  The variational quantum eigensolver (VQE) algorithm recently became a popular
method to compute quantum chemical properties of molecules on noisy
intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation
from the NISQ device in the circuit, it is important to keep the so-called
quantum depth of the circuit at a minimum, defined as the minimum number of
quantum gates that need to be operated sequentially. In the present work, we
introduce a modular 2-qubit cluster circuit that allows for the design of a
shallow-depth quantum circuit compared to previously proposed architectures
without loss of chemical accuracy. Moreover, by virtue of the simplicity of the
cluster circuit, it is possible to assign a valence bond chemical
interpretation to the cluster circuit. The design was tested on the H2, (H2)2
and LiH molecules, as well as the finite-size transverse-field Ising model, as
the latter provides additional insights in the construction of the circuit in a
resonating valence bond picture.


  Let $p$ be a rational prime, $v_p$ the normalized $p$-adic valuation on
$\mathbb{Z}$, $q>1$ a $p$-power and $A=\mathbb{F}_q[t]$. Let $\wp\in A$ be an
irreducible polynomial and $\mathfrak{n}\in A$ a non-zero element which is
prime to $\wp$. Let $k\geq 2$ and $r\geq 1$ be integers. We denote by
$S_k(\Gamma_1(\mathfrak{n}\wp^r))$ the space of Drinfeld cuspforms of level
$\Gamma_1(\mathfrak{n}\wp^r)$ and weight $k$ for $A$. Let $n\geq 1$ be an
integer and $a\geq 0$ a rational number. Suppose that $\mathfrak{n}\wp$ has a
prime factor of degree one and the generalized eigenspace in
$S_k(\Gamma_1(\mathfrak{n}\wp^r))$ of slope $a$ is one-dimensional. In this
paper, under an assumption that $a$ is sufficiently small, we construct a
family $\{F_{k'}\mid v_p(k'-k)\geq \log_p(p^n+a)\}$ of Hecke eigenforms
$F_{k'}\in S_{k'}(\Gamma_1(\mathfrak{n}\wp^r))$ of slope $a$ such that, for any
$Q\in A$, the Hecke eigenvalues of $F_k$ and $F_{k'}$ at $Q$ are congruent
modulo $\wp^\kappa$ with some $\kappa>p^{v_p(k'-k)}-p^n-a$.


  This paper deals with both the higher order Tur\'an inequalities and the
Laguerre inequalities for quasi-polynomial-like functions -- that are
expressions of the form $f(n)=c_l(n)n^l+\cdots+c_d(n)n^d+o(n^d)$, where
$d,l\in\mathbb{N}$ and $d\leqslant l$. A natural example of such a function is
the $A$-partition function $p_{A}(n)$, which enumerates the number of
partitions of $n$ with parts in the fixed finite multiset
$A=\{a_1,a_2,\ldots,a_k\}$ of positive integers. For an arbitrary positive
integer $d$, we present efficient criteria for both the order $d$ Tur\'an
inequality and the $d$th Laguarre inequality for quasi-polynomial-like
functions. In particular, we apply these results to deduce non-trivial
analogues for $p_A(n)$.


  Many different approaches for solving Constraint Satisfaction Problems (CSPs)
and related Constraint Optimization Problems (COPs) exist. However, there is no
single solver (nor approach) that performs well on all classes of problems and
many portfolio approaches for selecting a suitable solver based on simple
syntactic features of the input CSP instance have been developed. In this paper
we first present a simple portfolio method for CSP based on k-nearest neighbors
method. Then, we propose a new way of using portfolio systems --- training them
shortly in the exploitation time, specifically for the set of instances to be
solved and using them on that set. Thorough evaluation has been performed and
has shown that the approach yields good results. We evaluated several machine
learning techniques for our portfolio. Due to its simplicity and efficiency,
the selected k-nearest neighbors method is especially suited for our short
training approach and it also yields the best results among the tested methods.
We also confirm that our approach yields good results on SAT domain.


  It has been widely accepted that the introduction of titanium carbides into
titanium-based alloys can significantly enhance the oxidation resistance due to
their superior physicochemical stability at elevated temperatures. The present
study reported for the first time that the ordered C vacancies within titanium
carbides could lead to an uncommon phenomenon particularly at the very initial
stage of oxidation. The intrinsic micro-to-macro oxidation mechanisms were
systematically clarified with the aids of transmission electron microscope and
ab-initio molecular dynamics simulation.


  We present a numerical method for obtaining high-accuracy numerical solutions
of spatially localized time-periodic excitations on a nonlinear Hamiltonian
lattice. We compare these results with analytical considerations of the spatial
decay. We show that nonlinear contributions have to be considered, and obtain
very good agreement between the latter and the numerical results. We discuss
further applications of the method and results.


  We propose a realization of a transformation-based acoustic temporal cloak
using an active closed-loop control approach to an equivalent electromagnetic
problem. Unlike the more common spatial cloaks the goal of which is hiding
fixed objects from detection, the goal of the temporal cloak is hiding the
occurrence of events during a finite period of time. In electromagnetic
systems, in which events represent, for example, leakage of signals from
transmission lines or optical fibers, temporal cloaking solutions usually rely
on nonlinear phenomena related to the fibers properties, or on modulating the
properties of the propagation medium itself. In particular, the
transformation-based solution requires modulating the constitutive parameters
of the medium both in space and time. Our control approach is fully linear,
where the required change in the medium parameters is programmed into the
controllers and created by external actuators in real-time. This cloaking
system keeps the physical medium unchanged, and enables to reprogram the
cloaking parameters upon request. We demonstrate our solution in a simulation
of a one-dimensional water channel.


  The corrections of order (Z alpha)^6m_1/m_2 and (Z alpha)^7 from one-loop
two-photon exchange diagrams to the energy spectra of the hydrogenic atoms are
calculated with the help of the Taylor expansion of corresponding integrands.
The method of averaging the quasipotential over the wave functions in the
d-dimensional coordinate space is formulated. The numerical values of the
obtained contributions to the fine structure of muonium, hydrogen and
positronium are presented.


  This paper introduces the new interactive Java sketching software KamiWaAi,
recently developed at the University of Fukui. Its graphical user interface
enables the user without any knowledge of both mathematics or computer science,
to do full three dimensional "drawings" on the screen. The resulting
constructions can be reshaped interactively by dragging its points over the
screen. The programming approach is new. KamiWaAi implements geometric objects
like points, lines, circles, spheres, etc. directly as software objects (Java
classes) of the same name. These software objects are geometric entities
mathematically defined and manipulated in a conformal geometric algebra,
combining the five dimensions of origin, three space and infinity. Simple
geometric products in this algebra represent geometric unions, intersections,
arbitrary rotations and translations, projections, distance, etc. To ease the
coordinate free and matrix free implementation of this fundamental geometric
product, a new algebraic three level approach is presented. Finally details
about the Java classes of the new GeometricAlgebra software package and their
associated methods are given. KamiWaAi is available for free internet download.
  Key Words: Geometric Algebra, Conformal Geometric Algebra, Geometric Calculus
Software, GeometricAlgebra, Java Package, Interactive 3D Software, Geometric
Objects


  We study upper and lower bounds on the sample-complexity of learning
near-optimal behaviour in finite-state discounted Markov Decision Processes
(MDPs). For the upper bound we make the assumption that each action leads to at
most two possible next-states and prove a new bound for a UCRL-style algorithm
on the number of time-steps when it is not Probably Approximately Correct
(PAC). The new lower bound strengthens previous work by being both more general
(it applies to all policies) and tighter. The upper and lower bounds match up
to logarithmic factors.


  We study maximum-likelihood-type estimation for diffusion processes when the
coefficients are nonrandom and observation occurs in nonsynchronous manner. The
problem of nonsynchronous observations is important when we consider the
analysis of high-frequency data in a financial market. Constructing a
quasi-likelihood function to define the estimator, we adaptively estimate the
parameter for the diffusion part and the drift part. We consider the asymptotic
theory when the terminal time point $T_n$ and the observation frequency goes to
infinity, and show the consistency and the asymptotic normality of the
estimator. Moreover, we show local asymptotic normality for the statistical
model, and asymptotic efficiency of the estimator as a consequence. To show the
asymptotic properties of the maximum-likelihood-type estimator, we need to
control the asymptotic behaviors of some functionals of the sampling scheme.
Though it is difficult to directly control those in general, we study tractable
sufficient conditions when the sampling scheme is generated by mixing
processes.


  We introduce a logic, called LT, to express properties of transductions, i.e.
binary relations from input to output (finite) words. In LT, the input/output
dependencies are modelled via an origin function which associates to any
position of the output word, the input position from which it originates. LT is
well-suited to express relations (which are not necessarily functional), and
can express all regular functional transductions, i.e. transductions definable
for instance by deterministic two-way transducers. Despite its high expressive
power, LT has decidable satisfiability and equivalence problems, with tight
non-elementary and elementary complexities, depending on specific
representation of LT-formulas. Our main contribution is a synthesis result:
from any transduction R defined in LT , it is possible to synthesise a regular
functional transduction f such that for all input words u in the domain of R, f
is defined and (u,f(u)) belongs to R. As a consequence, we obtain that any
functional transduction is regular iff it is LT-definable. We also investigate
the algorithmic and expressiveness properties of several extensions of LT, and
explicit a correspondence between transductions and data words. As a
side-result, we obtain a new decidable logic for data words.


  The aim of this paper is to provide a general mathematical framework for
group equivariance in the machine learning context. The framework builds on a
synergy between persistent homology and the theory of group actions. We define
group-equivariant non-expansive operators (GENEOs), which are maps between
function spaces associated with groups of transformations. We study the
topological and metric properties of the space of GENEOs to evaluate their
approximating power and set the basis for general strategies to initialise and
compose operators. We begin by defining suitable pseudo-metrics for the
function spaces, the equivariance groups, and the set of non-expansive
operators. Basing on these pseudo-metrics, we prove that the space of GENEOs is
compact and convex, under the assumption that the function spaces are compact
and convex. These results provide fundamental guarantees in a machine learning
perspective. We show examples on the MNIST and fashion-MNIST datasets. By
considering isometry-equivariant non-expansive operators, we describe a simple
strategy to select and sample operators, and show how the selected and sampled
operators can be used to perform both classical metric learning and an
effective initialisation of the kernels of a convolutional neural network.


  We consider classes of dynamical systems admitting Markov induced maps. Under
general assumptions, which in particular guarantee the existence of SRB
measures, we prove that the entropy of the SRB measure varies continuously with
the dynamics. We apply our result to a vast class of non-uniformly expanding
maps of a compact manifold and prove the continuity of the entropy of the SRB
measure. In particular, we show that the SRB entropy of Viana maps varies
continuously with the map.


  We present the largest publicly available catalog of interacting dwarf
galaxies. It includes 177 nearby merging dwarf galaxies of stellar mass M$_{*}$
$<$ 10$^{10}$M$_{\sun}$ and redshifts z $<$ 0.02. These galaxies are selected
by visual inspection of publicly available archival imaging from two wide-field
optical surveys (SDSS III and the Legacy Survey), and they possess low surface
brightness features that are likely the result of an interaction between dwarf
galaxies. We list UV and optical photometric data which we use to estimate
stellar masses and star formation rates. So far, the study of interacting dwarf
galaxies has largely been done on an individual basis, and lacks a sufficiently
large catalog to give statistics on the properties of interacting dwarf
galaxies, and their role in the evolution of low mass galaxies. We expect that
this public catalog can be used as a reference sample to investigate the
effects of the tidal interaction on the evolution of star-formation,
morphology/structure of dwarf galaxies.
  Our sample is overwhelmingly dominated by star-forming galaxies, and they are
generally found significantly below the red-sequence in the color-magnitude
relation. The number of early-type galaxies is only 3 out of 177. We classify
them, according to observed low surface brightness features, into various
categories including shells, stellar streams, loops, antennae or simply
interacting. We find that dwarf-dwarf interactions tend to prefer the low
density environment. Only 41 out of the 177 candidate dwarf-dwarf interaction
systems have giant neighbors within a sky projected distance of 700 kpc and a
line of sight radial velocity range $\pm$700 km/s and, compared to the LMC-SMC,
they are generally located at much larger sky-projected distances from their
nearest giant neighbor.


  In this paper we present two semi-implicit-type second order Compact
Approximate Taylor (CAT2) numerical schemes and blend them with a local a
posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve
hyperbolic systems of balance laws with relaxed source term. The resulting
scheme presents high accuracy when applied to smooth solutions, essentially
non-oscillatory behavior for irregular ones, and offers a nearly fail-safe
property in terms of ensuring positivity. The numerical results obtained from a
variety of test cases, including smooth and non-smooth well-prepared and
unprepared initial condition, assessing the appropriate behavior of the
semi-implicit-type second order CATMOOD schemes. These results have been
compared in accuracy and efficiency with a second order semi-implicit
Runge-Kutta (RK) method.


  Maximal connected grading classes of a finite-dimensional algebra $A$ are in
one-to-one correspondence with Galois covering classes of $A$ which admit no
proper Galois covering and therefore are key in computing the intrinsic
fundamental group $\pi_1(A)$. Our first concern here is the algebras
$A=M_n(\mathbb{C})$. Their maximal connected gradings turn out to be in
one-to-one correspondence with the Aut$(G)$-orbits of non-degenerate classes in
$H^2(G,\C^*)$, where $G$ runs over all groups of central type whose orders
divide $n^2$. We show that there exist groups of central type $G$ such that
$H^2(G,\C^*)$ admits more than one such orbit of non-degenerate classes. We
compute the family $\Lambda$ of positive integers $n$ such that there is a
unique group of central type of order $n^2$, namely $C_n\times C_n$. The family
$\Lambda$ is of square-free integers and contains all prime numbers. It is
obtained by a full description of all groups of central type whose orders are
cube-free. We establish the maximal connected gradings of all finite
dimensional semisimple complex algebras using the fact that such gradings are
determined by dimensions of complex projective representations of finite
groups. In some cases we give a description of the corresponding fundamental
groups.


  I review lattice calculations of quantities that involve light quarks,
including light quark masses, the vector form factor f_+(0) needed for
semileptonic kaon decays, and kaon mixing. Results for most of these quantities
are now available from multiple groups. Averages of these results are
presented, along with a discussion of the methodology behind the averaging
procedure. Recent progress in calculations of K->pi pi matrix elements is also
reviewed.


  In this paper, we propose a fast and accurate numerical method based on
Fourier transform to solve Kolmogorov forward equations of symmetric scalar
L\'evy processes. The method is based on the accurate numerical formulas for
Fourier transform proposed by Ooura. These formulas are combined with
nonuniform fast Fourier transform (FFT) and fractional FFT to speed up the
numerical computations. Moreover, we propose a formula for numerical indefinite
integration on equispaced grids as a component of the method. The proposed
integration formula is based on the sinc-Gauss sampling formula, which is a
function approximation formula. This integration formula is also combined with
the FFT. Therefore, all steps of the proposed method are executed using the FFT
and its variants. The proposed method allows us to be free from some special
treatments for a non-smooth initial condition and numerical time integration.
The numerical solutions obtained by the proposed method appeared to be
exponentially convergent on the interval if the corresponding exact solutions
do not have sharp cusps. Furthermore, the real computational times are
approximately consistent with the theoretical estimates.


  For scalar semilinear wave equations, we analyze the interaction of two
(distorted) plane waves at an interface between media of different nonlinear
properties. We show that new waves are generated from the nonlinear
interactions, which might be responsible for the observed nonlinear effects in
applications. Also, we show that the incident waves and the nonlinear responses
determine the location of the interface and some information of the nonlinear
properties of the media. In particular, for the case of a jump discontinuity at
the interface, we can determine the magnitude of the jump.


  CMS reports on the recently updated, preliminary results with the full
datasets of 2011 and 2012 in the analysis of the Higgs-like Boson at 125 GeV.
Utilizing 5.1$fb^{-1}$ of 7 TeV data and 19.6$fb^{-1}$ of 8 TeV data, a signal
strength of $0.78^{+0.28}_{-0.26}$ times the Standard Model (SM) expectations
with a mass of $125.4\pm0.8$ GeV is observed. The significance of this
resonance with respect to the background only prediction is $3.2\sigma$. The
cut-based cross-check analysis observes signal strength of
$1.11^{+0.32}_{-0.30}$ times the SM expectations with a significance of
$3.9\sigma$ at 124.5 GeV.


  We exhibit a large class of symbols $m$ on $\R^d$, $d\geq 2$, for which the
corresponding Fourier multipliers $T_m$ satisfy the following inequality. If
$D$, $E$ are measurable subsets of $\R^d$ with $E\subseteq D$ and $|D|<\infty$,
then $$ \int_{D\setminus E} |T_{m}\chi_E(x)|\mbox{d}x\leq \begin{cases}
|E|+|E|\ln\left(\frac{|D|}{2|E|}\right), & \mbox{if}|E|<|D|/2, |D\setminus
E|+\frac{1}{2}|D \setminus E|\ln \left(\frac{|E|}{|D\setminus E|}\right), &
\mbox{if}|E|\geq |D|/2. \end{cases}. $$ Here $|\cdot|$ denotes the Lebesgue
measure on $\bR^d$. When $d=2$, these multipliers include the real and
imaginary parts of the Beurling-Ahlfors operator $B$ and hence the inequality
is also valid for $B$ with the right-hand side multiplied by $\sqrt{2}$. The
inequality is sharp for the real and imaginary parts of $B$. This work is
motivated by K. Astala's celebrated results on the Gehring-Reich conjecture
concerning the distortion of area by quasiconformal maps. The proof rests on
probabilistic methods and exploits a family of appropriate novel sharp
inequalities for differentially subordinate martingales. These martingale
bounds are of interest on their own right.


  The title page of Chapter 9 in Fundamentals of Physics (Halliday, Resnick,
and Walker, 8th Edition, p. 201) shows a dramatic photograph of two Big Horn
sheep butting heads and promises to explain how sheep survive such violent
clashes without serious injury. However, the answer presented in sample problem
9-4 (p. 213) errs in presuming an interaction time of 0.27 s which results in
an unrealistically long stopping distance of 0.62 m. Furthermore, the assertion
that the horns provide necessary cushioning of the blow is inconsistent with
the absence of concussions in domestic breeds of hornless sheep. Results from
traumatic brain injury (TBI) research allow acceleration tolerance of sheep to
be estimated as 450 g facilitating an analysis of sheep collisions that is more
consistent with available observations (stopping distance less than 1 cm,
impact time of roughly 2 ms).


  We study the two-dimensional topological abelian BF theory in the Lorenz
gauge and, surprisingly, we find that the gauged-fixed theory is a free type B
twisted N=(2,2) superconformal theory with odd linear target space, with the
ghost field c being the pullback of the linear holomorphic coordinate on the
target. The BRST operator of the gauge-fixed theory equals the total Q of type
B twisted theory. This unexpected identification of two different theories
opens a way for nontrivial deformations of both of these theories.


  We construct a translating solution to anisotropic curve shortening flow and
show that for a given anisotropic factor $g:S^1\to\mathbb{R}_+$, and a given
direction and speed, this translator is unique. We then construct an ancient
compact solution to anisotropic curve shortening flow, and show that this
solution, along with the appropriate translating solution, are the unique
solutions to anisotropic curve shortening flow that lie in a slab of a given
width and no smaller.


  Objective assessment of image quality is fundamentally important in many
image processing tasks. In this work, we focus on learning blind image quality
assessment (BIQA) models which predict the quality of a digital image with no
access to its original pristine-quality counterpart as reference. One of the
biggest challenges in learning BIQA models is the conflict between the gigantic
image space (which is in the dimension of the number of image pixels) and the
extremely limited reliable ground truth data for training. Such data are
typically collected via subjective testing, which is cumbersome, slow, and
expensive. Here we first show that a vast amount of reliable training data in
the form of quality-discriminable image pairs (DIP) can be obtained
automatically at low cost by exploiting large-scale databases with diverse
image content. We then learn an opinion-unaware BIQA (OU-BIQA, meaning that no
subjective opinions are used for training) model using RankNet, a pairwise
learning-to-rank (L2R) algorithm, from millions of DIPs, each associated with a
perceptual uncertainty level, leading to a DIP inferred quality (dipIQ) index.
Extensive experiments on four benchmark IQA databases demonstrate that dipIQ
outperforms state-of-the-art OU-BIQA models. The robustness of dipIQ is also
significantly improved as confirmed by the group MAximum Differentiation (gMAD)
competition method. Furthermore, we extend the proposed framework by learning
models with ListNet (a listwise L2R algorithm) on quality-discriminable image
lists (DIL). The resulting DIL Inferred Quality (dilIQ) index achieves an
additional performance gain.


  The automatic detection and localization of anatomical features in retinal
imaging data are relevant for many aspects. In this work, we follow a
data-centric approach to optimize classifier training for optic nerve head
detection and localization in optical coherence tomography en face images of
the retina. We examine the effect of domain knowledge driven spatial complexity
reduction on the resulting optic nerve head segmentation and localization
performance. We present a machine learning approach for segmenting optic nerve
head in 2D en face projections of 3D widefield swept source optical coherence
tomography scans that enables the automated assessment of large amounts of
data. Evaluation on manually annotated 2D en face images of the retina
demonstrates that training of a standard U-Net can yield improved optic nerve
head segmentation and localization performance when the underlying pixel-level
binary classification task is spatially relaxed through domain knowledge.


  I consider the task of experimental data fitting. Unlike the traditional
approach I do not try to minimize any functional based on available
experimental information, instead the minimization problem is replaced with
constraint satisfaction procedure, which produces the interval hull of
solutions of desired type. The method, called 'box slicing algorithm', is
described in details. The results obtained this way need not to be labeled with
confidence level of any kind, they are simply certain (guaranteed). The method
easily handles the case with uncertainties in one or both variables. There is
no need for, always more or less arbitrary, weighting the experimental data.
The approach is directly applicable to other experimental data processing
problems like outliers detection or finding the straight line, which is tangent
to the experimental curve.


  We discuss the open string ending on D $p$-branes in IKKT framework. First we
determine the boundary conditions of Green-Schwarz superstring which are
consistent with supersymmetry and $\kappa$-symmetry. We point out some
subtleties arising from taking the Schild gauge and show that in this gauge the
system incorporates the limited dimensional D $p$-branes ($p=3,7$). The matrix
regularization for the Dirichlet open string is given by gauge group SO(N).
When $p=3$, the matrix model becomes the dimensional reduction of a 6
dimensional ${\cal N}=1$ super Yang-Mills theory.


  Swift, Chandra and XMM have found a weak but nearly constant X-ray component
from Swift J1644+57 that appeared at ~500 days and was visible at least until ~
1400 days after the stellar capture, which cannot be explained by standard
tidal disruption theories. We suggest that this X-ray afterglow component may
result from Thomson scattering between the primary X-rays and its surrounding
plasma, i.e. the Compton echo effect. Similar phenomena has also been observed
from molecular clouds in our Galactic Center, which were caused by the past
activity of Srg A*. If this interpretation of Swift J1644+57 afterglow is
correct, this is the first Compton Echo effect observed in the cosmological
distances.


  The multimodal models used in the emerging field at the intersection of
computational linguistics and computer vision implement the bottom-up
processing of the `Hub and Spoke' architecture proposed in cognitive science to
represent how the brain processes and combines multi-sensory inputs. In
particular, the Hub is implemented as a neural network encoder. We investigate
the effect on this encoder of various vision-and-language tasks proposed in the
literature: visual question answering, visual reference resolution, and
visually grounded dialogue. To measure the quality of the representations
learned by the encoder, we use two kinds of analyses. First, we evaluate the
encoder pre-trained on the different vision-and-language tasks on an existing
diagnostic task designed to assess multimodal semantic understanding. Second,
we carry out a battery of analyses aimed at studying how the encoder merges and
exploits the two modalities.


  It was proved by Fan--Lee and Fan that the absolute Gromov--Witten invariants
of two projective bundles $\mathbb P(V_i)\rightarrow X$ are identified
canonically when the total Chern classes $c(V_1)=c(V_2)$ for two bundles $V_1$
and $V_2$ over a smooth projective variety $X$. In this note we show that for
the two projective completions $\mathbb P(V_i\oplus\mathcal O)$ of $V_i$ and
their infinity divisors $\mathbb P(V_i)$, the relative Gromov--Witten
invariants of $(\mathbb P(V_i\oplus\mathcal O),\mathbb P(V_i))$ are identified
canonically when $c(V_1)=c(V_2)$.


  A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal
with high-dimensional datasets. This happens primarily due to the use of
T-norm, particularly, product or minimum (or a softer version of it). Thus,
there are hardly any work dealing with datasets with dimensions more than
hundred or so. Here, we propose a neuro-fuzzy framework that can handle
datasets with dimensions even more than 7000! In this context, we propose an
adaptive softmin (Ada-softmin) which effectively overcomes the drawbacks of
``numeric underflow" and ``fake minimum" that arise for existing fuzzy systems
while dealing with high-dimensional problems. We call it an Adaptive
Takagi-Sugeno-Kang (AdaTSK) fuzzy system. We then equip the AdaTSK system to
perform feature selection and rule extraction in an integrated manner. In this
context, a novel gate function is introduced and embedded only in the
consequent parts, which can determine the useful features and rules, in two
successive phases of learning. Unlike conventional fuzzy rule bases, we design
an enhanced fuzzy rule base (En-FRB), which maintains adequate rules but does
not grow the number of rules exponentially with dimension that typically
happens for fuzzy neural networks. The integrated Feature Selection and Rule
Extraction AdaTSK (FSRE-AdaTSK) system consists of three sequential phases: (i)
feature selection, (ii) rule extraction, and (iii) fine tuning. The
effectiveness of the FSRE-AdaTSK is demonstrated on 19 datasets of which five
are in more than 2000 dimension including two with dimension greater than 7000.
This may be the first time fuzzy systems are realized for classification
involving more than 7000 input features.


  Two-dimensional van der Waals compounds with magnetic ions on a honeycomb
lattice are hosts to a variety of exotic behavior. The magnetic interactions in
one such compound, MnPSe$_3$, are investigated with elastic and inelastic
neutron scattering. Magnetic excitations are observed in the magnetically
ordered regime and persist to temperatures well above the ordering temperature,
$\rm T_N$ = 74 K, consistent with low dimensional magnetic interactions. The
inelastic neutron scattering results allow a model spin Hamiltonian to be
presented that includes dominant intralayer interactions of $J_{1ab}$=0.45 meV,
$J_{2ab}$=0.03 meV, $J_{3ab}$=0.19 meV, and appreciable interlayer interactions
of $J_c$=0.031(5) meV. No evidence for anisotropy in the form of a spin-gap is
observed in the data collected. The measurements on MnPSe$_3$ are contrasted
with those on MnPS$_3$ and reveal a large increase in the interlayer exchange
interactions in MnPSe$_3$, despite the quasi-2D magnetic behavior.


  We study statistical characterization of the many-body states in the exactly
solvable model with internal degree of freedom in more than one dimension. The
model exhibits the Mott metal-insulator transition. It is shown that the ground
state is described by that of a generalized ideal gas of particles (called
exclusons) which have mutual exclusion statistics between different species. In
addition to giving a perspective view of spin-charge separation, the model
constitutes an explicit example of mutual exclusion statistics in more than two
dimensions.


  The many-anyons wavefunction is constructed via the superposition of all the
permutations on the direct product of single anyon states and its interchange
properties are examined. The phase of permutation is not a representation but
the word metric of the permutation group . Amazingly the interchange phase
yields a finite capacity of one quantum state interpolating between Fermion and
Boson and the mutual exchange phase has no explicit effect on statistics.
Finite capacity of quantum state is defined as Gentile statistics and it is
different from the fractional exclusion statistics. Some discussion on the
general model is also given.


  We have measured the fraction of bars in nearby spiral galaxies using
near-infrared J, H, and K_s images of 151 spiral galaxies from 2MASS. This
local sample provides an anchor for the study of the evolution of the bar
fraction and bar properties with redshift. We identify bars by analyzing the
full two-dimensional light distribution and requiring a combined ellipticity
and position angle signature. The combined bar signature is found in 59% of the
galaxies. The bar fraction increases to 67% when we include "candidate" bars,
where only the ellipticity signature is present. We also measure the change in
the bar fraction as a function of bar size; the bar fraction drops to 36% for
bars with a semi-major axis larger than 4 kpc. We find that infrared bars
typically extend to one-third of the galactic disk, with a deprojected relative
size of <a_{bar}/R_{25}> ~ 0.3 +/- 0.2. Early-type spirals host significantly
larger bars, consistent with earlier studies. The <a_{bar}/R_{25}> is two times
larger in early-types than in late-types. The typical bar axial ratio (b/a) is
\~0.5, with a weak trend of higher axial ratios for larger bars.


  The luminosities of the centers of nearby elliptical galaxies are very low
compared to models of thin disc accretion to their black holes at the Bondi
rate, typically a few hundredths to a few tenths of a solar mass per year. This
has motivated models of inefficiently-radiated accretion that invoke weak
electron-ion thermal coupling, and/or inhibited accretion rates due to
convection or outflows. Here we point out that even if such processes are
operating, a significant fraction of the accreting gas is prevented from
reaching the central black hole because it condenses into stars in a
gravitationally unstable disc. Star formation occurs inside the Bondi radius
(typically ~100pc in giant ellipticals), but still relatively far from the
black hole in terms of Schwarzschild radii. Star formation depletes and heats
the gas disc, eventually leading to a marginally stable, but much reduced,
accretion flow to the black hole. We predict the presence of cold (~100K),
dusty gas discs, containing clustered H-alpha emission and occasional type II
supernovae, both resulting from the presence of massive stars. Star formation
accounts for several features of the M87 system: a thin disc, traced by H-alpha
emission, is observed on scales of about 100pc, with features reminiscent of
spiral arms and dust lanes; the star formation rate inferred from the intensity
of H-alpha emission is consistent with the Bondi accretion rate of the system.
Star formation may therefore help suppress accretion onto the central engines
of massive ellipticals. We also discuss some implications for the fueling of
the Galactic center and quasars.


  In clinical and epidemiological research doubly truncated data often appear.
This is the case, for instance, when the data registry is formed by interval
sampling. Double truncation generally induces a sampling bias on the target
variable, so proper corrections of ordinary estimation and inference procedures
must be used. Unfortunately, the nonparametric maximum likelihood estimator of
a doubly truncated distribution has several drawbacks, like potential
non-existence and non-uniqueness issues, or large estimation variance.
Interestingly, no correction for double truncation is needed when the sampling
bias is ignorable, which may occur with interval sampling and other sampling
designs. In such a case the ordinary empirical distribution function is a
consistent and fully efficient estimator that generally brings remarkable
variance improvements compared to the nonparametric maximum likelihood
estimator. Thus, identification of such situations is critical for the simple
and efficient estimation of the target distribution. In this paper we introduce
for the first time formal testing procedures for the null hypothesis of
ignorable sampling bias with doubly truncated data. The asymptotic properties
of the proposed test statistic are investigated. A bootstrap algorithm to
approximate the null distribution of the test in practice is introduced. The
finite sample performance of the method is studied in simulated scenarios.
Finally, applications to data on onset for childhood cancer and Parkinson's
disease are given. Variance improvements in estimation are discussed and
illustrated.


  In this work, we propose trait-based merge trees a generalization of merge
trees to feature level sets, targeting the analysis of tensor field or general
multi-variate data. For this, we employ the notion of traits defined in
attribute space as introduced in the feature level sets framework. The
resulting distance field in attribute space induces a scalar field in the
spatial domain that serves as input for topological data analysis. The leaves
in the merge tree represent those areas in the input data that are closest to
the defined trait and thus most closely resemble the defined feature. Hence,
the merge tree yields a hierarchy of features that allows for querying the most
relevant and persistent features. The presented method includes different query
methods for the tree which enable the highlighting of different aspects. We
demonstrate the cross-application capabilities of this approach with three case
studies from different domains.


  Interacting quantum systems in the chaotic domain are at the core of various
ongoing studies of many-body physics, ranging from the scrambling of quantum
information to the onset of thermalization. We propose a minimum model for
chaos that can be experimentally realized with cold atoms trapped in
one-dimensional multi-well potentials. We explore the emergence of chaos as the
number of particles is increased, starting with as few as two, and as the
number of wells is increased, ranging from a double well to a multi-well
Kronig-Penney-like system. In this way, we illuminate the narrow boundary
between integrability and chaos in a highly tunable few-body system. We show
that the competition between the particle interactions and the periodic
structure of the confining potential reveals subtle indications of quantum
chaos for 3 particles, while for 4 particles stronger signatures are seen. The
analysis is performed for bosonic particles and could also be extended to
distinguishable fermions.


  Whenever applicable, the Stochastic Gradient Descent (SGD) has shown itself
to be unreasonably effective. Instead of underperforming and getting trapped in
local minima due to the batch noise, SGD leverages it to learn to generalize
better and find minima that are good enough for the entire dataset. This led to
numerous theoretical and experimental investigations, especially in the context
of Artificial Neural Networks (ANNs), leading to better machine learning
algorithms. However, SGD is not applicable in a non-differentiable setting,
leaving all that prior research off the table.
  In this paper, we show that a class of evolutionary algorithms (EAs) inspired
by the Gillespie-Orr Mutational Landscapes model for natural evolution is
formally equivalent to SGD in certain settings and, in practice, is well
adapted to large ANNs. We refer to such EAs as Gillespie-Orr EA class (GO-EAs)
and empirically show how an insight transfer from SGD can work for them. We
then show that for ANNs trained to near-optimality or in the transfer learning
setting, the equivalence also allows transferring the insights from the
Mutational Landscapes model to SGD.
  We then leverage this equivalence to experimentally show how SGD and GO-EAs
can provide mutual insight through examples of minima flatness, transfer
learning, and mixing of individuals in EAs applied to large models.


  Volumetric ultrasound has great potentials in promoting prenatal
examinations. Automated solutions are highly desired to efficiently and
effectively analyze the massive volumes. Segmentation and landmark localization
are two key techniques in making the quantitative evaluation of prenatal
ultrasound volumes available in clinic. However, both tasks are non-trivial
when considering the poor image quality, boundary ambiguity and anatomical
variations in volumetric ultrasound. In this paper, we propose an effective
framework for simultaneous segmentation and landmark localization in prenatal
ultrasound volumes. The proposed framework has two branches where informative
cues of segmentation and landmark localization can be propagated
bidirectionally to benefit both tasks. As landmark localization tends to suffer
from false positives, we propose a distance based loss to suppress the noise
and thus enhance the localization map and in turn the segmentation. Finally, we
further leverage an adversarial module to emphasize the correspondence between
segmentation and landmark localization. Extensively validated on a volumetric
ultrasound dataset of fetal femur, our proposed framework proves to be a
promising solution to facilitate the interpretation of prenatal ultrasound
volumes.


  The lack of evidence for the production of colored supersymmetric particles
at the LHC has increased interest in searches for superpartners of the
electroweak SM gauge bosons, namely the neutralinos and charginos. These are
challenging due to the weak nature of the production process, and the existing
discovery reach has significant gaps in due to the difficulty of separating the
supersymmetric signal from SM diboson events that produce similar final states
and kinematics. We apply the Recursive Jigsaw Reconstruction technique to study
final states enriched in charged leptons and missing transverse momentum,
focusing on compressed topologies with direct production of charginos and
neutralinos decaying to the lightest neutral supersymmetric particle through
the emission of W and Z bosons. After presenting prototype analysis designs for
future LHC runs, we demonstrate that its detectors have the potential to probe
a significant amount of unexplored parameter space for chargino-neutralino
associated production within the next few years, and show that the very
challenging successful search for chargino pair production with compressed
spectra might be possible by the end of the LHC lifetime.


  We define the algebraic Dirac induction map $\Ind_D$ for graded affine Hecke
algebras. The map $\Ind_D$ is a Hecke algebra analog of the explicit
realization of the Baum-Connes assembly map in the $K$-theory of the reduced
$C^*$-algebra of a real reductive group using Dirac operators. The definition
of $\Ind_D$ is uniform over the parameter space of the graded affine Hecke
algebra. We show that the map $\Ind_D$ defines an isometric isomorphism from
the space of elliptic characters of the Weyl group (relative to its reflection
representation) to the space of elliptic characters of the graded affine Hecke
algebra. We also study a related analytically defined global elliptic Dirac
operator between unitary representations of the graded affine Hecke algebra
which are realized in the spaces of sections of vector bundles associated to
certain representations of the pin cover of the Weyl group. In this way we
realize all irreducible discrete series modules of the Hecke algebra in the
kernels (and indices) of such analytic Dirac operators. This can be viewed as a
graded Hecke algebra analogue of the construction of discrete series
representations for semisimple Lie groups due to Parthasarathy and
Atiyah-Schmid.


  We examine the effect of an accretion disc on the orbits of stars in the
central star cluster surrounding a central massive black hole by performing a
suite of 39 high-accuracy direct N-body simulations using state-of-the art
software and accelerator hardware, with particle numbers up to 128k. The
primary focus is on the accretion rate of stars by the black hole (equivalent
to their tidal disruption rate for black holes in the small to medium mass
range) and the eccentricity distribution of these stars. Our simulations vary
not only the particle number, but disc model (two models examined), spatial
resolution at the centre (characterised by the numerical accretion radius) and
softening length. The large parameter range and physically realistic modelling
allow us for the first time to confidently extrapolate these results to real
galactic centres. While in a real galactic centre both particle number and
accretion radius differ by a few orders of magnitude from our models, which are
constrained by numerical capability, we find that the stellar accretion rate
converges for models with N > 32k. The eccentricity distribution of accreted
stars, however, does not converge. We find that there are two competing effects
at work when improving the resolution: larger particle number leads to a
smaller fraction of stars accreted on nearly-circular orbits, while higher
spatial resolution increases this fraction. We scale our simulations to some
nearby galaxies and find that the expected boost in stellar accretion (or tidal
disruption, which could be observed as X-ray flares) in the presence of a gas
disc is about a factor of 10. Even with this boost, the accretion of mass from
stars is still a factor of ~ 100 slower than the accretion of gas from the
disc. Thus, it seems accretion of stars is not a major contributor to black
hole mass growth.


  Discrete dynamical systems defined on the state space {0,1,...,p-1}^n have
been used in multiple applications, most recently for the modeling of gene and
protein networks. In this paper we study to what extent well-known theorems by
Smale and Hirsch, which form part of the theory of (continuous) monotone
dynamical systems, generalize or fail to do so in the discrete case.
  We show that that arbitrary m-dimensional systems cannot necessarily be
embedded into n-dimensional cooperative systems for n=m+1, as in the Smale
theorem for the continuous case, but we show that this is possible for n=m+2 as
long as p is sufficiently large.
  We also prove that a natural discrete analogue of strong cooperativity
implies nontrivial bounds on the lengths of periodic orbits and imposes a
condition akin to Lyapunov stability on all attractors. Finally, we explore
several natural candidates for definitions of irreducibility of a discrete
system. While some of these notions imply the strong cooperativity of a given
cooperative system and impose even tighter bounds on the lengths of periodic
orbits than strong cooperativity alone, other plausible definitions allow the
existence of exponentially long periodic orbits.


  We present results from direct measurements of the $^{27}{\rm Al}(\alpha,n)$
thick target yield from laboratory incident energies $E_{\alpha}\approx$
3$-$5~MeV, performed with the $^{3}$HeBF$_{3}$ Giant Barrel (HeBGB) neutron
detector at the Edwards Accelerator Laboratory. Our measurements have a small
energy cadence in order to address discrepancies and sparseness of thick-target
yield data sets existing for this energy region. We find general agreement with
existing data sets, including yields derived from cross section data, while
resolving a discrepancy between existing thick-target yield data sets for
$E_{\alpha}\approx4-5$~MeV. However, for $E_{\alpha}<3.5$~MeV, our results are
substantially lower than previous thick-target yield data and somewhat larger
than yields calculated from existing cross section data. Our data complete the
energy-range needed for estimates of the $^{27}{\rm Al}(\alpha,n)$ contribution
to neutrino and dark matter detector backgrounds and result in increased
viability of $^{27}{\rm Al}(\alpha,n)$ as a plasma diagnostic tool at fusion
facilities such as the National Ignition Facility.


  We propose a method to achieve quantum supremacy using ensembles of qubits,
using only spin squeezing, basis rotations, and Fock state measurements. Each
ensemble is assumed to be controllable only with its total spin. Using a
repeated sequence of random basis rotations followed by squeezing, we show that
the probability distribution of the final measurements quickly approaches a
Porter-Thomas distribution. We show that the sampling probability can be
related to a #P-hard problem with a complexity scaling as $(N+1)^M$, where $N$
is the number of qubits in an ensemble and $ M $ is the number of ensembles.
The scheme can be implemented with hot or cold atomic ensembles. Due to the
large number of atoms in typical atomic ensembles, this allows access to the
quantum supremacy regime with a modest number of ensembles or gate depth.


  A regularization-independent universal formula for the energy--momentum
tensor in gauge theory in the flat spacetime can be written down by employing
the so-called Yang--Mills gradient flow. We examine a possible use of the
formula in the calculation of the axial $U(1)$ anomaly in a gravitational
field, the anomaly first obtained by Toshiei Kimura [Prog.\ Theor.\ Phys.\ {\bf
42}, 1191 (1969)]. As a general argument indicates, the formula reproduces the
correct non-local structure of the (axial $U(1)$ current)--(energy--momentum
tensor)--(energy--momentum tensor) triangle diagram in a way that is consistent
with the axial $U(1)$ anomaly. On the other hand, the formula does not
automatically reproduce the general coordinate (or translation) Ward--Takahashi
relation, requiring corrections by local counterterms. This analysis thus
illustrates the fact that the universal formula as it stands can be used only
in on-shell correlation functions, in which the energy--momentum tensor does
not coincide with other composite operators in coordinate space.


  We construct a dg-enhancement of KLRW algebras that categorifies the tensor
product of a universal $\mathfrak{sl}_2$ Verma module and several integrable
irreducible modules. When the integrable modules are two-dimensional, we
construct a categorical action of the blob algebra on derived categories of
these dg-algebras which intertwines the categorical action of
$\mathfrak{sl}_2$. From the above we derive a categorification of the blob
algebra.


  In this study, we introduce a novel variant and application of the
Collaborative Representation based Classification in spectral domain for
recognition of the hand gestures using the raw surface Electromyography
signals. The intuitive use of spectral features are explained via circulant
matrices. The proposed Spectral Collaborative Representation based
Classification (SCRC) is able to recognize gestures with higher levels of
accuracy for a fairly rich gesture set. The worst recognition result which is
the best in the literature is obtained as 97.3\% among the four sets of the
experiments for each hand gestures. The recognition results are reported with a
substantial number of experiments and labeling computation.


  This thesis discusses the phenomenological parton recombination approach to
describe hadronization in heavy ion collisions. The very good agreement to RHIC
data for the flow coefficients v_2 and v_4 is shown and extrapolations are used
to make predictions for the LHC.


  Partial, frustrated synchronization and chimera-like states are expected to
occur in Kuramoto-like models if the spectral dimension of the underlying graph
is low: $d_s < 4$. We provide numerical evidence that this really happens in
case of the high-voltage power grid of Europe ($d_s < 2$), a large human
connectome (KKI113) and in case of the largest, exactly known brain network
corresponding to the fruit-fly (FF) connectome ($d_s < 4$), even though their
graph dimensions are much higher, i.e.: $d^{EU}_g\simeq 2.6(1)$ and
$d^{FF}_g\simeq 5.4(1)$, $d^{\mathrm{KKI113}}_g\simeq 3.4(1)$. We provide local
synchronization results of the first- and second-order (Shinomoto) Kuramoto
models by numerical solutions on the FF and the European power-grid graphs,
respectively, and show the emergence of \red{chimera-like} patterns on the
graph community level as well as by the local order parameters.


  The X-ray Polarization Probe (XPP) is a second generation X-ray polarimeter
following up on the Imaging X-ray Polarimetry Explorer (IXPE). The XPP will
offer true broadband polarimetery over the wide 0.2-60 keV bandpass in addition
to imaging polarimetry from 2-8 keV. The extended energy bandpass and
improvements in sensitivity will enable the simultaneous measurement of the
polarization of several emission components. These measurements will give
qualitatively new information about how compact objects work, and will probe
fundamental physics, i.e. strong-field quantum electrodynamics and strong
gravity.


  We present new exact solutions of the warped spherical compactifications in
the higher-dimensional gravitational theory coupled to scalar and several form
field strengths. We find two classes of solutions. One has a de Sitter
spacetime with a static warp factor. The other gives an accelerating universe
in the non-Einstein conformal frame with a time-dependent warp factor.


  We give an elementary proof that Davie's definition of a solution to a rough
differential equation and the notion of solution given by Bailleul in (Flows
driven by rough paths) coincide. This provides an alternative point on view on
the deep algebraic insights of Cass and Weidner in their work (Tree algebras
over topological vector spaces in rough path theory).


  Suppose that F/F+ is a CM extension of number fields in which the prime p
splits completely and every other prime is unramified. Fix a place w|p of F.
Suppose that rbar : Gal(F-bar/F) -> GL_3(Fp-bar) is a continuous irreducible
Galois representation such that rbar|_{Gal(F_w-bar/F_w)} is upper-triangular,
maximally non-split, and generic. If rbar is automorphic, and some suitable
technical conditions hold, we show that rbar|_{\Gal(F_w-bar/F_w)} can be
recovered from the GL_3(F_w)-action on a space of mod p automorphic forms on a
compact unitary group. On the way we prove results about weights in Serre's
conjecture for rbar, show the existence of an ordinary lifting of rbar, and
prove the freeness of certain Taylor-Wiles patched modules in this context. We
also show the existence of many Galois representations rbar to which our main
theorem applies.


  The flat bone develops through intramembranous ossification, in which the
mesenchymal cells are directly driven towards osteogenic lineage without the
formation of cartilage template. While long bone develops through endochondral
ossification, where cartilage template act as an intermediate stage between
mesenchymal and bone tissues. Although the avian sternum is a flat bone, some
studies describe formation of a cartilage template during its development. The
aim of the current study was to observe the mechanism of ossification in quail
sternum during embryonic development. Thirty quail embryos were collected for
the current study (5 embryos/ day) during the period between Day (D) 5 and D10
of embryonic development and processed for light microscopy. The
differentiation of mesenchymal condensation in to the chondrogenic cells was
observed at D5 whereas the secretion of extracellular matrix could be evident
at D6. The cartilage primordia were observed by D7 which were consisted of
chondrocytes, embedded in matrix and surrounded by perichondrium. Later these
primordia were developed in to cartilage template by D8 where the chondrocytes
were present in their lacuna. This template attained the shape of future
sternum by D9, which was more distinct at D10. These preliminary observations
suggested that the quail sternum grows through endochondral ossification. The
future study will further explore the histological changes of quail sternum
during post-hatching development.


  A detailed investigation by one-step photoemission calculations of the
GaN(0001)-(1x1) surface in comparison with recent experiments is presented in
order to clarify its structural properties and electronic structure. The
discussion of normal and off-normal spectra reveals through the identified
surface states clear fingerprints for the applicability of a surface model
proposed by Smith et al. Especially the predicted metallic bonds are confirmed.
In the context of direct transitions the calculated spectra allow to determine
the valence band width and to argue in favor of one of two theoretical bulk
band structures. Furthermore a commonly used experimental method to fix the
valence band maximum is critically tested.


  We have developed a theoretical analysis to systematically study the
late-time evolution of the Rayleigh-Taylor instability in a finite-sized
spatial domain. The nonlinear dynamics of fluids with similar and contrasting
densities are considered for two-dimensional flows driven by sustained
acceleration. The flows are periodic in the plane normal to the direction of
acceleration and have no external mass sources. Group theory analysis is
applied to accurately account for the mode coupling. Asymptotic nonlinear
solutions are found to describe the inter-facial dynamics far from and near the
boundaries. The influence of the size of the domain on the diagnostic
parameters of the flow is identified. In particular, it is shown that in a
finite-sized domain the flow is slower compared to the spatially extended case.
The direct link between the multiplicity of solutions and the inter-facial
shear function is explored. It is suggested that the inter-facial shear
function acts as a natural parameter to the family of analytic solutions.


  We provide upper bounds of the expected Wasserstein distance between a
probability measure and its empirical version, generalizing recent results for
finite dimensional Euclidean spaces and bounded functional spaces. Such a
generalization can cover Euclidean spaces with large dimensionality, with the
optimal dependence on the dimensionality. Our method also covers the important
case of Gaussian processes in separable Hilbert spaces, with rate-optimal upper
bounds for functional data distributions whose coordinates decay geometrically
or polynomially. Moreover, our bounds of the expected value can be combined
with mean-concentration results to yield improved exponential tail probability
bounds for the Wasserstein error of empirical measures under Bernstein-type or
log Sobolev-type conditions.


  6G will exploit satellite, aerial and terrestrial platforms jointly to
improve radio access capability and to unlock the support of on-demand edge
cloud services in the three dimensional space (3D) by incorporating Mobile Edge
Computing (MEC) functionalities on aerial platforms and low orbit satellites.
This will extend the MEC support to devices and network elements in the sky and
will forge a space borne MEC enabling intelligent personalized and distributed
on demand services. 3D end users will experience the impression of being
surrounded by a distributed computer fulfilling their requests in apparently
zero latency. In this paper, we consider an architecture providing
communication, computation, and caching (C3) services on demand, anytime and
everywhere in 3D space, building on the integration of conventional ground
(terrestrial) base stations and flying (non-terrestrial) nodes. Given the
complexity of the overall network, the C3 resources and the management of the
aerial devices need to be jointly orchestrated via AI-based algorithms,
exploiting virtualized networks functions dynamically deployed in a distributed
manner across terrestrial and non-terrestrial nodes.


  We present a systematic study on the physical properties of
EuFe$_{2-x}$Ni$_{x}$As$_{2}$ (0$\leq$\emph{x}$\leq$0.2) by electrical
resistivity, magnetic susceptibility and thermopower measurements. The undoped
compound EuFe$_{2}$As$_{2}$ undergoes a spin-density-wave (SDW) transition
associated with Fe moments at 195 K, followed by antiferromagnetic (AFM)
ordering of Eu$^{2+}$ moments at 20 K. Ni doping at the Fe site simultaneously
suppresses the SDW transition and AFM ordering of Eu$^{2+}$ moments. For
$x\geq$0.06, the magnetic ordering of Eu$^{2+}$ moments evolves from
antiferromagnetic to ferromagnetic (FM). The SDW transition is completely
suppressed for $x\geq$0.16, however, no superconducting transition was observed
down to 2 K. The possible origins of the AFM-to-FM transition and the absence
of superconductivity in EuFe$_{2-x}$Ni$_{x}$As$_{2}$ system are discussed.


  The topological pressure introduced by Ruelle and similar quantities describe
dynamical multifractal properties of dynamical systems. These are important
characteristics of mesoscopic systems in the classical regime. Original
definition of these quantities are based on the symbolic description of the
dynamics. It is hard or impossible to find symbolic description and generating
partition to a general dynamical system, therefore these quantities are often
not accessible for further studies. Here we present a new method by which the
symbolic description can be omitted. We apply the method for a mixing and an
intermittent system.


  Local stochastic gradient descent (SGD) is a fundamental approach in
achieving communication efficiency in Federated Learning (FL) by allowing
individual workers to perform local updates. However, the presence of
heterogeneous data distributions across working nodes causes each worker to
update its local model towards a local optimum, leading to the phenomenon known
as ``client-drift" and resulting in slowed convergence. To address this issue,
previous works have explored methods that either introduce communication
overhead or suffer from unsteady performance. In this work, we introduce a
novel metric called ``degree of divergence," quantifying the angle between the
local gradient and the global reference direction. Leveraging this metric, we
propose the divergence-based adaptive aggregation (DRAG) algorithm, which
dynamically ``drags" the received local updates toward the reference direction
in each round without requiring extra communication overhead. Furthermore, we
establish a rigorous convergence analysis for DRAG, proving its ability to
achieve a sublinear convergence rate. Compelling experimental results are
presented to illustrate DRAG's superior performance compared to
state-of-the-art algorithms in effectively managing the client-drift
phenomenon. Additionally, DRAG exhibits remarkable resilience against certain
Byzantine attacks. By securely sharing a small sample of the client's data with
the FL server, DRAG effectively counters these attacks, as demonstrated through
comprehensive experiments.


  Consider the focusing cubic semilinear Schroedinger equation in R^3 i
\partial_t \psi + \Delta \psi + | \psi |^2 \psi = 0. It admits an
eight-dimensional manifold of special solutions called ground state solitons.
  We exhibit a codimension-one critical real-analytic manifold N of
asymptotically stable solutions in a neighborhood of the soliton manifold. We
then show that N is centre-stable, in the dynamical systems sense of
Bates-Jones, and globally-in-time invariant.
  Solutions in N are asymptotically stable and separate into two asymptotically
free parts that decouple in the limit --- a soliton and radiation. Conversely,
in a general setting, any solution that stays close to the soliton manifold for
all time is in N.
  The proof uses the method of modulation. New elements include a different
linearization and an endpoint Strichartz estimate for the time-dependent
linearized equation.
  The proof also uses the fact that the linearized Hamiltonian has no nonzero
real eigenvalues or resonances. This has recently been established in the case
treated here --- of the focusing cubic NLS in R^3 --- by the work of
Marzuola-Simpson and Costin-Huang-Schlag.


  A Model Intercomparison Project (MIP) consists of teams who each estimate the
same underlying quantity (e.g., temperature projections to the year 2070), and
the spread of the estimates indicates their uncertainty. It recognizes that a
community of scientists will not agree completely but that there is value in
looking for a consensus and information in the range of disagreement. A simple
average of the teams' outputs gives a consensus estimate, but it does not
recognize that some outputs are more variable than others. Statistical analysis
of variance (ANOVA) models offer a way to obtain a weighted consensus estimate
of outputs with a variance that is the smallest possible and hence the tightest
possible 'one-sigma' and 'two-sigma' intervals. Modulo dependence between MIP
outputs, the ANOVA approach weights a team's output inversely proportional to
its variation. When external verification data are available for evaluating the
fidelity of each MIP output, ANOVA weights can also provide a prior
distribution for Bayesian Model Averaging to yield a consensus estimate. We use
a MIP of carbon dioxide flux inversions to illustrate the ANOVA-based weighting
and subsequent consensus inferences.


  We combine analytical understanding of resonant dynamics in two-planet
systems with machine learning techniques to train a model capable of robustly
classifying stability in compact multi-planet systems over long timescales of
$10^9$ orbits. Our Stability of Planetary Orbital Configurations Klassifier
(SPOCK) predicts stability using physically motivated summary statistics
measured in integrations of the first $10^4$ orbits, thus achieving speed-ups
of up to $10^5$ over full simulations. This computationally opens up the
stability constrained characterization of multi-planet systems. Our model,
trained on $\approx 100,000$ three-planet systems sampled at discrete
resonances, generalizes both to a sample spanning a continuous period-ratio
range, as well as to a large five-planet sample with qualitatively different
configurations to our training dataset. Our approach significantly outperforms
previous methods based on systems' angular momentum deficit, chaos indicators,
and parametrized fits to numerical integrations. We use SPOCK to constrain the
free eccentricities between the inner and outer pairs of planets in the
Kepler-431 system of three approximately Earth-sized planets to both be below
0.05. Our stability analysis provides significantly stronger eccentricity
constraints than currently achievable through either radial velocity or transit
duration measurements for small planets, and within a factor of a few of
systems that exhibit transit timing variations (TTVs). Given that current
exoplanet detection strategies now rarely allow for strong TTV constraints
(Hadden et al., 2019), SPOCK enables a powerful complementary method for
precisely characterizing compact multi-planet systems. We publicly release
SPOCK for community use.


  Using transmission electron microscopy, we investigate the thermally
activated motion of domain walls (DWs) between two positions in permalloy
(Ni80Fe20) nanowires at room temperature. We show that this purely thermal
motion is well described by an Arrhenius law, allowing for a description of the
DW as a quasi-particle in a 1D potential landscape. By injecting small
currents, the potential is modified, allowing for the determination of the
non-adiabatic spin torque: the non-adiabatic coefficient is 0.010 +/- 0.004 for
a transverse DW and 0.073 +/- 0.026 for a vortex DW. The larger value is
attributed to the higher magnetization gradients present.


  This article deals with a stochastic control problem for certain fluids of
non-Newtonian type. More precisely, the state equation is given by the
two-dimensional stochastic second grade fluids perturbed by a multiplicative
white noise. The control acts through an external stochastic force and we
search for a control that minimizes a cost functional. We show that the
G\^ateaux derivative of the control to state map is a stochastic process being
the unique solution of the stochastic linearized state equation. The
well-posedness of the corresponding stochastic backward adjoint equation is
also established, allowing to derive the first order optimality condition.


  We perform a computational study of a variant of the ``train'' model for
earthquakes [PRA 46, 6288 (1992)], where we assume a static friction that is a
stochastic function of position rather than being velocity dependent. The model
consists of an array of blocks coupled by springs, with the forces between
neighbouring blocks balanced by static friction. We calculate the probability,
P(s), of the occurrence of avalanches with a size s or greater, finding that
our results are consistent with the phenomenology and also with previous models
which exhibit a power law over a wide range. We show that the train model may
be mapped onto a stochastic sandpile model and study a variant of the latter
for non-spherical grains. We show that, in this case, the model has critical
behaviour only for grains with large aspect ratio, as was already shown in
experiments with real ricepiles. We also demonstrate a way to introduce
randomness in a physically motivated manner into the model.


  It follows from Oseledec Multiplicative Ergodic Theorem (or Kingmans
Subadditional Ergodic Theorem) that the Lyapunov-irregular set of points for
which the Oseledec averages of a given continuous cocycle diverge has zero
measure with respect to any invariant probability measure. In strong contrast,
for any dynamical system f with exponential specification property and a Holder
continuous matrix cocycle A, we show here that if there exist ergodic measures
with different Lyapunov spectrum, then the Lyapunov-irregular set of A displays
distributional chaos of type 1.


  The search for non-Gaussian signatures in the Cosmic Microwave Background
(CMB) is crucial for understanding the physics of the early Universe. Given the
possibility of non-Gaussian fluctuations in the CMB, a recent revision to the
standard $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model has been proposed,
dubbed "Super-$\Lambda$CDM". This model introduces additional free parameters
to account for the potential effects of a trispectrum in the primordial
fluctuations. In this study, we explore the impact of the Super-$\Lambda$CDM
model on current constraints on neutrino physics. In agreement with previous
research, our analysis reveals that for most of the datasets, the
Super-$\Lambda$CDM parameter $A_0$ significantly deviates from zero at over a
$95\%$ confidence level. We then demonstrate that this signal might influence
current constraints in the neutrino sector. Specifically, we find that the
current constraints on neutrino masses may be relaxed by over a factor of two
within the Super-$\Lambda$CDM framework, thanks to the correlation present with
$A_0$. Consequently, locking $A_0=0$ might introduce a bias, leading to overly
stringent constraints on the total neutrino mass.


  We find multicenter (Majumdar-Papapetrou type) solutions of
Eddington-inspired Born-Infeld gravity coupled to electromagnetic fields
governed by a Born-Infeld-like Lagrangian. We construct the general solution
for an arbitrary number of centers in equilibrium and then discuss the
properties of their one-particle configurations, including the existence of
bounces and the regularity (geodesic completeness) of these spacetimes. Our
method can be used to construct multicenter solutions in other theories of
gravity.


  We propose a characterisation of the effects of bistable coherent impurities
in solid state qubits. We introduce an effective impurity description in terms
of a tunable spin-boson environment and solve the dynamics for the qubit
coherences. The dominant rate characterizing the asymptotic time limit is
identified and signatures of non-Gaussian behavior of the quantum impurity at
intermediate times are pointed out. An alternative perspective considering the
qubit as a measurement device for the spin-boson impurity is proposed.


  Dynamic comparators are the core of high-speed, high-resolution
analog-to-digital converters (ADCs) used for communication applications. Most
of the dynamic comparators attain high-speed operation only for sufficiently
high input difference voltages. The comparator performance degrades at small
input difference voltages due to a limited pre-amplifier gain, which is
undesirable for high-speed, high-resolution ADCs. To overcome this drawback, a
cascode cross-coupled dynamic comparator is presented. The proposed comparator
improves the differential gain of the pre-amplifier and reduces the common-mode
voltage seen by the latch, which leads to a much faster regeneration at small
input difference voltages. The proposed comparator is designed, simulated, and
compared with the state-of-the-art techniques in 65 nm CMOS technology. The
results demonstrate that the proposed comparator achieves a delay of 46.5 ps at
1 mV input difference, and a supply of 1.1 V.


  The present study uses Galinstan as a test fluid to investigate the
shock-induced aerobreakup of a liquid metal droplet in a high Weber number
regime (We ~ 400 - 8000). Atomization dynamics is examined for three test
environments: oxidizing (Galinstan-air), inert (Galinstan-nitrogen), and
conventional fluids (DI water-air). Due to the readily oxidizing nature of
liquid metals, their atomization in an industrial scale system is generally
carried in inert atmosphere conditions. However, no previous study has
considered gas-induced secondary atomization of liquid metals in inert
conditions. Due to experimental challenges associated with molten metals,
laboratory scale models are generally tested for conventional fluids like DI
water, liquid fuels, etc. The translation of results obtained from conventional
fluid to liquid metal atomization is rarely explored. Here a direct multi-scale
spatial and temporal comparison is provided between the atomization dynamics of
conventional fluid and liquid metals under oxidizing and inert conditions. The
liquid metal droplet undergoes breakup through Shear-Induced Entrainment (SIE)
mode for the studied range of Weber number values. The prevailing mechanism is
explained based on the relative dominance of droplet deformation and KH wave
formation. The study provides quantitative and qualitative similarities for the
three test cases and explains the differences in morphology of fragmenting
secondary droplets in the oxidizing test case (Galinstan-air) due to rapid
oxidation of the fragmenting ligaments. A phenomenological framework is
postulated for predicting the morphology of secondary droplets. The formation
of flake-like secondary droplets in the Galinstan air test case is based on the
oxidation rate of liquid metals and the properties of the oxide layer formed on
the atomizing ligament surface.


  The first light curve solutions of the stars EW and HN in Pisces
constellation are presented. Photometry, and its' periodic changes are
calculated and discussed. The analysis of O-C diagram done by MCMC approach in
OCFit code and the new ephemeris provided for two binary systems. The light
curve solutions obtained. The results show that EW Psc is a near contact
eclipsing binary system with a photometric mass ratio q = 0.587, and the
fillout factor -0.034 and -0.018 for primary and secondary components,
respectively. The solution results also show that the system HN Psc is a
weak-contact W UMa eclipsing binary with a photometric mass ratio q = 0.853,
and with fillout factor 5.6%. The light curves solutions required the cold spot
accounting for the O'Connell effect.


  The proliferation of deep learning applications in healthcare calls for data
aggregation across various institutions, a practice often associated with
significant privacy concerns. This concern intensifies in medical image
analysis, where privacy-preserving mechanisms are paramount due to the data
being sensitive in nature. Federated learning, which enables cooperative model
training without direct data exchange, presents a promising solution.
Nevertheless, the inherent vulnerabilities of federated learning necessitate
further privacy safeguards. This study addresses this need by integrating
differential privacy, a leading privacy-preserving technique, into a federated
learning framework for medical image classification. We introduce a novel
differentially private federated learning model and meticulously examine its
impacts on privacy preservation and model performance. Our research confirms
the existence of a trade-off between model accuracy and privacy settings.
However, we demonstrate that strategic calibration of the privacy budget in
differential privacy can uphold robust image classification performance while
providing substantial privacy protection.


  High-frequency gravitational waves can be detected by observing the frequency
modulation they impart on photons. We discuss fundamental limitations to this
method related to the fact that it is impossible to construct a perfectly rigid
detector. We then propose several novel methods to search for O(MHz-GHz)
gravitational waves based on the frequency modulation induced in the spectrum
of an intense laser beam, by applying optical frequency demodulation
techniques, or by using optical atomic clock technology. We find promising
sensitivities across a broad frequency range.


  The goal of this work is to showcase the clinical value that portable MRI can
provide in crowded events and major sports competitions. We temporarily
installed a low-field and low-cost portable MRI system for extremity imaging in
the medical facilities of the Ricardo Tormo Motor Racing Circuit during the
four days of the Motorcycle Grand Prix held in Valencia (Spain), which closed
the 2022 season of the MotoGP. During this time, we scanned 14 subjects,
running a total of 21 protocols for wrist, knee and ankle imaging. Each
protocol included a minimum of one T1-weighted 3D-RARE sequence for general
anatomical information, and one 3D-STIR sequence to highlight fluid
accumulation and inflammation. The circuit medical staff were able to visualize
a number of lesions and conditions in the low-field reconstructions, including
gonarthrosis, effusion, or Haglund's syndrome, as well as metallic implants and
tissue changes due to surgical interventions. Out of eight low-field
acquisitions on previously diagnosed lesions, only two (a meniscus tear and a
Baker cyst) were not detected by the experts that evaluated our images. The
main highlight was that a low-field MRI scan on a subject reporting pain in a
wrist revealed a traumatic arthritis which an X-ray radiograph and visual
inspection had missed. We have operated in a scenario where high-field MRI is
unlikely to play a role but where a low-field system can lead to improved
medical attention. In the case reported here, system transport, installation in
the circuit facilities and calibration were all uncomplicated. The images
presented to the medical staff were mostly unprocessed and there is thus room
for improvement. In conclusion, this work supports the claim that low-field MRI
can likely provide added value whenever concepts such as accessibility,
portability and low-cost outweigh exquisite detail in images.


  The NuMI neutrino beam line and the MINOS experiment represent a major
investment of US High Energy Physics in the area of neutrino physics. The
forthcoming results could decisively establish neutrino oscillations as the
underlying physics mechanism for the atmospheric $\numu$ deficit and provide a
precise measurement of the corresponding oscillation parameters, $\dmsq23$ and
$\sinsq2t23$.neutrino sector may well be within our reach. The full potential
of the NuMI neutrino beam can be exploited by complementing the MINOS detector,
under construction, with a new detector(s) placed at some off-axis position and
collecting data in parallel with MINOS. The first phase of the proposed program
includes a new detector, optimized for $\nue$ detection, with a fiducial mass
of the order of 20 kton and exposed to neutrino and antineutrino beams. In a
five year run its sensitivity to the $\numutonue$ oscillations will be at least
a factor of ten beyond the current limit.
  The future direction of the program will depend on the results of this first
phase, but it is very likely that it will be a combination of a significant
increase of the neutrino beam intensity via an upgraded proton source and an
increase of the detector mass by a factor of five or so. Depending on the
circumstances, the goals of Phase II may be a further increase of the
sensitivity of a search for $\numutonue$ oscillations, or, perhaps, a
measurement of the CP violating phase $\delta$ in the lepton sector.


  A (bounded) manifold of circular type is a complex manifold M of dimension n
admitting a (bounded) exhaustive real function u, defined on M minus a point
x_o, so that: a) it is a smooth solution on $M\setminus {x_o}$ to the
Monge-Amp\`ere equation $(d d^c u)^n = 0$; b) x_o is a singular point for u of
logarithmic type and e^u extends smoothly on the blow up of M at x_o; c) $d d^c
(e^u) >0$ at any point of $M\setminus {x_o}$. This class of manifolds naturally
includes all smoothly bounded, strictly linearly convex domains and all
smoothly bounded, strongly pseudoconvex circular domains of $\bC^n$. The moduli
spaces of bounded manifolds of circular type are studied. In particular, for
each biholomorphic equivalence class of them it is proved the existence of an
essentially unique manifold in normal form. It is also shown that the class of
normalizing maps for an n-dimensional manifold M is a new holomorphic invariant
with the following property: it is parameterized by the points of a finite
dimensional real manifold of dimension n^2 when M is a (non-convex) circular
domain while it is of dimension $n^2 + 2 n$ when M is a strictly convex domain.
New characterizations of the circular domains and of the unit ball are also
obtained.


  In this paper we discuss the restrictions of the spacetime for the standard
model of cosmology by using results of the differential topology of 3- and
4-manifolds. The smoothness of the cosmic evolution is the strongest
restriction. The Poincare model (dodecaeder model), the Picard horn and the
3-torus are ruled out by the restrictions but a sum of two Poincare spheres is
allowed.


  We present G-MSM (Graph-based Multi-Shape Matching), a novel unsupervised
learning approach for non-rigid shape correspondence. Rather than treating a
collection of input poses as an unordered set of samples, we explicitly model
the underlying shape data manifold. To this end, we propose an adaptive
multi-shape matching architecture that constructs an affinity graph on a given
set of training shapes in a self-supervised manner. The key idea is to combine
putative, pairwise correspondences by propagating maps along shortest paths in
the underlying shape graph. During training, we enforce cycle-consistency
between such optimal paths and the pairwise matches which enables our model to
learn topology-aware shape priors. We explore different classes of shape graphs
and recover specific settings, like template-based matching (star graph) or
learnable ranking/sorting (TSP graph), as special cases in our framework.
Finally, we demonstrate state-of-the-art performance on several recent shape
correspondence benchmarks, including real-world 3D scan meshes with topological
noise and challenging inter-class pairs.


  Differential cross sections and photon beam asymmetries for the gamma p ->
pi+ n reaction have been measured for 0.6<cos(theta)<1 and Egamma=1.5-2.95 GeV
at SPring-8/LEPS. The cross sections monotonically decrease as the photon beam
energy increases for 0.6<cos(theta)<0.9. However, the energy dependence of the
cross sections for 0.9<cos(theta)<1 and Egamma=1.5-2.2 GeV (W=1.9-2.2 GeV) is
different, which may be due to a nucleon or Delta resonance. The present cross
sections agree well with the previous cross sections measured by other groups
and show forward peaking, suggesting significant t-channel contributions in
this kinematical region. The asymmetries are found to be positive, which can be
explained by rho-exchange in the t-channel. Large positive asymmetries in the
small |t| region, where the rho-exchange contribution becomes small, could be
explained by introducing pi-exchange interference with the s-channel.


  The spectrum of virtual photons for nuclei of Pb-208 at big hadron collider
energy is analysed. Cross-sections of inelastic Coulomb collisions accompanied
with evaporation of one to four neutrons by one of the partners are calculated.
By making use of the Glauber's method, executed estimates of neutron
multiplicity resulting from the Coulomb desintehration of the nuclei. The
predicted neutron multiplicity reaches 30-40 and more for each of the partners.
Neutrons are accompanied by emitted fast protons and other charged particles,
on the average three-five particles for each partner. The majority of the
particles of a kulonovsky origin are characterized with small rapiditty and can
thus be registered with ZDCs.


  Aoristic data can be described by a marked point process in time in which the
points cannot be observed directly but are known to lie in observable
intervals, the marks. We consider Bayesian state estimation for the latent
points when the marks are modelled in terms of an alternating renewal process
in equilibrium and the prior is a Markov point point process. We derive the
posterior distribution, estimate its parameters and present some examples that
illustrate the influence of the prior distribution.


  These are expanded notes of four introductory talks on A-infinity algebras,
their modules and their derived categories.


  We explore the possible impact of galactic and extragalactic foregrounds on
measurements of the cosmic microwave background (CMB). We find that, given our
present understanding of the foregrounds, they are unlikely to qualitatively
affect the ability of the MAP and Planck satellites to determine the angular
power spectrum of the CMB, the key statistic for constraining cosmological
parameters. Sufficiently far from the galactic plane, the only foregrounds that
will affect power spectrum determination with any significance are the
extragalactic ones. For MAP we find the most troublesome foregrounds are radio
point sources and the thermal Sunyaev-Zeldovich (SZ) effect. For Planck they
are these same radio point sources and the Far Infrared Background. Prior
knowledge of the statistics of the SZ component (either via theoretical
calculation, or higher frequency observations of just a few percent of the sky,
such as will be done by balloon-borne experiments) may significantly improve
MAP's determination of the CMB power spectrum. We also explore the foreground
impact on MAP and Planck polarization power spectrum measurements.


  The half-life of the $^{20}$F ground state has been measured using a
radioactive beam implanted in a plastic scintillator and recording
$\beta\gamma$ coincidences together with four CsI(Na) detectors. The result,
$T_{1/2} = 11.0011(69)_{\rm stat}(30)_{\rm sys}$~s, is at variance by 17
combined standard deviations with the two most precise results. The present
value revives the poor consistency of results for this half-life and calls for
a new measurement, with a technique having different sources of systematic
effects, to clarify the discrepancy.


  We discuss the lift of certain D6-antiD6-brane systems to M-theory. These are
purely gravitational configurations with a bolt singularity. When reduced along
a trivial circle, and for large bolt radius, the bolt is related to a
non-supersymmetric orbifold type of singularity where some closed string
tachyons are expected in the twisted sectors. This is a kind of open-closed
string duality that relates open string tachyons on one side and localised
tachyons in the other. We consider the evolution of the system of branes from
M-theory point of view. This evolution gives rise to a brane-antibrane
annihilation on the brane side. On the gravity side, the evolution is related
to a reduction of the order of the orbifold and to a contraction of the bolt to
a nut or flat space if the system has non-vanishing or vanishing charge,
respectively. We also consider the inverse process of reducing a
non-supersymmetric orbifold to a D6-brane system. For $C^2/Z_N\times Z_M$, the
reduced system is a fractional D6-brane at an orbifold singularity $C/Z_M$.


  In this paper is considered a problem of defining natural star-products on
symplectic manifolds, admissible for quantization of classical Hamiltonian
systems. First, a construction of a star-product on a cotangent bundle to an
Euclidean configuration space is given with the use of a sequence of pair-wise
commuting vector fields. The connection with a covariant representation of such
a star-product is also presented. Then, an extension of the construction to
symplectic manifolds over flat and non-flat pseudo-Riemannian configuration
spaces is discussed. Finally, a coordinate free construction of related quantum
mechanical operators from Hilbert space over respective configuration space is
presented.


  The chromomagnetic vacuum of SU(2) gluodynamics is considered in the
background of a finite radius flux tube (center-vortex) with homogeneous field
inside and zero field outside. In this background there are tachyonic modes.
These modes cause an instability. It is assumed that the selfinteraction of
these modes stops the creation of gluons and that a condensate will be formed.
For constant condensates, the minimum of the effective potential is found on
the tree level. In the background of these condensates, all tachyonic modes
acquire nonzero, real masses which will result in a real effective potential of
this system.
  Considering only the tachyonic modes and adding the energy of the background
field, the total energy is found to have a minimum at some value of the
background field, which depends on the coupling of the initial SU(2) model. For
small coupling, this dependence is polynomial in distinction from the Savvidy
vacuum where it is exponentially suppressed. The minimum of this energy will
deepens with shrinking radius of the flux tube. It can be expected that this
process can be stopped by adding quantum effects. Using the high temperature
expansion of the effective potential, it can be expected that the symmetry,
which is broken by the condensate, will be restored at sufficiently high
temperature.


  We investigate the vortex phase diagram in untwinned YBaCuO single crystals
with columnar defects. These randomly distributed defects, produced by heavy
ion irradiation, are expected to induce a ``Bose Glass'' phase of localized
vortices characterized by a vanishing resistance and a Meissner effect for
magnetic fields transverse to the defect axis. We directly observe the
transverse Meissner effect using an array of Hall probe magnetometers. As
predicted, the Meissner state breaks down at temperatures Ts that decrease
linearly with increasing transverse magnetic field. However, Ts falls well
below the conventional melting temperature Tm determined by a vanishing
resistivity, suggesting an intermediate regime where flux lines are effectively
localized even when rotated off the columnar defects.


  We generalize the Chebotarev density formulas of Dawsey (2017) and Alladi
(1977) to the setting of arbitrary finite Galois extensions of number fields
$L/K$. In particular, if $C \subset G = \textrm{Gal}(L/K)$ is a conjugacy
class, then we establish that the Chebotarev density is the following limit of
partial sums of ideals of $K$: \[ -\lim_{X\rightarrow\infty}
\sum_{\substack{2\leq N(I)\leq X \\ I \in S(L/K; C)}} \frac{\mu_K(I)}{N(I)} =
\frac{|C|}{|G|}, \] where $\mu_K(I)$ denotes the generalized M\"obius function
and $S(L/K;C)$ is the set of ideals $I\subset \mathcal{O}_K$ such that $I$ has
a unique prime divisor $\mathfrak{p}$ of minimal norm and the Artin symbol
$\left[\frac{L/K}{\mathfrak{p}}\right]$ is $C$. To obtain this formula, we
generalize several results from classical analytic number theory, as well as
Alladi's concept of duality for minimal and maximal prime divisors, to the
setting of ideals in number fields.


  We present a novel approximate inference method for diffusion processes,
based on the Wasserstein gradient flow formulation of the diffusion. In this
formulation, the time-dependent density of the diffusion is derived as the
limit of implicit Euler steps that follow the gradients of a particular free
energy functional. Existing methods for computing Wasserstein gradient flows
rely on discretization of the domain of the diffusion, prohibiting their
application to domains in more than several dimensions. We propose instead a
discretization-free inference method that computes the Wasserstein gradient
flow directly in a space of continuous functions. We characterize approximation
properties of the proposed method and evaluate it on a nonlinear filtering
task, finding performance comparable to the state-of-the-art for filtering
diffusions.


  Bayesian Optimization (BO) has shown significant success in tackling
expensive low-dimensional black-box optimization problems. Many optimization
problems of interest are high-dimensional, and scaling BO to such settings
remains an important challenge. In this paper, we consider generalized additive
models in which low-dimensional functions with overlapping subsets of variables
are composed to model a high-dimensional target function. Our goal is to lower
the computational resources required and facilitate faster model learning by
reducing the model complexity while retaining the sample-efficiency of existing
methods. Specifically, we constrain the underlying dependency graphs to tree
structures in order to facilitate both the structure learning and optimization
of the acquisition function. For the former, we propose a hybrid graph learning
algorithm based on Gibbs sampling and mutation. In addition, we propose a novel
zooming-based algorithm that permits generalized additive models to be employed
more efficiently in the case of continuous domains. We demonstrate and discuss
the efficacy of our approach via a range of experiments on synthetic functions
and real-world datasets.


  The simplest orientifolds of the WZW models are obtained by gauging a Z_2
symmetry group generated by a combined involution of the target Lie group G and
of the worldsheet. The action of the involution on the target is by a twisted
inversion g \mapsto (\zeta g)^{-1}, where \zeta is an element of the center of
G. It reverses the sign of the Kalb-Ramond torsion field H given by a
bi-invariant closed 3-form on G. The action on the worldsheet reverses its
orientation. An unambiguous definition of Feynman amplitudes of the orientifold
theory requires a choice of a gerbe with curvature H on the target group G,
together with a so-called Jandl structure introduced in hep-th/0512283. More
generally, one may gauge orientifold symmetry groups \Gamma = Z_2 \ltimes Z
that combine the Z_2-action described above with the target symmetry induced by
a subgroup Z of the center of G. To define the orientifold theory in such a
situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We
reduce the study of the existence of such structures and of their inequivalent
choices to a problem in group-\Gamma cohomology that we solve for all simple
simply-connected compact Lie groups G and all orientifold groups \Gamma = Z_2
\ltimes Z.


  In this paper we have studied the influence of reversed shear on the
improvement of the confinement's quality in the plasma of tokamak and
especially in reducing the anomalous transport. For that, we have used a
special model for the drift wave fields. Comparison between particles
trajectories for normal and reversed shear is carried out in 2 D and 3 D
presentation. Also, the diffusion coefficient of particles for the two cases,
normal and negative shear, is evaluated.


  Cloud computing for high performance computing resources is an emerging
topic. This service is of interest to researchers who care about reproducible
computing, for software packages with complex installations, and for companies
or researchers who need the compute resources only occasionally or do not want
to run and maintain a supercomputer on their own. The connection between HPC
and containers is exemplified by the fact that Microsoft Azure's Eagle cloud
service machine is number three on the November 23 Top 500 list. For cloud
services, the HPC application and dependencies are installed in containers,
e.g. Docker, Singularity, or something else, and these containers are executed
on the physical hardware. Although containerization leverages the existing
Linux kernel and should not impose overheads on the computation, there is the
possibility that machine-specific optimizations might be lost, particularly
machine-specific installs of commonly used packages. In this paper, we will use
an astrophysics application using HPX-Kokkos and measure overheads on
homogeneous resources, e.g. Supercomputer Fugaku, using CPUs only and on
heterogenous resources, e.g. LSU's hybrid CPU and GPU system. We will report on
challenges in compiling, running, and using the containers as well as
performance performance differences.


  The Hubble tension, revealed by a $\sim 5\sigma$ discrepancy between
measurements of the Hubble-Lemaitre constant from early- and local-Universe
observations, is one of the most significant problems in modern cosmology. In
order to better understand the origin of this mismatch, independent techniques
to measure $H_0$, such as strong lensing time delays, are required. Notably,
the sample size of such systems is key to minimising statistical uncertainties
and cosmic variance, which can be improved by exploring the datasets of
large-scale sky surveys like DESI (Dark Energy Spectroscopic Instrument). We
identify possible strong lensing time-delay systems within DESI by selecting
candidate multiply imaged lensed quasars from a catalogue of 24,440,816
candidate QSOs contained in the 9th data release of the DESI Legacy Imaging
Surveys (DESI-LS). Using a friend-of-friends-like algorithm on spatial
co-ordinates, our method generates an initial list of compact quasar groups.
This list is subsequently filtered using a measure of the similarity of colours
of a group's members and the likelihood that they are quasars. A visual
inspection finally selects candidate strong lensing systems based on the
spatial configuration of the group members. We identify 620 new candidate
multiply imaged lensed quasars (101 Grade-A, 214 Grade-B, 305 Grade-C). This
number excludes 53 known spectroscopically confirmed systems and existing
candidate systems identified in other similar catalogues. When available, these
new candidates will be further checked by combining the spectroscopic and
photometric data from DESI. The catalogues and images of the candidates in this
work are available online
(https://github.com/EigenHermit/lensed_qso_cand_catalogue_He-22/).