  This paper continues the study of metastable behaviour in disordered mean
field models initiated in [2], [3]. We consider the generalized Hopfield model
with finitely many independent patterns $\xi_1,...,\xi_p$ where the patterns
have i.i.d. components and follow discrete distributions on $[-1,1]$. We show
that metastable behaviour occurs and provide sharp asymptotics on metastable
exit times and the corresponding capacities. We apply the potential theoretic
approach developed by Bovier et al. in the space of appropriate order
parameters and use an analysis of the discrete Laplacian to obtain lower bounds
on capacities. Moreover, we include the possibility of multiple saddle points
with the same value of the rate function and the case that the energy surface
is degenerate around critical points.


  We present a path integral Monte Carlo study of the global superfluid
fraction and local superfluid density in cylindrically-symmetric reservoirs of
liquid $^{4}$He separated by nanoaperture arrays. The superfluid response to
both translations along the axis of symmetry (longitudinal response) and
rotations about the cylinder axis (transverse response) are computed, together
with radial and axial density distributions that reveal the microscopic
inhomogeneity arising from the combined effects of the confining external
potential and the $^4$He-$^4$He interatomic potentials. We make a microscopic
determination of the length-scale of decay of superfluidity at the radial
boundaries of the system by analyzing the local superfluid density distribution
to extract a displacement length that quantifies the superfluid mass
displacement away from the boundary. We find that the longitudinal superfluid
response is reduced in reservoirs separated by a septum containing sufficiently
small apertures compared to a cylinder with no intervening aperture array, for
all temperatures below $T_{\lambda}$. For a single aperture in the septum, a
significant drop in the longitudinal superfluid response is seen when the
aperture diameter is made smaller than twice the empirical
temperature-dependent $^4$He healing length, consistent with the formation of a
weak link between the reservoirs. Increasing the diameter of a single aperture
or the number of apertures in the array results in an increase of the
superfluid density toward the expected bulk value.


  The Compact Linear Collider (CLIC) is a proposed future high-luminosity
linear electron-positron collider operating at three energy stages, with
nominal centre-of-mass energies: 380 GeV, 1.5 TeV, and 3 TeV. Its aim is to
explore the energy frontier, providing sensitivity to physics beyond the
Standard Model (BSM) and precision measurements of Standard Model processes
with an emphasis on Higgs boson and top-quark physics. The opportunities for
top-quark physics at CLIC are discussed in this paper. The initial stage of
operation focuses on top-quark pair production measurements, as well as the
search for rare flavour-changing neutral current (FCNC) top-quark decays. It
also includes a top-quark pair production threshold scan around 350 GeV which
provides a precise measurement of the top-quark mass in a well-defined
theoretical framework. At the higher-energy stages, studies are made of
top-quark pairs produced in association with other particles. A study of ttH
production including the extraction of the top Yukawa coupling is presented as
well as a study of vector boson fusion (VBF) production, which gives direct
access to high-energy electroweak interactions. Operation above 1 TeV leads to
more highly collimated jet environments where dedicated methods are used to
analyse the jet constituents. These techniques enable studies of the top-quark
pair production, and hence the sensitivity to BSM physics, to be extended to
higher energies. This paper also includes phenomenological interpretations that
may be performed using the results from the extensive top-quark physics
programme at CLIC.


  Using first principle calculations, we study the structural, optical and
electronic properties of two-dimensional silicene-like structures of CSi7
(carbosilicene) and GeSi7 (germasilicene) monolayers. We show that both CSi7
and GeSi7 monolayers have different buckling that promises a new way to control
the buckling in silicene-like structures. Carbon impurity decreases the
silicene buckling, whereas germanium impurity increases it. The CSi7 has
semiconducting properties with 0.25 eV indirect band gap, but GeSi7 is a
semimetal. Also, under uniaxial tensile strain, the semiconducting properties
of CSi7 convert to metallic properties which shows that CSi7 can be used in
straintronic devices such as strain sensor and strain switch. There is no
important response for GeSi7 under strain. The GeSi7 has higher dielectric
constant relative to CSi7, silicene and graphene and it can be used as a
2D-material in high performance capacitors. Calculation of cohesive and
formation energies show that CSi7 is more stable than GeSi7. Furthermore, we
investigate the optical properties of these new materials and we show that CSi7
and GeSi7 can significantly increase the light absorption of silicene. The
obtained results can pave a new route for tuning the electronic and optical
properties of silicene like structures for different applications in
nanoelectronic devices.


  One-shot federated learning (OSFL) has gained attention in recent years due
to its low communication cost. However, most of the existing methods require
auxiliary datasets or training generators, which hinders their practicality in
real-world scenarios. In this paper, we explore the novel opportunities that
diffusion models bring to OSFL and propose FedCADO, utilizing guidance from
client classifiers to generate data that complies with clients' distributions
and subsequently training the aggregated model on the server. Specifically, our
method involves targeted optimizations in two aspects. On one hand, we
conditionally edit the randomly sampled initial noises, embedding them with
specified semantics and distributions, resulting in a significant improvement
in both the quality and stability of generation. On the other hand, we employ
the BN statistics from the classifiers to provide detailed guidance during
generation. These tailored optimizations enable us to limitlessly generate
datasets, which closely resemble the distribution and quality of the original
client dataset. Our method effectively handles the heterogeneous client models
and the problems of non-IID features or labels. In terms of privacy protection,
our method avoids training any generator or transferring any auxiliary
information on clients, eliminating any additional privacy leakage risks.
Leveraging the extensive knowledge stored in the pre-trained diffusion model,
the synthetic datasets can assist us in surpassing the knowledge limitations of
the client samples, resulting in aggregation models that even outperform the
performance ceiling of centralized training in some cases, which is
convincingly demonstrated in the sufficient quantification and visualization
experiments conducted on three large-scale multi-domain image datasets.


  We consider the multifractal formalism for the dynamics of semigroups of
rational maps on the Riemann sphere and random complex dynamical systems. We
elaborate a multifractal analysis of level sets given by quotients of Birkhoff
sums with respect to the skew product associated with a semigroup of rational
maps. Applying these results, we perform a multifractal analysis of the
H\"older regularity of limit state functions of random complex dynamical
systems.


  For a field k$with an automorphism \sigma and a derivation \delta, we
introduce the notion of liouvillian solutions of linear difference-differential
systems {\sigma(Y) = AY, \delta(Y) = BY} over k and characterize the existence
of liouvillian solutions in terms of the Galois group of the systems. We will
give an algorithm to decide whether such a system has liouvillian solutions
when k = C(x,t), \sigma(x) = x+1, \delta = d/dt$ and the size of the system is
a prime.


  Name-based gender prediction has traditionally categorized individuals as
either female or male based on their names, using a binary classification
system. That binary approach can be problematic in the cases of gender-neutral
names that do not align with any one gender, among other reasons. Relying
solely on binary gender categories without recognizing gender-neutral names can
reduce the inclusiveness of gender prediction tasks. We introduce an additional
gender category, i.e., "neutral", to study and address potential gender biases
in Large Language Models (LLMs). We evaluate the performance of several
foundational and large language models in predicting gender based on first
names only. Additionally, we investigate the impact of adding birth years to
enhance the accuracy of gender prediction, accounting for shifting associations
between names and genders over time. Our findings indicate that most LLMs
identify male and female names with high accuracy (over 80%) but struggle with
gender-neutral names (under 40%), and the accuracy of gender prediction is
higher for English-based first names than non-English names. The experimental
results show that incorporating the birth year does not improve the overall
accuracy of gender prediction, especially for names with evolving gender
associations. We recommend using caution when applying LLMs for gender
identification in downstream tasks, particularly when dealing with non-binary
gender labels.


  This paper is concerned with the problem of comparing the population means of
two groups of independent observations. An approximate randomization test
procedure based on the test statistic of Chen and Qin (2010) is proposed. The
asymptotic behavior of the test statistic as well as the randomized statistic
is studied under weak conditions. In our theoretical framework, observations
are not assumed to be identically distributed even within groups. No condition
on the eigenstructure of the covariance matrices is imposed. And the sample
sizes of the two groups are allowed to be unbalanced. Under general conditions,
all possible asymptotic distributions of the test statistic are obtained. We
derive the asymptotic level and local power of the approximate randomization
test procedure. Our theoretical results show that the proposed test procedure
can adapt to all possible asymptotic distributions of the test statistic and
always has correct test level asymptotically. Also, the proposed test procedure
has good power behavior. Our numerical experiments show that the proposed test
procedure has favorable performance compared with several alternative test
procedures.


  Neural architecture search methods seek optimal candidates with efficient
weight-sharing supernet training. However, recent studies indicate poor ranking
consistency about the performance between stand-alone architectures and
shared-weight networks. In this paper, we present Prior-Guided One-shot NAS
(PGONAS) to strengthen the ranking correlation of supernets. Specifically, we
first explore the effect of activation functions and propose a balanced
sampling strategy based on the Sandwich Rule to alleviate weight coupling in
the supernet. Then, FLOPs and Zen-Score are adopted to guide the training of
supernet with ranking correlation loss. Our PGONAS ranks 3rd place in the
supernet Track Track of CVPR2022 Second lightweight NAS challenge. Code is
available in
https://github.com/pprp/CVPR2022-NAS?competition-Track1-3th-solution.


  Estimating causal effects from observational data is not always possible due
to confounding. Identifying a set of appropriate covariates (adjustment set)
and adjusting for their influence can remove confounding bias; however, such a
set is typically not identifiable from observational data alone. Experimental
data do not have confounding bias, but are typically limited in sample size and
can therefore yield imprecise estimates. Furthermore, experimental data often
include a limited set of covariates, and therefore provide limited insight into
the causal structure of the underlying system. In this work we introduce a
method that combines large observational and limited experimental data to
identify adjustment sets and improve the estimation of causal effects. The
method identifies an adjustment set (if possible) by calculating the marginal
likelihood for the experimental data given observationally-derived prior
probabilities of potential adjustmen sets. In this way, the method can make
inferences that are not possible using only the conditional dependencies and
independencies in all the observational and experimental data. We show that the
method successfully identifies adjustment sets and improves causal effect
estimation in simulated data, and it can sometimes make additional inferences
when compared to state-of-the-art methods for combining experimental and
observational data.


  The essence of the path planning problems is multi-modality constraint.
However, most of the current literature has not mentioned this issue. This
paper introduces the research progress of path planning based on the
multi-modality constraint. The path planning of multi-modality constraint
research can be classified into three stages in terms of its basic ingredients
(such as shape, kinematics and dynamics et al.): Route Planning, Trajectory
Planning and Motion Planning. It then reviews the research methods and
classical algorithms, especially those applied to the Unmanned Surface Vehicle
(USV) in every stage. Finally, the paper points out some existing problems in
every stage and suggestions for future research.


  In less than two years of operation, the James Webb Space Telescope (JWST)
has already accelerated significantly our quest to identify active massive
black holes (BHs) in the first billion years of the Universe's history. At the
time of writing, about 50 AGN detections and candidates have been identified
through spectroscopy, photometry, and/or morphology. Broad-line AGN are about a
hundred times more numerous than the faint end of the UV-bright quasar
population at z~5-6. In this paper, we compare the observational constraints on
the abundance of these AGN at z~5 to the populations of AGN produced in
large-scale cosmological simulations. Assuming a null fraction of obscured
simulated AGN, we find that while some simulations produce more AGN than
discovered so far, some others produce a similar abundance or even fewer AGN in
the bolometric luminosity range probed by JWST. Keeping in mind the large
uncertainty on the constraints, we discuss the implications for the theoretical
modeling of BH formation and evolution in case similar constraints continue to
accumulate. At the redshift of interest, the simulated AGN populations diverge
the most at Lbol~1e44 erg/s (by more than a dex in the bolometric luminosity
function). This regime is most affected by incompleteness in JWST surveys.
However, it holds significant potential for constraining the physical processes
determining the assembly of BHs (e.g., seeding, feedback from supernova and
AGN) and the current abundance of broad-line AGN with >1e44.5 erg/s.


  Prompt isolated leptons are essential in many analyses in high-energy
particle physics but are subject to fake-lepton background, i.e. objects that
mimic the lepton signature. The fake-lepton background is difficult to estimate
from simulation and is often directly determined from data. A popular method is
the matrix method, which however suffers from several limitations. This paper
recapitulates an alternative approach based on a likelihood with Poisson
constraints and reformulates the problem from a different starting point in the
framework of Bayesian statistics. The equality of both approaches is shown and
several cases are studied in which the matrix method is limited. In addition,
the fake lepton background is recalculated and compared to the estimate with
the matrix method in an example top-quark measurement.


  The optical conductivity, $\sigma(\omega)$, of the two dimensional one-band
Hubbard model is calculated at finite temperature using exact diagonalization
techniques on finite clusters. The in-plane d.c. resistivity, $\rho_{ab}$, is
also evaluated. We find that at large U/t and temperature T, $\rho_{ab}$ is
approximately linear with temperature, in reasonable agreement with experiments
on high-T$_c$ superconductors. Moreover, we note that $\sigma(\omega)$ displays
charge excitations, a mid-infrared (MIR) band and a Drude peak, also as
observed experimentally. The combination of the Drude peak and the MIR
oscillator strengths leads to a conductivity that decays slower than
$1/\omega^2$ at energies smaller than the insulator gap near half-filling.


  It is today acknowledged that neural network language models outperform
backoff language models in applications like speech recognition or statistical
machine translation. However, training these models on large amounts of data
can take several days. We present efficient techniques to adapt a neural
network language model to new data. Instead of training a completely new model
or relying on mixture approaches, we propose two new methods: continued
training on resampled data or insertion of adaptation layers. We present
experimental results in an CAT environment where the post-edits of professional
translators are used to improve an SMT system. Both methods are very fast and
achieve significant improvements without overfitting the small adaptation data.


  The relativistically broadened Fe K$\alpha$ line, originating from the
accretion disc in a vicinity of a super massive black hole, is observed in only
less than 50\% of type 1 Active Galactic Nuclei (AGN). In this study we
investigate could this lack of detections be explained by the effects of
certain parameters of the accretion disc and black hole, such as the
inclination, the inner and outer radius of disc and emissivity index. In order
to determine how these parameters affect the Fe K $\alpha$ line shape, we
simulated about 60,000 Fe K $\alpha$ line profiles emitted from the
relativistic disc.
  Based on simulated line profiles, we conclude that the lack of the Fe
K$\alpha$ line detection in type 1 AGN could, be caused by the specific
emitting disc parameters, but also by the limits in the spectral resolution and
sensitivity of the X-ray detectors.


  A Hadamard matrix is a scaled orthogonal matrix with $\pm 1$ entries. Such
matrices exist in certain dimensions: the Hadamard conjecture is that such a
matrix always exists when $n$ is a multiple of 4. A conjecture attributed to
Ryser is that no circulant Hadamard matrices exist when $n > 4$. Recently, Dong
and Rudelson proved the existence of approximate Hadamard matrices in all
dimensions: there exist universal $0< c < C < \infty$ so that for all $n \geq
1$, there is a matrix $A \in \left\{-1,1\right\}^{n \times n}$ satisfying, for
all $x \in \mathbb{R}^n$, $$ c \sqrt{n} \|x\|_2 \leq \|Ax\|_2 \leq C \sqrt{n}
\|x\|_2.$$ We observe that, as a consequence of the existence of flat
Littlewood polynomials, circulant approximate Hadamard matrices exist for all
$n \geq 1$.


  For any $\Lambda>0$, let $\mathcal{M}_{n,\Lambda}$ denote the space
containing all locally Lipschitz minimal graphs of dimension $n$ and of
arbitrary codimension $m$ in Euclidean space $\mathbb{R}^{n+m}$ with uniformly
bounded 2-dilation $\Lambda$ of their graphic functions. In this paper, we show
that this is a natural class to extend structural results known for codimension
one. In particular, we prove that any tangent cone $C$ of
$M\in\mathcal{M}_{n,\Lambda}$ at infinity has multiplicity one. This enables us
to get a Neumann-Poincar$\mathrm{\acute{e}}$ inequality on stationary
indecomposable components of $C$. A corollary is a Liouville theorem for $M$.
For small $\Lambda>1$(we can take any $\Lambda<\sqrt{2}$), we prove that (i)
for $n\leq7$, $M$ is flat; (2) for $n>8$ and a non-flat $M$, any tangent cone
of $M$ at infinity is a multiplicity one quasi-cylindrical minimal cone in
$\mathbb{R}^{n+m}$ whose singular set has dimension $\leq n-7$.


  The project concerns the interplay among quantum mechanics, statistical
mechanics and thermodynamics, in isolated quantum systems. The underlying goal
is to improve our understanding of the concept of thermal equilibrium in
quantum systems. First, I investigated the role played by observables and
measurements in the emergence of thermal behaviour. This led to a new notion of
thermal equilibrium which is specific for a given observable, rather than for
the whole state of the system. The equilibrium picture that emerges is a
generalization of statistical mechanics in which we are not interested in the
state of the system but only in the outcome of the measurement process. I
investigated how this picture relates to one of the most promising approaches
for the emergence of thermal behaviour in isolated quantum systems: the
Eigenstate Thermalization Hypothesis. Then, I applied the results to study some
equilibrium properties of many-body localised systems. Despite the localization
phenomenon, which prevents thermalization of subsystems, I was able to show
that we can still use the predictions of statistical mechanics to describe the
equilibrium of some observables. Moreover, the intuition developed in the
process led me to propose an experimentally accessible way to unravel the
interacting nature of many-body localised systems. Second, I exploited the
"Concentration of Measure" phenomenon to study the macroscopic properties of
the basis states of Loop Quantum Gravity. These techniques were previously used
to explain why the thermal behaviour in quantum systems is such an ubiquitous
phenomenon, at the macroscopic scale. I focused on the local properties, their
thermodynamic behaviour and interplay with the semiclassical limit. This was
motivated by the necessity to understand, from a quantum gravity perspective,
how and why a classical horizon exhibits thermal properties.


  We study a 2D potential flow of an ideal fluid with a free surface with
decaying conditions at infinity. By using the conformal variables approach, we
study a particular solution of Euler equations having a pair of square-root
branch points in the conformal plane, and find that the analytic continuation
of the fluid complex potential and conformal map define a flow in the entire
complex plane, excluding a vertical cut between the branch points. The expanded
domain is called the "virtual" fluid, and it contains a vortex sheet whose
dynamics is equivalent to the equations of motion posed at the free surface.
The equations of fluid motion are analytically continued to both sides of the
vertical branch cut (the vortex sheet), and additional time-invariants
associated with the topology of conformal plane and Kelvin's theorem for
virtual fluid are explored. We called them "winding" and virtual circulation.
This result can be generalized to a system of many cuts connecting many branch
points, and resulting in a pair of invariants for each pair of branch points.
We develop an asymptotic theory that shows how a solution originating from a
single vertical cut forms a singularity at the free surface in infinite time,
the rate of singularity approach is double-exponential, and supercedes the
previous result of the short branch cut theory with finite time singularity
formation. The present work offers a new look at fluid dynamics with free
surface by unifying the problem of motion of vortex sheets, and the problem of
2D water waves. A particularly interesting question that arises in this context
is whether instabilities of the virtual vortex sheet are related to breaking of
steep ocean waves when gravity effects are included.


  It is predicted that strongly interacting spins on a frustrated lattice may
lead to a quantum disordered ground state or even form a quantum spin liquid
with exotic low-energy excitations. However, a thorough tuning of the
frustration strength, separating its effects from those of disorder and other
factors, is pending. Here we break the symmetry of a kagome-lattice compound in
a controlled manner by applying $in$ $situ$ uniaxial stress. The transition
temperature of $\rm Y_3Cu_9(OH)_{18}OCl_8$ is linearly enhanced with strain,
$\Delta T_{\rm N}/T_{\rm N} \approx 10\%$ upon in-plane compression of order
$1\%$, providing clear evidence for a release of frustration and its pivotal
role for magnetic order. Our comprehensive $^1$H NMR results suggest a
$\overrightarrow{Q}=(1/3\times 1/3)$ state under unstrained conditions and
further reveal an incomplete antiferromagnetic transition with fluctuating
moments in this strongly frustrated system.


  The theory of optical thermodynamics provides a comprehensive framework that
enables a self-consistent description of the intricate dynamics of nonlinear
multimoded photonic systems. This theory, among others, predicts a
pressure-like intensive quantity ($\hat{p}$) that is conjugate to the system's
total number of modes ($M$) - its corresponding extensive variable. Yet at this
point, the nature of this intensive quantity is still nebulous. In this Letter,
we elucidate the physical origin of the optical thermodynamic pressure and
demonstrate its dual essence. In this context, we rigorously derive an
expression that splits $\hat{p}$ into two distinct components, a term that is
explicitly tied to the electrodynamic radiation pressure and a second entropic
part that is responsible for the entropy change. We utilize this result to
establish a formalism that simplifies the quantification of radiation pressure
under nonlinear equilibrium conditions, thus eliminating the need for a tedious
evaluation of the Maxwell stress tensor. Our theoretical analysis is
corroborated by numerical simulations carried out in highly multimoded
nonlinear optical structures. These results may provide a novel way in
predicting and controlling radiation pressure processes in a variety of
nonlinear electromagnetic settings.


  A variety of complex systems exhibit different types of relationships
simultaneously that can be modeled by multiplex networks. A typical problem is
to determine the community structure of such systems that, in general, depend
on one or more parameters to be tuned. In this study we propose one measure,
grounded on information theory, to find the optimal value of the relax rate
characterizing Multiplex Infomap, the generalization of the Infomap algorithm
to the realm of multilayer networks. We evaluate our methodology on synthetic
networks, to show that the most representative community structure can be
reliably identified when the most appropriate relax rate is used. Capitalizing
on these results, we use this measure to identify the most reliable meso-scale
functional organization in the human protein-protein interaction multiplex
network and compare the observed clusters against a collection of independently
annotated gene sets from the Molecular Signatures Database (MSigDB). Our
analysis reveals that modules obtained with the optimal value of the relax rate
are biologically significant and, remarkably, with higher functional content
than the ones obtained from the aggregate representation of the human proteome.
Our framework allows us to characterize the meso-scale structure of those
multilayer systems whose layers are not explicitly interconnected each other --
as in the case of edge-colored models -- the ones describing most biological
networks, from proteomes to connectomes.


  In view of interpreting the cosmological observations precisely, especially
when they involve narrow light beams, it is crucial to understand how light
propagates in our statistically homogeneous, clumpy, Universe. Among the
various approaches to tackle this issue, Swiss-cheese models propose an
inhomogeneous spacetime geometry which is an exact solution of Einstein's
equation, while the Dyer-Roeder approximation deals with inhomogeneity in an
effective way. In this article, we demonstrate that the distance-redshift
relation of a certain class of Swiss-cheese models is the same as the one
predicted by the Dyer-Roeder approach, at a well-controlled level of
approximation. Both methods are therefore equivalent when applied to the
interpretation of, e.g., supernova observations. The proof relies on completely
analytical arguments, and is illustrated by numerical results.


  This paper derives the asymptotic behavior of the following ruin probability
$$P\{\exists t \in G(\delta):B_H(t)-c_1t>q_1u,B_H(t)-c_2t>q_2u\},
  \ \ \ u \rightarrow \infty,$$ where $B_H$ is a standard fractional Brownian
motion, $c_1,q_1,c_2,q_2>0$ and $G(\delta)$ denotes a regular grid $\{0,\delta,
2\delta,...\}$ for some $\delta>0$. The approximation depends on $H$, $\delta$
(only when $H\leq 1/2$) and the relations between parameters $c_1,q_1,c_2,q_2$.


  We propose fractional Fokker-Planck equation for the kinetic description of
relaxation and superdiffusion processes in constant magnetic and random
electric fields. We assume that the random electric field acting on a test
charged particle is isotropic and possesses non-Gaussian Levy stable
statistics. These assumptions provide us with a straightforward possibility to
consider formation of anomalous stationary states and superdiffusion processes,
both properties are inherent to strongly non-equilibrium plasmas of solar
systems and thermonuclear devices. We solve fractional kinetic equations, study
the properties of the solution, and compare analytical results with those of
numerical simulation based on the solution of the Langevin equations with the
noise source having Levy stable probability density. We found, in particular,
that the stationary states are essentially non-Maxwellian ones and, at the
diffusion stage of relaxation, the characteristic displacement of a particle
grows superdiffusively with time and is inversely proportional to the magnetic
field.


  We study the formula complexity of Iterated Sub-Permutation Matrix
Multiplication, the logspace-complete problem of computing the product of $k$
$n$-by-$n$ Boolean matrices with at most a single $1$ in each row and column.
For all $d \le \log k$, this problem is solvable by $n^{O(dk^{1/d})}$ size
monotone formulas of two distinct types: (unbounded fan-in) $AC^0$ formulas of
depth $d+1$ and (semi-unbounded fan-in) $SAC^0$ formulas of $\bigwedge$-depth
$d$ and $\bigwedge$-fan-in $k^{1/d}$. The results of this paper give matching
$n^{\Omega(dk^{1/d})}$ lower bounds for monotone $AC^0$ and $SAC^0$ formulas
for all $k \le \log\log n$, as well as slightly weaker $n^{\Omega(dk^{1/2d})}$
lower bounds for non-monotone $AC^0$ and $SAC^0$ formulas. These size-depth
tradeoffs converge at $d = \log k$ to tight $n^{\Omega(\log k)}$ lower bounds
for both unbounded-depth monotone formulas [Ros15] and bounded-depth
non-monotone formulas [Ros18]. Our non-monotone lower bounds extend to the more
restricted Iterated Permutation Matrix Multiplication problem, improving the
previous $n^{k^{1/\exp(O(d))}}$ tradeoff for this problem [BIP98].


  One of the fundamental challenges in the deep learning community is to
theoretically understand how well a deep neural network generalizes to unseen
data. However, current approaches often yield generalization bounds that are
either too loose to be informative of the true generalization error or only
valid to the compressed nets. In this study, we present a simple yet
non-vacuous generalization bound from the optimization perspective. We achieve
this goal by leveraging that the hypothesis set accessed by stochastic gradient
algorithms is essentially fractal-like and thus can derive a tighter bound over
the algorithm-dependent Rademacher complexity. The main argument rests on
modeling the discrete-time recursion process via a continuous-time stochastic
differential equation driven by fractional Brownian motion. Numerical studies
demonstrate that our approach is able to yield plausible generalization
guarantees for modern neural networks such as ResNet and Vision Transformer,
even when they are trained on a large-scale dataset (e.g. ImageNet-1K).


  Sampling errors are inevitable when measuring the ocean; thus, to achieve a
trustable set of observations requires a quality control (QC) procedure capable
to detect spurious data. While manual QC by human experts minimizes errors, it
is inefficient to handle large datasets and vulnerable to inconsistencies
between different experts. Although automatic QC circumvents those issues, the
traditional methods results in high rates of false positives. Here, I propose a
novel approach to automatically QC oceanographic data based on the anomaly
detection technique. Multiple tests are combined into a single,
multidimensional criterion that learns the behavior of the good measurements,
and identifies bad samples as outliers. When applied to 13 years of
hydrographic profiles, the anomaly detection resulted in the best
classification performance, reducing the error by at least 50%. An open source
Python package, CoTeDe, was developed to provide state of the art tools to
quality control oceanographic data.


  Cross sections from low-energy neutron-nucleus scattering have been evaluated
using a coupled channel theory of scattering. Both a coordinate-space and a
momentum-space formalism of that coupled-channel theory are considered.A simple
rotational model of the channel interaction potentials is used to find results
using two relevant codes, ECIS97 and MCAS, so that they may be compared. The
very same model is then used in the MCAS approach to quantify the changes that
occur when allowance is made for effects of the Pauli principle.


  Using the pure spinor master action for 10D super-Yang-Mills in the gauge
$b_{0}V = Q\Xi$, tree-level scattering amplitudes are calculated through the
perturbiner method, and shown to match those obtained from pure spinor CFT
techniques. We find kinematic numerators made of nested $b$-ghost operators,
and show that the Siegel gauge condition $b_{0}V = 0$ gives rise to
color-kinematics duality satisfying numerators whose Jacobi identity follows
from the Jacobi identity of a kinematic algebra.


  Spatial symmetries in crystals are distinguished by whether they preserve the
spatial origin. We show how this basic geometric property gives rise to a new
topology in band insulators. We study spatial symmetries that translate the
origin by a fraction of the lattice period, and find that these nonsymmorphic
symmetries protect a novel surface fermion whose dispersion is shaped like an
hourglass; surface bands connect one hourglass to the next in an unbreakable
zigzag pattern. These exotic fermions are materialized in the large-gap
insulators: KHgX (X=As,Sb,Bi), which we propose as the first material class
whose topology relies on nonsymmorphic symmetries. Beside the hourglass
fermion, another surface of KHgX manifests a 3D generalization of the quantum
spin Hall effect, which has only been observed in 2D crystals. To describe the
bulk topology of nonsymmorphic crystals, we propose a non-Abelian
generalization of the geometric theory of polarization. Our nontrivial topology
originates from an inversion of the rotational quantum numbers, which we
propose as a fruitful criterion in the search for topological materials.


  User-generated content (UGC) on social media can act as a key source of
information for emergency responders in crisis situations. However, due to the
volume concerned, computational techniques are needed to effectively filter and
prioritise this content as it arises during emerging events. In the literature,
these techniques are trained using annotated content from previous crises. In
this paper, we investigate how this prior knowledge can be best leveraged for
new crises by examining the extent to which crisis events of a similar type are
more suitable for adaptation to new events (cross-domain adaptation). Given the
recent successes of transformers in various language processing tasks, we
propose CAST: an approach for Crisis domain Adaptation leveraging
Sequence-to-sequence Transformers. We evaluate CAST using two major
crisis-related message classification datasets. Our experiments show that our
CAST-based best run without using any target data achieves the state of the art
performance in both in-domain and cross-domain contexts. Moreover, CAST is
particularly effective in one-to-one cross-domain adaptation when trained with
a larger language model. In many-to-one adaptation where multiple crises are
jointly used as the source domain, CAST further improves its performance. In
addition, we find that more similar events are more likely to bring better
adaptation performance whereas fine-tuning using dissimilar events does not
help for adaptation. To aid reproducibility, we open source our code to the
community.


  Computable analysis and effective descriptive set theory are both concerned
with complete metric spaces, functions between them and subsets thereof in an
effective setting. The precise relationship of the various definitions used in
the two disciplines has so far been neglected, a situation this paper is meant
to remedy.
  As the role of the Cauchy completion is relevant for both effective
approaches to Polish spaces, we consider the interplay of effectivity and
completion in some more detail.


  In the era of large language models, model merging is a promising way to
combine multiple task-specific models into a single multitask model without
extra training. However, two challenges remain: (a) interference between
different models and (b) heterogeneous data during testing. Traditional model
merging methods often show significant performance gaps compared to fine-tuned
models due to these issues. Additionally, a one-size-fits-all model lacks
flexibility for diverse test data, leading to performance degradation. We show
that both shared and exclusive task-specific knowledge are crucial for merging
performance, but directly merging exclusive knowledge hinders overall
performance. In view of this, we propose Twin-Merging, a method that
encompasses two principal stages: (1) modularizing knowledge into shared and
exclusive components, with compression to reduce redundancy and enhance
efficiency; (2) dynamically merging shared and task-specific knowledge based on
the input. This approach narrows the performance gap between merged and
fine-tuned models and improves adaptability to heterogeneous data. Extensive
experiments on $12$ datasets for both discriminative and generative tasks
demonstrate the effectiveness of our method, showing an average improvement of
$28.34\%$ in absolute normalized score for discriminative tasks and even
surpassing the fine-tuned upper bound on the generative tasks. (Our
implementation is available in https://github.com/LZY-the-boys/Twin-Mergin.)


  We present the results of a detailed investigation of the Galactic supernova
remnant RCW 86 using the XMM-Newton X-ray telescope. RCW 86 is the probable
remnant of SN 185 A.D, a supernova that likely exploded inside a wind-blown
cavity. We use the XMM-Newton Reflection Grating Spectrometer (RGS) to derive
precise temperatures and ionization ages of the plasma, which are an indication
of the interaction history of the remnant with the presumed cavity. We find
that the spectra are well fitted by two non-equilibrium ionization models,
which enables us to constrain the properties of the ejecta and interstellar
matter plasma. Furthermore, we performed a principal component analysis on EPIC
MOS and pn data to find regions with particular spectral properties. We present
evidence that the shocked ejecta, emitting Fe-K and Si line emission, are
confined to a shell of approximately 2 pc width with an oblate spheroidal
morphology. Using detailed hydrodynamical simulations, we show that general
dynamical and emission properties at different portions of the remnant can be
well-reproduced by a type Ia supernova that exploded in a non-spherically
symmetric wind-blown cavity. We also show that this cavity can be created using
general wind properties for a single degenerate system. Our data and
simulations provide further evidence that RCW 86 is indeed the remnant of SN
185, and is the likely result of a type Ia explosion of single degenerate
origin.


  We show that there exists a surjection from the set of effective divisors of
degree $g$ on a tropical curve of genus $g$ to its Jacobian by using a tropical
version of the Riemann-Roch theorem. We then show that the restriction of the
surjection is reduced to the bijection on an appropriate subset of the set of
effective divisors of degree $g$ on the curve. Thus the subset of effective
divisors has the additive group structure induced from the Jacobian. We finally
realize the addition in Jacobian of a tropical hyperelliptic curve of genus $g$
via the intersection with a tropical curve of degree $3g/2$ or $3(g-1)/2$.


  Extracting activation patterns from functional Magnetic Resonance Images
(fMRI) datasets remains challenging in rapid-event designs due to the inherent
delay of blood oxygen level-dependent (BOLD) signal. The general linear model
(GLM) allows to estimate the activation from a design matrix and a fixed
hemodynamic response function (HRF). However, the HRF is known to vary
substantially between subjects and brain regions. In this paper, we propose a
model for jointly estimating the hemodynamic response function (HRF) and the
activation patterns via a low-rank representation of task effects.This model is
based on the linearity assumption behind the GLM and can be computed using
standard gradient-based solvers. We use the activation patterns computed by our
model as input data for encoding and decoding studies and report performance
improvement in both settings.


  A new way is proposed to cancel the cosmological constant. The proposal
involves the metric determinant acting as a type of self-adjusting $q$-field
without need of a fine-tuned chemical potential. Since the determinant of the
metric now plays a role in the physics, the allowed coordinate transformations
are restricted to those with unit Jacobian. This approach to the cosmological
constant problem is, therefore, similar to the unimodular-gravity approach of
the previous literature. The resulting cosmology has been studied and the
obtained results show the natural cancellation of an initial cosmological
constant if quantum-dissipative effects are included.


  Finding the number 2H6 of directed Hamiltonian cycles in 6-cube is problem 43
in Section 7.2.1.1 of Knuth's ' The Art of Computer Programming'; various
proposed estimates are surveyed below. We computed exact value:
H6=14,754,666,508,334,433,250,560=6*2^4*217,199*1,085,989*5,429,923. Also the
number Aut6 of those cycles up to automorphisms of 6-cube was computed as
147,365,405,634,413,085


  We describe the canonical phase space of asymptotically flat gravity in
Ashtekar-Barbero variables. We show that the Gauss constraint multiplier must
fall off slower than previously considered in order to recover ADM phase space.
The generators of the asymptotic Poincare group are derived within the
Ashtekar-Barbero phase space without reference to the ADM generators. The
resulting expressions are shown to agree, modulo Gauss constraint terms, with
those obtained from the ADM generators. A payoff of this procedure is a new
expression for the generator of asymptotic rotations which is polynomial in the
triad and hence better suited for quantum theory. Our treatment complements
earlier description by Thiemann in the context of self-dual variables.


  We show that a tachyon condensate phase replaces the spacelike singularity in
certain cosmological and black hole spacetimes in string theory. We analyze
explicitly a set of examples with flat spatial slices in various dimensions
which have a winding tachyon condensate, using worldsheet path integral methods
from Liouville theory. In a vacuum with no excitations above the tachyon
background in the would-be singular region, we analyze the production of closed
strings in the resulting state in the bulk of spacetime. We find a thermal
result reminiscent of the Hartle-Hawking state, with tunably small energy
density. The amplitudes exhibit a self-consistent truncation of support to the
weakly-coupled small-tachyon region of spacetime. We argue that the background
is accordingly robust against back reaction, and that the resulting string
theory amplitudes are perturbatively finite, indicating a resolution of the
singularity and a mechanism to start or end time in string theory. Finally, we
discuss the generalization of these methods to examples with positively curved
spatial slices.


  Rogue nodes broadcasting false information in beacon messages may lead to
catastrophic consequences in Vehicular Ad Hoc Networks (VANETs). Previous
researchers used either cryptography, trust scores, or past vehicle data to
detect rogue nodes; however, these methods suffer from high processing delay,
overhead, and False-Positive Rate (FPR). We propose herein Greenshield's
traffic model-based fog computing scheme called Fog-based Rogue Nodes Detection
(F-RouND), which dynamically utilizes the On-Board Units (OBUs) of all vehicles
in the region for rogue node detection. We aim to reduce the data processing
delays and FPR in detecting rogue nodes at high vehicle densities. The
performance of the F-RouND framework was evaluated via simulations. Results
show that the F-RouND framework ensures 45% lower processing delays, 12% lower
overhead, and 36% lower FPR at the urban scenario compared to the existing
rogue node detection schemes even when the number of rogue nodes increases by
up to 40% in the region.


  The room acoustic theory was established based on Sabine's reverberation
theory. However, in Sabine's theory, the reverberation time does not reach
zero, even if the absolute absorption condition is satisfied. This is a
contradiction of Sabine's theory, and Eyring revised the reverberation theory
to resolve this contradiction. In this paper, a theoretical framework for the
consistent reverberation theory is presented. Using this framework, it was
demonstrated that Eyring's theory has a contradiction between the sound energy
density in the steady state and energy decay from the steady state, which is
absent in Sabine's theory. Based on the proposed theoretical framework,
Sabine's reverberation theory was revised using an approach that is different
from that of Eyring. The reverberation time obtained using the revised theory
was shorter than that obtained using Sabine's theory and longer than that
obtained using Eyring's theory. Results of sound ray tracing simulations were
in better agreement with the values calculated using the revised theory rather
than those calculated using Sabine's and Eyring's theories.


  In a recent paper [Phys. Rev. Lett. 86, 63 (2001)], Li et al have reported
that the nonequilibrium heat conducting steady state of a disordered harmonic
chain is not unique. In this comment we point out that for a large class of
stochastic heat baths the uniqueness of the steady state can be proved, and
therefore the findings of Li et al could be either due to their use of
deterministic heat baths or insufficient equilibration times in the
simulations. We give a simple example where the uniquness of the steady state
can be explicitly demonstrated.


  We quantify the effects of light spin-zero particles with pseudoscalar
couplings to leptons and scalar couplings to nucleons on the evolution of solar
neutrinos. In this scenario the matter potential sourced by the nucleons in the
Sun's matter gives rise to spin precession of the relativistic neutrino
ensemble. As such the effects in the solar observables are different if
neutrinos are Dirac or Majorana particles. For Dirac neutrinos the spin-flavour
precession results into left-handed neutrino to right-handed neutrino (i.e.,
active-sterile) oscillations, while for Majorana neutrinos it results into
left-handed neutrino to right-handed antineutrino (i.e., active-active)
oscillations. In both cases this leads to distortions in the solar neutrino
spectrum which we use to derive constraints on the allowed values of the
mediator mass and couplings via a global analysis of the solar neutrino data.
In addition for Majorana neutrinos spin-flavour precession results into a
potentially observable flux of solar electron antineutrinos at the Earth which
we quantify and constrain with the existing bounds from Borexino and KamLAND.


  We report field-effect transistors (FETs) with single-crystal molybdenum
disulfide (MoS2) channels synthesized by chemical vapor deposition (CVD). For a
bilayer MoS2 FET, the mobility is ~17 cm2V-1s-1 and the on/off current ratio is
~108, which are much higher than those of FETs based on CVD polycrystalline
MoS2 films. By avoiding the detrimental effects of the grain boundaries and the
contamination introduced by the transfer process, the quality of the CVD MoS2
atomic layers deposited directly on SiO2 is comparable to the best exfoliated
MoS2 flakes. It shows that CVD is a viable method to synthesize high quality
MoS2 atomic layers.


  Efficient and accurate BRDF acquisition of real world materials is a
challenging research problem that requires sampling millions of incident light
and viewing directions. To accelerate the acquisition process, one needs to
find a minimal set of sampling directions such that the recovery of the full
BRDF is accurate and robust given such samples. In this paper, we formulate
BRDF acquisition as a compressed sensing problem, where the sensing operator is
one that performs sub-sampling of the BRDF signal according to a set of optimal
sample directions. To solve this problem, we propose the Fast and Robust
Optimal Sampling Technique (FROST) for designing a provably optimal
sub-sampling operator that places light-view samples such that the recovery
error is minimized. FROST casts the problem of designing an optimal
sub-sampling operator for compressed sensing into a sparse representation
formulation under the Multiple Measurement Vector (MMV) signal model. The
proposed reformulation is exact, i.e. without any approximations, hence it
converts an intractable combinatorial problem into one that can be solved with
standard optimization techniques. As a result, FROST is accompanied by strong
theoretical guarantees from the field of compressed sensing. We perform a
thorough analysis of FROST-BRDF using a 10-fold cross-validation with publicly
available BRDF datasets and show significant advantages compared to the
state-of-the-art with respect to reconstruction quality. Finally, FROST is
simple, both conceptually and in terms of implementation, it produces
consistent results at each run, and it is at least two orders of magnitude
faster than the prior art.


  In this study, we delve into the generation of high-resolution images from
pre-trained diffusion models, addressing persistent challenges, such as
repetitive patterns and structural distortions, that emerge when models are
applied beyond their trained resolutions. To address this issue, we introduce
an innovative, training-free approach FouriScale from the perspective of
frequency domain analysis. We replace the original convolutional layers in
pre-trained diffusion models by incorporating a dilation technique along with a
low-pass operation, intending to achieve structural consistency and scale
consistency across resolutions, respectively. Further enhanced by a
padding-then-crop strategy, our method can flexibly handle text-to-image
generation of various aspect ratios. By using the FouriScale as guidance, our
method successfully balances the structural integrity and fidelity of generated
images, achieving an astonishing capacity of arbitrary-size, high-resolution,
and high-quality generation. With its simplicity and compatibility, our method
can provide valuable insights for future explorations into the synthesis of
ultra-high-resolution images. The code will be released at
https://github.com/LeonHLJ/FouriScale.


  We suggest that the mass of four compact stars SAX J1808.4$-$3658, KS
1731$-$260, SAX J1750.8$-$2900 and IGR J17191$-$2821 can be determined from the
difference in the observed kiloHertz quasi periodic oscillations (kHz QPO-s) of
these stars. The stellar radius is very close to the marginally stable orbit
$R_{ms}$ as predicted by Einstein's general relativity. It may be noted that
the first of these stars was suggested to be a strange star more than a decade
back by Li \emph{et al.} (1999) from the unique millisecond X-ray pulsations
with an accurate determination of its rotation period. It showed kHz QPO-s
eight years back and so far it is the only set that has been observed. This is
the first time we give an estimate of the mass of the star and of three other
compact stars in Low-Mass X-ray Binaries using their observed kHz QPO-s.


  We show how LIGO is expected to detect coalescing binary black holes at
$z>1$, that are lensed by the intervening galaxy population. Gravitational
magnification, $\mu$, strengthens gravitational wave signals by $\sqrt{\mu}$,
without altering their frequencies, which if unrecognised leads to an
underestimate of the event redshift and hence an overestimate of the binary
mass. High magnifications can be reached for coalescing binaries because the
region of intense gravitational wave emission during coalescence is so small
($\sim$100km), permitting very close projections between lensing caustics and
gravitational-wave events. Our simulations incorporate accurate waveforms
convolved with the LIGO power spectral density. Importantly, we include the
detection dependence on sky position and orbital orientation, which for the
LIGO configuration translates into a wide spread in observed redshifts and
chirp masses. Currently we estimate a detectable rate of lensed events
\rateEarly{}, that rises to \rateDesign{}, at LIGO's design sensitivity limit,
depending on the high redshift rate of black hole coalescence.


  Several topics related to phenomenology of the Higgs sector in the
supersymmetric standard model are reviewed. The upper bound of the lightest
Higgs mass in the minimal supersymmetric standard model as well as extended
version of it is discussed and it is shown that an $e^+ e^-$ linear collider
with $\sqrt{s}\sim300 - 500$ GeV can find at least one Higgs boson in these
models. It is also pointed out that the heavy Higgs mass scale may be
determined from measurements of the Higgs boson decay branching ratios even if
we only discover the lightest Higgs boson at early stage of the linear collider
experiment.


  Recently, Bafekry et al. [J. Appl. Phys. 130, 114301(2021)] reported their
density functional theory (DFT) results on the structural, phonon dispersion,
elastic constants and electronic properties of a BCN monolayer. The
aforementioned theoretical work however includes erroneous results and
discussions, as will be explained in the following.


  Software testing is an important and essential part of the software
development life cycle and accounts for almost one-third of system development
costs. In the software industry, testing costs can account for about 35% to 40%
of the total cost of a software project. Therefore, providing efficient ways to
test software is critical to reduce cost, time, and effort. Black-box testing
and White-box testing are two essential components of software testing.
Black-box testing focuses on the software's functionality, while White-box
testing examines its internal structure. These tests contribute significantly
to ensuring program coverage, which remains one of the main goals of the
software testing paradigm. One of the main problems in this area is the
identification of appropriate paths for program coverage, which are referred to
as test sequences. Creating an automated and effective test sequence is a
challenging task in the software testing process. In the proposed methodology,
the challenge of "test sequence generation" is considered a multi-objective
optimization problem that includes the Oracle cost and the path, both of which
are optimized in a symmetrical manner to achieve optimal software testing.
Multi-Objective Particle Swarm Optimization (MOPSO) is used to represent the
test sequences with the highest priority and the lowest Oracle cost as optimal.
The performance of the implemented approach is compared with the
Multi-Objective Firefly Algorithm (MOFA) for generating test sequences. The
MOPSO-based solution outperforms the MOFA-based approach and simultaneously
provides the optimal solution for both objectives.


  Context. G29.96-0.02 is a high-mass star-forming cloud observed at 70, 160,
250, 350, and 500 microns as part of the Herschel survey of the Galactic Plane
during the Science Demonstration Phase. Aims. We wish to conduct a far-infrared
study of the sources associated with this star-forming region by estimating
their physical properties and evolutionary stage, and investigating the clump
mass function, the star formation efficiency and rate in the cloud. Methods. We
have identified the Hi-GAL sources associated with the cloud, searched for
possible counterparts at centimeter and infrared wavelengths, fitted their
spectral energy distribution and estimated their physical parameters. Results.
A total of 198 sources have been detected in all 5 Hi-GAL bands, 117 of which
are associated with 24 microns emission and 87 of which are not associated with
24 microns emission. We called the former sources 24 microns-bright and the
latter ones 24 microns-dark. The [70-160] color of the 24 microns-dark sources
is smaller than that of the 24 microns-bright ones. The 24 microns-dark sources
have lower L_bol and L_bol/M_env than the 24 microns-bright ones for similar
M_env, which suggests that they are in an earlier evolutionary phase. The
G29-SFR cloud is associated with 10 NVSS sources and with extended centimeter
continuum emission well correlated with the 70 microns emission. Most of the
NVSS sources appear to be early B or late O-type stars. The most massive and
luminous Hi-GAL sources in the cloud are located close to the G29-UC region,
which suggests that there is a privileged area for massive star formation
towards the center of the G29-SFR cloud. Almost all the Hi-GAL sources have
masses well above the Jeans mass but only 5% have masses above the virial mass,
which indicates that most of the sources are stable against gravitational
collapse. The sources with M_env > M_virial and that ...


  This work presents a novel framework for spherical mesh parameterization. An
efficient angle-preserving spherical parameterization algorithm is introduced,
which is based on dynamic Yamabe flow and the conformal welding method with
solid theoretic foundation. An area-preserving spherical parameterization is
also discussed, which is based on discrete optimal mass transport theory.
Furthermore, a spherical parameterization algorithm, which is based on the
polar decomposition method, balancing angle distortion and area distortion is
presented. The algorithms are tested on 3D geometric data and the experiments
demonstrate the efficiency and efficacy of the proposed methods.


  The purpose of this study is to clarify what kind of news is easily retweeted
and what kind of news is easily Liked. We believe these actions, retweeting and
Liking, have different meanings for users. Understanding this difference is
important for understanding people's interest in Twitter. To analyze the
difference between retweets (RT) and Likes on Twitter in detail, we focus on
word appearances in news titles. First, we calculate basic statistics and
confirm that tweets containing news URLs have different RT and Like tendencies
compared to other tweets. Next, we compared RTs and Likes for each category and
confirmed that the tendency of categories is different. Therefore, we propose
metrics for clarifying the differences in each action for each category used in
the $\chi$-square test in order to perform an analysis focusing on the topic.
The proposed metrics are more useful than simple counts and TF-IDF for
extracting meaningful words to understand the difference between RTs and Likes.
We analyzed each category using the proposed metrics and quantitatively
confirmed that the difference in the role of retweeting and Liking appeared in
the content depending on the category. Moreover, by aggregating tweets
chronologically, the results showed the trend of RT and Like as a list of words
and clarified how the characteristic words of each week were related to current
events for retweeting and Liking.


  We present a new algorithm for maintaining a DFS tree of an arbitrary
directed graph under any sequence of edge insertions. Our algorithm requires a
total of $O(m\cdot n)$ time in the worst case to process a sequence of edge
insertions, where $n$ is the number of vertices in the graph and $m$ is the
total number of edges in the final graph. We also prove lower bounds for
variations of this problem.


  In $\mathbb{R}^d$, the characterization of the \mbox{lack of compactness of
the continuous Sobolev injection $ \mathring{H}^s \hookrightarrow L^p $}, with
$ \displaystyle{\frac{s}{d} + \frac{1}{p} = \frac{1}{2}} $ and $\displaystyle{0


  Terahertz (THz) radiation with its spectrum extending up to 1 THz has been
observed by an illumination of femtosecond optical pulses to optical switching
devices fabricated on magnetoresistive manganite thin films;
Pr$_{0.7}$Ca$_{0.3}$MnO$_3$. The THz radiation strongly depends on temperature
$T$ and its $T$ trend reverses sign across charge-orbital and spin ordering
$T$'s.


  We study the Gribov problem within a Hamiltonian formulation of pure
Yang-Mills theory. For a particular gauge fixing, a finite volume modification
of the axial gauge, we find an exact characterization of the space of
gauge-inequivalent gauge configurations.


  Black holes can be produced in collapse of small-scale dark matter
structures, which can happen at any time from the early to present-day
universe. Microstructure black holes (MSBHs) can have a wide range of masses.
Small MSBHs evaporate via Hawking radiation with lifetimes shorter than the age
of the universe, but they are not subject to the usual early-universe bounds on
the abundance of small primordial black holes. We investigate the possible
signal of such a population of exploding, late-forming black holes,
constraining their abundance with observations from diffuse extragalactic
gamma- and x-ray sources, the galactic center, and dwarf spheroidal galaxies.


  Saturable absorption is a nonlinear effect where a material's ability to
absorb light is frustrated due to a high influx of photons and the creation of
electron vacancies. Experimentally induced saturable absorption in copper
revealed a reduction in the temporal duration of transmitted X-ray laser
pulses, but a complete understanding of this process is still missing. In this
computational work, we employ non-local thermodynamic equilibrium plasma
simulations to study the interaction of femtosecond X-rays and copper.
Following the onset of frustrated absorption, we find that a $K\text{--}M$
resonant transition occurring at highly charged states turns copper opaque
again. The changes in absorption generate a transient transparent window
responsible for the shortened transmission signal. We also propose using
fluorescence induced by the incident beam as an alternative source to achieve
shorter X-ray pulses. Intense femtosecond X-ray pulses are valuable to probe
the structure and dynamics of biological samples or to reach extreme states of
matter. Shortened pulses could be relevant for emerging imaging techniques.


  Comment on "Fe valency-induced effect on the magnetic and electrotransport
properties in Nd$_{0.67}$Sr$_{0.33}$Mn$_{1-x}$Fe$_x$O$_3$ polycrystalline
system" [Appl. Phys. Lett. 82, 1721 (2003)]


  The sensitivity of trajectories over finite time intervals t to perturbations
of the initial conditions can be associated with a finite-time Lyapunov
exponent lambda, obtained from the elements M_{ij} of the stability matrix M.
For globally chaotic dynamics lambda tends to a unique value (the usual
Lyapunov exponent lambda_infty) as t is sent to infinity, but for finite t it
depends on the initial conditions of the trajectory and can be considered as a
statistical quantity. We compute for a particle moving in a random
time-dependent potential how the distribution function P(lambda;t) approaches
the limiting distribution P(lambda;infty)=delta(lambda-lambda_infty). Our
method also applies to the tail of the distribution, which determines the
growth rates of positive moments of M_{ij}. The results are also applicable to
the problem of wave-function localization in a disordered one-dimensional
potential.


  We study the entanglement of quantum states associated with submanifolds of
Kaehler manifolds. As a motivating example, we discuss the semiclassical
asymptotics of entanglement entropy of pure states on the two dimensional
sphere with the standard metric.


  We extend our previous studies [PhysRevD.90.054509, PhysRevD.92.094510] of
the pion quasiparticle in the low-temperature phase of two-flavor QCD with
support from chiral effective theory. This includes the analysis performed on a
finite temperature ensemble of size $20\times 64^3$ at $T\approx 151$MeV and a
lighter zero-temperature pion mass $m_{\pi} \approx 185$ MeV. Furthermore, we
investigate the Gell-Mann--Oakes-Renner relation at finite temperature and the
Dey-Eletsky-Ioffe mixing theorem at finite quark mass.


  For loops with UV divergences, finite physical results obtained via $\infty -
\infty$ mean the physical transition amplitudes of loops are not well-defined.
In this paper, a presumption that the physical contributions of loops from UV
regions are insignificant is proposed, and a method of UV-free scheme described
by an equation is introduced to derive loop results without UV divergences.
This scheme provides a new perspective to an open question of the hierarchy
problem of Higgs mass, i.e., an alternative interpretation without fine-tuning
within the standard model.


  The host star metallicity provide a measure of the conditions in
protoplanetary disks at the time of planet formation. Using a sample of over
20,000 Kepler stars with spectroscopic metallicities from the LAMOST survey, we
explore how the exoplanet population depends on host star metallicity as a
function of orbital period and planet size. We find that exoplanets with
orbital periods less than 10 days are preferentially found around metal-rich
stars ([Fe/H]~ 0.15 +- 0.05 dex). The occurrence rates of these hot exoplanets
increases to ~30% for super-solar metallicity stars from ~10% for stars with a
sub-solar metallicity. Cooler exoplanets, that resides at longer orbital
periods and constitute the bulk of the exoplanet population with an occurrence
rate of >~ 90%, have host-star metallicities consistent with solar. At short
orbital periods, P<10 days, the difference in host star metallicity is largest
for hot rocky planets (<1.7 R_Earth), where the metallicity difference is
[Fe/H] =~ 0.25 +- 0.07 dex. The excess of hot rocky planets around metal-rich
stars implies they either share a formation mechanism with hot Jupiters, or
trace a planet trap at the protoplanetary disk inner edge which is
metallicity-dependent. We do not find statistically significant evidence for a
previously identified trend that small planets toward the habitable zone are
preferentially found around low-metallicity stars. Refuting or confirming this
trend requires a larger sample of spectroscopic metallicities.


  Copper ferrite thin films were deposited on amorphous quartz substrates. The
as deposited films were annealed in air and either quenched or slow cooled.
Magnetization studies were carried out on the as deposited as well as annealed
films using a SQUID magnetometer. The M-H curves were measured up to a field of
7T, at temperatures varying from 5K to 300K. The magnetization in the films did
not saturate, even at the highest field. The expression, M(H)= Q(1- a/H^n)
fitted the approach to saturation best with n=1/2, for all films and at all
temperatures. The coefficient a was the highest for the as deposited film and
was the smallest for the quenched film. In the case of as deposited film, the
value of coefficient a increased with increasing temperature, while for the
annealed films, the value of a showed a decrease as temperature increases.


  The exceptional mechanical properties of graphene have made it attractive for
nano-mechanical devices and functional composite materials. Two key aspects of
graphene's mechanical behavior are its elastic and adhesive properties. These
are generally determined in separate experiments, and it is moreover typically
difficult to extract parameters for adhesion. In addition, the mechanical
interplay between graphene and other elastic materials has not been well
studied. Here, we demonstrate a technique for studying both the elastic and
adhesive properties of few-layer graphene (FLG) by placing it on deformable,
micro-corrugated substrates. By measuring deformations of the composite
graphene-substrate structures, and developing a related linear elasticity
theory, we are able to extract information about graphene's bending rigidity,
adhesion, critical stress for interlayer sliding, and sample-dependent tension.
The results are relevant to graphene-based mechanical and electronic devices,
and to the use of graphene in composite, flexible, and strain-engineered
materials.


  For many spin-0 target nuclei neutron capture measurements yield information
on level densities at the neutron separation energy. Also the average photon
width has been determined from capture data as well as Maxwellian average cross
sections for the energy range of unresolved resonances. Thus it is challenging
to use this data set for a test of phenomenological prescriptions for the
prediction of radiative processes. An important ingredient for respective
calculations is the photon strength function for which a parameterization was
proposed using a fit to giant dipole resonance shapes on the basis of
theoretically determined ground state deformations including triaxiality.
Deviations from spherical and axial symmetry also influence level densities and
it is suggested to use a combined parameterization for both, level density and
photon strength. The formulae presented give a good description of the data for
low spin capture into 124 nuclei with 72<A<244 and only very few global
parameters have to be adjusted when the predetermined information on ground
state shapes of the nuclei involved is accounted for.


  Graph Contrastive Learning (GCL) has emerged as a popular unsupervised graph
representation learning method. However, it has been shown that GCL is
vulnerable to adversarial attacks on both the graph structure and node
attributes. Although empirical approaches have been proposed to enhance the
robustness of GCL, the certifiable robustness of GCL is still remain
unexplored. In this paper, we develop the first certifiably robust framework in
GCL. Specifically, we first propose a unified criteria to evaluate and certify
the robustness of GCL. We then introduce a novel technique, RES (Randomized
Edgedrop Smoothing), to ensure certifiable robustness for any GCL model, and
this certified robustness can be provably preserved in downstream tasks.
Furthermore, an effective training method is proposed for robust GCL. Extensive
experiments on real-world datasets demonstrate the effectiveness of our
proposed method in providing effective certifiable robustness and enhancing the
robustness of any GCL model. The source code of RES is available at
https://github.com/ventr1c/RES-GCL.


  We studied the crystal and magnetic structure of the
La$_{1-x}$Ca$_{x}$MnO$_{3}$ compound for $(0.11\leq x\leq 0.175)$ using
stoichiometric samples. For $x<0.13$ the system's ground state is insulating
canted antiferromagnetic. For $0.13\le x \le 0.175$ e below the Jahn Teller
transition temperature ($T_{\rm JT}$) the crystal structure undergoes a
monoclinic distortion. The crystal structure can be described with $P 2_1/c$
space group which permits two Mn sites. The unit cell strain parameter
$s=2(a-c)/(a+c)$ increases for $T<T_{\rm JT}$, taking the maximum value at the
Curie point, and then decreases. Below $T_{\rm M^/M^{//}}\approx 60 $ K $s$
abruptly changes slope and finally approaches T=0 K with nearly zero slope. The
change of $s$ at $T_{\rm M^/M^{//}}$ is connected to a characteristic feature
in the magnetic measurements. As $x$ increases towards the ferromagnetic
metallic boundary, although $s$ is reduced appreciably, the monoclinic
structure is preserved. The monoclinic structure is discussed with relation to
the orbital ordering, which can produce the ferromagnetic insulating ground
state. We also studied samples that were prepared in air atmosphere. This
category of samples shows ferromagnetic insulating behavior without following
the particular variation of the $s$ parameter. The crystal structure of these
samples is related to the so-called O$^{*}$ ($c>a>b/\sqrt{2}$) structure.


  Adomian polynomials (AP's) are expressed in terms of new objects called
reduced polynomials (RP's). These new objects, which carry two subscripts, are
independent of the form of the nonlinear operator. Apart from the well-known
two properties of AP's, curiously enough no further properties are discussed in
the literature. We derive and discuss in full detail the properties of the RP's
and AP's. We focus on the case where the nonlinear operator depends on one
variable and construct the most general analytical expressions of the RP's for
small values of the difference of their subscripts. It is shown that each RP
depends on a number of functions equal to the difference of its subscripts plus
one. These new properties lead to implement a dramatically simple and compact
Mathematica program for the derivation of individual RP's and AP's in their
general forms and provide useful hints for elegant hand calculations of AP's.
Application of the program is considered.


  We investigate the thermodynamic limit of the su(n)-invariant spin chain
models with unparallel boundary fields. It is found that the contribution of
the inhomogeneous term in the associated T-Q relation to the ground state
energy does vanish in the thermodynamic limit. This fact allows us to calculate
the boundary energy of the system. Taking the su(2) (or the XXX) spin chain and
the su(3) spin chain as concrete examples, we have studied the corresponding
boundary energies of the models. The method used in this paper can be
generalized to study the thermodynamic properties and boundary energy of other
high rank models with non-diagonal boundary fields.


  We propose a 3D meshless method to compute mean pressure fields in turbulent
flows from image velocimetry. The method is an extension of the constrained
Radial Basis Function (RBF) formulation by \citet{Sperotto2022} to a Reynolds
Averaged Navier Stokes (RANS) framework. This is designed to handle both
scattered data as in Particle Tracking Velocimetry (PTV) and data in uniform
grids as in correlation-based Particle Image Velocimetry (PIV). The RANS
extension includes the Reynolds stresses into the constrained least square
problem. We test the approach on a numerical database featuring a Backward
Facing Step (BFS) with a Reynolds number of 6400 (defined with respect to the
inlet velocity and step height), obtained via Direct Numerical Simulation
(DNS).


  The Gaia satellite is cataloging the astrometric properties of an
unprecedented number of stars in the Milky Way with extraordinary precision.
This provides a gateway for conducting extensive surveys of transient
astrometric lensing events caused by dark compact objects. In this work, we
establish a data analysis pipeline capable of searching for such events in the
upcoming Gaia Data Release 4 (DR4). We use Gaia Early Data Release 3 (EDR3) and
current dark matter and astrophysical black hole population models to create
mock DR4 catalogs containing stellar trajectories perturbed by lensing. Our
analysis of these mock catalogs suggests that Gaia DR4 will contain about 4
astrometric lensing events from astrophysical black holes at a $5\sigma$
significance level. Furthermore, we project that our data analysis pipeline
applied to Gaia DR4 will result in leading constraints on compact dark matter
in the mass range $1$-$10^3~M_\odot$ down to a dark matter fraction of about
one percent.


  We experimentally demonstrate an optically-pumped III-V/Si vertical-cavity
laser with lateral emission into a silicon waveguide. This on-chip hybrid laser
comprises a distributed Bragg reflector, a III-V active layer, and a
high-contrast grating reflector, which simultaneously funnels light into the
waveguide integrated with the laser. This laser has the advantages of
long-wavelength vertical-cavity surface-emitting lasers, such as low threshold
and high side-mode suppression ratio, while allowing integration with silicon
photonic circuits, and is fabricated using CMOS-compatible processes. It has
the potential for ultrahigh-speed operation beyond 100 Gbit/s and features a
novel mechanism for transverse mode control.


  A relativistic topological insulator model in three spatial dimensions which
is a non trivial extension of the non-abelian Landau problem is proposed. The
model is exactly soluble and energy levels have both a discrete and a
continuous degeneracy. The chromomagnetic field is strong and the fermions are
confined in a plane and the physical effects that appear reflects the ${\bm
Z}_2$ symmetry.


  The realizations of the Lie algebra corresponding to the dynamical symmetry
group SO(2,1) of the Schr\"{o}dinger equations for the Morse and the
$V=u^2+1/u^2$ potentials were known to be related by a canonical
transformation. q-deformed analog of this transformation connecting two
different realizations of the sl_q(2) algebra is presented. By the virtue of
the q-canonical transformation a q-deformed Schr\"{o}dinger equation for the
Morse potential is obtained from the q-deformed $V=u^2+ 1/u^2$ Schr\"{o}dinger
equation. Wave functions and eigenvalues of the q-Schr\"{o}dinger equations
yielding a new definition of the q-Laguerre polynomials are studied.


  We study the problem of identifying the unknown intervention targets in
structural causal models where we have access to heterogeneous data collected
from multiple environments. The unknown intervention targets are the set of
endogenous variables whose corresponding exogenous noises change across the
environments. We propose a two-phase approach which in the first phase recovers
the exogenous noises corresponding to unknown intervention targets whose
distributions have changed across environments. In the second phase, the
recovered noises are matched with the corresponding endogenous variables. For
the recovery phase, we provide sufficient conditions for learning these
exogenous noises up to some component-wise invertible transformation. For the
matching phase, under the causal sufficiency assumption, we show that the
proposed method uniquely identifies the intervention targets. In the presence
of latent confounders, the intervention targets among the observed variables
cannot be determined uniquely. We provide a candidate intervention target set
which is a superset of the true intervention targets. Our approach improves
upon the state of the art as the returned candidate set is always a subset of
the target set returned by previous work. Moreover, we do not require
restrictive assumptions such as linearity of the causal model or performing
invariance tests to learn whether a distribution is changing across
environments which could be highly sample inefficient. Our experimental results
show the effectiveness of our proposed algorithm in practice.


  We present and compare two high-pressure, high-frequency electric-discharge
sources for the generation of supersonic beams of fluorine radicals. The
sources are based on dielectric-barrier-discharge (DBD) and plate-discharge
units attached to a pulsed solenoid valve. The corrosion-resistant discharge
sources were operated with fluorine gas seeded in helium up to backing
pressures as high as 30 bar. We employed a (3+1) resonance-enhanced multiphoton
ionization combined with velocity-map imaging for the optimization,
characterization and comparison of the fluorine beams. Additionally, universal
femtosecond-laser-ionization detection was used for the characterization of the
discharge sources at experimental repetition rates up to 200 Hz. Our results
show that the plate discharge is more efficient in F$_{2}$ dissociation than
the DBD by a factor of 8-9, whereas the DBD produces internally colder fluorine
radicals.


  Extending the U(1) slave-rotor representation\cite{FG_SRR} of the repulsive
Hubbard model, we propose an SU(2) slave-rotor decomposition for the attractive
Hubbard model, where the SU(2) slave-rotor variables represent order parameter
fluctuations associated with superconductivity and charge density wave. This
decomposition method allows us to modify the standard Hartree-Fock mean field
theory by incorporating order parameter fluctuations on an equal footing.
Deriving an effective SU(2) slave-rotor action from the attractive Hubbard
model, and analyzing it at the mean field level, we demonstrate a second order
phase transition driven by softening of the slave-rotor variables.


  We investigate the valence intraband transitions in p-doped self-assembled
InAs quantum dots using far-infrared magneto-optical technique with polarized
radiation. We show that a purely electronic model is unable to account for the
experimental data. We calculate the coupling between the mixed hole LO-phonon
states using the Fr\"ohlich Hamiltonian, from which we determine the polaron
states as well as the energies and oscillator strengths of the valence
intraband transitions. The good agreement between the experiments and
calculations provides strong evidence for the existence of hole-polarons and
demonstrates that the intraband magneto-optical transitions occur between
polaron states.


  This paper was removed due to an error in the proof (Claim 4.12 as stated is
not true). The authors would like to thank Ilya Volkovich for pointing out a
counterexample to this paper's main result in positive characteristic: If $F$
is a field with prime characteristic $p$, then the polynomial $x_1^p + x_2^p +
\ldots + x^n^p$ has the following factor: $(x_1+x_2+ \ldots + x_n)^{p-1}$,
which has sparsity $n^p$.


  We study topology optimization governed by the incompressible Navier-Stokes
flows using a phase field model. Novel stabilized semi-implicit schemes for the
gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving
the resulting optimal control problem. Unconditional energy stability is shown
for the gradient flow schemes in continuous and discrete spaces. Numerical
experiments of computational fluid dynamics in 2d and 3d show the effectiveness
and robustness of the optimization algorithms proposed.


  We introduce Graph-Sparse Logistic Regression, a new algorithm for
classification for the case in which the support should be sparse but connected
on a graph. We val- idate this algorithm against synthetic data and benchmark
it against L1-regularized Logistic Regression. We then explore our technique in
the bioinformatics context of proteomics data on the interactome graph. We make
all our experimental code public and provide GSLR as an open source package.


  Effective field theories (EFTs) require regularization and renormalization to
gain predictive power. While regularization is inconsequential from the point
of view of the observable predictions of EFT -- in a renormalized theory we
expect predictions to be regulator-independent once the cutoff is removed --
the particular details of regulator dependence might provide interesting
insights into the inner workings of an EFT. In fact, the analysis of regulator
dependence has been frequently suggested as a tool to study the ordering scheme
or power counting of EFTs. We show here that the choice of the regulator might
impact the power law properties of the residual cutoff dependence. If this
conclusion were to be confirmed, it would have consequences on the validity of
this method as a tool to analyze power counting.


  One part of Sylow's famous theorem in group theory states that the number of
Sylow p-subgroups of a finite group is always congruent to 1 modulo p.
Conversely, Marshall Hall has shown that not every positive integer $n\equiv
1\pmod{p}$ occurs as the number of Sylow p-subgroups of some finite group.
While Hall's proof relies on deep knowledge of modular representation theory,
we show by elementary means that no finite group has exactly 35 Sylow
17-subgroups.


  A search for the Standard Model Higgs boson has been performed with the OPAL
detector at LEP based on the full data sample collected at sqrt(s) = 192-209
GeV in 1999 and 2000, corresponding to an integrated luminosity of
approximately 426 pb-1. The data are examined for their consistency with the
background-only hypothesis and various Higgs boson mass hypotheses. A lower
bound of 109.7 GeV is obtained on the Higgs boson mass at the 95% confidence
level. At higher masses, the data are consistent with both the background and
the signal-plus-background hypotheses.


  Demand forecasting in the online fashion industry is particularly amendable
to global, data-driven forecasting models because of the industry's set of
particular challenges. These include the volume of data, the irregularity, the
high amount of turn-over in the catalog and the fixed inventory assumption.
While standard deep learning forecasting approaches cater for many of these,
the fixed inventory assumption requires a special treatment via controlling the
relationship between price and demand closely. In this case study, we describe
the data and our modelling approach for this forecasting problem in detail and
present empirical results that highlight the effectiveness of our approach.


  We investigate the one- to two-dimensional zigzag transition in clusters
consisting of a small number of particles interacting through a Yukawa (Debye)
potential and confined in a two-dimensional biharmonic potential well. Dusty
(complex) plasma clusters with $n \le 19$ monodisperse particles are
characterized experimentally for two different confining wells. The well
anisotropy is accurately measured, and the Debye shielding parameter is
determined from the longitudinal breathing frequency. Debye shielding is shown
to be important. A model for this system is used to predict equilibrium
particle configurations. The experiment and model exhibit excellent agreement.
The critical value of $n$ for the zigzag transition is found to be less than
that predicted for an unshielded Coulomb interaction. The zigzag transition is
shown to behave as a continuous phase transition from a one-dimensional to a
two-dimensional state, where the state variables are the number of particles,
the well anisotropy and the Debye shielding parameter. A universal critical
exponent for the zigzag transition is identified for transitions caused by
varying the Debye shielding parameter.


  We develop the model theory of omega-stable K-loops and 'sym\'etrons'.
Continuing Poizat's seminal work, we notably establish an appropriate version
of the indecomposability theorem and we adapt Lascar's analysis to this
context.
  --
  Nous d\'eveloppons la th\'eorie des mod\`eles des K-boucles et des
sym\'etrons omega-stables. En poursuivant le travail s\'eminal de Poizat, nous
\'etablissons notamment une version appropri\'ee du th\'eor\`eme des
ind\'ecomposables et nous adaptons l'analyse de Lascar \`a ce contexte.


  Existence of bound states in the continuum (BIC) manifests a general wave
phenomenon firstly predicted in quantum mechanics in 1929 by J. von Neumann and
E. Wigner. Today it is being actively explored in photonics, radiophysics,
acoustics, and hydrodynamics. In this paper, we report the first experimental
observation of electromagnetic bound state in the radiation continuum in 1D
array of dielectric particles. By measurement of the transmission spectra of
the ceramic disk chain at GHz frequencies we demonstrate how a resonant state
in the vicinity of the center of the Brillouin zone turns into a
symmetry-protected BIC with increase the number of the disks. We estimate a
number of the disks when the radiation losses become negligible in comparison
to material absorption and, therefore, the chain could be considered
practically as infinite. The presented analysis is supplemented by measurements
of the near fields of the symmetry protected BIC. All measurements are in a
good agreement with the results of numerical simulation and analytical model
based on tight-binding approximation. The obtained results provide useful
guidelines for practical implementations of structures with bound states in the
continuum that opens up new horizons for the development of optical and
radiofrequency metadevices.


  This paper studies two variants of defective acyclic coloring of planar
graphs. For a graph $G$ and a coloring $\varphi$ of $G$, a 2CC transversal is a
subset $E'$ of $E(G)$ that intersects every 2-colored cycle. Let $k$ be a
positive integer. We denote by $m_k(G)$ the minimum integer $m$ such that $G$
has a proper $k$-coloring which has a 2CC transerval of size $m$, and by
$m'_k(G)$ the minimum size of a subset $E'$ of $E(G)$ such that $G-E'$ is
acyclic $k$-colorable. We prove that for any $n$-vertex $3$-colorable planar
graph $G$, $m_3(G) \le n - 3$ and for any planar graph $G$, $m_4(G) \le n - 5$
provided that $n \ge 5$. We show that these upper bounds are sharp: there are
infinitely many planar graphs attaining these upper bounds. Moreover, the
minimum 2CC transversal $E'$ can be chosen in such a way that $E'$ induces a
forest. We also prove that for any planar graph $G$, $m'_3(G) \le (13n - 42) /
10$ and $m'_4(G) \le (3n - 12) / 5$.


  We develop method that allows to derive reductions and solutions to
hyperbolic systems of partial differential equations. The method is based on
using functions that are constant in the direction of characteristics of the
system. These functions generalize well-known Riemann invariants. As
applications we consider the gas dynamics system and ideal magnetohydrodynamics
equations. In special cases we find solutions of these equations depending on
some arbitrary functions.


  In this paper, we develop a simple model describing inherent photon-number
noise in Rarity-Tapster type interferometers. This noise is caused by
generating photon pairs in the process of spontaneous parametric
down-conversion and adding a third photon by attenuating fundamental laser mode
to single-photon level. We experimentally verify our model and present
resulting signal to noise ratios as well as obtained three-photon generation
rates as functions of various setup parameters. Subsequently we evaluate impact
of this particular source of noise on quantum teleportation which is a key
quantum information protocol using this interferometric configuration.


  Introducing a Clebsch-like parameterization, we have formulated a canonical
Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An
interesting structure of the equations is in that the Lorentz-force, which is a
quadratic nonlinear term in the conventional formulation, appears as a linear
term -{\Delta}Q, just representing the current density (Q is a Clebsch
variable, and {\Delta} is the two-dimensional Laplacian); omitting this term
reduces the system into the two-dimensional Euler vorticity equation of a
neutral fluid. A heuristic estimate shows that current sheets grow
exponentially (even in a fully nonlinear regime) together with the action
variable P that is conjugate to Q. By numerical simulation, the predicted
behavior of the canonical variables, yielding exponential growth of current
sheets, has been demonstrated.


  We construct a meta-generalized-gradient approximation which properly
balances the nonlocality contributions to the exchange and correlation at the
semilocal level. This non-empirical functional shows good accuracy for a broad
palette of properties (thermochemistry, structural properties) and systems
(molecules, metal clusters, surfaces and bulk solids). The accuracy for several
well known problems in electronic structure calculations, such as the bending
potential of the silver trimer and the dimensional crossover of anionic gold
clusters, is also demonstrated. The inclusion of empirical dispersion
corrections is finally discussed and analyzed.


  We argue that multiple point principle (MPP) can be used to ensure CP
conservation and the absence of flavour changing neutral currents within the
two Higgs doublet model (2HDM). We also discuss Higgs phenomenology in the MPP
inspired 2HDM.


  In recent years, twisted Alexander polynomial has been playing an important
role in low-dimensional topology.
  For Montesinos links, we develop an efficient method to compute the twisted
Alexander polynomial associated to any linear representation.
  In particular, formulas for multi-variable Alexander polynomials of these
links can be easily derived.


  We formulate a new bootstrap principle which allows for the construction of
particle spectra involving unstable as well as stable particles. We comment on
the general Lie algebraic structure which underlies theories with unstable
particles and propose several new scattering matrices. We find a new Lie
algebraic decoupling rule, which predicts the renormalization group flow in
dependence of the relative ordering of the resonance parameters. The proposals
are exemplified for some concrete theories which involve unstable particles,
such as the homogeneous sine-Gordon models and their generalizations. The new
decoupling rule can be validated by means of our new bootstrap principle and
also via the renormalization group flow, which we obtain from a thermodynamic
Bethe ansatz analysis.


  We characterize integral homology classes of the product of two projective
planes which are representable by a subvariety.


  We apply the Nash-Moser theorem for exact sequences of R. Hamilton to the
context of deformations of Lie algebras and we discuss some aspects of the
scope of this theorem in connection with the polynomial ideal associated to the
variety of nilpotent Lie algebras. This allows us to introduce the space
$H_{k-nil}^2(\mathfrak{g},\mathfrak{g})$, and certain subspaces of it, that
provide fine information about the deformations of $\mathfrak{g}$ in the
variety of $k$-step nilpotent Lie algebras.
  Then we focus on degenerations and rigidity in the variety of $k$-step
nilpotent Lie algebras of dimension $n$ with $n\le7$ and, in particular, we
obtain rigid Lie algebras and rigid curves in the variety of 3-step nilpotent
Lie algebras of dimension 7. We also recover some known results and point out a
possible error in a published article related to this subject.


  We investigate compatibility of the pure gravity mediation (or the minimal
split supersymmetry) with chaotic inflation models in supergravity. We find
that an approximate Z2 parity of the inflaton is useful to suppress gravitino
production from thermal bath and to obtain consistent inflation dynamics. We
discuss production of the lightest supersymmetric particle through the decay of
the inflaton with the approximate Z2 symmetry and find that a large gravitino
mass is favored to avoid the overproduction of the lightest supersymmetric
particle, while a lower gravitino mass requires tuning of parameters. This may
explain why the nature has chosen the gravitino mass of O(100) TeV rather than
O(100) GeV.


  We have studied large deviations of the height of the pile from its mean
value in the Oslo ricepile model. We sampled these very rare events with
probabilities of order $10^{-100}$ by Monte Carlo simulations using importance
sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf
73}, 021303, 2006] that in steady state of the Oslo ricepile model, the
probability of large negative height fluctuations $\Delta h=-\alpha L$ about
the mean varies as $\exp(-\kappa {\alpha}^4 L^3)$ as $L \to \infty$ with
$\alpha $ held fixed, and $\kappa > 0$.


  A recent study by one of the authors has demonstrated the importance of
profile vectors in DNA-based data storage. We provide exact values and lower
bounds on the number of profile vectors for finite values of alphabet size $q$,
read length $\ell$, and word length $n$.Consequently, we demonstrate that for
$q\ge 2$ and $n\le q^{\ell/2-1}$, the number of profile vectors is at least
$q^{\kappa n}$ with $\kappa$ very close to one.In addition to enumeration
results, we provide a set of efficient encoding and decoding algorithms for
each of two particular families of profile vectors.


  In recent years, the Douglas-Rachford splitting method has been shown to be
effective at solving many non-convex optimization problems. In this paper we
present a local convergence analysis for non-convex feasibility problems and
show that both finite termination and local linear convergence are obtained.
For a generalization of the Sudoku puzzle, we prove that the local linear rate
of convergence of Douglas-Rachford is exactly $\frac{\sqrt{5}}{5}$ and
independent of puzzle size. For the $s$-queens problem we prove that
Douglas-Rachford converges after a finite number of iterations. Numerical
results on solving Sudoku puzzles and $s$-queens puzzles are provided to
support our theoretical findings.


  The microscopic structure and movement of reaction fronts in reaction
diffusion systems far from equilibrium are investigated. We show that some
three-site interaction models exhibit exact diffusive shock measures, i.e.
domains of different densities connected by a sharp wall without correlations.
In all cases fluctuating domains grow at the expense of ordered domains, the
absence of growth is possible between ordered domains. It is shown that these
models give rise to aspects not seen in nearest neighbor models, viz. double
shocks and additional symmetries. A classification of the systems by their
symmetries is given and the link of domain wall motion and a free fermion
description is discussed.


  It has been shown for low-spin fields that the use of only the self-dual part
of the connection as basic variable does not lead to spurious equations or
inconsistencies. We slightly generalize the form of the chiral Lagrangian of
half-integer spin fields and express its imaginary part in a simple form. If
the imaginary part is non-vanishing, it will lead to spurious equations. As an
example, for (Majorana) Rarita-Schwinger fields the equations of motion of the
torsion is solved and it is shown that it vanishes owing to the Fierz identity.