  The SKA will be a unique instrument with which to study the evolution of the
gas content of galaxies. A proposed deep (~8 Msec) 'pencil-beam' survey is
simulated using recently updated specifications for SKA sensitivity and survey
speed. Almost 10^7 galaxies could be detected in the redshifted 21cm line, most
at redshifts in excess of two. This will enable confident statements to be made
about the evolution of the cosmic HI density and the HI mass function to z=3,
corresponding to a lookback time of 11 Gyr. However, galaxies or groups of
galaxies with masses the same as the most HI-massive galaxies at z=0 will be
detectable at redshifts of 6, if they exist. The ideal instrument for studying
HI evolution would have an instantaneous sensitivity at least a factor of two
higher than current specifications in the critical frequency range 200-500 MHz,
or A/T > 2x10^4 m^2/K. The capabilities of the SKA will be highly complementary
to ALMA which will be able to study the evolution of the molecular gas
component over the same redshift range.


  We propose a novel knowledge distillation framework for effectively teaching
a sensorimotor student agent to drive from the supervision of a privileged
teacher agent. Current distillation for sensorimotor agents methods tend to
result in suboptimal learned driving behavior by the student, which we
hypothesize is due to inherent differences between the input, modeling
capacity, and optimization processes of the two agents. We develop a novel
distillation scheme that can address these limitations and close the gap
between the sensorimotor agent and its privileged teacher. Our key insight is
to design a student which learns to align their input features with the
teacher's privileged Bird's Eye View (BEV) space. The student then can benefit
from direct supervision by the teacher over the internal representation
learning. To scaffold the difficult sensorimotor learning task, the student
model is optimized via a student-paced coaching mechanism with various
auxiliary supervision. We further propose a high-capacity imitation learned
privileged agent that surpasses prior privileged agents in CARLA and ensures
the student learns safe driving behavior. Our proposed sensorimotor agent
results in a robust image-based behavior cloning agent in CARLA, improving over
current models by over 20.6% in driving score without requiring LiDAR,
historical observations, ensemble of models, on-policy data aggregation or
reinforcement learning.


  The analyticity of response functions and scattering amplitudes implies
powerful relations between low-energy observables and the underlying
short-distance dynamics. These 'IR/UV' relations are rooted in basic physical
principles, such as causality and unitarity. In this paper, we seek similar
connections in inflation, relating cosmological observations to the physics
responsible for the accelerated expansion. We assume that the inflationary
theory is Lorentz invariant at short distances, but allow for non-relativistic
interactions and a non-trivial speed of propagation at low energies. Focusing
on forward scattering, we derive a 'sum rule' which equates a combination of
low-energy parameters to an integral which is sensitive to the high-energy
behavior of the theory. While for relativistic amplitudes unitarity is
sufficient to prove positivity of the sum rule, this is not guaranteed in the
non-relativistic case. We discuss the conditions under which positivity still
applies, and show that they are satisfied by all known UV completions of
single-field inflation. In that case, we obtain a consistency condition for
primordial non-Gaussianity, which constrains the size and the sign of the
equilateral four-point function in terms of the amplitude of the three-point
function. The resulting bound rules out about half of the parameter space that
is still allowed by current observations. Finding a violation of our
consistency condition would point towards less conventional theories of
inflation, or violations of basic physical principles.


  Weakening the Euclidean assumption in special relativity and the
coordinate-independence hypothesis in general relativity for the de Sitter
space, we propose a de Sitter invariant special relativity with two universal
constants of speed $c$ and length $R$ based on the principle of relativity and
the postulate of universal constants $c$ and $R$ on de Sitter space with
Beltrami metric. We also propose a postulate on the origin of the inertial
motions and inertial systems as a base of the principle of relativity. We show
that the Beltrami-de Sitter space provides such a model that the origin of
inertia should be determined by the cosmological constant $\Lambda$ if the
length $R$ is linked with $\Lambda$. In addition, via the `gnomonic' projection
the uniform straight-line motion on Beltrami-de Sitter space is linked with the
uniform motion along a great `circle' on de Sitter space embedded in 5-d
Minkowski space.


  When a thick cylindrical coin is tossed in the air and lands without bouncing
on an inelastic substrate, it ends up on its face or its side. We account for
the rigid body dynamics of spin and precession and calculate the probability
distribution of heads, tails, and sides for a thick coin as a function of its
dimensions and the distribution of its initial conditions. Our theory yields a
simple expression for the aspect ratio of homogeneous coins with a prescribed
frequency of heads/tails compared to sides, which we validate by tossing
experiments using coins of different aspect ratios.


  Governments across the world are currently facing the task of selecting
suitable intervention strategies to cope with the effects of the COVID-19
pandemic. This is a highly challenging task, since harsh measures may result in
economic collapse while a relaxed strategy might lead to a high death toll.
Motivated by this, we consider the problem of forming intervention strategies
to mitigate the impact of the COVID-19 pandemic that optimize the trade-off
between the number of deceases and the socio-economic costs. We demonstrate
that the healthcare capacity and the testing rate highly affect the optimal
intervention strategies. Moreover, we propose an approach that enables
practical strategies, with a small number of policies and policy changes, that
are close to optimal. In particular, we provide tools to decide which policies
should be implemented and when should a government change to a different
policy. Finally, we consider how the presented results are affected by
uncertainty in the initial reproduction number and infection fatality rate and
demonstrate that parametric uncertainty has a more substantial effect when
stricter strategies are adopted.


  We examine several definitions of soficity for monoids obtained by
generalizing various definitions of sofic groups. They are not all equivalent
and include the definition recently introduced by Ceccherini-Silberstein and
Coornaert. One of these definitions readily generalizes to semigroups (albeit
in an arguably unsatisfying way), thus addressing a question asked by Kambites.
We conclude by proposing a definition of soficity for a general dynamical
system consisting of a semigroup acting by measure-preserving transformations
on a probability space.


  Recently Kawabata found that the conductance in Tomonaga-Luttinger (TL)
liquids should not be renormalized if one incorporates the renormalization of
applied fields correctly. This claim is generalized to include the interactions
which carry the large momentum transfer. We thus find that Kawabata's
conclusion holds generally for the class of TL liquids. A key observation is
that such irrelevant interactions merely renormalize the velocity and the TL
parameter at the massless TL fixed point.


  The paper presents a proof of the Hodge Riemann relations for the
combinatorial intersection cohomology of a polytope, as fist given by K.Karu,
in terms of geometric operations on polytopes.


  High-temperature phase behavior in the system LixNa1-xNbO3 has been studied
by using high-resolution powder neutron diffraction. Each of the three
compositions studied in the Na-rich part of the phase diagram (x = 0.03, 0.08
and 0.12) shows evidence for distinct and complex structural modulations based
on different tilting schemes of NbO6 octahedral units. Whilst octahedral
tilting is prevalent in the structural chemistry of perovskites the nature of
complexity of the phases observed here is unprecedented. Neither of the
long-range tilt phases observed in NaNbO3 itself occurs here; instead a novel
phase with a well-defined 4-fold superlattice is observed for the composition
Li0.12Na0.88NbO3, and yet more complex phases with modulations based on 20-fold
and 30-fold repeats are observed for Li0.03Na0.97NbO3 and Li0.08Na0.92NbO3,
respectively. This peculiar structural behavior makes the system LixNa1-xNbO3
the most structurally complex 'simple' perovskite known.


  We investigated the spatial correlation between the arrival directions of the
highest energy cosmic rays (HECRs) detected by the Akeno Giant Air Shower Array
(AGASA) with energies above $4 \times 10^{19}$ eV and the positions of galaxies
observed by the Sloan Digital Sky Survey (SDSS) within $z = 0.024$. We
systematically tested the dependence of the correlation on the redshift ranges
and properties of the galaxies, i.e., absolute luminosity, color, and
morphology, to understand where HECR sources are and what objects are HECR
sources. In the systematic survey, we found potential signals of the positive
correlation at small angular scale ($<10^{\circ}$) with the (non-penalized)
chance probability less than 5% in intermediate redshift ranges. Then, we
estimated penalized probabilities to compensate the trial effects of angular
scan, and found that the strongest correlation is produced by early-type
galaxies in $0.012 \leq z < 0.018$ at 90% C.L. The possible origin of HECRs
which correlating galaxies imply is also discussed.


  The present study is both a reanalysis and an extension of the approach
initiated by Eremin and Voloshin(referenced in the text). We attempt to
interpret here the rapidity-spectra of the various particles produced in both
$Pb+Pb$ and $Au+Au$ collisions at CERN-SPS and RHIC-BNL. The study made here is
wider in scope and is more species-specific than the earlier ones for which the
results obtained here have been compared with those suggested by some previous
works based on HIJING, VENUS etc, at various centralities. The study reconfirms
that the constituent parton picture of the particles provides a better and more
unified description of the rapidity-density yields for the various secondaries,
including some light cluster particles like deuteron even in heavy ion
collisions.


  We study properties of a parafermionic generalization of the hyperbolic
hypergeometric function appearing as the most important part in the fusion
matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev
modular double. We show that this generalized hypergeometric function is a
limiting form of the rarefied elliptic hypergeometric function $V^{(r)}$ and
derive its transformation properties and a mixed difference-recurrence equation
satisfied by it. At the intermediate level we describe symmetries of a more
general rarefied hyperbolic hypergeometric function. An important $r=2$ case
corresponds to the supersymmetric hypergeometric function given by the integral
appearing in the fusion matrix of $N=1$ super Liouville field theory and the
Racah-Wigner symbols of the quantum algebra ${\rm U}_q({\rm osp}(1|2))$. We
indicate relations to the standard Regge symmetry and prove some previous
conjectures for the supersymmetric Racah-Wigner symbols by establishing their
different parametrizations.


  In the biology field of botany, leaf shape recognition is an important task.
One way of characterising the leaf shape is through the centroid contour
distances (CCD). Each CCD path might have different resolution, so
normalisation is done by considering that they are circular densities.
Densities are rotated by subtracting the mean preferred direction. Distance
measures between densities are used to produce a hierarchical clustering method
to classify the leaves. We illustrate our approach with a real dataset.


  We clarify some properties of projective superspace by using a manifestly
superconformal notation. In particular, we analyze the N=2 scalar multiplet in
detail, including its action, and the propagator and its super-Schwinger
parameters. The internal symmetry is taken to be noncompact (after Wick
rotation), allowing boundary conditions that preserve it off shell.
Generalization to N=4 suggests the coset superspace PSU(2,2|4)/OSp(4|4) for the
AdS/CFT superstring.


  Using a PT symmetric regularization technique we reminad the reader that and
how (a) the SUSY is re-established between the two shifted harmonic oscillator
potentials $ V(q)=q^2+{G}/{q^2}+ const$ and (b) many non-equivalent Hermitian
and non-Hermitian (PT symmetric) systems may often be studied in parallel (with
a schematic solvable illustrative example added).


  Understanding protein sequences is vital and urgent for biology, healthcare,
and medicine. Labeling approaches are expensive yet time-consuming, while the
amount of unlabeled data is increasing quite faster than that of the labeled
data due to low-cost, high-throughput sequencing methods. In order to extract
knowledge from these unlabeled data, representation learning is of significant
value for protein-related tasks and has great potential for helping us learn
more about protein functions and structures. The key problem in the protein
sequence representation learning is to capture the co-evolutionary information
reflected by the inter-residue co-variation in the sequences. Instead of
leveraging multiple sequence alignment as is usually done, we propose a novel
method to capture this information directly by pre-training via a dedicated
language model, i.e., Pairwise Masked Language Model (PMLM). In a conventional
masked language model, the masked tokens are modeled by conditioning on the
unmasked tokens only, but processed independently to each other. However, our
proposed PMLM takes the dependency among masked tokens into consideration,
i.e., the probability of a token pair is not equal to the product of the
probability of the two tokens. By applying this model, the pre-trained encoder
is able to generate a better representation for protein sequences. Our result
shows that the proposed method can effectively capture the inter-residue
correlations and improves the performance of contact prediction by up to 9%
compared to the MLM baseline under the same setting. The proposed model also
significantly outperforms the MSA baseline by more than 7% on the TAPE contact
prediction benchmark when pre-trained on a subset of the sequence database
which the MSA is generated from, revealing the potential of the sequence
pre-training method to surpass MSA based methods in general.


  For each infinite series of the classical Lie groups of type B,C or D, we
introduce a family of polynomials parametrized by the elements of the
corresponding Weyl group of infinite rank. These polynomials represent the
Schubert classes in the equivariant cohomology of the appropriate flag variety.
They satisfy a stability property, and are a natural extension of the (single)
Schubert polynomials of Billey and Haiman, which represent non-equivariant
Schubert classes. They are also positive in a certain sense, and when indexed
by maximal Grassmannian elements, or by the longest element in a finite Weyl
group, these polynomials can be expressed in terms of the factorial analogues
of Schur's Q- or P-functions defined earlier by Ivanov.


  The magnetically ordered ground state of CeRhIn$_{5}$ at ambient pressure and
zero magnetic field is an incomensurate helicoidal phase with the propagation
vector $\bf{k}$=(1/2, 1/2, 0.298) and the magnetic moment in the basal plane of
the tetragonal structure. We determined by neutron diffraction the two
different magnetically ordered phases of CeRhIn$_{5}$ evidenced by bulk
measurements under applied magnetic field in its basal plane. The low
temperature high magnetic phase corresponds to a sine-wave structure of the
magnetization being commensurate with $\bf{k}$=(1/2, 1/2, 1/4). At high
temperature, the phase is incommensurate with $\bf{k}$=(1/2, 1/2, 0.298) and a
possible small ellipticity. The propagation vector of this phase is the same as
the one of the zero-field structure.


  We consider type IIB (p,q) 5-branes in constant non-zero background tensor
potentials, or equivalently, with finite constant field strength on the brane.
At linear level, zero-modes are introduced and the physical degrees of freedom
are found to be parametrised by a real 2- or 4-form field strength on the
brane. An exact, SL(2;Z)-covariant solution to the full non-linear supergravity
equations is then constructed. The resulting metric space-times are analysed,
with special emphasis on the limiting cases with maximal values of the tensor.
The analysis provides an answer to how the various background tensor fields are
related to Born-Infeld degrees of freedom and to non-commutativity parameters.


  We present a determination of the Hubble constant from measurements of the
Sunyaev-Zeldovich Effect (SZE) in an orientation-unbiased sample of 7 z < 0.1
galaxy clusters. With improved X-ray models and a more accurate 32-GHz
calibration, we obtain H_O = 64+14-11 +/- 14_sys km/s/Mpc. for a standard CDM
cosmology, or 66+14-11 +/- 15_sys km/s/Mpc for a flat LambdaCDM cosmology. In
combination with X-ray cluster measurements and the BBN value for Omega_B, we
find Omega_M = 0.32 +/- 0.05.


  Closed-form expressions for the distributions of the order statistics on the
spacings between order statistics for the uniform distribution are obtained.
This generalizes a result by Fisher concerning tests of significance in the
harmonic analysis of a series.


  At low energies or temperatures, maximally supersymmetric Yang-Mills theory
on $\mathbb R^{(t)}\times S^1$ with large $N$ gauge group $SU(N)$ and strong
t'Hooft coupling is conjectured to be dual to the low energy dynamics of a
collection of D0-branes on a circle. We construct thermal states in the
gravitational side of the correspondence where we find a first-order phase
transition between states that are uniform on the $S^1$ and states that are
localised on it. When compared with lattice computations that are now
available, these critical values provide the first instance where a first-order
phase transition is tested on both sides of gauge/gravity duality.


  It is known that the performance of speaker identification systems is high
under the neutral talking condition; however, the performance deteriorates
under the shouted talking condition. In this paper, second-order circular
hidden Markov models (CHMM2s) have been proposed and implemented to enhance the
performance of isolated-word text-dependent speaker identification systems
under the shouted talking condition. Our results show that CHMM2s significantly
improve speaker identification performance under such a condition compared to
the first-order left-to-right hidden Markov models (LTRHMM1s), second-order
left-to-right hidden Markov models (LTRHMM2s), and the first-order circular
hidden Markov models (CHMM1s). Under the shouted talking condition, our results
show that the average speaker identification performance is 23% based on
LTRHMM1s, 59% based on LTRHMM2s, and 60% based on CHMM1s. On the other hand,
the average speaker identification performance under the same talking condition
based on CHMM2s is 72%.


  We present a new determination of the QCD strong coupling constant based on
precise lattice calculations of the $\Upsilon$ spectrum. The largest systematic
uncertainty in previous such determinations resulted from the absence of vacuum
polarization from light quarks. We substantially reduce this error by including
two flavors of dynamical light quarks and extrapolating to three. We find
$\alphathree_\V(8.2~\GeV) = 0.196(3)$ for three light flavors, corresponding to
$\alphafive_\msbar(M_Z) = 0.115(2)$. This is significantly more accurate than
previous determinations using this or any other technique.


  We propose an efficient algorithm for estimation of possibility based
qualitative expected utility. It is useful for decision making mechanisms where
each possible decision is assigned a multi-attribute possibility distribution.
The computational complexity of ordinary methods calculating the expected
utility based on discretization is growing exponentially with the number of
attributes, and may become infeasible with a high number of these attributes.
We present series of theorems and lemmas proving the correctness of our
algorithm that exibits a linear computational complexity. Our algorithm has
been applied in the context of selecting the most prospective partners in
multi-party multi-attribute negotiation, and can also be used in making
decisions about potential offers during the negotiation as other similar
problems.


  In Extended Reality (XR) applications, high data rates and low latency are
crucial for immersive experiences. Uplink transmission in XR is challenging due
to the limited antennas and power of lightweight XR devices. To improve data
transmission rates, we investigate a relay-assisted carrier aggregation (RACA)
system. The XR device simultaneously transmits data to an access point (AP) and
a relay in proximity over low-frequency and high-frequency bands, respectively.
Then, the relay down-converts and amplifies the signals to the AP, effectively
acting as an additional transmit antenna for the XR device. In this paper, we
propose two algorithms to maximize the data rate of the XR device in their
respective protocols. In the centralized protocol, the rate maximization
problem is equivalently transformed as a weighted mean square error
minimization (WMMSE) problem which can be solved iteratively by alternative
optimization. In the distributed protocol, the rate maximization problem is
decomposed into two independent sub-problems where the rate of the direct link
and the rate of the relay link are maximized by singular value decomposition
(SVD)-based methods with water-filling (WF). Simulation results show that the
rate of the RACA system is improved by $32\%$ compared to that of the
conventional carrier aggregation scheme.


  Two labeled point configurations $\{p_1,\ldots,p_n\}$ and
$\{q_1,\ldots,q_n\}$ are of the same order type if, for every $i,j,k$, the
triples $(p_i,p_j,p_k)$ and $(q_i,q_j,q_k)$ have the same orientation. In the
1980's, Goodman, Pollack and Sturmfels showed that (i) the number of order
types on $n$ points is of order $4^{n+o(n)}$, (ii) all order types can be
realized with double-exponential integer coordinates, and that (iii) certain
order types indeed require double-exponential integer coordinates. In 2018,
Caraballo, D\'iaz-B\'a{\~n}ez, Fabila-Monroy, Hidalgo-Toscano, Lea{\~n}os,
Montejano showed that at least $n^{3n+o(n)}$ order types can be realized on an
integer grid of polynomial size. In this article, we improve their result by
showing that at least $n^{4n+o(n)}$ order types can be realized on an integer
grid of polynomial size, which is essentially best possible.


  We report the experimental observation of the recently predicted peaks on the
I-V curve of the superconducting single-electron transistor at relatively high
temperatures. The peaks are due to the matching of singularities in the
quasiparticle density of states in two electrodes of a tunnel junction. The
energy shift due to Coulomb blockade provides the matching at finite voltage.


  Two families of quasi exactly solvable 2*2 matrix Schroedinger operators are
constructed. The first one is based on a polynomial matrix potential and
depends on three parameters. The second is a one-parameter generalisation of
the scalar Lame equation. The relationship between these operators and QES
Hamiltonians already considered in the literature is pointed out.


  We present the first detailed spatio-kinematical analysis of the planetary
nebula HaTr 4, one of few known to contain a post-Common-Envelope central star
system. Based on high spatial and spectral resolution spectroscopy of the
[OIII]5004.84 angstrom nebular emission line, in combination with deep,
narrow-band imagery, a spatio-kinematical model was developed in order to
accurately determine the three-dimensional morphology and orientation of HaTr
4. The nebula is found to display an extended ovoid morphology with an
equatorial enhancement consistent with a toroidal waist - a feature believed to
be typical of central star binarity. The nebular inclination is found to be in
good agreement with that determined for the binary plane, providing strong
evidence that shaping and evolution of HaTr 4 has been influenced by its
central binary system - making HaTr 4 one of only 5 planetary nebulae to have
had this observationally proven.


  An analysis of $B^{\pm}\to DK^{\pm}$ and $B^{\pm}\to D\pi^{\pm}$ decays is
presented where the $D$ meson is reconstructed in the four-body final state
$K^{\pm}\pi^{\mp} \pi^+ \pi^-$. Using LHCb data corresponding to an integrated
luminosity of $1.0{\rm \,fb}^{-1}$, first observations are made of the
suppressed ADS modes $B^{\pm}\to [\pi^{\pm} K^{\mp}\pi^+\pi^-]_D K^{\pm}$ and
$B^{\pm}\to [\pi^{\pm} K^{\mp} \pi^+\pi^- ]_D\pi^{\pm}$ with a significance of
$5.1\sigma$ and greater than $10\sigma$, respectively. Measurements of CP
asymmetries and CP-conserving ratios of partial widths from this family of
decays are also performed. The magnitude of the ratio between the suppressed
and favoured $B^{\pm}\to DK^{\pm}$ amplitudes is determined to be $r^K_B =
0.097 \pm{0.011}$.


  We bring a new perspective to semi-supervised semantic segmentation by
providing an analysis on the labeled and unlabeled distributions in training
datasets. We first figure out that the distribution gap between labeled and
unlabeled datasets cannot be ignored, even though the two datasets are sampled
from the same distribution. To address this issue, we theoretically analyze and
experimentally prove that appropriately boosting uncertainty on unlabeled data
can help minimize the distribution gap, which benefits the generalization of
the model. We propose two strategies and design an uncertainty booster
algorithm, specially for semi-supervised semantic segmentation. Extensive
experiments are carried out based on these theories, and the results confirm
the efficacy of the algorithm and strategies. Our plug-and-play uncertainty
booster is tiny, efficient, and robust to hyperparameters but can significantly
promote performance. Our approach achieves state-of-the-art performance in our
experiments compared to the current semi-supervised semantic segmentation
methods on the popular benchmarks: Cityscapes and PASCAL VOC 2012 with
different train settings.


  We investigate theoretically the effects of intrinsic spin-relaxation on the
spin-dependent transport through a single-molecule magnet (SMM), which is
weakly coupled to ferromagnetic leads. The tunnel magnetoresistance (TMR) is
obtained by means of the rate-equation approach including not only the
sequential but also the cotunneling processes. It is shown that the TMR is
strongly suppressed by the fast spin-relaxation in the sequential region and
can vary from a large positive to slight negative value in the cotunneling
region. Moreover, with an external magnetic field along the easy-axis of SMM, a
large negative TMR is found when the relaxation strength increases. Finally, in
the high bias voltage limit the TMR for the negative bias is slightly larger
than its characteristic value of the sequential region, however it can become
negative for the positive bias caused by the fast spin-relaxation.


  The notion of Einstein causality, i.e. the limiting role of the velocity of
light in the transmission of signals, is discussed. It is pointed out that
Nimtz and coworkers use the notion of signal velocity in a different sense from
Einstein and that their experimental results are in full agreement with
Einstein causality in its ordinary sense. We also show that under quite general
assumptions instantaneous spreading of particle localization occurs in quantum
theory, relativistic or not, with fields or without. We discuss if this affects
Einstein causality.


  We address the subject of transport in one-dimensional ballistic polygon
loops subject to Rashba spin-orbit coupling. We identify the role played by the
polygon vertices in the accumulation of spin-related phases by studying
interference effects as a function of the spin-orbit coupling strength. We find
that the vertices act as strong spin-scattering centers that hinder the
developing of Aharovov-Casher and Berry phases. In particular, we show that the
oscillation frequency of interference pattern can be doubled by modifying the
shape of the loop from a square to a circle.


  In quantum theory, symmetry has to be defined necessarily in terms of the
family of unit rays, the state space. The theorem of Wigner asserts that a
symmetry so defined at the level of rays can always be lifted into a linear
unitary or an antilinear antiunitary operator acting on the underlying Hilbert
space. We present a proof of this theorem which is both elementary and
economical. Central to our proof is the recognition that a given Wigner
symmetry can, by post-multiplication by a unitary symmetry, be taken into
either the identity or complex conjugation. Our analysis involves a judicious
interplay between the effect a given Wigner symmetry has on certain
two-dimensional subspaces and the effect it has on the entire Hilbert space.


  The biased Dicke model describes a system of biased two-level atoms coupled
to a bosonic field, and is expected to produce new phenomena that are not
present in the original Dicke model. In this paper, we study the critical
properties of the biased Dicke model in the classical oscillator limits. For
the finite-biased case in this limit, We present analytical results
demonstrating that the excitation energy does not vanish for arbitrary
coupling. This indicates that the second order phase transition is avoided in
the biased Dicke model, which contrasts to the original Dicke model. We also
analyze the squeezing and the entanglement in the ground state, and find that a
finite bias will strongly modify their behaviors in the vicinity of the
critical coupling point.


  End-to-end learning refers to training a possibly complex learning system by
applying gradient-based learning to the system as a whole. End-to-end learning
system is specifically designed so that all modules are differentiable. In
effect, not only a central learning machine, but also all "peripheral" modules
like representation learning and memory formation are covered by a holistic
learning process. The power of end-to-end learning has been demonstrated on
many tasks, like playing a whole array of Atari video games with a single
architecture. While pushing for solutions to more challenging tasks, network
architectures keep growing more and more complex.
  In this paper we ask the question whether and to what extent end-to-end
learning is a future-proof technique in the sense of scaling to complex and
diverse data processing architectures. We point out potential inefficiencies,
and we argue in particular that end-to-end learning does not make optimal use
of the modular design of present neural networks. Our surprisingly simple
experiments demonstrate these inefficiencies, up to the complete breakdown of
learning.


  We conduct a theoretical examination of the electronic and magnetic
characteristics of end-modified 7-atom wide armchair graphene nanoribbons
(AGNRs). Our investigation is performed within the framework of a single-band
Hubbard model, beyond a mean-field approximation. First, we carry out a
comprehensive comparison of various approaches for accommodating
di-hydrogenation configurations at the AGNR ends. We demonstrate that the
application of an on-site potential to the modified carbon atom, coupled with
the addition of an electron, replicates phenomena such as the experimentally
observed reduction in the bulk-states (BS) gap. These results for the density
of states (DOS) and electronic densities align closely with those obtained
through a method explicitly designed to account for the orbital properties of
hydrogen atoms. Furthermore, our study enables a clear differentiation between
mean-field (MF) magnetic moments, which are spatially confined to the same
sites as the topological end-states (ES), and correlation-induced magnetic
moments, which exhibit localization along all edges of the AGNRs. Notably, we
find the robustness of these correlation-induced magnetic moments relative to
end modifications, within the scope of the method we employ.


  The correctness of Harrods model in the differential form is studied. The
inadequacy of exponential growth of economy is shown; an alternative result is
obtained. By example of Phillips model, an approach to correction of
macroeconomic models (in terms of initial prerequisites) is generalized. A
methodology based on balance relations for modelling of economic dynamics,
including obtaining forecast estimates, is developed. The problems thus
considered are reduced to the solution of Volterra and Fredholm integral
equations of the second kind.


  Business Process Management (BPM) aims to improve organizational activities
and their outcomes by managing the underlying processes. To achieve this, it is
often necessary to consider information from various sources, including
unstructured textual documents. Therefore, researchers have developed several
BPM-specific solutions that extract information from textual documents using
Natural Language Processing techniques. These solutions are specific to their
respective tasks and cannot accomplish multiple process-related problems as a
general-purpose instrument. However, in light of the recent emergence of Large
Language Models (LLMs) with remarkable reasoning capabilities, such a
general-purpose instrument with multiple applications now appears attainable.
In this paper, we illustrate how LLMs can accomplish text-related BPM tasks by
applying a specific LLM to three exemplary tasks: mining imperative process
models from textual descriptions, mining declarative process models from
textual descriptions, and assessing the suitability of process tasks from
textual descriptions for robotic process automation. We show that, without
extensive configuration or prompt engineering, LLMs perform comparably to or
better than existing solutions and discuss implications for future BPM research
as well as practical usage.


  We analyse the parity violation issue in the Poincar\'e gauge theory of
gravity for the two classes of models which are built as natural extensions of
the Einstein-Cartan theory. The conservation laws of the matter currents are
revisited and we clarify the derivation of the effective Einstein field
equation and the structure of the effective energy-momentum current for
arbitrary matter sources.


  The even--even and even--odd nuclei $^{126}$Xe-$^{132}$Xe and
$^{131}$Ba-$^{137}$Ba are shown to have a well-realized $SO_8 \supset SO_6
\supset SO_3$ fermion dynamical symmetry. Their low-lying energy levels can be
described by a unified analytical expression with two (three) adjustable
parameters for even--odd (even--even) nuclei that is derived from the fermion
dynamical symmetry model. Analytical expressions are given for wavefunctions
and for $E2$ transition rates that agree well with data. The distinction
between the FDSM and IBM $SO_6$ limits is discussed. The experimentally
observed suppression of the the energy levels with increasing $SO_5$ quantum
number $\tau$ can be explained as a perturbation of the pairing interaction on
the $SO_6$ symmetry, which leads to an $SO_5$ Pairing effect for $SO_6$ nuclei.


  We present a comprehensive multiwavelength photometric analysis of the
innermost (3x3 square kpc) 110 globular clusters (GCs) of M87. Their spectral
energy distributions (SEDs) were built taking advantage of new ground-based
high resolution near-IR imaging aided by adaptive optics at the Very Large
Telescope (VLT) combined with Hubble Space Telescope (HST) ultraviolet--optical
archival data. These GC SEDs are among the best photometrically sampled
extragalactic GC SEDs. To compare with our SEDs we constructed equally sampled
SEDs of Milky Way GCs. Using both these Milky Way cluster templates and
different stellar population models, ages of >10 Gyr and metallicities of
[Fe/H] -0.6 dex are consistently inferred for the inner GCs of M87. In
addition, the metallicity of these GCs is low (Dif([Fe/H]) 0.8 dex) compared to
that of their host galaxy. These results agree with the idea that the GC
formation in M87 ceased earlier than that of the bulk of the stars of the
central part of the galaxy. The ages of the inner GCs of M87 support the idea
that these central parts of the galaxy formed first. Our data do not support
evidence of recent wet merging.


  We report a comprehensive study of low-power, octave-bandwidth,
single-soliton microresonator frequency combs in both the 1550 nm and 1064 nm
bands. Our experiments utilize fully integrated silicon-nitride Kerr
microresonators, and we demonstrate direct soliton generation with widely
available distributed-Bragg-reflector lasers that provide less than 40 mW of
chip-coupled laser power. We report measurements of soliton thermal dynamics
and demonstrate how rapid laser-frequency control, consistent with the thermal
timescale of a microresonator, facilitates stabilization of octave-bandwidth
soliton combs. Moreover, since soliton combs are completely described by
fundamental linear and nonlinear dynamics of the intraresonator field, we
demonstrate the close connection between modeling and generation of
octave-bandwidth combs. Our experiments advance the development of
self-referenced frequency combs with integrated-photonics technology, and
comb-laser sources with tens of terahertz pulse bandwidth across the
near-infrared.


  Organic aerosol (OA) is a key component to total submicron particulate matter
(PM1), and comprehensive knowledge of OA sources across Europe is crucial to
mitigate PM1 levels. Europe has a well-established air quality research
infrastructure from which yearlong datasets using 21 aerosol chemical
speciation monitors (ACSMs) and 1 aerosol mass spectrometer (AMS) were gathered
during 2013-2019. It includes 9 non-urban and 13 urban sites. This study
developed a state-of-the-art source apportionment protocol to analyse long-term
OA mass spectrum data by applying the most advanced source apportionment
strategies (i.e., rolling PMF, ME-2, and bootstrap). This harmonised protocol
enables the quantifications of the most common OA components such as
hydrocarbon-like OA (HOA), biomass burning OA (BBOA), cooking-like OA (COA),
more oxidised-oxygenated OA (MO-OOA), and less oxidised-oxygenated OA (LO-OOA).
Other components such as coal combustion OA (CCOA), solid fuel OA (SFOA: mainly
mixture of coal and peat combustion), cigarette smoke OA (CSOA), sea salt
(mostly inorganic but part of the OA mass spectrum), coffee OA, and ship
industry OA could also be separated at a few specific sites. Oxygenated OA
(OOA) components make up most of the submicron OA mass (average = 71.1%, a
range of 43.7-100%). Solid fuel combustion-related OA components (i.e., BBOA,
CCOA, and SFOA) are still considerable with in total 16.0% yearly contribution
to the OA, yet mainly during winter months (21.4%). Overall, this comprehensive
protocol works effectively across all sites governed by different sources and
generates robust and consistent source apportionment results. Our work presents
a comprehensive overview of OA sources in Europe with a unique combination of
high time resolution and long-term data coverage (9-36 months), providing
essential information to improve/validate air quality, health impact, and
climate models.


  Beyond Standard Model scenarios addressing the flavor puzzle and the
hierarchy problem generally predict dominant new physics couplings with
fermions of the third generation. In this Letter, we explore the collider and
astrophysical signatures of new light scalar and pseudoscalar particles
dominantly coupled to the $\tau$-lepton. The best experimental prospects are
expected at Belle II through the $e^+e^-\to\tau^+\tau^-\gamma\gamma$,
$\tau^+\tau^-\gamma$, $3\gamma$, mono-$\gamma$ processes, and the $\tau$
anomalous magnetic moment. The correlated effects in these searches can
unambiguously point toward the underlying new physics dynamics. Moreover, we
study astrophysics bounds - especially from core-collapse supernovae and
neutron star mergers - finding them particularly effective and complementary to
collider bounds. We carry out this program in the well-motivated context of
axion-like particles as well as generic CP-even and CP-odd particles,
highlighting possible ways to discriminate among them.


  The early-time interface instabilities in high intensity (high Weber number
and high Reynolds number) aero-breakup of a liquid drop are investigated by
numerical simulations. A combined analysis based on simulation results and
linear-instability theory show that both RT (Rayleigh-Taylor) and KH
(Kelvin-Helmholtz) instabilities contributes the dominant disturbances
originate from about the half way from the stagnation point to the equator.
This is verified further with a specially modified simulation, which decreases
the effect of KH instability while keeps other flow properties unchanged.


  During physical human robot collaboration, it is important to be able to
implement a time-varying interactive behaviour while ensuring robust stability.
Admittance control and passivity theory can be exploited for achieving these
objectives. Nevertheless, when the admittance dynamics is time-varying, it can
happen that, for ensuring a passive and stable behaviour, some spurious
dissipative effects have to be introduced in the admittance dynamics. These
effects are perceived by the user and degrade the collaborative performance. In
this paper we exploit the task redundancy of the manipulator in order to
harvest energy in the null space and to avoid spurious dynamics on the
admittance. The proposed architecture is validated by simulations and by
experiments onto a collaborative robot.


  We discuss intrinsic inhomogeneities of superconductive properties of
uniformly disordered thin films with large dimensionless conductance g. It is
shown that mesoscopic fluctuations, which usually contain a small factor 1/g,
are crucially enhanced near the critical conductance g_c >> 1 where
superconductivity is destroyed at T=0 due to Coulomb suppression of the Cooper
attraction. This leads to strong spatial fluctuations of the local transition
temperature and thus to percolative nature of the thermal superconductive
transition.


  Optimization with nonnegative orthogonality constraints has wide applications
in machine learning and data sciences. It is NP-hard due to some combinatorial
properties of the constraints. We first propose an equivalent optimization
formulation with nonnegative and multiple spherical constraints and an
additional single nonlinear constraint. Various constraint qualifications, the
first- and second-order optimality conditions of the equivalent formulation are
discussed. By establishing a local error bound of the feasible set, we design a
class of (smooth) exact penalty models via keeping the nonnegative and multiple
spherical constraints. The penalty models are exact if the penalty parameter is
sufficiently large other than going to infinity. A practical penalty algorithm
with postprocessing is then developed. It uses a second-order method to
approximately solve a series of subproblems with nonnegative and multiple
spherical constraints. We study the asymptotic convergence of the penalty
algorithm and establish that any limit point is a weakly stationary point of
the original problem and becomes a stationary point under some additional mild
conditions. Extensive numerical results on the projection problem, orthogonal
nonnegative matrix factorization problems and the K-indicators model show the
effectiveness of our proposed approach.


  This paper examines the global regularity problem on the two-dimensional
incompressible Boussinesq equations with fractional dissipation, given by
$\Lambda^\alpha u$ in the velocity equation and by $\Lambda^\beta \theta$ in
the temperature equation, where $\Lambda=\sqrt{-\Delta}$ denotes the Zygmund
operator. We establish the global existence and smoothness of classical
solutions when $(\alpha,\beta)$ is in the critical range:
$\alpha>\frac{\sqrt{1777}-23}{24} =0.798103..$, $\beta>0$ and $\alpha+ \beta
=1$. This result improves the previous work of Jiu, Miao, Wu and Zhang
\cite{JMWZ} which obtained the global regularity for $\alpha>
\frac{23-\sqrt{145}}{12} \approx 0.9132$, $\beta>0$ and $\alpha+ \beta =1$.


  Organisms in nature have evolved to exhibit flexibility in face of changes to
the environment and/or to themselves. Artificial neural networks (ANNs) have
proven useful for controlling of artificial agents acting in environments.
However, most ANN models used for reinforcement learning-type tasks have a
rigid structure that does not allow for varying input sizes. Further, they fail
catastrophically if inputs are presented in an ordering unseen during
optimization. We find that these two ANN inflexibilities can be mitigated and
their solutions are simple and highly related. For permutation invariance, no
optimized parameters can be tied to a specific index of the input elements. For
size invariance, inputs must be projected onto a common space that does not
grow with the number of projections. Based on these restrictions, we construct
a conceptually simple model that exhibit flexibility most ANNs lack. We
demonstrate the model's properties on multiple control problems, and show that
it can cope with even very rapid permutations of input indices, as well as
changes in input size. Ablation studies show that is possible to achieve these
properties with simple feedforward structures, but that it is much easier to
optimize recurrent structures.


  We compare the structural properties of galaxies formed in cosmological
simulations using the smoothed particle hydrodynamics (SPH) code GADGET with
those using the moving-mesh code AREPO. Both codes employ identical gravity
solvers and the same sub-resolution physics but use very different methods to
track the hydrodynamic evolution of gas. This permits us to isolate the effects
of the hydro solver on the formation and evolution of galactic gas disks in
GADGET and AREPO haloes with comparable numerical resolution. In a matching
sample of GADGET and AREPO haloes we fit simulated gas disks with exponential
profiles. We find that the cold gas disks formed using the moving mesh approach
have systematically larger disk scale lengths and higher specific angular
momenta than their GADGET counterparts across a wide range in halo masses. For
low mass galaxies differences between the properties of the simulated galaxy
disks are caused by an insufficient number of resolution elements which lead to
the artificial angular momentum transfer in our SPH calculation. We however
find that galactic disks formed in massive halos, resolved with 10^6
particles/cells, are still systematically smaller in the GADGET run by a factor
of ~2. The reasons for this are: 1) The excessive heating of haloes close to
the cooling radius due to spurious dissipation of the subsonic turbulence in
GADGET; and 2) The efficient delivery of low angular momentum gaseous blobs to
the bottom of the potential well. While this large population of gaseous blobs
in GADGET originates from the filaments which are pressure confined and
fragment due to the SPH surface tension while infalling into hot halo
atmospheres, it is essentially absent in the moving mesh calculation, clearly
indicating numerical rather than physical origin of the blob material.


  We construct a set of new epidemiological thresholds to address the general
problem of spreading and containment of a disease with influx of infected
individuals when the classic $\mathcal R_0$ is no longer meaningful. We provide
analytical properties of these indices and illustrate their usefulness in a
compartmental model of COVID-19 with data taken from Chile showing a good
predictive potential when contrasted with the recorded disease behaviour. This
approach and the associated analytical and numerical results allow us to
quantify the severity of an immigration of infectious individuals into a
community, and identification of the key parameters that are capable of
changing or reversing the spread of an infectious disease in specific models.


  We analyze the connection between the autocorrelation of a binary sequence
and its run structure given by the run length encoding. We show that both the
periodic and the aperiodic autocorrelation of a binary sequence can be
formulated in terms of the run structure. The run structure is given by the
consecutive runs of the sequence. Let C=(C(0), C(1),...,C(n)) denote the
autocorrelation vector of a binary sequence. We prove that the kth component of
the second order difference operator of C can be directly calculated by using
the consecutive runs of total length k. In particular this shows that the kth
autocorrelation is already determined by all consecutive runs of total length
L<k. In the aperiodic case we show how the run vector R can be efficiently
calculated and give a characterization of skew-symmetric sequences in terms of
their run length encoding.


  We study the model of a strongly non-linear chain of particles coupled to two
heat baths at different temperatures. Our main result is the existence and
uniqueness of a stationary state at all temperatures. This result extends those
of Eckmann, Pillet, Rey-Bellet to potentials with essentially arbitrary growth
at infinity. This extension is possible by introducing a stronger version of
H\"ormander's theorem for Kolmogorov equations to vector fields with
polynomially bounded coefficients on unbounded domains.


  In object recognition applications, object images usually appear with
different quality levels. Practically, it is very important to indicate object
image qualities for better application performance, e.g. filtering out
low-quality object image frames to maintain robust video object recognition
results and speed up inference. However, no previous works are explicitly
proposed for addressing the problem. In this paper, we define the problem of
object quality assessment for the first time and propose an effective approach
named Object-QA to assess high-reliable quality scores for object images.
Concretely, Object-QA first employs a well-designed relative quality assessing
module that learns the intra-class-level quality scores by referring to the
difference between object images and their estimated templates. Then an
absolute quality assessing module is designed to generate the final quality
scores by aligning the quality score distributions in inter-class. Besides,
Object-QA can be implemented with only object-level annotations, and is also
easily deployed to a variety of object recognition tasks. To our best knowledge
this is the first work to put forward the definition of this problem and
conduct quantitative evaluations. Validations on 5 different datasets show that
Object-QA can not only assess high-reliable quality scores according with human
cognition, but also improve application performance.


  Integrable equations with second order Lax pair like KdV and Camassa-Holm
(CH) exhibit interesting conformal properties and can be written in terms of
the so-called conformal invariants (Schwarz form). These properties for the CH
hierarchy are discussed in this contribution.
  The squared eigenfunctions of the spectral problem, associated to the
Camassa-Holm equation represent a complete basis of functions, which helps to
describe the Inverse Scattering Transform (IST) for the Camassa-Holm hierarchy
as a Generalised Fourier Transform (GFT). Using GFT we describe explicitly some
members of the CH hierarchy, including integrable deformations for the CH
equation. Also we show that solutions of some 2+1-dimensional generalizations
of CH can be constructed via the IST for the CH hierarchy.


  Let $\mathfrak{g}$ be a finite dimensional complex simple Lie algebra,
$\mathbb{K}$ a commutative field and $q$ a nonzero element of $\mathbb{K}$
which is not a root of unity. To each reduced decomposition of the longest
element $w_0$ of the Weyl group $W$ corresponds a PBW basis of the quantised
enveloping algebra $\mathcal{U}_q^+(\mathfrak{g})$, and one can apply the
theory of deleting-derivation to this iterated Ore extension. In particular,
for each decomposition of $w_0$, this theory constructs a bijection between the
set of prime ideals in $\mathcal{U}_q^+(\mathfrak{g})$ that are invariant under
a natural torus action and certain combinatorial objects called Cauchon
diagrams. In this paper, we give an algorithmic description of these Cauchon
diagrams when the chosen reduced decomposition of $w_0$ corresponds to a good
ordering (in the sense of Lusztig \cite{Lu2}) of the set of positive roots.
This algorithmic description is based on the constraints that are coming from
Lusztig's admissible planes \cite{Lu2}: each admissible plane leads to a set of
constraints that a diagram has to satisfy to be Cauchon. Moreover, we
explicitely describe the set of Cauchon diagrams for explicit reduced
decomposition of $w_0$ in each possible type. In any case, we check that the
number of Cauchon diagrams is always equal to the cardinal of $W$. In
\cite{CM}, we use these results to prove that Cauchon diagrams correspond
canonically to the positive subexpressions of $w_0$. So the results of this
paper also give an algorithmic description of the positive subexpressions of
any reduced decomposition of $w_0$ corresponding to a good ordering.


  Resolution, usually defined by the Rayleigh criterion or the Full Width at
Half Maximum of a Point Spread Function, is a basic property of an image. Here,
we present a new statistical definition of image resolution based on the
cross-correlation properties of the pixels in an image. It is shown that the
new definition of image resolution depends not only on the PSF of an imaging
device, but also on the signal-to-noise ratio of the data and on the structures
of an object. In an image, the resolution does not have to be uniform. Our new
definition is also suitable for the interpretation of the result of a
deconvolution. We illustrate this, in this paper, with a Wiener deconvolution.
It is found that weak structures can be extracted from low signal-to-noise
ratio data, but with low resolution; a high-resolution image was obtained from
high signal-to-noise ratio data after a Wiener deconvolution. The new
definition can also be used to compare various deconvolution algorithms on
their processing effects, such as resolution, sensitivity and sidelobe level,
etc.


  We argue that cosmic strings with high winding numbers generally form in
first-order gauge symmetry breaking phase transitions, and we demonstrate this
using computer simulations. These strings are heavier than single-winding
strings and therefore more easily observable. Their cosmological evolution may
also be very different.


  The reaction rates of neutron capture reactions on light nuclei are important
for reliably simulating nucleosynthesis in a variety of stellar scenarios.
Neutron capture reaction rates on neutron-rich C-, N-, and O-isotopes are
calculated in the framework of a hybrid compound and direct capture model. The
results are tabulated and compared with the results of previous calculations as
well as with experimental results.


  Biomedical association studies are increasingly done using clinical concepts,
and in particular diagnostic codes from clinical data repositories as
phenotypes. Clinical concepts can be represented in a meaningful, vector space
using word embedding models. These embeddings allow for comparison between
clinical concepts or for straightforward input to machine learning models.
Using traditional approaches, good representations require high dimensionality,
making downstream tasks such as visualization more difficult. We applied
Poincar\'e embeddings in a 2-dimensional hyperbolic space to a large-scale
administrative claims database and show performance comparable to
100-dimensional embeddings in a euclidean space. We then examine disease
relationships under different disease contexts to better understand potential
phenotypes.


  This paper introduces a new representation method that is mainly based on
chemical bonds among atoms in materials. Each chemical bond and its surrounded
atoms are considered as a unified unit or a local structure that is expected to
reflect a part of materials' nature. First, a material is separated into local
structures; and then represented as matrices, each of which is computed by
using information about the corresponding chemical bond as well as
orbital-field matrices of two related atoms. After that, all local structures
of the material are utilized by using the statistics point of view. In the
experiment, the new method was applied into a materials informatics application
that aims at predicting atomization energies using QM7 data set. The results of
the experiment show that the new method is more effective than two
state-of-the-art representation methods in most of the cases.


  In this paper, we propose a gradient difference based approach to text
localization in videos and scene images. The input video frame/ image is first
compressed using multilevel 2-D wavelet transform. The edge information of the
reconstructed image is found which is further used for finding the maximum
gradient difference between the pixels and then the boundaries of the detected
text blocks are computed using zero crossing technique. We perform logical AND
operation of the text blocks obtained by gradient difference and the zero
crossing technique followed by connected component analysis to eliminate the
false positives. Finally, the morphological dilation operation is employed on
the detected text blocks for scene text localization. The experimental results
obtained on publicly available standard datasets illustrate that the proposed
method can detect and localize the texts of various sizes, fonts and colors.


  In Thermal Field Dynamics, thermal states are obtained from restrictions of
vacuum states on a doubled field algebra. It is shown that the suitably doubled
Fock representations of the Heisenberg algebra do not need to be introduced by
hand but can be canonically handed down from deformations of the extended
Heisenberg bialgebra. No artificial redefinitions of fields are necessary to
obtain the thermal representations and the case of arbitrary dimension is
considered from the beginning. Our results support a possibly fundamental role
of bialgebra structures in defining a general framework for Thermal Field
Dynamics.


  The quantum mechanical formalism doesn't support our intuition, nor does it
elucidate the key concepts that govern the behaviour of the entities that are
subject to the laws of quantum physics. The arrays of complex numbers are kin
to the arrays of 0s and 1s of the early days of computer programming practice.
In this review we present steps towards a diagrammatic `high-level' alternative
for the Hilbert space formalism, one which appeals to our intuition. It allows
for intuitive reasoning about interacting quantum systems, and trivialises many
otherwise involved and tedious computations. It clearly exposes limitations
such as the no-cloning theorem, and phenomena such as quantum teleportation. As
a logic, it supports `automation'. It allows for a wider variety of underlying
theories, and can be easily modified, having the potential to provide the
required step-stone towards a deeper conceptual understanding of quantum
theory, as well as its unification with other physical theories. Specific
applications discussed here are purely diagrammatic proofs of several quantum
computational schemes, as well as an analysis of the structural origin of
quantum non-locality. The underlying mathematical foundation of this high-level
diagrammatic formalism relies on so-called monoidal categories, a product of a
fairly recent development in mathematics. These monoidal categories do not only
provide a natural foundation for physical theories, but also for proof theory,
logic, programming languages, biology, cooking, ... The challenge is to
discover the necessary additional pieces of structure that allow us to predict
genuine quantum phenomena.


  Feit and Tits (1978) proved that a nontrivial projective representation of
minimal dimension of a finite extension of a finite nonabelian simple group $G$
factors through a projective representation of $G$, except for some groups of
Lie type in characteristic 2; the exact exceptions for $G$ were determined by
Kleidman and Liebeck (1989). We generalise this result in two ways. First we
consider all low-dimensional projective representations, not just those of
minimal dimension. Second we consider all characteristically simple groups, not
just simple groups.


  Following an approach developed by Paczy\'nski & Stanek, we derive a distance
to the Large Magellanic Cloud (LMC) by comparing red clump stars from the
Hipparcos catalog with the red clump stars observed in two fields in the LMC
that were selected from the ongoing photometric survey of the Magellanic Clouds
to lie in low extinction regions. The use of red clump stars allows a single
step determination of the distance modulus to the LMC, $\mu_{0,LMC} = 18.065\pm
0.031\pm 0.09 $mag (statistical plus systematic error), and the corresponding
distance, $R_{LMC}= 41.02\pm 0.59\pm 1.74 kpc$. This measurement is in
excellent agreement with the recent determination by Udalski et al., also based
on the red clump stars, but is $\sim 0.4 $mag smaller than the generally
accepted value of $\mu_{0,LMC} = 18.50\pm 0.15 $mag. We discuss possible
reasons for this discrepancy and how it can be resolved.


  Although General Relativity (GR) has been tested extensively in the weak
gravity regime, similar tests in the strong gravity regime are still missing.
In this paper we explore the possibility to use X-ray spectropolarimetric
observations of black holes in X-ray binaries to distinguish between the Kerr
metric and the phenomenological metrics introduced by Johannsen and Psaltis
(2011) (which are not vacuum solutions of Einstein's equation) and thus to test
the no-hair theorem of GR. To this end, we have developed a numerical code that
calculates the radial brightness profiles of accretion disks and parallel
transports the wave vector and polarization vector of photons through the Kerr
and non-GR spacetimes. We used the code to predict the observational appearance
of GR and non-GR accreting black hole systems. We find that the predicted
energy spectra and energy dependent polarization degree and polarization
direction do depend strongly on the underlying spacetime. However, for large
regions of the parameter space, the GR and non-GR metrics lead to very similar
observational signatures, making it difficult to observationally distinguish
between the two types of models.


  The results from three ASCA observations of AX J0051.6-7311 = RX J0051.9-7311
are reported. Coherent pulsations with a barycentric period of 172.40 +/- 0.03
s were discovered in the third observation, with an exceptionally long exposure
time of ~177 ks. The X-ray spectrum was found to remain unchanged through these
observations, with a photon index of ~0.9. Energy-resolved pulse profiles in
the third observation reveal that the pulsations are mostly due to photons with
an energy above ~2 keV. Archival data of ROSAT and Einstein indicate that AX
J0051.6-7311 exhibits a flux variation having a factor ~> 20.


  Thermalisation is a probabilistic process. As such, it is generally expected
that when we increase the temperature of a system its classical behaviour
dominates its quantum coherences. By employing the Gibbs state of a
translationally invariant quantum spin liquid - Kitaev's honeycomb lattice
model - we demonstrate that an insulating phase at $T=0$ becomes metallic
purely by increasing temperature. In particular, we compute the finite
temperature distribution of energies and show that it diverges logarithmically,
as we move to small energies. The corresponding wave functions become critical
alike as at Anderson transitions. These characteristics are obtained within a
new exact Monte Carlo method that simulates the finite temperature behaviour of
the Kitaev model. In particular, we take into account the projection onto the
physical parity sectors, required for identifying the topological degeneracy of
the model. Our work opens the possibility to detect thermal metal behaviour in
spin liquid experiments.


  This paper is devoted to strictly hyperbolic systems and equations with
non-smooth coefficients. Below a certain level of smoothness, distributional
solutions may fail to exist. We construct generalised solutions in the
Colombeau algebra of generalised functions. Extending earlier results on
symmetric hyperbolic systems, we introduce generalised strict hyperbolicity,
construct symmetrisers, prove an appropriate G\r{a}rding inequality and
establish existence, uniqueness and regularity of generalised solutions. Under
additional regularity assumptions on the coefficients, when a classical
solution of the Cauchy problem (or of a transmission problem in the piecewise
regular case) exists, the generalised solution is shown to be associated with
the classical solution (or the piecewise classical solution satisfying the
appropriate transmission conditions).


  This paper is concerned with the steady-state propagation of an antiplane
semi-infinite crack in couple stress elastic materials. A distributed loading
applied at the crack faces and moving with the same velocity of the crack tip
is considered, and the influence of the loading profile variations and
microstructural effects on the dynamic energy release rate is investigated. The
behaviour of both energy release rate and maximum total shear stress when the
crack tip speed approaches the critical speed (either that of the shear waves
or that of the localised surface waves) is studied. The limit case
corresponding to vanishing characteristic scale lengths is addressed both
numerically and analytically by means of a comparison with classical elasticity
results.


  We study large uniform random quadrangulations whose genus grow linearly with
the number of faces, whose local convergence was recently established by
Budzinski and the author arXiv:1902.00492,arXiv:2012.05813. Here we study
several properties of these objects which are not captured by the local
topology. Namely we show that balls around the root are planar whp up to
logarithmic radius, and we prove that there exists short non-contractible
cycles with positive probability.


  Edge computing enables smart IoT-based systems via concurrent and continuous
execution of latency-sensitive machine learning (ML) applications. These
edge-based machine learning systems are often battery-powered (i.e.,
energy-limited). They use heterogeneous resources with diverse computing
performance (e.g., CPU, GPU, and/or FPGAs) to fulfill the latency constraints
of ML applications. The challenge is to allocate user requests for different ML
applications on the Heterogeneous Edge Computing Systems (HEC) with respect to
both the energy and latency constraints of these systems. To this end, we study
and analyze resource allocation solutions that can increase the on-time task
completion rate while considering the energy constraint. Importantly, we
investigate edge-friendly (lightweight) multi-objective mapping heuristics that
do not become biased toward a particular application type to achieve the
objectives; instead, the heuristics consider "fairness" across the concurrent
ML applications in their mapping decisions. Performance evaluations demonstrate
that the proposed heuristic outperforms widely-used heuristics in heterogeneous
systems in terms of the latency and energy objectives, particularly, at low to
moderate request arrival rates. We observed 8.9% improvement in on-time task
completion rate and 12.6% in energy-saving without imposing any significant
overhead on the edge system.


  We develop theory and methodology for the problem of nonparametric
registration of functional data that have been subjected to random deformation
(warping) of their time scale. The separation of this phase variation
("horizontal" variation) from the amplitude variation ("vertical" variation) is
crucial in order to properly conduct further analyses, which otherwise can be
severely distorted. We determine precise nonparametric conditions under which
the two forms of variation are identifiable. These show that the
identifiability delicately depends on the underlying rank. By means of several
counterexamples, we demonstrate that our conditions are sharp if one wishes a
genuinely nonparametric setup; and in doing so we caution that popular remedies
such as structural assumptions or roughness penalties can easily fail. We then
propose a nonparametric registration method based on a "local variation
measure", the main element in elucidating identifiability. A key advantage of
the method is that it is free of any tuning or penalisation parameters
regulating the amount of alignment, thus circumventing the problem of
over/under-registration often encountered in practice. We provide asymptotic
theory for the resulting estimators under the identifiable regime, but also
under mild departures from identifiability, quantifying the resulting bias in
terms of the amplitude variation's spectral gap.


  We present an approach to the factorization method for second order
difference equations on time scales. We construct Hilbert spaces of functions
on the time scale and show how to construct a chain of intertwined first order
$\Delta$-difference operators $\mathcal A_k$ in the sense that $\mathcal A_k$
and $\mathcal A_k^*$ act as ladder operators generating new solutions of
eigenproblem of $\mathcal A_k\mathcal A_k^*$.


  In this paper we study the regularity of the non-centered fractional maximal
operator $M_{\beta}$. As the main result, we prove that there exists
$C(n,\beta)$ such that if $q=n/(n-\beta)$ and $f$ is a radial function, then
$\|DM_{\beta}f\|_{L^{q}(\mathbb{R}^n)}\leq
C(n,\beta)\|Df\|_{L^{1}(\mathbb{R}^n)}$. The corresponding result was
previously known only if $n=1$ or $\beta=0$. Our proofs are almost free from
one-dimensional arguments. Therefore, we believe that the new approach may be
very useful when trying to extend the result for all $f\in
W^{1,1}(\mathbb{R}^n)$.


  This paper introduces our approach to the EmotioNet Challenge 2020. We pose
the AU recognition problem as a multi-task learning problem, where the
non-rigid facial muscle motion (mainly the first 17 AUs) and the rigid head
motion (the last 6 AUs) are modeled separately. The co-occurrence of the
expression features and the head pose features are explored. We observe that
different AUs converge at various speed. By choosing the optimal checkpoint for
each AU, the recognition results are improved. We are able to obtain a final
score of 0.746 in validation set and 0.7306 in the test set of the challenge.


  We investigate the effects of relative motion on entanglement harvesting by
considering a pair of Unruh-Dewitt detectors moving at arbitrary, but
independent and constant velocities, both linearly interacting with the vacuum
scalar field. Working within the weak coupling approximation, we find that the
Negativity is a (non-elementary) function of the relative velocity of the
detectors, as well as their energy gaps and minimal separation. We find
parameter regions where Negativity increases with velocity up to a maximum and
then decreases, reaching zero at some sublight velocity. At any given relative
velocity, the harvested entanglement is inversely correlated with the detector
energy gap (at sufficiently high values) and the distance of closest approach
of two detectors.


  We observe sharp step-down discontinuities in the magnetic susceptibility of
NH$_4$H$_2$PO$_4$ and NH$_4$H$_2$PO$_4$-$d$$_{60}$ (60% deuterated) along the
$a$ and $c$-axes occurring exactly at their antiferroelectric transition
temperatures. For the case of KH$_2$PO$_4$, less pronounced discontinuities
occur at the ferroelectric transition temperature. To explain this, we treat
the acid protons as individual oscillators that generate current elements which
translate to magnetic forces in near resonance with each other. With decreasing
temperature, the resonant forces become more commensurate which amplifies a
disproportionate drop off of two types of magnetic forces to eventually trigger
the structural phase transitions. For the case of NH$_4$H$_2$PO$_4$, the
associated internal magnetic field appears to aid the NH$_4$$^+$ to order at
higher temperature. At 49 K, a shoulder-like anomaly in both NH$_4$H$_2$PO$_4$
and KH$_2$PO$_4$ is attributed to a possible onset of macroscopic quantum
tunneling of protons. Our findings bring forth a new category of intrinsic
multiferroic systems.


  We study a $2d$ Hamiltonian fluid made of particles carrying spins coupled to
their velocities. At low temperatures and intermediate densities, this
conservative system exhibits phase coexistence between a collectively moving
droplet and a still gas. The particle displacements within the droplet have
remarkably similar correlations to those of birds flocks. The center of mass
behaves as an effective self-propelled particle, driven by the droplet's total
magnetization. The conservation of a generalized angular momentum leads to
rigid rotations, opposite to the fluctuations of the magnetization orientation
that, however small, are responsible for the shape and scaling of the
correlations.


  The relative entropy of the massive free bosonic field theory is studied on
various compact Riemann surfaces as a universal quantity with physical
significance, in particular, for gravitational phenomena. The exact expression
for the sphere is obtained, as well as its asymptotic series for large mass and
its Taylor series for small mass. One can also derive exact expressions for the
torus but not for higher genus. However, the asymptotic behaviour for large
mass can always be established-up to a constant-with heat-kernel methods. It
consists of an asymptotic series determined only by the curvature, hence common
for homogeneous surfaces of genus higher than one, and exponentially vanishing
corrections whose form is determined by the concrete topology. The coefficient
of the logarithmic term in this series gives the conformal anomaly.


  Kenmotsu geometry is a valuable part of contact geometry with nice
applications in other fields such as theoretical physics. In this article, we
study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu
statistical manifold with some related examples. We investigate some
statistical curvature properties of Kenmotsu statistical manifolds. We prove
that a Kenmotsu statistical manifold is not a Ricci-flat statistical manifold
with an example. Finally, we prove a very well-known Chen-Ricci inequality for
statistical submanifolds in Kenmotsu statistical manifolds of constant
$\phi-$sectional curvature by adopting optimization techniques on submanifolds.
This article ends with some concluding remarks.


  This paper investigates non-myopic path planning of mobile sensors for
multi-target tracking. Such problem has posed a high computational complexity
issue and/or the necessity of high-level decision making. Existing works tackle
these issues by heuristically assigning targets to each sensing agent and
solving the split problem for each agent. However, such heuristic methods
reduce the target estimation performance in the absence of considering the
changes of target state estimation along time. In this work, we detour the
task-assignment problem by reformulating the general non-myopic planning
problem to a distributed optimization problem with respect to targets. By
combining alternating direction method of multipliers (ADMM) and local
trajectory optimization method, we solve the problem and induce consensus
(i.e., high-level decisions) automatically among the targets. In addition, we
propose a modified receding-horizon control (RHC) scheme and edge-cutting
method for efficient real-time operation. The proposed algorithm is validated
through simulations in various scenarios.


  Social network alignment, aligning different social networks on their common
users, is receiving dramatic attention from both academic and industry. All
existing studies consider the social network to be static and neglect its
inherent dynamics. In fact, the dynamics of social networks contain the
discriminative pattern of an individual, which can be leveraged to facilitate
social network alignment. Hence, we for the first time propose to study the
problem of aligning dynamic social networks. Towards this end, we propose a
novel Dynamic social Network Alignment (DNA) framework, a unified optimization
approach over deep neural architectures, to unfold the fruitful dynamics to
perform alignment. However, it faces tremendous challenges in both modeling and
optimization: (1) To model the intra-network dynamics, we explore the local
dynamics of the latent pattern in friending evolvement and the global
consistency of the representation similarity with neighbors. We design a novel
deep neural architecture to obtain the dual embedding capturing local dynamics
and global consistency for each user. (2) To model the inter-network alignment,
we exploit the underlying identity of an individual from the dual embedding in
each dynamic social network. We design a unified optimization approach
interplaying proposed deep neural architectures to construct a common subspace
of identity embeddings. (3) To address this optimization problem, we design an
effective alternating algorithm with solid theoretical guarantees.We conduct
extensive experiments on real-world datasets and show that the proposed DNA
framework substantially outperforms the state-of-the-art methods.


  Ordered configurations of hydrogen adatoms on graphene have long been
proposed, calculated and searched for. Here we report direct observation of
several ordered configurations of H adatoms on graphene by scanning tunneling
microscopy. On the top side of the graphene plane, H atoms in the
configurations appear to stick to carbon atoms in the same sublattice. A gap
larger than 0.6 eV in the local density of states of the configurations was
revealed by scanning tunneling spectroscopy measurements. These findings can be
well explained by density functional theory calculations based on double sided
H configurations. In addition, factors that may influence H ordering are
discussed.


  We present preliminary results on a study of the 2--850 micron SEDs of a
sample of 30 FIRBACK galaxies selected at 170 micron. These sources are
representative of the brightest ~10% of the Cosmic Infrared Background. They
are a mixture of mostly local (z<~0.3) starforming galaxies, and a tail of
ULIGs that extend up to z~1, and are likely to be a similar population to faint
SCUBA sources. We use archival Spitzer IRAC and MIPS data to extend the
spectral coverage to the mid-IR regime, resulting in an unprecended (for this
redshift range) census of their infrared SEDs. This allows us to study in far
greater detail this important population linking the near-IR stellar emission
with PAH and thermal dust emission. We do this using a Markov Chain Monte Carlo
method, which easily allows for the inclusion of ~6 free parameters, as well as
an estimate of parameter uncertainties and correlations.


  Our aim in this note is to show that, for any $\epsilon>0$, there exists a
union-closed family $\mathcal F$ with (unique) smallest set $S$ such that no
element of $S$ belongs to more than a fraction $\epsilon$ of the sets in
$\mathcal F$. More precisely, we give an example of a union-closed family with
smallest set of size $k$ such that no element of this set belongs to more than
a fraction $(1+o(1))\frac{\log_2 k}{2k}$ of the sets in $\mathcal F$. We also
give explicit examples of union-closed families containing `small' sets for
which we have been unable to verify the Union-Closed Conjecture.


  We analyze, using experiments and 3D MHD numerical simulations, the dynamics
and radiative properties of a plasma ablated by a laser (1 ns,
10$^{12}$-10$^{13}$ W/cm$^2$) from a solid target, as it expands into a
homogeneous, strong magnetic field (up to 30 T) transverse to its main
expansion axis. We find that as soon as 2 ns after the start of the expansion,
the plasma becomes constrained by the magnetic field. As the magnetic field
strength is increased, more plasma is confined close to the target and is
heated by magnetic compression. We also observe a dense slab that rapidly
expands into vacuum after ~ 8 ns; however, this slab contains only ~ 2 % of the
total plasma. As a result of the higher density and increased heating of the
confined plasma, there is a net enhancement of the total x-ray emissivity
induced by the magnetization.


  We present the results of a radial velocity survey of a sample of Hyades
stars, and discuss the effects of stellar activity on radial velocity
measurements. The level of radial velocity scatter due to rotational modulation
of stellar surface features for the Hyades is in agreement with the predictions
of Saar & Donahue (1997)- the maximum radial velocity rms of up to ~50 m/s,
with an average rms of ~16 m/s. In this sample of 94 stars, we find 1 new
binary, 2 stars with linear trends indicative of binary companions, and no
close-in giant planets. We discuss the limits on extrasolar planet detection in
the Hyades and the constraints imposed on radial velocity surveys of young
stars.


  The birth kicks of black holes, arising from asymmetric mass ejection or
neutrino emission during core-collapse supernovae, are of great interest for
both observationally constraining supernova models and population-synthesis
studies of binary evolution. Recently, several efforts were undertaken to
estimate black hole birth kicks from observations of black-hole low-mass X-ray
binaries. We follow up on this work, specifically focussing on the highest
estimated black-hole kick velocities. We find that existing observations do not
require black hole birth kicks in excess of approximately 100 km/s, although
higher kicks are not ruled out.


  Objective: To simultaneously deblur and supersample prostate specific
membrane antigen (PSMA) positron emission tomography (PET) images using neural
blind deconvolution. Approach: Blind deconvolution is a method of estimating
the hypothetical "deblurred" image along with the blur kernel (related to the
point spread function) simultaneously. Traditional \textit{maximum a
posteriori} blind deconvolution methods require stringent assumptions and
suffer from convergence to a trivial solution. A method of modelling the
deblurred image and kernel with independent neural networks, called "neural
blind deconvolution" had demonstrated success for deblurring 2D natural images
in 2020. In this work, we adapt neural blind deconvolution for PVE correction
of PSMA PET images with simultaneous supersampling. We compare this methodology
with several interpolation methods, using blind image quality metrics, and test
the model's ability to predict kernels by re-running the model after applying
artificial "pseudokernels" to deblurred images. The methodology was tested on a
retrospective set of 30 prostate patients as well as phantom images containing
spherical lesions of various volumes. Results: Neural blind deconvolution led
to improvements in image quality over other interpolation methods in terms of
blind image quality metrics, recovery coefficients, and visual assessment.
Predicted kernels were similar between patients, and the model accurately
predicted several artificially-applied pseudokernels. Localization of activity
in phantom spheres was improved after deblurring, allowing small lesions to be
more accurately defined. Significance: The intrinsically low spatial resolution
of PSMA PET leads to PVEs which negatively impact uptake quantification in
small regions. The proposed method can be used to mitigate this issue, and can
be straightforwardly adapted for other imaging modalities.


  Nonlinear sigma models appear in a wide variety of physics contexts, such as
the long-range order with spontaneously broken continuous global symmetries.
There are also large classes of quantum criticality admit sigma model
descriptions in their phase diagrams without known ultraviolet complete quantum
field theory descriptions. We investigate defects in general nonlinear sigma
models in any spacetime dimensions, which include the "electric" defects that
are characterized by topological interactions on the defects, and the
"magnetic" defects that are characterized by the isometries and homotopy
groups. We use an analogue of the charge-flux attachment to show that the
magnetic defects are in general non-invertible, and the electric and magnetic
defects form junctions that combine defects of different dimensions into
analogues of higher-group symmetry. We explore generalizations that couple
nonlinear sigma models to topological quantum field theories by defect
attachment, which modifies the non-invertible fusion and braiding of the
defects. We discuss several applications, including constraints on energy
scales and scenarios of low energy dynamics with spontaneous symmetry breaking
in gauge theories, and axion gauge theories.


  We incorporate heavy-light mesons into staggered chiral perturbation theory,
working to leading order in 1/m_Q, where m_Q is the heavy quark mass. At first
non-trivial order in the chiral expansion, staggered taste violations affect
the chiral logarithms for heavy-light quantities only through the light meson
propagators in loops. There are also new analytic contributions coming from
additional terms in the Lagrangian involving heavy-light and light mesons.
Using this heavy-light staggered chiral perturbation theory, we perform the
one-loop calculation of the B (or D) meson leptonic decay constant in the
partially quenched and full QCD cases. In our treatment, we assume the validity
both of the "fourth root trick" to reduce four staggered tastes to one, and of
the prescription to represent this trick in the chiral theory by insertions of
factors of 1/4 for each sea quark loop.


  We propose a new class of determinantal point processes (DPPs) which can be
manipulated for inference and parameter learning in potentially sublinear time
in the number of items. This class, based on a specific low-rank factorization
of the marginal kernel, is particularly suited to a subclass of continuous DPPs
and DPPs defined on exponentially many items. We apply this new class to
modelling text documents as sampling a DPP of sentences, and propose a
conditional maximum likelihood formulation to model topic proportions, which is
made possible with no approximation for our class of DPPs. We present an
application to document summarization with a DPP on $2^{500}$ items.


  In this note we present a new short and direct proof of L\'{e}vy's continuity
theorem in arbitrary dimension $d$, which does not rely on Prohorov's theorem,
Helly's selection theorem or the uniqueness theorem for characteristic
functions. Instead, it is based on convolution with a small (scalar) Gaussian
distribution as well as on basic facts about weak convergence and measure
theory. Moreover, we show how, by similar means, one may prove the fact that a
distribution with integrable characteristic function is absolutely continuous
with respect to $d$-dimensional Lebesgue measure and derive the formula for its
density.


  Initiated by the recent observation of a flattened lineshape of
$IJ^{PC}=00^{-+}$ around $1.4\sim 1.5$ GeV in the $K_S K_S \pi^0$ invariant
mass spectrum by BESIII, we make a systematic partial wave analysis of $J/\psi
\to\gamma\eta_X\to \gamma K\bar{K}\pi$ based on an isobaric approach. We
demonstrate that in the scenario of the first radial excitations of the
isoscalar pseudoscalar from the $K\bar{K}\pi$ threshold to about 1.6 GeV the
non-trivial $K_S K_S \pi^0$ invariant mass spectrum can be explained by the
coupled-channel effects with the presence of the triangle singularity
mechanism. It shows that a combined fit of the three-body and two-body spectra
can be achieved which suggests that the one-state solution around $1.4\sim 1.5$
GeV proposed before still holds well. In particular, we show that the
coupled-channel effects between the two most important quasi-two-body decay
channels, $K^*\bar{K}+c.c.$ and $a_0(980)\pi$, can be well described by taking
into account the one-loop corrections in the isobaric approach. This is because
the isoscalar pseudoscalar states are coupled to the $K^*\bar{K}+c.c.$ and
$a_0(980)\pi$ channels via the $P$ and $S$ waves, respectively. As a
consequence, the coupled-channel effects can be largely absorbed into the
redefinition of the tree-level effective couplings with the transition
amplitudes computed to the order of one-loop corrections. Then, the
coupled-channel effects can be estimated by the contributions from the one-loop
rescattering amplitudes in comparison with the tree-level ones, where we find
that the rescattering contributions from the $P$-wave into the $S$-wave, or
vice verse, are apparently suppressed in the kinematic region near threshold.


  We describe a joint high contrast imaging survey for planets at Keck and VLT
of the last large sample of debris disks identified by the Spitzer Space
Telescope. No new substellar companions were discovered in our survey of 30
Spitzer-selected targets. We combine our observations with data from four
published surveys to place constraints on the frequency of planets around 130
debris disk single stars, the largest sample to date. For a control sample, we
assembled contrast curves from several published surveys targeting 277 stars
which do not show infrared excesses. We assumed a double power law distribution
in mass and semi-major axis of the form f(m,a) = $Cm^{\alpha}a^{\beta}$, where
we adopted power law values and logarithmically flat values for the mass and
semi-major axis of planets. We find that the frequency of giant planets with
masses 5-20 $M_{\rm Jup}$ and separations 10-1000 AU around stars with debris
disks is 6.27% (68% confidence interval 3.68 - 9.76%), compared to 0.73% (68%
confidence interval 0.20 - 1.80%) for the control sample of stars without
disks. These distributions differ at the 88% confidence level, tentatively
suggesting distinctness of these samples.


  Planck scale corrections arising from deformed special relativity on Hawking
radiation in Parikh and Wilczk's tunneling framework are studied. We calculate
the emission rate of massless particles tunneling though the corrected horizon
of modified black holes from gravity's rainbow. In the tunneling process, when
a particle get across the quantum horizon, the metric fluctuation not only due
to the energy conservation but also quantum effects of the space-time are taken
into account. Our results show that, the emission rate is related to the
changes of the black hole's quantum corrected entropy and consistent with an
underlying unitary theory. In the modified black hole, by using black hole
thermodynamics, a series of quantum correction terms including a logarithmic
term to the Bekenstein-Hawking entropy are obtained. Correspondingly, the
Planck scale corrected emission spectrum is obtained and it deviates from the
thermal spectrum.


  Correspondence selection aims to correctly select the consistent matches
(inliers) from an initial set of putative correspondences. The selection is
challenging since putative matches are typically extremely unbalanced, largely
dominated by outliers, and the random distribution of such outliers further
complicates the learning process for learning-based methods. To address this
issue, we propose to progressively prune the correspondences via a
local-to-global consensus learning procedure. We introduce a ``pruning'' block
that lets us identify reliable candidates among the initial matches according
to consensus scores estimated using local-to-global dynamic graphs. We then
achieve progressive pruning by stacking multiple pruning blocks sequentially.
Our method outperforms state-of-the-arts on robust line fitting, camera pose
estimation and retrieval-based image localization benchmarks by significant
margins and shows promising generalization ability to different datasets and
detector/descriptor combinations.


  The Hartman-Watson distribution with density $f_r(t)$ is a probability
distribution defined on $t \geq 0$ which appears in several problems of applied
probability. The density of this distribution is expressed in terms of an
integral $\theta(r,t)$ which is difficult to evaluate numerically for small
$t\to 0$. Using saddle point methods, we obtain the first two terms of the
$t\to 0$ expansion of $\theta(\rho/t,t)$ at fixed $\rho >0$. An error bound is
obtained by numerical estimates of the integrand, which is furthermore uniform
in $\rho$. As an application we obtain the leading asymptotics of the density
of the time average of the geometric Brownian motion as $t\to 0$. This has the
form $\mathbb{P}(\frac{1}{t} \int_0^t e^{2(B_s+\mu s)} ds \in da) = (2\pi
t)^{-1/2} g(a,\mu) e^{-\frac{1}{t} J(a)} (1 + O(t))$, with an exponent $J(a)$
which reproduces the known result obtained previously using Large Deviations
theory.


  A fundamental question in the study of water waves is the existence and
stability of solitary waves. Solitary waves have been proved to exist and have
been studied in many interesting situations, and often arise from the balance
of different forces/factors influencing the fluid dynamics, e.g. gravity,
surface tension or the fluid bottom. However, the existence of solitary waves
has remained an open problem in two of the simplest cases, namely for either
pure gravity waves or pure capillary waves in infinite depth. In this article
we settle both of these questions in two space dimensions. Precisely, we
consider incompressible, irrotational, infinite depth water wave equation,
either with gravity and without surface tension, or without gravity but with
surface tension. In both of these cases we prove that there are no solitary
waves.


  The aim of this work is to study the structure and properties of the binary
LCD codes having an automorphisms of odd prime order and to present a method
for their construction.


  Let G be a unitary group of a signed-Hermitian form h given over a
non-Archimedian local field k of residue characteristic not two. Let V be the
vector space on which h is defined. We consider minimal skew-strata, more
precisely pairs (b,a) consisting of a Lie algebra element b and a hereditary
order $a$ stable under the adjoint involution of h, such that b generates a
field whose multiplicative group is a subset of the normalizer of $a$, and some
more conditions. We prove that if two minimal skew-strata (b_i,a), i=1,2
interwine by an element of G, then they are conjugate under G, and we give a
natural generalization for minimal semisimple skew-strata.


  Counterfactual explanations provide a popular method for analyzing the
predictions of black-box systems, and they can offer the opportunity for
computational recourse by suggesting actionable changes on how to change the
input to obtain a different (i.e.\ more favorable) system output. However,
recent work highlighted their vulnerability to different types of
manipulations.
  This work studies the vulnerability of counterfactual explanations to data
poisoning. We formally introduce and investigate data poisoning in the context
of counterfactual explanations for increasing the cost of recourse on three
different levels: locally for a single instance, or a sub-group of instances,
or globally for all instances. In this context, we characterize and prove the
correctness of several different data poisonings. We also empirically
demonstrate that state-of-the-art counterfactual generation methods and
toolboxes are vulnerable to such data poisoning.


  Let $M$ be a compact connected surface with boundary. We prove that the
signal condition given by the Gauss-Bonnet theorem is necessary and sufficient
for a given smooth function $f$ on $\partial M$ (resp. on $M$) to be geodesic
curvature of the boundary (resp. the Gauss curvature) of some flat metric on
$M$ (resp. metric on $M$ with geodesic boundary). In order to provide analogous
results for this problem with $n\geq 3,$ we prove some topological restrictions
which imply, among other things, that any function that is negative somewhere
on $\partial M$ (resp. on $M$) is a mean curvature of a scalar flat metric on
$M$ (resp. scalar curvature of a metric on $M$ and minimal boundary with
respect to this metric). As an application of our results, we obtain a
classification theorem for manifolds with boundary.


  Domain-specific languages raise the level of abstraction in software
development. While it is evident that programmers can more easily reason about
very high-level programs, the same holds for compilers only if the compiler has
an accurate model of the application domain and the underlying target platform.
Since mapping high-level, general-purpose languages to modern, heterogeneous
hardware is becoming increasingly difficult, DSLs are an attractive way to
capitalize on improved hardware performance, precisely by making the compiler
reason on a higher level. Implementing efficient DSL compilers is a daunting
task however, and support for building performance-oriented DSLs is urgently
needed. To this end, we present the Delite Framework, an extensible toolkit
that drastically simplifies building embedded DSLs and compiling DSL programs
for execution on heterogeneous hardware. We discuss several building blocks in
some detail and present experimental results for the OptiML machine-learning
DSL implemented on top of Delite.


  We argue that relativistic hydrodynamics is able to make robust predictions
for soft particle production in Xe+Xe collisions at the CERN Large Hadron
Collider (LHC). The change of system size from Pb+Pb to Xe+Xe provides a unique
opportunity to test the scaling laws inherent to fluid dynamics. Using
event-by-event hydrodynamic simulations, we make quantitative predictions for
several observables: mean transverse momentum, anisotropic flow coefficients,
and their fluctuations. Results are shown as function of collision centrality.