  The mathematical relations between the regular Coulomb function
$F_{\eta\ell}(\rho)$ and the irregular Coulomb functions
$H^\pm_{\eta\ell}(\rho)$ and $G_{\eta\ell}(\rho)$ are obtained in the complex
plane of the variables $\eta$ and $\rho$ for integer or half-integer values of
$\ell$. These relations, referred to as "connection formulas", form the basis
of the theory of Coulomb wave functions, and play an important role in many
fields of physics, especially in the quantum theory of charged particle
scattering. As a first step, the symmetry properties of the regular function
$F_{\eta\ell}(\rho)$ are studied, in particular under the transformation
$\ell\mapsto-\ell-1$, by means of the modified Coulomb function
$\Phi_{\eta\ell}(\rho)$, which is entire in the dimensionless energy
$\eta^{-2}$ and the angular momentum $\ell$. Then, it is shown that, for
integer or half-integer $\ell$, the irregular functions
$H^\pm_{\eta\ell}(\rho)$ and $G_{\eta\ell}(\rho)$ can be expressed in terms of
the derivatives of $\Phi_{\eta,\ell}(\rho)$ and $\Phi_{\eta,-\ell-1}(\rho)$
with respect to $\ell$. As a consequence, the connection formulas directly lead
to the description of the singular structures of $H^\pm_{\eta\ell}(\rho)$ and
$G_{\eta\ell}(\rho)$ at complex energies in their whole Riemann surface. The
analysis of the functions is supplemented by novel graphical representations in
the complex plane of $\eta^{-1}$.


  The dynamic polarization for kekul\'e-patterned graphene is studied within
the Random Phase Approximation (RPA). It is shown how the breaking of the
valley degeneracy by the lattice modulation is manifested through the
dielectric spectrum, the plasmonic dispersion, the static screening and the
optical conductivity. The valley-dependent splitting of the Fermi velocities
due to the kekul\'e distortion leads to a similar splitting in the dielectric
spectrum of graphene, introducing new characteristic frequencies, which are
given in terms of the valley-coupling amplitude. The valley coupling also
splits the plasmonic dispersion, introducing a second branch in the Landau
damping region. Finally, the signatures of the broken valley degeneracy in the
optical conductivity are studied. The characteristic step-like spectrum of
graphene is split into two half steps due to the onset of absorption in each
valley occurring at different characteristic frequencies. Also, it was found an
absorption phenomenon where a resonance peak related to intervalley transport
emerges at a "beat frequency", determined by the difference between the
characteristic frequencies of each valley. Some of these mechanisms are
expected to be present in other space-modulated 2D materials and suggest how
optical or electrical response measurements can be suitable to detect spatial
modulation.


  Oriented Strontium Ferrite films with the c axis orientation were deposited
with varying oxygen partial pressure on Al2O3(0001) substrate using PLD
technique. The angle dependent magnetic hysteresis, remanent coercivity and
temperature dependent coercivity had been employed to understand the
magnetization reversal of these films. It was found that the Strontium Ferrite
thin film grown at lower (higher) oxygen partial pressure shows
Stoner-Wohlfarth type (Kondorsky like) reversal. The relative importance of
pinning and nucleation processes during magnetization reversal is used to
explain the type of the magnetization reversal with different oxygen partial
pressure during growth.


  We study a new formulation for the eikonal equation |grad u| =1 on a bounded
subset of R^2. Instead of a vector field grad u, we consider a field P of
orthogonal projections on 1-dimensional subspaces, with div P in L^2. We prove
existence and uniqueness for solutions of the equation P div P=0. We give a
geometric description, comparable with the classical case, and we prove that
such solutions exist only if the domain is a tubular neighbourhood of a regular
closed curve. The idea of the proof is to apply a generalized method of
characteristics introduced in Jabin, Otto, Perthame, "Line-energy
Ginzburg-Landau models: zero-energy states", Ann. Sc. Norm. Super. Pisa Cl.
Sci. (5) 1 (2002), to a suitable vector field m satisfying P = m \otimes m.
  This formulation provides a useful approach to the analysis of stripe
patterns. It is specifically suited to systems where the physical properties of
the pattern are invariant under rotation over 180 degrees, such as systems of
block copolymers or liquid crystals.


  The manipulation of LIBOR by a group of banks became one of the major blows
to the remaining confidence in financial industry. Yet, despite an enormous
amount of popular literature on the subject, rigorous time-series studies are
few. In my paper, I discuss the following hypothesis. Namely, if we should
assume for a statistical null, the quotes, which were submitted by the member
banks were true, the deviations from the LIBOR should have been entirely random
because they were determined by idiosyncratic conditions by the member banks.
This hypothesis can be statistically verified. Serial correlations of the
rates, which cannot be explained by the differences in credit qualities of the
member banks or the domicile Governments, were subjected to correlation tests.
A new econometric method--the analysis of the Wigner-Ville function borrowed
from quantum mechanics and signal processing--is used and explained for the
statistical interpretation of regression residuals.


  We first show that the braid group over a graph topologically containing no
$\Theta$-shape subgraph has a presentation related only by commutators. Then
using discrete Morse theory and triple Massey products, we prove that a graph
topologically contains none of four prescribed graphs if and only if its
4-braid groups is a right-angled Artin group.


  The ITER ICRF system will gain in complexity relative to the existing systems
on modern devices, and the same will hold true for DEMO. The accumulated
experience can help greatly in designing an ICRF system for DEMO. In this paper
the current status of the pre-conceptual design of the DEMO ICRF antenna and
some related components is presented. While many aspects strongly resemble the
ITER system, in some design solutions we had to take an alternative route to be
able to adapt to DEMO specific. One of the key points is the toroidal antenna
extent needed for the requested ICRF heating performance, achieved by splitting
the antenna in halves, with appropriate installation. Modelling of the so far
largest ICRF antenna in RAPLICASOL and associated challenges are presented.
Calculation are benchmarked with TOPICA. Results of the analysis of the latest
model and an outlook for future steps are given.


  The dust component of the interstellar medium (ISM) has been extensively
studied in the past decades. Late-type stars have been assumed as the main
source of dust to the ISM, but recent observations show that supernova remnants
may play a role on the ISM dust feedback. In this work, I study the importance
of low and high mass stars, as well as their evolutionary phase, on the ISM
dust feedback process. I also determine the changes on the obtained results
considering different mass distribution functions and star formation history.
We describe a semi-empirical calculation of the relative importance of each
star at each evolutionary phase in the dust ejection to the ISM. I compare the
obtained results for two stellar mass distribution functions, the classic
Salpeter initial mass function and the present day mass function. I used the
evolutionary track models for each stellar mass, and the empirical mass-loss
rates and dust-to-gas ratio. The relative contribution of each stellar mass
depends on the used distribution. Ejecta from massive stars represent the most
important objects for the ISM dust replenishment using the Salpeter IMF. On the
other hand, for the present day mass function low and intermediate mass stars
are dominant. Late-type giant and supergiant stars dominate the ISM dust
feedback in our actual Galaxy, but this may not the case of galaxies
experiencing high star formation rates, or at high redshifts. In those cases,
SNe are dominant in the dust feedback process.


  We use recent HST colour-magnitude diagrams of the resolved stellar
populations of a sample of local dSph galaxies (Carina, LeoI, LeoII, Ursa Minor
and Draco) to infer the star formation histories of these systems, $SFR(t)$.
Applying a new variational calculus maximum likelihood method which includes a
full Bayesian analysis and allows a non-parametric estimate of the function one
is solving for, we infer the star formation histories of the systems studied.
This method has the advantage of yielding an objective answer, as one need not
assume {\it a priori} the form of the function one is trying to recover. The
results are checked independently using Saha's $W$ statistic. The total
luminosities of the systems are used to normalize the results into physical
units and derive SN type II rates. We derive the luminosity weighted mean star
formation history of this sample of galaxies.


  We convincingly argue that the true dynamical and gauge structures of the QCD
ground state are much more complicated than its Lagrangian exact gauge symmetry
supposes to be. The dynamical source of these complications has been identified
with the tadpole/seagull term, which renormalized version called, {\sl the mass
gap}. It is explicitly present in the full gluon self-energy. The true
dynamical role of the mass gap was hidden in the QCD ground state. To disclose
it the splintering between the transverse conditions for the full gluon
self-energy and its subtracted counterpart has been derived. We have
established the equation of motion for the full gluon propagator on account of
the mass gap. It allows to fix the dynamical and gauge structures of the full
gluon propagator with a newly-derived generalized gauge. It is uniquely given
as a function of the gluon momentum. All this makes it possible to present
novel non-perturbative analytical approach to QCD, which we call the mass gap
approach. It extends the mass gap concept to be accounted for the QCD ground
state as well. We have found the general non-perturbative solution for the full
gluon propagator with exactly defined finite gluon pole mass, and it is
different from the excitations with the effective gluon masses. Despite the
exact gauge symmetry is broken in the ground state, the renormalizability of
the theory is not affected due to the important role of the Slavnov-Taylor
identity in the renormalization beyond the perturbation theory. For this the
non-perturbative multiplicative renormalization program for the full massive
gluon propagator has been formulated. Our approach does not allow the massive
gluons to be the mass-shell objects, and thus prevents them to appear as
physical states at large distances (confinement of massive gluons).


  We construct a conformal map from $\mathbb{R}^3$ to a three-dimensional
spheriod, which includes $\mathbb{S}^3$, a double-cover of the 3-ball, and
$\mathbb{R} \times \mathbb{S}^2$ as limiting cases. Using the data of the
critical three-dimensional Ising model on $\mathbb{R}^3$ that was computed
using the conformal bootstrap method, we numerically estimate the fourth-order
Binder cumulant of the critical three-dimensional $\phi^4$ theory on
$\mathbb{S}^3$. We expect this estimate will enable an interesting comparison
between the conformal bootstrap and future calculations of critical $\phi^4$
theory on $\mathbb{S}^3$ using the Quantum Finite Element (QFE) method.


  We show that for any po sitive integer $m$, there exist order $n$ Stein
corks. The boundaries are cyclic branched covers of slice knots embedded in the
boundary of corks. By applying these corks to generalized forms, we give a
method producing examples of many finite order corks, which are possibly not
Stein cork.


  One of the most effective algorithms for differentially private learning and
optimization is objective perturbation. This technique augments a given
optimization problem (e.g. deriving from an ERM problem) with a random linear
term, and then exactly solves it. However, to date, analyses of this approach
crucially rely on the convexity and smoothness of the objective function,
limiting its generality. We give two algorithms that extend this approach
substantially. The first algorithm requires nothing except boundedness of the
loss function, and operates over a discrete domain. Its privacy and accuracy
guarantees hold even without assuming convexity. This gives an oracle-efficient
optimization algorithm over arbitrary discrete domains that is comparable in
its generality to the exponential mechanism. The second algorithm operates over
a continuous domain and requires only that the loss function be bounded and
Lipschitz in its continuous parameter. Its privacy analysis does not require
convexity. Its accuracy analysis does require convexity, but does not require
second order conditions like smoothness. Even without convexity, this algorithm
can be generically used as an oracle-efficient optimization algorithm, with
accuracy evaluated empirically. We complement our theoretical results with an
empirical evaluation of the non-convex case, in which we use an integer program
solver as our optimization oracle. We find that for the problem of learning
linear classifiers, directly optimizing for 0/1 loss using our approach can
out-perform the more standard approach of privately optimizing a
convex-surrogate loss function on the Adult dataset.


  Wildfires are natural disasters capable of damaging economies and
communities. When wildfires become uncontrollable, Incident Manager Teams
(IMT's) dispatch response vehicles to key assets to undertake protective tasks
and so mitigate the risk to these assets. In developing a deployment plan under
severe time pressure, IMT's need to consider the special requirements of each
asset, the resources (vehicles and their teams), as well as uncertainties
associated with the wildfire. A common situation that arises in southern
Australian wildfires is a wind change. There is a reliable forecast of a wind
change, but some uncertainty around the timing of that change. To assist IMT's
to deal with this situation we develop a two-stage stochastic model to
integrate such an uncertainty with the complexities of asset protection
operations. This is the first time a mathematical model is proposed which
considers uncertainty in the timing of a scenario change. The model is
implemented for a case study that uses the context of the 2009 Black Saturday
bushfires in Victoria. A new set of benchmark instances is generated using
realistic wildfire attributes to test the computational tractability of our
model and the results compared to a dynamic rerouting approach. The
computations reveal that, compared with dynamic rerouting, the new model can
generate better deployment plans. The model can achieve solutions in
operational time for realistic-sized problems, although for larger problems the
sub-optimal rerouting algorithm would still need to be deployed.


  We develop a non-perturbative bosonization approach for bilayer quantum Hall
systems at \nu_T = 1, which allows us to systematically study the existence of
an exciton condensate in these systems. An effective boson model is derived and
the excitation spectrum is calculated both in the Bogoliubov and in the Popov
approximations. In the latter case, we show that the ground state of the system
is an exciton condensate only when the distance between the layers is very
small compared to the magnetic length, indicating that the system possibly
undergoes another phase transition before the incompressible-compressible one.
The effect of a finite electron interlayer tunnelling is included and a
quantitative phase diagram is proposed.


  We investigate the analogue effect of the Aharonov-Bohm effect for bound
states in two relativistic quantum systems in a spacetime with a space-like
dislocation. We assume that the topological defect has an internal magnetic
flux. Then, we analyse the interaction of a charged particle with a uniform
magnetic field in this topological defect spacetime, and thus, we extend this
analysis to the confinement to a hard-wall potential and a linear scalar
potential. Later, the interaction of the Klein-Gordon oscillator with a uniform
magnetic field is analysed. We first focus on the effects of torsion that stem
from the spacetime with a space-like dislocation and the geometric quantum
phase. Then, we analyse the effects of torsion and the geometric quantum phase
under the presence of a hard-wall potential and a linear scalar potential.


  We start by asking an interesting yet challenging question, "If an eyewitness
can only recall the eye features of the suspect, such that the forensic artist
can only produce a sketch of the eyes (e.g., the top-left sketch shown in Fig.
1), can advanced computer vision techniques help generate the whole face
image?" A more generalized question is that if a large proportion (e.g., more
than 50%) of the face/sketch is missing, can a realistic whole face
sketch/image still be estimated. Existing face completion and generation
methods either do not conduct domain transfer learning or can not handle large
missing area. For example, the inpainting approach tends to blur the generated
region when the missing area is large (i.e., more than 50%). In this paper, we
exploit the potential of deep learning networks in filling large missing region
(e.g., as high as 95% missing) and generating realistic faces with
high-fidelity in cross domains. We propose the recursive generation by
bidirectional transformation networks (r-BTN) that recursively generates a
whole face/sketch from a small sketch/face patch. The large missing area and
the cross domain challenge make it difficult to generate satisfactory results
using a unidirectional cross-domain learning structure. On the other hand, a
forward and backward bidirectional learning between the face and sketch domains
would enable recursive estimation of the missing region in an incremental
manner (Fig. 1) and yield appealing results. r-BTN also adopts an adversarial
constraint to encourage the generation of realistic faces/sketches. Extensive
experiments have been conducted to demonstrate the superior performance from
r-BTN as compared to existing potential solutions.


  The stochastic protein kinetic equations can be stiff for certain parameters,
which makes their numerical simulation rely on very small time step sizes,
resulting in large computational cost and accumulated round-off errors. For
such situation, we provide a method of reducing stiffness of the stochastic
protein kinetic equation by means of a kind of variable transformation.
Theoretical and numerical analysis show effectiveness of this method. Its
generalization to a more general class of stochastic differential equation
models is also discussed.


  We propose a mechanism displaying confinement, as defined by the behavior of
the propagators, for 4 dimensional, N = 1 supersymmetric Yang-Mills theory in
superfield formalism. In this work we intend to verify the possibility of
extending the known Gribov problem of quantization of Yang-Mills theories and
the implementation of a local action with auxiliary superfields like
Gribov-Zwanziger approach to this problem.


  In this paper, the nilspace approach to higher-order Fourier analysis is
developed in the setting of vector spaces over a prime field $\mathbb{F}_p$,
with applications mainly in ergodic theory. A key requisite for this
development is to identify a class of nilspaces adequate for this setting. We
introduce such a class, whose members we call $p$-homogeneous nilspaces. One of
our main results characterizes these objects in terms of a simple algebraic
property. We then prove various further results on these nilspaces, leading to
a structure theorem describing every finite $p$-homogeneous nilspace as the
image, under a nilspace fibration, of a member of a simple family of filtered
finite abelian $p$-groups. The applications include a description of the
Host-Kra factors of ergodic $\mathbb{F}_p^\omega$-systems as $p$-homogeneous
nilspace systems. This enables the analysis of these factors to be reduced to
the study of such nilspace systems, with central questions on the factors thus
becoming purely algebraic problems on finite nilspaces. We illustrate this
approach by proving that for $k\leq p+1$ the $k$-th Host-Kra factor is an
Abramov system of order $\leq k$, extending a result of Bergelson-Tao-Ziegler
that holds for $k< p$. We illustrate the utility of $p$-homogeneous nilspaces
also by showing that the above-mentioned structure theorem yields a new proof
of the Tao-Ziegler inverse theorem for Gowers norms on $\mathbb{F}_p^n$.


  S. Banach, in particular, proved that for any function, even $f(x) = 1,$
where $x\in[0,1],$ the convergence of its Fourier series with respect to the
general orthonormal systems (ONS) is not guaranteed. In this paper, we find
conditions for the functions $\varphi_{n}$ of an ONS $(\varphi_n),$ under which
the Fourier series of functions $f\in Lip_1$ are unconditionally convergent
almost everywhere. During our research, we mainly used the properties of the
sequences of linear functionals on the Banach spaces to prove the main theorems
we presented in this article. Our research has concluded that the
aforementioned conditions do exist and are the best possible in a certain
sense. We have also found that any ONS contains a subsystem such that the
Fourier series of any function $f\in Lip_1$ is unconditionally convergent.
Further, the precondition presented in Theorem \ref{theorem1.1}, which demands
that the Fourier series of the function $f=1$ be convergent, is adequate,
meaning that it does not make the actual conditions of Theorem \ref{theorem1.1}
redundant. We have shown that the solution for these types of problems for the
general ONS is trivial for the classical ONS (trigonometric, Haar, and Walsh
systems).


  Pre-trained multilingual language models show significant performance gains
for zero-shot cross-lingual model transfer on a wide range of natural language
understanding (NLU) tasks. Previously, for zero-shot cross-lingual evaluation,
pre-trained models are only fine-tuned on English data and tested on a variety
of target languages. In this paper, we do cross-lingual evaluation on various
NLU tasks (sentence classification, sequence labeling, question answering)
using prompt-tuning and compare it with fine-tuning. The results show that
prompt tuning achieves much better cross-lingual transfer than fine-tuning
across datasets, with only 0.1% to 0.3% tuned parameters. Additionally, we
demonstrate through the analysis that prompt tuning can have better
cross-lingual transferability of representations on downstream tasks with
better aligned decision boundaries.


  In online display advertising, selecting the most effective ad creative (ad
image) for each impression is a crucial task for DSPs (Demand-Side Platforms)
to fulfill their goals (click-through rate, number of conversions, revenue, and
brand improvement). As widely recognized in the marketing literature, the
effect of ad creative changes with the number of repetitive ad exposures. In
this study, we propose an efficient and easy-to-implement ad creative selection
algorithm that explicitly considers user's psychological status when selecting
ad creatives. The proposed system was deployed in a real-world production
environment and tested against the baseline algorithms. The results show
superiority of the proposed algorithm.


  Two steps phase shifting interferometry has been a hot topic in the recent
years. We present a comparison study of 12 representative self--tunning
algorithms based on two-steps phase shifting interferometry. We evaluate the
performance of such algorithms by estimating the phase step of synthetic and
experimental fringe patterns using 3 different normalizing processes: Gabor
Filters Bank (GFB), Deep Neural Networks (DNNs) and Hilbert Huang Transform
(HHT); in order to retrieve the background, the amplitude modulation and noise.
We present the variants of state-of-the-art phase step estimation algorithms by
using the GFB and DNNs as normalization preprocesses, as well as the use of a
robust estimator such as the median to estimate the phase step. We present
experimental results comparing the combinations of the normalization processes
and the two steps phase shifting algorithms. Our study demonstrates that the
quality of the retrieved phase from of two-step interferograms is more
dependent of the normalizing process than the phase step estimation method.


  We define discrete flat surfaces in hyperbolic 3-space from the perspective
of discrete integrable systems and prove properties that justify the
definition. We show how these surfaces correspond to previously defined
discrete constant mean curvature 1 surfaces in hyperbolic 3-space, and we also
describe discrete focal surfaces (discrete caustics) that can be used to define
singularities on discrete flat surfaces. We also examine discrete linear
Weingarten surfaces of Bryant type in hyperbolic 3-space, and consider an
example of a discrete flat surface related to the Airy equation that exhibits
swallowtail singularities and a Stokes phenomenon.


  We have revisited the fragment-asperity interaction model recently introduced
by Sotolongo-Costa and Posadas (Physical Review Letters 92, 048501, 2004) by
considering a different definition for mean values in the context of Tsallis
nonextensive statistics and introducing a new scale between the earthquake
energy and the size of fragment $\epsilon \propto r^3$. The energy distribution
function (EDF) deduced in our approach is considerably different from the one
obtained in the above reference. We have also tested the viability of this new
EDF with data from two different catalogs (in three different areas), namely,
NEIC and Bulletin Seismic of the Revista Brasileira de Geof\'{\i}sica. Although
both approaches provide very similar values for the nonextensive parameter $q$,
other physical quantities, e.g., the energy density differs considerably, by
several orders of magnitude.


  Graphene has attracted much attention as one of promising candidates of
future high-speed transistor materials because of its high carrier mobility of
more than 10,000 cm2 V-1 s-1. Up to this point, we have focused on the contact
properties as performance killers, as a very small density of states in
graphene might suppress the current injection from metal to graphene. This
paper systematically reviews the metal/graphene contact properties and
discusses the present status and future requirements of the specific contact
resistivity.


  In this paper, a novel optimal technique for joint angles trajectory tracking
control with energy optimization for a biped robot with toe foot is proposed.
For the task of climbing stairs by a 9-link biped model, a cycloid trajectory
for swing phase is proposed in such a way that the cycloid variables depend on
the staircase dimensions. Zero Moment Point(ZMP) criteria is taken for
satisfying stability constraint. This paper mainly can be divided into 3 steps:
1) Planning stable cycloid trajectory for initial step and subsequent step for
climbing upstairs and Inverse Kinematics using an unsupervised artificial
neural network with knot shifting procedure for jerk minimization. 2) Modeling
Dynamics for Toe foot biped model using Lagrange Dynamics along with contact
modeling using spring-damper system followed by developing Neural Network
Temporal Quantized Lagrange Dynamics which takes inverse kinematics output from
neural network as its inputs. 3) Using Ant Colony Optimization to tune PD
(Proportional Derivative) controller parameters and torso angle with the
objective to minimize joint space trajectory errors and total energy consumed.
Three cases with variable staircase dimensions have been taken and a brief
comparison is done to verify the effectiveness of our proposed work Generated
patterns have been simulated in MATLAB .


  Bacterial conglomerates such as biofilms and microcolonies are ubiquitous in
nature and play an important role in industry and medicine. In contrast to
well-mixed, diluted cultures routinely used in microbial research, bacteria in
a microcolony interact mechanically with one another and with the substrate to
which they are attached. Despite their ubiquity, little is known about the role
of such mechanical interactions on growth and biological evolution of microbial
populations. Here we use a computer model of a microbial colony of rod-shaped
cells to investigate how physical interactions between cells determine their
motion in the colony, this affects biological evolution. We show that the
probability that a faster-growing mutant "surfs" at the colony's frontier and
creates a macroscopic sector depends on physical properties of cells (shape,
elasticity, friction). Although all these factors contribute to the surfing
probability in seemingly different ways, they all ultimately exhibit their
effects by altering the roughness of the expanding frontier of the colony and
the orientation of cells. Our predictions are confirmed by experiments in which
we measure the surfing probability for colonies of different front roughness.
Our results show that physical interactions between bacterial cells play an
important role in biological evolution of new traits, and suggest that these
interaction may be relevant to processes such as de novo evolution of
antibiotic resistance.


  By leveraging the hyperfine interaction between the rotational and nuclear
spin degrees of freedom, we demonstrate extensive magnetic control over the
electric dipole moments, electric dipolar interactions, and ac Stark shifts of
ground-state alkali-dimer molecules such as KRb$(X^1\Sigma)$. The control is
enabled by narrow avoided crossings and the highly ergodic character of
molecular eigenstates at low magnetic fields, offering a general and robust way
of continuously tuning the intermolecular electric dipolar interaction for
applications in quantum simulation and sensing.


  Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime and a
uniform magnetic field are studied in the context of the so called,
metaphorically speaking, position-dependent mass (PDM) settings. We show that
the corresponding KG-equation collapses into a two-dimensional radial
Schr\"{o}dinger-Coulomb like model. The exact textbook solution of which is
used to find the energies and wave functions of KG-Coulombic particles (both
constant mass and PDM ones). In so doing, we consider, with $y=E/E_{P}$, four
pairs of rainbow functions: (a) $% g_{_{0}}\left( y\right) =1$, $g_{_{1}}\left(
y\right) =\sqrt{1-\epsilon y^{2}% }$, (b) $g_{_{0}}\left( y\right) =1$,
$g_{_{1}}\left( y\right) =\sqrt{% 1-\epsilon y}$, (c) $g_{_{0}}\left( y\right)
=g_{_{1}}\left( y\right) =\left( 1-\epsilon y\right) ^{-1}$, and (d) $g_{_{0}}(
y) =(e^{\epsilon y}-1) /\epsilon y$, $g_{_{1}}\left( y\right) =1$.
Interestingly, we observe that the first pair in (a) introduces the Planck
energy $E_{p}$ as a maximum possible KG-particle/antiparticle energy value.


  In quantum information processing, two primary research directions have
emerged: one based on discrete variables (DV) and the other on the structure of
quantum states in a continuous-variable (CV) space. It is increasingly
recognized that integrating these two approaches could unlock new potentials,
overcoming the inherent limitations of each. Here, we show that such a DV-CV
hybrid approach, applied to superconducting Kerr parametric oscillators (KPOs),
enables us to entangle a pair of Schr\"odinger's cat states by two
straightforward methods. The first method involves the entanglement-preserving
and deterministic conversion between Bell states in the Fock-state basis (DV
encoding) and those in the cat-state basis (CV encoding). This method would
allow us to construct quantum networks in the cat-state basis using
conventional schemes originally developed for the Fock-state basis. In the
second method, the $\sqrt{\textrm{iSWAP}}$ gate operation is implemented
between two cat states following the procedure used for Fock-state encoding.
This DV-like gate operation on CV encoding not only completes the demonstration
of a universal quantum gate set in a KPO system but also enables faster and
simpler gate operations compared to previous SWAP gate implementations on
bosonic modes. Our work offers a simple yet powerful application of DV-CV
hybridization while also highlighting the scalability of this planar KPO
system.


  We derive upper and lower bounds for the Assouad and lower dimensions of
self-affine measures in $\mathbb{R}^d$ generated by diagonal matrices and
satisfying suitable separation conditions. The upper and lower bounds always
coincide for $d=2,3$ yielding precise explicit formulae for the dimensions.
Moreover, there are easy to check conditions guaranteeing that the bounds
coincide for $d \geq 4$.
  An interesting consequence of our results is that there can be a `dimension
gap' for such self-affine constructions, even in the plane. That is, we show
that for some self-affine carpets of `Bara\'nski type' the Assouad dimension of
all associated self-affine measures strictly exceeds the Assouad dimension of
the carpet by some fixed $\delta>0$ depending only on the carpet. We also
provide examples of self-affine carpets of `Bara\'nski type' where there is no
dimension gap and in fact the Assouad dimension of the carpet is equal to the
Assouad dimension of a carefully chosen self-affine measure.


  The results of the first generation of submillimeter-wave surveys have been
published. The opening of this new window on the distant Universe has added
considerably to our understanding of the galaxy formation process, by revealing
a numerous population of very luminous distant galaxies. Most would have been
very difficult to identify using other methods. The potential importance of
selection effects, especially those connected with the spectral energy
distributions of the detected galaxies, for the interpretation of the results
are highlighted.


  A novel intelligent reflecting surface (IRS)-aided multi-robot network is
proposed, where multiple mobile wheeled robots are served by an access point
(AP) through non-orthogonal multiple access (NOMA). The goal is to maximize the
sum-rate of all robots by jointly optimizing trajectories and NOMA decoding
orders of robots, reflecting coefficients of the IRS, and the power allocation
of the AP, subject to the quality of service (QoS) of each robot. To tackle
this problem, a dueling double deep Q-network (D^{3}QN) based algorithm is
invoked for jointly determining the phase shift matrix and robots'
trajectories. Specifically, the trajectories for robots contain a set of local
optimal positions, which reveals that robots make the optimal decision at each
step. Numerical results demonstrated that the proposed D^{3}QN algorithm
outperforms the conventional algorithm, while the performance of IRS-NOMA
network is better than the orthogonal multiple access (OMA) network.


  Let $c, k_1,..., k_N $ be non-negative numbers, and define a measure $\mu $
in the wedge $W:= \{x\in \mathbb{R} ^N :\, x_i >0, i=1,...,N\} $ by $d\mu =
e^{c|x|^2} x_1 ^{k_1}...x_N ^{k_N} \, dx $. It is shown that among all
measurable subsets of $W$ with fixed $\mu$ -measure, the intersection of $W$
with a ball centered at the origin renders the weighted perimeter relative to
$W$ a minimum.


  The coupling between antiferromagnetic spins and infrared-active phonons in
solids is responsible for many intriguing phenomena and is a field of intense
research with extensive potential applications in the modern devices based on
antiferromagnetic spintronics and phononics. Insulating rutile
antiferromagnetic crystal CoF$_2$ is one of the model materials for studying
nonlinear magnetophononics due to the strong spin-lattice coupling as a result
of the orbitally degenerate ground state of Co$^{2+}$ ions manifested in the
plethora of static and induced piezomagnetic effects. Here we report results on
the complete infrared spectroscopy study of lattice and magnetic dynamics in
CoF$_2$ in a wide temperature range and their careful analysis. We observed
that infrared-active phonons demonstrate frequency shifts at the
antiferromagnetic ordering. Furthermore, using first-principles calculations,
we examined the lattice dynamics and disclosed that these frequency shifts are
rather due to the spin-phonon coupling than geometrical lattice effects. Next
we found that the low-frequency dielectric permittivity demonstrates distinct
changes at the antiferromagnetic ordering due to the spontaneous
magnetodielectric effect caused by the behavior of infrared-active phonons. In
addition, we have observed magnetic excitations in the infrared spectra and
identified their magnetodipole origin. To strengthen our conclusions, we
analyze the theoretical phonon-magnon coupling overall phonons at the $\Gamma$
point. We conclude that the largest effect comes from the $A_{1g}$ and $B_{2g}$
Raman-active modes. As such, our results establish a solid basis for further
investigations and more deeper understanding of the coupling of phonons with
spins and magnetic excitations in antiferromagnets.


  Meta-analysis techniques have been widely developed and applied in genomic
applications, especially for combining multiple transcriptomic studies. In this
paper we propose an order statistic of $p$-values ($r$th ordered $p$-value,
rOP) across combined studies as the test statistic. We illustrate different
hypothesis settings that detect gene markers differentially expressed (DE) 'in
all studies," "in the majority of studies"' or "in one or more studies," and
specify rOP as a suitable method for detecting DE genes "in the majority of
studies." We develop methods to estimate the parameter $r$ in rOP for real
applications. Statistical properties such as its asymptotic behavior and a
one-sided testing correction for detecting markers of concordant expression
changes are explored. Power calculation and simulation show better performance
of rOP compared to classical Fisher's method, Stouffer's method, minimum
$p$-value method and maximum $p$-value method under the focused hypothesis
setting. Theoretically, rOP is found connected to the na\"{i}ve vote counting
method and can be viewed as a generalized form of vote counting with better
statistical properties. The method is applied to three microarray meta-analysis
examples including major depressive disorder, brain cancer and diabetes. The
results demonstrate rOP as a more generalizable, robust and sensitive
statistical framework to detect disease-related markers.


  Partial difference sets with parameters $(v,k,\lambda,\mu)=(v, (v-1)/2,
(v-5)/4, (v-1)/4)$ are called Paley type partial difference sets. In this note
we prove that if there exists a Paley type partial difference set in an abelian
group $G$ of an order not a prime power, then $|G|=n^4$ or $9n^4$, where $n>1$
is an odd integer. In 2010, Polhill \cite{Polhill} constructed Paley type
partial difference sets in abelian groups with those orders. Thus, combining
with the constructions of Polhill and the classical Paley construction using
non-zero squares of a finite field, we completely answer the following
question: "For which odd positive integer $v > 1$, can we find a Paley type
partial difference set in an abelian group of order $v$?"


  Graph Contrastive Learning (GCL) aims to learn node representations by
aligning positive pairs and separating negative ones. However, few of
researchers have focused on the inner law behind specific augmentations used in
graph-based learning. What kind of augmentation will help downstream
performance, how does contrastive learning actually influence downstream tasks,
and why the magnitude of augmentation matters so much? This paper seeks to
address these questions by establishing a connection between augmentation and
downstream performance. Our findings reveal that GCL contributes to downstream
tasks mainly by separating different classes rather than gathering nodes of the
same class. So perfect alignment and augmentation overlap which draw all
intra-class samples the same can not fully explain the success of contrastive
learning. Therefore, in order to understand how augmentation aids the
contrastive learning process, we conduct further investigations into the
generalization, finding that perfect alignment that draw positive pair the same
could help contrastive loss but is poisonous to generalization, as a result,
perfect alignment may not lead to best downstream performance, so specifically
designed augmentation is needed to achieve appropriate alignment performance
and improve downstream accuracy. We further analyse the result by information
theory and graph spectrum theory and propose two simple but effective methods
to verify the theories. The two methods could be easily applied to various GCL
algorithms and extensive experiments are conducted to prove its effectiveness.
The code is available at https://github.com/somebodyhh1/GRACEIS


  For a contravariant 4-metric which changes signature from Lorentzian to
Riemannian across a spatial hypersurface, the mixed Einstein tensor is
manifestly non-singular. In Gaussian normal coordinates, the metric contains a
step function and the Einstein tensor contains the Dirac delta function with
support at the junction. The coefficient of the Dirac function is a linear
combination of the second fundamental form (extrinsic curvature) of the
junction. Thus, unless the junction has vanishing extrinsic curvature, the
physical interpretation of the metric is that it describes a layer of matter
(with stresses but no energy or momentum) at the junction. In particular, such
metrics do not satisfy the vacuum Einstein equations, nor the
Einstein-Klein-Gordon equations and so on. Similarly, the d'Alembertian of a
Klein-Gordon field contains the Dirac function with coefficient given by the
momentum of the field. Thus, if the momentum of the field does not vanish at
the junction, the physical interpretation is that there is a source (with step
potential) at the junction. In particular, such fields do not satisfy the
massless Klein-Gordon equation. These facts contradict claims in the
literature.


  In this short note we try to generalize the Clemens-Griffiths criterion of
non-rationality for smooth cubic threefolds to the case of smooth cubic
fourfolds.


  We study Fourier and Laplace transforms for Fourier hyperfunctions with
values in a complex locally convex Hausdorff space. Since any hyperfunction
with values in a wide class of locally convex Hausdorff spaces can be extended
to a Fourier hyperfunction, this gives simple notions of asymptotic Fourier and
Laplace transforms for vector-valued hyperfunctions, which improves the
existing models of Komatsu, B\"aumer, Lumer and Neubrander and Langenbruch.


  We investigate the structure of the core surrounding the recently identified
deeply embedded young stellar object Barnard 1c which has an unusual
polarization pattern as traced in submillimeter dust emission. Barnard 1c lies
within the Perseus molecular cloud at a distance of 250 pc. It is a deeply
embedded core of 2.4 solar masses (Kirk et al.) and a luminosity of 4 +/- 2
solar luminosities. Observations of CO, 13CO, C18O, HCO+ and N2H+ were obtained
with the BIMA array, together with the continuum at 3.3 mm and 2.7 mm.
Single-dish measurements of N2H+ and HCO+ with FCRAO reveal the larger scale
emission in these lines, The CO and HCO+ emission traces the outflow, which
coincides in detail with the S-shaped jet recently found in Spitzer IRAC
imaging. The N2H+ emission, which anticorrelates spatially with the C18O
emission, originates from a rotating envelope with effective radius ~ 2400 AU
and mass 2.1 - 2.9 solar masses. N2H+ emission is absent from a 600 AU diameter
region around the young star. The remaining N2H+ emission may lie in a coherent
torus of dense material. With its outflow and rotating envelope, B1c closely
resembles the previously studied object L483-mm, and we conclude that it is a
protostar in an early stage of evolution. We hypothesize that heating by the
outflow and star has desorbed CO from grains which has destroyed N2H+ in the
inner region and surmise that the presence of grains without ice mantles in
this warm inner region can explain the unusual polarization signature from B1c.


  We study the contribution of B_c mesons to the search for B->tau nu decays.
We find that at LEP the contributions from B_u and B_c mesons can be
comparable. This observation can have a relevant impact on the extraction of
constraints on new physics (such as charged-Higgs contributions) from current
LEP limits on B->tau nu final states. Inclusion of the B_c contribution can
reduce the current L3 limit on Tan(beta)/M_H from 0.38/GeV (90%CL) down to
0.27/GeV (90%CL).


  While the common environment representation in structure from motion is given
by a sparse point cloud, the community has also investigated the use of lines
to better enforce the inherent regularities in man-made surroundings. Following
the potential of this idea, the present paper introduces a more flexible
higher-order extension of points that provides a general model for structural
edges in the environment, no matter if straight or curved. Our model relies on
linked B\'ezier curves, the geometric intuition of which proves great benefits
during parameter initialization and regularization. We present the first fully
automatic pipeline that is able to generate spline-based representations
without any human supervision. Besides a full graphical formulation of the
problem, we introduce both geometric and photometric cues as well as
higher-level concepts such overall curve visibility and viewing angle
restrictions to automatically manage the correspondences in the graph. Results
prove that curve-based structure from motion with splines is able to outperform
state-of-the-art sparse feature-based methods, as well as to model curved edges
in the environment.


  The capability to simulate a hydraulic fracturing process is an essential
tool that can be used to optimize treatment design and increase the efficiency
of field operations. In most practical cases, hydraulic fractures propagate in
a multi-layered rock formation. As a result, there is a need to incorporate the
effect of such heterogeneities in fracturing models to achieve an accurate
prediction. To capture the layered structure of rocks, a hydraulic fracture
simulator typically requires a fine mesh, which leads to a drastic reduction in
computational performance. An alternative is to use more sophisticated models
that are capable of providing reasonably accurate predictions even on a
relatively coarse mesh. In the case of fracture growth modeling, the pivotal
component of the simulation is a fracture front tracking algorithm that
accounts for the layered structure of the formation. Consequently, this paper
aims to extend the established Implicit Level Set Algorithm (ILSA) to account
for the effect of multiple stress layers within the tip asymptote. The enhanced
front tracking algorithm involves the stress-corrected asymptote that
incorporates the influence of stress layers within the near-tip region. To
further increase the validity region of the stress-corrected asymptote, the
stress relaxation factor is introduced, and its accuracy is examined. The
numerical algorithm is validated against the reference semi-analytical
solutions as well as experimental observations. In addition, we investigate the
sensitivity of the fracture geometry to mesh size to demonstrate that the front
tracking algorithm based on the stress-corrected asymptote retains its accuracy
on a coarse mesh.


  This paper considers a two-person zero-sum continuous-time Markov pure jump
game in Borel state and action spaces over a fixed finite horizon. The main
assumption on the model is the existence of a drift function, which bounds the
reward rate. Under some regularity conditions, we show that the game has a
value, and both of the players have their optimal policies.


  We study two correlated electrons in a nearest neighbour tight- binding
chain, with both on site and nearest neighbour interaction. Both the cases of
parallel and antiparallel spins are considered. In addition to the free
electron band for two electrons, there are correlated bands with positive or
negative energy, depending on wheather the interaction parameters are repulsive
or attractive. Electrons form bound states, with amplitudes that decay
exponentially with separation. Conditions for such states to be filled at low
temperatures are discussed.


  Effective expression feature representations generated by a triplet-based
deep metric learning are highly advantageous for facial expression recognition
(FER). The performance of triplet-based deep metric learning is contingent upon
identifying the best threshold for triplet loss. Threshold validation, however,
is tough and challenging, as the ideal threshold changes among datasets and
even across classes within the same dataset. In this paper, we present the
multi-threshold deep metric learning technique, which not only avoids the
difficult threshold validation but also vastly increases the capacity of
triplet loss learning to construct expression feature representations. We find
that each threshold of the triplet loss intrinsically determines a distinctive
distribution of inter-class variations and corresponds, thus, to a unique
expression feature representation. Therefore, rather than selecting a single
optimal threshold from a valid threshold range, we thoroughly sample thresholds
across the range, allowing the representation characteristics manifested by
thresholds within the range to be fully extracted and leveraged for FER. To
realize this approach, we partition the embedding layer of the deep metric
learning network into a collection of slices and model training these embedding
slices as an end-to-end multi-threshold deep metric learning problem. Each
embedding slice corresponds to a sample threshold and is learned by enforcing
the corresponding triplet loss, yielding a set of distinct expression features,
one for each embedding slice. It makes the embedding layer, which is composed
of a set of slices, a more informative and discriminative feature, hence
enhancing the FER accuracy. Extensive evaluations demonstrate the superior
performance of the proposed approach on both posed and spontaneous facial
expression datasets.


  We review results of the last two years concerning caloron solutions of unit
charge with non-trivial holonomy, revealing the constituent monopole nature of
these instantons. For SU(n) there are n such BPS constituents. New is the
presentation of the exact values for the Polyakov loop at the three constituent
locations for the SU(3) caloron with arbitrary holonomy. At these points two
eigenvalues coincide, extending earlier results for SU(2) to a situation more
generic for general SU(n).


  The charged and neutral kaon form factors are calculated as a
phenomenological application of the QCD Dyson-Schwinger equations. The results
are compared with the pion form factor calculated in the same framework and
yield \mbox{$F_{K^\pm}(Q^2) > F_{\pi^\pm}(Q^2)$} on
\mbox{$Q^2\in[0,3]$~GeV$^2$}; and a neutral kaon form factor that is similar in
form and magnitude to the neutron charge form factor. These results are
sensitive to the difference between the kaon and pion Bethe-Salpeter amplitude
and the $u$- and $s$-quark propagation characteristics.


  Let K be the subgroup of the extended mapping class group, Mod(S), generated
by Dehn twists about separating curves. Assuming that S is a closed, orientable
surface of genus at least 4, we confirm a conjecture of Farb that Comm(K),
Aut(K) and Mod(S) are all isomorphic. More generally, we show that any
injection of a finite index subgroup of K into the Torelli group I of S is
induced by a homeomorphism. In particular, this proves that K is co-Hopfian and
is characteristic in I. Further, we recover the result of Farb and Ivanov that
any injection of a finite index subgroup of I into I is induced by a
homeomorphism. Our method is to reformulate these group theoretic statements in
terms of maps of curve complexes.


  We show that a reduced form of the structural requirements for deterministic
hidden variables used in Bell-Kochen-Specker theorems is already sufficient for
the no-go results. Those requirements are captured by the following principle:
an observable takes a spectral value x if and only if the spectral projector
associated with x takes the value 1. We show that the only if part of this
condition suffices. The proof identifies an important structural feature behind
the no-go results; namely, if at least one projector is assigned the value 1 in
any resolution of the identity, then at most one is.


  The formation mechanism of globular clusters (GCs) has long been debated by
astronomers. It was recently proposed that Supersonically Induced Gas Objects
(SIGOs), which formed in the early Universe due to the supersonic relative
motion of baryons and dark matter at recombination, could be the progenitors of
early globular clusters. In order to become GCs, SIGOs must form stars
relatively efficiently despite forming outside of dark matter halos. We
investigate the potential for star formation in SIGOs using cosmological
hydrodynamic simulations, including the aforementioned relative motions of
baryons and dark matter, molecular hydrogen cooling in primordial gas clouds,
and including explicit star formation. We find that SIGOs do form stars and
that the nascent star clusters formed through this process are accreted by dark
matter halos on short timescales (a few hundreds of Myr). Thus, SIGOs may be
found as intact substructures within these halos, analogous to many present-day
GCs. From this result, we conclude that SIGOs are capable of forming star
clusters with similar properties to globular clusters in the early Universe and
we discuss their detectablity by upcoming JWST surveys.


  Golo is a simple dynamically-typed language for the Java Virtual Machine.
Initially implemented as a ahead-of-time compiler to JVM bytecode, it leverages
invokedy-namic and JSR 292 method handles to implement a reasonably efficient
runtime. Truffle is emerging as a framework for building interpreters for JVM
languages with self-specializing AST nodes. Combined with the Graal compiler,
Truffle offers a simple path towards writing efficient interpreters while
keeping the engineering efforts balanced. The Golo project is interested in
experimenting with a Truffle interpreter in the future, as it would provides
interesting comparison elements between invokedynamic versus Truffle for
building a language runtime.


  We discuss B-meson signatures of a Supersymmetric U(2) flavor model, with
relatively light (electroweak scale masses) third generation right-handed
scalars. We impose current B and K meson experimental constraints on such a
theory, and obtain expectations for B->X_s gamma, B->X_s glue, B->X_s l+ l-,
B->phi K_s, B_s-B_sbar mixing, and the dilepton asymmetry in B_s. We show that
such a theory is compatible with all current data, and furthermore, could
reconcile the apparent deviations from Standard Model predictions that have
been found in some experiments.


  In ultrarelativistic heavy-ion collisions, the Fourier decomposition of the
relative azimuthal angle, \Delta \phi, distribution of particle pairs yields a
large cos(3\Delta \phi) component, extending out to large rapidity separations
\Delta \eta >1. This component captures a significant portion of the ridge and
shoulder structures in the \Delta \phi distribution, which have been observed
after contributions from elliptic flow are subtracted. An average finite
triangularity due to event-by-event fluctuations in the initial matter
distribution, followed by collective flow, naturally produces a cos(3\Delta
\phi) correlation. Using ideal and viscous hydrodynamics, and transport theory,
we study the physics of triangular (v_3) flow in comparison to elliptic (v_2),
quadrangular (v_4) and pentagonal (v_5) flow. We make quantitative predictions
for v_3 at RHIC and LHC as a function of centrality and transverse momentum.
Our results for the centrality dependence of v_3 show a quantitative agreement
with data extracted from previous correlation measurements by the STAR
collaboration. This study supports previous results on the importance of
triangular flow in the understanding of ridge and shoulder structures.
Triangular flow is found to be a sensitive probe of initial geometry
fluctuations and viscosity.


  We address the problem of maintaining resource availability in a networked
multi-robot team performing distributed tracking of unknown number of targets
in an environment of interest. Based on our model, robots are equipped with
sensing and computational resources enabling them to cooperatively track a set
of targets in an environment using a distributed Probability Hypothesis Density
(PHD) filter. We use the trace of a robot's sensor measurement noise covariance
matrix to quantify its sensing quality. While executing the tracking task, if a
robot experiences sensor quality degradation, then robot team's communication
network is reconfigured such that the robot with the faulty sensor may share
information with other robots to improve the team's target tracking ability
without enforcing a large change in the number of active communication links. A
central system which monitors the team executes all the network reconfiguration
computations. We consider two different PHD fusion methods in this paper and
propose four different Mixed Integer Semi-Definite Programming (MISDP)
formulations (two formulations for each PHD fusion method) to accomplish our
objective. All four MISDP formulations are validated in simulation.


  We report on a 95ks Chandra observation of the TeV emitting High Mass X-ray
Binary LSI +61 303, using the ACIS-S camera in Continuos Clocking mode to
search for a possible X-ray pulsar in this system. The observation was
performed while the compact object was passing from phase 0.94 to 0.98 in its
orbit around the Be companion star (hence close to the apastron passage). We
did not find any periodic or quasi-periodic signal (at this orbital phase) in a
frequency range of 0.005-175 Hz. We derived an average pulsed fraction 3 sigma
upper limit for the presence of a periodic signal of ~10% (although this limit
is strongly dependent on the frequency and the energy band), the deepest limit
ever reached for this object. Furthermore, the source appears highly variable
in flux and spectrum even in this very small orbital phase range, in particular
we detect two flares, lasting thousands of seconds, with a very hard X-ray
spectrum with respect to the average source spectral distribution. The X-ray
pulsed fraction limits we derived are lower than the pulsed fraction of any
isolated rotational-powered pulsar, in particular having a TeV counterpart. In
this scenario most of the X-ray emission of LSI +61 303 should necessarily come
from the interwind or inner-pulsar wind zone shock rather than from the
magnetosphere of the putative pulsar. Furthermore, we did not find evidence for
the previously suggested extended X-ray emission (abridged).


  Spatial Monte Carlo integration (SMCI) is an extension of standard Monte
Carlo integration and can approximate expectations on Markov random fields with
high accuracy. SMCI was applied to pairwise Boltzmann machine (PBM) learning,
with superior results to those from some existing methods. The approximation
level of SMCI can be changed, and it was proved that a higher-order
approximation of SMCI is statistically more accurate than a lower-order
approximation. However, SMCI as proposed in the previous studies suffers from a
limitation that prevents the application of a higher-order method to dense
systems.
  This study makes two different contributions as follows. A generalization of
SMCI (called generalized SMCI (GSMCI)) is proposed, which allows relaxation of
the above-mentioned limitation; moreover, a statistical accuracy bound of GSMCI
is proved. This is the first contribution of this study. A new PBM learning
method based on SMCI is proposed, which is obtained by combining SMCI and the
persistent contrastive divergence. The proposed learning method greatly
improves the accuracy of learning. This is the second contribution of this
study.


  We count the number of all Rota-Baxter operators on a finite direct sum $A =
F\oplus F\oplus \ldots \oplus F$ of fields and count all of them up to
conjugation with an automorphism. We also study Rota-Baxter operators on $A$
corresponding to a decomposition of $A$ into a direct vector space sum of two
subalgebras. We show that every algebra structure induced on $A$ by a
Rota-Baxter of nonzero weight is isomorphic to $A$.


  We consider interacting population systems of predator-prey type, presenting
four models of control strategies for epidemics among the prey. In particular
to contain the transmissible disease, safety niches are considered, assuming
they lessen the disease spread, but do not protect prey from predators. This
represents a novelty with respect to standard ecosystems where the refuge
prevents predators' attacks. The niche is assumed either to protect the healthy
individuals, or to hinder the infected ones to get in contact with the
susceptibles, or finally to reduce altogether contacts that might lead to new
cases of the infection. In addition a standard culling procedure is also
analysed. The effectiveness of the different strategies are compared. Probably
the environments providing a place where disease carriers cannot come in
contact with the healthy individuals, or where their contact rates are lowered,
seem to preferable for disease containment.


  A probability distribution over the Boolean cube is monotone if flipping the
value of a coordinate from zero to one can only increase the probability of an
element. Given samples of an unknown monotone distribution over the Boolean
cube, we give (to our knowledge) the first algorithm that learns an
approximation of the distribution in statistical distance using a number of
samples that is sublinear in the domain.
  To do this, we develop a structural lemma describing monotone probability
distributions. The structural lemma has further implications to the sample
complexity of basic testing tasks for analyzing monotone probability
distributions over the Boolean cube: We use it to give nontrivial upper bounds
on the tasks of estimating the distance of a monotone distribution to uniform
and of estimating the support size of a monotone distribution. In the setting
of monotone probability distributions over the Boolean cube, our algorithms are
the first to have sample complexity lower than known lower bounds for the same
testing tasks on arbitrary (not necessarily monotone) probability
distributions.
  One further consequence of our learning algorithm is an improved sample
complexity for the task of testing whether a distribution on the Boolean cube
is monotone.


  We show that the nonuniform state (Fulde-Ferrel-Larkin-Ovchinnikov (FFLO)
state) of the spin triplet superconductivity in noncentrosymmetric systems is
stabilized by antisymmetric spin-orbit coupling even if the magnetic field is
absent. The transition temperature of the spin triplet superconductivity is
reduced by the antisymmetric spin-orbit coupling in general. This pair breaking
effect is shown to be similar to the Pauli pair breaking effect due to magnetic
field for the spin singlet superconductivity, in which FFLO state is stabilized
near the Pauli limit (or Chandrasekhar-Clogston limit) of external magnetic
field. Since there are gapless excitations in nonuniform superconducting state,
some physical quantities such as specific heat and penetration depth should
obey the power low temperature-dependences. We discuss the possibility of the
realization of nonuniform state in CePt$_3$Si.


  We present a quantum theory of cooling of a mechanical resonator using
back-action with constant electron current. The resonator device is based on a
doubly clamped nanotube, which mechanically vibrates and acts as a double
quantum dot for electron transport. Mechanical vibrations and electrons are
coupled electrostatically using an external gate. The fundamental eigenmode is
cooled by absorbing phonons when electrons tunnel through the double quantum
dot. We identify the regimes in which ground state cooling can be achieved for
realistic experimental parameters.


  The creation of a vulnerable node has been demonstrated through the analysis
and implementation of the MS17-010 (CVE-2017-0144) vulnerability, affecting the
SMBv1 protocol on various Windows operating systems. The principle and
methodology of exploiting the vulnerability are described, with a formalized
representation of the exploitation in the form of a Meta Attack Language (MAL)
graph. Additionally, the attacker's implementation is outlined as the execution
of an automated script in Python using the Metasploit Framework. Basic security
measures for systems utilizing the SMBv1 protocol are provided.


  LHCb presents studies of particle production in minimum bias events in pp
collisions at \sqrt{s} = 7 TeV. These studies include measurements of
strangeness production, particle ratios, baryon-antibaryon ratios and charged
particle production. The forward coverage and low pT acceptance of the
experiment makes these measurements very complementary to those performed by
the central detectors at the LHC. Further benefits arise from the powerful
particle identification capabilities provided by the LHCb RICH system. The
measurements are compared with theoretical predictions.


  We use the generalized Konishi anomaly equations and R-symmetry anomaly to
compute the exact perturbative and non-perturbative gravitational F-terms of
four-dimensional N=1 supersymmetric gauge theories. We formulate the general
procedure for computation and consider chiral and non-chiral SU(N) gauge
theories.


  For a given connected graph $G$, the edge Mostar index $Mo_e(G)$ is defined
as $Mo_e(G)=\sum_{e=uv \in E(G)}|m_u(e|G) - m_v(e|G)|$, where $m_u(e|G)$ and
$m_v(e|G)$ are respectively, the number of edges of $G$ lying closer to vertex
$u$ than to vertex $v$ and the number of edges of $G$ lying closer to vertex
$v$ than to vertex $u$. We determine a sharp upper bound for the edge Mostar
index on bicyclic graphs and identify the graphs that attain the bound, which
disproves a conjecture proposed by Liu et al. [Iranian J. Math. Chem. 11(2)
(2020) 95--106].


  ESCAPE is a free python package and framework for creating applications for
simulating and fitting of X-ray and neutron scattering data with current
support for specular reflectivity, polarized neutron reflectometry, high
resolution X-ray diffraction, small angle scattering with future support for
off-specular scattering from structured samples with complicated morphology.
Utilizing current features of Jupyter project, it allows to create highly
customized applications in the format of notebooks. These notebooks, being
shared with other users, can be used directly or started as web applications
with graphical user interface. This paper is a brief overview of the core and
scattering packages providing description of the major features with code
examples. The following features make ESCAPE different from other projects:
independent from scattering applications core, which provides access to models
building blocks like parameters, variables, functors, data objects, models and
optimizers; support of arithmetic operations and algebraic expressions on
parameters and functors, offering models with complex dependencies of
parameters; math module with standard mathematical functors and special
functors which perform numerical integration over variable or parameter,
supplying customization of intensity model; simultaneous fit of several models,
also for models with different dimensions. Check our web site
https://escape-app.net/ for further information.


  A geodesic bicombing on a metric space selects for every pair of points a
geodesic connecting them. We prove existence and uniqueness results for
geodesic bicombings satisfying different convexity conditions. In combination
with recent work by the second author on injective hulls, this shows that every
word hyperbolic group acts geometrically on a proper, finite dimensional space
X with a unique (hence equivariant) convex geodesic bicombing of the strongest
type. Furthermore, the Gromov boundary of X is a Z-set in the closure of X, and
the latter is a metrizable absolute retract, in analogy with the Bestvina--Mess
theorem on the Rips complex.


  Let $\mathbb{E}(H)$ and $\mathbb{V}(H)$ denote the edge set and the vertex
set of the simple connected graph $H$, respectively. The mixed metric dimension
of the graph $H$ is the graph invariant, which is the mixture of two important
graph parameters, the edge metric dimension and the metric dimension. In this
article, we compute the mixed metric dimension for the two families of the
plane graphs viz., the Web graph $\mathbb{W}_{n}$ and the Prism allied graph
$\mathbb{D}_{n}^{t}$. We show that the mixed metric dimension is non-constant
unbounded for these two families of the plane graph. Moreover, for the Web
graph $\mathbb{W}_{n}$ and the Prism allied graph $\mathbb{D}_{n}^{t}$, we
unveil that the mixed metric basis set $M_{G}^{m}$ is independent.


  We extend partially the Kakutani-Zygmund dichotomy theorem to a class of
generalized Riesz-product type measures by proving that the generalized
Riesz-product is singular if and only if its Mahler measure is zero. As a
consequence, we exhibit a new subclass of rank one maps acting on a finite
measure space with singular spectrum. In our proof the $H^p$ theory coming to
play. Furthermore, by appealing to a deep result of Bourgain, we prove that the
Mahler measure of the spectrum of rank one map with cutting parameter
$p_n=O(n^\beta)$, $\beta \leq 1$ is zero, and we establish that the integral of
the absolute part of any generalized Riesz-product is strictly less than 1.
This answer partially a question asked by M. Nadkarni.


  This study presents a theoretical analysis on the efficiency of interleaving,
an efficient online evaluation method for rankings. Although interleaving has
already been applied to production systems, the source of its high efficiency
has not been clarified in the literature. Therefore, this study presents a
theoretical analysis on the efficiency of interleaving methods. We begin by
designing a simple interleaving method similar to ordinary interleaving
methods. Then, we explore a condition under which the interleaving method is
more efficient than A/B testing and find that this is the case when users leave
the ranking depending on the item's relevance, a typical assumption made in
click models. Finally, we perform experiments based on numerical analysis and
user simulation, demonstrating that the theoretical results are consistent with
the empirical results.


  The visual signal compression is a long-standing problem. Fueled by the
recent advances of deep learning, exciting progress has been made. Despite
better compression performance, existing end-to-end compression algorithms are
still designed towards better signal quality in terms of rate-distortion
optimization. In this paper, we show that the design and optimization of
network architecture could be further improved for compression towards machine
vision. We propose an inverted bottleneck structure for the encoder of the
end-to-end compression towards machine vision, which specifically accounts for
efficient representation of the semantic information. Moreover, we quest the
capability of optimization by incorporating the analytics accuracy into the
optimization process, and the optimality is further explored with generalized
rate-accuracy optimization in an iterative manner. We use object detection as a
showcase for end-to-end compression towards machine vision, and extensive
experiments show that the proposed scheme achieves significant BD-rate savings
in terms of analysis performance. Moreover, the promise of the scheme is also
demonstrated with strong generalization capability towards other machine vision
tasks, due to the enabling of signal-level reconstruction.


  Significant temperature effects on the electrokinetic transport in a
nanochannel with a slab geometry are demonstrated using a molecular dynamics
(MD) model. A system consisting of Na+ and Cl- ions dissolved in water and
confined between fixed crystalline silicon walls with negatively charged inner
surfaces in an external electric field was investigated. Lennard-Jones (LJ)
force fields and Coulomb electrostatic interactions with Simple Point Charge
Extended (SPC/E) model were used to represent the interactions between ions,
water molecules, and channel wall atoms. Dependence of the flow of water and
ions on the temperature was examined. The magnitude of the water flux and even
its direction are shown to be significantly affected by temperature. In
particular, the previously reported flow reversal phenomenon does not occur at
higher temperature. Temperature dependence of the flux was attributed to the
charge redistribution and to the changes in viscosity of water.


  Regression models for dichotomous data are ubiquitous in statistics. Besides
being useful for inference on binary responses, these methods serve also as
building blocks in more complex formulations, such as density regression,
nonparametric classification and graphical models. Within the Bayesian
framework, inference proceeds by updating the priors for the coefficients,
typically set to be Gaussians, with the likelihood induced by probit or logit
regressions for the responses. In this updating, the apparent absence of a
tractable posterior has motivated a variety of computational methods, including
Markov Chain Monte Carlo routines and algorithms which approximate the
posterior. Despite being routinely implemented, Markov Chain Monte Carlo
strategies face mixing or time-inefficiency issues in large p and small n
studies, whereas approximate routines fail to capture the skewness typically
observed in the posterior. This article proves that the posterior distribution
for the probit coefficients has a unified skew-normal kernel, under Gaussian
priors. Such a novel result allows efficient Bayesian inference for a wide
class of applications, especially in large p and small-to-moderate n studies
where state-of-the-art computational methods face notable issues. These
advances are outlined in a genetic study, and further motivate the development
of a wider class of conjugate priors for probit models along with methods to
obtain independent and identically distributed samples from the unified
skew-normal posterior.


  Numerical modelling of quantum effects caused by bosonic or fermionic
character of secondaries produced in high energy collisions of different sorts
is at the moment still far from being established. In what follows we propose
novel numerical method of modelling Bose-Einstein correlations (BEC) observed
among identical (bosonic) particles produced in such reactions. We argue that
the most natural approach is to work directly in the momentum space of produced
secondaries in which the Bose statistics reveals itself in their tendency to
bunch in a specific way in the available phase space. Fermionic particles can
also be treated in similar fashion.


  Power functions with low $c$-differential uniformity have been widely studied
not only because of their strong resistance to multiplicative differential
attacks, but also low implementation cost in hardware. Furthermore, the
$c$-differential spectrum of a function gives a more precise characterization
of its $c$-differential properties. Let $f(x)=x^{\frac{p^n+3}{2}}$ be a power
function over the finite field $\mathbb{F}_{p^{n}}$, where $p\neq3$ is an odd
prime and $n$ is a positive integer. In this paper, for all primes $p\neq3$, by
investigating certain character sums with regard to elliptic curves and
computing the number of solutions of a system of equations over
$\mathbb{F}_{p^{n}}$, we determine explicitly the $(-1)$-differential spectrum
of $f$ with a unified approach. We show that if $p^n \equiv 3 \pmod 4$, then
$f$ is a differentially $(-1,3)$-uniform function except for
$p^n\in\{7,19,23\}$ where $f$ is an APcN function, and if $p^n \equiv 1 \pmod
4$, the $(-1)$-differential uniformity of $f$ is equal to $4$. In addition, an
upper bound of the $c$-differential uniformity of $f$ is also given.


  We study the dependency of the concentration on mass and redshift using three
large N-body cosmological hydrodynamic simulations carried out by the
Magneticum project. We constrain the slope of the mass-concentration relation
with an unprecedented mass range for hydrodynamic simulations and find a
negative trend on the mass-concentration plane and a slightly negative redshift
dependency, in agreement with observations and other numerical works. We also
show how the concentration correlates with the fossil parameter, defined as the
stellar mass ratio between the central galaxy and the most massive satellite,
in agreement with observations. We find that haloes with high fossil parameter
have systematically higher concentration and investigate the cause in two
different ways. First we study the evolution of haloes that lives unperturbed
for a long period of time, where we find that the internal region keeps
accreting satellites as the fossil parameter increases and the scale radius
decreases (which increases the concentration). We also study the dependency of
the concentration on the virial ratio and the energy term from the surface
pressure $E_s$. We conclude that fossil objects have higher concentration
because they are dynamically relaxed, with no in-fall/out-fall material and had
time to accrete their satellites.


  Shapley (1953) introduced two-player zero-sum discounted stochastic games,
henceforth stochastic games, a model where a state variable follows a
two-controlled Markov chain, the players receive rewards at each stage which
add up to $0$, and each maximizes the normalized $\la$-discounted sum of stage
rewards, for some fixed discount rate $\la\in(0,1]$. In this paper, we study
asymptotic occupation measures arising in these games, as the discount rate
goes to $0$.


  We generalize optimal inequalities of C. Loewner and M. Gromov, by proving
lower bounds for the total volume in terms of the homotopy systole and the
stable systole. Our main tool is the construction of an area-decreasing map to
the Jacobi torus, streamlining and generalizing the construction of the first
author in collaboration with D. Burago. It turns out that one can successfully
combine this construction with the coarea formula, to yield new optimal
inequalities.


  In this work we review the precursors of catastrophic avalanches (global
failures) in several failure models, namely (a) Fiber Bundle Model (FBM), (b)
Random Fuse Model (RFM), (c) Sandpile Models and (d) Fractal Overlap Model. The
precursor parameters identified here essentially reflect the growing
correlations within such systems as they approach their respective failure
points. As we show, often they help us to predict the global failure points in
advance.


  By means of Monte Carlo simulations we show that there are two qualitatively
different modes of localization of classical waves in 1-{\em D} random
periodic-on-average systems. States from pass bands and band edges of the
underlying band structure demonstrate single parameter scaling with universal
behavior. States from the interior of the band gaps do not have universal
behavior and require two parameters to describe their scaling properties. The
transition between these two types of behavior occurs in an extremely narrow
region of frequencies. When the degree of disorder exceeds a certain critical
value the single parameter scaling is restored for an entire band-gap.


  Deep Reinforcement Learning has been very successful recently with various
works on complex domains. Most works are concerned with learning a single
policy that solves the target task, but is fixed in the sense that if the
environment changes the agent is unable to adapt to it. Successor Features
(SFs) proposes a mechanism that allows learning policies that are not tied to
any particular reward function. In this work we investigate how SFs may be
pre-trained without observing any reward in a custom environment that features
resource collection, traps and crafting. After pre-training we expose the SF
agents to various target tasks and see how well they can transfer to new tasks.
Transferring is done without any further training on the SF agents, instead
just by providing a task vector. For training the SFs we propose a task
relabelling method which greatly improves the agent's performance.


  Quantum monotone metric was introduced by Petz,and it was proved that quantum
monotone metrics on the set of quantum states with trace one were characterized
by operator monotone functions. Later, these were extended to monotone metrics
on the set of positive operators whose traces are not always one based on
completely positive, trace preserving (CPTP) maps. It was shown that these
extended monotone metrics were characterized by operator monotone functions
continuously parameterized by traces of positive operators,and did not have
some ideal properties such as monotonicity and convexity with respect to the
positive operators. In this paper, we introduce another extension of quantum
monotone metrics which have monotonicity under completely positive, trace
non-increasing (CPTNI) maps and additive noise. We prove that our extended
monotone metrics can be characterized only by static operator monotone
functions from few assumptions without assuming continuities of metrics. We
show that our monotone metrics have some natural properties such as additivity
of direct sum, convexity and monotonicity with respect to positive operators.


  New red and violet system line lists for the CN isotopologues 13C14N and
12C15N have been generated. These new transition data are combined with those
previously derived for 12C14N, and applied to the determination of CNO
abundances in the solar photosphere and in four red giant stars: Arcturus, the
bright very low-metallicity star HD 122563, and carbon-enhanced metal-poor
stars HD 196944 and HD 201626. When lines of both red and violet system lines
are detectable in a star, their derived N abundances are in good agreement. The
mean N abundances determined in this work generally are also in accord with
published values.


  Signal analysis is built upon various resolutions of the identity in signal
vector spaces, e.g. Fourier, Gabor, wavelets, etc. Similar resolutions are used
as quantizers of functions or distributions, paving the way to a time-frequency
or time-scale quantum formalism and revealing interesting or unexpected
features. Extensions to classical electromagnetism viewed as a quantum theory
for waves and not for photons are mentioned.


  We study the relations of the positive frequency mode functions of Dirac
field in 4-dimensional Minkowski spacetime covered with Rindler and Kasner
coordinates, and describe the explicit form of the Minkowski vacuum state with
the quantum states in Kasner and Rindler regions, and analytically continue the
solutions. As a result, we obtain the correspondence of the positive frequency
mode functions in Kasner region and Rindler region in a unified manner which
derives vacuum entanglement.


  The classical shooting-method is about finding a suitable initial shooting
positions to shoot to the desired target. The new approach formulated here,
with the introduction and the analysis of the `target map' as its core,
naturally connects the classical shooting-method to the simple and beautiful
topological degree theory.
  We apply the new approach, to a motivating example, to derive the existence
of global positive solutions of the Hardy-Littlewood-Sobolev (also known as
Lane-Emden) type system: [{{aligned}
  &(-\triangle)^ku(x) = v^p(x), \,\, u(x)>0 \quad\text{in}\quad\mathbb{R}^n,
  & (-\triangle)^k v(x) =u^q(x), \,\, v(x)>0 \quad\text{in}\quad\mathbb{R}^n,
p, q>0,
  {aligned}.] in the critical and supercritical cases
$\frac{1}{p+1}+\frac{1}{q+1}\leq\frac{n-2k}{n}$. Here we derive the existence
with the computation of the topological degree of a suitably defined target
map. This and some other results presented in this article completely solved
several long-standing open problems about the existence or non-existence of
positive entire solutions.


  Object detection has made substantial progress in the last decade, due to the
capability of convolution in extracting local context of objects. However, the
scales of objects are diverse and current convolution can only process
single-scale input. The capability of traditional convolution with a fixed
receptive field in dealing with such a scale variance problem, is thus limited.
Multi-scale feature representation has been proven to be an effective way to
mitigate the scale variance problem. Recent researches mainly adopt partial
connection with certain scales, or aggregate features from all scales and focus
on the global information across the scales. However, the information across
spatial and depth dimensions is ignored. Inspired by this, we propose the
multi-scale convolution (MSConv) to handle this problem. Taking into
consideration scale, spatial and depth information at the same time, MSConv is
able to process multi-scale input more comprehensively. MSConv is effective and
computationally efficient, with only a small increase of computational cost.
For most of the single-stage object detectors, replacing the traditional
convolutions with MSConvs in the detection head can bring more than 2.5\%
improvement in AP (on COCO 2017 dataset), with only 3\% increase of FLOPs.
MSConv is also flexible and effective for two-stage object detectors. When
extended to the mainstream two-stage object detectors, MSConv can bring up to
3.0\% improvement in AP. Our best model under single-scale testing achieves
48.9\% AP on COCO 2017 \textit{test-dev} split, which surpasses many
state-of-the-art methods.


  Fundamental issues involving nuclei in the celebrated solar neutrino problem
are discussed in terms of an effective field theory adapted to nuclear few-body
systems, with a focus on the proton fusion process and the hep process. Our
strategy in addressing these questions is to combine chiral perturbation theory
-- an effective field theory of QCD -- with an accurate nuclear physics
approach to arrive at a more effective effective field theory that reveals and
exploits a subtle role of the chiral-symmetry scale in short-distance effects
encoded in short-range nuclear correlations. Our key argument is drawn from the
close analogy of the principal weak matrix element figuring in the hep process
to the suppressed matrix elements in the polarized neutron-proton capture at
threshold currently being measured in the laboratories.


  We discover weak antilocalization effect of two-dimensional electron gas with
one electric subband occupied in the inversion layer on p-type HgCdTe crystal.
By fitting the model of Iordanskii, Lyanda-Geller and Pikus to data at varies
temperatures and gate voltages, we extract phase coherence and spin-orbit
scattering times as functions of temperature and carrier density. We find that
Elliot-Yafet mechanism and Nyquist mechanism are the dominating spin
decoherence and dephasing mechanisms, respectively. We also find that the
Rashba parameter is relatively large and the dependence of Rashba parameter
upon carrier density is not monotonic and an optimal carrier density exists for
the maximization of spin-orbit coupling.


  Using a generalized model of interaction between a two-level system (TLS) and
an arbitrary deformation of the material, we calculate the interaction of Lamb
modes with TLSs in amorphous nanoscopic membranes. We compare the mean free
paths of the Lamb modes with different symmetries and calculate the heat
conductivity $\kappa$. In the limit of an infinitely wide membrane, the heat
conductivity is divergent. Nevertheless, the finite size of the membrane
imposes a lower cut-off for the phonons frequencies, which leads to the
temperature dependence $\kappa\propto T(a+b\ln T)$. This temperature dependence
is a hallmark of the TLS-limited heat conductance at low temperature.


  On the graphene moire on Ir(111) a variety of highly perfect cluster
superlattices can be grown as shown is for Ir, Pt, W, and Re. Even materials
that do not form cluster superlattices upon room temperature deposition may be
grown into such by low temperature deposition or the application of cluster
seeding through Ir as shown for Au, AuIr, FeIr. Criteria for the suitability of
a material to form a superlattice are given and largely confirmed. It is proven
that at least Pt and Ir even form epitaxial cluster superlattices. The
temperature stability of the cluster superlattices is investigated and
understood on the basis of positional fluctuations of the clusters around their
sites of minimum potential energy. The binding sites of Ir, Pt, W and Re
cluster superlattices are determined and the ability to cover samples
macroscopically with a variety of superlattices is demonstrated.


  We combine the well known Shortest Paths (SP) problem and the Bottleneck
Paths (BP) problem to introduce a new problem called the Shortest Paths for All
Flows (SP-AF) problem that has relevance in real life applications. We first
solve the Single Source Shortest Paths for All Flows (SSSP-AF) problem on
directed graphs with unit edge costs in $O(mn)$ worst case time bound. We then
present two algorithms to solve SSSP-AF on directed graphs with integer edge
costs bounded by $c$ in $O(m^2 + nc)$ and $O(m^2 + mn\log{(\frac{c}{m})})$ time
bounds. Finally we extend our algorithms for the SSSP-AF problem to solve the
All Pairs Shortest Paths for All Flows (APSP-AF) problem in $O(m^{2}n + nc)$
and $O(m^{2}n + mn^{2}\log{(\frac{c}{mn})})$ time bounds. All algorithms
presented in this paper are practical for implementation.


  Developing an educational test can be expensive and time-consuming, as each
item must be written by experts and then evaluated by collecting hundreds of
student responses. Moreover, many tests require multiple distinct sets of
questions administered throughout the school year to closely monitor students'
progress, known as parallel tests. In this study, we focus on tests of silent
sentence reading efficiency, used to assess students' reading ability over
time. To generate high-quality parallel tests, we propose to fine-tune large
language models (LLMs) to simulate how previous students would have responded
to unseen items. With these simulated responses, we can estimate each item's
difficulty and ambiguity. We first use GPT-4 to generate new test items
following a list of expert-developed rules and then apply a fine-tuned LLM to
filter the items based on criteria from psychological measurements. We also
propose an optimal-transport-inspired technique for generating parallel tests
and show the generated tests closely correspond to the original test's
difficulty and reliability based on crowdworker responses. Our evaluation of a
generated test with 234 students from grades 2 to 8 produces test scores highly
correlated (r=0.93) to those of a standard test form written by human experts
and evaluated across thousands of K-12 students.


  We analyse the role played by system-environment correlations in the
emergence of non-Markovian dynamics. By working within the framework developed
in Breuer et al., Phys. Rev. Lett. 103, 210401 (2009), we unveil a fundamental
connection between non-Markovian behaviour and dynamics of system-environment
correlations. We derive an upper bound to the rate of change of the
distinguishability between different states of the system that explicitly
depends on the development and establishment of correlations between system and
environment. We illustrate our results using a fully solvable spin-chain model,
which allows us to gain insight on the mechanisms triggering non-Markovian
evolution.


  We propose and analyze a reliable and efficient a posteriori error estimator
for the pointwise tracking optimal control problem of the Stokes equations.
This linear-quadratic optimal control problem entails the minimization of a
cost functional that involves point evaluations of the velocity field that
solves the state equations. This leads to an adjoint problem with a linear
combination of Dirac measures as a forcing term and whose solution exhibits
reduced regularity properties. We also consider constraints on the control
variable. The proposed a posteriori error estimator can be decomposed as the
sum of four contributions: three contributions related to the discretization of
the state and adjoint equations, and another contribution that accounts for the
discretization of the control variable. On the basis of the devised a
posteriori error estimator, we design a simple adaptive strategy that
illustrates our theory and exhibits a competitive performance.


  In this paper, we propose a practical integrated sensing and communications
(ISAC) framework to sense dynamic targets from clutter environment while
ensuring users communications quality. To implement communications function and
sensing function simultaneously, we design multiple communications beams that
can communicate with the users as well as one sensing beam that can rotate and
scan the entire space. To minimize the interference of sensing beam on existing
communications systems, we divide the service area into sensing beam for
sensing (S4S) sector and communications beam for sensing (C4S) sector, and
provide beamforming design and power allocation optimization strategies for
each type sector. Unlike most existing ISAC studies that ignore the
interference of static environmental clutter on target sensing, we construct a
mixed sensing channel model that includes both static environment and dynamic
targets. When base station receives the echo signals, the mean phasor
cancellation (MPC) method is employed to filter out the interference from
static environmental clutter and to extract the effective dynamic target
echoes. Then a complete and practical dynamic target sensing scheme is designed
to detect the presence of dynamic targets and to estimate their angles,
distances, and velocities. In particular, dynamic target detection and angle
estimation are realized through angle-Doppler spectrum estimation (ADSE) and
joint detection over multiple subcarriers (MSJD), while distance and velocity
estimation are realized through the extended subspace algorithm. Simulation
results demonstrate the effectiveness of the proposed scheme and its
superiority over the existing methods that ignore environmental clutter.


  We use the coupled cluster method (CCM) to study the zero-temperature phase
diagram of a 2D frustrated spin-half antiferromagnet, the so-called Union Jack
model. It is defined on a square lattice such that all nearest-neighbor bonds
are present with a strength $J_{1} > 0$, but only half the
next-nearest-neighbor bonds are present with a strength $J_{2} \equiv \kappa
J_{1} > 0$. The bonds are arranged such that on the $2 \times 2$ unit cell they
form the pattern of the Union Jack flag. We find strong evidence for a first
phase transition between a N\'{e}el phase and a canted ferrimagnetic phase at a
critical coupling $\kappa_{c_{1}} = 0.66 \pm 0.02$. At the transition the
energy and its first derivative seem continuous, thus providing a typical
scenario of a second-order transition, although a weakly first-order transition
cannot be excluded. By contrast, the average on-site magnetization $M$
approaches a nonzero value $M_{c_{1}}=0.195 \pm 0.005$ on both sides of the
transition, which is more typical of a first-order transition. The slope
$dM/d\kappa$ also appears to be continuous, or very nearly so, at the critical
point $\kappa_{c_{1}}$. We find strong evidence that the canted phase becomes
unstable at large values of $\kappa$, and hence we have also used the CCM with
a model collinear semi-stripe-ordered ferrimagnetic state in which alternating
rows (and columns) are ferromagnetically and antiferromagnetically ordered. We
find tentative evidence, based on the relative energies of the two states, for
a second (first-order) phase transition between the canted and
semi-stripe-ordered states at a large value of the coupling parameter around
$\kappa_{c_{2}} \approx 125 \pm 5$. This prediction, however, is based on an
extrapolation of the CCM results for the canted state into regimes where the
CCM equations at any level of approximation beyond the lowest have no
solutions.


  We present an optimization of the hadron focusing system for a low-energy
high-intensity conventional neutrino beam (Super-Beam) proposed on the basis of
the HP-SPL at CERN with a beam power of 4 MW and an energy of 4.5 GeV. The far
detector would be a 440 kton Water Cherenkov detector (MEMPHYS) located at a
baseline of 130 km in the Fr\'ejus site. The neutrino fluxes simulation relies
on a new GEANT4 based simulation coupled with an optimization algorithm based
on the maximization of the sensitivity limit on the $\theta_{13}$ mixing angle.
A new configuration adopting a multiple horn system with solid targets is
proposed which improves the sensitivity to $\theta_{13}$ and the CP violating
phase $\delta_{CP}$.


  Parity-violating (PV) elastic electron-proton scattering measures Q-weak for
the proton, $Q_W^p$. To extract $Q_W^p$ from data, all radiative corrections
must be well-known. Recently, disagreement on the gamma-Z box contribution to
$Q_W^p$ has prompted the need for further analysis of this term. Here, we
support one choice of a debated factor, go beyond the previously assumed
equality of electromagnetic and gamma-Z structure functions, and find an
analytic result for one of the gamma-Z box integrals. Our numerical evaluation
of the gamma-Z box is in agreement within errors with previous reports, albeit
somewhat larger in central value, and is within the uncertainty requirements of
current experiments.