  We construct a complete set of Wannier functions which are localized at both
given positions and momenta. This allows us to introduce the quantum phase
space, onto which a quantum pure state can be mapped unitarily. Using its
probability distribution in quantum phase space, we define an entropy for a
quantum pure state. We prove an inequality regarding the long time behavior of
our entropy's fluctuation. For a typical initial state, this inequality
indicates that our entropy can relax dynamically to a maximized value and stay
there most of time with small fluctuations. This result echoes the quantum
H-theorem proved by von Neumann in [Zeitschrift f\"ur Physik {\bf 57}, 30
(1929)]. Our entropy is different from the standard von Neumann entropy, which
is always zero for quantum pure states. According to our definition, a system
always has bigger entropy than its subsystem even when the system is described
by a pure state. As the construction of the Wannier basis can be implemented
numerically, the dynamical evolution of our entropy is illustrated with an
example.


  The known bijections on Dyck paths are either involutions or have notoriously
intractable cycle structure. Here we present a size-preserving bijection on
Dyck paths whose cycle structure is amenable to complete analysis. In
particular, each cycle has length a power of 2. A new manifestation of the
Catalan numbers as labeled forests crops up enroute as does the Pascal matrix
mod 2. We use the bijection to show the equivalence of two known manifestations
of the Motzkin numbers. Finally, we consider some statistics on the new Catalan
manifestation.


  On neutral atom platforms, preparing specific quantum states is usually
achieved by pulse shaping, i.e., by optimizing the time-dependence of the
Hamiltonian related to the system. This process can be extremely costly, as it
requires sampling of the final state in the quantum processor many times.
Hence, determining a good pulse, as well as a good embedding, to solve specific
combinatorial graph problems is one of the most important bottlenecks of the
analog approach. In this work, we propose a novel protocol for solving hard
combinatorial graph problems that combines variational analog quantum computing
and machine learning. Our numerical simulations show that the proposed protocol
can reduce dramatically the number of iterations to be run on the quantum
device. Finally, we assess the quality of the proposed approach by estimating
the related Q-score, a recently proposed metric aimed at benchmarking QPUs.


  We define a reduction covariant for the representations a la Vinberg
associated to stably graded Lie algebras. We then give an analogue of the LLL
algorithm for the odd split special orthogonal group and show how this can be
combined with our theory to effectively reduce the coefficients of vectors in a
representation connected to 2-descent for odd hyperelliptic curves.


  In this paper, we propose a computable error estimate of the Gross-Pitaevskii
equation for ground state solution of Bose-Einstein condensates by general
conforming finite element methods on general meshes. Based on the proposed
error estimate, asymptotic lower bounds of the smallest eigenvalue and ground
state energy can be obtained. Several numerical examples are presented to
validate our theoretical results in this paper.


  The equation of state of cold baryonic matter is studied within a
relativistic mean-field model with hadron masses and coupling constants
depending on a scalar field. We demonstrate that if the effective nucleon mass
stops to decrease with a density increase at densities $n>n_*>n_0$, where $n_0$
is the nuclear saturation density, the equation of state stiffens for these
densities and the limiting neutron star mass increases. The stabilization of
the nucleon mass can be realised if in the equation of motion for the scalar
mean-field there appear a term sharply varying in a narrow vicinity of the
field value corresponding to the density $n_*$. We show several possible
realizations of this mechanism getting sufficiently stiff equations of state.
The appearance of hyperons in dense neutron star interiors is accounted for.
The obtained equations of state remain sufficiently stiff if the reduction of
the $\phi$ meson mass is incorporated. Thereby, the hyperon puzzle can be
resolved.


  We investigate a stationary random coefficient autoregressive process.
  Using renewal type arguments tailor-made for such processes, we show that the
stationary distribution has a power-law tail. When the model is normal, we show
that the model is in distribution equivalent to an autoregressive process with
ARCH errors. Hence, we obtain the tail behavior of any such model of arbitrary
order.


  We discuss lepton flavour violating processes induced in the production and
decay of heavy right-handed neutrinos at the LHC. Such particles appear in
left-right symmetrical extensions of the Standard Model as the messengers of
neutrino mass generation, and can have masses at the TeV scale. We determine
the expected sensitivity on the right-handed neutrino mixing matrix, as well as
on the right-handed gauge boson and heavy neutrino masses. By comparing the
sensitivity of the LHC with that of searches for low energy LFV processes, we
identify favourable areas of the parameter space to explore the complementarity
between LFV at low and high energies.


  Reusing code is a common practice in software development: It helps
developers speedup the implementation task while also reducing the chances of
introducing bugs, given the assumption that the reused code has been tested,
possibly in production. Despite these benefits, opportunities for reuse are not
always in plain sight and, thus, developers may miss them. We present our
preliminary steps in building RETIWA, a recommender able to automatically
identify custom implementations in a given project that are good candidates to
be replaced by open source APIs. RETIWA relies on a ``knowledge base''
consisting of real examples of custom implementation-to-API replacements. In
this work, we present the mining strategy we tailored to automatically and
reliably extract replacements of custom implementations with APIs from open
source projects. This is the first step towards building the envisioned
recommender.


  We present results from offline searches of Fermi Gamma-ray Burst Monitor
(GBM) data for gamma-ray transients coincident with the compact binary
coalescences observed by the gravitational-wave (GW) detectors Advanced LIGO
and Advanced Virgo during their first and second observing runs. In particular,
we perform follow-up for both confirmed events and low significance candidates
reported in the LIGO/Virgo catalog GWTC-1. We search for temporal coincidences
between these GW signals and GBM triggered gamma-ray bursts (GRBs). We also use
the GBM Untargeted and Targeted subthreshold searches to find coincident
gamma-rays below the on-board triggering threshold. This work implements a
refined statistical approach by incorporating GW astrophysical source
probabilities and GBM visibilities of LIGO/Virgo sky localizations to search
for cumulative signatures of coincident subthreshold gamma-rays. All search
methods recover the short gamma-ray burst GRB 170817A occurring ~1.7 s after
the binary neutron star merger GW170817. We also present results from a new
search seeking GBM counterparts to LIGO single-interferometer triggers. This
search finds a candidate joint event, but given the nature of the GBM signal
and localization, as well as the high joint false alarm rate of $1.1 \times
10^{-6}$ Hz, we do not consider it an astrophysical association. We find no
additional coincidences.


  Grasping objects of different shapes and sizes - a foundational, effortless
skill for humans - remains a challenging task in robotics. Although model-based
approaches can predict stable grasp configurations for known object models,
they struggle to generalize to novel objects and often operate in a
non-interactive open-loop manner. In this work, we present a reinforcement
learning framework that learns the interactive grasping of various
geometrically distinct real-world objects by continuously controlling an
anthropomorphic robotic hand. We explore several explicit representations of
object geometry as input to the policy. Moreover, we propose to inform the
policy implicitly through signed distances and show that this is naturally
suited to guide the search through a shaped reward component. Finally, we
demonstrate that the proposed framework is able to learn even in more
challenging conditions, such as targeted grasping from a cluttered bin.
Necessary pre-grasping behaviors such as object reorientation and utilization
of environmental constraints emerge in this case. Videos of learned interactive
policies are available at https://maltemosbach.github.
io/geometry_aware_grasping_policies.


  Using the coherent-state representation we show that the classical Einstein
equation for the FRW cosmological model with a general minimal scalar field can
be derived from the semiclassical quantum Einstein equation.


  Since the appearance of H. Robbins article (1948), the central limit theorems
for random sums have been studied for about 70 years. The central limit
theorems for random sums of independent random variables play a very important
role in various disciplines such as statistics, financial mathematics,
insurance, etc. The purpose of this paper is to randomize some well-known
classical and non-classical central limit theorems for sums of independent (not
necessarily identically distributed) random variables of a double sequence,
with the conditions for determining their validity. The results obtained in
this paper are extensions and generalizations of known ones.


  We give a negative answer to the Newman--Shapiro problem on weighted
approximation for entire functions formulated in 1966 and motivated by the
theory of operators on the Fock space. There exists a function in the Fock
space such that its exponential multiples do not approximate some entire
multiples in the space. Furthermore, we establish several positive results
under different restrictions on the function in question.


  I review the progress that has been made in light hadron spectroscopy from
lattice QCD, since the LATTICE'94 conference in Bielefeld.


  Object detectors often suffer from the domain gap between training (source
domain) and real-world applications (target domain). Mean-teacher self-training
is a powerful paradigm in unsupervised domain adaptation for object detection,
but it struggles with low-quality pseudo-labels. In this work, we identify the
intriguing alignment and synergy between mean-teacher self-training and
contrastive learning. Motivated by this, we propose Contrastive Mean Teacher
(CMT) -- a unified, general-purpose framework with the two paradigms naturally
integrated to maximize beneficial learning signals. Instead of using
pseudo-labels solely for final predictions, our strategy extracts object-level
features using pseudo-labels and optimizes them via contrastive learning,
without requiring labels in the target domain. When combined with recent
mean-teacher self-training methods, CMT leads to new state-of-the-art
target-domain performance: 51.9% mAP on Foggy Cityscapes, outperforming the
previously best by 2.1% mAP. Notably, CMT can stabilize performance and provide
more significant gains as pseudo-label noise increases.


  Pre-mRNA splicing relies on the poorly understood dynamic interplay between
>150 protein components of the spliceosome. The steps at which splicing can be
regulated remain largely unknown. We systematically analyzed the effect of
knocking down the components of the splicing machinery on alternative splicing
events relevant for cell proliferation and apoptosis and used this information
to reconstruct a network of functional interactions. The network accurately
captures known physical and functional associations and identifies new ones,
revealing remarkable regulatory potential of core spliceosomal components,
related to the order and duration of their recruitment during spliceosome
assembly. In contrast with standard models of regulation at early steps of
splice site recognition, factors involved in catalytic activation of the
spliceosome display regulatory properties. The network also sheds light on the
antagonism between hnRNP C and U2AF, and on targets of antitumor drugs, and can
be widely used to identify mechanisms of splicing regulation.


  The aim of this note is to show that the properties like motivic
decomposability, Chow theoretic decomposition of the diagonal etc. happens for
the special member of a family if it happens for a general member of the
family.


  The {\em Tur\'an number} of an $r$-uniform graph $F$, denoted by $ex(n,F)$,
is the maximum number of edges in an $F$-free $r$-uniform graph on $n$
vertices. The {\em Tur\'{a}n density} of $F$ is defined as
$\pi(F)=\underset{{n\rightarrow\infty}}{\lim}{ex(n,F) \over {n \choose r }}.$
For graphs, Erd\H{o}s-Stone-Simonovits (\cite{ESi}, \cite{ES}) showed that
$\Pi_{\infty}^{(2)}=\Pi_{fin}^{(2)}=\Pi_{1}^{(2)}=\{0, {1 \over 2}, {2 \over
3}, \ldots,{l-1 \over l}, ...\}.$ We know quite few about the Tur\'an density
of an $r$-uniform graph for $r\ge 3$. Baber and Talbot \cite{BT}, and Pikhurko
\cite{Pikhurko2} showed that there is an irrational number in $\Pi_{3}^{(3)}$
and $\Pi_{fin}^{(3)}$ respectively, disproving a conjecture of Chung and Graham
\cite{FG}. Baber and Talbot \cite{BT} asked whether $\Pi_{1}^{(r)}$ contains an
irrational number. In this paper, we show that the Lagrangian density of
$F=\{123, 124, 134, 234, 567\}$ (the disjoint union of $K_4^3$ and an edge) is
${\sqrt 3\over 3}$, consequently, the Tur\'an density of the extension of $F$
is an irrational number, answering the question of Baber and Talbot.


  We investigate dynamics of the chiral transition in expanding quark-antiquark
plasma produced in an ultra-relativistic heavy ion collision. The chiral
symmetry break-down and dynamical generation of the constituent quark mass are
studied within the linear sigma model and Nambu-Jona-Lasinio model. Time
dependence of the quark and antiquark densities is obtained from the scaling
solution of the relativistic Vlasov equation. Fast initial growth and strong
oscillations of the constituent quark mass are found in the linear sigma model
as well as in the NJL model, when derivative terms are taken into account.


  It has been shown in the last few years that 3-form fields present viable
cosmological solutions for inflation and dark energy with particular observable
signatures distinct from those of canonical single scalar field inflation. The
aim of this work is to explore the dynamics of a single 3-form in five
dimensional Randall-Sundrum II braneworld scenario, in which a 3-form is
confined to the brane and only gravity propagates in the bulk. We compare the
solutions with the standard four dimensional case already studied in the
literature. In particular, we evaluate how the spectral index and the ratio of
tensor to scalar perturbations are influenced by the presence of the bulk and
put constraints on the parameters of the models in the light of the recent
Planck 2015 data.


  It is sometimes claimed that Lorentz invariant wave equations which allow
superluminal propagation exhibit worse predictability than subluminal
equations. To investigate this, we study the Born-Infeld scalar in two
spacetime dimensions. This equation can be formulated in either a subluminal or
a superluminal form. Surprisingly, we find that the subluminal theory is less
predictive than the superluminal theory in the following sense. For the
subluminal theory, there can exist multiple maximal globally hyperbolic
developments arising from the same initial data. This problem does not arise in
the superluminal theory, for which there is a unique maximal globally
hyperbolic development. For a general quasilinear wave equation, we prove
theorems establishing why this lack of uniqueness occurs, and identify
conditions on the equation that ensure uniqueness. In particular, we prove that
superluminal equations always admit a unique maximal globally hyperbolic
development. In this sense, superluminal equations exhibit better
predictability than generic subluminal equations.


  We review the main features and results of thermal leptogenesis within the
type I seesaw mechanism, the minimal extension of the Standard Model explaining
neutrino masses and mixing. After presenting the simplest approach, the vanilla
scenario, we discuss various important developments in recent years, such as
the inclusion of lepton and heavy neutrino flavour effects, a description
beyond a hierarchical heavy neutrino mass spectrum and an improved kinetic
description within the density matrix and the closed-time-path formalisms. We
also discuss how leptogenesis can ultimately represent an important
phenomenological tool to test the seesaw mechanism and the underlying model of
new physics.


  $\beta$-Ga$_2$O$_3$ is an ultra-wide bandgap semiconductor and is thus
expected to be optically transparent to light of sub-bandgap wavelengths well
into the ultraviolet. Contrary to this expectation, it is found here that free
electrons in n-doped $\beta$-Ga$_2$O$_3$ absorb light from the IR to the UV
wavelength range via intra- and inter-conduction band optical transitions.
Intra-conduction band absorption occurs via an indirect optical phonon mediated
process with a $1/\omega^{3}$ dependence in the visible to near-IR wavelength
range. This frequency dependence markedly differs from the $1/\omega^{2}$
dependence predicted by the Drude model of free-carrier absorption. The
inter-conduction band absorption between the lowest conduction band and a
higher conduction band occurs via a direct optical process at $\lambda \sim
349$ nm (3.55 eV). Steady state and ultrafast optical spectroscopy measurements
unambiguously identify both these absorption processes and enable quantitative
measurements of the inter-conduction band energy, and the frequency dependence
of absorption. Whereas the intra-conduction band absorption does not depend on
light polarization, inter-conduction band absorption is found to be strongly
polarization dependent. The experimental observations, in excellent agreement
with recent theoretical predictions for $\beta$-Ga$_2$O$_3$, provide important
limits of sub-bandgap transparency for optoelectronics in the deep-UV to
visible wavelength range, and are also of importance for high electric field
transport effects in this emerging semiconductor.


  Computational searches for stable and metastable structures of water ice and
other H:O compositions at TPa pressures have led us to predict that H$_2$O
decomposes into H$_2$O$_2$ and a hydrogen-rich phase at pressures of a little
over 5 TPa. The hydrogen-rich phase is stable over a wide range of hydrogen
contents, and it might play a role in the erosion of the icy component of the
cores of gas giants as H$_2$O comes into contact with hydrogen. Metallization
of H$_2$O is predicted at a higher pressure of just over 6 TPa, and therefore
H$_2$O does not have a thermodynamically stable low-temperature metallic form.
We have also found a new and rich mineralogy of complicated water ice phases
which are more stable in the pressure range 0.8--2 TPa than any predicted
previously.


  The field of generating recommendations within the framework of causal
inference has seen a recent surge, with recommendations being likened to
treatments. This approach enhances insights into the influence of
recommendations on user behavior and helps in identifying the underlying
factors. Existing research has often leveraged propensity scores to mitigate
bias, albeit at the risk of introducing additional variance. Others have
explored the use of unbiased data from randomized controlled trials, although
this comes with assumptions that may prove challenging in practice. In this
paper, we first present the causality-aware interpretation of recommendations
and reveal how the underlying exposure mechanism can bias the maximum
likelihood estimation (MLE) of observational feedback. Recognizing that
confounders may be elusive, we propose a contrastive self-supervised learning
to minimize exposure bias, employing inverse propensity scores and expanding
the positive sample set. Building on this foundation, we present a novel
contrastive counterfactual learning method (CCL) that incorporates three unique
positive sampling strategies grounded in estimated exposure probability or
random counterfactual samples. Through extensive experiments on two real-world
datasets, we demonstrate that our CCL outperforms the state-of-the-art methods.


  In this paper we apply the self-consistent generalized Langevin equation
theory (SCGLE) of dynamic arrest for colloidal mixtures to predict the glass
transition of a colloidal fluid permeating a porous matrix of obstacles with
random distribution. We obtained the transition diagrams for different size
asymmetries and so we give an asserted description of recent simulations
results [K. Kim, K. Miyazaki, and S. Saito, Europhys. Lett. 88, 36002 (2009)]
of Quenched-Annealed and Equilibrated-Mixture systems which reveal very
different qualitative scenarios which are in apparent contradiction with
theoretical predictions of Mode Coupling Theory (MCT) [V. Krakoviack. Phys.
Rev. E 75, 031503 (2007)]. We show that SCGLE theory predicts the existence of
a reentrant region in EM systems as predicted using MC theory. However,
opposite to MCT predictions, we show that it is practically impossible to
distinguish a rentrant region in QA systems if it would exist. Qualitative
comparisons are in good agreement with simulation results and thus, we propose
SCGLE theory as a useful tool for the interpretation of the arrest transition
in ideal porous systems.


  This paper is devoted to study the existence of a solution to Hilfer
fractional differential equation with nonlocal boundary condition. We use the
equivalent integral equation to study the considered Hilfer differential
problem with nonlocal boundary condition. The Monch type fixed point theorem
and the measure of the noncompactness technique are the main tools in this
study. We demonstrate the existence of a solution with a suitable illustrative
example.


  Exchange bias (EB) refers to a shift of the hysteresis loop along the field
axis in materials consisting of ferromagnetic (FM) and antiferromagnetic (AFM)
layers, generally after a cooling procedure in high magnetic field. This effect
is highly desirable for technological applications ranging from spintronics to
magnetic recording. Achieving giant EB effect near room temperature in a small
cooling field is thus an on-going technologically relevant challenge for the
materials science community. In this work, we present the experimental
realization of such a fundamental goal by demonstrating the existence of giant
EB after a zero field cooled (ZFC) procedure in antiperovskite Mn3.5Co0.5N
below 256 K. We found that it exhibits an EB field of 0.28 T at 50 K after a
ZFC procedure accompanied by a large vertical magnetization shift (VMS).
Interestingly, this EB field can be elevated up to 1.2 T after a cooling
procedure with a small applied field of just 500 Oe. Mn3:5Co0:5N bears the
first intermetallic material showing a strong correlation between EB and VMS.We
attribute the observed EB effect to a completely new canted triangular magnetic
structure determined by neutron diffraction experiment. Finally, we discuss the
striking effect of Co substitution on the physical properties of antiperovskite
materials and put forward a new strategy for antiperovskite lattice to exploit
new single phase materials showing large EB effect at room temperature.


  In the present paper a novel graph-based approach to the shape decomposition
problem is addressed. The shape is appropriately transformed into a visibility
graph enriched with local neighborhood information. A two-step diffusion
process is then applied to the visibility graph that efficiently enhances the
information provided, thus leading to a more robust and meaningful graph
construction. Inspired by the notion of a clique as a strict cluster
definition, the dominant sets algorithm is invoked, slightly modified to
comport with the specific problem of defining shape parts. The cluster
cohesiveness and a node participation vector are two important outputs of the
proposed graph partitioning method. Opposed to most of the existing techniques,
the final number of the clusters is determined automatically, by estimating the
cluster cohesiveness on a random network generation process. Experimental
results on several shape databases show the effectiveness of our framework for
graph based shape decomposition.


  Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe
through a bounce in the high energy region. But LQC has an ambiguity about the
quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)]
proposed a new quantization scheme. Similar to others, this new quantization
scheme also replaces the big bang singularity with the quantum bounce. More
interestingly, it introduces a quantum singularity, which is traversable. We
investigate this novel dynamics quantitatively with a tachyon scalar field,
which gives us a concrete example. Our result shows that our universe can
evolve through the quantum singularity regularly, which is different from the
classical big bang singularity. So this singularity is only a week singularity.


  This paper deals with stability of discrete-time switched linear systems
whose all subsystems are unstable. We present sufficient conditions on the
subsystems matrices such that a switched system is globally exponentially
stable under a set of purely time-dependent switching signals that are allowed
to activate all subsystems. The main apparatuses for our analysis are (matrix)
commutation relations between certain products of the subsystems matrices and
graph-theoretic arguments. We present a numerical experiment to demonstrate our
results.


  We provide a framework to analyze the convergence of discretized kinetic
Langevin dynamics for $M$-$\nabla$Lipschitz, $m$-convex potentials. Our
approach gives convergence rates of $\mathcal{O}(m/M)$, with explicit stepsize
restrictions, which are of the same order as the stability threshold for
Gaussian targets and are valid for a large interval of the friction parameter.
We apply this methodology to various integration schemes which are popular in
the molecular dynamics and machine learning communities. Further, we introduce
the property ``$\gamma$-limit convergent" (GLC) to characterize underdamped
Langevin schemes that converge to overdamped dynamics in the high-friction
limit and which have stepsize restrictions that are independent of the friction
parameter; we show that this property is not generic by exhibiting methods from
both the class and its complement. Finally, we provide asymptotic bias
estimates for the BAOAB scheme, which remain accurate in the high-friction
limit by comparison to a modified stochastic dynamics which preserves the
invariant measure.


  Most classification methods are based on the assumption that data conforms to
a stationary distribution. The machine learning domain currently suffers from a
lack of classification techniques that are able to detect the occurrence of a
change in the underlying data distribution. Ignoring possible changes in the
underlying concept, also known as concept drift, may degrade the performance of
the classification model. Often these changes make the model inconsistent and
regular updatings become necessary. Taking the temporal dimension into account
during the analysis of Web usage data is a necessity, since the way a site is
visited may indeed evolve due to modifications in the structure and content of
the site, or even due to changes in the behavior of certain user groups. One
solution to this problem, proposed in this article, is to update models using
summaries obtained by means of an evolutionary approach based on an intelligent
clustering approach. We carry out various clustering strategies that are
applied on time sub-periods. To validate our approach we apply two external
evaluation criteria which compare different partitions from the same data set.
Our experiments show that the proposed approach is efficient to detect the
occurrence of changes.


  Thermal noise generally greatly exceeds quantum noise in optomechanical
devices unless the mechanical frequency is very high or the thermodynamic
temperature is very low. This paper addresses the design concept for a novel
optomechanical device capable of ultrahigh quality factors in the audio
frequency band with negligible thermal noise. The proposed system consists of a
minimally supported millimeter scale pendulum mounted in a Double End-Mirror
Sloshing (DEMS) cavity that is topologically equivalent to a
Membrane-in-the-Middle (MIM) cavity. The radiation pressure inside the
high-finesse cavity allows for high optical stiffness, cancellation of terms
which lead to unwanted negative damping and suppression of quantum radiation
pressure noise. We solve for the optical spring dynamics of the system using
the Hamiltonian, find the noise spectral density and show that stable optical
trapping is possible. We also assess various loss mechanisms, one of the most
important being the acceleration loss due to the optical spring. We show that
practical devices, starting from a centre-of-mass pendulum frequency of 0.1 Hz,
could achieve a maximum quality factor of $10^{14}$ with optical spring
stiffened frequency 1-10 kHz. Small resonators of mass 1 $\mu$g or less could
achieve a Q-factor of $10^{11}$ at a frequency of 100 kHz. Applications for
such devices include white light cavities for improvement of gravitational wave
detectors, or sensors able to operate near the quantum limit.


  We study an optimal control problem associated to the conformal Laplacian
obstacle problem on closed n-dimensional Riemannian manifolds with n >2. When
the Yamabe invariant of the Riemannian manifold is positive, we show that the
optimal controls are equal to their associated optimal states and show the
existence of a smooth optimal control which induces a conformal metric with
constant scalar curvature. For the standard sphere, we prove that the standard
bubbles -- namely conformal factor of metrics conformal to the standard one
with constant positive scalar curvature -- are the only optimal controls and
hence equal to their associated optimal state.


  For a polynomial $f(x)\in \mathbb Z[x]$ we study an analogue of Jacobsthal
function, defined by the formula \[ j_f(N)=\max_{m}\{\text{For some } x\in
\mathbb N \text{ the inequality } (x+f(i),N)>1 \text{ holds for all }i\leq m\}.
\] We prove a lower bound \[ j_f(P(y))\gg y(\ln
y)^{\ell_f-1}\left(\frac{(\ln\ln y)^2}{\ln\ln\ln y}\right)^{h_f}\left(\frac{\ln
y\ln\ln\ln y}{(\ln\ln y)^2}\right)^{M(f)}, \] where $P(y)$ is the product of
all primes $p$ below $y$, $\ell_f$ is the number of distinct linear factors of
$f(x)$, $h_f$ is the number of distinct non-linear irreducible factors and
$M(f)$ is the average size of the maximal preimage of a point under a map
$f:\mathbb F_p\to \mathbb F_p$. The quantity $M(f)$ is computed in terms of
certain Galois groups.


  The internal phase dynamics of a quantum system is revealed in details.
Theoretical and experimental evidences of existence of a causal relation of the
phase of the wave function with the dynamics of the quantum system are
presented sistematically for the first time. A new, dynamics-statistical
interpretation of the quantum mechanics is introduced. A particle-wave duality
picture incorporated in the wave function through its phase and amplitude is
considered.


  We compute the light hadron mass spectrum in quenched lattice QCD at $\beta =
6.0$ using the Sheikholeslami-Wohlert fermionic action. The calculation is done
for several choices of the coefficient $c_{SW}$, including $c_{SW} = 0$ and the
recently proposed optimal value $c_{SW} = 1.769$. We find that the individual
masses change by up to 30\% under $O(a)$ improvement. The spectrum calculation
suggests $c_{SW} \approx 1.4$ for the optimal value of the coefficient.


  We introduce a novel architecture for neural disparity refinement aimed at
facilitating deployment of 3D computer vision on cheap and widespread consumer
devices, such as mobile phones. Our approach relies on a continuous formulation
that enables to estimate a refined disparity map at any arbitrary output
resolution. Thereby, it can handle effectively the unbalanced camera setup
typical of nowadays mobile phones, which feature both high and low resolution
RGB sensors within the same device. Moreover, our neural network can process
seamlessly the output of a variety of stereo methods and, by refining the
disparity maps computed by a traditional matching algorithm like SGM, it can
achieve unpaired zero-shot generalization performance compared to
state-of-the-art end-to-end stereo models.


  The main aim of this paper is to study an analogue of the generalized divisor
function in a number field $\mathbb{K}$, namely,
$\sigma_{\mathbb{K},\alpha}(n)$. The Dirichlet series associated to this
function is $\zeta_{\mathbb{K}}(s)\zeta_{\mathbb{K}}(s-\alpha)$. We give an
expression for the Riesz sum associated to $\sigma_{\mathbb{K},\alpha}(n),$ and
also extend the validity of this formula by using convergence theorems. As a
special case, when $\mathbb{K}=\mathbb{Q}$, the Riesz sum formula for the
generalized divisor function is obtained, which, in turn, for $\alpha=0$, gives
the Vorono\"{\i} summation formula associated to the divisor counting function
$d(n)$. We also obtain a big $O$-estimate for the Riesz sum associated to
$\sigma_{\mathbb{K},\alpha}(n)$.


  By a metric fractal we understand a compact metric space $K$ endowed with a
finite family $\mathcal F$ of contracting self-maps of $K$ such that
$K=\bigcup_{f\in\mathcal F}f(K)$. If $K$ is a subset of a metric space $X$ and
each $f\in\mathcal F$ extends to a contracting self-map of $X$, then we say
that $(K,\mathcal F)$ is a fractal in $X$. We prove that each metric fractal
$(K,\mathcal F)$ is
  $\bullet$ isometrically equivalent to a fractal in the Banach spaces $C[0,1]$
and $\ell_\infty$;
  $\bullet$ bi-Lipschitz equivalent to a fractal in the Banach space $c_0$;
  $\bullet$ isometrically equivalent to a fractal in the Hilbert space $\ell_2$
if $K$ is an ultrametric space.
  We prove that for a metric fractal $(K,\mathcal F)$ with the doubling
property there exists $k\in\mathbb N$ such that the metric fractal $(K,\mathcal
F^{\circ k})$ endowed with the fractal structure $\mathcal F^{\circ
k}=\{f_1\circ\dots\circ f_k:f_1,\dots,f_k\in\mathcal F\}$ is equi-H\"older
equivalent to a fractal in a Euclidean space $\mathbb R^d$. This result is used
to prove our main result saying that each finite-dimensional compact metrizable
space $K$ containing an open uncountable zero-dimensional space $Z$ is
homeomorphic to a fractal in a Euclidean space $\mathbb R^d$. For $Z$, being a
copy of the Cantor set, this embedding result was proved by Duvall and Husch in
1992.


  We extend to semi-abelian categories the notion of characteristic subobject,
which is widely used in group theory and in the theory of Lie algebras.
Moreover, we show that many of the classical properties of characteristic
subgroups of a group hold in the general semi-abelian context, or in stronger
ones.


  We investigate the long-time dynamics and optimal control problem of a
diffuse interface model that describes the growth of a tumor in presence of a
nutrient and surrounded by host tissues. The state system consists of a
Cahn-Hilliard type equation for the tumor cell fraction and a
reaction-diffusion equation for the nutrient. The possible medication that
serves to eliminate tumor cells is in terms of drugs and is introduced into the
system through the nutrient. In this setting, the control variable acts as an
external source in the nutrient equation. First, we consider the problem of
`long-time treatment' under a suitable given source and prove the convergence
of any global solution to a single equilibrium as $t\to+\infty$. Then we
consider the `finite-time treatment' of a tumor, which corresponds to an
optimal control problem. Here we also allow the objective cost functional to
depend on a free time variable, which represents the unknown treatment time to
be optimized. We prove the existence of an optimal control and obtain first
order necessary optimality conditions for both the drug concentration and the
treatment time. One of the main aim of the control problem is to realize in the
best possible way a desired final distribution of the tumor cells, which is
expressed by the target function $\phi_\Omega$. By establishing the Lyapunov
stability of certain equilibria of the state system (without external source),
we see that $\phi_{\Omega}$ can be taken as a stable configuration, so that the
tumor will not grow again once the finite-time treatment is completed.


  A charged particle in the presence of a magnetic field is studied in the
position dependent operator formalism. Instead of a quantum harmonic
oscillator, the solution of the resulting Schr\"odinger-like equation is the
one for the Morse oscillator. The anharmonicity that shows up naturally from
the theory is analogous to the corrections introduced by relativistic ones.The
degeneracy of the spin up and down levels is lifted due to the non-Euclidean
space. It is shown that the Fermi energy and the total ground state energy of
the 2DEG is also modified.


  Processes with three external electroweak gauge boson allow for a measurement
of triple and quartic gauge couplings. They can be used to constrain anomalous
gauge couplings, where new physics might predominantly couple to electroweak
gauge bosons. In this paper we chose a class of such processes where we
consider two photons and an additional vector boson in the final state. As
additional vector boson we consider either a third photon or a $W$ or $Z$
boson. For the latter two cases we assume a leptonic decay of the boson. We
calculate the next-to-leading order QCD and electroweak corrections to these
processes with a particular emphasis on the until now unknown electroweak
corrections. We find that the electroweak corrections to the total cross
section are moderate in the range of a few per cent at most, but can reach
several tens of per cent in regions of phase space that are particularly
interesting in the context of new physics searches. In addition we investigate
the difference between additive and multiplicative scheme when combining QCD
and electroweak corrections and we assess the importance of photon induced
contributions to these processes.


  A nanophotonic waveguide coupled with an atomic array forms one of the
strongly-coupled quantum interfaces to showcase many fascinating collective
features of quantum dynamics. In particular for a dissimilar array of two
different interparticle spacings with competing photon-mediated dipole-dipole
interactions and directionality of couplings, we study the steady-state phases
of atomic excitations under a weakly-driven condition of laser field. We
identify a partial set of steady-state phases of the driven system composed of
combinations of steady-state solutions in a homogeneous array. We also reveal
an intricate role of the atom at the interface of the dissimilar array in
determining the steady-state phases and find an alteration in the dichotomy of
the phases strongly associated with steady-state distributions with crystalline
orders. We further investigate in detail the interaction-induced depletion in
half of the dissimilar array. This blockaded region results from two
contrasting interparticle spacings near the reciprocal coupling regime, which
is evidenced from the analytical solutions under the reciprocal coupling. Our
results can provide insights in the driven-dissipative quantum phases of atomic
excitations with nonreciprocal couplings and pave the avenues toward quantum
simulations of exotic many-body states essential for quantum information
applications.


  Recent work in adversarial machine learning started to focus on the visual
perception in autonomous driving and studied Adversarial Examples (AEs) for
object detection models. However, in such visual perception pipeline the
detected objects must also be tracked, in a process called Multiple Object
Tracking (MOT), to build the moving trajectories of surrounding obstacles.
Since MOT is designed to be robust against errors in object detection, it poses
a general challenge to existing attack techniques that blindly target objection
detection: we find that a success rate of over 98% is needed for them to
actually affect the tracking results, a requirement that no existing attack
technique can satisfy. In this paper, we are the first to study adversarial
machine learning attacks against the complete visual perception pipeline in
autonomous driving, and discover a novel attack technique, tracker hijacking,
that can effectively fool MOT using AEs on object detection. Using our
technique, successful AEs on as few as one single frame can move an existing
object in to or out of the headway of an autonomous vehicle to cause potential
safety hazards. We perform evaluation using the Berkeley Deep Drive dataset and
find that on average when 3 frames are attacked, our attack can have a nearly
100% success rate while attacks that blindly target object detection only have
up to 25%.


  Current Spoken Dialogue Systems (SDSs) often serve as passive listeners that
respond only after receiving user speech. To achieve human-like dialogue, we
propose a novel future prediction architecture that allows an SDS to anticipate
future affective reactions based on its current behaviors before the user
speaks. In this work, we investigate two scenarios: speech and laughter. In
speech, we propose to predict the user's future emotion based on its temporal
relationship with the system's current emotion and its causal relationship with
the system's current Dialogue Act (DA). In laughter, we propose to predict the
occurrence and type of the user's laughter using the system's laughter
behaviors in the current turn. Preliminary analysis of human-robot dialogue
demonstrated synchronicity in the emotions and laughter displayed by the human
and robot, as well as DA-emotion causality in their dialogue. This verifies
that our architecture can contribute to the development of an anticipatory SDS.


  Current language models can generate high-quality text. Are they simply
copying text they have seen before, or have they learned generalizable
linguistic abstractions? To tease apart these possibilities, we introduce
RAVEN, a suite of analyses for assessing the novelty of generated text,
focusing on sequential structure (n-grams) and syntactic structure. We apply
these analyses to four neural language models (an LSTM, a Transformer,
Transformer-XL, and GPT-2). For local structure - e.g., individual dependencies
- model-generated text is substantially less novel than our baseline of
human-generated text from each model's test set. For larger-scale structure -
e.g., overall sentence structure - model-generated text is as novel or even
more novel than the human-generated baseline, but models still sometimes copy
substantially, in some cases duplicating passages over 1,000 words long from
the training set. We also perform extensive manual analysis showing that
GPT-2's novel text is usually well-formed morphologically and syntactically but
has reasonably frequent semantic issues (e.g., being self-contradictory).


  In this short review, we pay attention to some subtleties in the study of
projective representations, contrasting local to global properties and their
interplay. The analysis is exposed rigorously, showing and demonstrating the
main necessary theorems. We discuss the implementation of useful algebraic
topology tools to characterize representations.


  The goal of this paper is to adapt speaker embeddings for solving the problem
of speaker diarisation. The quality of speaker embeddings is paramount to the
performance of speaker diarisation systems. Despite this, prior works in the
field have directly used embeddings designed only to be effective on the
speaker verification task. In this paper, we propose three techniques that can
be used to better adapt the speaker embeddings for diarisation: dimensionality
reduction, attention-based embedding aggregation, and non-speech clustering. A
wide range of experiments is performed on various challenging datasets. The
results demonstrate that all three techniques contribute positively to the
performance of the diarisation system achieving an average relative improvement
of 25.07% in terms of diarisation error rate over the baseline.


  I apply recent work on "learning to think" (2015) and on PowerPlay (2011) to
the incremental training of an increasingly general problem solver, continually
learning to solve new tasks without forgetting previous skills. The problem
solver is a single recurrent neural network (or similar general purpose
computer) called ONE. ONE is unusual in the sense that it is trained in various
ways, e.g., by black box optimization / reinforcement learning / artificial
evolution as well as supervised / unsupervised learning. For example, ONE may
learn through neuroevolution to control a robot through environment-changing
actions, and learn through unsupervised gradient descent to predict future
inputs and vector-valued reward signals as suggested in 1990. User-given tasks
can be defined through extra goal-defining input patterns, also proposed in
1990. Suppose ONE has already learned many skills. Now a copy of ONE can be
re-trained to learn a new skill, e.g., through neuroevolution without a
teacher. Here it may profit from re-using previously learned subroutines, but
it may also forget previous skills. Then ONE is retrained in PowerPlay style
(2011) on stored input/output traces of (a) ONE's copy executing the new skill
and (b) previous instances of ONE whose skills are still considered worth
memorizing. Simultaneously, ONE is retrained on old traces (even those of
unsuccessful trials) to become a better predictor, without additional expensive
interaction with the enviroment. More and more control and prediction skills
are thus collapsed into ONE, like in the chunker-automatizer system of the
neural history compressor (1991). This forces ONE to relate partially analogous
skills (with shared algorithmic information) to each other, creating common
subroutines in form of shared subnetworks of ONE, to greatly speed up
subsequent learning of additional, novel but algorithmically related skills.


  IGR J11305-6256 is one of the numerous sources discovered through the
INTEGRAL scan of the Galactic Plane. Thanks to the Swift-BAT survey, that
allows the frequent sampling of any sky region, we have discovered in the hard
X-ray emission of this source a modulation with a period of ~120.83 d. The
significance of this periodic modulation is ~4 standard deviations in Gaussian
statistics. We interpret it as the orbital period of the binary system. We
derive an orbital separation between IGR J11305-6256 and its companion star of
~286 R$_{\odot}$ corresponding to ~19 times the radius of the companion star.
The broadband XRT-BAT (0.3-150 keV) spectrum is described either by the sum of
a black-body and a cut-off power-law or by a partially absorbed cut-off
power-law. The temporal and spectral characteristics of the source indicate its
possible association with the class of persistent, but faint, Be X-ray binary
systems.


  E commerce refers to the utilization of electronic data transmission for
enhancing business processes and implementing business strategies. Explicit
components of e commerce include providing after sales services, promoting
services or products to services, processing payment, engaging in transaction
processes, identifying customer needs, processing payment and creating services
or products. In recent times, the use of e commerce has become too common among
the people. However, the growing demand of e commerce sites have made essential
for the databases to support direct querying of the Web page. This research
aims to explore and evaluate the integration of database queries and their uses
in searching of electronic commerce products. It has been analyzed that e
commerce is one of the most outstanding trends, which have been emerged in the
commerce world, for the last decades. Therefore, this study was undertaken to
examine the benefits of integrating database queries with e commerce product
searches. The findings of this study suggested that database queries are
extremely valuable for e commerce sites as they make product searches simpler
and accurate. In this context, the approach of integrating database queries is
found to be the most suitable and satisfactory, as it simplifies the searching
of e commerce products.


  At the prime $2$, Behrens, Hill, Hopkins and Mahowald showed $M_2(1,4)$
admits $32$-periodic $v_2$-self-map and more recently authors joint with
Mahowald showed $A_1$ also admits $32$-periodic $v_2$-self-map. This leads to
the question, whether there exists a finite $2$-local complex with periodicity
less than $32$. This paper will answer the question by producing a class of
finite $2$-local spectra $\widetilde{\mathcal{Z}}$ all of which admit
$1$-periodic $v_2$-self-map.


  In the works of A. Ach\'ucarro and P. K. Townsend and also by E. Witten, a
duality between three-dimensional Chern-Simons gauge theories and gravity was
established. In all cases, the results made use of the field equations. In a
previous work, we were capable to generalize Witten's work to the off-shell
cases, as well as to four dimensional Yang-Mills theory with de Sitter gauge
symmetry. The price we paid is that curvature and torsion must obey some
constraints under the action of the interior derivative. These constraints
implied on the partial breaking of diffeomorphism invariance. In the present
work, we, first, formalize our early results in terms of fiber bundle theory by
establishing the formal aspects of the map between a principal bundle (gauge
theory) and a coframe bundle (gravity) with partial breaking of diffeomorphism
invariance. Then, we study the effect of the constraints on the homology
defined by the interior derivative. The main result is the emergence of a
nontrivial homology in Riemann-Cartan manifolds.


  In discrete time, $\ell$-blocks of red lights are separated by $\ell$-blocks
of green lights. Cars arrive at random. \ We seek the distribution of maximum
line length of idle cars, and justify conjectured probabilistic asymptotics
algebraically for $2\leq\ell\leq3$ and numerically for $\ell\geq4$.


  It is commonly believed that area laws for entanglement entropies imply that
a quantum many-body state can be faithfully represented by efficient tensor
network states - a conjecture frequently stated in the context of numerical
simulations and analytical considerations. In this work, we show that this is
in general not the case, except in one dimension. We prove that the set of
quantum many-body states that satisfy an area law for all Renyi entropies
contains a subspace of exponential dimension. Establishing a novel link between
quantum many-body theory and the theory of communication complexity, we then
show that there are states satisfying area laws for all Renyi entropies but
cannot be approximated by states with a classical description of small
Kolmogorov complexity, including polynomial projected entangled pair states
(PEPS) or states of multi-scale entanglement renormalisation (MERA). Not even a
quantum computer with post-selection can efficiently prepare all quantum states
fulfilling an area law, and we show that not all area law states can be
eigenstates of local Hamiltonians. We also prove translationally invariant and
isotropic instances of these results, and show a variation with decaying
correlations using quantum error-correcting codes.


  We explore the effects coming from the nested structures on propagation of
radial light rays going through them in the simple self-similar configuration
containing pairs of voids and overdense regions. Each pair can be described
with the Lemaitre-Tolman-Bondi metric and is composed of interior dust ball and
exterior Schwarzschild region. A relation between the redshift and amount of
nested pairs is studied numerically in order to answer a question whether a
strong relativistic effect can be obtained when every component of the
structure can be described by the weak field approximation of general
relativity.


  Previous studies have shown how the three generations of the Standard Model
fermions can arise from a single generation in more than four dimensions, and
how off-diagonal neutral couplings arise for gauge-boson Kaluza-Klein
recurrences. These couplings conserve family number in the leading
approximation. While an existing example, built on a spherical geometry,
suggests a high compactification scale, we conjecture that the overall
structure is generic, and work out possible signatures at colliders, compatible
with rare decays data.


  Let $({\bf X},\omega_{\bf X}^*)$ be a separated, $-2$-shifted symplectic
derived $\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie
arXiv:1111.3209, of complex virtual dimension ${\rm vdim}_{\mathbb C}{\bf
X}=n\in\mathbb Z$, and $X_{\rm an}$ the underlying complex analytic topological
space. We prove that $X_{\rm an}$ can be given the structure of a derived
smooth manifold ${\bf X}_{\rm dm}$, of real virtual dimension ${\rm
vdim}_{\mathbb R}{\bf X}_{\rm dm}=n$. This ${\bf X}_{\rm dm}$ is not canonical,
but is independent of choices up to bordisms fixing the underlying topological
space $X_{\rm an}$. There is a 1-1 correspondence between orientations on
$({\bf X},\omega_{\bf X}^*)$ and orientations on ${\bf X}_{\rm dm}$.
  Because compact, oriented derived manifolds have virtual classes, this means
that proper, oriented $-2$-shifted symplectic derived $\mathbb C$-schemes have
virtual classes, in either homology or bordism. This is surprising, as
conventional algebro-geometric virtual cycle methods fail in this case. Our
virtual classes have half the expected dimension, and from purely complex
algebraic input, can yield a virtual class of odd real dimension.
  Now derived moduli schemes of coherent sheaves on a Calabi-Yau 4-fold are
expected to be $-2$-shifted symplectic (this holds for stacks). We propose to
use our virtual classes to define new Donaldson-Thomas style invariants
'counting' (semi)stable coherent sheaves on Calabi-Yau 4-folds $Y$ over
$\mathbb C$, which should be unchanged under deformations of $Y$.


  A scheme to optimally design a beam combiner is discussed for any
pre-determined fixed geometry nulling interferometer aimed at detection and
characterization of exoplanets with multiple telescopes or a single telescope
(aperture masking). We show that considerably higher order nulls can be
achieved with 1-D interferometer geometries than possible with 2-D geometries
with the same number of apertures. Any 1-D interferometer with N apertures can
achieve a 2(N-1)-order null, while the order of the deepest null for a random
2-D aperture geometry interferometer is the order of the N-th term in the
Taylor expansion of e^{i(x^2+y^2)} around x=0, y=0 (2nd order null for N=2,3;
4th order null for N=4,5,6). We also show that an optimal beam combiner for
nulling interferometry relies only 0 or Pi phase shifts. Examples of nulling
interferometer designs are shown to illustrate these findings.


  Dispersive deformations of the Monge equation u_u=uu_x are studied using
ideas originating from topological quantum field theory and the deformation
quantization programme. It is shown that, to a high-order, the symmetries of
the Monge equation may also be appropriately deformed, and that, if they exist
at all orders, they are uniquely determined by the original deformation. This
leads to either a new class of integrable systems or to a rigorous notion of an
approximate integrable system. Quasi-Miura transformations are also constructed
for such deformed equations.


  The Douglas-Rachford splitting algorithm is a classical optimization method
that has found many applications. When specialized to two normal cone
operators, it yields an algorithm for finding a point in the intersection of
two convex sets. This method for solving feasibility problems has attracted a
lot of attention due to its good performance even in nonconvex settings.
  In this paper, we consider the Douglas-Rachford algorithm for finding a point
in the intersection of two subspaces. We prove that the method converges
strongly to the projection of the starting point onto the intersection.
Moreover, if the sum of the two subspaces is closed, then the convergence is
linear with the rate being the cosine of the Friedrichs angle between the
subspaces. Our results improve upon existing results in three ways: First, we
identify the location of the limit and thus reveal the method as a best
approximation algorithm; second, we quantify the rate of convergence, and
third, we carry out our analysis in general (possibly infinite-dimensional)
Hilbert space. We also provide various examples as well as a comparison with
the classical method of alternating projections.


  Online metric learning has been widely exploited for large-scale data
classification due to the low computational cost. However, amongst online
practical scenarios where the features are evolving (e.g., some features are
vanished and some new features are augmented), most metric learning models
cannot be successfully applied to these scenarios, although they can tackle the
evolving instances efficiently. To address the challenge, we develop a new
online Evolving Metric Learning (EML) model for incremental and decremental
features, which can handle the instance and feature evolutions simultaneously
by incorporating with a smoothed Wasserstein metric distance. Specifically, our
model contains two essential stages: a Transforming stage (T-stage) and a
Inheriting stage (I-stage). For the T-stage, we propose to extract important
information from vanished features while neglecting non-informative knowledge,
and forward it into survived features by transforming them into a low-rank
discriminative metric space. It further explores the intrinsic low-rank
structure of heterogeneous samples to reduce the computation and memory burden
especially for highly-dimensional large-scale data. For the I-stage, we inherit
the metric performance of survived features from the T-stage and then expand to
include the new augmented features. Moreover, a smoothed Wasserstein distance
is utilized to characterize the similarity relationships among the
heterogeneous and complex samples, since the evolving features are not strictly
aligned in the different stages. In addition to tackling the challenges in
one-shot case, we also extend our model into multishot scenario. After deriving
an efficient optimization strategy for both T-stage and I-stage, extensive
experiments on several datasets verify the superior performance of our EML
model.


  In this work, we present a novel, machine-learning approach for constructing
Multiclass Interpretable Scoring Systems (MISS) - a fully data-driven
methodology for generating single, sparse, and user-friendly scoring systems
for multiclass classification problems. Scoring systems are commonly utilized
as decision support models in healthcare, criminal justice, and other domains
where interpretability of predictions and ease of use are crucial. Prior
methods for data-driven scoring, such as SLIM (Supersparse Linear Integer
Model), were limited to binary classification tasks and extensions to
multiclass domains were primarily accomplished via one-versus-all-type
techniques. The scores produced by our method can be easily transformed into
class probabilities via the softmax function. We demonstrate techniques for
dimensionality reduction and heuristics that enhance the training efficiency
and decrease the optimality gap, a measure that can certify the optimality of
the model. Our approach has been extensively evaluated on datasets from various
domains, and the results indicate that it is competitive with other machine
learning models in terms of classification performance metrics and provides
well-calibrated class probabilities.


  A precise interpretation of the Universe wave function is forbidden in the
spirit of the Copenhagen School since a precise notion of measure operation
cannot be satisfactorily defined. Here we propose a Bohmian interpretation of
the isotropic Universe quantum dynamics, in which the Hamilton-Jacobi equation
is restated by including quantum corrections, which lead to a classical
trajectory containing effects of order $\hbar^2$. This solution is then used to
determine the spectrum of gauge-invariant quantum fluctuations living on the
obtained background model. The analysis is performed adopting the wave function
approach to describe the fluctuation dynamics, which gives a time-dependent
harmonic oscillator for each Fourier mode and whose frequency is affected by
the $\hbar^2$ corrections. The properties of the emerging spectrum are
discussed, outlining the modification induced with respect to the
scale-invariant result and the hierarchy of the spectral index running is
discussed.


  Gravitational waves (GWs) from the inspiral of a neutron star (NS) or
stellar-mass black hole (BH) into an intermediate-mass black hole (IMBH) with
mass between ~50 and ~350 solar masses may be detectable by the planned
advanced generation of ground-based GW interferometers. Such intermediate mass
ratio inspirals (IMRIs) are most likely to be found in globular clusters. We
analyze four possible IMRI formation mechanisms: (1) hardening of an NS-IMBH or
BH-IMBH binary via three-body interactions, (2) hardening via Kozai resonance
in a hierarchical triple system, (3) direct capture, and (4) inspiral of a
compact object from a tidally captured main-sequence star; we also discuss
tidal effects when the inspiraling object is an NS. For each mechanism we
predict the typical eccentricities of the resulting IMRIs. We find that IMRIs
will have largely circularized by the time they enter the sensitivity band of
ground-based detectors. Hardening of a binary via three-body interactions,
which is likely to be the dominant mechanism for IMRI formation, yields
eccentricities under 10^-4 when the GW frequency reaches 10 Hz. Even among
IMRIs formed via direct captures, which can have the highest eccentricities,
around 90% will circularize to eccentricities under 0.1 before the GW frequency
reaches 10 Hz. We estimate the rate of IMRI coalescences in globular clusters
and the sensitivity of a network of three Advanced LIGO detectors to the
resulting GWs. We show that this detector network may see up to tens of IMRIs
per year, although rates of one to a few per year may be more plausible. We
also estimate the loss in signal-to-noise ratio that will result from using
circular IMRI templates for data analysis and find that, for the eccentricities
we expect, this loss is negligible.


  We explore dynamics of a density pulse induced by a local quench in a
one-dimensional electron system. The spectral curvature leads to an "overturn"
(population inversion) of the wave. We show that beyond this time the density
profile develops strong oscillations with a period much larger than the Fermi
wave length. The effect is studied first for the case of free fermions by means
of direct quantum simulations and via semiclassical analysis of the evolution
of Wigner function. We demonstrate then that the period of oscillations is
correctly reproduced by a hydrodynamic theory with an appropriate dispersive
term. Finally, we explore the effect of different types of electron-electron
interaction on the phenomenon. We show that sufficiently strong interaction
[$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial
scale] determines the dominant dispersive term in the hydrodynamic equations.
Hydrodynamic theory reveals crucial dependence of the density evolution on the
relative sign of the interaction and the density perturbation.


  We present the first study of the cusp effect (the movement of resonant poles
due to the proximity of multiparticle thresholds) caused by the creation of
diquark-antidiquark pairs. The cusp profile for such states is obtained from
constituent counting rules. We compare the effectiveness of diquark cusps in
moving resonant poles with that from a phenomenological form commonly used for
meson-pair creation, and find that mesons tend to be more effective at lower
energies $({\it e.g.}$, the $K\overline{K}$ threshold), while diquarks tend to
be more effective at the charm [$X(3872)$] scales and above.


  We show that linear complexity is the threshold for the emergence of Kakutani
inequivalence for measurable systems supported on a minimal subshift. In
particular, we show that there are minimal subshifts of arbitrarily low
super-linear complexity that admit both loosely Bernoulli and non-loosely
Bernoulli ergodic measures and that no minimal subshift with linear complexity
can admit inequivalent measures.


  We present long term H$\alpha$ monitoring results of five Be/X-ray binaries
to study the Be disc size variations and their influence on Type II (giant)
X-ray outbursts. The work is done in the context of the viscous decretion disc
model which predicts that Be discs in binary systems are truncated by resonant
torques induced by the neutron star in its orbit. Our observations show that
type II outbursts are not correlated(nor anti-correlated) with the disc size,
as they are seen to occur both at relatively small and large Be disc radii. We
discuss these observations in context of alternate interpretation of Be disc
behaviour, such as precession, elongation and density effects, and with
cognisance of the limitations of our disc size estimates.


  Within a dynamical transport approach we investigate charged current
interactions in neutrino-nucleus reactions for neutrino energies of 0.3 - 1.5
GeV with particular emphasis on resonant pion production channels via the
$\Delta_{33}(1232)$ resonance. The final-state-interactions of the resonance as
well as of the emitted pions are calculated explicitly for $^{12}C$ and
$^{56}Fe$ nuclei and show a dominance of pion suppression at moderate momenta
$p_\pi >$ 0.2 GeV/c. A comparison to integrated $\pi^+$ spectra for $\nu_\mu +
^{12}C$ reactions with the available (preliminary) data demonstrates a
reasonable agreement.


  We propose a multi-agent logic of knowledge, public and arbitrary
announcements, that is interpreted on topological spaces in the style of subset
space semantics. The arbitrary announcement modality functions similarly to the
effort modality in subset space logics, however, it comes with intuitive and
semantic differences. We provide axiomatizations for three logics based on this
setting, and demonstrate their completeness.


  We demonstrate a heuristic optimization algorithm based on the game tree
search for multi-component materials design. The algorithm searches for the
largest spin polarization of seven-component Heusler alloys. The algorithm can
find the peaks quickly and is more robust against local optima than Bayesian
optimization approaches using the expected improvement or upper confidence
bound approaches. We also investigate Heusler alloys including anti-site
disorder and show that
[Fe$_{0.9}$Co$_{0.1}$]$_{2}$Cr$_{0.95}$Mn$_{0.05}$Si$_{0.3}$Ge$_{0.7}$ has the
potential to be a high spin polarized material with robustness against
anti-site disorder.


  One approach to the development of quantum search algorithms is the quantum
walk. A spatial search can be effected by the continuous-time evolution of a
single quantum particle on a graph containing a marked site. In many physical
implementations, however, one might expect to have multiple particles. In
interacting bosonic systems at zero temperature, the dynamics is well-described
by a discrete nonlinear Schrodinger equation. We investigate the role of
nonlinearity in determining the efficiency of the spatial search algorithm
within the quantum walk model, for the complete graph. The analytical
calculations reveal that the nonlinear search time scales with size of the
search space N like the square root of N, equivalent to the linear case though
with a different overall constant. The results indicate that interacting
Bose-Einstein condensates at zero temperature could be natural systems for the
implementation of the quantum search algorithm.


  The dynamics of an association of interactive biological species is studied
theoretically. We explore a mean field approximation to describe the temporal
evolution of an ecological system with the basic prey-predator interspecies
relation, as well as an approximation to introduce time correlations in the
dynamics. We start by discussing the solution of the Volterra-Lotka model in a
mean field approximation based in an analogy with the Weiss solution to the
Ising model for ferromagnetic materials. In order to explore the effects of
long-range time correlations, we describe the time evolution of the system
within a kind of Bragg-Williams approximation. This approach allows us to
evaluate a characteristic life-time of the ecosystem. This quantity could be
very useful to discuss the time evolution of the system under a wide diversity
of environmental conditions of the ecosystem which is not usually considered.
We discuss the general trends of the temporal evolution of the association with
some data from real ecosystems.


  We establish the equivalence of conjectures concerning the pair correlation
of zeros of $L$-functions in the Selberg class and the variances of sums of a
related class of arithmetic functions over primes in short intervals. This
extends the results of Goldston & Montgomery [7] and Montgomery & Soundararajan
[11] for the Riemann zeta-function to other $L$-functions in the Selberg class.
Our approach is based on the statistics of the zeros because the analogue of
the Hardy-Littlewood conjecture for the auto-correlation of the arithmetic
functions we consider is not available in general. One of our main findings is
that the variances of sums of these arithmetic functions over primes in short
intervals have a different form when the degree of the associated $L$-functions
is 2 or higher to that which holds when the degree is 1 (e.g. the Riemann
zeta-function). Specifically, when the degree is 2 or higher there are two
regimes in which the variances take qualitatively different forms, whilst in
the degree-1 case there is a single regime.


  Let $K$ be a field of characteristic not two and $K(x,y,z)$ the rational
function field over $K$ with three variables $x,y,z$. Let $G$ be a finite group
of acting on $K(x,y,z)$ by monomial $K$-automorphisms. We consider the
rationality problem of the fixed field $K(x,y,z)^G$ under the action of $G$,
namely whether $K(x,y,z)^G$ is rational (that is, purely transcendental) over
$K$ or not. We may assume that $G$ is a subgroup of $\mathrm{GL}(3,\mathbb{Z})
and the problem is determined up to conjugacy in $\mathrm{GL}(3,\mathbb{Z})$.
There are 73 conjugacy classes of $G$ in $\mathrm{GL}(3,\mathbb{Z})$. By
results of Endo-Miyata, Voskresenski\u\i, Lenstra, Saltman, Hajja, Kang and
Yamasaki, 8 conjugacy classes of 2-groups in $\mathrm{GL}(3,\mathbb{Z})$ have
negative answers to the problem under certain monomial actions over some base
field $K$, and the necessary and sufficient condition for the rationality of
$K(x,y,z)^G$ over $K$ is given. In this paper, we show that the fixed field
$K(x,y,z)^G$ under monomial action of $G$ is rational over $K$ except for
possibly negative 8 cases of 2-groups and unknown one case of the alternating
group of degree four. Moreover we give explicit transcendental bases of the
fixed fields over $K$. For unknown case, we obtain an affirmative solution to
the problem under some conditions. In particular, we show that if $K$ is
quadratically closed field then $K(x,y,z)^G$ is rational over $K$. We also give
an application of the result to 4-dimensional linear Noether's problem.


  Today, deep learning is an essential technology for our life. To solve more
complex problems with deep learning, both sizes of training datasets and neural
networks are increasing. To train a model with large datasets and networks,
distributed deep neural network (DDNN) training technique is necessary. For
large-scale DDNN training, HPC clusters are a promising computation
environment. In large-scale DDNN on HPC clusters, I/O performance is critical
because it is becoming a bottleneck. Most flagship-class HPC clusters have
hierarchical storage systems. For designing future HPC storage systems, it is
necessary to quantify the performance improvement effect of the hierarchical
storage system on the workloads. This paper demonstrates the quantitative
performance analysis of the hierarchical storage system for DDNN workload in a
flagship-class supercomputer. Our analysis shows how much performance
improvement and volume increment of the storage will be required to meet the
performance goal.


  Background: The quantitative analysis of microscope videos often requires
instance segmentation and tracking of cellular and subcellular objects. The
traditional method consists of two stages: (1) performing instance object
segmentation of each frame, and (2) associating objects frame-by-frame.
Recently, pixel-embedding-based deep learning approaches these two steps
simultaneously as a single stage holistic solution. In computer vision,
annotated training data with consistent segmentation and tracking is resource
intensive, the severity of which is multiplied in microscopy imaging due to (1)
dense objects (e.g., overlapping or touching), and (2) high dynamics (e.g.,
irregular motion and mitosis). Adversarial simulations have provided successful
solutions to alleviate the lack of such annotations in dynamics scenes in
computer vision, such as using simulated environments (e.g., computer games) to
train real-world self-driving systems. Methods: In this paper, we propose an
annotation-free synthetic instance segmentation and tracking (ASIST) method
with adversarial simulation and single-stage pixel-embedding based learning.
Contribution: The contribution of this paper is three-fold: (1) the proposed
method aggregates adversarial simulations and single-stage pixel-embedding
based deep learning; (2) the method is assessed with both the cellular (i.e.,
HeLa cells) and subcellular (i.e., microvilli) objects; and (3) to the best of
our knowledge, this is the first study to explore annotation-free instance
segmentation and tracking study for microscope videos. Results: The ASIST
method achieved an important step forward, when compared with fully supervised
approaches: ASIST shows 7% to 11% higher segmentation, detection and tracking
performance on microvilli relative to fully supervised methods, and comparable
performance on Hela cell videos.


  In this paper, a Step-wise Refinement model is proposed to elicit
requirements in a more effective manner.


  In this paper, we mainly consider about the existence and uniqueness of
global weak solutions for the two-component Novikov system. We first recall
some results and definitions of strong solutions and weak solutions for the
system, then by using the method of approximation of smooth solutions, we prove
the existence and uniqueness of global weak solutions of the system.


  In this paper we study how all the physical "constants" vary in the framework
described by a model in which we have taken into account the generalize
conservation principle for its stress-energy tensor. This possibility enable us
to take into account the adiabatic matter creation in order to get rid of the
entropy problem. We try to generalize this situation by contemplating
multi-fluid components. To validate all the obtained results we explore the
possibility of considering the variation of the"constants" in the quantum
cosmological scenario described by the Wheeler-DeWitt equation. For this
purpose we explore the Wheeler-DeWitt equation in different contexts but from a
dimensional point of view. We end by presenting the Wheeler-DeWitt equation in
the case of considering all the constants varying. The quantum potential is
obtained and the tunneling probability is studied.


  The outcomes of this paper are twofold. Implicit complexity.
  We provide an implicit characterization of polynomial time computation in
terms of ordinary differential equations: we characterize the class PTIME of
languages computable in polynomial time in terms of differential equations with
polynomial right-hand side. This result gives a purely continuous elegant and
simple characterization of PTIME. We believe it is the first time complexity
classes are characterized using only ordinary differential equations. Our
characterization extends to functions computable in polynomial time over the
reals in the sense of computable analysis. Our results may provide a new
perspective on classical complexity, by giving a way to define complexity
classes, like PTIME, in a very simple way, without any reference to a notion of
(discrete) machine. This may also provide ways to state classical questions
about computational complexity via ordinary differential equations.
  Continuous-Time Models of Computation.
  Our results can also be interpreted in terms of analog computers or analog
models of computation: As a side effect, we get that the 1941 General Purpose
Analog Computer (GPAC) of Claude Shannon is provably equivalent to Turing
machines both in terms of computability and complexity, a fact that has never
been established before. This result provides arguments in favour of a
generalised form of the Church-Turing Hypothesis, which states that any
physically realistic (macroscopic) computer is equivalent to Turing machines
both in terms of computability and complexity.


  We investigate nonequilibrium behavior in (1+1)-dimensional stochastic field
theories in the context of Ginzburg-Landau models at varying cooling rates. We
argue that a reliable measure of the departure from thermal equilibrium can be
obtained from the absolute value of the rate of change of the
momentum-integrated structure function, $\Delta S_{\rm{tot}}$. We show that the
peak of $\Delta S_{\rm{tot}}$ scales with the cooling, or quench, time-scale,
$\tau_q$, in agreement with the prediction by Laguna and Zurek for the scaling
of freeze-out time in both over and under-damped regimes. Furthermore, we show
that the amplitude of the peak scales as $\tau_q^{-6/5}$ independent of the
viscosity.


  We determine some classes of varieties X - that include the varieties with
numerically effective tangent bundle - satisfying the following property: if E
is a Higgs bundle such that f*E is semistable for any morphism f from a smooth
projective curve to X, then E is slope semistable and the discriminant of E is
zero in H4(X,R). We also characterize some classes of varieties such that the
underlying vector bundle of a slope semistable Higgs bundle is always slope
semistable.


  Light transport in superdiffusive media of finite size is studied
theoretically. The intensity Green's function for a slab geometry is found by
discretizing the fractional diffusion equation and employing the eigenfunction
expansion method. Truncated step length distributions and complex boundary
conditions are considered. The profile of a coherent backscattering cone is
calculated in the superdiffusion approximation.


  A heterogenous network with base stations (BSs), small base stations (SBSs)
and users distributed according to independent Poisson point processes is
considered. SBS nodes are assumed to possess high storage capacity and to form
a distributed caching network. Popular files are stored in local caches of
SBSs, so that a user can download the desired files from one of the SBSs in its
vicinity. The offloading-loss is captured via a cost function that depends on
the random caching strategy proposed here. The popularity profile of cached
content is unknown and estimated using instantaneous demands from users within
a specified time interval. An estimate of the cost function is obtained from
which an optimal random caching strategy is devised. The training time to
achieve an $\epsilon>0$ difference between the achieved and optimal costs is
finite provided the user density is greater than a predefined threshold, and
scales as $N^2$, where $N$ is the support of the popularity profile. A transfer
learning-based approach to improve this estimate is proposed. The training time
is reduced when the popularity profile is modeled using a parametric family of
distributions; the delay is independent of $N$ and scales linearly with the
dimension of the distribution parameter.


  Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov
functions for SYM theories in different dimensions, are all incorporated into
network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This
lifting is especially simple for what we call balanced networks. Then, the Ward
identities (known under the names of Virasoro/W-constraints or loop equations
or regularity condition for qq-characters) are also promoted to the DIM level,
where they all become corollaries of a single identity.


  Task-oriented dialogue (TOD) systems have assisted users on many tasks,
including ticket booking and service inquiries. While existing TOD systems have
shown promising performance in serving customer needs, these systems mostly
assume that users would interact with the dialogue agent politely. This
assumption is unrealistic as impatient or frustrated customers may also
interact with TOD systems impolitely. This paper aims to address this research
gap by investigating impolite users' effects on TOD systems. Specifically, we
constructed an impolite dialogue corpus and conducted extensive experiments to
evaluate the state-of-the-art TOD systems on our impolite dialogue corpus. Our
experimental results show that existing TOD systems are unable to handle
impolite user utterances. We also present a data augmentation method to improve
TOD performance in impolite dialogues. Nevertheless, handling impolite
dialogues remains a very challenging research task. We hope by releasing the
impolite dialogue corpus and establishing the benchmark evaluations, more
researchers are encouraged to investigate this new challenging research task.


  Chromospheric differential rotation is a key component in comprehending the
atmospheric coupling between the chromosphere and the photosphere at different
phases of the solar cycle. In this study, we therefore utilize the newly
calibrated multidecadal Ca II K spectroheliograms (1907-2007) from the
Kodaikanal Solar Observatory (KoSO) to investigate the differential rotation of
the solar chromosphere using the technique of image cross-correlation. Our
analysis yields the chromospheric differential rotation rate $\Omega (\theta) =
(14.61\pm 0.04 - 2.18\pm 0.37\sin^2{\theta} - 1.10 \pm
0.61\sin^4{\theta})^\circ{\rm /day}$. These results suggest the chromospheric
plages exhibit an equatorial rotation rate 1.59% faster than the photosphere
when compared with the differential rotation rate measured using sunspots and
also a smaller latitudinal gradient compared to the same. To compare our
results to those from other observatories, we have applied our method on a
small sample of Ca II K data from Rome, Meudon, and Mt. Wilson observatories,
which support our findings from KoSO data. Additionally, we have not found any
significant north-south asymmetry or any systematic variation in chromospheric
differential rotation over the last century.


  For any distinct two primes $p_1\equiv p_2\equiv 3$ $(\text{mod }4)$, let
$h(-p_1)$, $h(-p_2)$ and $h(p_1p_2)$ be the class numbers of the quadratic
fields $\mathbb{Q}(\sqrt{-p_1})$, $\mathbb{Q}(\sqrt{-p_2})$ and
$\mathbb{Q}(\sqrt{p_1p_2})$, respectively. Let
$\omega_{p_1p_2}:=(1+\sqrt{p_1p_2})/2$ and let $\Psi(\omega_{p_1p_2})$ be the
Hirzebruch sum of $\omega_{p_1p_2}$. We show that $h(-p_1)h(-p_2)\equiv
h(p_1p_2)\Psi(\omega_{p_1p_2})/n$ $(\text{mod }8)$, where $n=6$ (respectively,
$n=2$) if $\min\{p_1,p_2\}>3$ (respectively, otherwise). We also consider the
real quadratic order with conductor $2$ in $\mathbb{Q}(\sqrt{p_1p_2})$.


  We have obtained echelle spectra with the Hubble Space Telescope (HST) of the
MgII 2800A region of ten stars whose metallicities range from 1/300 to 1/3 that
of the Sun, and whose space velocities suggest a halo or old thick-disk origin.
Spectra of all ten show double-peaked emission in the MgII core, very much like
the quiet Sun. A half-dozen non-rotating stars were observed more than once,
and show at most a low level of variability in the emission flux, comparable to
that of quiet stars of solar metallicity. For four stars, we have obtained
Lyman-alpha spectra at 0.2A resolution; all four show emission. The data thus
strongly suggest that chromospheric activity at a minimum level is present in
all stars of near-solar temperature, regardless of age or metallicity. While
this points to non-magnetic sources such as acoustic waves, a contribution from
globally-organized magnetic fields is possible at a low level. We plan a longer
series of MgII and Lyman alpha observations to constrain this.


  Binding energies of light, $A\leq 6$, $\Lambda\Lambda$ hypernuclei are
calculated using the stochastic variational method in a pionless effective
field theory (EFT) approach at leading order with the purpose of assessing
critically the onset of binding in the strangeness S=-2 hadronic sector. The
EFT input in this sector consists of (i) a $\Lambda\Lambda$ contact term
constrained by the $\Lambda\Lambda$ scattering length $a_{\Lambda\Lambda}$,
using a range of values compatible with $\Lambda\Lambda$ correlations observed
in relativistic heavy ion collisions, and (ii) a $\Lambda\Lambda N$ contact
term constrained by the only available $A\leq 6$ $\Lambda\Lambda$ hypernucler
binding energy datum of $^{6}_{\Lambda\Lambda}$He. The recently debated neutral
three-body and four-body systems $^{3}_{\Lambda\Lambda}$n and
$^{4}_{\Lambda\Lambda}$n are found unbound by a wide margin. A relatively large
value of $|a_{\Lambda\Lambda}| \gtrsim 1.5$ fm is needed to bind
$^{4}_{\Lambda\Lambda}$H, thereby questioning its particle stability. In
contrast, the particle stability of the $A=5$ $\Lambda\Lambda$ hypernuclear
isodoublet $^{5}_{\Lambda\Lambda} $H--$^{5}_{\Lambda\Lambda}$He is robust, with
$\Lambda$ separation energy of order 1 MeV.


  In central collisions at relativistic heavy ion colliders like the
Relativistic Heavy Ion Collider RHIC/Brookhaven and the Large Hadron Collider
LHC (in its heavy ion mode) at CERN/Geneva, one aims at detecting a new form of
hadronic matter - the Quark Gluon Plasma. We discuss here a complementary
aspect of these collisions, the very peripheral ones. Due to coherence, there
are strong electromagnetic fields of short duration in such collisions. They
give rise to photon-photon and photon-nucleus collisions with high flux up to
an invariant mass region hitherto unexplored experimentally. After a general
survey photon-photon luminosities in relativistic heavy ion collisions are
discussed. Special care is taken to include the effects of strong interactions
and nuclear size. Then photon-photon physics at various gamma-gamma-invariant
mass scales is discussed. The region of several GeV, relevant for RHIC is
dominated by QCD phenomena (meson and vector meson pair production). Invariant
masses of up to about 100 GeV can be reached at LHC, and the potential for new
physics is discussed. Photonuclear reactions and other important background
effects, especially diffractive processes are also discussed. Lepton-pair
production, especially electron-positron pair production is copious. Due to the
strong fields there will be new phenomena, especially multiple e+e- pair
production.


  When a quantum particle moves in a curved space, a geometric potential can
arise. In spite of a long history of extensive theoretical studies, to
experimentally observe the geometric potential remains to be a challenge. What
are the physically observable consequences of such a geometric potential?
Solving the Schrodinger equation on a truncated conic surface, we uncover a
class of quantum scattering states that bear a strong resemblance with the
quasi-resonant states associated with atomic collapse about a Coulomb impurity,
a remarkable quantum phenomenon in which an infinite number of quasi-resonant
states emerge. A characteristic defining feature of such collapse states is the
infinite oscillations of the local density of states (LDOS) about the zero
energy point separating the scattering from the bound states. The emergence of
such states in the curved (Riemannian) space requires neither a relativistic
quantum mechanism nor any Coulomb impurity: they have zero angular momentum and
their origin is purely geometrical - henceforth the term geometry-induced
wavefunction collapse. We establish the collapsing nature of these states
through a detailed comparative analysis of the behavior of the LDOS for both
the zero and finite angular-momentum states as well as the corresponding
classical picture. Potential experimental schemes to realize the
geometry-induced collapse states are articulated. Not only has our study
uncovered an intrinsic connection between the geometric potential and atomic
collapse, it also provides a method to experimentally observe and characterize
geometric potentials arising from different subfields of physics. For example,
in nanoscience and nanotechnology, curved geometry has become increasingly
common. Our finding suggests that wavefunction collapse should be an important
factor of consideration in designing and developing nanodevices.


  Teachers' mathematical content knowledge (CK) is of vital importance and need
in teacher professional development (PD) programs. Computer-aided asynchronous
PD systems are the most recent proposed PD techniques, which aim to help
teachers improve their PD equally with fewer concerns about costs and
limitations of time or location. However, current automatic CK identification
methods, which serve as one of the core techniques of asynchronous PD systems,
face challenges such as diversity of user responses, scarcity of high-quality
annotated data, and low interpretability of the predictions. To tackle these
challenges, we propose a Multi-Agent LLMs-based framework, LLMAgent-CK, to
assess the user responses' coverage of identified CK learning goals without
human annotations. By taking advantage of multi-agent LLMs in strong
generalization ability and human-like discussions, our proposed LLMAgent-CK
presents promising CK identifying performance on a real-world mathematical CK
dataset MaCKT. Moreover, our case studies further demonstrate the working of
the multi-agent framework.


  We theoretically investigate the plasmonic properties of mid-infrared
graphene-based metamaterials and apply deep learning of a neural network for
the inverse design. These artificial structures have square periodic arrays of
graphene plasmonic resonators deposited on dielectric thin films. Optical
spectra vary significantly with changes in structural parameters. Our numerical
results are in accordance with previous experiments. Then, the theoretical
approach is employed to generate data for training and testing deep neural
networks. By merging the pre-trained neural network with the inverse network,
we implement calculations for inverse design of the graphene-based
metameterials. We also discuss the limitation of the data-driven approach.


  Effective machine learning models learn both robust features that directly
determine the outcome of interest (e.g., an object with wheels is more likely
to be a car), and shortcut features (e.g., an object on a road is more likely
to be a car). The latter can be a source of error under distributional shift,
when the correlations change at test-time. The prevailing sentiment in the
robustness literature is to avoid such correlative shortcut features and learn
robust predictors. However, while robust predictors perform better on
worst-case distributional shifts, they often sacrifice accuracy on majority
subpopulations. In this paper, we argue that shortcut features should not be
entirely discarded. Instead, if we can identify the subpopulation to which an
input belongs, we can adaptively choose among models with different strengths
to achieve high performance on both majority and minority subpopulations. We
propose COnfidence-baSed MOdel Selection (CosMoS), where we observe that model
confidence can effectively guide model selection. Notably, CosMoS does not
require any target labels or group annotations, either of which may be
difficult to obtain or unavailable. We evaluate CosMoS on four datasets with
spurious correlations, each with multiple test sets with varying levels of data
distribution shift. We find that CosMoS achieves 2-5% lower average regret
across all subpopulations, compared to using only robust predictors or other
model aggregation methods.


  Past studies of the Brauer group of a scheme tells us the importance of the
interrelationship among Brauer groups of its finite \'etale coverings. In this
paper, we consider these groups simultaneously, and construct an integrated
object "Brauer-Mackey functor".
  We realize this as a {\it cohomological Mackey functor} on the Galois
category of finite \'etale coverings. For any finite \'etale covering of
schemes, we can associate two homomorphisms for Brauer groups, namely the
pull-back and the norm map. These homomorphisms make Brauer groups into a
bivariant functor ($=$ Mackey functor) on the Galois category.
  As a corollary, Restricting to a finite Galois covering of schemes, we obtain
a cohomological Mackey functor on its Galois group. This is a generalization of
the result for rings by Ford. Moreover, applying Bley and Boltje's theorem, we
can derive certain isomorphisms for the Brauer groups of intermediate
coverings.


  Hierarchical assembly models predict a population of supermassive black hole
(SMBH) binaries. These are not resolvable by direct imaging but may be
detectable via periodic variability (or nanohertz frequency gravitational
waves). Following our detection of a 5.2 year periodic signal in the quasar PG
1302-102 (Graham et al. 2015), we present a novel analysis of the optical
variability of 243,500 known spectroscopically confirmed quasars using data
from the Catalina Real-time Transient Survey (CRTS) to look for close (< 0.1
pc) SMBH systems. Looking for a strong Keplerian periodic signal with at least
1.5 cycles over a baseline of nine years, we find a sample of 111 candidate
objects. This is in conservative agreement with theoretical predictions from
models of binary SMBH populations. Simulated data sets, assuming stochastic
variability, also produce no equivalent candidates implying a low likelihood of
spurious detections. The periodicity seen is likely attributable to either jet
precession, warped accretion disks or periodic accretion associated with a
close SMBH binary system. We also consider how other SMBH binary candidates in
the literature appear in CRTS data and show that none of these are equivalent
to the identified objects. Finally, the distribution of objects found is
consistent with that expected from a gravitational wave-driven population. This
implies that circumbinary gas is present at small orbital radii and is being
perturbed by the black holes. None of the sources is expected to merge within
at least the next century. This study opens a new unique window to study a
population of close SMBH binaries that must exist according to our current
understanding of galaxy and SMBH evolution.


  Recently, we have struck the balance between the information freshness, in
terms of age of information (AoI), experienced by users and energy consumed by
sensors, by appropriately activating sensors to update their current status in
caching enabled Internet of Things (IoT) networks [1]. To solve this problem,
we cast the corresponding status update procedure as a continuing Markov
Decision Process (MDP) (i.e., without termination states), where the number of
state-action pairs increases exponentially with respect to the number of
considered sensors and users. Moreover, to circumvent the curse of
dimensionality, we have established a methodology for designing deep
reinforcement learning (DRL) algorithms to maximize (resp. minimize) the
average reward (resp. cost), by integrating R-learning, a tabular reinforcement
learning (RL) algorithm tailored for maximizing the long-term average reward,
and traditional DRL algorithms, initially developed to optimize the discounted
long-term cumulative reward rather than the average one. In this technical
report, we would present detailed discussions on the technical contributions of
this methodology.


  The aim of our paper is to generalize the tangent prolongation of Lie groups
to non-associative multiplications and to examine how the weak associative and
weak inverse properties are transferred to the multiplication defined on the
tangent bundle. We obtain that the tangent prolongation of a
$\mathcal{C}^r$-differentiable loop ($r\geq 1$) is a
$\mathcal{C}^{r-1}$-differentiable loop that acquires the classical weak
inverse and weak associative properties of the initial loop.


  We construct a classical dynamical system whose phase space is a certain
infinite-dimensional Grassmannian manifold, and propose that it is equivalent
to the large N limit of two-dimensional QCD with an O(2N+1) gauge group. In
this theory, we find that baryon number is a topological quantity that is
conserved only modulo 2. We also relate this theory to the master field
approach to matrix models.