  This article is devoted to the analysis of inverse source problems for Stokes
systems in unbounded domains where the corresponding velocity flow is observed
on a surface. Our main objective is to study the unique determination of
general class of time-dependent and vector-valued source terms with potentially
unknown divergence. Taking into account the challenges inherent in this class
of inverse source problems, we aim to identify the most precise conditions that
ensure their resolution. Motivated by various fluid motion problems, we explore
several class of boundary measurements. Our proofs are based on different
arguments, including unique continuation properties for Stokes systems,
approximate controllability, complex analysis, and the application of explicit
harmonic functions and explicit solutions for Stokes systems. This analysis is
complemented by a reconstruction algorithm and examples of numerical
computations.


  The security and robustness of deep neural networks (DNNs) have become
increasingly concerning. This paper aims to provide both a theoretical
foundation and a practical solution to ensure the reliability of DNNs. We
explore the concept of Lipschitz continuity to certify the robustness of DNNs
against adversarial attacks, which aim to mislead the network with adding
imperceptible perturbations into inputs. We propose a novel algorithm that
remaps the input domain into a constrained range, reducing the Lipschitz
constant and potentially enhancing robustness. Unlike existing adversarially
trained models, where robustness is enhanced by introducing additional examples
from other datasets or generative models, our method is almost cost-free as it
can be integrated with existing models without requiring re-training.
Experimental results demonstrate the generalizability of our method, as it can
be combined with various models and achieve enhancements in robustness.
Furthermore, our method achieves the best robust accuracy for CIFAR10,
CIFAR100, and ImageNet datasets on the RobustBench leaderboard.


  The field of continual deep learning is an emerging field and a lot of
progress has been made. However, concurrently most of the approaches are only
tested on the task of image classification, which is not relevant in the field
of intelligent vehicles. Only recently approaches for class-incremental
semantic segmentation were proposed. However, all of those approaches are based
on some form of knowledge distillation. At the moment there are no
investigations on replay-based approaches that are commonly used for object
recognition in a continual setting. At the same time while unsupervised domain
adaption for semantic segmentation gained a lot of traction, investigations
regarding domain-incremental learning in an continual setting is not
well-studied. Therefore, the goal of our work is to evaluate and adapt
established solutions for continual object recognition to the task of semantic
segmentation and to provide baseline methods and evaluation protocols for the
task of continual semantic segmentation. We firstly introduce evaluation
protocols for the class- and domain-incremental segmentation and analyze
selected approaches. We show that the nature of the task of semantic
segmentation changes which methods are most effective in mitigating forgetting
compared to image classification. Especially, in class-incremental learning
knowledge distillation proves to be a vital tool, whereas in domain-incremental
learning replay methods are the most effective method.


  Spectral population synthesis (PS) is a fundamental tool in extragalactic
research that aims to decipher the assembly history of galaxies from their SED.
However, until recently all PS codes were restricted to purely stellar fits,
neglecting the essential contribution of nebular emission (NE). With the advent
of FADO, the now possible self-consistent modelling of stellar and NE opens new
routes to the exploration of galaxy SFHs. The main goal of this study is to
quantitatively explore the accuracy to which FADO can recover physical and
evolutionary properties of galaxies and compare its output with that from
purely stellar PS codes. With this in mind, FADO and STARLIGHT were applied to
synthetic SEDs that track the spectral evolution of stars and gas in
extinction-free mock galaxies that form their stellar mass ($M_\star$)
according to different parametric SFHs. Spectral fits were computed for two
different set-ups that approximate the spectral range of SDSS and CALIFA data.
Our analysis indicates that FADO can recover the key physical and evolutionary
properties of galaxies, such as $M_\star$ and mass- and light-weighted mean age
and metallicity, with an accuracy better than 0.2 dex. This is the case even in
phases of strongly elevated sSFR and thus with considerable NE contamination.
As for STARLIGHT, our analysis documents a moderately good agreement with
theoretical values only for evolutionary phases for which NE drops to low
levels. Indeed, fits with STARLIGHT during phases of high sSFR severely
overestimate both $M_\star$ and the mass-weighted stellar age, whereas strongly
underestimate the light-weighted age and metallicity. The insights from this
study suggest that the neglect of nebular continuum emission in STARLIGHT and
similar purely stellar PS codes could systematically impact $M_\star$ and SFH
estimates for star-forming galaxies.


  One of the most criticized features of Bayesian statistics is the fact that
credible intervals, especially when open likelihoods are involved, may strongly
depend on the prior shape and range. Many analyses involving open likelihoods
are affected by the eternal dilemma of choosing between linear and logarithmic
prior, and in particular in the latter case the situation is worsened by the
dependence on the prior range under consideration. In this letter, we revive a
simple method to obtain constraints that depend neither on the prior shape nor
range and, using the tools of Bayesian model comparison, extend it to overcome
the possible dependence of the bounds on the choice of free parameters in the
numerical analysis. An application to the case of cosmological bounds on the
sum of the neutrino masses is discussed as an example.


  We suggest a technique based on the transfer of topological charge from
applied laser radiation to directional and coherent optical fields generated in
ladder-type excited atomic media to identify the major processes responsible
for their appearance. As an illustration, in Rb vapours we analyse transverse
intensity and phase profiles of the forward-directed collimated blue and
near-IR light using self-interference and astigmatic transformation techniques
when either or both of two resonant laser beams carry orbital angular momentum.
Our observations unambiguously demonstrate that emission at 1.37 {\mu}m is the
result of a parametric four-wave mixing process involving only one of the two
applied laser fields.


  As a prospective key technology for the next-generation wireless
communications, reconfigurable intelligent surfaces (RISs) have gained
tremendous research interest in both the academia and industry in recent years.
Only limited knowledge, however, has been obtained about the channel eigenvalue
characteristics and spatial degrees of freedom (DoF) of systems containing
RISs, especially when mutual coupling (MC) is present between the array
elements. In this paper, we focus on the small-scale spatial correlation and
eigenvalue properties excluding and including MC effects, for RISs with a
quasi-continuous aperture (i.e., holographic RISs). Specifically, asymptotic
behaviors of far-field and near-field eigenvalues of the spatial correlation
matrix of holographic RISs without MC are first investigated, where the
counter-intuitive observation of a lower DoF with more elements is explained by
leveraging the power spectrum of the spatial correlation function. Second, a
novel metric is proposed to quantify the inter-element correlation or coupling
strength in RISs and ordinary antenna arrays. Furthermore, in-depth analysis is
performed regarding the MC effects on array gain, effective spatial
correlation, and eigenvalue architectures for a variety of element intervals
when a holographic RIS works in the radiation and reception mode, respectively.
The analysis and numerical results demonstrate that a considerable amount of
the eigenvalues of the spatial correlation matrix correspond to evanescent
waves that are promising for near-field communication and sensing. More
importantly, holographic RISs can potentially reach an array gain conspicuously
larger than conventional arrays by exploiting MC, and MC has discrepant impacts
on the effective spatial correlation and eigenvalue structures at the
transmitter and receiver.


  In this paper we show that, for any fixed $1<c<967/805$, every sufficiently
large positive number $N$ and a small constant $\varepsilon>0$, the diophantine
inequality \begin{equation*} |p_1^c+p_2^c+p_3^c+p_4^c-N|<\varepsilon
\end{equation*} has a solution in prime numbers $p_1,\,p_2,\,p_3,\,p_4$, such
that $p_1=x^2 + y^2 +1$.


  We are concerned with the linearized, isotropic and homogeneous elastic
scattering problem by many small rigid obstacles of arbitrary, Lipschitz
regular, shapes in 3D case. We prove that there exists two constant $a_0$ and
$c_0$, depending only on the Lipschitz character of the obstacles, such that
under the conditions $a\leq a_0$ and $\sqrt{M-1}\frac{a}{d} \leq c_0$ on the
number $M$ of the obstacles, their maximum diameter $a$ and the minimum
distance between them $d$, the corresponding Foldy-Lax approximation of the
farfields is valid. In addition, we provide the error of this approximation
explicitly in terms of the three parameters $M, a$ and $d$. These
approximations can be used, in particular, in the identification problems (i.e.
inverse problems) and in the design problems (i.e. effective medium theory).


  Groundwater flow in Washington DC greatly influences the surface water
quality in urban areas. The current methods of flow estimation, based on
Darcy's Law and the groundwater flow equation, can be described by the
diffusion equation (the transient flow) and the Laplace equation (the
steady-state flow). The Laplace equation is a simplification of the diffusion
equation under the condition that the aquifer has a recharging boundary. The
practical way of calculation is to use numerical methods to solve these
equations. The most popular system is called MODFLOW, which was developed by
USGS. MODFLOW is based on the finite-difference method in rectangular Cartesian
coordinates. MODFLOW can be viewed as a "quasi 3D" simulation since it only
deals with the vertical average (no z-direction derivative). Flow calculations
between the 2D horizontal layers use the concept of leakage. In this project,
we have established a mathematical model based on gradually varied functions
for groundwater data volume reconstruction. These functions do not rely on the
rectangular Cartesian coordinate system. A gradually varied function can be
defined in a general graph or network. Gradually varied functions are suitable
for arbitrarily shaped aquifers. Two types of models are designed and
implemented for real data processing: (1) the gradually varied model for
individual (time) groundwater flow data, (2) the gradually varied model for
sequential (time) groundwater flow data. In application, we also established a
MySQL database to support the related research. The advantage of the gradually
varied fitting and its related method does not need the strictly defined
boundary condition as it is required in MODFLOW.


  While improving prediction accuracy has been the focus of machine learning in
recent years, this alone does not suffice for reliable decision-making.
Deploying learning systems in consequential settings also requires calibrating
and communicating the uncertainty of predictions. To convey instance-wise
uncertainty for prediction tasks, we show how to generate set-valued
predictions from a black-box predictor that control the expected loss on future
test points at a user-specified level. Our approach provides explicit
finite-sample guarantees for any dataset by using a holdout set to calibrate
the size of the prediction sets. This framework enables simple,
distribution-free, rigorous error control for many tasks, and we demonstrate it
in five large-scale machine learning problems: (1) classification problems
where some mistakes are more costly than others; (2) multi-label
classification, where each observation has multiple associated labels; (3)
classification problems where the labels have a hierarchical structure; (4)
image segmentation, where we wish to predict a set of pixels containing an
object of interest; and (5) protein structure prediction. Lastly, we discuss
extensions to uncertainty quantification for ranking, metric learning and
distributionally robust learning.


  We motivate a measurement of various ratios of $W$ and $Z$ cross sections at
the Large Hadron Collider (LHC) at large values of the boson transverse
momentum ($p_T\gtrsim M_{W,Z}$). We study the dependence of predictions for
these cross-section ratios on the multiplicity of associated jets, the boson
$p_T$ and the LHC centre-of-mass energy. We present the flavour decomposition
of the initial-state partons and an evaluation of the theoretical
uncertainties. We show that the $W^+/W^-$ ratio is sensitive to the up-quark to
down-quark ratio of parton distribution functions (PDFs), while other
theoretical uncertainties are negligible, meaning that a precise measurement of
the $W^+/W^-$ ratio at large boson $p_T$ values could constrain the PDFs at
larger momentum fractions $x$ than the usual inclusive $W$ charge asymmetry.
The $W^\pm/Z$ ratio is insensitive to PDFs and most other theoretical
uncertainties, other than possibly electroweak corrections, and a precise
measurement will therefore be useful in validating theoretical predictions
needed in data-driven methods, such as using $W(\to\ell\nu)$+jets events to
estimate the $Z(\to\nu\bar{\nu})$+jets background in searches for new physics
at the LHC. The differential $W$ and $Z$ cross sections themselves, ${\rm
d}\sigma/{\rm d}p_T$, have the potential to constrain the gluon distribution,
provided that theoretical uncertainties from higher-order QCD and electroweak
corrections are brought under control, such as by inclusion of anticipated
next-to-next-to-leading order QCD corrections.


  We discuss the relationship between bosonic stimulation, density
fluctuations, and matter wave gratings. It is shown that enhanced stimulated
scattering, matter wave amplification and atomic four-wave mixing are in
principle possible for fermionic or non-degenerate samples if they are prepared
in a cooperative state. In practice, there are limitations by short coherence
times.


  We consider the defocusing, $\dot{H}^1$-critical Hartree equation for the
radial data in all dimensions $(n\geq 5)$. We show the global well-posedness
and scattering results in the energy space. The new ingredient in this paper is
that we first take advantage of the term $\displaystyle - \int_{I}\int_{|x|\leq
A|I|^{1/2}}|u|^{2}\Delta \Big(\frac{1}{|x|}\Big)dxdt$ in the localized Morawetz
identity to rule out the possibility of energy concentration, instead of the
classical Morawetz estimate dependent of the nonlinearity.


  In this work we consider Bayesian inference problems with intractable
likelihood functions. We present a method to compute an approximate of the
posterior with a limited number of model simulations. The method features an
inverse Gaussian Process regression (IGPR), i.e., one from the output of a
simulation model to the input of it. Within the method, we provide an adaptive
algorithm with a tempering procedure to construct the approximations of the
marginal posterior distributions. With examples we demonstrate that IGPR has a
competitive performance compared to some commonly used algorithms, especially
in terms of statistical stability and computational efficiency, while the price
to pay is that it can only compute a weighted Gaussian approximation of the
marginal posteriors.


  Using a radio-quiet subsample of the Sloan Digital Sky Survey spectroscopic
quasar catalogue, spanning redshifts 0.5-3.5, we derive the mean millimetre and
far-infrared quasar spectral energy distributions (SEDs) via a stacking
analysis of Atacama Cosmology Telescope and Herschel-Spectral and Photometric
Imaging REceiver data. We constrain the form of the far-infrared emission and
find 3$\sigma$-4$\sigma$ evidence for the thermal Sunyaev-Zel'dovich (SZ)
effect, characteristic of a hot ionized gas component with thermal energy $(6.2
\pm 1.7)\times 10^{60}$ erg. This amount of thermal energy is greater than
expected assuming only hot gas in virial equilibrium with the dark matter
haloes of $(1-5)\times 10^{12}h^{-1}$M$_\odot$ that these systems are expected
to occupy, though the highest quasar mass estimates found in the literature
could explain a large fraction of this energy. Our measurements are consistent
with quasars depositing up to $(14.5 \pm 3.3)~\tau_8^{-1}$ per cent of their
radiative energy into their circumgalactic environment if their typical period
of quasar activity is $\tau_8\times~10^8$ yr. For high quasar host masses,
$\sim10^{13}h^{-1}$M$_\odot$, this percentage will be reduced. Furthermore, the
uncertainty on this percentage is only statistical and additional systematic
uncertainties enter at the 40 per cent level. The SEDs are dust dominated in
all bands and we consider various models for dust emission. While sufficiently
complex dust models can obviate the SZ effect, the SZ interpretation remains
favoured at the 3$\sigma$-4$\sigma$ level for most models.


  We study punctual quot-schemes of torsion-free sheaves $E_Y$ on smooth
projective curves, surfaces and Calabi--Yau fourfolds via their virtual
geometry. Our goal is to give a complete description of the virtual fundamental
classes and their tautological integrals. In the fourfold case, we first
construct these classes under additional conditions. We use novel methods
relying on the wall-crossing of Joyce. Our results include -the dependence of
the cobordism classes on the torsion-free sheaf $E_Y$ where $Y$ is a surface,
-relations to the previous results in the literature, which addressed the case
of a trivial $E_Y$, -a new 12-fold correspondence relating Segre and Verlinde
invariants for curves, surfaces and Calabi-Yau fourfolds based on the one
observed by Arbesfeld-Johnson-Lim-Oprea-Pandharipande in dimensions one and
two, -a closed formula for the Nekrasov genus, which gives a compact analogue
of Nekrasov's conjecture. As our techniques are orthogonal to the original
literature, we make our work independent by proving a new combinatorial
identity in arXiv:2111.09868


  The creation of a next generation internet (semantic web) is impossible
without attributes, allowing the semantic association of documents and their
integration into information context. To achieve these goals, the Universal
Metadata Standard (ums) may be an ultimative tool, which could serve as a basis
for documentography, and is functionally required for interpretation of
documents by the automatic operating systems.


  We are presenting the first ab initio structure investigation of the loosely
bound 11-Be nucleus, together with a study of the lighter isotope 9-Be. The
nuclear structure of these isotopes is particularly interesting due to the
appearance of a parity-inverted ground state in 11-Be. Our study is performed
in the framework of the ab initio no-core shell model. Results obtained using
four different, high-precision two-nucleon interactions, in model spaces up to
9\hbar\Omega, are shown. For both nuclei, and all potentials, we reach
convergence in the level ordering of positive- and negative-parity spectra
separately. Concerning their relative position, the positive-parity states are
always too high in excitation energy, but a fast drop with respect to the
negative-parity spectrum is observed when the model space is increased. This
behavior is most dramatic for 11-Be. In the largest model space we were able to
reach, the 1/2+ level has dropped down to become either the first or the second
excited state, depending on which interaction we use. We also observe a
contrasting behavior in the convergence patterns for different two-nucleon
potentials, and argue that a three-nucleon interaction is needed to explain the
parity inversion. Furthermore, large-basis calculations of 13-C and 11-B are
performed. This allows us to study the systematics of the position of the first
unnatural-parity state in the N=7 isotone and the A=11 isobar. The 11-B run in
the 9\hbar\Omega model space involves a matrix with dimension exceeding 1.1 x
10^9, and is our largest calculation so far. We present results on binding
energies, excitation spectra, level configurations, radii, electromagnetic
observables, and 10-Be+n overlap functions.


  It is well-known that a dilute one-dimensional (1D) gas of bosons with
infinitely strong repulsive interactions behaves like a gas of free fermions.
Just as with conduction electrons in metals, we consider a single-particle
picture of the resulting dynamics, when the gas is isolated by enclosing it
into a box with hard walls and preparing it in a special initial state. We
show, by solving the nonstationary problem of a free particle in a 1D hard-wall
box, that the single-particle state recurs in time, signaling the intuitively
expected back-and-forth motion of a free particle moving in a confined space.
Under suitable conditions, the state of the whole gas can then be made to recur
if all the particles are put in the same initial momentum superposition. We
introduce this problem here as a modern instance of the discussions giving rise
to the famous recurrence paradox in statistical mechanics: on one hand, our
results may be used to develop a poor man's interpretation of the recurrence of
the initial state observed [T. Kinoshita et al, Nature 440, 900 (2006)] in
trapped 1D Bose gases of cold atoms, for which our estimated recurrence time is
in fair agreement with the period of the oscillations observed; but this
experiment, on the other hand, has been substantially influential on the belief
that an isolated quantum many-body system can equilibrate as a consequence of
its own unitary nonequilibrium dynamics. Some ideas regarding the latter are
discussed.


  The concept of drone corridors is recently getting more attention to enable
connected, safe, and secure flight zones in the national airspace. To support
beyond visual line of sight (BVLOS) operations of aerial vehicles in a drone
corridor, cellular base stations (BSs) serve as a convenient infrastructure,
since such BSs are widely deployed to provide seamless wireless coverage.
However, antennas in the existing cellular networks are down-tilted to
optimally serve their ground users, which results in coverage holes if they are
also used to serve drones. In this letter, we consider the use of additional
uptilted antennas at cellular BSs and optimize the uptilt angle to minimize
outage probability for a given drone corridor. Our numerical results show how
the beamwidth and the maximum drone corridor height affect the optimal value of
the antenna uptilt angle.


  We classify isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$ and
thereby reprove a result of Dorfmeister and Neher.


  The level-truncation analysis of open string field theory for a class of
periodic marginal deformations indicates that a branch of solutions in Siegel
gauge exists only for a finite range of values of the marginal field. The
periodicity in the deformation parameter is thus obscure. We use the relation
between gauge-invariant observables and the closed string tadpole on a disk
conjectured by Ellwood to construct a map between the deformation parameter of
the boundary conformal field theory and the parameter labeling classical
solutions of open string field theory. We evaluate the gauge-invariant
observables for the numerical solutions in Siegel gauge up to level 12 and find
that our results qualitatively agree with the analysis by Sen using the
energy-momentum tensor and are consistent with the picture that the finite
range of the branch covers one fundamental domain of the periodic moduli space.


  Large-scale quantum information processing requires the use of quantum error
correcting codes to mitigate the effects of noise in quantum devices.
Topological error-correcting codes, such as surface codes, are promising
candidates as they can be implemented using only local interactions in a
two-dimensional array of physical qubits. Procedures such as defect braiding
and lattice surgery can then be used to realize a fault-tolerant universal set
of gates on the logical space of such topological codes. However, error
correction also introduces a significant overhead in computation time, the
number of physical qubits, and the number of physical gates. While optimizing
fault-tolerant circuits to minimize this overhead is critical, the
computational complexity of such optimization problems remains unknown. This
ambiguity leaves room for doubt surrounding the most effective methods for
compiling fault-tolerant circuits for a large-scale quantum computer. In this
paper, we show that the optimization of a special subset of braided quantum
circuits is NP-hard by a polynomial-time reduction of the optimization problem
into a specific problem called Planar Rectilinear 3SAT.


  We study elementary processes for production of dileptons from nucleons,
either through NN bremsstrahlung or through photon-induced reactions. We
emphasize the dependence of the expected cross-sections on the electromagnetic
formfactor of the nucleon in the time-like regime and point out that the
mentioned reactions can provide important information on the validity of vector
meson dominance for the nucleon. We also study the off-shell dependence of the
formfactors.


  We have measured the current-voltage characteristics of a single Josephson
junction placed in a high impedance environment. The transfer of Cooper pairs
through the junction is governed by overdamped quasicharge dynamics, leading to
Coulomb blockade and Bloch oscillations. Exact duality exists to the standard
overdamped phase dynamics of a Josephson junction, resulting in a dual shape of
the current-voltage characteristic, with current and voltage changing roles. We
demonstrate this duality with experiments which allow for a quantitative
comparison with a theory that includes the effect of fluctuations due to finite
temperature of the electromagnetic environment.


  I summarize the prospects for discovering Higgs bosons at future $pp$ and
$\ee$ colliders both in the Standard Model and its Minimal Supersymmetric
extension.


  High energy CW electron beams at new accelerator facilities allow
electromagnetic production and precision study of hypernuclear structure, and
we report here on the first experiment demonstrating the usefulness of the
(e,e'K+) reaction. This experiment is also the first to take advantage of the
enhanced virtual photon flux available when electrons are scattered at
approximately zero degrees. The observed resolution, ~900 keV, of the
12B(hypernuclear) spectrum is the best yet attained using magnetic
spectrometers. The positions of the major excitations are in agreement with
theoretical predictions and the previous binding energy measurements.


  For curves of genus bigger than one we prove that Buium's first arithmetic
jet spaces (p-jet spaces) admit the structure of a torsor under some line
bundle.
  This result lifts a known constructions in characteristic p where the first
$p$-jet space modulo p is a sheaf under the Frobenius tangent sheaf
(parametrizing Frobenius linear derivations).
  In particular we show there is a natural family of lifts of the Frobenius
tangent bundle so that the first $p$-jet space (and hence higher order lifts of
the Frobenius) form torsor a under this bundle.
  The Cech cohomology classes associated to this torsor structure, which we
call the Deligne-Illusie class, has strong analogies with the classical
Kodaira-Spencer class from deformation theory.


  We present the neural-integrated meshfree (NIM) method, a differentiable
programming-based hybrid meshfree approach within the field of computational
mechanics. NIM seamlessly integrates traditional physics-based meshfree
discretization techniques with deep learning architectures. It employs a hybrid
approximation scheme, NeuroPU, to effectively represent the solution by
combining continuous DNN representations with partition of unity (PU) basis
functions associated with the underlying spatial discretization. This
neural-numerical hybridization not only enhances the solution representation
through functional space decomposition but also reduces both the size of DNN
model and the need for spatial gradient computations based on automatic
differentiation, leading to a significant improvement in training efficiency.
Under the NIM framework, we propose two truly meshfree solvers: the strong
form-based NIM (S-NIM) and the local variational form-based NIM (V-NIM). In the
S-NIM solver, the strong-form governing equation is directly considered in the
loss function, while the V-NIM solver employs a local Petrov-Galerkin approach
that allows the construction of variational residuals based on arbitrary
overlapping subdomains. This ensures both the satisfaction of underlying
physics and the preservation of meshfree property. We perform extensive
numerical experiments on both stationary and transient benchmark problems to
assess the effectiveness of the proposed NIM methods in terms of accuracy,
scalability, generalizability, and convergence properties. Moreover,
comparative analysis with other physics-informed machine learning methods
demonstrates that NIM, especially V-NIM, significantly enhances both accuracy
and efficiency in end-to-end predictive capabilities.


  We analyze spectral properties of the ultrarelativistic (Cauchy) operator
$|\Delta |^{1/2}$, provided its action is constrained exclusively to the
interior of the interval $[-1,1] \subset R$. To this end both analytic and
numerical methods are employed. New high-accuracy spectral data are obtained. A
direct analytic proof is given that trigonometric functions $\cos(n\pi x/2)$
and $\sin(n\pi x)$, for integer $n$ are {\it not} the eigenfunctions of
$|\Delta |_D^{1/2}$, $D=(-1,1)$. This clearly demonstrates that the traditional
Fourier multiplier representation of $|\Delta |^{1/2}$ becomes defective, while
passing from $R$ to a bounded spatial domain $D\subset R$.


  Gauged $U(1)_{L_\mu - L_\tau}$ model has been advocated for a long time in
light of muon $g-2$ anomaly, which is a more than $3\sigma$ discrepancy between
the experimental measurement and the standard model prediction. We augment this
model with three right-handed neutrinos $(N_e, N_\mu, N_\tau)$ and a
vector-like singlet fermion $(\chi)$ to explain simultaneously the non-zero
neutrino mass and dark matter content of the Universe, while satisfying
anomalous muon $g-2$ constraints. It is shown that in a large parameter space
of this model we can explain positron excess, observed at PAMELA, Fermi-LAT and
AMS-02, through dark matter annihilation, while satisfying the relic density
and direct detection constraints.


  We explore the thermodynamic properties of homogeneous cold
(zero-temperature) nuclear matter including nucleons and $\alpha$-particle
condensation at low densities by using a generalized nonlinear relativistic
mean-field (gNL-RMF) model. In the gNL-RMF model, the $\alpha$-particle is
included as explicit degree of freedom and treated as point-like particle with
its interaction described by meson exchanges and the in-medium effects on the
$\alpha$ binding energy is described by density- and temperature-dependent
energy shift with the parameters obtained by fitting the experimental Mott
density. We find that below the dropping density $n_{\rm{drop}}$ ($\sim 3\times
10^{-3}$ fm$^{-3}$), the zero-temperature symmetric nuclear matter is in the
state of pure Bose-Einstein condensate (BEC) of $\alpha$ particles while the
neutron-rich nuclear matter is composed of $\alpha$-BEC and neutrons. Above the
$n_{\rm{drop}}$, the fraction of $\alpha$-BEC decreases with density and
vanishes at the transition density $n_t$ ($\sim 8\times 10^{-3}$ fm$^{-3}$).
Above the $n_t$, the nuclear matter becomes pure nucleonic matter. Our results
indicate that the empirical parabolic law for the isospin asymmetry dependence
of nuclear matter equation of state is heavily violated by the
$\alpha$-particle condensation in the zero-temperature dilute nuclear matter,
making the conventional definition of the symmetry energy meaningless. We
investigate the symmetry energy defined under parabolic approximation for the
zero-temperature dilute nuclear matter with $\alpha$-particle condensation, and
find it is significantly enhanced compared to the case without clusters and
becomes saturated at about $7$ MeV at very low densities ($\lesssim 10^{-3}$
fm$^{-3}$). The critical temperature for $\alpha$-condensation in homogeneous
dilute nuclear matter is also discussed.


  Existing and missing calculations of standard model processes producing large
transverse energy in electron-proton interactions at HERA are reviewed. The
adequacy of the existing standard model Monte Carlo programs for generic
searches of exotic processes is analyzed.


  Fake news on social media is increasingly regarded as one of the most
concerning issues. Low cost, simple accessibility via social platforms, and a
plethora of low-budget online news sources are some of the factors that
contribute to the spread of false news. Most of the existing fake news
detection algorithms are solely focused on the news content only but engaged
users prior posts or social activities provide a wealth of information about
their views on news and have significant ability to improve fake news
identification. Graph Neural Networks are a form of deep learning approach that
conducts prediction on graph-described data. Social media platforms are
followed graph structure in their representation, Graph Neural Network are
special types of neural networks that could be usually applied to graphs,
making it much easier to execute edge, node, and graph-level prediction.
Therefore, in this paper, we present a comparative analysis among some commonly
used machine learning algorithms and Graph Neural Networks for detecting the
spread of false news on social media platforms. In this study, we take the UPFD
dataset and implement several existing machine learning algorithms on text data
only. Besides this, we create different GNN layers for fusing graph-structured
news propagation data and the text data as the node feature in our GNN models.
GNNs provide the best solutions to the dilemma of identifying false news in our
research.


  The sensitivity of deep neural networks to compressed images hinders their
usage in many real applications, which means classification networks may fail
just after taking a screenshot and saving it as a compressed file. In this
paper, we argue that neglected disposable coding parameters stored in
compressed files could be picked up to reduce the sensitivity of deep neural
networks to compressed images. Specifically, we resort to using one of the
representative parameters, quantization steps, to facilitate image
classification. Firstly, based on quantization steps, we propose a novel
quantization aware confidence (QAC), which is utilized as sample weights to
reduce the influence of quantization on network training. Secondly, we utilize
quantization steps to alleviate the variance of feature distributions, where a
quantization aware batch normalization (QABN) is proposed to replace batch
normalization of classification networks. Extensive experiments show that the
proposed method significantly improves the performance of classification
networks on CIFAR-10, CIFAR-100, and ImageNet. The code is released on
https://github.com/LiMaPKU/QSAM.git


  We have developed a new tool for numerical work in General Relativity:
GRworkbench. While past tools have been ad hoc, GRworkbench closely follows the
framework of Differential Geometry to provide a robust and general way of
computing on analytically defined space-times. We discuss the relationship
between Differential Geometry and C++ classes in GRworkbench, and demonstrate
their utility.


  We consider radial oscillations of supertube probes in the Godel-type
background which is U-dual to the compactified pp-wave obtained from the
Penrose limit of the NS five-brane near horizon geometry. The supertube probe
computation can be carried over directly to a string probe calculation on the
U-dual background. The classical equations of motion are solved explicitly. In
general, the probe is not restricted to travel unidirectionally through any
global time coordinate. In particular, we find geodesics that close.


  Whilst there is a generally accepted evolutionary scheme for the formation of
low-mass stars, the analogous processes when moving down in mass to the brown
dwarfs regime are not yet well understood. In this first paper we try to build
the most complete and unbiased spectroscopically confirmed census of the
population of Collinder 69, the central cluster of the Lambda Orionis star
forming region, as a first step in addressing the question of how brown dwarfs
and planetary mass objects form. We have studied age dependent features in
optical and near-infrared spectra of candidate members to the cluster (such as
alkali lines and accretion associated indicators). In addition, we have
complemented that study with the analysis of other youth indicators like X-ray
emission or mid-infrared excess. We have confirmed the membership to Collinder
69 of \sim90 photometric candidate members. As a byproduct we have determined a
temperature scale for young M, very low-mass stars and brown dwarfs. We have
assembled one of the most complete Initial Mass Functions from 0.016 to 20
M\odot. And, finally, we have studied the implications of the spatial
distribution of the confirmed members on the proposed mechanisms of brown
dwarfs formation.


  We start a program of background independent quantum gravity in eight
dimensions. We begin by considering canonical gravity \textit{a la}
"Kaluza-Klein" in $D=d+1$ dimensions. We show that our canonical gravity
approach can be applied to the case of self-dual gravity in four dimensions.
Further, by using our previously proposed classical action of Ashtekar
self-dual gravity formalism in eight dimensions, we proceed to develop the
canonical approach in eight dimensions. Our construction considers different
SO(8) symmetry breakings. In particular, the breaking $SO(8)=S_{R}^{7}% \times
S_{L}^{7}\times G_{2}$ plays an important role in our discussion.


  Pre-training a diverse set of neural network controllers in simulation has
enabled robots to adapt online to damage in robot locomotion tasks. However,
finding diverse, high-performing controllers requires expensive network
training and extensive tuning of a large number of hyperparameters. On the
other hand, Covariance Matrix Adaptation MAP-Annealing (CMA-MAE), an evolution
strategies (ES)-based quality diversity algorithm, does not have these
limitations and has achieved state-of-the-art performance on standard QD
benchmarks. However, CMA-MAE cannot scale to modern neural network controllers
due to its quadratic complexity. We leverage efficient approximation methods in
ES to propose three new CMA-MAE variants that scale to high dimensions. Our
experiments show that the variants outperform ES-based baselines in benchmark
robotic locomotion tasks, while being comparable with or exceeding
state-of-the-art deep reinforcement learning-based quality diversity
algorithms.


  The most interesting experimental results obtained in studies of 2D and 3D
topological insulators (TIs) based on HgTe quantum wells and films are
reviewed. In the case of 2D TIs, these include the observation of nonlocal
ballistic and diffusion transport, the magnetic breakdown of 2D TIs, and an
anomalous temperature dependence of edge-channel resistance. In 3D TIs, a
record-setting high mobility of surface two-dimensional Dirac fermions (DFs)
has been attained. This enabled determining all the main TI parameters (the
bulk gap and the density of DFs on both of its surfaces) and provided
information on the phase of the Shubnikov - de Haas oscillations of DFs, which
indicates the rigid topological coupling between the fermion spin and momentum.
Prospects for further research are discussed in the conclusion.


  The Tri-Bimaximal (TBM) mixing predicts a vanishing $\theta_{13}$. This can
be attributed to the inherited $\mu-\tau$ symmetry of TBM mixing. We break its
$\mu-\tau$ symmetry by adding a complex magic matrix with one variable to TBM
neutrino mass matrix with one vanishing eigenvalue. We present two such
textures and study their phenomenological implications.


  Using excitation energies to isobaric analog states (IAS) and charge
invariance, we extract nuclear symmetry coefficients, from a mass formula, on a
nucleus-by-nucleus basis. Consistently with charge invariance, the coefficients
vary weakly across an isobaric chain. However, they change strongly with
nuclear mass and range from a_a~10 MeV at mass A~10 to a_a~22 MeV at A~240.
Following the considerations of a Hohenberg-Kohn functional for nuclear
systems, we determine how to find in practice the symmetry coefficient using
neutron and proton densities, even when those densities are simultaneously
affected by significant symmetry-energy and Coulomb effects. These results
facilitate extracting the symmetry coefficients from Skyrme-Hartree-Fock (SHF)
calculations, that we carry out using a variety of Skyrme parametrizations in
the literature. For the parametrizations, we catalog novel short-wavelength
instabilities. In comparing the SHF and IAS results for the symmetry
coefficients, we arrive at narrow (+-2.4 MeV) constraints on the symmetry
energy values S(rho) at 0.04<rho<0.13 fm^-3. Towards normal density the
constraints significantly widen, but the normal value of energy a_a^V and the
slope parameter L are found to be strongly correlated. To narrow the
constraints, we reach for the measurements of asymmetry skins and arrive at
a_a^V=(30.2-33.7) MeV and L=(35-70) MeV, with those values being again strongly
positively correlated along the diagonal of their combined region. Inclusion of
the skin constraints allows to narrow the constraints on S(rho), at
0.04<rho<0.13 fm^-3, down to +-1.1 MeV. Several microscopic calculations,
including variational, Bruckner-Hartree-Fock and Dirac-Bruckner-Hartree-Fock,
are consistent with our constraint region on S(rho).


  Pb$_2$CoOsO$_6$ is a newly synthesized polar metal in which inversion
symmetry is broken by the magnetic frustration in an antiferromagnetic ordering
of Co and Os sublattices. The coupled magnetic and structural transition occurs
at 45 K at ambient pressure. Here we perform transport measurements and
first-principles calculations to study the pressure effects on the
magnetic/structural coupled transition of Pb$_2$CoOsO$_6$. Experimentally we
monitor the resistivity anomaly at $T_N$ under various pressures up to 11 GPa
in a cubic anvil cell apparatus. We find that $T_N$ determined from the
resistivity anomaly first increases quickly with pressure in a large slope of
$dT_N/dP$ = +6.8(8) K/GPa for $P < 4$ GPa, and then increases with a much
reduced slope of 1.8(4) K/GPa above 4 GPa. Our first-principles calculations
suggest that the observed discontinuity of $dT_N/dP$ around 4 GPa may be
attributed to the vanishing of Os magnetic moment under pressure. Pressure
substantially reduces the Os moment and completely suppresses it above a
critical value, which relieves the magnetic frustration in the
antiferromagnetic ordering of Pb$_2$CoOsO$_6$. The Co and Os polar distortions
decrease with the increasing pressure and simultaneously vanish at the critical
pressure. Therefore above the critical pressure a new centrosymmetric
antiferromagnetic state emerges in Pb$_2$CoOsO$_6$, distinct from the one under
ambient pressure, thus showing a discontinuity in $dT_N/dP$.


  An accelerated universe should naturally have a vacuum energy density
determined by its dynamical curvature. The cosmological constant is most likely
a temporary description of a dynamical variable that has been drastically
evolving from the early inflationary era to the present. In this Essay we
propose a unified picture of the cosmic history implementing such an idea, in
which the cosmological constant problem is fixed at early times. All the main
stages, from inflation and its ("graceful") exit into a standard radiation
regime, as well as the matter and dark energy epochs, are accounted for.
Finally, we show that for a generic Grand Unified Theory associated to the
inflationary phase, the amount of entropy generated from primeval vacuum decay
can explain the huge measured value today.


  Addressing the limitations of individual attribution scores via the Shapley
value (SV), the field of explainable AI (XAI) has recently explored intricate
interactions of features or data points. In particular, extensions of the SV,
such as the Shapley Interaction Index (SII), have been proposed as a measure to
still benefit from the axiomatic basis of the SV. However, similar to the SV,
their exact computation remains computationally prohibitive. Hence, we propose
with SVARM-IQ a sampling-based approach to efficiently approximate
Shapley-based interaction indices of any order. SVARM-IQ can be applied to a
broad class of interaction indices, including the SII, by leveraging a novel
stratified representation. We provide non-asymptotic theoretical guarantees on
its approximation quality and empirically demonstrate that SVARM-IQ achieves
state-of-the-art estimation results in practical XAI scenarios on different
model classes and application domains.


  Adiabatic passage is a standard tool for achieving robust transfer in quantum
systems. We show that, in the context of driven nonlinear Hamiltonian systems,
adiabatic passage becomes highly non-robust when the target is unstable. We
show this result for a generic (1:2) resonance, for which the complete transfer
corresponds to a hyperbolic fixed point in the classical phase space featuring
an adiabatic connectivity strongly sensitive to small perturbations of the
model. By inverse engineering, we devise high-fidelity and robust partially
non-adiabatic trajectories. They localize at the approach of the target near
the stable manifold of the separatrix, which drives the dynamics towards the
target in a robust way. These results can be applicable to atom-molecule
Bose-Einstein condensate conversion and to nonlinear optics.


  We consider the problem of classification of all W algebras which commute
with a set of exponential screening operators. Assuming that the W algebra has
a nontrivial current of spin 3, we find equations satisfied by the screening
operators and classify their solutions.


  Quantum amplitudes for $s=1$ at Maxwell fields and for $s=2$ linearised
gravitational wave perturbations of a spherically symmetric Einstein/massless
scalar background, describing gravitational collapse to a black hole, are
treated by analogy with a previous treatment of $s=0$ scalar-field
perturbations of gravitational collapse at late times. In both the $s=1$ and
$s=2$ cases, we isolate suitable 'co-ordinate' variables which can be taken as
boundary data on a final space-like hypersurface $\Sigma_F$. For simplicity, we
take the data on an initial pre-collapse surface $\Sigma_I$ to be exactly
spherically symmetric. The (large) Lorentzian proper-time interval between
$\Sigma_{I}, \Sigma_{F}$, measured at spatial infinity, is denoted by $T$. The
complexified classical boundary-value problem is expected to be well-posed,
provide that the time interval $T$ has been rotated into the complex:
$T\to{\mid}T{\mid}\exp(-i\theta)$, for $0<\theta\leq{\pi}/2$. We calculate the
second-variation classical Lorenztian action $S ^{(2)}_{\rm class}$. Following
Feynman, we recover the Lorentzian quantum amplitude by taking the limit as
$\theta\to 0_+$ of the semi-classical amplitude $\exp(iS^{(2)}_{\rm class})$.
The boundary data for $ s=1$ involve the Maxwell magnetic field; the data for
$s=2$ involve the magnetic part of the Weyl curvature tensor. The magnetic
boundary conditions are related to each other and to the natural $s={1 \over
2}$ boundary conditions by supersymmetry.


  A quantum phase transition in strongly correlated Fermi systems beyond the
topological quantum critical point is studied within the Fermi liquid approach.
The transition occurs between two topologically equivalent states, each with
three sheets of the Fermi surface. One of these states possesses a
quasiparticle halo in the quasiparticle momentum distribution $n(p)$, while the
other, the hole pocket. The transition is found to be of the first order with
respect to both the coupling constant $g$ and the temperature $T$. The phase
diagram of the system in the vicinity of this transition is constructed.


  In the fields of Experimental and Computational Aesthetics, numerous image
datasets have been created over the last two decades. In the present work, we
provide a comparative overview of twelve image datasets that include aesthetic
ratings (beauty, liking or aesthetic quality) and investigate the
reproducibility of results across different datasets. Specifically, we examine
how consistently the ratings can be predicted by using either (A) a set of 20
previously studied statistical image properties, or (B) the layers of a
convolutional neural network developed for object recognition. Our findings
reveal substantial variation in the predictability of aesthetic ratings across
the different datasets. However, consistent similarities were found for
datasets containing either photographs or paintings, suggesting different
relevant features in the aesthetic evaluation of these two image genres. To our
surprise, statistical image properties and the convolutional neural network
predict aesthetic ratings with similar accuracy, highlighting a significant
overlap in the image information captured by the two methods. Nevertheless, the
discrepancies between the datasets call into question the generalizability of
previous research findings on single datasets. Our study underscores the
importance of considering multiple datasets to improve the validity and
generalizability of research results in the fields of experimental and
computational aesthetics.


  We obtain a nonperturbative, analytical solution to integral equation of
scattering theory by assuming the field within the scattering object is a
spherical wave with a scattering amplitude equal to that of the far field. This
approximation transforms the integral equation into a simple algebraic equation
which can be readily solved to obtain a closed-form expression for the
scattering amplitude. We show this approximation is valid for homogeneous
potentials of compact support, namely circular and square cylinders, and that
the calculated scattering cross sections for spheres and square cylinders are
accurate for frequencies through the fundamental resonance. Then we apply our
analytical expression to the inverse scattering problem for spheres and show
that accurate reconstructions are possible even under resonance conditions. The
simplicity and accuracy of our method suggest it can be a reliable and
efficient tool for understanding a wide range of scattering problems in optics.


  Relativistic jets launched by supermassive black holes, so-called as active
galactic nuclei (AGNs), are known as the most energetic particle accelerators
in the universe. However, the baryon loading efficiency onto the jets from the
accretion flows and their particle acceleration efficiencies have been veiled
in mystery. With the latest data sets, we perform multi-wavelength spectral
analysis of quiescent spectra of 13 TeV gamma-ray detected
high-frequency-peaked BL Lacs (HBLs) following one-zone static
synchrotron-self-Compton (SSC) model. We determine the minimum, cooling break,
and maximum electron Lorentz factors following the diffusive shock acceleration
(DSA) theory. We find that HBLs have $P_B/P_e\sim6.3\times10^{-3}$ and the
radiative efficiency $\epsilon_{\rm rad,jet}\sim6.7\times10^{-4}$ where $P_B$
and $P_e$ is the Poynting and electron power, respectively. By assuming 10
leptons per one proton, the jet power relates to the black hole mass as $P_{\rm
jet}/L_{\rm Edd}\sim0.18$ where $P_{\rm jet}$ and $L_{\rm Edd}$ is the jet
power and the Eddington luminosity, respectively. Under our model assumptions,
we further find that HBLs have the jet production efficiency of $\eta_{\rm
jet}\sim1.5$ and the mass loading efficiency of $\xi_{\rm
jet}\gtrsim5\times10^{-2}$. We also investigate the particle acceleration
efficiency in the blazar zone by including the most recent Swift/BAT data. Our
samples ubiquitously have the particle acceleration efficiency of
$\eta_g\sim10^{4.5}$, which is inefficient to accelerate particles up to the
ultra-high-energy-cosmic-ray (UHECR) regime. This implies that the UHECR
acceleration sites should be other than the blazar zones of quiescent low power
AGN jets, if one assumes the one-zone SSC model based on the DSA theory.


  The properties of precessing, coalescing binary black holes are presently
inferred through comparison with two approximate models of compact binary
coalescence. In this work we show these two models often disagree substantially
when binaries have modestly large spins ($a\gtrsim 0.4$) and modest mass ratios
($q\gtrsim 2$). We demonstrate these disagreements using standard figures of
merit and the parameters inferred for recent detections of binary black holes.
By comparing to numerical relativity, we confirm these disagreements reflect
systematic errors. We provide concrete examples to demonstrate that these
systematic errors can significantly impact inferences about astrophysically
significant binary parameters. For the immediate future, parameter inference
for binary black holes should be performed with multiple models (including
numerical relativity), and carefully validated by performing inference under
controlled circumstances with similar synthetic events.


  Most deep learning methods that achieve high segmentation accuracy require
deep network architectures that are too heavy and complex to run on embedded
devices with limited storage and memory space. To address this issue, this
paper proposes an efficient Generative Adversarial Transfomer (GATrans) for
achieving high-precision semantic segmentation while maintaining an extremely
efficient size. The framework utilizes a Global Transformer Network (GTNet) as
the generator, efficiently extracting multi-level features through residual
connections. GTNet employs global transformer blocks with progressively linear
computational complexity to reassign global features based on a learnable
similarity function. To focus on object-level and pixel-level information, the
GATrans optimizes the objective function by combining structural similarity
losses. We validate the effectiveness of our approach through extensive
experiments on the Vaihingen dataset, achieving an average F1 score of 90.17%
and an overall accuracy of 91.92%.


  We study the convergence of the Ginzburg-Landau (GL) expansion in the context
of the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity and the
Nambu-Jona-Lasinio (NJL) model for chiral symmetry breaking at finite
temperature $T$ and chemical potential $\mu$. We present derivations of the
all-order formulas for the coefficients of the GL expansions in both systems
under the mean-field approximation. We show that the convergence radii for the
BCS gap $\Delta$ and dynamical quark mass $M$ are given by $\Delta_\text{conv}
= \pi T$ and $M_\text{conv} = \sqrt{\mu^2 + (\pi T)^2}$, respectively. We also
discuss the implications of these results and the quantitative reliability of
the GL expansion near the first-order chiral phase transition.


  Linear optics is a promising candidate for the implementation of quantum
information processing protocols. In such systems single photons are employed
to represent qubits. In practice, single photons produced from different
sources will not be perfectly temporally and frequency matched. Therefore
understanding the effects of temporal and frequency mismatch is important for
characterising the dynamics of the system. In this paper we discuss the effects
of temporal and frequency mismatch, how they differ, and what their effect is
upon a simple linear optics quantum gate. We show that temporal and frequency
mismatch exhibit inherently different effects on the operation of the gate. We
also consider the spectral effects of the photo-detectors, focusing on
time-resolved detection, which we show has a strong impact on the operation of
such protocols.


  We review the existing proposals to detect relic neutrinos using the coherent
scattering of a neutrino wind on a test mass. By considering the transformation
of the neutrino momentum between reference frames, we demonstrate that the
induced acceleration scales with the square of the neutrino mass for
unclustered neutrinos, contrary to the existing literature. In addition, we
show that there is a large contribution to this effect from coherent
neutrino-electron scattering, which can exceed the neutrino-nucleus component
by nearly an order of magnitude. Unfortunately, we find that even with this
enhancement there are no existing experiments or proposals capable of detecting
relic neutrinos using this method.


  We propose a technique for interpolating between probability distributions on
discrete surfaces, based on the theory of optimal transport. Unlike previous
attempts that use linear programming, our method is based on a dynamical
formulation of quadratic optimal transport proposed for flat domains by Benamou
and Brenier [2000], adapted to discrete surfaces. Our structure-preserving
construction yields a Riemannian metric on the (finite-dimensional) space of
probability distributions on a discrete surface, which translates the so-called
Otto calculus to discrete language. From a practical perspective, our technique
provides a smooth interpolation between distributions on discrete surfaces with
less diffusion than state-of-the-art algorithms involving entropic
regularization. Beyond interpolation, we show how our discrete notion of
optimal transport extends to other tasks, such as distribution-valued Dirichlet
problems and time integration of gradient flows.


  The fine-tuning of Large Language Models (LLMs) specialized in code
generation has seen notable advancements through the use of open-domain coding
queries. Despite the successes, existing methodologies like Evol-Instruct
encounter performance limitations, impeding further enhancements in code
generation tasks. This paper examines the constraints of existing prompt
evolution techniques and introduces a novel approach, Instruction Fusion (IF).
IF innovatively combines two distinct prompts through a hybridization process,
thereby enhancing the evolution of training prompts for code LLMs. Our
experimental results reveal that the proposed novel method effectively
addresses the shortcomings of prior methods, significantly improving the
performance of Code LLMs across five code generation benchmarks, namely
HumanEval, HumanEval+, MBPP, MBPP+ and MultiPL-E, which underscore the
effectiveness of Instruction Fusion in advancing the capabilities of LLMs in
code generation.


  We demonstrate dual-comb spectroscopy based on difference frequency
generation of frequency-agile near-infrared frequency combs, produced with the
help of electro-optic modulators. The combs have a remarkably flat intensity
distribution and their positions and line spacings can be selected freely by
simply dialing a knob. We record, in the 3-micron region, Doppler-limited
absorption spectra with resolved comb lines within milliseconds. Precise
molecular line parameters are retrieved. Our technique holds promise for fast
and sensitive time-resolved studies e.g. of trace gases.


  The Alexandria system under development at IBM Research provides an
extensible framework and platform for supporting a variety of big-data
analytics and visualizations. The system is currently focused on enabling rapid
exploration of text-based social media data. The system provides tools to help
with constructing "domain models" (i.e., families of keywords and extractors to
enable focus on tweets and other social media documents relevant to a project),
to rapidly extract and segment the relevant social media and its authors, to
apply further analytics (such as finding trends and anomalous terms), and
visualizing the results. The system architecture is centered around a variety
of REST-based service APIs to enable flexible orchestration of the system
capabilities; these are especially useful to support knowledge-worker driven
iterative exploration of social phenomena. The architecture also enables rapid
integration of Alexandria capabilities with other social media analytics
system, as has been demonstrated through an integration with IBM Research's
SystemG. This paper describes a prototypical usage scenario for Alexandria,
along with the architecture and key underlying analytics.


  Despite extraordinary progress, current machine learning systems have been
shown to be brittle against adversarial examples: seemingly innocuous but
carefully crafted perturbations of test examples that cause machine learning
predictors to misclassify. Can we learn predictors robust to adversarial
examples? and how? There has been much empirical interest in this contemporary
challenge in machine learning, and in this thesis, we address it from a
theoretical perspective.
  In this thesis, we explore what robustness properties can we hope to
guarantee against adversarial examples and develop an understanding of how to
algorithmically guarantee them. We illustrate the need to go beyond traditional
approaches and principles such as empirical risk minimization and uniform
convergence, and make contributions that can be categorized as follows: (1)
introducing problem formulations capturing aspects of emerging practical
challenges in robust learning, (2) designing new learning algorithms with
provable robustness guarantees, and (3) characterizing the complexity of robust
learning and fundamental limitations on the performance of any algorithm.


  Deep Learning models based on heatmap regression have revolutionized the task
of facial landmark localization with existing models working robustly under
large poses, non-uniform illumination and shadows, occlusions and
self-occlusions, low resolution and blur. However, despite their wide adoption,
heatmap regression approaches suffer from discretization-induced errors related
to both the heatmap encoding and decoding process. In this work we show that
these errors have a surprisingly large negative impact on facial alignment
accuracy. To alleviate this problem, we propose a new approach for the heatmap
encoding and decoding process by leveraging the underlying continuous
distribution. To take full advantage of the newly proposed encoding-decoding
mechanism, we also introduce a Siamese-based training that enforces heatmap
consistency across various geometric image transformations. Our approach offers
noticeable gains across multiple datasets setting a new state-of-the-art result
in facial landmark localization. Code alongside the pretrained models will be
made available at https://www.adrianbulat.com/face-alignment


  Due to factors such as low population density and expansive geographical
distances, network deployment falls behind in rural regions, leading to a
broadband divide. Wireless spectrum serves as the blood and flesh of wireless
communications. Shared white spaces such as those in the TVWS and CBRS spectrum
bands offer opportunities to expand connectivity, innovate, and provide
affordable access to high-speed Internet in under-served areas without
additional cost to expensive licensed spectrum. However, the current methods to
utilize these white spaces are inefficient due to very conservative models and
spectrum policies, causing under-utilization of valuable spectrum resources.
This hampers the full potential of innovative wireless technologies that could
benefit farmers, small Internet Service Providers (ISPs) or Mobile Network
Operators (MNOs) operating in rural regions. This study explores the challenges
faced by farmers and service providers when using shared spectrum bands to
deploy their networks while ensuring maximum system performance and minimizing
interference with other users. Additionally, we discuss how spatiotemporal
spectrum models, in conjunction with database-driven spectrum-sharing
solutions, can enhance the allocation and management of spectrum resources,
ultimately improving the efficiency and reliability of wireless networks
operating in shared spectrum bands.


  We show that if there exists a topologically expansive homeomorphism on a
uniform space, then the space is always a regular space. Through examples we
show that in general composition of topologically expansive homeomorphisms need
not be topological expansive and also that conjugate of topologically expansive
homeomorphism need not be topological expansive. Further, we obtain a
characterization of orbit expansivity in terms of topological expansivity and
conclude that if there exists a topologically expansive homeomorphism on a
compact uniform space then the space must be metrizable. We also study
positively expansive maps on topological space and obtain condition for maps to
be positively topological expansive in terms of finite open cover. Further, we
show that if there exists a continuous, one-to-one, positively topological
expansive map on a compact uniform space, then the space is finite. We also
give an example of a positively topological expansive map on a non--Hausdorff
space.


  Spectra of thermal fluctuations of a wide range of interfaces, from
liquid/air, viscoelastic material/air, liquid/liquid, to liquid/viscoelastic
material interfaces, were measured over 100 Hz to 10 MHz frequency range. The
obtained spectra were compared with the fluctuation theory of interfaces, and
found to be mostly in quite good agreement, when the theory was generalized to
apply to thermal fluctuations of liquid/viscoelastic material interfaces. The
spectra were measured using a system that combines light reflection,
statistical noise reduction through averaged correlations, and confocal
microscopy. It requires only a small area of the interface ($\sim1\,\mu$m$^2$)
, relatively short times for measurements ($\lesssim$few min), and can also be
applied to highly viscous materials.


  In this paper, we propose an energy-efficient spatial modulation based
molecular communication (SM-MC) scheme, in which a transmitted symbol is
composed of two parts, i.e., a space derived symbol and a concentration derived
symbol. The space symbol is transmitted by embedding the information into the
index of a single activated transmitter nanomachine. The concentration symbol
is drawn according to the conventional concentration shift keying (CSK)
constellation. Befitting from a single active transmitter during each symbol
transmission period, SM-MC can avoid the inter-link interference problem
existing in the current multiple-input multiple-output (MIMO) MC schemes, which
hence enables low-complexity symbol detection and performance improvement.
Specifically, in our low-complexity scheme, the space symbol is first detected
by energy comparison, and then the concentration symbol is detected by the
equal gain combining assisted CSK demodulation. In this paper, we analyze the
symbol error rate (SER) of the SM-MC and its special case, namely the space
shift keying based MC (SSK-MC), where only space symbol is transmitted and no
CSK modulation is invoked. Finally, the analytical results are validated by
computer simulations, and our studies demonstrate that both the SM-MC and
SSK-MC are capable of achieving better SER performance than the conventional
MIMO-MC and single-input single-output MC (SISO-MC) when the same symbol rate
is assumed.


  The split basis of an irreducible representation of the symmetric group,
$S_{n+m}$, is the basis which is adapted to direct product subgroups of the
form $S_{n} \times S_{m}$. In this article we have calculated symmetric group
subduction coefficients relating the standard Young-Yamanouchi basis for the
symmetric group to the split basis by means of a novel version of the
Schur-Weyl duality. We have also directly obtained matrix representations in
the split basis using these techniques. The advantages of this approach are
that we obtain analytical expressions for the subduction coefficients and
matrix representations and directly resolve issues of multiplicity in the
subduction of $S_{n} \times S_{m}$ irreducible representations from $S_{n+m}$
irreducible representations. Our method is applicable to $S_{n+m}$ irreducible
representations labelled by Young diagrams with large row length differences.
We provide evidence for a systematic expansion in the inverse row length
difference and tools to compute the leading contribution, which is exact when
row length differences are infinite.


  Internet of things (IoT) is a revolutionizing technology which aims to create
an ecosystem of connected objects and embedded devices and provide ubiquitous
connectivity between trillions of not only smart devices but also simple
sensors and actuators. Although recent advancements in miniaturization of
devices with higher computational capabilities and ultra-low power
communication technologies have enabled the vast deployment of sensors and
actuators everywhere, such an evolution calls for fundamental changes in
hardware design, software, network architecture, data analytic, data storage
and power sources. A large portion of IoT devices cannot be powered by
batteries only anymore, as they will be installed in hard to reach areas and
regular battery replacement and maintenance are infeasible. A viable solution
is to scavenge and harvest energy from environment and then provide enough
energy to the devices to perform their operations. This will significantly
increase the device life time and eliminate the need for the battery as an
energy source. This survey aims at providing a comprehensive study on energy
harvesting techniques as alternative and promising solutions to power IoT
devices. We present the main design challenges of IoT devices in terms of
energy and power and provide design considerations for a successful
implementations of self-powered IoT devices. We then specifically focus on
piezoelectric energy harvesting and RF energy harvesting as most promising
solutions to power IoT devices and present the main challenges and research
directions. We also shed light on the security challenges of energy harvesting
enabled IoT systems and green big data.


  The properties of the B-meson light-cone wave function up to next-to-leading
order Fock state expansion have been studied through a comparative study of the
$B\to \pi$, $K$ transition form factors within the $k_T$ factorization approach
and the light-cone sum rule analysis. The transition form factors
$F^{B\to\pi}_{+,0,T}$ and $F^{B\to K}_{+,0,T}$ are carefully re-calculated up
to ${\cal O}(1/m_b^2)$ within the $k_T$ factorization approach in the large
recoil region, in which the main theoretical uncertainties are discussed. The
QCD light-cone sum rule is applicable in the large and intermediate energy
regions, and the QCD light-cone sum rule results in Ref.\cite{sumrule} are
adopted for such a comparative study. It is found that when the two
phenomenological parameters $\bar\Lambda\in [0.50,0.55]$ and
$\delta\in[0.25,0.30]$, the results of $F^{B\to\pi}_{+,0,T}(Q^2)$ and $F^{B\to
K}_{+,0,T}(Q^2)$ from these two approaches are consistent with each other in
the large recoil energy region.


  Fully-supervised polyp segmentation has accomplished significant triumphs
over the years in advancing the early diagnosis of colorectal cancer. However,
label-efficient solutions from weak supervision like scribbles are rarely
explored yet primarily meaningful and demanding in medical practice due to the
expensiveness and scarcity of densely-annotated polyp data. Besides, various
deployment issues, including data shifts and corruption, put forward further
requests for model generalization and robustness. To address these concerns, we
design a framework of Spatial-Spectral Dual-branch Mutual Teaching and
Entropy-guided Pseudo Label Ensemble Learning (S$^2$ME). Concretely, for the
first time in weakly-supervised medical image segmentation, we promote the
dual-branch co-teaching framework by leveraging the intrinsic complementarity
of features extracted from the spatial and spectral domains and encouraging
cross-space consistency through collaborative optimization. Furthermore, to
produce reliable mixed pseudo labels, which enhance the effectiveness of
ensemble learning, we introduce a novel adaptive pixel-wise fusion technique
based on the entropy guidance from the spatial and spectral branches. Our
strategy efficiently mitigates the deleterious effects of uncertainty and noise
present in pseudo labels and surpasses previous alternatives in terms of
efficacy. Ultimately, we formulate a holistic optimization objective to learn
from the hybrid supervision of scribbles and pseudo labels. Extensive
experiments and evaluation on four public datasets demonstrate the superiority
of our method regarding in-distribution accuracy, out-of-distribution
generalization, and robustness, highlighting its promising clinical
significance. Our code is available at https://github.com/lofrienger/S2ME.


  Excited band structures recently observed in $^{156}$Dy are investigated
using the microscopic triaxial projected shell model (TPSM) approach and the
quasiparticle random phase approximation (QRPA) based on the rotating
mean-field. It is demonstrated that new observed excited bands, tracking the
ground-state band, are the $\gamma$-bands based on the excited two-quasineutron
configurations as conjectured in the experimental work.


  This paper proposes a new approach to model the temporal dynamics of a
sequence of facial expressions. To this purpose, a sequence of Face Image
Descriptors (FID) is regarded as the output of a Linear Time Invariant (LTI)
system. The temporal dynamics of such sequence of descriptors are represented
by means of a Hankel matrix. The paper presents different strategies to compute
dynamics-based representation of a sequence of FID, and reports classification
accuracy values of the proposed representations within different standard
classification frameworks. The representations have been validated in two very
challenging application domains: emotion recognition and pain detection.
Experiments on two publicly available benchmarks and comparison with
state-of-the-art approaches demonstrate that the dynamics-based FID
representation attains competitive performance when off-the-shelf
classification tools are adopted.


  Task-oriented dialogues must maintain consistency both within the dialogue
itself, ensuring logical coherence across turns, and with the conversational
domain, accurately reflecting external knowledge. We propose to conceptualize
dialogue consistency as a Constraint Satisfaction Problem (CSP), wherein
variables represent segments of the dialogue referencing the conversational
domain, and constraints among variables reflect dialogue properties, including
linguistic, conversational, and domain-based aspects. To demonstrate the
feasibility of the approach, we utilize a CSP solver to detect inconsistencies
in dialogues re-lexicalized by an LLM. Our findings indicate that: (i) CSP is
effective to detect dialogue inconsistencies; and (ii) consistent dialogue
re-lexicalization is challenging for state-of-the-art LLMs, achieving only a
0.15 accuracy rate when compared to a CSP solver. Furthermore, through an
ablation study, we reveal that constraints derived from domain knowledge pose
the greatest difficulty in being respected. We argue that CSP captures core
properties of dialogue consistency that have been poorly considered by
approaches based on component pipelines.


  As the multi-view data grows in the real world, multi-view clus-tering has
become a prominent technique in data mining, pattern recognition, and machine
learning. How to exploit the relation-ship between different views effectively
using the characteristic of multi-view data has become a crucial challenge.
Aiming at this, a hidden space sharing multi-view fuzzy clustering (HSS-MVFC)
method is proposed in the present study. This method is based on the classical
fuzzy c-means clustering model, and obtains associ-ated information between
different views by introducing shared hidden space. Especially, the shared
hidden space and the fuzzy partition can be learned alternatively and
contribute to each other. Meanwhile, the proposed method uses maximum entropy
strategy to control the weights of different views while learning the shared
hidden space. The experimental result shows that the proposed multi-view
clustering method has better performance than many related clustering methods.


  The implications of conformal invariance, as relevant in quantum field
theories at a renormalisation group fixed point, are analysed with particular
reference to results for correlation functions involving conserved currents and
the energy momentum tensor. Ward identities resulting from conformal invariance
are discussed. Explicit expressions for two and three point functions, which
are essentially determined by conformal invariance, are obtained. As special
cases we consider the three point functions for two vector and an axial current
in four dimensions, which realises the usual anomaly simply and unambiguously,
and also for the energy momentum tensor in general dimension $d$. The latter is
shown to have two linearly independent forms in which the Ward identities are
realised trivially, except if $d = 4$, when the two forms become degenerate.
This is necessary in order to accommodate the two independent forms present in
the trace of the energy momentum tensor on curved space backgrounds for
conformal field theories in four dimensions. The coefficients of the two trace
anomaly terms are related to the three parameters describing the general energy
momentum tensor three point function. The connections with gravitational
effective actions depending on a background metric are described. A particular
form due to Riegert is shown to be unacceptable. Conformally invariant
expressions for the effective action in four dimensions are obtained using the
Green function for a differential operator which has simple properties under
local rescalings of the metric.


  We study a one-dimensional model of interacting bosons on a lattice with two
flat bands. Regular condensation is suppressed due to the absence of a well
defined minimum in the single particle spectrum. We find that interactions
stabilize a number of non-trivial phases like a pair (quasi-) condensate, a
supersolid at incommensurable fillings and valence bond crystals at
commensurability. We support our analytical calculations with numerical
simulations using the density matrix renormalization group technique.
Implications for cold-atoms and extensions to higher dimensions are discussed.


  This paper presents a methodology for building daily profiles of wind
generation and load for different seasons to assess their impacts on voltage
violations. The measurement-based wind models showed very high accuracy when
validated against several years of actual wind power data. System load modeling
was carried out by analyzing the seasonal trends that occur in residential,
commercial, and industrial loads. When the proposed approach was implemented on
the IEEE 118-bus system, it could identify violations in bus voltage profiles
that the season-independent model could not capture. The results of the
proposed approach are expected to provide better visualization of the problems
that seasonal variations in wind power and load might cause to the electric
power grid.


  Let $\Theta = (\theta_1,\theta_2,\theta_3)\in \mathbb{R}^3$. Suppose that
$1,\theta_1,\theta_2,\theta_3$ are linearly independent over $\mathbb{Z}$. For
Diophantine exponents $$ \alpha(\Theta) = \sup \{\gamma >0:\,\,\, \limsup_{t\to
+\infty} t^\gamma \psi_\Theta (t) <+\infty \} ,$$ $$\beta(\Theta) = \sup
\{\gamma >0:\,\,\, \liminf_{t\to +\infty} t^\gamma \psi_\Theta (t) <+\infty\}
$$ we prove $$ \beta (\Theta) \ge {1/2} ({\alpha (\Theta)}/{1-\alpha(\Theta)}
+\sqrt{{\alpha(\Theta)}/{1-\alpha(\Theta)})^2
+{4\alpha(\Theta)}/{1-\alpha(\Theta)}}) \alpha (\Theta) $$


  Based on our observation that there exists a dramatic drop for the singular
values of the fully connected layers or a single feature map of the
convolutional layer, and that the dimension of the concatenated feature vector
almost equals the summation of the dimension on each feature map, we propose a
singular value decomposition (SVD) based approach to estimate the dimension of
the deep manifolds for a typical convolutional neural network VGG19. We choose
three categories from the ImageNet, namely Persian Cat, Container Ship and
Volcano, and determine the local dimension of the deep manifolds of the deep
layers through the tangent space of a target image. Through several
augmentation methods, we found that the Gaussian noise method is closer to the
intrinsic dimension, as by adding random noise to an image we are moving in an
arbitrary dimension, and when the rank of the feature matrix of the augmented
images does not increase we are very close to the local dimension of the
manifold. We also estimate the dimension of the deep manifold based on the
tangent space for each of the maxpooling layers. Our results show that the
dimensions of different categories are close to each other and decline quickly
along the convolutional layers and fully connected layers. Furthermore, we show
that the dimensions decline quickly inside the Conv5 layer. Our work provides
new insights for the intrinsic structure of deep neural networks and helps
unveiling the inner organization of the black box of deep neural networks.


  Bandlimited approaches to quantum field theory offer the tantalizing
possibility of working with fields that are simultaneously both continuous and
discrete via the Shannon Sampling Theorem from signal processing. Conflicting
assumptions in general relativity and quantum field theory motivate the use of
such an appealing analytical tool that could thread the needle to meet both
requirements. Bandlimited continuous quantum fields are isomorphic to lattice
theories, yet without requiring a fixed lattice. Any lattice with a required
minimum spacing can be used. This is an isomorphism that avoids taking the
limit of the lattice spacing going to zero. In this work, we explore the
consequences of this isomorphism, including the emergence of effectively
continuous symmetries in quantum lattice theories. One obtains conserved
lattice observables for these continuous symmetries, as well as a duality of
locality from the two perspectives. We expect this work and its extensions to
provide useful tools for considering numerical lattice models of continuous
quantum fields arising from the availability of discreteness without a fixed
lattice, as well as offering new insights into emergent continuous symmetries
in lattice models and possible laboratory demonstrations of these phenomena.


  We investigate the production of Higgs particles in association with the
supersymmetric scalar partners of the top quark at proton colliders. In the
minimal supersymmetric extension of the Standard Model, the cross sections for
the production of the lightest neutral Higgs boson in association with top
squark pairs can be rather large, substantially exceeding the rate for the
associated Higgs boson production with top quarks. If the lightest top squark
is not much heavier than the top quark, this process will enhance the potential
of the CERN Large Hadron Collider to discover the lightest neutral Higgs boson,
and will open a window to the study of the Higgs-stop coupling, the potentially
largest electroweak coupling in the supersymmetric theory.


  Using fourth-order perturbation theory, a general formula for the van der
Waals potential of two neutral, unpolarized, ground-state atoms in the presence
of an arbitrary arrangement of dispersing and absorbing magnetodielectric
bodies is derived. The theory is applied to two atoms in bulk material and in
front of a planar multilayer system, with special emphasis on the cases of a
perfectly reflecting plate and a semi-infinite half space. It is demonstrated
that the enhancement and reduction of the two-atom interaction due to the
presence of a perfectly reflecting plate can be understood, at least in the
nonretarded limit, by using the method of image charges. For the semi-infinite
half space, both analytical and numerical results are presented.


  Many round or nearly roundish Planetary Nebulae (PNe) show multiple shells
and halo structures during their evolutionary stage near the maximum
temperature of their central star. Controversial debate is currently ongoing if
these structures are recombination halos, as suggested by hydrodynamic
modelling efforts, or ionized material. Recently we discovered a halo with even
somewhat unusual structures around the sparsely studied PN IC~5148 and present
for the first time spectroscopy going out to the halo of such a PN.} resolution
spectroscopy is used to derive dust chemistry and mineralogy. We investigate
the spatial distribution of material and its ionization state from the center
of the nebula up to the very outskirts of the halo. We obtained long-slit low
resolution spectroscopy (FORS2@VLT) of the nebula in two position angles, which
we used to investigate the nebular structure and its halo in the optical range
from 450 to 880\,nm. In addition we used medium resolution spectra taken with
X-SHOOTER@VLT ranging from 320 nm to 2.4 mu to derive atmospheric parameters
for the central star. We obtained the distance and position in the Galaxy from
various methods combined with GAIA DR2 data. We also applied Cloudy models to
the nebula in order to derive physical parameters of the various regions. We
obtained spatially resolved structures and detailed descriptions of the
outrunning shock front and a set of unusual halo structures denoted to further
shock. The halo structures appears clearly as hot ionized material. Furthermore
we derived a reliable photometric value for the central star at a GAIA distance
of D=1.3kpc. Considering the large distance $z=1.0$\,kpc from the galactic
plane together to its non-circular motion in the galaxy and, a metallicity only
slightly below that of typical disk PNe, most likely IC 5148 originates from a
thick disk population star.


  We consider a two-component, two-dimensional nonlinear Schr\"{o}dinger system
with unequal dispersion coefficients and self-defocusing nonlinearities,
chiefly with equal strengths of the self- and cross-interactions. In this
setting, a natural waveform with a nonvanishing background in one component is
a vortex, which induces an effective potential well in the second component,
via the nonlinear coupling of the two components. We show that the potential
well may support not only the fundamental bound state, but also multi-ring
excited radial state complexes for suitable ranges of values of the dispersion
coefficient of the second component. We systematically explore the existence,
stability, and nonlinear dynamics of these states. The complexes involving the
excited radial states are weakly unstable, with a growth rate depending on the
dispersion of the second component. Their evolution leads to transformation of
the multi-ring complexes into stable VB solitons ones with the fundamental
state in the second component. The excited states may be stabilized by a
harmonic-oscillator trapping potential, as well as by unequal strengths of the
self- and cross-repulsive nonlinearities.


  The recently proposed pair-interaction model is applied to study a series of
refractory high entropy alloys. The results demonstrate the simplicity,
robustness, and high accuracy of this model in predicting the configuration
energies of NbMoTaW, NbMoTaWV and NbMoTaWTi. The element-element pair
interaction parameters obtained from the linear regression of first-principle
data provide a new perspective to understand the strengthening mechanism in
HEAs, as revealed by comparing the effects of adding vanadium and titanium.
Using the pair-interaction model, an expression for the intrinsic energy
fluctuation is derived, which provides guidance on both theoretical modeling
and first principles calculation.


  Using the annealed approach we investigate the asymptotic behavior of the
survival probability of a critical multitype branching process evolving in
i.i.d. random environment. We show under rather general assumptions on the form
of the offspring generating functions of particles that the probability of
survival up to generation $n$ of the process initiated at moment zero by a
single particle of type $i$ is equivalent to $c_{i}n^{-1/2}$ for large $n,$
where $c_{i}$ is a positive constant. Earlier such asymptotic representation
was known only for the case of the fractional linear offspring generating
functions.


  In this article, we show that if $X$ is a Stein space of dimension $n$ and,
if $D$ is a locally $q$-complete open set in $X$, then $D$ is $q$-complete.
This gives, in particular, a positive answer to the local Steinness problem,
which is one of the most classical problem in complex analytic geometry,
namely, if $D$ is a locally Stein open set in a Stein space $X$, then $D$ is
Stein


  In [1], we have presented the theoretical background for finding the
Elementary Invariants for a 3D system of first order rational differential
equations (1ODEs). We have also provided an algorithm to find such Invariants.
Here we introduce new theoretical results that will lead to a novel, more
efficient, approach to determine these invariants. Furthermore, one important
aspect of such dynamical systems is that the integrability can be an issue. We
will show that the present theoretical development allows for an Integrability
analysis in the case where the system has free parameters.


  Using a graph-theoretic approach, we derive a new sufficient condition for
observability of a Boolean control network (BCN). Based on this condition, we
describe two algorithms: the first selects a set of nodes so that observing
this set makes the BCN observable. The second algorithm builds an observer for
the observable BCN. Both algorithms are sub-optimal, as they are based on a
sufficient but not necessary condition for observability. Yet their
time-complexity is linear in the length of the description of the BCN,
rendering them feasible for large-scale networks. We discuss how these results
can be used to provide a sub-optimal yet polynomial-complexity algorithm for
the minimal observability problem in BCNs. Some of the theoretical results are
demonstrated using a BCN model of the core network regulating the mammalian
cell cycle.


  Let A be an n by n random matrix with iid entries taken from the p-adic
integers or Z/NZ. Then under mild non-degeneracy conditions the cokernel of A
has a universal probability distribution. In particular, the p-part of an iid
random matrix over the integers has cokernel distributed according to the
Cohen-Lenstra measure up to an exponentially small error.


  In this paper we observe that for geometrically integral projective varieties
$X$, admitting a full weak exceptional collection consisting of pure vector
bundles, the existence of a $k$-rational point implies $\mathrm{rdim}(X)=0$. We
also study the symmetric power $S^n(X)$ of Brauer--Severi and involution
varieties over $\mathbb{R}$ and prove that the equivariant derived category
$D^b_{S_n}(X^n)$ admits a full weak exceptional collection. As a consequence,
we find $\mathrm{rdim}(X)=0$ if and only if $\mathrm{rdim}(D^b_{S_n}(X^n))=0$
for $1\leq n\leq 3$. If $X$ is Brauer--Severi, the existence of a
$\mathbb{R}$-rational point on $X$ or $S^3(X)$ is equivalent to
$\mathrm{rdim}(D^b_{S_3}(X^3))=0$.


  Clickbait is a pejorative term describing web content that is aimed at
generating online advertising revenue, especially at the expense of quality or
accuracy, relying on sensationalist headlines or eye-catching thumbnail
pictures to attract click-throughs and to encourage forwarding of the material
over online social networks. We use distributed word representations of the
words in the title as features to identify clickbaits in online news media. We
train a machine learning model using linear regression to predict the cickbait
score of a given tweet. Our methods achieve an F1-score of 64.98\% and an MSE
of 0.0791. Compared to other methods, our method is simple, fast to train, does
not require extensive feature engineering and yet moderately effective.


  We study the condensation of fluids confined by a pair of non-parallel plates
of finite height $H$. We show that such a system experiences two types of
condensation, termed single- and double-pinning, which can be characterized by
one (single-pinning) or two (double-pinning) edge contact angles describing the
shape of menisci pinned at the system edges. For both types of capillary
condensation we formulate the Kelvin-like equation and determine the conditions
under which the given type of condensation occurs. We construct the global
phase diagram revealing a reentrant phenomenon pertinent to the change of the
capillary condensation type upon varying the inclination of the walls.
Asymptotic properties of the system are discussed and a link with related phase
phenomena in different systems is made. Finally, we show that the change from a
single- to a double-pinned state is a continuous transition, the character of
which depends on the wetting properties of the walls.


  Recently, the CMS collaboration has reported a di-tau excess with a local
significance of 2.6-3.1$\sigma$ where the invariant mass is
$m_{\tau\tau}=$95-100 GeV. This excess can be interpreted as a light scalar
boson that couples to the third generation fermions, particularly top and
$\tau$. Based on the simplest model that can account for the CMS di-tau excess,
we evaluate experimental sensitivities to the additional light resonance, using
the results reported by the ATLAS collaboration. We see that a search for the
top-quark associated production of the SM Higgs boson that decays into
$\tau\bar\tau$ sets a strong model-independent limit. We also find that the
CP-even scalar interpretation of the light resonance is excluded by the ATLAS
results, while the CP-odd interpretation is not.


  This paper investigates the problem of guessing subject to distortion, which
was introduced by Arikan and Merhav. While the primary concern of the previous
study was asymptotic analysis, our primary concern is non-asymptotic analysis.
We prove non-asymptotic achievability and converse bounds of the moment of the
number of guesses without side information (resp. with side information) by
using a quantity based on the R\'enyi entropy (resp. the Arimoto-R\'enyi
conditional entropy). Also, we introduce an error probability and show similar
results. Further, from our bounds, we derive a single-letter characterization
of the asymptotic exponent of guessing moment for a stationary memoryless
source.


  We consider the possibility of a bosonic (meta)stabilization of a cosmic
gauge string loop due to the presence of a gas of low mass bosonic particles
which become trapped within the string core. This boson gas exerts a pressure
which tends to counteract the string tension, allowing a circular string loop
to find a finite equilibrium radius, provided that gas particles do not escape
the string core. However, high energy bosons do escape, and consequently the
loop shrinks and the temperature rises. Estimates indicate that the bosonic
stabilization mechanism is ineffective, and the loop is unstable against decay.


  A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks
often used in TS modeling and forecasting. Because of its "black box" aspect,
many researchers refuse to use it. Moreover, the optimization (often based on
the exhaustive approach where "all" configurations are tested) and learning
phases of this artificial intelligence tool (often based on the
Levenberg-Marquardt algorithm; LMA) are weaknesses of this approach
(exhaustively and local minima). These two tasks must be repeated depending on
the knowledge of each new problem studied, making the process, long, laborious
and not systematically robust. In this paper a pruning process is proposed.
This method allows, during the training phase, to carry out an inputs selecting
method activating (or not) inter-nodes connections in order to verify if
forecasting is improved. We propose to use iteratively the popular damped
least-squares method to activate inputs and neurons. A first pass is applied to
10% of the learning sample to determine weights significantly different from 0
and delete other. Then a classical batch process based on LMA is used with the
new MLP. The validation is done using 25 measured meteorological TS and
cross-comparing the prediction results of the classical LMA and the 2-stage
LMA.