  This paper uses the relation of the cosmic scale factor and scalar field to
solve Wheeler-DeWitt equation, gives the tunnel effect of the cosmic scale
factor a and quantum potential well of scalar field, and makes it fit with the
physics of cosmic quantum birth. By solving Wheeler-DeWitt equation we achieve
a general probability distribution of the cosmic birth, and give the analysis
of cosmic quantum birth.


  Beam splitters allow us to superpose two continuous single mode quantum
systems. To study the behaviour of their strongly mode mixing dynamics we
consider variable beam splitters and their dynamics using Wigner's phase space
distribution, W, the evolution of which is governed by the continuity-equation
$ \frac{\partial}{\partial \tau} W = - {\nabla } \cdot {J}$. We derive the form
of the corresponding Wigner current, J, of each outgoing mode after tracing out
the other. The influence of the modes on each other is analyzed and visualized
using their respective Wigner distributions and Wigner currents. This allows us
to perform geometrical analyses of the mode interactions, casting new light on
beam splitter behaviour. Several of the presented results should be immediately
testable in experiments.


  We present an algorithm of quantum engineering of large-amplitude>5
high-fidelity>0.99 even/odd Schrodinger cat states (SCSs) using a single mode
squeezed vacuum (SMSV) state as resource. Set of k beam splitters (BSs) with
arbitrary transmittance and reflectance coefficients sequentially following
each other acts as a hub that redirects a multiphoton state into the measuring
modes simultaneously measured by photon number resolving (PNR) detectors. We
show that the multiphoton state splitting guarantees significant increase of
the success probability of the cat state generator compared to its
implementation in a single PNR detector version and imposes less requirements
on ideal PNR detectors. We prove that the fidelity of the output SCSs and its
success probability are in conflict with each other (which can be quantified)
in a scheme with ineffective PNR detectors, especially when subtracting large
(say, 100) number of photons, i.e., increasing the fidelity to perfect values
leads to a sharp decrease in the success probability. In general, the strategy
of subtracting up to 20 photons from initial SMSV in setup with two BSs is
acceptable for achieving sufficiently high values of the fidelity and success
probability at the output of the generator of the SCSs of amplitude <3 with two
inefficient PNR detectors.


  In this article we focus our attention on the principle of energy
conservation within the context of systems of fluid dynamics. We give an
overview of results concerning the resolution of the famous Onsager conjecture
- which states regularity requirements for weak solutions of the incompressible
Euler system to conserve energy. Further we survey results providing optimal
sufficient regularity conditions for energy conservation for other balance
laws: compressible Euler, Navier-Stokes, magnetohydrodynamics and general
conservation laws.


  We investigate the nature of HI-rich galaxies from the ALFALFA and GASS
surveys, which are defined as galaxies in the top 10th percentile in atomic gas
fraction at a given stellar mass. We analyze outer (R>1.5 Re) stellar
populations for a subset of face-on systems using optical g-r versus r-z
colour/colour diagrams. The results are compared with those from control
samples that are defined without regard to atomic gas content, but are matched
in redshift, stellar mass and structural parameters. HI-rich early-type (C>2.6)
and late-type (C<2.6) galaxies are studied separately. When compared to the
control sample, the outer stellar populations of the majority of HI-rich
early-type galaxies are shifted in the colour/colour plane along a locus
consistent with younger stellar ages, but similar metallicities. The outer
colours of HI-rich late-type galaxies are much bluer in r-z than the HI-rich
early types, and we infer that they have outer disks which are both younger and
more metal-poor. We then proceed to analyze the galaxy environments of HI-rich
galaxies on scales of 500 kpc. HI-rich early-type galaxies with low (log M* <
10.5) stellar masses differ significantly from the control sample in that they
are more likely to be central rather than satellite systems. Their satellites
are also less massive and have younger stellar populations. Similar, but weaker
effects are found for low mass HI-rich late-type galaxies. In addition, we find
that the satellites of HI-rich late-types exhibit a greater tendency to align
along the major axis of the primary. No environmental differences are found for
massive (log M* > 10.5) HI-rich galaxies, regardless of type.


  Symmetries and conservation laws of energy, linear momentum and angular
momentum play a central role in physics, in particular in nonlinear optics.
Recently, light fields with non trivial topology, such as polarization M\"obius
strips or torus-knot beams, have been unveiled. They cannot be associated to
well-defined values of orbital and spin angular momenta (OAM and SAM), but are
invariant under coordinated rotations, i.e. rotational symmetries that are
generated by the generalized angular momentum (GAM) operator, a mixture of the
OAM and SAM operators. The discovery of the GAM, which at variance with
integer-valued OAM and SAM, can have arbitrary value, and raises the question
of its conservation in nonlinear optical processes. By driving high harmonic
generation with a polarization M\"obius strip and implementing novel OAM
characterization methods in the XUV range, we experimentally observe the
conservation of the GAM, each harmonic carrying a precise half-integer GAM
charge equal to that of the fundamental field multiplied by the harmonic order.
The GAM is thus revealed as the appropriate quantum number to describe
nonlinear processes driven by light fields containing topological polarization
singularities.


  Data collected at very frequent intervals is usually extremely sparse and has
no structure that is exploitable by modern tensor decomposition algorithms.
Thus the utility of such tensors is low, in terms of the amount of
interpretable and exploitable structure that one can extract from them. In this
paper, we introduce the problem of finding a tensor of adaptive aggregated
granularity that can be decomposed to reveal meaningful latent concepts
(structures) from datasets that, in their original form, are not amenable to
tensor analysis. Such datasets fall under the broad category of sparse point
processes that evolve over space and/or time. To the best of our knowledge,
this is the first work that explores adaptive granularity aggregation in
tensors. Furthermore, we formally define the problem and discuss what different
definitions of "good structure" can be in practice, and show that optimal
solution is of prohibitive combinatorial complexity. Subsequently, we propose
an efficient and effective greedy algorithm called IceBreaker, which follows a
number of intuitive decision criteria that locally maximize the "goodness of
structure", resulting in high-quality tensors. We evaluate our method on
synthetic, semi-synthetic and real datasets. In all the cases, our proposed
method constructs tensors that have very high structure quality.


  Ultrasound (US) imaging is based on the time-reversal principle, in which
individual channel RF measurements are back-propagated and accumulated to form
an image after applying specific delays. While this time reversal is usually
implemented as a delay-and-sum (DAS) beamformer, the image quality quickly
degrades as the number of measurement channels decreases. To address this
problem, various types of adaptive beamforming techniques have been proposed
using predefined models of the signals. However, the performance of these
adaptive beamforming approaches degrade when the underlying model is not
sufficiently accurate. Here, we demonstrate for the first time that a single
universal deep beamformer trained using a purely data-driven way can generate
significantly improved images over widely varying aperture and channel
subsampling patterns. In particular, we design an end-to-end deep learning
framework that can directly process sub-sampled RF data acquired at different
subsampling rate and detector configuration to generate high quality ultrasound
images using a single beamformer. Experimental results using B-mode focused
ultrasound confirm the efficacy of the proposed methods.


  We complete the computation of the Yang-Mills vacuum wave functional in three
dimensions at weak coupling with O(e^2) precision. We use two different methods
to solve the functional Schroedinger equation. One of them generalizes to
O(e^2) the method followed by Hatfield at O(e). The other uses the weak
coupling version of the gauge invariant formulation of the Schroedinger
equation and the ground state wave functional followed by Karabali, Nair, and
Yelnikov. These methods need to be carefully regularized to yield correct
results. This is done in this paper with full detail.


  We propose a new approach to high-intensity laser-driven electron
acceleration in a plasma. Here, we demonstrate that a plasma wave generated by
a stimulated forward-scattering of an incident laser pulse can be in a longest
acceleration phase with an incident laser wave. This is why the plasma wave has
the maximum amplification coefficient which is determined by the breakdown
(overturn) electric field in which the acceleration of injected relativistic
beam electrons occurs. We estimate qualitatively the acceleration parameters of
relativistic electrons in the field of a plasma wave generated at the
stimulated forward scattering of a high-intensity laser pulse in a plasma.


  In this paper we prove the following theorem. Let $f:\mathbb{A}^2\rightarrow
\mathbb{A}^2$ be a dominate polynomial endomorphisms defined over an
algebraically closed field $k$ of characteristic $0$. If there are no
nonconstant rational function $g:\mathbb{A}^2-rightarrow \mathbb{P}^1$
satisfying $g\circ f=g$, then there exists a point $p\in \mathbb{A}^2(k)$ whose
orbit under $f$ is Zariski dense in $\mathbb{A}^2$.
  This result gives us a positive answer to a conjecture of Amerik, Bogomolov
and Rovinsky ( and Zhang) for polynomial endomorphisms on the affine plane.


  We examine the mechanism of bundling of cytoskeletal actin filaments by two
representative bundling proteins, fascin and espin. Small-angle X-ray studies
show that increased binding from linkers drives a systematic \textit{overtwist}
of actin filaments from their native state, which occurs in a linker-dependent
fashion. Fascin bundles actin into a continuous spectrum of intermediate twist
states, while espin only allows for untwisted actin filaments and
fully-overtwisted bundles. Based on a coarse-grained, statistical model of
protein binding, we show that the interplay between binding geometry and the
intrinsic \textit{flexibility} of linkers mediates cooperative binding in the
bundle. We attribute the respective continuous/discontinous bundling mechanisms
of fascin/espin to differences in the stiffness of linker bonds themselves.


  We show that there is a general sort of models in which it is possible to
have large magnetic dipole moments for neutrinos while keeping their masses
arbitrarily small. Some examples of these models are considered.


  The chromopolarizability of a quarknonium describes the quarknonium's
interaction with soft gluonic fields and can be measured in the heavy
quarkonium decays. Within the framework of dispersion theory which consider the
$\pi\pi$ final state interaction (FSI) model-independently, we analyze the
transition $\psi^\prime\to J/\psi\pi^+\pi^-$ and obtain the
chromopolarizability $\alpha_{\psi^\prime \psi}$ and the parameter $\kappa$. It
is found that the $\pi\pi$ FSI plays an important role in extracting the
chromopolarizability from the experimental data. The obtained
chromopolarizability with the FSI is reduced to about 1/2 of that without the
FSI. With the FSI, we determine the chromopolarizability
$|\alpha_{\psi^\prime\psi}|=(1.44\pm 0.02)$ GeV$^{-3}$ and the parameter
$\kappa=0.139\pm 0.005.$ Our results could be useful in studying the
interactions of charmonium with light hadrons.


  We analyse the electromagnetic coupling in the Kemmer-Duffin-Petiau (KDP)
equation. Since the KDP--equation which describes spin-0 and spin-1 bosons is
of Dirac-type, we examine some analogies and differences from the Dirac
equation. The main difference to the Dirac equation is that the KDP equation
contains redundant components. We will show that as a result certain
interaction terms in the Hamilton form of the KDP equation do not have a
physical meaning and will not affect the calculation of physical observables.
We point out that a second order KDP equation derived by Kemmer as an analogy
to the second order Dirac equation is of limited physical applicability as (i)
it belongs to a class of second order equations which can be derived from the
original KDP equation and (ii) it lacks a back-transformation which would allow
one to obtain solutions of the KDP equation out of solutions of the second
order equation. We therefore suggest a different higher order equation which,
as far as the solutions for the wave functions are concerned, is equivalent to
the orginal first order KDP wave equation.


  We introduce the notions of infinitesimal extension and square-zero extension
in the context of simplicial commutatie algebras. We next investigate their
mutual relationship and we show that the Postnikov tower of a simplicial
commutative algebra is built out of square-zero extensions. We conclude the
notes with two applications: we give connectivity estimates for the cotangent
complex and we show how obstructions can be seen as deformations over
simplicial rings.


  We study the pure compact U(1) gauge theory with the extended Wilson action
(\beta, \gamma couplings) by finite size scaling techniques, in lattices
ranging from L=6 to L=24 in the region of \gamma <= 0 with toroidal and
spherical topologies. The phase transition presents a double peak structure
which survives in the thermodynamical limit in the torus. In the sphere the
evidence support the idea of a weaker, but still first order, phase transition.
For negative values of gamma the transition becomes weaker and larger lattices
are needed to find its asymptotic behaviour. Along the transient region the
behaviour is the typical one of a weak first order transition for both
topologies, with a region where 1/d < nu < 0.5, which becomes nu compatible
with 1/d when larger lattices are used.


  This paper analyzes the use of 3D Convolutional Neural Networks for brain
tumor segmentation in MR images. We address the problem using three different
architectures that combine fine and coarse features to obtain the final
segmentation. We compare three different networks that use multi-resolution
features in terms of both design and performance and we show that they improve
their single-resolution counterparts.


  The 2-Handed Assembly Model (2HAM) is a tile-based self-assembly model in
which, typically beginning from single tiles, arbitrarily large aggregations of
static tiles combine in pairs to form structures. The Signal-passing Tile
Assembly Model (STAM) is an extension of the 2HAM in which the tiles are
dynamically changing components which are able to alter their binding domains
as they bind together. For our first result, we demonstrate useful techniques
and transformations for converting an arbitrarily complex STAM$^+$ tile set
into an STAM$^+$ tile set where every tile has a constant, low amount of
complexity, in terms of the number and types of ``signals'' they can send, with
a trade off in scale factor.
  Using these simplifications, we prove that for each temperature $\tau>1$
there exists a 3D tile set in the 2HAM which is intrinsically universal for the
class of all 2D STAM$^+$ systems at temperature $\tau$ (where the STAM$^+$ does
not make use of the STAM's power of glue deactivation and assembly breaking, as
the tile components of the 2HAM are static and unable to change or break
bonds). This means that there is a single tile set $U$ in the 3D 2HAM which
can, for an arbitrarily complex STAM$^+$ system $S$, be configured with a
single input configuration which causes $U$ to exactly simulate $S$ at a scale
factor dependent upon $S$. Furthermore, this simulation uses only two planes of
the third dimension. This implies that there exists a 3D tile set at
temperature $2$ in the 2HAM which is intrinsically universal for the class of
all 2D STAM$^+$ systems at temperature $1$. Moreover, we show that for each
temperature $\tau>1$ there exists an STAM$^+$ tile set which is intrinsically
universal for the class of all 2D STAM$^+$ systems at temperature $\tau$,
including the case where $\tau = 1$.


  (abridged) Quasar absorption lines provide a precise test of the assumed
constancy of the fundamental constants of physics. We have investigated
potential changes in the fine-structure constant, alpha, and the
proton-to-electron mass ratio, mu.
  The many-multiplet method allows one to use optical fine-structure
transitions to constrain (Delta alpha)/alpha at better than the 10^(-5) level.
We present a new analysis of 154 quasar absorbers with 0.2 < z <3.7 in VLT/UVES
spectra. From these absorbers we find 2.2 sigma evidence for angular variations
in alpha under a dipole+monopole model. Combined with previous Keck/HIRES
observations, we find 4.1 sigma evidence for angular (and therefore spatial)
variations in alpha, with maximal increase of alpha occurring in the direction
RA=(17.3 +/- 1.0) hr, dec=(-61 +/- 10) deg. Under a model where the observed
effect is proportional to the lookback-time distance the significance increases
to 4.2 sigma. Dipole models fitted to the VLT and Keck samples and models
fitted to z<1.6 and z>1.6 sub-samples independently yield consistent estimates
of the dipole direction, which suggests that the effect is not caused by
telescope systematics. We consider a number of systematic effects and show that
they are unable to explain the observed dipole effect.
  We have used spectra of the quasars Q0405-443, Q0347-383 and Q0528-250 from
VLT/UVES to investigate the absorbers at z=2.595, 3.025 and 2.811 in these
spectra respectively. We find that (Delta mu)/mu=(10.1 +/- 6.6) x 10^(-6), (8.2
+/- 7.5) x 10^(-6) and (-1.4 +/- 3.9) x 10^(-6) in these absorbers
respectively. A second spectrum of Q0528-250 provides an additional constraint
of (Delta mu)/mu=(0.2 +/- 3.2_stat +/- 1.9_sys) x 10^(-6). The weighted mean of
these values yields (Delta mu)/mu=(1.7 +/- 2.4) x 10^(-6), the most precise
constraint on evolution in mu at z>1.


  We study linear quadratic Gaussian (LQG) control design for linear
port-Hamiltonian systems. To this end, we exploit the freedom in choosing the
weighting matrices and propose a specific choice which leads to an LQG
controller which is port-Hamiltonian and, thus, in particular stable and
passive. Furthermore, we construct a reduced-order controller via balancing and
subsequent truncation. This approach is closely related to classical LQG
balanced truncation and shares a similar a priori error bound with respect to
the gap metric. By exploiting the non-uniqueness of the Hamiltonian, we are
able to determine an optimal pH representation of the full-order system in the
sense that the error bound is minimized. In addition, we discuss consequences
for pH-preserving balanced truncation model reduction which results in two
different classical H-infinity-error bounds. Finally, we illustrate the
theoretical findings by means of two numerical examples.


  This paper deals with the dynamical system that generalizes the MIC-Kepler
system. It is shown that the Schr\"{o}dinger equation for this generalized
MIC-Kepler system can be separated in prolate spheroidal coordinates. The
coefficients of the interbasis expansions between three bases (spherical,
parabolic and spheroidal) are studied in detail. It is found that the
coefficients for this expansion of the parabolic basis in terms of the
spherical basis, and vice-versa, can be expresses through the Clebsch-Gordan
coefficients for the group SU(2) analytically continued to real values of their
arguments. The coefficients for the expansions of the prolate spheroidal basis
in terms of the spherical and parabolic bases are proved to satisfy three-term
recursion relations.


  The color connection of the parton system is an important bridge to connect
the perturbative process and the hadronization one. The special color
connection of four-heavy-quark system in $e^+e^-$ annihilation, which is the
necessary one for the doubly heavy baryon and tetraquark productions is
revisited. The hadronization effects, investigated with the help of the Quark
Combination Model are compared with the corresponding results employing the
Lund String Model in our previous work. The global properties related to a
certain color connection are not sensitive to various hadronization models.


  We present an analytical study of the loss of quantum coherence at absolute
zero. Our model consists of a harmonic oscillator coupled to an environment of
harmonic oscillators at absolute zero. We find that for an Ohmic bath, the
offdiagonal elements of the density matrix in the position representation decay
as a power law in time at late times. This slow loss of coherence in the
quantum domain is qualitatively different from the exponential decay observed
in studies of high temperature environments.


  Terpai [22] proved the Nordhaus-Gaddum bound that $\mu(G) + \mu(\overline{G})
\le 4n/3 - 1$, where $\mu(G)$ is the spectral radius of a graph $G$ with $n$
vertices. Let $s^+$ denote the sum of the squares of the positive eigenvalues
of $G$. We prove that $\sqrt{s^{+}(G)} + \sqrt{s^+(\overline{G})} < \sqrt{2}n$
and conjecture that $\sqrt{s^{+}(G)} + \sqrt{s^+(\overline{G})} \le 4n/3 - 1.$
We have used AutoGraphiX and Wolfram Mathematica to search for a
counter-example. We also consider Nordhaus-Gaddum bounds for $s^+$ and bounds
for the Randi\'c index.


  We investigate the valence quark distribution function of the pion
$v^{\pi}(x,Q^2)$ in the framework of the chiral constituent quark model and
evaluate the meson cloud effects on $v^{\pi}(x,Q^2)$. We explicitly demonstrate
how the meson cloud effects affect $v^{\pi}(x,Q^2)$ in detail. We find that the
meson cloud correction causes an overall 32\% reduction of the valence quark
distribution and an enhancement at the small Bjorken $x$ regime. Besides, we
also find that the dressing effect of the meson cloud will make the valence
quark distribution to be softer in the large $x$ region.


  The discovery of multiple stellar populations in Milky Way globular clusters
(GCs) has stimulated various follow-up studies on helium-enhanced stellar
populations. Here we present the evolutionary population synthesis models for
the spectro-photometric evolution of simple stellar populations (SSPs) with
varying initial helium abundance ($Y_{\rm ini}$). We show that $Y_{\rm ini}$
brings about {dramatic} changes in spectro-photometric properties of SSPs. Like
the normal-helium SSPs, the integrated spectro-photometric evolution of
helium-enhanced SSPs is also dependent on metallicity and age for a given
$Y_{\rm ini}$. {We discuss the implications and prospects for the
helium-enhanced populations in relation to the second-generation populations
found in the Milky Way GCs.} All of the models are available at
\url{http://web.yonsei.ac.kr/cosmic/data/YEPS.htm}.


  Considering the challenges posed by the space and time complexities in
handling extensive scientific volumetric data, various data representations
have been developed for the analysis of large-scale scientific data.
Multivariate functional approximation (MFA) is an innovative data model
designed to tackle substantial challenges in scientific data analysis. It
computes values and derivatives with high-order accuracy throughout the spatial
domain, mitigating artifacts associated with zero- or first-order
interpolation. However, the slow query time through MFA makes it less suitable
for interactively visualizing a large MFA model. In this work, we develop the
first scalable interactive volume visualization pipeline, MFA-DVV, for the MFA
model encoded from large-scale datasets. Our method achieves low input latency
through distributed architecture, and its performance can be further enhanced
by utilizing a compressed MFA model while still maintaining a high-quality
rendering result for scientific datasets. We conduct comprehensive experiments
to show that MFA-DVV can decrease the input latency and achieve superior
visualization results for big scientific data compared with existing
approaches.


  In this paper, we introduce a novel semantic generative communication (SGC)
framework, where generative users leverage text-to-image (T2I) generators to
create images locally from downloaded text prompts, while non-generative users
directly download images from a base station (BS). Although generative users
help reduce downlink transmission energy at the BS, they consume additional
energy for image generation and for uploading their generator state information
(GSI). We formulate the problem of minimizing the total energy consumption of
the BS and the users, and devise a generative user selection algorithm.
Simulation results corroborate that our proposed algorithm reduces total energy
by up to 54% compared to a baseline with all non-generative users.


  Future wireless communication systems are envisioned to share radio frequency
(RF) spectrum, with other services such as radars, in order to meet the growing
spectrum demands. In this paper, we consider co-channel spectrum sharing
between cellular systems and radars. We address the problem of target detection
by radars that are subject to shape its waveform in a way that it does not
cause interference to cellular systems. We consider a multiple-input
multiple-output (MIMO) radar and a MIMO cellular communication system with $\mc
K$ base stations (BS). We propose a spectrum sharing algorithm which steers
radar nulls, by projecting radar waveform onto the null space of interference
channel, towards a `selected' BS, thus, protecting it from radar interference.
This BS is selected, among $\mc K$ BSs, on the basis of guaranteeing minimum
waveform degradation. We study target detection capabilities of this null-space
projected (NSP) waveform and compare it with the orthogonal waveform. We derive
the generalized likelihood ratio test (GLRT) for target detection and derive
detector statistic for NSP and orthogonal waveform. The target detection
performance for NSP and orthogonal waveform is studied theoretically and via
Monte Carlo simulations.


  In STOC'16, Fraigniaud et al. consider the problem of finding a treasure
hidden in one of many boxes that are ordered by importance. That is, if a
treasure is in a more important box, then one would like to find it faster.
Assuming there are many searchers, the authors suggest that using an algorithm
that requires no coordination between searchers can be highly beneficial.
Indeed, besides saving the need for a communication and coordination mechanism,
such algorithms enjoy inherent robustness. The authors proceed to solve this
linear search problem in the case of countably many boxes and an adversary
placed treasure, and prove that the best speed-up possible by $k$
non-coordinating searchers is precisely $\frac{k}{4}(1+1/k)^2$. In particular,
this means that asymptotically, the speed-up is four times worse compared to
the case of full coordination.
  We suggest an important variant of the problem, where the treasure is placed
uniformly at random in one of a finite, large, number of boxes. We devise
non-coordinating algorithms that achieve a speed-up of $6/5$ for two searchers,
a speed-up of $3/2$ for three searchers, and in general, a speed-up of
$k(k+1)/(3k-1)$ for any $k \geq 1$ searchers. Thus, as $k$ grows to infinity,
the speed-up approaches three times worse compared to the case of full
coordination. Moreover, these bounds are tight in a strong sense as no
non-coordinating search algorithm for $k$ searchers can achieve better
speed-ups. We also devise non-coordinating algorithms that use only logarithmic
memory in the size of the search domain, and yet, asymptotically, achieve the
optimal speed-up. Finally, we note that all our algorithms are extremely simple
and hence applicable.


  It is shown that the quarks and leptons of the standard model, including a
right-handed neutrino, can be obtained by gauging the holonomy groups of
complex projective spaces of complex dimensions two and three. The spectrum
emerges as chiral zero modes of the Dirac operator coupled to gauge fields and
the demonstration involves an index theorem analysis on a general complex
projective space in the presence of topologically non-trivial SU(n)xU(1) gauge
fields. The construction may have applications in type IIA string theory and
non-commutative geometry.


  This paper introduces the real image Super-Resolution (SR) challenge that was
part of the Advances in Image Manipulation (AIM) workshop, held in conjunction
with ECCV 2020. This challenge involves three tracks to super-resolve an input
image for $\times$2, $\times$3 and $\times$4 scaling factors, respectively. The
goal is to attract more attention to realistic image degradation for the SR
task, which is much more complicated and challenging, and contributes to
real-world image super-resolution applications. 452 participants were
registered for three tracks in total, and 24 teams submitted their results.
They gauge the state-of-the-art approaches for real image SR in terms of PSNR
and SSIM.


  We present a new study of quasi-elastic $W$ and $Z$ scattering processes in
high-energy $e^+e^-$ collisions, based on and extrapolating the low-energy
effective theory which extends the Standard Model with a 125 GeV Higgs boson.
Besides parameterizing deviations in terms of the dimension-8 operators that
arise in the effective theory, we also study simplified models of new physics
in $W/Z$ scattering in terms of scalar and tensor resonance multiplets. The
high-energy asymptotics of all models is regulated by a universal unitarization
procedure. This enables us to provide benchmark scenarios which can be
meaningfully evaluated off-shell and in exclusive event samples, and to
determine the sensitivity of an $e^+e^-$ collider to the model parameters. We
analyze the longitudinal vector boson scattering modes, where we optimize the
cuts for the fiducial cross section for different collider scenarios. Here, we
choose energy stages of 1.0, 1.4 and 3 TeV, as motivated by the extendability
of the ILC project and the staging scenario of the CLIC project.


  We analyze the behavior of several renormalization group functions at
infrared fixed points for $SU(N)$ gauge theories with fermions in the
fundamental and two-indexed representations. This includes the beta function of
the gauge coupling, the anomalous dimension of the gauge parameter and the
anomalous dimension of the mass. The scheme in which the analysis is performed
is the minimal momentum subtraction scheme through third loop order. Due to the
fact that scheme dependence is inevitable once the perturbation theory is
truncated we compare to previous identical studies done in the minimal
subtraction scheme and the modified regularization invariant scheme. We find
only mild to moderate scheme dependence.


  I study some possibilities of analytically solving a particular
Sturm-Liouville problem with step-wise (piece-constant) coefficients with help
of an iterative procedure mentioned in my previous paper (Green's function sum
rules). I construct short, simple, but very accurate analytical formulae for
calculating the ground state eigenvalue and eigenfunction as well as for
calculating the first eigenfunction. I study numerical precision of the
obtained approximations together with the perturbation theory results.


  Uncrewed aerial vehicles (UAVs) have attracted recent attention for
sixth-generation (6G) networks due to their low cost and flexible deployment.
In order to maximize the ever-increasing data rates, spectral efficiency, and
wider coverage, technologies such as reconfigurable intelligent surface (RIS)
and non-orthogonal multiple access (NOMA) are adapted with UAVs (UAV-RIS NOMA).
However, the error performance of UAV-RIS NOMA has not been considered, yet. In
this letter, we investigate the error probability of UAV-RIS NOMA systems. We
also consider the practical constraints of hardware impairments (HWI) at the
transceivers, inter-cell interference (ICI), and imperfect successive
interference cancellation (SIC). The analytical derivations are validated by
Monte-Carlo simulations. Our results demonstrate that our proposed system
achieves higher performance gain (more than 5 dB with increasing the number of
RIS elements) with less error probability compared to UAVs without RIS.
Moreover, it is found that the HWI, ICI, and imperfect SIC have shown a
negative impact on the system performance.


  Entanglement detection is an important problem in quantum information theory
because quantum entanglement is a key resource in quantum information
processing. Realignment criteria is a powerful tool for detection of entangled
states in bipartite and multipartite quantum system. It is an important
criteria for entanglement detection because it works well; not only for
negative partial transpose entangled states (NPTES) but also for positive
partial transpose entangled states (PPTES). Since the matrix corresponding to
realignment map is indefinite so the experimental implementation of the map is
an obscure task. In this work, firstly, we have approximated the realignment
map to a positive map using the method of structural physical approximation
(SPA) and then we have shown that the structural physical approximation of
realignment map (SPA-R) is completely positive. Positivity of the constructed
map is characterized using moments which can be physically measured. Next, we
develop a separability criterion based on our SPA-R map in the form of an
inequality and have shown that the developed criterion not only detect NPTES
but also PPTES. We have provided some examples to support the results obtained.
Moreover, we have analysed the error that may occur because of approximating
the realignment map.


  We study a generalization of genus-zero $r$-spin theory in which exactly one
insertion has a negative-one twist, which we refer to as the "closed extended"
theory, and which is closely related to the open $r$-spin theory of Riemann
surfaces with boundary. We prove that the generating function of genus-zero
closed extended intersection numbers coincides with the genus-zero part of a
special solution to the system of differential equations for the wave function
of the $r$-th Gelfand-Dickey hierarchy. This parallels an analogous result for
the open $r$-spin generating function in the companion paper to this work.


  We show how a unified description of the various two-flavor neutrino
oscillation solutions, allowed by the atmospheric and solar neutrino
experiments, are naturally realized within the framework of $\nu$MSSM (MSSM
augmented with the seesaw mechanism) and beyond, especially grand unified
theories. A general mechanism for achieving maximal mixing to resolve the
atmospheric anomaly is discussed, and applied to the flipped SU(5) model.
Except in the case of MSSM and SU(5), a light sterile neutrino is an inevitable
consequence of our considerations. The bi-maximal neutrino mixing scenario is
one of the options considered. Neutrino hot dark matter can arise in models
with maximal $\nu_{\mu}-\nu_s$ oscillations. A ${\cal U}(1)$ flavor symmetry,
motivated by the charged fermion mass hierarchies and the magnitudes of the CKM
matrix elements, plays a central role.


  Stellar spectropolarimetry has become extremely popular during the last
decade, and has led to major advances in our understanding of stellar magnetic
fields and of their impact on stellar structure and evolution. Many important
discoveries have been obtained thanks to observations performed with the FORS
low-resolution spectropolarimeters of the ESO Very Large Telescope. We first
review and summarise the major results of a homogeneous re-reduction and
analysis of all single-slit FORS1 spectropolarimetric observations. This work
revealed a non-negligible dependence of the results upon the adopted reduction
and analysis procedure, as well as the presence of instabilities, revealing
that photon noise is not the only source of uncertainty. As a consequence of
our new analysis and assessment of the uncertainties, we are not able to
confirm a large number of magnetic field detections presented in the past for a
variety of stars. We further summarise the results of FORS2 spectropolarimetric
observations of the A0 supergiant HD92207 which allowed us to explore further
the nature of the instabilities, roughly constraining their maximum impact on
the derived Stokes profiles and magnetic field values. We finally present new
results obtained with a further independent pipeline on the FORS2 data of
HD92207, confirming our previous analysis, and discuss simple quality-check
controls which can be performed on the data in order to distinguish between
genuine and spurious signals. All together, our results reveal that the FORS
spectropolarimeters are indeed reliable instruments, when their capabilities
are not pushed beyond the limits of a Cassegrain mounted low-resolution
spectrograph.


  We present a novel semi-analytical methodology to construct optimal linear
optical circuits for heralded production of 3-photon GHZ and 2-photon Bell
states. We provide a detailed description and analysis of the resulting optical
schemes, which deliver success probabilities of 1/54 and 2/27 for dual-rail
encoded 3-GHZ and Bell states generation, respectively. Our results improve the
known constructive bounds on the success probabilities for 3-GHZ states and are
of particular importance for a ballistic quantum computing model, for which
these states provide an essential resource.


  We build a multiassets heterogeneous agents model with fundamentalists and
chartists, who make investment decisions by maximizing the constant relative
risk aversion utility function. We verify that the model can reproduce the main
stylized facts in real markets, such as fat-tailed return distribution and
long-term memory in volatility. Based on the calibrated model, we study the
impacts of the key strategies' parameters on investors' wealth shares. We find
that, as chartists' exponential moving average periods increase, their wealth
shares also show an increasing trend. This means that higher memory length can
help to improve their wealth shares. This effect saturates when the exponential
moving average periods are sufficiently long. On the other hand, the mean
reversion parameter has no obvious impacts on wealth shares of either type of
traders. It suggests that no matter whether fundamentalists take moderate
strategy or aggressive strategy on the mistake of stock prices, it will have no
different impact on their wealth shares in the long run.


  In this letter, we report the first experimental observation of a photonic
hook - a new type of near field curved light generated at the output of
dielectric cuboid with broken symmetry having dimensions comparable to the
electromagnetic wavelength. The radius of curvature associated with the
generated photonic hook is smaller than the wavelength used while its minimum
beam-waist is about 0.44 lamda. This represents the smallest radius of
curvature ever recorded for any alectromagnetic beams.


  Young stellar associations hold a star formation record that can persist for
millions of years, revealing the progression of star formation long after the
dispersal of the natal cloud. To identify nearby young stellar populations that
trace this progression, we have designed a comprehensive framework for the
identification of young stars, and use it to identify $\sim$3$\times 10^4$
candidate young stars within a distance of 333 pc using Gaia DR2. Applying the
HDBSCAN clustering algorithm to this sample, we identify 27 top-level groups,
nearly half of which have little to no presence in previous literature. Ten of
these groups have visible substructure, including notable young associations
such as Orion, Perseus, Taurus, and Sco-Cen. We provide a complete
subclustering analysis on all groups with substructure, using age estimates to
reveal each region's star formation history. The patterns we reveal include an
apparent star formation origin for Sco-Cen along a semicircular arc, as well as
clear evidence for sequential star formation moving away from that arc with a
propagation speed of $\sim$4 km s$^{-1}$ ($\sim$4 pc Myr$^{-1}$). We also
identify earlier bursts of star formation in Perseus and Taurus that predate
current, kinematically identical active star-forming events, suggesting that
the mechanisms that collect gas can spark multiple generations of star
formation, punctuated by gas dispersal and cloud regrowth. The large spatial
scales and long temporal scales on which we observe star formation offer a
bridge between the processes within individual molecular clouds and the broad
forces guiding star formation at galactic scales.


  The CALET Gamma-ray Burst Monitor (CGBM) is the secondary scientific
instrument of the CALET mission on the International Space Station (ISS), which
is scheduled for launch by H-IIB/HTV in 2014. The CGBM provides a broadband
energy coverage from 7 keV to 20 MeV, and simultaneous observations with the
primary instrument Calorimeter (CAL) in the GeV - TeV gamma-ray range and
Advanced Star Camera (ASC) in the optical for gamma-ray bursts (GRBs) and other
X-gamma-ray transients. The CGBM consists of two kinds of scintillators: two
LaBr$_3$(Ce) (7 keV - 1 MeV) and one BGO (100 keV - 20 MeV) each read by a
single photomultiplier. The LaBr$_3$(Ce) crystal, used in space for the first
time here for celestial gamma-ray observations, enables GRB observations over a
broad energy range from low energy X-ray emissions to gamma rays. The detector
performance and structures have been verified using the bread-board model (BBM)
via vibration and thermal vacuum tests. The CALET is currently in the
development phase of the proto-flight model (PFM) and the pre-flight
calibration of the CGBM is planned for August 2013. In this paper, we report on
the current status and expected performance of CALET for GRB observations.


  In this work, we present an adjoint-based method for discovering the
underlying governing partial differential equations (PDEs) given data. The idea
is to consider a parameterized PDE in a general form and formulate a
PDE-constrained optimization problem aimed at minimizing the error of the PDE
solution from data. Using variational calculus, we obtain an evolution equation
for the Lagrange multipliers (adjoint equations) allowing us to compute the
gradient of the objective function with respect to the parameters of PDEs given
data in a straightforward manner. In particular, we consider a family of
parameterized PDEs encompassing linear, nonlinear, and spatial derivative
candidate terms, and elegantly derive the corresponding adjoint equations. We
show the efficacy of the proposed approach in identifying the form of the PDE
up to machine accuracy, enabling the accurate discovery of PDEs from data. We
also compare its performance with the famous PDE Functional Identification of
Nonlinear Dynamics method known as PDE-FIND (Rudy et al., 2017), on both smooth
and noisy data sets. Even though the proposed adjoint method relies on
forward/backward solvers, it outperforms PDE-FIND for large data sets thanks to
the analytic expressions for gradients of the cost function with respect to
each PDE parameter.


  Mixed Reality (MR) is gaining prominence in manual task skill learning due to
its in-situ, embodied, and immersive experience. To teach manual tasks, current
methodologies break the task into hierarchies (tasks into subtasks) and
visualize the current subtask and future in terms of causality. Existing
psychology literature also shows that humans learn tasks by breaking them into
hierarchies. In order to understand the design space of information visualized
to the learner for better task understanding, we conducted a user study with 48
users. The study was conducted using a complex assembly task, which involves
learning of both actions and tool usage. We aim to explore the effect of
visualization of causality in the hierarchy for manual task learning in MR by
four options: no causality, event level causality, interaction level causality,
and gesture level causality. The results show that the user understands and
performs best when all the level of causality is shown to the user. Based on
the results, we further provide design recommendations and in-depth discussions
for future manual task learning systems.


  In this paper, we study the zero-delay source-channel coding problem, and
specifically the problem of obtaining the vector transformations that optimally
map between the m-dimensional source space and the k-dimensional channel space,
under a given transmission power constraint and for the mean square error
distortion. We first study the functional properties of this problem and show
that the objective is concave in the source and noise densities and convex in
the density of the input to the channel. We then derive the necessary
conditions for optimality of the encoder and decoder mappings. A well known
result in information theory pertains to the linearity of optimal encoding and
decoding mappings in the scalar Gaussian source and channel setting, at all
channel signal-to-noise ratios (CSNRs). In this paper, we study this result
more generally, beyond the Gaussian source and channel, and derive the
necessary and sufficient condition for linearity of optimal mappings, given a
noise (or source) distribution, and a specified power constraint. We also prove
that the Gaussian source-channel pair is unique in the sense that it is the
only source-channel pair for which the optimal mappings are linear at more than
one CSNR values. Moreover, we show the asymptotic linearity of optimal mappings
for low CSNR if the channel is Gaussian regardless of the source and, at the
other extreme, for high CSNR if the source is Gaussian, regardless of the
channel. Our numerical results show strict improvement over prior methods. The
numerical approach is extended to the scenario of source-channel coding with
decoder side information. The resulting encoding mappings are shown to be
continuous relatives of, and in fact subsume as special case, the Wyner-Ziv
mappings encountered in digital distributed source coding systems.


  We investigate a correlation between the dark matter content of elliptical
galaxies and their ellipticity that was initially reported in 2014. We use new
determinations of dark matter and ellipticities that are posterior to that
time. Our data set consists of 237 elliptical galaxies passing a strict set of
criteria. We find a relation between the mass-to-light ratio and ellipticity
that is well fit by M/L = (14.1 \pm 5.4)?, which agrees with the result
reported in 2014.


  Recent works in learning-integrated optimization have shown promise in
settings where the optimization problem is only partially observed or where
general-purpose optimizers perform poorly without expert tuning. By learning an
optimizer $\mathbf{g}$ to tackle these challenging problems with $f$ as the
objective, the optimization process can be substantially accelerated by
leveraging past experience. The optimizer can be trained with supervision from
known optimal solutions or implicitly by optimizing the compound function
$f\circ \mathbf{g}$. The implicit approach may not require optimal solutions as
labels and is capable of handling problem uncertainty; however, it is slow to
train and deploy due to frequent calls to optimizer $\mathbf{g}$ during both
training and testing. The training is further challenged by sparse gradients of
$\mathbf{g}$, especially for combinatorial solvers. To address these
challenges, we propose using a smooth and learnable Landscape Surrogate $M$ as
a replacement for $f\circ \mathbf{g}$. This surrogate, learnable by neural
networks, can be computed faster than the solver $\mathbf{g}$, provides dense
and smooth gradients during training, can generalize to unseen optimization
problems, and is efficiently learned via alternating optimization. We test our
approach on both synthetic problems, including shortest path and
multidimensional knapsack, and real-world problems such as portfolio
optimization, achieving comparable or superior objective values compared to
state-of-the-art baselines while reducing the number of calls to $\mathbf{g}$.
Notably, our approach outperforms existing methods for computationally
expensive high-dimensional problems.


  In this paper, a speech enhancement method based on noise compensation
performed on short time magnitude as well phase spectra is presented. Unlike
the conventional geometric approach (GA) to spectral subtraction (SS), here the
noise estimate to be subtracted from the noisy speech spectrum is proposed to
be determined by exploiting the low frequency regions of current frame of noisy
speech rather than depending only on the initial silence frames. This approach
gives the capability of tracking non-stationary noise thus resulting in a
non-stationary noise-driven geometric approach of spectral subtraction for
speech enhancement. The noise compensated magnitude spectrum from the GA step
is then recombined with unchanged phase of noisy speech spectrum and used in
phase compensation to obtain an enhanced complex spectrum, which is used to
produce an enhanced speech frame. Extensive simulations are carried out using
speech files available in the NOIZEUS database shows that the proposed method
consistently outperforms some of the recent methods of speech enhancement when
employed on the noisy speeches corrupted by street or babble noise at different
levels of SNR in terms of objective measures, spectrogram analysis and formal
subjective listening tests.


  With the rapid development of Internet and the sharp increase of network
crime, network security has become very important and received a lot of
attention. We model security issues as stochastic systems. This allows us to
find weaknesses in existing security systems and propose new solutions.
Exploring the vulnerabilities of existing security tools can prevent
cyber-attacks from taking advantages of the system weaknesses. We propose a
hybrid network security scheme including intrusion detection systems (IDSs) and
honeypots scattered throughout the network. This combines the advantages of two
security technologies. A honeypot is an activity-based network security system,
which could be the logical supplement of the passive detection policies used by
IDSs. This integration forces us to balance security performance versus cost by
scheduling device activities for the proposed system. By formulating the
scheduling problem as a decentralized partially observable Markov decision
process (DEC-POMDP), decisions are made in a distributed manner at each device
without requiring centralized control. The partially observable Markov decision
process (POMDP) is a useful choice for controlling stochastic systems. As a
combination of two Markov models, POMDPs combine the strength of hidden Markov
Model (HMM) (capturing dynamics that depend on unobserved states) and that of
Markov decision process (MDP) (taking the decision aspect into account).
Decision making under uncertainty is used in many parts of business and
science.We use here for security tools.We adopt a high-quality approximation
solution for finite-space POMDPs with the average cost criterion, and their
extension to DEC-POMDPs. We show how this tool could be used to design a
network security framework.


  We study analysis over infinite dimensional manifolds consisted by sequences
of almost K\"ahler manifolds. In particular we develop moduli theory of pseudo
holomorphic curves into the spaces with high symmetry.
  As applications, we study Hamiltonian dynamics over the infinite dimensional
manifolds, and induce some dynamical properties of Hamiltonian diffeomorphisms
on such spaces.


  Learning from small data sets is critical in many practical applications
where data collection is time consuming or expensive, e.g., robotics, animal
experiments or drug design. Meta learning is one way to increase the data
efficiency of learning algorithms by generalizing learned concepts from a set
of training tasks to unseen, but related, tasks. Often, this relationship
between tasks is hard coded or relies in some other way on human expertise. In
this paper, we frame meta learning as a hierarchical latent variable model and
infer the relationship between tasks automatically from data. We apply our
framework in a model-based reinforcement learning setting and show that our
meta-learning model effectively generalizes to novel tasks by identifying how
new tasks relate to prior ones from minimal data. This results in up to a 60%
reduction in the average interaction time needed to solve tasks compared to
strong baselines.


  The bright Seyfert 1 galaxy MCG-6-30-15 has provided some of the best
evidence to date for the existence of supermassive black holes in active
galactic nuclei. Observations with ASCA revealed an X-ray iron line profile
shaped by strong Doppler and gravitational effects. In this paper the shape of
the iron line, its variability characteristics and the robustness of this
spectral interpretation are examined using the long XMM-Newton observation
taken in 2001. A variety of spectral models, both including and excluding the
effects of strong gravity, are compared to the data in a uniform fashion. The
results strongly favour models in which the spectrum is shaped by emission from
a relativistic accretion disc. It is far more difficult to explain the 3-10 keV
spectrum using models dominated by absorption (either by warm or partially
covering cold matter), emission line blends, curved continua or additional
continuum components. These provide a substantially worse fit to the data and
fail to explain other observations (such as the simultaneous BeppoSAX
spectrum). This reaffirms the veracity of the relativistic `disc line'
interpretation. The short term variability in the shape of the energy spectrum
is investigated and explained in terms of a two-component emission model. Using
a combination of spectral variability analyses the spectrum is successfully
decomposed into a variable power-law component (PLC) and a reflection dominated
component (RDC). The former is highly variable while the latter is
approximately constant throughout the observation, leading to the well-known
spectral variability patterns. (Abridged)


  In this letter, we study a few properties of Complex Conjugate Pair Sums
(CCPSs) and Complex Conjugate Subspaces (CCSs). Initially, we consider an LTI
system whose impulse response is one period data of CCPS. For a given input
x(n), we prove that the output of this system is equivalent to computing the
first order derivative of x(n). Further, with some constraints on the impulse
response, the system output is also equivalent to the second order derivative.
With this, we show that a fine edge detection in an image can be achieved using
CCPSs as impulse response over Ramanujan Sums (RSs). Later computation of
projection for CCS is studied. Here the projection matrix has a circulant
structure, which makes the computation of projections easier. Finally, we prove
that CCS is shift-invariant and closed under the operation of circular
cross-correlation.


  Deep Neural Networks (DNN) have become a promising paradigm when developing
Artificial Intelligence (AI) and Machine Learning (ML) applications. However,
DNN applications are vulnerable to fake data that are crafted with adversarial
attack algorithms. Under adversarial attacks, the prediction accuracy of DNN
applications suffers, making them unreliable. In order to defend against
adversarial attacks, we introduce a novel noise-reduction procedure, Vector
Quantization U-Net (VQUNet), to reduce adversarial noise and reconstruct data
with high fidelity. VQUNet features a discrete latent representation learning
through a multi-scale hierarchical structure for both noise reduction and data
reconstruction. The empirical experiments show that the proposed VQUNet
provides better robustness to the target DNN models, and it outperforms other
state-of-the-art noise-reduction-based defense methods under various
adversarial attacks for both Fashion-MNIST and CIFAR10 datasets. When there is
no adversarial attack, the defense method has less than 1% accuracy degradation
for both datasets.


  We address the problem of camera pose estimation in visual localization.
Current regression-based methods for pose estimation are trained and evaluated
scene-wise. They depend on the coordinate frame of the training dataset and
show a low generalization across scenes and datasets. We identify the dataset
shift an important barrier to generalization and consider transfer learning as
an alternative way towards a better reuse of pose estimation models. We revise
domain adaptation techniques for classification and extend them to camera pose
estimation, which is a multi-regression task. We develop a deep adaptation
network for learning scene-invariant image representations and use adversarial
learning to generate such representations for model transfer. We enrich the
network with self-supervised learning and use the adaptability theory to
validate the existence of scene-invariant representation of images in two given
scenes. We evaluate our network on two public datasets, Cambridge Landmarks and
7Scene, demonstrate its superiority over several baselines and compare to the
state of the art methods.


  We calculate the interaction kernel K for two-dimensional diffusive
electrons. The screening of the Coulomb interaction together with the Fermi
statistics induces a spin selection rule for electron-electron scattering so
that in leading order in the inverse conductance only pairs of electrons with
antiparallel spins do scatter. At low temperature, this results in a larger
coherence length for fully polarized electrons and thus in a positive in-plane
magnetoresistance. An applied in-plane magnetic field also induces a
nonmonotonous behavior of K at finite temperature. Alternatively, the vanishing
of the scattering in the triplet channel strongly reduces ferromagnetism deep
in the metallic regime. These effects weaken as the density of charge carriers
is reduced.


  We find and analyze the exact time-dependent potential energy surface driving
the proton motion for a model of cavity-induced suppression of proton-coupled
electron-transfer. We show how, in contrast to the polaritonic surfaces, its
features directly correlate to the proton dynamics and discuss
cavity-modifications of its structure responsible for the suppression. The
results highlight the interplay between non-adiabatic effects from coupling to
photons and coupling to electrons, and suggest caution is needed when applying
traditional dynamics methods based on polaritonic surfaces.


  The three keys to autonomous driving are sensors, data integration, and 100%
safety decisions. In the past, due to the high latency and low reliability of
the network, many decisions had to be made locally in the vehicle. This puts
high demands on the vehicle itself, which results in the dilatory
commercialization of automatic driving. With the advent of 5G, these situations
will be greatly improved. In this paper, we present the improvements that 5G
technology brings to autonomous vehicles especially in terms of latency and
reliability amongst the multitude of other factors. The paper analyzes the
specific areas where 5G can improve for autonomous vehicles and Intelligent
Transport Systems in general (ITS) and looks forward to the application of 5G
technology in the future.


  We investigate the conditions under which a set $\SC$ of pure bipartite
quantum states on a $D\times D$ system can be locally cloned deterministically
by separable operations, when at least one of the states is full Schmidt rank.
We allow for the possibility of cloning using a resource state that is less
than maximally entangled. Our results include that: (i) all states in $\SC$
must be full Schmidt rank and equally entangled under the $G$-concurrence
measure, and (ii) the set $\SC$ can be extended to a larger clonable set
generated by a finite group $G$ of order $|G|=N$, the number of states in the
larger set. It is then shown that any local cloning apparatus is capable of
cloning a number of states that divides $D$ exactly. We provide a complete
solution for two central problems in local cloning, giving necessary and
sufficient conditions for (i) when a set of maximally entangled states can be
locally cloned, valid for all $D$; and (ii) local cloning of entangled qubit
states with non-vanishing entanglement. In both of these cases, a maximally
entangled resource is necessary and sufficient, and the states must be related
to each other by local unitary "shift" operations. These shifts are determined
by the group structure, so need not be simple cyclic permutations. Assuming
this shifted form and partially entangled states, then in D=3 we show that a
maximally entangled resource is again necessary and sufficient, while for
higher dimensional systems, we find that the resource state must be strictly
more entangled than the states in $\SC$. All of our necessary conditions for
separable operations are also necessary conditions for LOCC, since the latter
is a proper subset of the former. In fact, all our results hold for LOCC, as
our sufficient conditions are demonstrated for LOCC, directly.


  Sequential Monte Carlo (SMC) samplers form an attractive alternative to MCMC
for Bayesian computation. However, their performance depends strongly on the
Markov kernels used to rejuvenate particles. We discuss how to calibrate
automatically (using the current particles) Hamiltonian Monte Carlo kernels
within SMC. To do so, we build upon the adaptive SMC approach of Fearnhead and
Taylor (2013), and we also suggest alternative methods. We illustrate the
advantages of using HMC kernels within an SMC sampler via an extensive
numerical study.


  Models with similar performances exhibit significant disagreement in the
predictions of individual samples, referred to as prediction churn. Our work
explores this phenomenon in graph neural networks by investigating differences
between models differing only in their initializations in their utilized
features for predictions. We propose a novel metric called Influence Difference
(ID) to quantify the variation in reasons used by nodes across models by
comparing their influence distribution. Additionally, we consider the
differences between nodes with a stable and an unstable prediction, positing
that both equally utilize different reasons and thus provide a meaningful
gradient signal to closely match two models even when the predictions for nodes
are similar. Based on our analysis, we propose to minimize this ID in Knowledge
Distillation, a domain where a new model should closely match an established
one. As an efficient approximation, we introduce DropDistillation (DD) that
matches the output for a graph perturbed by edge deletions. Our empirical
evaluation of six benchmark datasets for node classification validates the
differences in utilized features. DD outperforms previous methods regarding
prediction stability and overall performance in all considered Knowledge
Distillation experiments.


  We present a discrete version of the two-dimensional nonlinear $O(3)$ sigma
model examined by Belavin and Polyakov. We formulate it by means of Mercat's
discrete complex analysis and its elaboration by Bobenko and G\"unther. We
define a weighted discrete Dirichlet energy and area on a planar quad-graph and
derive an inequality between them. We write $f$ for the complex function
obtained from the unit vector field of the model. The inequality is saturated
if and only if the $f$ is discrete (anti-)holomorphic. By using a weight $W$
obtained from a kind of tiling of the sphere $S^2$, the weighted discrete area
${\cal A}^{W}_{\diamondsuit}(f)$ admits a geometrical interpretation, namely,
${\cal A}^{W}_{\diamondsuit}(f)=4 \pi N $ for a topological quantum number $N
\in \pi_2(S^2)$. This ensures the topological stability of the solution
described by the $f$, and we have the quantized energy
$E^{W}_{\diamondsuit}(f)=|{\cal A}^{W}_{\diamondsuit}(f)|=4 \pi |N| $. For
quad-graphs with orthogonal diagonals, we show that the discrete
(anti-)holomorphic function $f$ satisfies the Euler--Lagrange equation derived
from the weighted discrete Dirichlet energy. On some rhombic lattices, the
discrete power functions $z^{(N)}$ give the topological quantum number $N$.
Moreover, the weighted discrete Dirichlet energy, area, and Euler--Lagrange
equation tend to their continuous forms as the lattice spacings tend to zero.


  We prove that, in a neighborhood of the Euclidean ball, there are no other
fixed points of the $p$-centroid body operator, using spherical harmonic
techniques. We also show that the Euclidean ball is locally the only body whose
centroid body is a dilate of its polar intersection body.


  Integrating cameras into wireless smart rings has been challenging due to
size and power constraints. We introduce IRIS, the first wireless
vision-enabled smart ring system for smart home interactions. Equipped with a
camera, Bluetooth radio, inertial measurement unit (IMU), and an onboard
battery, IRIS meets the small size, weight, and power (SWaP) requirements for
ring devices. IRIS is context-aware, adapting its gesture set to the detected
device, and can last for 16-24 hours on a single charge. IRIS leverages the
scene semantics to achieve instance-level device recognition. In a study
involving 23 participants, IRIS consistently outpaced voice commands, with a
higher proportion of participants expressing a preference for IRIS over voice
commands regarding toggling a device's state, granular control, and social
acceptability. Our work pushes the boundary of what is possible with ring
form-factor devices, addressing system challenges and opening up novel
interaction capabilities.


  Text in natural images contains rich semantics that are often highly relevant
to objects or scene. In this paper, we focus on the problem of fully exploiting
scene text for visual understanding. The main idea is combining word
representations and deep visual features into a globally trainable deep
convolutional neural network. First, the recognized words are obtained by a
scene text reading system. Then, we combine the word embedding of the
recognized words and the deep visual features into a single representation,
which is optimized by a convolutional neural network for fine-grained image
classification. In our framework, the attention mechanism is adopted to reveal
the relevance between each recognized word and the given image, which further
enhances the recognition performance. We have performed experiments on two
datasets: Con-Text dataset and Drink Bottle dataset, that are proposed for
fine-grained classification of business places and drink bottles, respectively.
The experimental results consistently demonstrate that the proposed method
combining textual and visual cues significantly outperforms classification with
only visual representations. Moreover, we have shown that the learned
representation improves the retrieval performance on the drink bottle images by
a large margin, making it potentially useful in product search.


  Transportation processes, which play a prominent role in the life and social
sciences, are typically described by discrete models on lattices. For studying
their dynamics a continuous formulation of the problem via partial differential
equations (PDE) is employed. In this paper we propose a symbolic computation
approach to derive mean-field PDEs from a lattice-based model. We start with
the microscopic equations, which state the probability to find a particle at a
given lattice site. Then the PDEs are formally derived by Taylor expansions of
the probability densities and by passing to an appropriate limit as the time
steps and the distances between lattice sites tend to zero. We present an
implementation in a computer algebra system that performs this transition for a
general class of models. In order to rewrite the mean-field PDEs in a
conservative formulation, we adapt and implement symbolic integration methods
that can handle unspecified functions in several variables. To illustrate our
approach, we consider an application in crowd motion analysis where the
dynamics of bidirectional flows are studied. However, the presented approach
can be applied to various transportation processes of multiple species with
variable size in any dimension, for example, to confirm several proposed
mean-field models for cell motility.


  In this chapter we explain briefly the fundamentals of the interactive scores
formalism. Then we develop a solution for implementing the ECO machine by
mixing petri nets and constraints propagation. We also present another solution
for implementing the ECO machine using concurrent constraint programming.
Finally, we present an extension of interactive score with conditional
branching.


  Detection of the first stars has remained elusive so-far but their presence
may soon be unveiled by upcoming JWST observations. Previous studies have not
investigated the entire possible range of halo masses and redshifts which may
help in their detection. Motivated by the prospects of detecting galaxies up to
$z\sim 20$ in JWST early data release, we quantify the contribution of Pop III
stars to high-redshift galaxies from $6 \leq z \leq 30$ by employing the
semi-analytical model A-SLOTH, which self-consistently models the formation of
Pop III and Pop II stars along with their feedback. Our results suggest that
the contribution of Pop III stars is the highest in low-mass halos of $\rm
10^7-10^9~M_{\odot}$. While high-mass halos $\rm \geq 10^{10}~M_{\odot}$
contain less than 1\% Pop III stars, they host galaxies with stellar masses of
$\rm 10^9~M_{\odot}$ as early as $z \sim 30$. Interestingly, the apparent
magnitude of Pop~III populations gets brighter towards higher redshift due to
the higher stellar masses, but Pop~III-dominated galaxies are too faint to be
directly detected with JWST. Our results predict JWST can detect galaxies up to
$z\sim 30$, which may help in constraining the IMF of Pop III stars and will
guide observers to discern the contribution of Pop~III stars to high-redshift
galaxies.


  In this paper, we first compute the Killing spinors of $AdS_4\times Q^{1, 1,
1}$ and its certain orbifolds. Based on this, two classes of $M2$-brane
solutions are found. The first class of solutions includes $M2$-branes dual to
Wilson loops in the fundamental representation as special cases. The second
class includes the candidates of the holographic description of vortex loops in
the dual field theories.


  The Hamiltonian Theory of the fractional quantum Hall effect is an operator
description that subsumes many properties of Composite Fermions, applies to
gapped and gapless cases, and has been found to provide results in quantitative
accord with data on gaps, relaxation rates and polarizations at temperatures of
$300mK$ and above. The only free parameter is $\lambda$, which is related to
the sample thickness and appears in the Zhang-Das Sarma potential $v(q) = {2\pi
e^2\over \kappa q} e^{-ql\lambda}$ where $l$ and $\kappa $ are the magnetic
length and dielectric constant. Here we examine the recent data of Tracy and
Eisenstein on the nuclear magnetic resonance relaxation rate at filling factor
$\nu=\half$ deduced from resistivity measurements at temperatures as low as
$45mK$. We find that their results can be satisfactorily described by this
theory, if in addition to a $v(q)$ with $\lambda \simeq 2$, a constant disorder
width $\Gamma\simeq 100 mK$ is incorporated.


  We present a workflow for clinical data analysis that relies on Bayesian
Structure Learning (BSL), an unsupervised learning approach, robust to noise
and biases, that allows to incorporate prior medical knowledge into the
learning process and that provides explainable results in the form of a graph
showing the causal connections among the analyzed features. The workflow
consists in a multi-step approach that goes from identifying the main causes of
patient's outcome through BSL, to the realization of a tool suitable for
clinical practice, based on a Binary Decision Tree (BDT), to recognize patients
at high-risk with information available already at hospital admission time. We
evaluate our approach on a feature-rich COVID-19 dataset, showing that the
proposed framework provides a schematic overview of the multi-factorial
processes that jointly contribute to the outcome. We discuss how these
computational findings are confirmed by current understanding of the COVID-19
pathogenesis. Further, our approach yields to a highly interpretable tool
correctly predicting the outcome of 85% of subjects based exclusively on 3
features: age, a previous history of chronic obstructive pulmonary disease and
the PaO2/FiO2 ratio at the time of arrival to the hospital. The inclusion of
additional information from 4 routine blood tests (Creatinine, Glucose, pO2 and
Sodium) increases predictive accuracy to 94.5%.


  In earlier work, we introduced three families of polynomials where the
generating function of each set includes one of the three Jackson $q$-analogs
of the Bessel function. This paper gives determinant representation for each
family, their large $n $ asymptotics, and two expansion theorems for specific
classes of entire functions. We include two examples.


  In this study, we present a Bayesian hierarchical framework to model
fluid-induced seismicity. The framework is based on a non-homogeneous Poisson
process (NHPP) with a fluid-induced seismicity rate proportional to the rate of
injected fluid. The fluid-induced seismicity rate model depends upon a set of
physically meaningful parameters, and has been validated for six fluid-induced
case studies. In line with the vision of hierarchical Bayesian modeling, the
rate parameters are considered as random variables. We develop both the
Bayesian inference and updating rules, which are used to develop a
probabilistic forecasting model. We tested the Basel 2006 fluid-induced seismic
case study to prove that the hierarchical Bayesian model offers a suitable
framework to coherently encode both epistemic uncertainty and aleatory
variability. Moreover, it provides a robust and consistent short-term seismic
forecasting model suitable for online risk quantification and mitigation.


  We study the central extensions of Lie algebras graded by an irreducible
locally finite root system.


  The paper is devoted to the geometry of transportation cost spaces and their
generalizations introduced by Melleray, Petrov, and Vershik (2008).
Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or
Wasserstein $1$ spaces. In this work, the existence of metric spaces with the
following properties is proved: (1) uniformly discrete infinite metric spaces
transportation cost spaces on which do not contain isometric copies of
$\ell_1$, this result answers a question raised by Cuth and Johanis (2017); (2)
locally finite metric spaces which admit isometric embeddings only into Banach
spaces containing isometric copies of $\ell_1$; (3) metric spaces for which the
double-point norm is not a norm. In addition, it is proved that the
double-point norm spaces corresponding to trees are close to $\ell_\infty^d$ of
the corresponding dimension, and that for all finite metric spaces $M$, except
a very special class, the infimum of all seminorms for which the embedding of
$M$ into the corresponding seminormed space is isometric, is not a seminorm.


  Prompt and $\beta$-delayed fission observables, such as the average number of
prompt and delayed neutrons, the independent and cumulative fission product
yields, and the prompt $\gamma$-ray energy spectra for the photonuclear
reactions on $^{235,238}$U and $^{239}$Pu are calculated with the
Hauser-Feshbach Fission Fragment Decay (HF$^3$D) model and compared with
available experimental data. In the analysis of neutron-induced fission
reactions to the case of photo-induced fission, an excellent reproduction of
the delayed neutron yields supports a traditional assumption that the
photo-fission might be similar to the neutron-induced fission at the same
excitation energies regardless of the spin and parity of the fissioning
systems.


  The standard equilibrium Green-Kubo and nonequilibrium molecular dynamics
(MD) methods for computing thermal transport coefficients in solids typically
require relatively long simulation times and large system sizes. To this end,
we revisit here the homogeneous nonequilibrium MD method by Evans [Phys. Lett.
A \textbf{91}, 457 (1982)] and generalize it to many-body potentials that are
required for more realistic materials modeling. We also propose a method for
obtaining spectral conductivity and phonon mean free path from the simulation
data. This spectral decomposition method does not require lattice dynamics
calculations and can find important applications in spatially complex
structures. We benchmark the method by calculating thermal conductivities of
three-dimensional silicon, two-dimensional graphene, and a
quasi-one-dimensional carbon nanotube and show that the method is about one to
two orders of magnitude more efficient than the Green-Kubo method. We apply the
spectral decomposition method to examine the long-standing dispute over thermal
conductivity convergence vs divergence in carbon nanotubes.


  When linear regression generates a relationship between a (dependent) scalar
response and one or multiple independent variables, various datasets providing
distinct graphical trends can develop resembling relationships based on the
same statistical properties. Advanced statistical approaches, such as neural
networks and machine learning methods, are of great necessity to process,
characterize, and analyze these degenerate datasets. On the other hand, the
accurate creation of purposedly degenerate datasets is essential to test new
models in the research and education of applied statistics. In this light, the
present study characterizes the famous Anscombe datasets and provides a general
algorithm for creating multiple paired datasets of identical statistical
properties.


  We propose explicit expressions for the form factors, including their
normalization constants, of topologically charged (or soliton-creating)
operators in the sine-Gordon model. The normalization constants, which
constitute the main content of our proposal, allow one to find exact relations
between the short- and long-distance asymptotics of the correlation functions.
We make predictions concerning asymptotics of fermion correlation functions in
the massive Thirring model, SU(2)-Thirring model with anisotropy, and in the
half-filled Hubbard chain.


  In this paper, we study free holomorphic functions on regular polyballs and
provide analogues of several classical results from complex analysis such as:
Abel theorem, Hadamard formula, Cauchy inequality, Schwarz lemma, and maximum
principle. These results are used together with a class of noncommutative
Berezin transforms to obtain a complete description of the group Aut(B_n) of
all free holomorphic automorphisms of the polyball. The abstract polyball B_n
has a universal model S consisting of left creation operators acting on tensor
products of full Fock spaces. We determine: the group of automorphisms of the
Cuntz-Toeplitz algebra C*(S) which leaves invariant the noncommutative polyball
algebra A_n; the group of unitarily implemented automorphisms of the polyball
algebra A_n and the noncommutative Hardy algebra F_n^\infty, respectively. We
prove that the free holomorphic automorphism group Aut(B_n) is a sigma-compact,
locally compact topological group with respect to the topology induced by an
appropriate metric. Finally, we obtain a concrete unitary projective
representation of the topological group Aut(B_n)in terms of noncommutative
Berezin kernels associated with regular polyballs.


  The chase procedure, an algorithm proposed 25+ years ago to fix constraint
violations in database instances, has been successfully applied in a variety of
contexts, such as query optimization, data exchange, and data integration. Its
practicability, however, is limited by the fact that - for an arbitrary set of
constraints - it might not terminate; even worse, chase termination is an
undecidable problem in general. In response, the database community has
proposed sufficient restrictions on top of the constraints that guarantee chase
termination on any database instance. In this paper, we propose a novel
sufficient termination condition, called inductive restriction, which strictly
generalizes previous conditions, but can be checked as efficiently.
Furthermore, we motivate and study the problem of data-dependent chase
termination and, as a key result, present sufficient termination conditions
w.r.t. fixed instances. They are strictly more general than inductive
restriction and might guarantee termination although the chase does not
terminate in the general case.


  This paper summarises the recent results of the Run IIa D0 experiment at the
Tevatron Collider at Fermilab on the observable parameters of the $B_{s}$
meson. A measurement of the branching fraction $B_s->D_s^{(*)}D_s^{(*)}$ is
reported, which provides an estimate of the width difference
$\Delta\Gamma_{s}^{CP}/\Delta\Gamma_{s}$. Through the decay $B_{s} \to J/\psi
\phi$ the width difference $\Delta\Gamma_{s}$ is extracted, and for the first
time a constraint is set on the CP-violating phase $\phi_{s}$, although a
four-fold ambiguity remains. This result is combined with other D0 measurements
to yield $\Delta\Gamma_{s}=0.13\pm0.09 {\rm ps^{-1}}$, $\phi_{s} =
-0.70^{+0.47}_{-0.39}$.


  In this article we address the problem of Euler's buckling instability in a
charged semi-flexible polymer that is under the action of a compressive force.
We consider this instability as a phase transition and investigate the role of
thermal fluctuations in the buckling critical force. By performing molecular
dynamic simulations, we show that the critical force decreases when the
temperature increases. Repulsive electrostatic interaction in the finite
temperature is in competition with thermal fluctuations to increase the
buckling threshold.


  In fault-tolerant quantum computing schemes, the overhead is often dominated
by the cost of preparing codewords reliably. This cost generally increases
quadratically with the block size of the underlying quantum error-correcting
code. In consequence, large codes that are otherwise very efficient have found
limited fault-tolerance applications. Fault-tolerant preparation circuits
therefore are an important target for optimization.
  We study the Golay code, a 23-qubit quantum error-correcting code that
protects the logical qubit to a distance of seven. In simulations, even using a
naive ancilla preparation procedure, the Golay code is competitive with other
codes both in terms of overhead and the tolerable noise threshold. We provide
two simplified circuits for fault-tolerant preparation of Golay code-encoded
ancillas. The new circuits minimize error propagation, reducing the overhead by
roughly a factor of four compared to standard encoding circuits. By adapting
the malignant set counting technique to depolarizing noise, we further prove a
threshold above 1.32 x 10^{-3} noise per gate.


  We consider the problem of predictive density estimation under
Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity
constraints on the location parameters. We study the first order asymptotic
minimax risk of Bayes predictive density estimates based on product discrete
priors where the proportion of non-zero coordinates converges to zero as
dimension increases. Discrete priors that are product of clustered univariate
priors provide a tractable configuration for diversification of the future risk
and are used for constructing efficient predictive density estimates. We
establish that the Bayes predictive density estimate from an appropriately
designed clustered discrete prior is asymptotically minimax optimal. The
marginals of our proposed prior have infinite clusters of identical sizes. The
within cluster support points are equi-probable and the clusters are
periodically spaced with geometrically decaying probabilities as they move away
from the origin. The cluster periodicity depends on the decay rate of the
cluster probabilities. Under different sparsity regimes, through numerical
experiments, we compare the maximal risk of the Bayes predictive density
estimates from the clustered prior with varied competing estimators including
those based on geometrically decaying non-clustered priors of Johnstone (1994)
and Mukherjee & Johnstone (2017) and obtain encouraging results.


  The classical optimal investment and consumption problem with infinite
horizon is studied in the presence of transaction costs. Both proportional and
fixed costs as well as general utility functions are considered. Weak dynamic
programming is proved in the general setting and a comparison result for
possibly discontinuous viscosity solutions of the dynamic programming equation
is provided. Detailed numerical experiments illustrate several properties of
the optimal investment strategies.


  We observe hadronic W decays in t-tbar -> W (-> l nu) + >= 4 jet events using
a 109 pb-1 data sample of p-pbar collisions at sqrt{s} = 1.8 TeV collected with
the Collider Detector at Fermilab (CDF). A peak in the dijet invariant mass
distribution is obtained that is consistent with W decay and inconsistent with
the background prediction by 3.3 standard deviations. From this peak we measure
the W mass to be 77.2 +- 4.6 (stat+syst) GeV/c^2. This result demonstrates the
presence of two W bosons in t-tbar candidates in the W (-> l nu) + >= 4 jet
channel.


  The hadron inclusive spectra in pp collisions at high energies are analyzed
within a soft QCD model, namely the quark-gluon string model. In addition to
the sea quark distribution in the incoming proton we consider also the
unintegrated gluon distribution that has an increasing behaviour when the gluon
transverse momentum grows. It leads to an increase of the inclusive spectra of
hadrons and their multiplicity in the central rapidity region of pp collision
at LHC energies.


  We show, both numerically and analytically, that the consequences of 'wiring
up' a competitive population depend quite dramatically on the interplay between
the local connectivity and the global resources. With modest global resources,
adding small amounts of local connectivity yields an increasingly heterogeneous
population. With substantial global resources, high-performing yet reasonably
homogenous collective states emerge instead.


  We consider magnetic billiards under a strong constant magnetic field. The
purpose of this paper is two-folded. We examine the question of existence of
polynomial integral of billiard magnetic flow. We succeed to reduce this
question to algebraic geometry test on existence of polynomial integral, which
shows polynomial non-integrability for all but finitely many values of the
magnitude. In the second part of the paper we construct examples of magnetic
billiards which have the so called $\delta$-Gutkin property, meaning that any
Larmor circle entering the domain with angle $\delta$ exits the domain with the
same angle $\delta$. For ordinary Birkhoff billiard in the plane such examples
were introduced by E. Gutkin and are very explicit. Our construction of Gutkin
magnetic billiards relies on beautiful examples by F.Wegner of the so called
Zindler curves, which are related to the problem of floating bodies in
equilibrium, which goes back to S.Ulam. We prove that Gutkin magnetic billiard
can be obtained as a parallel curve to a Wegner curve. Wegner curves can be
written by elliptic functions in polar coordinates so the construction of
magnetic Gutkin billiard is rather explicit but much more complicated.


  In this paper, we propose an efficient decoding algorithm for short
low-density parity check (LDPC) codes by carefully combining the belief
propagation (BP) decoding and order statistic decoding (OSD) algorithms.
Specifically, a modified BP (mBP) algorithm is applied for a certain number of
iterations prior to OSD to enhance the reliability of the received message,
where an offset parameter is utilized in mBP to control the weight of the
extrinsic information in message passing. By carefully selecting the offset
parameter and the number of mBP iterations, the number of errors in the most
reliable positions (MRPs) in OSD can be reduced by mBP, thereby significantly
improving the overall decoding performance of error rate and complexity.
Simulation results show that the proposed algorithm can approach the
maximum-likelihood decoding (MLD) for short LDPC codes with only a slight
increase in complexity compared to BP and a significant decrease compared to
OSD. Specifically, the order-(m-1) decoding of the proposed algorithm can
achieve the performance of the order-m OSD.


  We examine evaluations of the contributions of Matrix Mechanics and Max Born
to the formulation of quantum mechanics from Heisenberg's Helgoland paper of
1925 to Born's Nobel Prize of 1954. We point out that the process of evaluation
is continuing in the light of recent interpretations of the theory that
deemphasize the importance of the wave function.


  Consider a bounded solution of the focusing, energy-critical wave equation
that does not scatter to a linear solution. We prove that this solution
converges in some weak sense, along a sequence of times and up to scaling and
space translation, to a sum of solitary waves. This result is a consequence of
a new general compactness/rigidity argument based on profile decomposition. We
also give an application of this method to the energy-critical Schr\"odinger
equation.


  We study the effective theory of slowly rotating black holes at the infinite
limit of the spacetime dimension D. This large D effective theory is obtained
by integrating the Einstein equation with respect to the radial direction. The
effective theory gives equations for non-linear dynamical deformations of the
slowly rotating black hole as effective equations. The effective equations
contain the slowly rotating Myers-Perry black hole, slowly boosted black
string, non-uniform black string and black ring as stationary solutions. We
obtain an analytic solution of the black ring by solving the effective
equations. Furthermore, by perturbation analysis of the effective equations, we
find a quasinormal mode condition of the black ring in analytic way. As a
result we confirm that thin black ring is unstable against non-axisymmetric
perturbations. We also include 1/D corrections to the effective equations and
discuss the effects by 1/D corrections.


  We present a novel fully Bayesian analysis to constrain short gamma-ray burst
jet structures associated with cocoon, wide-angle and simple top-hat jet
models, as well as the binary neutron star merger rate. These constraints are
made given the distance and inclination information from GW170817, observed
flux of GRB170817A, observed rate of short gamma-ray bursts detected by Swift,
and the neutron star merger rate inferred from LIGO's first and second
observing runs. A separate analysis is conducted where a fitted short gamma-ray
burst luminosity function is included to provide further constraints. The jet
structure models are further constrained using the observation of GW190425 and
we find that the assumption that it produced a GRB170817-like short gamma-ray
burst that went undetected due to the jet geometry is consistent with previous
observations. We find and quantify evidence for low luminosity and wide-angled
jet structuring in the short gamma-ray burst population, independently from
afterglow observations, with log Bayes factors of $0.45{-}0.55$ for such models
when compared to a classical top-hat jet. Slight evidence is found for a
Gaussian jet structure model over all others when the fitted luminosity
function is provided, producing log Bayes factors of $0.25{-}0.9\pm0.05$ when
compared to the other models. However without considering GW190425 or the
fitted luminosity function, the evidence favours a cocoon-like model with log
Bayes factors of $0.14\pm0.05$ over the Gaussian jet structure. We provide new
constraints to the binary neutron star merger rates of
$1{-}1300$Gpc$^{-3}$yr$^{-1}$ or $2{-}680$Gpc$^{-3}$yr$^{-1}$ when a fitted
luminosity function is assumed.


  In this paper, we present the clockwise-algorithm that solves the extension
in $k$-dimensions of the infamous nine-dot problem, the well-known
two-dimensional thinking outside the box puzzle. We describe a general strategy
that constructively produces minimum length covering trails, for any $k \in
\mathbb{N}-\{0\}$, solving the NP-complete $(3 \times 3 \times \cdots \times
3)$-point problem inside $3 \times 3 \times \cdots \times 3$ hypercubes. In
particular, using our algorithm, we explicitly draw different covering trails
of minimal length $h(k)=\frac{3^k-1}{2}$, for $k=3, 4, 5$. Furthermore, we
conjecture that, for every $k \geq 1$, it is possible to solve the $3^k$-point
problem with $h(k)$ lines starting from any of the $3^k$ nodes, except from the
central one. Finally, we cover a $3 \times 3 \times 3$ grid with a tree of size
$12$.


  The Sz.-Nagy Foias characteristic function for a contraction has had a
rejuvenation in recent times due to a number of authors. Such a classical
object relates to an object of very contemporary interest, viz., the complete
Nevanlinna-Pick kernels. Indeed, a unitarily invariant kernel on the unit ball
{\em admits} a characteristic function if and only if it is a complete
Nevanlinna-Pick kernel. However, what has captured our curiosity are the recent
advancements in constructing characteristic functions for kernels that do not
have complete Nevanlinna-Pick property. In such cases, the reproducing kernel
Hilbert space which has served as the domain of the multiplication operator has
always been the vector-valued Drury-Arveson space (thus the Hardy space in case
of the unit disc).
  We present a unified framework for deriving characteristic functions for
kernels that allow a complete Nevanlinna-Pick factor. Notably, our approach not
only encapsulates all previously documented cases but also achieves a
remarkable level of generalization, thereby expanding the concept of the
characteristic function substantially. We also provide an explanation for the
prominence of the Drury-Arveson kernel in all previously established results by
showing that the Drury-Arveson kernel was the natural choice inherently
suitable for those situations.


  Motivated by the inherent value of packets arising in many cyber-physical
applications (e.g., due to precision of the information content or an alarm
message), we consider status update systems with update packets carrying values
as well as their generation time stamps. Once generated, a status update packet
has a random initial value and a deterministic deadline after which it is not
useful (ultimate staleness). In our model, value of a packet decreases in time
(even after reception) starting from its generation to ultimate staleness when
it vanishes. The value of information (VoI) at the receiver is additive in that
the VoI is the sum of the current values of all packets held by the receiver.
We investigate various queuing disciplines under potential dependence between
value and service time and provide closed form expressions for average VoI at
the receiver. Numerical results illustrate the average VoI for different
scenarios and the contrast between average age of information (AoI) and average
VoI.


  We determine the asymptotics for the variance of the number of zeros of
random linear combinations of orthogonal polynomials of degree $\leq n$ in
subintervals $\left [ a,b\right ] $ of the support of the underlying
orthogonality measure $\mu $. We show that, as $n\rightarrow \infty $, this
variance is asymptotic to $cn$, for some explicit constant $c>0$.


  Primordial Black Holes (PBHs) could explain some fraction of dark matter and
shed light on many areas of early-universe physics. Despite over half a century
of research interest, a PBH population has so far eluded detection. The most
competitive constraints on the fraction of dark matter comprised of PBHs
($f_{\rm DM}$) in the $(10^{-9}-10)M_{\odot}$ mass-ranges come from photometric
microlensing and bound $f_{\rm DM}\lesssim10^{-2}-10^{-1}$. With the advent of
the Roman Space Telescope with its sub-milliarcsecond (mas) astrometric
capabilities and its planned Galactic Bulge Time Domain Survey (GBTDS),
detecting astrometric microlensing signatures will become routine. Compared
with photometric microlensing, astrometric microlensing signals are sensitive
to different lens masses-distance configurations and contains different
information, making it a complimentary lensing probe. At sub-mas astrometric
precision, astrometric microlensing signals are typically detectable at larger
lens-source separations than photometric signals, suggesting a microlensing
detection channel of pure astrometric events. We use a Galactic simulation to
predict the number of detectable microlensing events during the GBTDS via this
pure astrometric microlensing channel. Assuming an absolute astrometric
precision floor for bright stars of 0.1 mas for the GBTDS, we find that the
number of detectable events peaks at $\approx 10^{3} f_{\rm DM}$ for a
population of $ 1 M_{\odot}$ PBHs and tapers to $\approx 10f_{\rm DM}$ and
$\approx 100f_{\rm DM}$ at $10^{-4}M_{\odot}$ and $10^{3}M_{\odot}$,
respectively. Accounting for the distinguishability of PBHs from Stellar
lenses, we conclude the GBTDS will be sensitive to a PBH population at $f_{\rm
DM}$ down to $\approx10^{-1}-10^{-3}$ for $(10^{-1}-10^{2})M_{\odot}$ likely
yielding novel PBH constraints.