  We derive sharp Adams inequalities with exact growth condition for the Riesz
potential as well as more general Riesz-like potentials on R^n. We also obtain
Moser-Trudinger inequalities with exact growth condition for the fractional
Laplacian, and for general homogeneous elliptic differential operators with
constant coefficients.


  Given a convex body K in R^n and p in R, we introduce and study the extremal
inner and outer affine surface areas
  IS_p(K) = sup_{K'\subseteq K} (as_p(K') ) and os_p(K)=inf_{K'\supseteq K}
(as_p(K') ), where as_p(K') denotes the L_p-affine surface area of K', and the
supremum is taken over all convex subsets of K and the infimum over all convex
compact subsets containing K.
  The convex body that realizes IS_1(K) in dimension 2 was determined by
Barany. He also showed that this body is the limit shape of lattice polytopes
in K. In higher dimensions no results are known about the extremal bodies.
  We use a thin shell estimate of Guedon and Milman and the L\"owner ellipsoid
to give asymptotic estimates on the size of IS_p(K) and os_p(K). Surprisingly,
both quantities are proportional to a power of volume.


  In this paper, we study the problem of joint active and passive beamforming
for reconfigurable intelligent surface (RIS)-assisted massive multiple-input
multiple-output systems towards the extension of the wireless cellular coverage
in 3D, where multiple RISs, each equipped with an array of passive elements,
are deployed to assist a base station (BS) to simultaneously serve multiple
unmanned aerial vehicles (UAVs) in the same time-frequency resource of 5G
wireless communications. With a focus on ensuring fairness among UAVs, our
objective is to maximize the minimum signal-to-interference-plus-noise ratio
(SINR) at UAVs by jointly optimizing the transmit beamforming parameters at the
BS and phase shift parameters at RISs. We propose two novel algorithms to
address this problem. The first algorithm aims to mitigate interference by
calculating the BS beamforming matrix through matrix inverse operations once
the phase shift parameters are determined. The second one is based on the
principle that one RIS element only serves one UAV and the phase shift
parameter of this RIS element is optimally designed to compensate the phase
offset caused by the propagation and fading. To obtain the optimal parameters,
we utilize one state-of-the-art reinforcement learning algorithm, deep
deterministic policy gradient, to solve these two optimization problems.
Simulation results are provided to illustrate the effectiveness of our proposed
solution and some insightful remarks are observed.


  Emphatic algorithms are temporal-difference learning algorithms that change
their effective state distribution by selectively emphasizing and
de-emphasizing their updates on different time steps. Recent works by Sutton,
Mahmood and White (2015), and Yu (2015) show that by varying the emphasis in a
particular way, these algorithms become stable and convergent under off-policy
training with linear function approximation. This paper serves as a unified
summary of the available results from both works. In addition, we demonstrate
the empirical benefits from the flexibility of emphatic algorithms, including
state-dependent discounting, state-dependent bootstrapping, and the
user-specified allocation of function approximation resources.


  Graphene nanoribbons (GNR) in mutually perpendicular electric and magnetic
fields are shown to exhibit dramatic changes in their band structure and
electron transport properties. A strong electric field across the ribbon
induces multiple chiral Dirac points, closing the semiconducting gap in
armchair GNR's. A perpendicular magnetic field induces partially formed Landau
levels as well as dispersive surface-bound states. Each of the applied fields
on its own preserves the even symmetry $E_{k} = E_{-k}$ of the subband
dispersion. When applied together, they reverse the dispersion parity to be odd
and gives $E_{e,k} = -E_{h,-k}$ and mix the electron and hole subbands within
the energy range corresponding to the change in potential across the ribbon.
This leads to oscillations of the ballistic conductance within this energy
range.


  The theory of quantum information processing for macroscopic qubits is based
on the fact that every macroscopic qubit has a conserved number of particles.
However, from an experimental point of view, every such qubit experiences
processes of decoherence that impact the possibilities for entanglement
generation between such qubits and use in quantum information processing
efficiently. One of the most prospective methods for generating entanglement
between distant atomic BECs is quantum nondemolition measurements. Here, we
study how the effects of photon measurement impact the entanglement when photon
loss decoherence is included. We employ the thermally entangled state
representation (TESR) and integral within the ordered operator(IWOP) approach
to obtain the accurate density matrix in a photon loss channel. We demonstrate
that varying outcomes of photon number measurements lead to the generation of
distinct entangled states, each exhibiting unique characteristics. We find that
using the Hofmann-Takeuchi and Duan-Giedke-Cirac-Zoller criterion provides
advantages in entanglement detection compared to the Wineland squeezing and EPR
steering criterion in such settings.


  A brief survey of theoretical approaches to description of multiplicity
distributions in high energy processes is given. It is argued that the
multicomponent nature of these processes leads to some peculiar characteristics
observed experimentally. Predictions for LHC energies are presented. It is
shown that similarity of the energy dependence of average multiplicities in
different reactions is not enough alone to suggest the universal mechanism of
particle production in strongly-interacting systems. Other characteristics of
multiplicity distributions depend on the nature of colliding partners.


  After a short analysis of the main problems involved in the construction of a
Far Infrared polarimeter with very low instrumental noise, we describe the
instrument that will be employed at MITO telescope to search for calibration
sources and investigate polarization near the CMB anisotropy peaks in the next
campaign (Winter 2002-03).


  Graph Neural Networks (GNNs) have been a powerful tool for node
classification tasks in complex networks. However, their decision-making
processes remain a black-box to users, making it challenging to understand the
reasoning behind their predictions. Counterfactual explanations (CFE) have
shown promise in enhancing the interpretability of machine learning models.
Prior approaches to compute CFE for GNNS often are learning-based approaches
that require training additional graphs. In this paper, we propose a
semivalue-based, non-learning approach to generate CFE for node classification
tasks, eliminating the need for any additional training. Our results reveals
that computing Banzhaf values requires lower sample complexity in identifying
the counterfactual explanations compared to other popular methods such as
computing Shapley values. Our empirical evidence indicates computing Banzhaf
values can achieve up to a fourfold speed up compared to Shapley values. We
also design a thresholding method for computing Banzhaf values and show
theoretical and empirical results on its robustness in noisy environments,
making it superior to Shapley values. Furthermore, the thresholded Banzhaf
values are shown to enhance efficiency without compromising the quality (i.e.,
fidelity) in the explanations in three popular graph datasets.


  We present an end-to-end machine-human image annotation system where each
component can be attached in a plug-and-play fashion. These components include
Feature Extraction, Machine Classifier, Task Sampling and Crowd Consensus.


  Geometric description of quantum correlations are favored for their distinct
physical significance. Geometric discord based on the trace distance and the
Bures distance are shown to be well-defined quantum correlation measures. Here,
we examine their particular dynamical behaviors under independent as well as
common structured reservoirs, and reveal their robustness against decoherence.
We showed that the two well-defined geometric discord may be preserved well, or
even be improved and generated by the noisy process of the common reservoir.
Moreover, we also provided a strategy for long-time preservation of these two
geometric discord in independent reservoirs.


  In the 1990s, Richard Lewontin referred to what appeared to be the twilight
of determinism in biology. He pointed out that DNA determines only a little
part of life phenomena, which are very complex. In fact, organisms determine
the environment and vice versa in a nonlinear way. Very recently,
biophysicists, Shimon Marom and Erez Braun, have demonstrated that controlled
biophysical systems have shown a relative autonomy and flexibility in response
which could not be predicted. Within the boundaries of some restraints, most of
them genetic, this freedom from determinism is well maintained. Marom and Braun
have challenged not only biophysical determinism but also reverse-engineering,
naive reductionism, mechanism, and systems biology.


  Warm inflationary universe models in the context of intermediate expansion,
between power law and exponential, are studied. General conditions required for
these models to be realizable are derived and discussed. This study is done in
the weak and strong dissipative regimes. The inflaton potentials considered in
this study are negative-power-law and powers of logarithms, respectively. The
parameters of our models are constrained from the WMAP three and five year
data.


  Present and future large scale surveys offer promising probes of cosmology.
For example the Dark Energy Survey (DES) is forecast to detect ~300 millions
galaxies and thousands clusters up to redshift ~1.3. I here show ongoing work
to combine two probes of large scale structure : cluster number counts and
galaxy 2-point function (in real or harmonic space). The halo model (coupled to
a Halo Occupation Distribution) can be used to model the cross-covariance
between these probes, and I introduce a diagrammatic method to compute easily
the different terms involved. Furthermore, I compute the joint non-Gaussian
likelihood, using the Gram-Charlier series. Then I show how to extend the
methods of Bayesian hyperparameters to Poissonian distributions, in a first
step to include them in this joint likelihood.


  Atmospheric Carbon Monoxide (CO) provides a window on the chemistry of the
atmosphere since it is one of few chemical constituents that can be remotely
sensed, and it can be used to determine budgets of other greenhouse gases such
as ozone and OH radicals. Remote sensing platforms in geostationary Earth orbit
will soon provide regional observations of CO at several vertical layers with
high spatial and temporal resolution. However, cloudy locations cannot be
observed and estimates of the complete CO concentration fields have to be
estimated based on the cloud-free observations. The current state-of-the-art
solution of this interpolation problem is to combine cloud-free observations
with prior information, computed by a deterministic physical model, which might
introduce uncertainties that do not derive from data. While sharing features
with the physical model, this paper suggests a Bayesian hierarchical model to
estimate the complete CO concentration fields. The paper also provides a direct
comparison to state-of-the-art methods. To our knowledge, such a model and
comparison have not been considered before.


  We present a time-dependent calculation of the velocity-dependent forces
which act on an excited atomic dipole in relative motion with respect to ground
state atoms of a different kind. Both, its interaction with a single atom and
with a dilute atomic plate are evaluated. In either case, the total force
consists of a conservative van der Waals component and a non-conservative
Rontgen component. On physical grounds, the former corresponds to the
velocity-dependent recoil experienced by the excited atom in the processes of
absorption and emission of the photons that it exchanges with the ground state
atoms on a periodic basis. The latter corresponds to the time-variation of the
Rontgen momentum, which is also mediated by the periodic exchange of
quasi-resonant photons. We find that, at leading order, all these interactions
are linear in the velocity. In the non-retarded regime the van der Waals force
dominates, being antiparallel to the velocity. On the contrary, in the retarded
regime the velocity-dependent forces oscillate in space, van der Waals and
Rontgen forces are of the same order in the atom-atom interaction, and the
Rontgen component dominates in the atom-surface interaction.


  We present a new step in the foundation of quantum field theory with the
tools of scale relativity. Previously, quantum motion equations (Schr\"odinger,
Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written
with a quantum-covariant derivative operator. Then, the nature of gauge
transformations, of gauge fields and of conserved charges have been given a
geometric meaning in terms of a scale-covariant derivative tool. Finally, the
electromagnetic Klein-Gordon equation has been recovered with a covariant
derivative constructed by combining the quantum-covariant velocity operator and
the scale-covariant derivative. We show here that if one tries to derive the
electromagnetic Dirac equation from the Klein-Gordon one as for the free
particle motion, i.e. as a square root of the time part of the Klein-Gordon
operator, one obtains an additional term which is the relativistic analog of
the spin-magnetic field coupling term of the Pauli equation. However, if one
first applies the quantum covariance, then implements the scale covariance
through the scale-covariant derivative, one obtains the electromagnetic Dirac
equation in its usual form. This method can also be applied successfully to the
derivation of the electromagnetic Klein-Gordon equation. This suggests it rests
on more profound roots of the theory, since it encompasses naturally the
spin-charge coupling.


  The first quantum technology, which harnesses uniquely quantum mechanical
effects for its core operation, has arrived in the form of commercially
available quantum key distribution systems that achieve enhanced security by
encoding information in photons such that information gained by an eavesdropper
can be detected. Anticipated future quantum technologies include large-scale
secure networks, enhanced measurement and lithography, and quantum information
processors, promising exponentially greater computation power for particular
tasks. Photonics is destined for a central role in such technologies owing to
the need for high-speed transmission and the outstanding low-noise properties
of photons. These technologies may use single photons or quantum states of
bright laser beams, or both, and will undoubtably apply and drive
state-of-the-art developments in photonics.


  The Galaxy Evolution Explorer (GALEX) detected ultraviolet emission in about
50% of multi-spin early-type galaxies (ETGs), suggesting the occurrence of a
recent rejuvenation episode connected to the formation of these kinematical
features. With the aim at investigating the complex evolutionary scenario
leading to the formation of counter rotating ETGs (CR-ETGs) we use our Smooth
Particle Hydrodynamic (SPH) code with chemo-photometric implementation. We
discuss here the UV evolutionary path of two CR-ETGs, NGC 3593 and NGC 5173,
concurrently best fitting their global observed properties, i.e., morphology,
dynamics, as well as their total B-band absolute magnitude and spectral energy
distribution (SED) extended over three orders of magnitude in wavelength. These
simulations correspond to our predictions about the target evolution which we
follow in the color-magnitude diagram (CMD), near-UV (NUV) versus r-band
absolute magnitude, as a powerful diagnostic tool to emphasize rejuvenation
episodes.


  Heterogeneous graph neural networks aim to discover discriminative node
embeddings and relations from multi-relational networks.One challenge of
heterogeneous graph learning is the design of learnable meta-paths, which
significantly influences the quality of learned embeddings.Thus, in this paper,
we propose an Attributed Multi-Order Graph Convolutional Network (AMOGCN),
which automatically studies meta-paths containing multi-hop neighbors from an
adaptive aggregation of multi-order adjacency matrices. The proposed model
first builds different orders of adjacency matrices from manually designed node
connections. After that, an intact multi-order adjacency matrix is attached
from the automatic fusion of various orders of adjacency matrices. This process
is supervised by the node semantic information, which is extracted from the
node homophily evaluated by attributes. Eventually, we utilize a one-layer
simplifying graph convolutional network with the learned multi-order adjacency
matrix, which is equivalent to the cross-hop node information propagation with
multi-layer graph neural networks. Substantial experiments reveal that AMOGCN
gains superior semi-supervised classification performance compared with
state-of-the-art competitors.


  We present combinatorial bijections and identities between certain skew Young
tableaux, Dyck paths, triangulations, and dissections.


  In the framework of the Tsallis statistical mechanics, for the spin-1/2 and
the harmonic oscillator, we study the change of the population of states when
the parameter $q$ is varied; the results show that the difference between
predictions of the Boltzmann--Gibbs and Tsallis Statistics can be much smaller
than the precision of any existing experiment. Also, the relation between the
privilege of rare/frequent event and the value of $q$ is restudied. This
relation is shown to be more complicated than the common belief about it.
Finally, the convergence criteria of the partition function of some simple
model systems, in the framework of Tsallis Statistical Mechanics, is studied;
based on this study, we conjecture that $q \leq 1$, in the thermodynamic limit.


  The wide dissemination of fake news is increasingly threatening both
individuals and society. Fake news detection aims to train a model on the past
news and detect fake news of the future. Though great efforts have been made,
existing fake news detection methods overlooked the unintended entity bias in
the real-world data, which seriously influences models' generalization ability
to future data. For example, 97\% of news pieces in 2010-2017 containing the
entity `Donald Trump' are real in our data, but the percentage falls down to
merely 33\% in 2018. This would lead the model trained on the former set to
hardly generalize to the latter, as it tends to predict news pieces about
`Donald Trump' as real for lower training loss. In this paper, we propose an
entity debiasing framework (\textbf{ENDEF}) which generalizes fake news
detection models to the future data by mitigating entity bias from a
cause-effect perspective. Based on the causal graph among entities, news
contents, and news veracity, we separately model the contribution of each cause
(entities and contents) during training. In the inference stage, we remove the
direct effect of the entities to mitigate entity bias. Extensive offline
experiments on the English and Chinese datasets demonstrate that the proposed
framework can largely improve the performance of base fake news detectors, and
online tests verify its superiority in practice. To the best of our knowledge,
this is the first work to explicitly improve the generalization ability of fake
news detection models to the future data. The code has been released at
https://github.com/ICTMCG/ENDEF-SIGIR2022.


  We consider CFTs conjectured to be dual to higher spin theories of gravity in
AdS_3 and AdS_4. Two dimensional CFTs with W_N symmetry are considered in the
lambda=0 (k --> infinity) limit, where they are conjectured to be described by
continuous orbifolds. The torus partition function is computed, using
reasonable assumptions, and equals that of a free field theory. We find no
phase transition at temperatures of order one; the usual Hawking-Page phase
transition is removed by the highly degenerate light states associated with
conical defect states in the bulk. Three dimensional Chern-Simons-matter CFTs
with vector-like matter are considered on T^3, where the dynamics is described
by an effective theory for the eigenvalues of the holonomies. Likewise, we find
no evidence for a Hawking-Page phase transition at large level k.


  In this paper, the time fractional reaction-diffusion equations with the
Caputo fractional derivative are solved by using the classical $L1$-formula and
the finite volume element (FVE) methods on triangular grids. The existence and
uniqueness for the fully discrete FVE scheme are given. The stability result
and optimal \textit{a priori} error estimate in $L^2(\Omega)$-norm are derived,
but it is difficult to obtain the corresponding results in $H^1(\Omega)$-norm,
so another analysis technique is introduced and used to achieve our goal.
Finally, two numerical examples in different spatial dimensions are given to
verify the feasibility and effectiveness.


  The 120-year old so-called Painleve paradox involves the loss of determinism
in models of planar rigid bodies in point contact with a rigid surface, subject
to Coulomb-like dry friction. The phenomenon occurs due to coupling between
normal and rotational degrees-of-freedom such that the effective normal force
becomes attractive rather than repulsive. Despite a rich literature, the
forward evolution problem remains unsolved other than in certain restricted
cases in 2D with single contact points. Various practical consequences of the
theory are revisited, including models for robotic manipulators, and the
strange behaviour of chalk when pushed rather than dragged across a blackboard.
  Reviewing recent theory, a general formulation is proposed, including a
Poisson or energetic impact law. The general problem in 2D with a single point
of contact is discussed and cases or inconsistency or indeterminacy enumerated.
Strategies to resolve the paradox via contact regularisation are discussed from
a dynamical systems point of view. By passing to the infinite stiffness limit
and allowing impact without collision, inconsistent and indeterminate cases are
shown to be resolvable for all open sets of conditions. However, two
unavoidable ambiguities that can be reached in finite time are discussed in
detail, so called dynamic jam and reverse chatter. A partial review is given of
2D cases with two points of contact showing how a greater complexity of
inconsistency and indeterminacy can arise. Extension to fully three-dimensional
analysis is briefly considered and shown to lead to further possible
singularities. In conclusion, the ubiquity of the \pain paradox is highlighted
and open problems are discussed.


  We study the Markowitz portfolio selection problem with unknown drift vector
in the multidimensional framework. The prior belief on the uncertain expected
rate of return is modeled by an arbitrary probability law, and a Bayesian
approach from filtering theory is used to learn the posterior distribution
about the drift given the observed market data of the assets. The Bayesian
Markowitz problem is then embedded into an auxiliary standard control problem
that we characterize by a dynamic programming method and prove the existence
and uniqueness of a smooth solution to the related semi-linear partial
differential equation (PDE). The optimal Markowitz portfolio strategy is
explicitly computed in the case of a Gaussian prior distribution. Finally, we
measure the quantitative impact of learning, updating the strategy from
observed data, compared to non-learning, using a constant drift in an uncertain
context, and analyze the sensitivity of the value of information w.r.t. various
relevant parameters of our model.


  By using two primary doublets and one induced bidoublet Higgs fields as a
result of the interactions of the two doublets, we evaluate the predictive
power of the left-right symmetry model based on $SU(2)_{L}\otimes
SU(2)_{R}\otimes U(1)$ gauge group to the gauge bosons masses, leptons masses,
and the structure of electroweak interactions. We found that the contribution
of the right charge-current to the electroweak interaction is only around
0.0073 percent. The neutrino mass emerges naturally without introducing exotic
particles. We obtain that the mixing angle $\theta = 45^{0}$ for boson sector,
$\theta \approx 45^{0}$ for neutrino sector, and $\theta = 0^{0}$ for electron
sector. The parity violation in our model could be associated with the mass
mixing in the bosons and leptons masses arise from the induced bidoublet Higgs
via symmetry breaking.
  PACs: 12.60.Cn; 12.60.Fr


  A brief survey of real algebraic structures on topological spaces is given.
This article is written for the Gokova Gemetry/Topology Conference proceedings.


  For a rational number $q$, a rational $D(q)$-$n$-tuple is a set of $n$
distinct nonzero rationals $\{a_1, a_2, \dots, a_n\}$ such that $a_ia_j+q$ is a
rational square for all $1 \leqslant i < j \leqslant n$. For every $q$ we find
all rational $m$ such that there exists a $D(q)$-quadruple with product
$abcd=m$. We describe all such quadruples using points on a specific elliptic
curve depending on $(q,m).$


  We investigate the Fefferman spaces of conformal type which are induced, via
parabolic geometry, by the quaternionic contact (qc) manifolds introduced by
O.Biquard. Equivalent characterizations of these spaces are proved: as
conformal manifolds with symplectic conformal holonomy of the appropriate
signature; as pseudo-Riemannian manifolds admitting conformal Killing fields
satisfying a conformally invariant system of conditions analog to G. Sparling's
criteria; and as the total space of a SO(3)- or $S^3$-bundle over a qc manifold
with the conformally equivalent metrics defined directly by Biquard. Global as
well as local results are acquired.


  We have analyzed all the archival X-ray data of 134 unidentified (unID)
gammaray sources listed in the first Fermi/LAT (1FGL) catalog and subsequently
followed up by Swift/XRT. We constructed the spectral energy distributions
(SEDs) from radio to gamma-rays for each X-ray source detected, and tried to
pick up unique objects that display anomalous spectral signatures. In these
analysis, we target all the 1FGL unID sources, using updated data from the
second Fermi/LAT (2FGL) catalog on their LAT position and spectra. We found
several potentially interesting objects, particularly three sources, 1FGL
J0022.2-1850, 1FGL J0038.0+1236 and 1FGL J0157.0-5259, which were then more
deeply observed with Suzaku as a part of an AO7 program in 2012. We
successfully detected an X-ray counterpart for each source whose X-ray spectra
were well fitted by a single power-law function. The positional coincidence
with a bright radio counterpart (currently identified as AGN) in the 2FGL error
circles suggests these are definitely the X-ray emission from the same AGN, but
their SEDs show a wide variety of behavior. In particular, the SED of 1FGL
J0038.0+1236 is difficult to be explained by conventional emission models of
blazars. The source 1FGL J0022.2-1850 may be in a transition state between a
low-frequency peaked BL Lac and a high-frequency peaked BL Lac object, and 1FGL
J0157.0-5259 could be a rare kind of extreme blazar. We discuss the possible
nature of these three sources observed with Suzaku, together with the X-ray
identification results and SEDs of all 134 sources observed with Swift/XRT.


  The analysis of perturbative quantities is a powerful tool to distinguish
between different Dark Energy models and gravity theories degenerated at the
background level. In this work, we generalise the integral solution of the
matter density contrast for General Relativity gravity to a wide class of
Modified Gravity (MG) theories. To calculate this solution is necessary prior
knowledge of the Hubble rate, the density parameter at the present epoch
($\Omega_{m0}$) and the functional form of the effective Newton's constant that
characterises the gravity theory. We estimate in a model-independent way the
Hubble expansion rate by applying a non-parametric reconstruction method to
model-independent cosmic chronometer data and high-$z$ quasar data. In order to
compare our generalised solution of the matter density contrast, using the
non-parametric reconstruction of $H(z)$ from observational data, with purely
theoretical one, we choose a parameterisation of the Screened MG and the
$\Omega_{m0}$ from WMAP-9 collaborations. Finally, we calculate the growth
index for the analysed cases, finding very good agreement between theoretical
values and the obtained ones using the approach presented in this work.


  We introduce a novel ridge detection algorithm for time-frequency (TF)
analysis, particularly tailored for intricate nonstationary time series
encompassing multiple non-sinusoidal oscillatory components. The algorithm is
rooted in the distinctive geometric patterns that emerge in the TF domain due
to such non-sinusoidal oscillations. We term this method \textit{shape-adaptive
mode decomposition-based multiple harmonic ridge detection}
(\textsf{SAMD-MHRD}). A swift implementation is available when supplementary
information is at hand. We demonstrate the practical utility of
\textsf{SAMD-MHRD} through its application to a real-world challenge. We employ
it to devise a cutting-edge walking activity detection algorithm, leveraging
accelerometer signals from an inertial measurement unit across diverse body
locations of a moving subject.


  In this work we investigate time varying networks with complex dynamics at
the nodes. We consider two scenarios of network change in an interval of time:
first, we have the case where each link can change with probability pt, i.e.
the network changes occur locally and independently at each node. Secondly we
consider the case where the entire connectivity matrix changes with probability
pt, i.e. the change is global. We show that network changes, occurring both
locally and globally, yield an enhanced range of synchronization. When the
connections are changed slowly (i.e. pt is low) the nodes display nearly
synchronized intervals interrupted by intermittent unsynchronized chaotic
bursts. However when the connections are switched quickly (i.e. pt is large),
the intermittent behavior quickly settles down to a steady synchronized state.
Furthermore we find that the mean time taken to reach synchronization from
generic random initial states is significantly reduced when the underlying
links change more rapidly. We also analyze the probabilistic dynamics of the
system with changing connectivity and the stable synchronized range thus
obtained is in broad agreement with those observed numerically.


  The intermittent dissipation of interstellar turbulence is an important
energy source in the diffuse ISM. Though on average smaller than the heating
rates due to cosmic rays and the photoelectric effect on dust grains, the
turbulent cascade can channel large amounts of energy into a relatively small
fraction of the gas that consequently undergoes significant heating and
chemical enrichment. In particular, this mechanism has been proposed as a
solution to the long-standing problem of the high abundance of CH+ along
diffuse molecular sight lines, which steady-state, low temperature models
under-produce by over an order of magnitude. While much work has been done on
the structure and chemistry of these small-scale dissipation zones,
comparatively little attention has been paid to relating these zones to the
properties of the large-scale turbulence. In this paper, we attempt to bridge
this gap by estimating the temperature and CH+ column density along diffuse
molecular sight-lines by post-processing 3-dimensional MHD turbulence
simulations. Assuming reasonable values for the cloud density (30 / cm^3), size
(20 pc), and velocity dispersion (2.3 km / s), we find that our computed
abundances compare well with CH+ column density observations, as well as with
observations of emission lines from rotationally excited H2 molecules.


  We derive the chiral effective Lagrangian for excited heavy-light mesons from
QCD under proper approximations. We focus on the chiral partners with
$j_l^P=\frac{3}{2}^+$ and $j_l^P=\frac{3}{2}^-$ which amounts to ($1^+,2^+$)
and ($1^-,2^-$) states respectively. The low energy constants including the
masses of the chiral partners are calculated. The calculated spectrum for the
excited mesons are found roughly consistent with experimental data. In
addition, our results indicate that quantum numbers of $B_J(5970)$ can be
identified with $1^-$ or $2^-$.


  Functional near-infrared spectroscopy (fNIRS) is a non-invasive technique for
monitoring brain activity. To better understand the brain, researchers often
use deep learning to address the classification challenges of fNIRS data. Our
study shows that while current networks in fNIRS are highly accurate for
predictions within their training distribution, they falter at identifying and
excluding abnormal data which is out-of-distribution, affecting their
reliability. We propose integrating metric learning and supervised methods into
fNIRS research to improve networks capability in identifying and excluding
out-of-distribution outliers. This method is simple yet effective. In our
experiments, it significantly enhances the performance of various networks in
fNIRS, particularly transformer-based one, which shows the great improvement in
reliability. We will make our experiment data available on GitHub.


  The paper presents a data-driven model of self-adaptivity for multiparty
sessions. System choreography is prescribed by a global type. Participants are
incarnated by processes associated with monitors, which control their
behaviour. Each participant can access and modify a set of global data, which
are able to trigger adaptations in the presence of critical changes of values.
  The use of the parallel composition for building global types, monitors and
processes enables a significant degree of flexibility: an adaptation step can
dynamically reconfigure a set of participants only, without altering the
remaining participants, even if the two groups communicate.


  Behavior Trees (BTs) got the robotics society attention not least thanks to
their modularity and reusability. The subtrees of BTs could be treated as
separate behaviors and therefore reused. We address the following research
question: do we exploit the full power of BT on these properties? We suggest to
generalise the idea of subtree reuse to "node templates" concept, which allows
to represent an arbitrary nodes collection. In addition, previously hardcoded
behaviors such as Node* and many Decorator nodes could be implemented in a
memory-based BT by node templates.


  The X-ray thermal isolated neutron star (XTINS) RX J0806.4--4123 shows
interesting multiwavelength properties that seemingly deviate from those of
similar neutron stars. An accurate determination of the spin frequency change
over time can assist in interpreting RX J0806.4-4123's properties in comparison
to those of other XTINSs and the wider pulsar population. From 2019 to 2023 we
carried out a tailored X-ray timing campaign of RX J0806.4-4123 with the NICER
instrument. We used statistical properties of the Fourier coefficients and the
$Z_K^2$ test for phase-connecting separate observations and finding a timing
solution for the entire dataset. We also developed a simple and universal
method for estimating the uncertainties of frequency $\nu$ and its derivative
$\dot{\nu}$ from the empirical dependencies of $Z_K^2$ on trial values of these
parameters, with account of all significant harmonics of the frequency.
Applying this method, we determined a spin-down rate $\dot{\nu} =
-7.3(1.2)\times 10^{-17}\,{\rm Hz\, s}^{-1}$. The resulting spin-down power
$\dot{E}=2.6\times 10^{29}$ erg s$^{-1}$ is the lowest among the XTINSs, and it
is a factor of 60 lower than the X-ray luminosity of this neutron star. RX
J0806.4-4123 is also among the pulsars with the lowest measured $\dot{E}$ in
general.


  The efficiency of wireless information and power transfer (WIPT) systems
requires an essential reevaluation and rethinking of the entire transceiver
chain, which is characterized by a bottom-up multi-layer design approach. In
this paper, we introduce and describe the key design layers: i) "Mathematical
modeling", associated with the investigation of mathematical models for the
wireless power transfer process, ii) "Information-theoretic limits", which
refers to the fundamental limits of the WIPT channel, iii) "Link design",
corresponding to signal processing techniques that make WIPT feasible, iv)
"System-level perspective", which studies the developed WIPT techniques from a
macroscopic system-level point-of-view, and v) "Experimental studies", that
refers to real-world implementation of WIPT systems. These layers are
well-connected and their interplay is imperative for the effective design of
WIPT systems. Specific case studies are discussed, which demonstrates the
interdisciplinary nature of the aforementioned multi-layer design framework.


  An accurate knowledge of the scattering length is fundamental in ultracold
quantum gas experiments and essential for the characterisation of the system as
well as for a meaningful comparison to theoretical models. Here, we perform a
careful characterisation of the s-wave scattering length $a_s$ for the four
highest-abundance isotopes of erbium, in the magnetic field range from 0G to
5G. We report on cross-dimensional thermalization measurements and apply the
Enskog equations of change to numerically simulate the thermalization process
and to analytically extract an expression for the so-called number of
collisions per re-thermalization (NCPR) to obtain $a_s$ from our experimental
data. We benchmark the applied cross-dimensional thermalization technique with
the experimentally more demanding lattice modulation spectroscopy and find good
agreement for our parameter regime. Our experiments are compatible with a
dependence of the NCPR with $a_s$, as theoretically expected in the case of
strongly dipolar gases. Surprisingly, we experimentally observe a dependency of
the NCPR on the density, which might arise due to deviations from an ideal
harmonic trapping configuration. Finally, we apply a model for the dependency
of the background scattering length with the isotope mass, allowing to estimate
the number of bound states of erbium.


  Double parking that often negatively affects traffic operations and safety is
not a new phenomenon on urban streets. This study proposes a novel data-driven
integrated framework for estimating the actual frequency of double parking so
that both microscopic and macroscopic models can be utilized to quantify
area-wide impacts in the presence of double parking. The findings of the study
can provide transportation agencies with useful insights on identifying
locations that will experience the greatest benefits by removing problematic
double parking. As a result, various parking enforcement and management
strategies can be planned more effectively.


  A Hopf algebra is co-Frobenius when it has a nonzero integral. It is proved
that the composition length of the indecomposable injective comodules over a
co-Frobenius Hopf algebra is bounded. As a consequence, the coradical
filtration of a co-Frobenius Hopf algebra is finite; this confirms a conjecture
by Sorin D\u{a}sc\u{a}lescu and the first author. The proof is of categorical
nature and the same result is obtained for Frobenius tensor categories of
subexponential growth. A family of co-Frobenius Hopf algebras that are not of
finite type over their Hopf socles is constructed, answering so in the negative
another question by the same authors.


  The aim of this work is to explore the combined effect of polydispersity and
roughness on the partial energy production rates and on the total cooling rate
of a granular fluid mixture. We consider a mixture of inelastic rough hard
spheres of different number densities, masses, diameters, moments of inertia,
and mutual coefficients of normal and tangential restitution. Starting from the
first equation of the BBGKY hierarchy, the collisional energy production rates
associated with the translational and rotational temperatures ($T_i^\text{tr}$
and $T_i^\text{rot}$) are expressed in terms of two-body average values. Next,
those average values are estimated by assuming a velocity distribution function
based on maximum-entropy arguments, allowing us to express the energy
production rates and the total cooling rate in terms of the partial
temperatures and the parameters of the mixture. Finally, the results are
applied to the homogeneous cooling state of a binary mixture and the influence
of inelasticity and roughness on the temperature ratios
$T_1^\text{tr}/T_1^\text{rot}$, $T_2^\text{tr}/T_1^\text{tr}$, and
$T_2^\text{rot}/T_1^\text{rot}$ is analyzed.


  We formulate a kinetic theory of self-interacting meson fields with an aim to
describe the freezeout stage of the space-time evolution of matter in
ultrarelativistic nuclear collisions. Kinetic equations are obtained from the
Heisenberg equation of motion for a single component real scalar quantum field
taking the mean field approximation for the non-linear interaction. The mesonic
mean field obeys the classical non-linear Klein-Gordon equation with a
modification due to the coupling to mesonic quasi-particle excitations which
are expressed in terms of the Wigner functions of the quantum fluctuations of
the meson field, namely the statistical average of the bilinear forms of the
meson creation and annihilation operators. In the long wavelength limit, the
equations of motion of the diagonal components of the Wigner functions take a
form of Vlasov equation with a particle source and sink which arises due to the
non-vanishing off-diagonal components of the Wigner function expressing
coherent pair-creation and pair-annihilation process in the presence of
non-uniform condensate. We show that in the static homogeneous system, these
kinetic equations reduce to the well-known gap equation in the Hartree
approximation, and hence they may be considered as a generalization of the
Hartree approximation method to non-equilibrium systems. As an application of
these kinetic equations, we compute the dispersion relations of the collective
mesonic excitations in the system near equilibrium.


  Classical shadows are a versatile tool to probe many-body quantum systems,
consisting of a combination of randomised measurements and classical
post-processing computations. In a recently introduced version of the protocol,
the randomization step is performed via unitary circuits of variable depth $t$,
defining the so-called shallow shadows. For sufficiently large $t$, this
approach allows one to get around the use of non-local unitaries to probe
global properties such as the fidelity with respect to a target state or the
purity. Still, shallow shadows involve the inversion of a many-body map, the
measurement channel, which requires non-trivial computations in the
post-processing step, thus limiting its applicability when the number of qubits
$N$ is large. In this work, we put forward a simple approximate post-processing
scheme where the infinite-depth inverse channel is applied to the finite-depth
classical shadows and study its performance for fidelity and purity estimation.
The scheme allows for different circuit connectivity, as we illustrate for
geometrically local circuits in one and two spatial dimensions and
geometrically non-local circuits made of two-qubit gates. For the fidelity, we
find that the resulting estimator coincides with a known linear cross-entropy,
achieving an arbitrary small approximation error $\delta$ at depth $t=O(\log
(N/\delta))$ (independent of the circuit connectivity). For the purity, we show
that the estimator becomes accurate at a depth $O(N)$. In addition, at those
depths, the variances of both the fidelity and purity estimators display the
same scaling with $N$ as in the case of global random unitaries. We establish
these bounds by analytic arguments and extensive numerical computations in
several cases of interest. Our work extends the applicability of shallow
shadows to large system sizes and general circuit connectivity.


  We present a strong form, meshless point collocation explicit solver for the
numerical solution of the transient, incompressible, viscous Navier-Stokes
(N-S) equations in two dimensions. We numerically solve the governing flow
equations in their stream function-vorticity formulation. We use a uniform
Cartesian embedded grid to represent the flow domain. We compute the spatial
derivatives using the Meshless Point Collocation (MPC) method. We verify the
accuracy of the numerical scheme for commonly-used benchmark problems including
lid-driven cavity flow, flow over a backward-facing step and vortex shedding
behind a cylinder. We have examined the applicability of the proposed scheme by
considering flow cases with complex geometries, such as flow in a duct with
cylindrical obstacles, flow in a bifurcated geometry, and flow past
complex-shaped obstacles. Our method offers high accuracy and excellent
computational efficiency as demonstrated by the verification examples, while
maintaining a stable time step comparable to that used in unconditionally
stable implicit methods.


  We prove sharp uniform $L^p$-bounds for low-lying eigenfunctions of
non-self-adjoint semiclassical pseudodifferential operators $P$ on
$\mathbb{R}^{n}$ whose principal symbols are doubly-characteristic at the
origin of $\mathbb{R}^{2n}$. Our bounds hold under two main assumptions on $P$:
(1) the total symbol of $P$ extends holomorphically to a neighborhood of
$\mathbb{R}^{2n}$ in $\mathbb{C}^{2n}$, and (2) the quadratic approximation to
the principal symbol of $P$ at the origin is elliptic along its singular space.
Most notably, our assumptions on the quadratic approximation are less
restrictive than those made in prior works, and our main theorem improves the
already known results in the case when the symbol of $P$ is analytic.


  The ability to isolate a quantum system from its environment is of
fundamental interest and importance in optical quantum science and technology.
Here we propose an experimentally feasible scheme for beating
environment-induced dissipation in an open two-level system coupled to a
parametrically driven cavity. The mechanism relies on a novel cooperation
between light-matter coupling enhancement and frequent measurements. We
demonstrate that, in the presence of the cooperation, the system dynamics can
be completely dominated by the effective system-cavity interaction and the
dissipative effects from the system-environment coupling can be surprisingly
ignored. This work provides a generic method of dissipation suppression in a
variety of quantum mechanical platforms, including natural atoms and
superconducting circuits.


  Traditional magnetic sub-Kelvin cooling relies on the nearly free local
moments in hydrate paramagnetic salts, whose utility is hampered by the dilute
magnetic ions and low thermal conductivity. Here we propose to use instead
fractional excitations inherent to quantum spin liquids (QSLs) as an
alternative, which are sensitive to external fields and can induce a very
distinctive magnetocaloric effect. With state-of-the-art tensor-network
approach, we compute low-temperature properties of Kitaev honeycomb model. For
the ferromagnetic case, strong demagnetization cooling effect is observed due
to the nearly free $Z_2$ vortices via spin fractionalization, described by a
paramagnetic equation of state with a renormalized Curie constant. For the
antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL
phase with very large spin entropy, possibly due to the emergence of spinon
Fermi surface. Potential realization of topological excitation cooling in
Kitaev materials is also discussed, which may offer a promising pathway to
circumvent existing limitations in the paramagnetic hydrates.


  The exact renormalization group is applied to the world sheet theory
describing bosonic open string backgrounds to obtain the equations of motion
for the fields of the open string. Using loop variable techniques the equations
can be constructed to be gauge invariant. Furthermore they are valid off the
(free) mass shell. This requires keeping a finite cutoff. Thus we have the
interesting situation of a scale invariant world sheet theory with a finite
world sheet cutoff. This is possible because there are an infinite number of
operators whose coefficients can be tuned. This is in the same sense that
"perfect actions" or "improved actions" have been proposed in lattice gauge
theory to reproduce the continuum results even while keeping a finite lattice
spacing.


  The amplitude of the roughness-induced energetic disorder at the
metal/organic interface is calculated. It was found that for moderately rough
electrodes, the correction to the electrostatic image potential at the charge
location is small. For this reason, roughness-induced energetic disorder cannot
noticeably affect charge carrier injection, contrary to the recent reports.


  We describe a new formula capable of quantitatively characterizing the Hubble
sequence of spiral galaxies including grand design and barred spirals. Special
shapes such as ring galaxies with inward and outward arms are also described by
the analytic continuation of the same formula. The formula is r(phi) = A/log[B
tan(phi/2N)]. This function intrinsically generates a bar in a continuous,
fixed relationship relative to an arm of arbitrary winding sweep. A is simply a
scale parameter while B, together with N, determine the spiral pitch. Roughly,
greater N results in tighter winding. Greater B results in greater arm sweep
and smaller bar/bulge while smaller B fits larger bar/bulge with a sharper
bar/arm junction. Thus B controls the "bar/bulge-to-arm" size, while N controls
the tightness much like the Hubble scheme. The formula can be recast in a form
dependent only on a unique point of turnover angle of pitch - essentially a
1-parameter fit, aside from a scale factor. The recast formula is remarkable
and unique in that a single parameter can define a spiral shape with either
constant or variable pitch capable of tightly fitting Hubble types from grand
design spirals to late type large-barred galaxies. We compare the correlation
of our pitch parameter to Hubble type with that of the traditional logarithmic
spiral for 21 well-shaped galaxies. The pitch parameter of our formula produces
a very tight correlation with ideal Hubble type suggesting it is a good
discriminator compared to logarithmic pitch, which shows poor correlation here
similar to previous works. Representative examples of fitted galaxies are
shown.


  To any moment graph G we assign a subcategory V of the category of sheaves on
G together with an exact structure. We show that in the case that the graph is
associated to a non-critical block of the equivariant category O over a
symmetrizable Kac-Moody algebra, V is equivalent (as an exact category) to the
subcategory of modules that admit a Verma flag. The projective modules
correspond under this equivalence to the intersection cohomology sheaves on the
graph.


  We use the Kobayashi-Hitchin correspondence for parabolic bundles to reprove
the results of Troyanov and Luo-Tian regarding existence and uniqueness of
conformal spherical metrics on the Riemann sphere with prescribed cone angles
in the interval $(0, 2\pi)$ at a given configuration of three or more points.


  Power distribution networks are approaching their voltage stability
boundaries due to the severe voltage violations and the inadequate reactive
power reserves caused by the increasing renewable generations and dynamic
loads. In the broad endeavor to resolve this concern, we focus on enhancing
voltage stability through stochastic distribution network reconfiguration
(SDNR), which optimizes the (radial) topology of a distribution network under
uncertain generations and loads. We propose a deep learning method to solve
this computationally challenging problem. Specifically, we build a
convolutional neural network model to predict the relevant voltage stability
index from the SDNR decisions. Then we integrate this prediction model into
successive branch reduction algorithms to reconfigure a radial network with
optimized performance in terms of power loss reduction and voltage stability
enhancement. Numerical results on two IEEE network models verify the
significance of enhancing voltage stability through SDNR and the computational
efficiency of the proposed method.


  In the past, two main approaches for the purpose of authentication, including
information-theoretic authentication codes and complexity-theoretic message
authentication codes (MACs), were almost independently developed. In this
paper, we propose a new cryptographic primitive, namely, artificial-noise-aided
MACs (ANA-MACs), which can be considered as both computationally secure and
information-theoretically secure. For ANA-MACs, we introduce artificial noise
to interfere with the complexity-theoretic MACs and quantization is further
employed to facilitate packet-based transmission. With a channel coding
formulation of key recovery in the MACs, the generation of standard
authentication tags can be seen as an encoding process for the ensemble of
codes, where the shared key between Alice and Bob is considered as the input
and the message is used to specify a code from the ensemble of codes. Then, we
show that the introduction of artificial noise in ANA-MACs can be well employed
to resist the key recovery attack even if the opponent has an unlimited
computing power. Finally, a pragmatic approach for the analysis of ANA-MACs is
provided, and we show how to balance the three performance metrics, including
the completeness error, the false acceptance probability, and the conditional
equivocation about the key. The analysis can be well applied to a class of
ANA-MACs, where MACs with Rijndael cipher are employed.


  A deep 75 ks {\it Chandra} ACIS--I data of NGC 2024 was analyzed, aiming at a
search for diffuse X-ray emission in this one of the most nearby (415 pc)
massive star-forming regions. After removing point sources, an extended
emission was detected in the central circular region with a radius of 0.5 pc.
It is spatially associated with the young massive stellar cluster. Its X-ray
spectrum exhibits a very hard continuum ($kT>8$ keV) and a sign of He-like Fe
K$_\alpha$ line with the 0.5--7 keV absorption corrected luminosity of
2$\times10^{31}$ \ergs. Undetected faint point sources, estimated from the
luminosity function of the detected sources, contribute less than 10% to this
emission. Hence the emission is truly diffuse in nature. Because of the
proximity of NGC 2024 and the long exposure, this discovery is one of the most
strong supports for the existence of the diffuse X-ray emission in massive
star-forming regions.


  We give a decomposition of the equivariant Kasparov category for discrete
quantum group with torsions. As an outcome, we show that the crossed product by
a discrete quantum group in a certain class preserves the UCT. We then show
that quasidiagonality of a reduced C*-algebra of a countable discrete quantum
group $\Gamma$ implies that $\Gamma$ is amenable, and deduce from the work of
Tikuisis, White and Winter, and the results in the first part of the paper, the
converse (i.e. the quantum Rosenberg Conjecture) for a large class of countable
discrete unimodular quantum groups. We also note that the unimodularity is a
necessary condition.


  We propose the full system of Baxter Q-functions (QQ-system) for the
integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this
QQ-system to derive new Weyl-type formulas expressing transfer matrices in all
symmetric and antisymmetric (fundamental) representations through $r+1$ basic
Q-functions. Our functional relations are consistent with the Q-operators
proposed recently by one of the authors and verified explicitly on the level of
operators at small finite length.


  In this paper, we prove uniqueness of solutions of mean field equations with
general boundary conditions for the critical and subcritical total mass regime,
extending the earlier results for null Dirichlet boundary condition. The proof
is based on new Bol's inequalities for weak radial solutions obtained from
rearrangement of the solutions.


  It is currently widely accepted that open star clusters and stellar
associations result from the evolution of embedded star clusters. Parameters
such star formation efficiency, time-scale of gas removal and velocity
dispersion can be determinants of their future as bound or unbound systems.
Finding objects at an intermediate evolution state can provide constraints to
model the embedded cluster evolution. In the HII region IC1396, Trumpler 37 is
an extended young cluster that presents characteristics of an association. We
employed the Two Micron All Sky Survey (2MASS) photometry to analysing its
structure and stellar content, and determining its astrophysical parameters. We
also analysed 11 bright-rimmed clouds in IC1396 in order to search for young
infrared star clusters, and the background open star cluster Teutsch 74, to
verify whether it has any contribution to the observed stellar density profile
of Trumpler 37. The derived parameters and comparison with template objects
from other studies lead us to conclude that Trumpler 37, rather than as a star
cluster, will probably emerge from its molecular cloud as an OB association.


  We consider a non-Hermitian yet $\mathcal{PT}$-symmetric Fermi liquid
($\mathcal{PT}$-FL) in external electric fields. Due to
$\mathcal{PT}$-symmetry, the system exhibits real spectrum, Fermi surface and
electric conductivity are well-defined through propagators. We find that, in
contrast to the conventional Fermi liquids (FL), the $\mathcal{PT}$-FL can
exhibit a zero resistance state in the longitudinal ($xx$) channel. Moreover,
the temperature dependence of the resistivity anomaly violates the conventional
FL scaling (it is not limited by $T^2$). These findings open route to further
exploration of transport anomalies beyond the conventional paradigm.


  Filling-control metal-insulator transition on the two-dimensional Hubbard
model is investigated by using the correlator projection method, which takes
into account momentum dependence of the free energy beyond the dynamical
mean-field theory. The phase diagram of metals and Mott insulators is analyzed.
Lifshitz transitions occur simultaneously with metal-insulator transitions at
large Coulomb repulsion. On the other hand, they are separated each other for
lower Coulomb repulsion, where the phase sandwiched by the Lifshitz and
metal-insulator transitions appears to show violation of the Luttinger sum
rule. Through the metal-insulator transition, quasiparticles retain nonzero
renormalization factor and finite quasi-particle weight in the both sides of
the transition. This supports that the metal-insulator transition is caused not
by the vanishing renormalization factor but by the relative shift of the Fermi
level into the Mott gap away from the quasiparticle band, in sharp contrast
with the original dynamical mean-field theory. Charge compressibility diverges
at the critical end point of the first-order Lifshitz transition at finite
temperatures. The origin of the divergence is ascribed to singular momentum
dependence of the quasiparticle dispersion.


  Among the approximation methods for the verification of counter systems, one
of them consists in model-checking their flat unfoldings. Unfortunately, the
complexity characterization of model-checking problems for such operational
models is not always well studied except for reachability queries or for Past
LTL. In this paper, we characterize the complexity of model-checking problems
on flat counter systems for the specification languages including first-order
logic, linear mu-calculus, infinite automata, and related formalisms. Our
results span different complexity classes (mainly from PTime to PSpace) and
they apply to languages in which arithmetical constraints on counter values are
systematically allowed. As far as the proof techniques are concerned, we
provide a uniform approach that focuses on the main issues.


  Let \Delta\subset \mathbb{R}^n be an n-dimensional Delzant polytope. It is
well-known that there exist the n-dimensional compact toric manifold X_\Delta
and the very ample (\mathbb{C}^\times)^n-equivariant line bundle L_\Delta on
X_\Delta associated with \Delta. In the present paper, we show that if
(X_\Delta,L_\Delta^i) is Chow semistable then the sum of integer points in
i\Delta is the constant multiple of the barycenter of \Delta. Using this result
we get a necessary condition for the polarized toric manifold
(X_\Delta,L_\Delta) being asymptotically Chow semistable. Moreover we can
generalize the result of Futaki, Sano and the author to the case when X_\Delta
is not necessarily Fano.


  With the constant growth of the World Wide Web and the number of documents in
different languages accordingly, the need for reliable language detection tools
has increased as well. Platforms such as Twitter with predominantly short texts
are becoming important information resources, which additionally imposes the
need for short texts language detection algorithms. In this paper, we show how
incorporating personalized user-specific information into the language
detection algorithm leads to an important improvement of detection results. To
choose the best algorithm for language detection for short text messages, we
investigate several machine learning approaches. These approaches include the
use of the well-known classifiers such as SVM and logistic regression, a
dictionary based approach, and a probabilistic model based on modified
Kneser-Ney smoothing. Furthermore, the extension of the probabilistic model to
include additional user-specific information such as evidence accumulation per
user and user interface language is explored, with the goal of improving the
classification performance. The proposed approaches are evaluated on randomly
collected Twitter data containing Latin as well as non-Latin alphabet languages
and the quality of the obtained results is compared, followed by the selection
of the best performing algorithm. This algorithm is then evaluated against two
already existing general language detection tools: Chromium Compact Language
Detector 2 (CLD2) and langid, where our method significantly outperforms the
results achieved by both of the mentioned methods. Additionally, a preview of
benefits and possible applications of having a reliable language detection
algorithm is given.


  With the general aim to classify BPS solutions in N=2, D=5 supergravities
interacting with an arbitrary number of vector, tensor and hypermultiplets,
here we begin considering the most general electrostatic, spherical-symmetric
BPS solutions in the presence of hypermultiplet couplings. We discuss the
properties of the BPS equations and the restrictions imposed by their
integrability conditions. We exhibit explicit solutions for the case of static
BPS black-holes coupled to one (the so called universal) hypermultiplet.


  Using the multiple scales method, the interaction between two bright and one
dark solitons is studied. Provided that a long wave-short wave resonance
condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO)
completely integrable system is obtained. By using a Madelung fluid
description, the one-soliton solutions of the corresponding ZYO system are
determined. Furthermore, a discussion on the interaction between one bright and
two dark solitons is presented. In particular, this problem is reduced to solve
a one-component ZYO system in the resonance conditions.


  October 2004 marks the 400th anniversary of the sighting of SN 1604, now
marked by the presence of an expanding nebulosity known as Kepler's supernova
remnant. Of the small number of remnants of historical supernovae, Kepler's
remnant remains the most enigmatic. The supernova type, and hence the type of
star that exploded, is still a matter of debate, and even the distance to the
remnant is uncertain by more than a factor of two. As new and improved
multiwavength observations become available, and as the time baseline of
observations gets longer, Kepler's supernova remnant is slowly revealing its
secrets. I review recent and current observations of Kepler's supernova remnant
and what they indicate about this intriguing object.


  We found cosmological solution of the 6D standing wave braneworld model
generated by gravity coupled to a massless scalar phantom-like field. By
obtaining a full exact solution of the model we found a novel dynamical
mechanism in which the anisotropic nature of the primordial metric gives rise
to expansion of three spatial brane dimensions and affectively reduction of
other spatial directions. This dynamical mechanism can be relevant for
dimensional reduction in string and other higher dimensional theories in the
attempt of getting a 4D isotropic expanding space-time.


  Aspect Sentiment Triplet Extraction (ASTE) is a burgeoning subtask of
fine-grained sentiment analysis, aiming to extract structured sentiment
triplets from unstructured textual data. Existing approaches to ASTE often
complicate the task with additional structures or external data. In this
research, we propose a novel tagging scheme and employ a contrastive learning
approach to mitigate these challenges. The proposed approach demonstrates
comparable or superior performance in comparison to state-of-the-art
techniques, while featuring a more compact design and reduced computational
overhead. Notably, even in the era of Large Language Models (LLMs), our method
exhibits superior efficacy compared to GPT 3.5 and GPT 4 in a few-shot learning
scenarios. This study also provides valuable insights for the advancement of
ASTE techniques within the paradigm of large language models.


  Despite the ever-strong demand for mental health care globally, access to
traditional mental health services remains severely limited expensive, and
stifled by stigma and systemic barriers. Thus, over the last few years, young
people are increasingly turning to content on video-sharing platforms (VSPs)
like TikTok and YouTube to help them navigate their mental health journey.
However, navigating towards trustworthy information relating to mental health
on these platforms is challenging, given the uncontrollable and unregulated
growth of dedicated mental health content and content creators catering to a
wide array of mental health conditions on these platforms. In this paper, we
attempt to define what constitutes as "mental health misinformation" through
examples. In addition, we also suggest some open questions to answer and
challenges to tackle regarding this important and timely research topic


  We translate notions and results of decomposition and dimension theories for
module categories, into the lattice environment. In particular we translate
dimension theory in module categories to complete modular upper-continuous
lattices.


  Planets smaller than Neptune and larger than Earth make up the majority of
the discovered exoplanets. Those with H$_2$-rich atmospheres are prime targets
for atmospheric characterization. The transition between the two main classes,
super-Earths and sub-Neptunes, is not clearly understood as the rocky surface
is likely not accessible to observations. Tracking several trace gases
(specifically the loss of ammonia (NH$_3$) and hydrogen cyanide (HCN)) has been
proposed as a proxy for the presence of a shallow surface. In this work, we
revisit the proposed mechanism of nitrogen conversion in detail and find its
timescale on the order of a million years. NH$_3$ exhibits dual paths
converting to N$_2$ or HCN, depending on the UV radiation of the star and the
stage of the system. In addition, methanol (CH$_3$OH) is identified as a robust
and complementary proxy for a shallow surface. We follow the fiducial example
of K2-18b with a 2D photochemical model (VULCAN) on an equatorial plane. We
find a fairly uniform composition distribution below 0.1 mbar controlled by the
dayside, as a result of slow chemical evolution. NH$_3$ and CH$_3$OH are
concluded to be the most unambiguous proxies to infer surfaces on sub-Neptunes
in the era of the James Webb Space Telescope (JWST).


  Recent literature has underscored the importance of dataset documentation
work for machine learning, and part of this work involves addressing
"documentation debt" for datasets that have been used widely but documented
sparsely. This paper aims to help address documentation debt for BookCorpus, a
popular text dataset for training large language models. Notably, researchers
have used BookCorpus to train OpenAI's GPT-N models and Google's BERT models,
even though little to no documentation exists about the dataset's motivation,
composition, collection process, etc. We offer a preliminary datasheet that
provides key context and information about BookCorpus, highlighting several
notable deficiencies. In particular, we find evidence that (1) BookCorpus
likely violates copyright restrictions for many books, (2) BookCorpus contains
thousands of duplicated books, and (3) BookCorpus exhibits significant skews in
genre representation. We also find hints of other potential deficiencies that
call for future research, including problematic content, potential skews in
religious representation, and lopsided author contributions. While more work
remains, this initial effort to provide a datasheet for BookCorpus adds to
growing literature that urges more careful and systematic documentation for
machine learning datasets.


  Magnetospheric accretion has been thoroughly studied in young stellar systems
with full non-evolved accretion disks, but it is poorly documented for
transition disk objects with large inner cavities. We aim at characterizing the
star-disk interaction and the accretion process onto the central star of LkCa
15, a transition disk system with an inner dust cavity. We obtained
quasi-simultaneous photometric and spectropolarimetric observations of the
system over several rotational periods. We analyzed the system light curve, as
well as changes in spectral continuum and line profile to derive the properties
of the accretion flow from the edge of the inner disk to the central star. We
also derived magnetic field measurements at the stellar surface. We find that
the system exhibits magnetic, photometric, and spectroscopic variability with a
period of about 5.70 days. The light curve reveals a periodic dip, which
suggests the presence of an inner disk warp that is located at the corotation
radius at about 0.06 au from the star. Line profile variations and veiling
variability are consistent with a magnetospheric accretion model where the
funnel flows reach the star at high latitudes. This leads to the development of
an accretion shock close to the magnetic poles. All diagnostics point to a
highly inclined inner disk that interacts with the stellar magnetosphere. The
spectroscopic and photometric variability of LkCa 15 is remarkably similar to
that of AA Tau, the prototype of periodic dippers. We therefore suggest that
the origin of the variability is a rotating disk warp that is located at the
inner edge of a highly inclined disk close to the star. This contrasts with the
moderate inclination of the outer transition disk seen on the large scale and
thus provides evidence for a significant misalignment between the inner and
outer disks of this planet-forming transition disk system.


  The model of the Universe in this paper uses equations of the unperturbed
Keplerian motion. They have been updated, complementied and generalized when
the solution of these equations is the characteristic function of a random
value from the theory of probabilities. Argument of the differential equation
in this case is any more time, an interval of time between sections of a random
stationary prosess. In this paper this time interval is referred to as flexible
(elastic) time due to its many non-trivial properties. It is proved flexible
time does not depend on the space which makes invalid the four dimensional
space-time concept. The Universe becomes stationary and Eucledian. It is
proved: 1. the advavce of Mercury's perihelion versus the predictions in
accordance with the universal gravity law results inequality of the
coefficients in the correlation equations of Keplerian moution along axes x, y
and z; 2. the velocity of propagation of harmonic oscillation in the Uneverse
is not constant; 3. long-range interaction, i.e. instantaneous communication
between any two points of space in tne Universe is possible; 4. the Universe is
a closed-loop informatiom-energy system which revives the nature and acts as a
barrier to the second law of thermodynamics where stars are treated as machines
which accumulate energy by moving. Physics in the Universe is conceptually
different from that of the Earth and, respectively, needs methods of
investigation different from the ones which are used today. Numerous
astronomical supervision and the researches lead by known astrophysicist
N.A.Kozyrev personally or under his management confirm adequacy of the model in
the present paper.


  Lake ice, as part of the Essential Climate Variable (ECV) lakes, is an
important indicator to monitor climate change and global warming. The
spatio-temporal extent of lake ice cover, along with the timings of key
phenological events such as freeze-up and break-up, provide important cues
about the local and global climate. We present a lake ice monitoring system
based on the automatic analysis of Sentinel-1 Synthetic Aperture Radar (SAR)
data with a deep neural network. In previous studies that used optical
satellite imagery for lake ice monitoring, frequent cloud cover was a main
limiting factor, which we overcome thanks to the ability of microwave sensors
to penetrate clouds and observe the lakes regardless of the weather and
illumination conditions. We cast ice detection as a two class (frozen,
non-frozen) semantic segmentation problem and solve it using a state-of-the-art
deep convolutional network (CNN). We report results on two winters ( 2016 - 17
and 2017 - 18 ) and three alpine lakes in Switzerland. The proposed model
reaches mean Intersection-over-Union (mIoU) scores >90% on average, and >84%
even for the most difficult lake. Additionally, we perform cross-validation
tests and show that our algorithm generalises well across unseen lakes and
winters.


  Circular orbits of a particle sliding on a frictionless surface of revolution
about a vertical axis are unstable below a critical radius if the curvature of
the surface satisfies a specified condition. This behavior can be realized in a
mechanical model, which give a glimpse of the greater complexity of particle
orbits in curved rather than flat spacetime.


  We find that temperature dependent screening can quantitatively explain the
metallic behaviour of the resistivity on the metallic side of the so-called
metal-insulator transition in p-SiGe. Interference and interaction effects
exhibit the usual insulating behaviour which is expected to overpower the
metallic background at sufficiently low temperatures. We find empirically that
the concept of a Fermi-liquid describes our data in spite of the large r_s = 8.


  Using the hamiltonian framework, we analyze the Gribov problem for U(N) and
SU(N) gauge theories on a cylinder (= (1+1) dimensional spacetime with compact
space S^1). The space of gauge orbits is found to be an orbifold. We show by
explicit construction that a proper treatment of the Gribov ambiguity leads to
a highly non-trivial structure of all physical states in these quantum field
theory models. The especially interesting example of massless QCD is discussed
in more detail: There, some of the special static gauge transformations which
are responsible for the Gribov ambiguity also lead to a spectral flow, and this
implies a chiral condensate in all physical states. We also show that the
latter is closely related to the Schwinger term and the chiral anomaly.


  Suppose there are two unknown parameters, each parameter is the solution to
an estimating equation, and the estimating equation of one parameter depends on
the other parameter. The parameters can be jointly estimated by "stacking"
their estimating equations and solving for both parameters simultaneously.
Asymptotic confidence intervals are readily available for stacked estimating
equations. We introduce a bootstrap-based hypothesis test for stacked
estimating equations which does not rely on asymptotic approximations. Test
statistics are constructed by splitting the sample in two, estimating the first
parameter on a portion of the sample then plugging the result into the second
estimating equation to solve for the next parameter using the remaining sample.
To reduce simulation variability from a single split, we repeatedly split the
sample and take the sample mean of all the estimates. For parametric models, we
derive the limiting distribution of sample splitting estimator and show they
are equivalent to stacked estimating equations.


  We consider house allocation with existing tenants in which each agent has
dichotomous preferences. We present strategyproof, polynomial-time, and
(strongly) individually rational algorithms that satisfy the maximum number of
agents. For the endowment only model, one of the algorithms also returns a
core-stable allocation.


  Cosmological simulations consistently predict specific properties of dark
matter halos, but these have not yet led to a physical understanding that is
generally accepted. This is especially true for the central regions of these
structures. Recently two major themes have emerged. In one, the dark matter
halo is primarily a result of the sequential accretion of primordial structure
(ie `Nature'); while in the other, dynamical relaxation (ie `Nurture')
dominates at least in the central regions. Some relaxation is however required
in either mechanism. In this paper we accept the recently established
scale-free sub-structure of halos as an essential part of both mechanisms.
Consequently; a simple model for the central relaxation based on a self-similar
cascade of tidal interactions, is contrasted with a model based on the
accretion of adiabatically self-similar, primordial structure. We conclude that
a weak form of this relaxation is present in the simulations, but that is
normally described as the radial orbit instability.


  First inclusive measurements of isolated prompt photons in photoproduction at
the HERA ep collider have been made with the ZEUS detector, using an integrated
luminosity of 38.4 pb$^{-1}$. Cross sections are given as a function of the
pseudorapidity and the transverse energy ($\eta^\gamma$, \eTg) of the photon,
for $\eTg > $ 5 GeV in the $\gamma p$ centre-of-mass energy range 134-285 GeV.
Comparisons are made with predictions from Monte Carlo models having
leading-logarithm parton showers, and with next-to-leading-order QCD
calculations, using currently available parameterisations of the photon
structure. For forward $\eta^\gamma$ (proton direction) good agreement is
found, but in the rear direction all predictions fall below the data.


  The progress in determining the coupling constants of mesonic chiral
Lagrangians is reviewed, with emphasis on the work performed in three
successive European Networks (Eurodaphne I and II, Euridice). Reliable
estimates of those constants are essential for making full use of
next-to-next-to-leading-order calculations in chiral perturbation theory. The
precision in the values of the strong coupling constants of O(p^4) has been
increasing steadily over the years. The situation is less satisfactory in the
nonleptonic weak sector where further phenomenological input and more
theoretical work are needed. A lot of progress has recently been achieved for
electromagnetic coupling constants occurring in radiative corrections for
mesonic processes at low energies.


  Taming quantum dynamical processes is the key to novel applications of
quantum physics, e.g. in quantum information science. The control of
light-matter interactions at the single-atom and single-photon level can be
achieved in cavity quantum electrodynamics, in particular in the regime of
strong coupling where atom and cavity form a single entity. In the optical
domain, this requires permanent trapping and cooling of an atom in a
micro-cavity. We have now realized three-dimensional cavity cooling and
trapping for an orthogonal arrangement of cooling laser, trap laser and cavity
vacuum. This leads to average single-atom trapping times exceeding 15 seconds,
unprecedented for a strongly coupled atom under permanent observation.


  Abelian anomaly is examined by means of the recently proposed gauge invariant
regularization for SO(10) chiral gauge theory and its generalization for a
theory of arbitrary gauge group with anomaly-free chiral fermion contents. For
both cases it is shown that the anomaly with correct normalization can be
obtained in a gauge invariant form without any counterterms.


  In this paper we study the holographic dual, in several spacetime dimensions,
of the Higgs branch of gauge theories with fundamental matter. These theories
contain defects of various codimensionalities, where the matter fields are
located. In the holographic description the matter is added by considering
flavor brane probes in the supergravity backgrounds generated by color branes,
while the Higgs branch is obtained when the color and flavor branes recombine
with each other. We show that, generically, the holographic dual of the Higgs
phase is realized by means of the addition of extra flux on the flavor branes
and by choosing their appropriate embedding in the background geometry. This
suggests a dielectric interpretation in terms of the color branes, whose vacuum
solutions precisely match the F- and D-flatness conditions obtained on the
field theory side. We further compute the meson mass spectra in several cases
and show that when the defect added has codimension greater than zero it
becomes continuous and gapless.


  In this paper, we study phase structure of a system of hard-core bosons with
a nearest-neighbor (NN) repulsive interaction in a stacked triangular lattice.
Hamiltonian of the system contains two parameters one of which is the hopping
amplitude $t$ between NN sites and the other is the NN repulsion $V$. We
investigate the system by means of the Monte-Carlo simulations and clarify the
low and high-temperature phase diagrams. There exist solid states with density
of boson $\rho={1 \over 3}$ and ${2\over 3}$, superfluid, supersolid and
phase-separated state. The result is compared with the phase diagram of the
two-dimensional system in a triangular lattice at vanishing temperature.


  We report on the current status of CLIO (Cryogenic Laser Interferometer
Observatory), which is a prototype interferometer for LCGT (Large Scale
Cryogenic Gravitational-Wave Telescope). LCGT is a Japanese next-generation
interferometric gravitational wave detector featuring the use of cryogenic
mirrors and a quiet underground site. The main purpose of CLIO is to
demonstrate a reduction of the mirror thermal noise by cooling the sapphire
mirrors. CLIO is located in an underground site of the Kamioka mine, 1000 m
deep from the mountain top, to verify its advantages. After a few years of
commissioning work, we have achieved a thermal-noise-limited sensitivity at
room temperature. One of the main results of noise hunting was the elimination
of thermal noise caused by a conductive coil-holder coupled with a pendulum
through magnets.


  We present the most recent cross section measurements for WW and WZ
production in proton-antiproton collisions with sqrt(s) = 1.96 TeV at the
Fermilab Tevatron in final states with two or three leptons, respectively,
along with limits on WWZ triple gauge couplings. We also present the combined
search for WW and WZ production in the lepton, neutrino, and dijet final state.
Finally, we present ZZ cross section measurements in both the fully leptonic
and the two lepton, two neutrino final states along with limits on anomalous
couplings ZZZ and ZZgamma. All results presented are based on data collected
with the Run II DO and CDF II detectors.


  Understanding and controlling the interfacial magnetic properties of
ferromagnetic thin films are crucial for spintronic device applications.
However, using conventional magnetometry, it is difficult to detect them
separately from the bulk properties. Here, by utilizing tunneling anisotropic
magnetoresistance in a single-barrier heterostructure composed of
La0.6Sr0.4MnO3 (LSMO)/ LaAlO3 (LAO)/ Nb-doped SrTiO3 (001), we reveal the
presence of a peculiar strong two-fold magnetic anisotropy (MA) along the
[110]c direction at the LSMO/LAO interface, which is not observed in bulk LSMO.
This MA shows unknown behavior that the easy magnetization axis rotates by
90{\deg} at an energy of 0.2 eV below the Fermi level in LSMO. We attribute
this phenomenon to the transition between the eg and t2g bands at the LSMO
interface. Our finding and approach to understanding the energy dependence of
the MA demonstrate a new possibility of efficient control of the interfacial
magnetic properties by controlling the band structures of oxide
heterostructures.


  We revisit the hadronic production of the four-lepton final state, e^- e^+
\mu^- \mu^+, through the fusion of initial state gluons. This process is
mediated by loops of quarks and we provide first full analytic results for
helicity amplitudes that account for both the effects of the quark mass in the
loop and off-shell vector bosons. The analytic results have been implemented in
the Monte Carlo program MCFM and are both fast, and numerically stable in the
region of low Z transverse momentum. We use our results to study the
interference between Higgs-mediated and continuum production of four-lepton
final states, which is necessary in order to obtain accurate theoretical
predictions outside the Higgs resonance region. We have confirmed and extended
a recent analysis of Caola and Melnikov that proposes to use a measurement of
the off-shell region to constrain the total width of the Higgs boson. Using a
simple cut-and-count method, existing LHC data should bound the width at the
level of 25-45 times the Standard Model expectation. We investigate the power
of using a matrix element method to construct a kinematic discriminant to
sharpen the constraint. In our analysis the bound on the Higgs width is
improved by a factor of about 1.6 using a simple cut on the MEM discriminant,
compared to an invariant mass cut m_{4l} > 300 GeV.


  For the first time, a wide range of collective magnetic g-factors g$_{\rm
R}$, obtained from a novel analysis of experimental data for
multi-quasiparticle configurations in high-K isomers, is shown to exhibit a
striking systematic variation with the relative number of proton and neutron
quasiparticles, N$_{\rm p}$ - N$_{\rm n}$. Using the principle of additivity,
the quasi-particle contribution to magnetism in high-K isomers of Lu - Re, Z =
71 - 75, has been estimated. Based on these estimates, band-structure branching
ratio data are used to explore the behaviour of the collective contribution as
the number and proton/neutron nature (N$_{\rm p}$, N$_{\rm n}$), of the
quasi-particle excitations, change. Basic ideas of pairing, its quenching by
quasi-particle excitation and the consequent changes to moment of inertia and
collective magnetism are discussed. Existing model calculations do not
reproduce the observed g$_{\rm R}$ variation adequately. The paired superfluid
system of nucleons in these nuclei, and their excitations, present properties
of general physics interest. The new-found systematic behaviour of g$_{\rm R}$
in multi-quasi-particle excitations of this unique system, showing variation
from close to zero for multi-neutron states to above 0.5 for multi-proton
states, opens a fresh window on these effects and raises the important question
of just which nucleons contribute to the `collective' properties of these
nuclei.


  We consider the problem of detecting communities or modules in networks,
groups of vertices with a higher-than-average density of edges connecting them.
Previous work indicates that a robust approach to this problem is the
maximization of the benefit function known as "modularity" over possible
divisions of a network. Here we show that this maximization process can be
written in terms of the eigenspectrum of a matrix we call the modularity
matrix, which plays a role in community detection similar to that played by the
graph Laplacian in graph partitioning calculations. This result leads us to a
number of possible algorithms for detecting community structure, as well as
several other results, including a spectral measure of bipartite structure in
networks and a new centrality measure that identifies those vertices that
occupy central positions within the communities to which they belong. The
algorithms and measures proposed are illustrated with applications to a variety
of real-world complex networks.


  In this paper we answer two recent questions from Charlier et al. and Harju
about self-shuffling words. An infinite word $w$ is called self-shuffling, if
$w=\prod_{i=0}^\infty U_iV_i=\prod_{i=0}^\infty U_i=\prod_{i=0}^\infty V_i$ for
some finite words $U_i$, $V_i$. Harju recently asked whether square-free
self-shuffling words exist. We answer this question affirmatively. Besides
that, we build an infinite word such that no word in its shift orbit closure is
self-shuffling, answering positively a question from Charlier et al.


  The prediction of salient areas in images has been traditionally addressed
with hand-crafted features based on neuroscience principles. This paper,
however, addresses the problem with a completely data-driven approach by
training a convolutional neural network (convnet). The learning process is
formulated as a minimization of a loss function that measures the Euclidean
distance of the predicted saliency map with the provided ground truth. The
recent publication of large datasets of saliency prediction has provided enough
data to train end-to-end architectures that are both fast and accurate. Two
designs are proposed: a shallow convnet trained from scratch, and a another
deeper solution whose first three layers are adapted from another network
trained for classification. To the authors knowledge, these are the first
end-to-end CNNs trained and tested for the purpose of saliency prediction.


  We propose a novel equation of state (EoS) which explains the evolutionary
history of a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe. The
uniqueness of this EoS lies in the fact that it incorporates the Lambert $W$
function in a special fashion. It is explicitly demonstrated that with
observationally relevant values of the unknown parameters
$\vartheta_\mathrm{1}$ and $\vartheta_\mathrm{2}$, all the evolutionary phases
of the Universe can be reproduced. Moreover, it also shows that the initial
singularity is unavoidable and asserts that the late-time acceleration of the
Universe would continue forever.


  We use time-resolved (TR) measurements based on the polar magneto-optical
Kerr effect (MOKE) to study the magnetization dynamics excited by spin orbit
torques in Py (Permalloy)/Pt and Ta/CoFeB bilayers. The analysis reveals that
the field-like (FL) spin orbit torque (SOT) dominates the amplitude of the
first oscillation cycle of the magnetization precession and the damping-like
(DL) torque determines the final steady-state magnetization. In our bilayer
samples, we have extracted the effective fields, hFL and hDL, of the two SOTs
from the time-resolved magnetization oscillation spectrum. The extracted values
are in good agreement with those extracted from time-integrated DCMOKE
measurements, suggesting that the SOTs do not change at high frequencies. We
also find that the amplitude ratio of the first oscillation to steady state is
linearly proportional to the ratio hFL/hDL. The first oscillation amplitude is
inversely proportional to, whereas the steady state value is independent of,
the applied external field along the current direction.


  This paper focuses on integer linear programs where solutions are binary
matrices, and the corresponding symmetry group is the set of all column
permutations. Orbitopal fixing, as introduced by Kaibel et al., is a technique
designed to break symmetries in the special case of partitioning (resp.
packing) formulations involving matrices with exactly (resp. at most) one
1-entry in each row.The main result of this paper is to extend orbitopal fixing
to the full orbitope, defined as the convex hull of binary matrices with
lexicographically nonincreasing columns.We determine all the variables whose
values are fixed in the intersection of an hypercube face with the full
orbitope.Sub-symmetries arising in a given subset of matrices are also
considered, thus leading to define the full sub-orbitope in the case of the
sub-symmetric group.We propose a linear time orbitopal fixing algorithm
handling both symmetries and sub-symmetries.We introduce a dynamic variant of
this algorithm where the lexicographical order follows the branching decisions
occurring alongthe B&B search. Experimental results for the Unit Commitment
Problem are presented. A comparison with state-of-the-art techniques is
considered to show the effectiveness of the proposed variants of the algorithm.


  Two-sample tests evaluate whether two samples are realizations of the same
distribution (the null hypothesis) or two different distributions (the
alternative hypothesis). We consider a new setting for this problem where
sample features are easily measured whereas sample labels are unknown and
costly to obtain. Accordingly, we devise a three-stage framework in service of
performing an effective two-sample test with only a small number of sample
label queries: first, a classifier is trained with samples uniformly labeled to
model the posterior probabilities of the labels; second, a novel query scheme
dubbed \emph{bimodal query} is used to query labels of samples from both
classes, and last, the classical Friedman-Rafsky (FR) two-sample test is
performed on the queried samples. Theoretical analysis and extensive
experiments performed on several datasets demonstrate that the proposed test
controls the Type I error and has decreased Type II error relative to uniform
querying and certainty-based querying. Source code for our algorithms and
experimental results is available at
\url{https://github.com/wayne0908/Label-Efficient-Two-Sample}.


  We investigate the existence of ground states with fixed mass for the
nonlinear Schr\"odinger equation with a pure power nonlinearity on periodic
metric graphs. Within a variational framework, both the $L^2$-subcritical and
critical regimes are studied. In the former case, we establish the existence of
global minimizers of the NLS energy for every mass and every periodic graph. In
the critical regime, a complete topological characterization is derived,
providing conditions which allow or prevent ground states of a certain mass
from existing. Besides, a rigorous notion of periodic graph is introduced and
discussed.


  We investigate the connection between the intrinsic C IV absorption line
variability and the continuum flux changes of broad absorption line (BAL)
quasars using a sample of 78 sources in the Stripe 82 region. The absorption
trough variability parameters are measured using the archival multi-epoch
spectroscopic data from the Sloan Digital Sky Survey (SDSS), and the continuum
flux variability parameters are estimated from the photometric light curves
obtained by the SDSS and the Catalina Real-Time Survey (CRTS) surveys. We find
evidence for weak correlations (\rho ~ 0.3) between the intrinsic C IV
absorption line variability and the quasar continuum variability for the final
sample of 78 BAL quasars. The correlation strengths improve (\rho ~0.5) for the
"high-SNR" sample sources that have higher spectral signal-to-noise ratio.
Using two sub-sets of the high-SNR sample differing on the absorption trough
depth, we find that the shallow trough sub-set shows an even stronger
correlation (\rho ~ 0.6), whereas the deep trough sub-set does not show any
correlation between the absorption line variability and the continuum
variability. These results point to the important role of saturation effects in
the correlation between the absorption line variability and the continuum
variability of BAL quasars. Considering other effects that can also smear the
correlation, we conclude that the actual correlation between the absorption
line and continuum variability is even stronger.


  We present a rigorous Ewald summation formula to evaluate the electrostatic
interactions in two-dimensionally periodic planar interfaces of
three-dimensional systems. By rewriting the Fourier part of the summation
formula of the original Ewald2D expression with an explicit order N2 complexity
to a closed form Fourier integral, we find that both the previously developed
electrostatic layer correction term and the boundary correction term naturally
arise from the expression of a rigorous trapezoidal summation of the Fourier
integral part. We derive the exact corrections to the trapezoidal summation in
a form of contour integrals offering precise error bounds with given parameter
sets of mesh size and system length. Numerical calculations of Madelung
constants in model ionic crystals of slab geometry have been performed to
support our analytical results.