H_2(G, \mathbb{Z})$ divides the
exponent of $G$. In this paper, we prove this conjecture for finite nilpotent
groups of odd exponent and of nilpotency class 5, $p$-central metabelian $p$
groups, and groups considered by L. E . Wilson in \cite{LEW}. Moreover, we
improve several bounds given by various authors.


  We propose a framework for tightly-coupled lidar inertial odometry via
smoothing and mapping, LIO-SAM, that achieves highly accurate, real-time mobile
robot trajectory estimation and map-building. LIO-SAM formulates lidar-inertial
odometry atop a factor graph, allowing a multitude of relative and absolute
measurements, including loop closures, to be incorporated from different
sources as factors into the system. The estimated motion from inertial
measurement unit (IMU) pre-integration de-skews point clouds and produces an
initial guess for lidar odometry optimization. The obtained lidar odometry
solution is used to estimate the bias of the IMU. To ensure high performance in
real-time, we marginalize old lidar scans for pose optimization, rather than
matching lidar scans to a global map. Scan-matching at a local scale instead of
a global scale significantly improves the real-time performance of the system,
as does the selective introduction of keyframes, and an efficient sliding
window approach that registers a new keyframe to a fixed-size set of prior
``sub-keyframes.'' The proposed method is extensively evaluated on datasets
gathered from three platforms over various scales and environments.