  Algebraic systems are constructed from which series of maximum distance
separable (mds) codes are derived. The methods use unit and idempotent schemes.


  When facing graph signal processing tasks, the workhorse assumption is that
the graph describing the support of the signals is known. However, in many
relevant applications the available graph suffers from observation errors and
perturbations. As a result, any method relying on the graph topology may yield
suboptimal results if those imperfections are ignored. Motivated by this, we
propose a novel approach for handling perturbations on the links of the graph
and apply it to the problem of robust graph filter (GF) identification from
input-output observations. Different from existing works, we formulate a
non-convex optimization problem that operates in the vertex domain and jointly
performs GF identification and graph denoising. As a result, on top of learning
the desired GF, an estimate of the graph is obtained as a byproduct. To handle
the resulting bi-convex problem, we design an algorithm that blends techniques
from alternating optimization and majorization minimization, showing its
convergence to a stationary point. The second part of the paper i) generalizes
the design to a robust setup where several GFs are jointly estimated, and ii)
introduces an alternative algorithmic implementation that reduces the
computational complexity. Finally, the detrimental influence of the
perturbations and the benefits resulting from the robust approach are
numerically analyzed over synthetic and real-world datasets, comparing them
with other state-of-the-art alternatives.


  Relation extraction is essential for extracting and understanding
biographical information in the context of digital humanities and related
subjects. There is a growing interest in the community to build datasets
capable of training machine learning models to extract relationships. However,
annotating such datasets can be expensive and time-consuming, in addition to
being limited to English. This paper applies guided distant supervision to
create a large biographical relationship extraction dataset for German. Our
dataset, composed of more than 80,000 instances for nine relationship types, is
the largest biographical German relationship extraction dataset. We also create
a manually annotated dataset with 2000 instances to evaluate the models and
release it together with the dataset compiled using guided distant supervision.
We train several state-of-the-art machine learning models on the automatically
created dataset and release them as well. Furthermore, we experiment with
multilingual and cross-lingual experiments that could benefit many low-resource
languages.


  One of the most important and challenging problems in coding theory is to
construct codes with best possible parameters and properties. The class of
quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing
on QC codes over the binary field, we have found 113 binary QC codes that are
new among the class of QC codes using an implementation of a fast cyclic
partitioning algorithm and the highly effective ASR algorithm. Moreover, these
codes have the following additional properties: a) they have the same
parameters as best known linear codes, and b) many of the have additional
desired properties such as being reversible, LCD, self-orthogonal or
dual-containing. Additionally, we present an algorithm for the generation of
new codes from QC codes using ConstructionX, and introduce 35 new record
breaking linear codes produced from this method.


  We study the Glashow resonance $\bar{\nu}_e + e^- \rightarrow W^-
\rightarrow$ hadrons at 6.3 PeV as diagnostic of the production processes of
ultra-high energy neutrinos. The focus lies on describing the physics of
neutrino production from pion decay as accurate as possible by including the
kinematics of weak decays and Monte Carlo simulations of pp and p$\gamma$
interactions. We discuss optically thick (to photohadronic interactions)
sources, sources of cosmic ray nuclei and muon damped sources. Even in the
proposed upgrade IceCube-Gen2, a discrimination of scenarios such as pp versus
p$\gamma$ is extremely challenging under realistic assumptions. Nonetheless,
the Glashow resonance can serve as a smoking gun signature of neutrino
production from photohadronic (A$\gamma$) interactions of heavier nuclei, as
the expected Glashow event rate exceeds that of pp interactions. We finally
quantify the exposures for which the non-observation of Glashow events exerts
pressure on certain scenarios.


  Over the past several years progress in designing better neural network
architectures for visual recognition has been substantial. To help sustain this
rate of progress, in this work we propose to reexamine the methodology for
comparing network architectures. In particular, we introduce a new comparison
paradigm of distribution estimates, in which network design spaces are compared
by applying statistical techniques to populations of sampled models, while
controlling for confounding factors like network complexity. Compared to
current methodologies of comparing point and curve estimates of model families,
distribution estimates paint a more complete picture of the entire design
landscape. As a case study, we examine design spaces used in neural
architecture search (NAS). We find significant statistical differences between
recent NAS design space variants that have been largely overlooked.
Furthermore, our analysis reveals that the design spaces for standard model
families like ResNeXt can be comparable to the more complex ones used in recent
NAS work. We hope these insights into distribution analysis will enable more
robust progress toward discovering better networks for visual recognition.


  In this paper we give a brief account of the main aspects of the theory of
associated and principal super bundles. As an application, we review the
Borel-Weil-Bott Theorem in the super setting, and some results on projective
embeddings of homogeneous spaces.


  Fourier analysis on a cut sky of the two-year COBE DMR 53 and 90 GHz sky maps
(in galactic coordinates) is used to determine the normalisation of an open
inflation model based on the cold dark matter scenario. The normalised model is
compared to measures of large-scale structure in the universe. Although the DMR
data alone does not provide sufficient discriminative power to prefer a
particular value of the mass density parameter, the open model appears to be
reasonably consistent with observations when Omega_0 ~ 0.3 - 0.4 and merits
further study.


  We investigate numerically the zero-temperature physics of the
one-dimensional Bose-Hubbard model in an incommensurate cosine potential,
recently realized in experiments with cold bosons in optical superlattices L.
Fallani et al., Phys. Rev. Lett. 98, 130404, (2007)]. An incommensurate cosine
potential has intermediate properties between a truly periodic and a fully
random potential, displaying a characteristic length scale (the quasi-period)
which is shown to set a finite lower bound to the excitation energy of the
system at special incommensurate fillings. This leads to the emergence of
gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass
(BG) phases for strong quasi-periodic potential, both for hardcore and softcore
bosons. Enriching the spatial features of the potential by the addition of a
second incommensurate component appears to remove the IBI regions, stabilizing
a continuous BG phase over an extended parameter range. Moreover we discuss the
validity of the local-density approximation in presence of a parabolic trap,
clarifying the notion of a local BG phase in a trapped system; we investigate
the behavior of first- and second-order coherence upon increasing the strength
of the quasi-periodic potential; and we discuss the ab-initio derivation of the
Bose-Hubbard Hamiltonian with quasi-periodic potential starting from the
microscopic Hamiltonian of bosons in an incommensurate superlattice.


  Boundary obstructed topological insulators are an unusual class of
higher-order topological insulators with topological characteristics determined
by the so-called Wannier bands. Boundary obstructed phases can harbor
hinge/corner modes, but these modes can often be destabilized by a phase
transition on the boundary instead of the bulk. While there has been much work
on the stability of topological insulators in the presence disorder, the
topology of a disordered Wannier band, and disorder-induced Wannier transitions
have not been extensively studied. In this work, we focus on the simplest
example of a Wannier topological insulator: a mirror-symmetric $\pi$-flux
ladder in 1D. We find that the Wannier topology is robust to disorder, and
derive a real-space renormalization group procedure to understand a new type of
strong disorder-induced transition between non-trivial and trivial Wannier
topological phases. We also establish a connection between the Wannier topology
of the ladder and the energy band topology of a related system with a physical
boundary cut, something which has generally been conjectured for clean models,
but has not been studied in the presence of disorder.


  We present a new type of brane inflation motivated by multi-kink solitonic
solutions of a scalar field in five dimensions. In the thin brane limit, we
analyze a non-static configuration in which the distance between two parallel
domain walls decreases. We show that the ensuing spacetime is inflationary,
both on the branes, and, for certain potentials, in the bulk. We argue that
this inflationary regime is transitory and can end via a brane merger into a
single kink solution - a flat, thick brane RS2 universe. This scenario is quite
general; we show that any potential which supports a single flat kink solution
is also likely to support an inflationary multi-kink configuration.


  We report interferometric imaging of CO(J=3-2) emission toward the z=2.846
submillimeter-selected galaxy SMM J04135+10277, using the Combined Array for
Research in Millimeter-wave Astronomy (CARMA). SMM J04135+10277 was previously
thought to be a gas-rich, submillimeter-selected quasar, with the highest
molecular gas mass among high-z quasars reported in the literature. Our maps at
~6x improved linear resolution relative to earlier observations spatially
resolve the emission on ~1.7" scales, corresponding to a (lensing-corrected)
source radius of ~5.2 kpc. They also reveal that the molecular gas reservoir,
and thus, likely the submillimeter emission, is not associated with the host
galaxy of the quasar, but with an optically faint gas-rich galaxy at 5.2", or
41.5 kpc projected distance from the active galactic nucleus (AGN). The
obscured gas-rich galaxy has a dynamical mass of M_dyn sin2(i)=5.6x10^11 M_sun,
corresponding to a gas mass fraction of ~21%. Assuming a typical M_BH/M* ratio
for z>2 quasars, the two galaxies in this system have an approximate mass ratio
of ~1.9. Our findings suggest that this quasar-starburst galaxy pair could
represent an early stage of a rare major, gas-rich/gas-poor ("wet-dry") merger
of two massive galaxies at z=2.8, rather than a single, gas-rich AGN host
galaxy. Such systems could play an important role in the early buildup of
present-day massive galaxies through a submillimeter-luminous starburst phase,
and may remain hidden in larger numbers among rest-frame far-infrared-selected
quasar samples at low and high redshift.


  A pre-Lie algebroid is an anchored bundle provided with an almost Lie bracket
such that the anchor is compatible with the Lie bracket of vector fields. We
firstly show how most geometrical structures intensively studied in the
framework of Lie algebroid can easily be extended in the pre-Lie algebroid
context. The principal purpose of this paper is to show that how all these
results only depend of the foliated structure and do not depend of the pre-Lie
algebroid structure that we can put on a foliated anchored bundle. As
application, we obtain a Finsler connection on a foliated anchored bundle which
induces the classical Finsler connection on each leaf and a similar result for
the Chern connection.


  The importance of nodes in a network constantly fluctuates based on changes
in the network structure as well as changes in external interest. We propose an
evolving teleportation adaptation of the PageRank method to capture how changes
in external interest influence the importance of a node. This framework
seamlessly generalizes PageRank because the importance of a node will converge
to the PageRank values if the external influence stops changing. We demonstrate
the effectiveness of the evolving teleportation on the Wikipedia graph and the
Twitter social network. The external interest is given by the number of hourly
visitors to each page and the number of monthly tweets for each user.


  In this paper, we continue our work in [15] to derive {\epsilon}-regularity
criteria at one scale without pressure for suitable weak solutions to the
Navier-Stokes equations. We establish a $\varepsilon$-regularity criterion
below of suitable weak solutions, for any $\delta>0$,
$$\iint_{Q(1)}|u|^{\frac{5}{2}+\delta}dxdt\leq \varepsilon.$$ As an
application, we extend the previous corresponding results concerning the
improvement of the classical Caffarelli--Kohn--Nirenberg theorem by a
logarithmic factor.


  There are few observed high-mass X-ray binaries (HMXBs) that harbor massive
black holes, and none are likely to result in a binary black hole (BBH) that
merges within a Hubble time; however, we know that massive merging BBHs exist
from gravitational-wave observations. We investigate the role that X-ray and
gravitational-wave observational selection effects play in determining the
properties of their respective detected binary populations. We find that, as a
result of selection effects, detectable HMXBs and detectable BBHs form at
different redshifts and metallicities, with detectable HMXBs forming at much
lower redshifts and higher metallicities than detectable BBHs. We also find
disparities in the mass distributions of these populations, with detectable
merging BBH progenitors pulling to higher component masses relative to the full
detectable HMXB population. Fewer than $3\%$ of detectable HMXBs host black
holes $> 35M_{\odot}$ in our simulated populations. Furthermore, we find the
probability that a detectable HMXB will merge as a BBH system within a Hubble
time is $\simeq 0.6\%$. Thus, it is unsurprising that no currently observed
HMXB is predicted to form a merging BBH with high probability.


  The processes responsible for the acceleration of solar energetic particles
(SEPs) are still not well understood, including whether SEP electrons and
protons are accelerated by common or separate processes. Using a numerical
particle transport model that includes both pitch-angle and perpendicular
spatial diffusion, we simulate, amongst other quantities, the onset delay for
MeV electrons and protons and compare the results to observations of SEPs from
widely-separated spacecraft. Such observations have previously been
interpreted, in a simple scenario assuming no perpendicular diffusion, as
evidence for different electron and proton sources. We show that, by assuming a
common particle source together with perpendicular diffusion, we are able to
simultaneously reproduce the onset delays for both electrons and protons. We
argue that this points towards a common accelerator for these particles.
Moreover, a relatively broad particle source is required in the model to
correctly describe the observations. This is suggestive of diffusive shock
acceleration occurring at large shock structures playing a significant role in
the acceleration of these SEPs.


  Despite the fact that the calculations of drag coefficient and pressure
distribution for airfoils can be completed by using Navier-Stoke's equation
with help of experimental parameters and advanced computer programming, a
simple theoretical approach to these classical problems is still lacked. In
this paper we show Schrodinger equation can in fact be a handy tool to describe
the mechanics of fluids using rigid sphere in air as an example and further
investigate the wave-like properties of fluids. We also provide computational
results for simulations of drag coefficient, as well as a comparison to
potential theory results of velocity distribution along the surface of a
sphere. The final discussion will be focusing on potential generalization of
the formulas to other geometrical objects (e.g. airfoils).


  We fabricated and characterized a new spin-functional MOSFET referred to as a
pseudo-spin-MOSFET (PS-MOSFET). The PS-MOSFET is a circuit using an ordinary
MOSFET and magnetic tunnel junction (MTJ) for reproducing functions of
spin-transistors. Device integration techniques for a bottom gate MOSFET using
a silicon-on-insulator (SOI) substrate and for an MTJ with a full-Heusler alloy
electrode and MgO tunnel barrier were developed. The fabricated PS-MOSFET
exhibited high and low transconductance controlled by the magnetization
configurations of the MTJ at room temperature. This is the first observation of
spin-transistor operations for spin-functional MOSFETs.


  Recently continuous rational maps between real algebraic varieties have
attracted the attention of several researchers. In this paper we continue the
investigation of approximation properties of continuous rational maps with
values in spheres. We propose a conjecture concerning such maps and show that
it follows from certain classical conjectures involving transformation of
compact smooth submanifolds of nonsingular real algebraic varieties onto
subvarieties. Furthermore, we prove our conjecture in a special case and obtain
several related results.


  We study the multi-dimensional Burgers equation $u_t + u u_{x_1} + \dots +
u^d u_{x_d} = 0$. We prove that the $L^\infty$ norm of entropy solutions of
this equation decays polynomially as $t \to \infty$ in terms of the $L^1$ norm
of the initial data only.


  The notion of symmetry is defined in the context of Linear and Integer
Programming. Symmetric integer programs are studied from a group theoretical
viewpoint. We investigate the structure of integer solutions of integer
programs and show that any integer program on n variables having an alternating
group A_n as a group of symmetries can be solved in linear time in the number
of variables.


  We study the so-called Gravitational Wave luminosity distance-redshift
relation $d_L^{\,GW}(z)$ during cosmological eras driven by non-perfect fluids.
In particular, we show that the presence of a shear viscosity in the energy
momentum tensor turns out to be the most relevant effect. Within this scenario,
a constant shear viscosity imprints the gravitational wave propagation through
a friction term $\delta(z)$ with a uniquely given redshift dependence. This
peculiar evolution predicts a specific shape for the ratio
$d_{L}^{GW}/d_{L}^{EM}$ which tends to a constant value when the sources are at
$z\gtrsim 1$, whereas scales linearly with the shear viscosity at lower
redshifts, regardless of the value of $\Omega_{m0}$. According to our final
discussion, the predicted redshift dependence $\delta(z)$ provided by a shear
viscosity could be tested by upcoming surveys of multi-messenger sources
against analogous scenarios provided by some widely studied theories of
modified gravity.


  Network data analysis is the fundamental basis for the development of methods
to increase service quality in mobile networks. This requires accurate data of
the current load in the network. The control channel analysis is a way to
monitor the resource allocations and the throughput of all active subscribers
in a public mobile radio cell. Previous open-source approaches require either
ideal radio conditions or long-term observations in order to obtain reliable
data. Otherwise, the revealed information is polluted by spurious assignments
with random content. In this paper, we present a new open-source instrument for
Fast Analysis of LTE Control channels (FALCON), which combines a novel
shortcut-decoding approach with the most reliable techniques known to us to
reduce the aforementioned requirements significantly. Long-term field
measurements reveal that FALCON reduces errors in average by three orders of
magnitude compared to currently the best approach. FALCON allows observations
at locations with interference and enables mobile applications with single
short-term tracking of the local load situation. It is compatible with numerous
software defined radios and can be used on standard computers for a reliable
real-time analysis.


  The prediction of the drop size distribution (DSD) resulting from liquid
atomization is key to the optimization of multi-phase flows, from gas-turbine
propulsion, through agriculture, to healthcare. Obtaining high-fidelity data of
liquid atomization, either experimentally or numerically, is expensive, which
makes the exploration of the design space difficult. First, to tackle these
challenges, we propose a framework to predict the DSD of a liquid spray based
on data as a function of the spray angle, the Reynolds number, and the Weber
number. Second, to guide the design of liquid atomizers, the model accurately
predicts the volume of fluid contained in drops of specific sizes whilst
providing uncertainty estimation. To do so, we propose a Gaussian process
regression (GPR) model, which infers the DSD and its uncertainty form the
knowledge of its integrals, and of its first moment, i.e., the mean drop
diameter. Third, we deploy multiple GPR models to estimate these quantities at
arbitrary points of the design space from data obtained from a large number of
numerical simulations of a flat fan spray. The kernel used for reconstructing
the DSD incorporates prior physical knowledge, which enables the prediction of
sharply peaked and heavy-tailed distributions. Fourth, we compare our method
with a benchmark approach, which estimates the DSD by interpolating the
frequency polygon of the binned drops with a GPR. We show that our integral
approach is significantly more accurate, especially in the tail of the
distribution (i.e., large, rare drops), and it reduces the bias of the density
estimator by up to ten times. Finally, we discuss physical aspects of the
model's predictions and interpret them against experimental results from the
literature. This work opens opportunities for modelling drop size distribution
in multiphase flows from data.


  We consider the problem of duplicate detection in noisy and incomplete data:
given a large data set in which each record has multiple entries (attributes),
detect which distinct records refer to the same real world entity. This task is
complicated by noise (such as misspellings) and missing data, which can lead to
records being different, despite referring to the same entity. Our method
consists of three main steps: creating a similarity score between records,
grouping records together into "unique entities", and refining the groups. We
compare various methods for creating similarity scores between noisy records,
considering different combinations of string matching, term frequency-inverse
document frequency methods, and n-gram techniques. In particular, we introduce
a vectorized soft term frequency-inverse document frequency method, with an
optional refinement step. We also discuss two methods to deal with missing data
in computing similarity scores.
  We test our method on the Los Angeles Police Department Field Interview Card
data set, the Cora Citation Matching data set, and two sets of restaurant
review data. The results show that the methods that use words as the basic
units are preferable to those that use 3-grams. Moreover, in some (but
certainly not all) parameter ranges soft term frequency-inverse document
frequency methods can outperform the standard term frequency-inverse document
frequency method. The results also confirm that our method for automatically
determining the number of groups typically works well in many cases and allows
for accurate results in the absence of a priori knowledge of the number of
unique entities in the data set.


  In this paper, we introduce a learning-based vision dynamics approach to
nonlinear model predictive control for autonomous vehicles, coined LVD-NMPC.
LVD-NMPC uses an a-priori process model and a learned vision dynamics model
used to calculate the dynamics of the driving scene, the controlled system's
desired state trajectory and the weighting gains of the quadratic cost function
optimized by a constrained predictive controller. The vision system is defined
as a deep neural network designed to estimate the dynamics of the images scene.
The input is based on historic sequences of sensory observations and vehicle
states, integrated by an Augmented Memory component. Deep Q-Learning is used to
train the deep network, which once trained can be used to also calculate the
desired trajectory of the vehicle. We evaluate LVD-NMPC against a baseline
Dynamic Window Approach (DWA) path planning executed using standard NMPC, as
well as against the PilotNet neural network. Performance is measured in our
simulation environment GridSim, on a real-world 1:8 scaled model car, as well
as on a real size autonomous test vehicle and the nuScenes computer vision
dataset.


  The firewall paradox for black holes is often viewed as indicating a conflict
between unitarity and the equivalence principle. We elucidate how the paradox
manifests as a limitation of semiclassical theory, rather than presents a
conflict between fundamental principles. Two principal features of the
fundamental and semiclassical theories address two versions of the paradox: the
entanglement and typicality arguments. First, the physical Hilbert space
describing excitations on a fixed black hole background in the semiclassical
theory is exponentially smaller than the number of physical states in the
fundamental theory of quantum gravity. Second, in addition to the Hilbert space
for physical excitations, the semiclassical theory possesses an unphysically
large Fock space built by creation and annihilation operators on the fixed
black hole background. Understanding these features not only eliminates the
necessity of firewalls but also leads to a new picture of Hawking emission
contrasting pair creation at the horizon.


  This paper investigates how accurately the prediction of being an introvert
vs. extrovert can be made with less than ten predictors. The study is based on
a previous data collection of 7161 respondents of a survey on 91 personality
and 3 demographic items. The results show that it is possible to effectively
reduce the size of this measurement instrument from 94 to 10 features with a
performance loss of only 1%, achieving an accuracy of 73.81% on unseen data.
Class imbalance correction methods like SMOTE or ADASYN showed considerable
improvement on the validation set but only minor performance improvement on the
testing set.


  We obtain a conceptually new differential geometric proof of P.F. Klembeck's
result that the holomorphic sectional curvature of a strictly pseudoconvex
domain approaches (in the boundary limit) the constant sectional curvature of
the Bergman metric of the unit ball.


  By exploiting the boundary state formalism we obtain the string correlator
between two internal points on the one loop open string world-sheet in the
presence of a constant background $B$-field. From this derivation it is clear
that there is an ambiguity when one tries to restrict the Green function to the
boundary of the surface. We fix this ambiguity by showing that there is a {\em
unique} form for the correlator between two points on the boundary which
reproduces the one loop field theory results of different noncommutative field
theories. In particular, we present the derivation of one loop diagrams for
$\phi^3_6$ and $\phi^4_4$ scalar interactions and for Yang--Mills theory. From
the 2-point function we are able to derive the one loop $\beta$-function for
noncommutative gauge theory.


  In this paper, we study one kind of stochastic recursive optimal control
problem with the obstacle constraints for the cost function where the cost
function is described by the solution of one reflected backward stochastic
differential equations. We will give the dynamic programming principle for this
kind of optimal control problem and show that the value function is the unique
viscosity solution of the obstacle problem for the corresponding
Hamilton-Jacobi-Bellman equations.


  We investigate in detail the structure of the simplest non-trivial F(\cal
R)-supergravity model, whose F-function is given by a generic quadratic
polynomial in terms of the scalar supercurvature (\cal R). This toy-model
admits a fully explicit derivation of the corresponding f(R)-gravity functions.
We apply the stability conditions for selecting the physical f(R)-gravity
functions, and discuss the phenomenological prospects of F(\cal R)-supergravity
in its application to cosmology.


  As one of the most striking features of quantum mechanics, quantum
correlations are at the heart of quantum information science. Detection of
correlations usually requires access to all the correlated subsystems. However,
in many realistic scenarios this is not feasible since only some of the
subsystems can be controlled and measured. Such cases can be treated as open
quantum systems interacting with an inaccessible environment. Initial
system-environment correlations play a fundamental role for the dynamics of
open quantum systems. Following a recent proposal, we exploit the impact of the
correlations on the open-system dynamics to detect system-environment quantum
correlations without accessing the environment. We use two degrees of freedom
of a trapped ion to model an open system and its environment. The present
method does not require any assumptions about the environment, the interaction
or the initial state and therefore provides a versatile tool for the study of
quantum systems.


  The lack of interpretability has hindered the large-scale adoption of AI
technologies. However, the fundamental idea of interpretability, as well as how
to put it into practice, remains unclear. We provide notions of
interpretability based on approximation theory in this study. We first
implement this approximation interpretation on a specific model (fully
connected neural network) and then propose to use MLP as a universal
interpreter to explain arbitrary black-box models. Extensive experiments
demonstrate the effectiveness of our approach.


  We study the modular symmetry anomaly in magnetized orbifold models. The
non-perturbative effects such as D-brane instanton effects can break tree-level
symmetry. We study which part of the modular symmetry is broken explicitly by
Majorana mass terms with three generations of neutrinos. The modular weight of
neutrino mass terms does not match with other coupling terms in tree-level
Lagrangian. In addition, the $Z_N$ symmetry of the modular flavor symmetry is
broken and a certain normal subgroup of the modular flavor symmetry remains in
neutrino mass terms.


  We study an operator-valued generalization of the Haagerup inequality for
Gromov hyperbolic groups. In 1978, U. Haagerup showed that if $f$ is a function
on the free group $\mathbb{F}_r$ which is supported on the $k$-sphere
$S_k=\{x\in \mathbb{F}_r:\ell(x)=k\}$, then the operator norm of its left
regular representation is bounded by $(k+1)\|f\|_2$. An operator-valued
generalization of it was started by U. Haagerup and G. Pisier. One of the most
complete form was given by A. Buchholz, where the $\ell^2$-norm in the original
inequality was replaced by $k+1$ different matrix norms associated to word
decompositions (this type of inequality is also called Khintchine-type
inequality). We provide a generalization of Buchholz's result for hyperbolic
groups.


  The ALICE experiment has measured charm and beauty production in pp and Pb-Pb
collisions at sqrt(s) = 2.76 and 7 TeV and sqrt(sNN) = 2.76 TeV, respectively,
via the exclusive reconstruction of hadronic D meson decays and semi-leptonic D
and B meson decays. In this contribution, recent results on the nuclear
modification factor for open charmed mesons and heavy-flavour decay electrons
at central rapidity and muons at forward rapidity are presented and discussed.


  We investigate a search for the oscillating current induced by axion dark
matter in an external magnetic field using optically pumped magnetometers
(OPMs). This experiment is based upon the LC circuit axion detection concept of
Sikivie, Sullivan, and Tanner. The modification of Maxwell's equations caused
by the axion-photon coupling results in a minute oscillating magnetic field at
the frequency equal to the axion mass in the presence of magnetic field. This
induced magnetic field could be searched for using an LC circuit amplifier with
an OPM, the most sensitive cryogen-free magnetic-field sensor, in a room
temperature experiment, avoiding the need for a complicated and expensive
cryogenic system. We discuss how an existing magnetic resonance imaging (MRI)
experiment can be modified to search for axions in a previously unexplored part
of the parameter space. Our existing detection setup, optimized for MRI, is
already sensitive to an axion-photon coupling of $10^{-7}$ GeV$^{-1}$ for an
axion mass near $3\times10^{-10}$ eV. While this is ruled out by limits from
astrophysics and solar axion searches, we show that realistic modifications,
and optimization of the experiment for axion detection, can set a new limit on
the axion-photon coupling up to three orders of magnitude beyond the current
best limit, for axion masses between $10^{-11}$ eV and $10^{-7}$ eV.ion masses
between $10^{-11}$ eV and $10^{-7}$ eV.


  Statistical modal Energy distribution Analysis (SmEdA) can be used as an
alternative to Statistical Energy Analysis for describing subsystems with low
modal overlap. In its original form, SmEdA predicts the power flow exchanged
between the resonant modes of different subsystems. In the case of sound
transmission through a thin structure, it is well-known that the non resonant
response of the structure plays a significant role in transmission below the
critical frequency. In this paper, we present an extension of SmEdA that takes
into account the contributions of the non resonant modes of a thin structure.
The dual modal formulation (DMF) is used to describe the behaviour of two
acoustic cavities separated by a thin structure, with prior knowledge of the
modal basis of each subsystem. Condensation in the DMF equations is achieved on
the amplitudes of the non resonant modes and a new coupling scheme between the
resonant modes of the three subsystems is obtained after several
simplifications. We show that the contribution of the non resonant panel mode
results in coupling the cavity modes of stiffness type, characterised by the
mode shapes of both the cavities and the structure. Comparisons with reference
results demonstrate that the present approach can take into account the non
resonant contributions of the structure in the evaluation of the transmission
loss.


  We investigate the factors that influence the usefulness of supersonic
collisions of Bose-Einstein condensates as a potential source of entangled
atomic pairs by analyzing the reduction of the number difference fluctuations
between regions of opposite momenta. We show that non-monochromaticity of the
mother clouds is typically the leading limitation on number squeezing, and that
the squeezing becomes less robust to this effect as the density of pairs grows.
We develop a simple model that explains the relationship between density
correlations and the number squeezing, allows one to estimate the squeezing
from properties of the correlation peaks, and shows how the multi-mode nature
of the scattering must be taken into account to understand the behavior of the
pairing. We analyze the impact of the Bose enhancement on the number squeezing,
by introducing a simplified low-gain model. We conclude that as far as
squeezing is concerned the preferable configuration occurs when atoms are
scattered not uniformly but rather into two well separated regions.


  This paper introduces our solution for the Track2 in AI City Challenge 2020
(AICITY20). The Track2 is a vehicle re-identification (ReID) task with both the
real-world data and synthetic data. Our solution is based on a strong baseline
with bag of tricks (BoT-BS) proposed in person ReID. At first, we propose a
multi-domain learning method to joint the real-world and synthetic data to
train the model. Then, we propose the Identity Mining method to automatically
generate pseudo labels for a part of the testing data, which is better than the
k-means clustering. The tracklet-level re-ranking strategy with weighted
features is also used to post-process the results. Finally, with multiple-model
ensemble, our method achieves 0.7322 in the mAP score which yields third place
in the competition. The codes are available at
https://github.com/heshuting555/AICITY2020_DMT_VehicleReID.


  With the advent of social networks and the web, the graph sizes have grown
too large to fit in main memory precipitating the need for alternative
approaches for an efficient, scalable evaluation of queries on graphs of any
size.
  Here, we use the divide and conquer approach by partitioning a graph and
process queries over partitions to obtain all or specified number of answers.
This entails correctly computing answers that span multiple partitions or even
need the same partition more than once. Given a set of partitions, there are
many approaches to evaluate a query: i) One Partition At a Time approach, ii)
Traditional use of Multiple Processors, and iii) using the Map/Reduce
Multi-Processor approach. Approach (i), detailed in this paper, has established
scalability through independent processing of partitions. The other two
approaches address response time in addition to scalability. For approach (i),
necessary minimal book keeping has been identified and its correctness
established in this paper. Query answering on partitioned graphs also requires
analyzing partitioning schemes for their impact on query processing and
determining the number and the sequence in which partitions need to be loaded
to reduce the response time to process queries. We correlate query properties
and partition characteristics to reduce query processing time in terms of the
resources available.
  We also identify a set of quantitative metrics and use them to formulate
heuristics to determine the order of loading partitions for efficient query
processing. For approach (i), experiments on large graphs (synthetic,
real-world) using different partitioning schemes analyze the proposed
heuristics on a variety of query types. The other two approaches are fleshed
out and analyzed. An existing graph querying system has been extended to
evaluate queries on partitioned graphs. Finally all approaches are contrasted.


  We present a new approach for transfer of dynamic robot control policies such
as biped locomotion from simulation to real hardware. Key to our approach is to
perform system identification of the model parameters {\mu} of the hardware
(e.g. friction, center-of-mass) in two distinct stages, before policy learning
(pre-sysID) and after policy learning (post-sysID). Pre-sysID begins by
collecting trajectories from the physical hardware based on a set of generic
motion sequences. Because the trajectories may not be related to the task of
interest, presysID does not attempt to accurately identify the true value of
{\mu}, but only to approximate the range of {\mu} to guide the policy learning.
Next, a Projected Universal Policy (PUP) is created by simultaneously training
a network that projects {\mu} to a low-dimensional latent variable {\eta} and a
family of policies that are conditioned on {\eta}. The second round of system
identification (post-sysID) is then carried out by deploying the PUP on the
robot hardware using task-relevant trajectories. We use Bayesian Optimization
to determine the values for {\eta} that optimizes the performance of PUP on the
real hardware. We have used this approach to create three successful biped
locomotion controllers (walk forward, walk backwards, walk sideways) on the
Darwin OP2 robot.


  We consider the effect on tipping from an additive periodic forcing in a
canonical model with a saddle node bifurcation and a slowly varying bifurcation
parameter. Here tipping refers to the dramatic change in dynamical behavior
characterized by a rapid transition away from a previously attracting state. In
the absence of the periodic forcing, it is well-known that a slowly varying
bifurcation parameter produces a delay in this transition, beyond the
bifurcation point for the static case. Using a multiple scales analysis, we
consider the effect of amplitude and frequency of the periodic forcing relative
to the drifting rate of the slowly varying bifurcation parameter.
  We show that a high frequency oscillation drives an earlier tipping when the
bifurcation parameter varies more slowly, with the advance of the tipping point
proportional to the square of the ratio of amplitude to frequency. In the low
frequency case the position of the tipping point is affected by the frequency,
amplitude and phase of the oscillation. The results are based on an analysis of
the local concavity of the trajectory, used for low frequencies both of the
same order as the drifting rate of the bifurcation parameter and for low
frequencies larger than the drifting rate. The tipping point location is
advanced with increased amplitude of the periodic forcing, with critical
amplitudes where there are jumps in the location, yielding significant advances
in the tipping point. We demonstrate the analysis for two applications with
saddle node-type bifurcations.


  We report on our three-dimensional (3D) magnetohydrodynamic (MHD) simulations
of cylindrical weakly twisted flux tubes emerging from 18 Mm below the
photosphere. We perform a parametric study, by varying the initial magnetic
field strength ($B_0$), radius ($R$), twist ($\alpha)$ and length of the
emerging part of the flux tube ($\lambda$) to investigate how these parameters
affect the transfer of the magnetic field from the convection zone to the
photosphere. We show that the efficiency of emergence at the photosphere (i.e.
how strong the photospheric field will be in comparison to $B_0$) depends not
only on the $B_0$ but also the morphology of the emerging field and the twist.
We show that parameters such as $B_0$ and magnetic flux cannot alone determine
whether a flux tube will emerge to the solar surface. For instance, high-$B_0$
(weak-$B_0$) fields may fail (succeed) to emerge at the photosphere, depending
on their geometrical properties. We also show that the photospheric magnetic
field strength can vary greatly for flux tubes with the same $B_0$ but
different geometric properties. Moreover, in some cases we have found scaling
laws, whereby the magnetic field strength scales with the local density as
$B\propto \rho^\kappa$, where $\kappa \approx 1$ deeper in the convection zone
and $\kappa <1$, close to the photosphere. The transition between the two
values occurs approximately when the local pressure scale ($H_p$) becomes
comparable to the diameter of the flux tube ($H_p\approx2R$). We derive forms
to explain how and when these scaling laws appear and compare them with the
numerical simulations.


  We characterize Willmore tori in the 4-sphere with nontrivial normal bundle
as Twistor projections of elliptic curves in complex projective space or as
inverted minimal tori (with planar ends) in Euclidean 4-space.


  Sexual education aims to foster a healthy lifestyle in terms of emotional,
mental and social well-being. In countries like India, where adolescents form
the largest demographic group, they face significant vulnerabilities concerning
sexual health. Unfortunately, sexual education is often stigmatized, creating
barriers to providing essential counseling and information to this at-risk
population. Consequently, issues such as early pregnancy, unsafe abortions,
sexually transmitted infections, and sexual violence become prevalent. Our
current proposal aims to provide a safe and trustworthy platform for sexual
education to the vulnerable rural Indian population, thereby fostering the
healthy and overall growth of the nation. In this regard, we strive towards
designing SUKHSANDESH, a multi-staged AI-based Question Answering platform for
sexual education tailored to rural India, adhering to safety guardrails and
regional language support. By utilizing information retrieval techniques and
large language models, SUKHSANDESH will deliver effective responses to user
queries. We also propose to anonymise the dataset to mitigate safety measures
and set AI guardrails against any harmful or unwanted response generation.
Moreover, an innovative feature of our proposal involves integrating ``avatar
therapy'' with SUKHSANDESH. This feature will convert AI-generated responses
into real-time audio delivered by an animated avatar speaking regional Indian
languages. This approach aims to foster empathy and connection, which is
particularly beneficial for individuals with limited literacy skills.
Partnering with Gram Vaani, an industry leader, we will deploy SUKHSANDESH to
address sexual education needs in rural India.


  We will present some results on the broad--band observations of BeppoSAX of
the bright Seyfert galaxies NGC 4151 and NGC 5548.


  An epitaxial semiconductor-superconductor nanowire is a superconducting
system with a complex level structure originating from hybridization: in
addition to a dense set of higher-energy states derived predominantly from the
metallic superconducting shell above the bulk gap $\Delta$, there is a smaller
number of lower-energy proximitized states from the semiconducting core that
define the induced gap $\Delta^*$. Nanostructures built from such nanowires can
furthermore incorporate quantum dots in order to obtain localized spins for
storing and manipulating quantum information. We discuss the magnetic field
dependence in three devices with different combinations of embedded quantum
dots and superconducting islands. For strong fields, they show pinning of
excitation energies to a uniform spacing, even if for weak fields they have
non-universal properties with different behaviors for even and odd number of
confined electrons. We propose a quantum impurity model for hybrid devices that
incorporates all relevant physical effects. We show that the model accounts for
the key observations and permits unambiguous interpretation in terms of
many-particle states. In particular, we study the replicas of the
Yu-Shiba-Rusinov states in the hybrid gap, their collapse and oscillation
around zero bias with increasing field, and the strong smoothing effect of the
spin-orbit coupling (SOC) on these oscillations. We propose that the
SOC-induced mixing of many-body states is a generic mechanism and that magnetic
pinning is likely to be a ubiquitous feature in hybrid nanowires.


  We construct the non-minimal linear representations of the N=4 Extended
Supersymmetry in one-dimension. They act on 8 bosonic and 8 fermionic fields.
Inequivalent representations are specified by the mass-dimension of the fields
and the connectivity of the associated graphs. The oxidation to minimal N=5
linear representations is given. Two types of N=4 sigma-models based on
non-minimal representations are obtained: the resulting off-shell actions are
either manifestly invariant or depend on a constrained prepotential. The
connectivity properties of the graphs play a decisive role in discriminating
inequivalent actions. These results find application in partial breaking of
supersymmetric theories.


  Dwarf galaxies are known to have remarkably low star formation efficiency due
to strong feedback. Adopting the dwarf galaxies of the Milky Way as a
laboratory, we explore a flexible semi-analytic galaxy formation model to
understand how the feedback processes shape the satellite galaxies of the Milky
Way. Using Markov-Chain Monte-Carlo, we exhaustively search a large parameter
space of the model and rigorously show that the general wisdom of strong
outflows as the primary feedback mechanism cannot simultaneously explain the
stellar mass function and the mass--metallicity relation of the Milky Way
satellites. An extended model that assumes that a fraction of baryons is
prevented from collapsing into low-mass halos in the first place can be
accurately constrained to simultaneously reproduce those observations. The
inference suggests that two different physical mechanisms are needed to explain
the two different data sets. In particular, moderate outflows with weak halo
mass dependence are needed to explain the mass--metallicity relation, and
prevention of baryons falling into shallow gravitational potentials of low-mass
halos (e.g. "pre-heating") is needed to explain the low stellar mass fraction
for a given subhalo mass.


  Invasion fronts in ecology are well studied but very few mathematical results
concern the case with variable motility (possibly due to mutations). Based on
an apparently simple reaction-diffusion equation, we explain the observed
phenomena of front acceleration (when the motility is unbounded) as well as
other quantitative results, such as the selection of the most motile
individuals (when the motility is bounded). The key argument for the
construction and analysis of traveling fronts is the derivation of the
dispersion relation linking the speed of the wave and the spatial decay. When
the motility is unbounded we show that the position of the front scales as
$t^{3/2}$. When the mutation rate is low we show that the canonical equation
for the dynamics of the fittest trait should be stated as a PDE in our context.
It turns out to be a type of Burgers equation with source term.


  We show that unification of the three gauge couplings can be realized
consistently in a class of non-supersymmetric SO(10) models with a one-step
breaking to the Standard Model if a color-sextet scalar field survives down to
the TeV scale. Such scalars, which should be accessible to the LHC for direct
detection, arise naturally in SO(10) as remnants of the seesaw mechanism for
neutrino masses. The diquark couplings of these scalars lead to \Delta B = 2
baryon number violating processes such as neutron-antineutron oscillation. We
estimate the free neutron-antineutron transition time to be \tau_{n-\bar{n}}
\approx (10^9-10^{12}) sec., which is in the interesting range for next
generation n-\bar{n} oscillation experiments. These models also realize
naturally the recently proposed (B-L)-violating GUT scale baryogenesis which
survives to low temperatures unaffected by the electroweak sphaleron
interactions.


  We devise experimental schemes able to mimic uniform and staggered magnetic
fluxes acting on ultracold two-electron atoms, such as ytterbium atoms,
propagating in a honeycomb lattice. The atoms are first trapped into two
independent state-selective triangular lattices and are further exposed to a
suitable configuration of resonant Raman laser beams. These beams induce hops
between the two triangular lattices and make atoms move in a honeycomb lattice.
Atoms traveling around each unit cell of this honeycomb lattice pick up a
nonzero phase. In the uniform case, the artificial magnetic flux sustained by
each cell can reach about two flux quanta, thereby realizing a cold atom
analogue of the Harper model with its notorious Hofstadter's butterfly
structure. Different condensed-matter phenomena such as the relativistic
integer and fractional quantum Hall effects, as observed in graphene samples,
could be targeted with this scheme.


  The alternating direction method with multipliers (ADMM) has been one of most
powerful and successful methods for solving various convex or nonconvex
composite problems that arise in the fields of image & signal processing and
machine learning. In convex settings, numerous convergence results have been
established for ADMM as well as its varieties. However, due to the absence of
convexity, the convergence analysis of nonconvex ADMM is generally very
difficult. In this paper we study the Bregman modification of ADMM (BADMM),
which includes the conventional ADMM as a special case and often leads to an
improvement of the performance of the algorithm. Under certain assumptions, we
prove that the iterative sequence generated by BADMM converges to a stationary
point of the associated augmented Lagrangian function. The obtained results
underline the feasibility of ADMM in applications under nonconvex settings.


  An error avoiding quantum code is presented which is capable of stabilizing
Grover's quantum search algorithm against a particular class of coherent
errors. This error avoiding code consists of states only which are factorizable
in the computational basis. Furthermore, its redundancy is smaller than the one
which is achievable with a general error correcting quantum code saturating the
quantum Hamming bound. The fact that this code consists of factorizable states
only may offer advantages for the implementation of quantum gates in the error
free subspace.


  Drug discovery is a highly complicated process, and it is unfeasible to fully
commit it to the recently developed molecular generation methods. Deep
learning-based lead optimization takes expert knowledge as a starting point,
learning from numerous historical cases about how to modify the structure for
better drug-forming properties. However, compared with the more established de
novo generation schemes, lead optimization is still an area that requires
further exploration. Previously developed models are often limited to resolving
one (or few) certain subtask(s) of lead optimization, and most of them can only
generate the two-dimensional structures of molecules while disregarding the
vital protein-ligand interactions based on the three-dimensional binding poses.
To address these challenges, we present a novel tool for lead optimization,
named Delete (Deep lead optimization enveloped in protein pocket). Our model
can handle all subtasks of lead optimization involving fragment growing,
linking, and replacement through a unified deleting (masking) strategy, and is
aware of the intricate pocket-ligand interactions through the geometric design
of networks. Statistical evaluations and case studies conducted on individual
subtasks demonstrate that Delete has a significant ability to produce molecules
with superior binding affinities to protein targets and reasonable
drug-likeness from given fragments or atoms. This feature may assist medicinal
chemists in developing not only me-too/me-better products from existing drugs
but also hit-to-lead for first-in-class drugs in a highly efficient manner.


  Galactic synchrotron emission exhibits large-angular-scale features known as
radio spurs and loops. Determining the physical size of these structures is
important for understanding the local interstellar structure and for modeling
the Galactic magnetic field. However, the distance to these structures is
either under debate or entirely unknown. We revisit a classical method of
finding the location of radio spurs by comparing optical polarization angles
with those of synchrotron emission as a function of distance. We consider three
tracers of the magnetic field: stellar polarization, polarized synchrotron
radio emission, and polarized thermal dust emission. We employ archival
measurements of optical starlight polarization and Gaia distances, and
construct a new map of polarized synchrotron emission from WMAP and Planck
data. We confirm that synchrotron, dust emission, and stellar polarization
angles all show a statistically significant alignment at high Galactic
latitude. We obtain distance limits to three regions towards Loop I of
112$\pm$17 pc, 135$\pm$20 pc, and $<105$ pc. Our results strongly suggest that
the polarized synchrotron emission towards the North Polar Spur at $b >
30^\circ$ is local. This is consistent with the conclusions of earlier work
based on stellar polarization and extinction, but in stark contrast with the
Galactic center origin recently revisited on the basis of X-ray data. We also
obtain a distance measurement towards part of Loop IV (180$\pm$15 pc) and find
evidence that its synchrotron emission arises from chance overlap of structures
located at different distances. Future optical polarization surveys will allow
the expansion of this analysis to other radio spurs.


  In this review we collect, for the first time in one paper, old and new
results and future perspectives of the research line that uses hadron
production, in high-energy scattering processes, to experimentally probe
fundamental questions of quantum gravity. The key observations, that ignited
the link between the two arenas, are the so-called ``color-event horizon'' of
quantum chromodynamics, and the enormous (de)accelerations involved in such
scattering processes: both phenomena point to the Unruh (and related Hawking)
type of effects. After the first pioneering investigations of this, such
research went on and on, including studies of the horizon entropy and other
``black-hole thermodynamical'' behaviors, which incidentally are also the
frontier of the analog gravity research itself. It is stressed in various
places here that the \textit{trait d'union} between the two phenomenologies is
that in both scenarios, hadron physics and black hole physics, ``thermal''
behaviors are more easily understood not as due to real thermalization
processes (sometimes just impossible, given the small number of particles
involved), but rather to a stochastic/quantum entanglement nature of such
temperature. Finally, other aspects, such as the self-critical organizations of
hadronic matter and of black-holes, have been recently investigated. The
results of those investigations are also summarized and commented upon here. As
a general remark, this research line shows that indeed we can probe quantum
gravity theoretical constructions with analog systems that are not confined to
belong only to the condensed matter arena. This is as it must be.


  The Complex Event Recognition (CER) group is a research team, affiliated with
the National Centre of Scientific Research "Demokritos" in Greece. The CER
group works towards advanced and efficient methods for the recognition of
complex events in a multitude of large, heterogeneous and interdependent data
streams. Its research covers multiple aspects of complex event recognition,
from efficient detection of patterns on event streams to handling uncertainty
and noise in streams, and machine learning techniques for inferring interesting
patterns. Lately, it has expanded to methods for forecasting the occurrence of
events. It was founded in 2009 and currently hosts 3 senior researchers, 5 PhD
students and works regularly with under-graduate students.


  Durda et al. (2004), using numerical models, suggested that binary asteroids
with large separation, called Escaping Ejecta Binaries (EEBs), can be created
by fragments ejected from a disruptive impact event. It is thought that six
binary asteroids recently discovered might be EEBs because of the high
separation between their components (~100 > a/Rp > ~20). However, the rotation
periods of four out of the six objects measured by our group and others and
presented here show that these suspected EEBs have fast rotation rates of 2.5
to 4 hours. Because of the small size of the components of these binary
asteroids, linked with this fast spinning, we conclude that the
rotational-fission mechanism, which is a result of the thermal YORP effect, is
the most likely formation scenario. Moreover, scaling the YORP effect for these
objects shows that its timescale is shorter than the estimated ages of the
three relevant Hirayama families hosting these binary asteroids. Therefore,
only the largest (D~19 km) suspected asteroid, (317) Roxane, could be, in fact,
the only known EEB. In addition, our results confirm the triple nature of
(3749) Balam by measuring mutual events on its lightcurve that match the
orbital period of a nearby satellite in addition to its distant companion.
Measurements of (1509) Esclangona at different apparitions show a unique shape
of the lightcurve that might be explained by color variations.


  The problem of heat conduction in one-dimensional piecewise homogeneous
composite materials is examined by providing an explicit solution of the
one-dimensional heat equation in each domain. The location of the interfaces is
known, but neither temperature nor heat flux are prescribed there. We find a
solution using the Unified Transform Method, due to Fokas and collaborators,
applied to interface problems and compute solutions numerically.


  We introduce $(s,t)$-uniform simplicial complexes. We show that the lengths
of spheres in minimal filling diagrams associated to loops in such complexes
are the terms of certain recurrence relations. We study the limit of the ratio
of the area of such spheres over their length as the radii of spheres grow.
Besides we compute the average Gaussian curvature for vertices inside these
spheres.


  We report the measurement of K$^-$ absorption processes in the $\Sigma^0$p
final state and the first exclusive measurement of the two nucleon absorption
(2NA) with the KLOE detector. The 2NA process without further interactions is
found to be 12\% of the sum of all other contributing processes, including
absorption on three and more nucleons or 2NA followed by final state
interactions with the residual nucleons. We also determine the possible
contribution of the ppK$^-$ bound state to the $\Sigma^0$p final state. A yield
of ppK$^- /\mathrm{K^-_{stop}}$ is found to be $(0.044 \pm 0.009\, stat ^{+
0.004} _{- 0.005} \,syst) \cdot 10^{-2}$ but its statistical significance based
on an F-test is only 1$\sigma$.


  The manipulation of quantum states of light has resulted in significant
advancements in both dark matter searches and gravitational wave detectors
[1-4]. Current dark matter searches operating in the microwave frequency range
use nearly quantum-limited amplifiers [3, 5, 6]. Future high frequency searches
will use photon counting techniques [1] to evade the standard quantum limit. We
present a signal enhancement technique that utilizes a superconducting qubit to
prepare a superconducting microwave cavity in a non-classical Fock state and
stimulate the emission of a photon from a dark matter wave. By initializing the
cavity in an $|n=4\rangle$ Fock state, we demonstrate a quantum enhancement
technique that increases the signal photon rate and hence also the dark matter
scan rate each by a factor of 2.78. Using this technique, we conduct a dark
photon search in a band around $\mathrm{5.965\, GHz \, (24.67\, \mu eV)}$,
where the kinetic mixing angle $\epsilon \geq 4.35 \times 10^{-13}$ is excluded
at the $90\%$ confidence level.


  The exponential decay rate of the semigroup $S(t)=e^{t\mathbb{A}}$ generated
by the abstract damped wave equation $$\ddot u + 2f(A) \dot u +A u=0 $$ is here
addressed, where $A$ is a strictly positive operator. The continuous function
$f$, defined on the spectrum of $A$, is subject to the constraints $$\inf
f(s)>0\qquad\text{and}\qquad \sup f(s)/s <\infty$$ which are known to be
necessary and sufficient for exponential stability to occur. We prove that the
operator norm of the semigroup fulfills the estimate $$\|S(t)\|\leq
Ce^{\sigma_*t}$$ being $\sigma_*<0$ the supremum of the real part of the
spectrum of $\mathbb{A}$. This estimate always holds except in the resonant
cases, where the negative exponential $e^{\sigma_*t}$ turns out to be penalized
by a factor $(1+t)$. The decay rate is the best possible allowed by the theory.


  We develop a novel method to extract key cosmological information, which is
primarily carried by the baryon acoustic oscillations and redshift space
distortions, from spectroscopic galaxy surveys based on a joint principal
component analysis (PCA) and massive optimized parameter estimation and data
compression (MOPED) algorithm. We apply this method to galaxy samples from BOSS
DR12, and find that a PCA manipulation is effective at extracting the
informative modes in the 2D correlation function, giving a tighter constraint
on BAO and RSD parameters compared to that using the lowest three multipole
moments by the traditional method; i.e. the Figure of Merit of BAO and RSD
parameters is improved by $\sim20\%$. We then perform a compression of the
informative PC modes for BAO and RSD parameters using the MOPED scheme,
reducing the dimension of the data vector to the number of interesting
parameters, manifesting the joint PCA and MOPED as a powerful tool for
clustering analysis with almost no loss of constraining power.


  In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary
surfaces and the boundary conditions imposed on those surfaces. However, AdS
can be foliated in various ways to give different boundaries. We show that the
CFTs obtained using certain distinct foliations are different. This difference
arises because the asymptotic region of a foliation overlaps with the deep
interior region of another. In particular we focus on the CFTs defined on
surfaces of large constant radius in global coordinates, Rindler-AdS
coordinates, and Poincar\'e coordinates for AdS$_3$. We refer to these as
global-CFT, Rindler-CFT and Poincar\'e-CFT respectively. We demonstrate that
the correlators for these CFTs are different and argue that the bulk duals to
these should agree up to very close to the respective horizons but then start
differing. Since the BTZ black hole is obtained as a quotient of AdS$_3$, we
discuss the implications of our results for bulk duals of
periodically-identified Poincar\'e and Rindler-CFTs. Our results are consistent
with some recent proposals suggesting a modification of the semi-classical BTZ
geometry close to the horizons.


  Metamagnetic transitions in single-crystal rare-earth nickel borocarbide
HoNi$_2$B$_2$C have been studied at T\approx 1.9 K with a Quantum Design torque
magnetometer. This compound is highly anisotropic with a variety of
metamagnetic states at low temperature which includes antiferromagnetic,
ferrimagnetic, non-collinear and ferromagnetic-like (saturated paramagnet)
states. The critical fields of the transitions depend crucially on the angle
$\theta$ between applied field and the easy axis [110]. Measurements of torque
along the c-axis have been made while changing the angular direction of the
magnetic field (parallel to basal tetragonal $ab$-planes) and with changing
field at fixed angle over a wide angular range. Two new phase boundaries in the
region of the non-collinear phase have been observed, and the direction of the
magnetization in this phase has been precisely determined. At low field the
antiferromagnetic phase is observed to be multidomain. In the angular range
very close to the hard axis [100] ($-6^{\circ} \lesssim\phi \lesssim
6^{\circ}$, where $\phi$ is the angle between field and the hard axis) the
magnetic behavior is found to be ``frustrated'' with a mixture of phases with
different directions of the magnetization.


  We use a combination of conventional density functional theory (DFT) and
post-DFT methods, including the local density approximation plus Hubbard $U$
(LDA+$U$), PBE0, and self-consistent $GW$ to study the electronic properties of
Ni-substituted PbTiO$_{3}$ (Ni-PTO) solid solutions. We find that LDA
calculations yield unreasonable band structures, especially for Ni-PTO solid
solutions that contain an uninterrupted NiO$_{2}$ layer. Accurate treatment of
localized states in transition-metal oxides like Ni-PTO requires post-DFT
methods. $B$-site Ni/Ti cation ordering is also investigated. The $B$-site
cation arrangement alters the bonding between Ni and O, and therefore strongly
affects the band gap ($E_{\rm g}$) of Ni-PTO. We predict that Ni-PTO solid
solutions should have a direct band gap in the visible light energy range, with
polarization similar to the parent PbTiO$_{3}$. This combination of properties
make Ni-PTO solid solutions promising candidate materials for solar energy
conversion devices.


  We show that each pseudoconvex domain $\Omega\subset {\mathbb C}^n$ admits a
holomorphic map $F$ to ${\mathbb C}^m$ with $|F|\le C_1 e^{C_2
\hat{\delta}^{-6}}$, where $\hat{\delta}$ is the minimum of the boundary
distance and $(1+|z|^2)^{-1/2}$, such that every boundary point is a
Casorati-Weierstrass point of $F$. Based on this fact, we introduce a new
anti-hyperbolic concept --- universal dominability. We also show that for each
$\alpha>6$ and each pseudoconvex domain $\Omega\subset {\mathbb C}^n$, there is
a holomorphic function $f$ on ${\Omega}$ with $|f|\le C_\alpha e^{C_\alpha'
\hat{\delta}^{-\alpha}}$, such that every boundary point is a Picard point of
$F$. Applications to the construction of holomorphic maps of a given domain
onto some ${\mathbb C}^m$ are given.


  In blind image deconvolution, priors are often leveraged to constrain the
solution space, so as to alleviate the under-determinacy. Priors which are
trained separately from the task of deconvolution tend to be instable, or
ineffective. We propose the Golf Optimizer, a novel but simple form of network
that learns deep priors from data with better propagation behavior. Like
playing golf, our method first estimates an aggressive propagation towards
optimum using one network, and recurrently applies a residual CNN to learn the
gradient of prior for delicate correction on restoration. Experiments show that
our network achieves competitive performance on GoPro dataset, and our model is
extremely lightweight compared with the state-of-art works.


  When machine learning models are deployed on a test distribution different
from the training distribution, they can perform poorly, but overestimate their
performance. In this work, we aim to better estimate a model's performance
under distribution shift, without supervision. To do so, we use a set of
domain-invariant predictors as a proxy for the unknown, true target labels.
Since the error of the resulting risk estimate depends on the target risk of
the proxy model, we study generalization of domain-invariant representations
and show that the complexity of the latent representation has a significant
influence on the target risk. Empirically, our approach (1) enables self-tuning
of domain adaptation models, and (2) accurately estimates the target error of
given models under distribution shift. Other applications include model
selection, deciding early stopping and error detection.


  Near-term quantum communication protocols suffer inevitably from channel
noises, whose alleviation has been mostly attempted with resources such as
multiparty entanglement or sophisticated experimental techniques. Generation of
multiparty higher dimensional entanglement is not easy. This calls for
exploring realistic solutions which are implementable with current devices.
Motivated particularly by the difficulty in generation of multiparty entangled
states, in this paper, we have investigated error-free information transfer
with minimal requirements. For this, we have proposed a new information
encoding scheme for communication purposes. The encoding scheme is based on the
fact that most noisy channels leave some quantities invariant. Armed with this
fact, we encode information in these invariants. These invariants are functions
of expectation values of operators. This information passes through the noisy
channel unchanged. Pertinently, this approach is not in conflict with other
existing error correction schemes. In fact, we have shown how standard quantum
error-correcting codes emerge if suitable restrictions are imposed on the
choices of logical basis states. As applications, for illustration, we propose
a quantum key distribution protocol and an error-immune information transfer
protocol.


  Video-based large language models (Video-LLMs) have been recently introduced,
targeting both fundamental improvements in perception and comprehension, and a
diverse range of user inquiries. In pursuit of the ultimate goal of achieving
artificial general intelligence, a truly intelligent Video-LLM model should not
only see and understand the surroundings, but also possess human-level
commonsense, and make well-informed decisions for the users. To guide the
development of such a model, the establishment of a robust and comprehensive
evaluation system becomes crucial. To this end, this paper proposes
\textit{Video-Bench}, a new comprehensive benchmark along with a toolkit
specifically designed for evaluating Video-LLMs. The benchmark comprises 10
meticulously crafted tasks, evaluating the capabilities of Video-LLMs across
three distinct levels: Video-exclusive Understanding, Prior Knowledge-based
Question-Answering, and Comprehension and Decision-making. In addition, we
introduce an automatic toolkit tailored to process model outputs for various
tasks, facilitating the calculation of metrics and generating convenient final
scores. We evaluate 8 representative Video-LLMs using \textit{Video-Bench}. The
findings reveal that current Video-LLMs still fall considerably short of
achieving human-like comprehension and analysis of real-world videos, offering
valuable insights for future research directions. The benchmark and toolkit are
available at: \url{https://github.com/PKU-YuanGroup/Video-Bench}.


  Ensemble Learning is an effective method for improving generalization in
machine learning. However, as state-of-the-art neural networks grow larger, the
computational cost associated with training several independent networks
becomes expensive. We introduce a fast, low-cost method for creating diverse
ensembles of neural networks without needing to train multiple models from
scratch. We do this by first training a single parent network. We then create
child networks by cloning the parent and dramatically pruning the parameters of
each child to create an ensemble of members with unique and diverse topologies.
We then briefly train each child network for a small number of epochs, which
now converge significantly faster when compared to training from scratch. We
explore various ways to maximize diversity in the child networks, including the
use of anti-random pruning and one-cycle tuning. This diversity enables "Prune
and Tune" ensembles to achieve results that are competitive with traditional
ensembles at a fraction of the training cost. We benchmark our approach against
state of the art low-cost ensemble methods and display marked improvement in
both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100.


  The hadronic $\kt$-spectrum inside a high energy jet is determined including
corrections of relative magnitude $\cO{\sqrt{\alpha_s}}$ with respect to the
Modified Leading Logarithmic Approximation (MLLA), in the limiting spectrum
approximation (assuming an infrared cut-off $Q_0 =\lqcd$) and beyond
($Q_0\ne\lqcd$). The results in the limiting spectrum approximation are found
to be, after normalization, in impressive agreement with measurements by the
CDF collaboration. A new integral representation for the "hump-backed" plateau
is also reported.


  Networks observed in real world like social networks, collaboration networks
etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear
over time. In this paper, we propose a generative, latent space based,
statistical model for such networks (called dynamic networks). We consider the
case where the number of nodes is fixed, but the presence of edges can vary
over time. Our model allows the number of communities in the network to be
different at different time steps. We use a neural network based methodology to
perform approximate inference in the proposed model and its simplified version.
Experiments done on synthetic and real world networks for the task of community
detection and link prediction demonstrate the utility and effectiveness of our
model as compared to other similar existing approaches.


  The asymptotic representations of the functions ${\rm Ai}_1(x), {\rm Gi}(x),
{\rm Ai}'(x), {\rm Ai}^2(x), {\rm Bi}^ 2(x)$ are obtained. As a by-product, the
factorial identity (21') is found. The derivation of asymptotic representations
of the integral $\int_v^{\infty}dx{\rm Ai}(x)h(x,v)$ for $v\to-\infty$ and
integrals, differing from it by the change of ${\rm Ai}(x)$ by ${\rm Ai}'(x)$
or ${\rm Ai_1(x)}$, is presented. For the Airy function ${\rm Ai}(z)$, as an
example, the Stokes' phenomenon is considered as a consequence of discontinuous
behavior of steepest descent lines over the passes. When $z$ crosses the Stokes
ray, the steepest descent line over the higher pass abruptly changes the
direction of its asymptotic approach to the steepest descent line over the
lower pass to the direction of approach to the opposite end of this line.
Therefore, when the integration contour, drawn along the steepest descent
lines, goes over the higher pass, it begins or stops to go over the lower pass
while $z$ crosses the Stokes ray, and as a result the recessive series
(contribution from the lower pass) discontinuously appears or disappears in the
asymptotic representation of a function containing the dominant series.


  The Mellin transform of fibre integral is calculated for certain isolated
singularities of quasihomogeneous complete intersections (especially the
unimodal singualrities of the list by Giusti and Wall). We show the property of
symmetry between spectra of Gauss-Manin and shed light on the lattice structure
of poles of the Mellin transform by means of topological data of the
singularity. As an application, Hodge numbers of the Milnor fibre are expressed
by counting the spectra of Gauss-Manin.


  Human action recognition refers to automatic recognizing human actions from a
video clip. In reality, there often exist multiple human actions in a video
stream. Such a video stream is often weakly-annotated with a set of relevant
human action labels at a global level rather than assigning each label to a
specific video episode corresponding to a single action, which leads to a
multi-label learning problem. Furthermore, there are many meaningful human
actions in reality but it would be extremely difficult to collect/annotate
video clips regarding all of various human actions, which leads to a zero-shot
learning scenario. To the best of our knowledge, there is no work that has
addressed all the above issues together in human action recognition. In this
paper, we formulate a real-world human action recognition task as a multi-label
zero-shot learning problem and propose a framework to tackle this problem in a
holistic way. Our framework holistically tackles the issue of unknown temporal
boundaries between different actions for multi-label learning and exploits the
side information regarding the semantic relationship between different human
actions for knowledge transfer. Consequently, our framework leads to a joint
latent ranking embedding for multi-label zero-shot human action recognition. A
novel neural architecture of two component models and an alternate learning
algorithm are proposed to carry out the joint latent ranking embedding
learning. Thus, multi-label zero-shot recognition is done by measuring
relatedness scores of action labels to a test video clip in the joint latent
visual and semantic embedding spaces. We evaluate our framework with different
settings, including a novel data split scheme designed especially for
evaluating multi-label zero-shot learning, on two datasets: Breakfast and
Charades. The experimental results demonstrate the effectiveness of our
framework.


  The Liouville problem for the stationary Navier-Stokes equations on the whole
space is a challenging open problem who has know several recent contributions.
We prove here some Liouville type theorems for these equations provided the
velocity field belongs to some Lorentz spaces and then in the more general
setting of Morrey spaces. Our theorems correspond to a improvement of some
recent result on this problem and contain some well-known results as a
particular case.


  Jet installation causes jet noise to be amplified significantly at low
frequencies and its physical mechanism must be understood to develop effective
aircraft noise reduction strategies. A hybrid semi-empirical prediction model
has recently been developed based on the instability-wave-scattering mechanism.
However, its validity and accuracy remain to be tested. To do so, in this paper
we carry out a systematic installed jet-noise experiment in the laboratory
using a flat plate instead of an aircraft wing. We show that reducing $H$ (the
separation distance between the flat plate and jet centreline) causes stronger
low-frequency noise enhancement while resulting in little change to the noise
shielding and enhancement at high frequencies. Decreasing $L$ (the axial
distance between the jet exit plane and the trailing edge of the plate) results
in reduced noise amplification at low frequencies and also weakens both the
shielding and enhancement at high frequencies. Increasing the jet Mach number
abates the installation effects. It is shown that the hybrid model developed in
the earlier work agrees with experimental measurements and can capture the
effects of varying $H$, $L$ and jet Mach number extremely well. It is concluded
that the model captures the correct physics and can serve as an accurate and
robust prediction tool. This new physical understanding provides insights into
innovative strategies for suppressing installed jet noise.


  With no evidence of any exotic particle detected so far beyond the Standard
Model, the new physics may lie above the presently accessible energies at
colliders and, at low-energies, can be accounted for via an effective
description. The interplay of flavour and Higgs physics data allows setting
stringent bounds on the parameters of the effective Lagrangian. In this paper,
we focus on $Z_2$-symmetric two Higgs doublet models near the decoupling limit:
the corresponding effective description relies on only a few parameters, thus
predicting many interesting correlations between observables that work as tests
of the theory. We present the results of a global fit to the existing data,
updating and extending over the past literature. We comment on the triple Higgs
coupling as a probe of an extended scalar sector and on the recent CDF II
measurement of the $W$-mass.


  The celebrated Diamond Lemma of Bergman gives an effectively verifiable
criterion of uniqueness of normal forms for term rewriting in associative
algebras. We present a new way to interpret and prove this result from the
viewpoint of homotopical algebra. Our main result states that every
multiplicative free resolution of an algebra with monomial relations gives rise
to its own Diamond Lemma, so that Bergman's condition of "resolvable
ambiguities" becomes the first non-trivial component of the Maurer--Cartan
equation in the corresponding tangent complex. The same approach works for many
other algebraic structures, emphasizing the relevance of computing
multiplicative free resolutions of algebras with monomial relations.


  We present SAGNet, a structure-aware generative model for 3D shapes. Given a
set of segmented objects of a certain class, the geometry of their parts and
the pairwise relationships between them (the structure) are jointly learned and
embedded in a latent space by an autoencoder. The encoder intertwines the
geometry and structure features into a single latent code, while the decoder
disentangles the features and reconstructs the geometry and structure of the 3D
model. Our autoencoder consists of two branches, one for the structure and one
for the geometry. The key idea is that during the analysis, the two branches
exchange information between them, thereby learning the dependencies between
structure and geometry and encoding two augmented features, which are then
fused into a single latent code. This explicit intertwining of information
enables separately controlling the geometry and the structure of the generated
models. We evaluate the performance of our method and conduct an ablation
study. We explicitly show that encoding of shapes accounts for both
similarities in structure and geometry. A variety of quality results generated
by SAGNet are presented. The data and code are at
https://github.com/zhijieW-94/SAGNet.


  We review recent results on QCD at finite temperature and non-vanishing
baryon number density. We focus on observables which are of immediate interest
to experimental searches for the Quark Gluon Plasma, i.e. the phase transition
temperature, the equation of state in two and three flavour QCD and thermal
effects on hadron masses. Some new developments in finite density QCD are also
presented.


  Unsupervised Domain Adaptation (UDA) is a learning technique that transfers
knowledge learned in the source domain from labelled training data to the
target domain with only unlabelled data. It is of significant importance to
medical image segmentation because of the usual lack of labelled training data.
Although extensive efforts have been made to optimize UDA techniques to improve
the accuracy of segmentation models in the target domain, few studies have
addressed the robustness of these models under UDA. In this study, we propose a
two-stage training strategy for robust domain adaptation. In the source
training stage, we utilize adversarial sample augmentation to enhance the
robustness and generalization capability of the source model. And in the target
training stage, we propose a novel robust pseudo-label and pseudo-boundary
(PLPB) method, which effectively utilizes unlabeled target data to generate
pseudo labels and pseudo boundaries that enable model self-adaptation without
requiring source data. Extensive experimental results on cross-domain fundus
image segmentation confirm the effectiveness and versatility of our method.
Source code of this study is openly accessible at
https://github.com/LinGrayy/PLPB.


  We consider a pair of one-parameter (alpha) families of generalized two-qubit
determinantal Hilbert-Schmidt probability distributions, p_{alpha}(|rho^{PT}|)
and q_{alpha}(|rho|), where rho is a 4 x 4 density matrix, rho^{PT}, its
partial transpose, with |rho^{PT}| \in [-1/16,1/256] and |rho| \in [0, 1/256].
The Dyson-index-like (random matrix) parameter alpha is 1/2 for the
9-dimensional generic two-rebit systems, 1 for the 15-dimensional generic
two-qubit systems,... Numerical (moment-based
probability-distribution-reconstruction) analyses suggest the conjecture that
the Fisher information--a measure over alpha--is identical for the two distinct
families. Further, we study the values of p_{alpha}(0), the probability
densities at the separability-entanglement boundary, with evidence strongly
indicating that p_2(0) =7425/34 and p_3(0)= 7696/69. Despite extensive results
of such a nature, we have not yet succeeded--in contrast with the corresponding
rational-valued separability probabilities (arXiv.org:1301.6617)--in generating
an underlying, explanatory ("concise") formula for p_{\alpha}(0), even though
the corresponding denominators of both sets of rational-valued results are
closely related, having almost identical (small) prime factors. The first
derivatives p_{alpha}^{'}(0) are positive for alpha = 1/2 and 1, but negative
for alpha > 1.


  In strongly correlated materials, quasiparticle excitations can carry
fractional quantum numbers. An intriguing possibility is the formation of
fractionalized, charge-neutral fermions, e.g., spinons and fermionic excitons,
that result in neutral Fermi surfaces and Landau quantization in an insulator.
While previous experiments in quantum spin liquids, topological Kondo
insulators, and quantum Hall systems have hinted at charge-neutral Fermi
surfaces, evidence for their existence remains far from conclusive. Here we
report experimental observation of Landau quantization in a two dimensional
(2D) insulator, i.e., monolayer tungsten ditelluride (WTe$_{2}$), a large gap
topological insulator. Using a detection scheme that avoids edge contributions,
we uncover strikingly large quantum oscillations in the monolayer insulator's
magnetoresistance, with an onset field as small as ~ 0.5 tesla. Despite the
huge resistance, the oscillation profile, which exhibits many periods, mimics
the Shubnikov-de Haas oscillations in metals. Remarkably, at ultralow
temperatures the observed oscillations evolve into discrete peaks near 1.6
tesla, above which the Landau quantized regime is fully developed. Such a low
onset field of quantization is comparable to high-mobility conventional
two-dimensional electron gases. Our experiments call for further investigation
of the highly unusual ground state of the WTe$_{2}$ monolayer. This includes
the influence of device components and the possible existence of mobile
fermions and charge-neutral Fermi surfaces inside its insulating gap.


  The fields of 8 X-ray sources in the Magellanic Clouds believed to be
Be/X-ray binaries have been searched for possible Be star counterparts. BVR and
H alpha CCD imaging was employed to identify early type emission stars through
colour indices and H alpha fluxes. Spectroscopy of 5 sources confirms the
presence of H alpha emission in each case. Based on the positional coincidence
of emission line objects with the X-ray sources, we identify Be star
counterparts to the {ROSAT} sources RX J0032.9-7348, RX J0049.1-7250, RX
J0054.9-7226 and RX J0101.0-7206, and to the recently discovered {ASCA} source
AX J0051-722. We confirm the Be star nature of the counterpart to the {HEAO1}
source H0544-66. In the field of the ROSAT source RX J0051.8-7231 we find that
there are three possible counterparts, each showing evidence for H alpha
emission. We find a close double in the error circle of the {EXOSAT} source EXO
0531.1-6609, each component of which could be a Be star associated with the
X-ray source.


  We present a two-step procedure to probe hotspots of plasmon-enhanced Raman
scattering with carbon nanotubes. Dielectrophoretic deposition places a small
carbon nanotube bundle on top of plasmonic Au nanodimer. After
'pre-characterising' both the nanotubes and dimer structure, we subsequently
use the tip of an AFM to push the bundle into the plasmonic hotspot located in
the 25nm wide dimer gap, characterize its location inside the gap, and observe
the onset of plasmon-enhanced Raman scattering. Evidence for the activation of
the carbon nanotube's double-resonant D-mode by the near-field of the plasmonic
hotspot is discussed.


  Consider a family f:A --> U of g-dimensional abelian varieties over a
quasiprojective manifold U. Suppose that the induced map from U to the moduli
scheme of polarized abelian varieties is generically finite and that there is a
projective manifold Y, containing U as the complement of a normal crossing
divisor S, such that the sheaf of logarithmic one forms is nef and that its
determinant is ample with respect to U. We characterize whether $U$ is a
Shimura variety by numerical data attached to the variation of Hodge
structures, rather than by properties of the map from U to the moduli scheme or
by the existence of CM points. More precisely, we show that U is a Shimura
variety, if and only if two conditions hold. First, each irreducible local
subsystem V of the complex weight one variation of Hodge structures is either
unitary or satisfies the Arakelov equality. Secondly, for each factor M in the
universal cover of U whose tangent bundle behaves like the one of a complex
ball, an iterated Kodaira-Spencer map associated with V has minimal possible
length in the direction of M.


  Generative adversarial imitation learning (GAIL) is a popular inverse
reinforcement learning approach for jointly optimizing policy and reward from
expert trajectories. A primary question about GAIL is whether applying a
certain policy gradient algorithm to GAIL attains a global minimizer (i.e.,
yields the expert policy), for which existing understanding is very limited.
Such global convergence has been shown only for the linear (or linear-type) MDP
and linear (or linearizable) reward. In this paper, we study GAIL under general
MDP and for nonlinear reward function classes (as long as the objective
function is strongly concave with respect to the reward parameter). We
characterize the global convergence with a sublinear rate for a broad range of
commonly used policy gradient algorithms, all of which are implemented in an
alternating manner with stochastic gradient ascent for reward update, including
projected policy gradient (PPG)-GAIL, Frank-Wolfe policy gradient (FWPG)-GAIL,
trust region policy optimization (TRPO)-GAIL and natural policy gradient
(NPG)-GAIL. This is the first systematic theoretical study of GAIL for global
convergence.


  Recent study shows that the accuracy of the k-shell method in determining
node coreness in a spreading process is largely impacted due to the existence
of core-like group, which has a large k-shell index but a low spreading
efficiency. Based on analysis of the structure of core-like groups in
real-world networks, we discover that nodes in the core-like group are mutually
densely connected with very few out-leaving links from the group. By defining a
measure of diffusion importance for each edge based on the number of
out-leaving links of its both ends, we are able to identify redundant links in
the spreading process, which have a relatively low diffusion importance but
lead to form the locally densely connected core-like group. After filtering out
the redundant links and applying the k-shell method to the residual network, we
obtain a renewed coreness for each node which is a more accurate index to
indicate its location importance and spreading influence in the original
network. Moreover, we find that the performance of the ranking algorithms based
on the renewed coreness are also greatly enhanced. Our findings help to more
accurately decompose the network core structure and identify influential nodes
in spreading processes.


  The main theme of this survey is the equivalence statements for quantum
scalar field vacuum states that have been recognized over the last couple of
decades as a powerful line of reasoning when discussing the highly academic
thermal-like Hawking effect and Unruh effect. An important ingredient in this
framework is the concept of vacuum field noise spectrum by which one can obtain
information about the curvature invariants of classical worldlines
(relativistic classical trajectories). It is argued, in the spirit of the free
fall type universality, that the preferred quantum field vacua with respect to
accelerated worldlines should be chosen in the class of all those possessing
stationary spectra for their quantum fluctuations. For scalar quantum field
vacua there are six stationary cases as shown by Letaw some time ago, these are
reviewed here. However, the non-stationary vacuum noises are not out of reach
and can be processed by a few mathematical methods that are mentioned as well.
Since the information about the kinematical curvature invariants of the
worldlines is of radiometric origin, hints are given on a more useful
application of such an academic formalism to radiation and beam radiometric
standards at high energy accelerators and in astrophysics. The survey ends up
with a quick look to related axiomatic quantum field topics and a few other
recent works


  The effect of the QCD phase transition is studied for the mass-radius
relation of compact stars and for hot and dense matter at a given proton
fraction used as input in core-collapse supernova simulations. The phase
transitions to the 2SC and CFL color superconducting phases lead to stable
hybrid star configurations with a pure quark matter core. In supernova
explosions quark matter could be easily produced due to $\beta$-equilibrium,
small proton fractions and nonvanishing temperatures. A low critical density
for the phase transition to quark matter is compatible with present pulsar mass
measurements.


  Recently, a kind of deterministic all-versus-nothing proof of Bell
nonlocality induced from the qubit non-stabilizer state was proposed, breaking
the tradition that deterministic all-versus-nothing proofs are always derived
from stabilizer states. A trivial generalization to the qudit (d is even)
version is by using a special basis map, but such a proof can still be reduced
to the qubit version. So far, whether high dimensional non-stabilizer states
can induce nontrivial deterministic all-versus-nothing proofs of Bell
nonlocality remains unknown. Here we present an example induced from a specific
four-qudit non-stabilizer state (with d = 4), showing that such proofs can be
constructed in high dimensional scenarios as well.


  It is shown that the idea of ``minimal'' coupling to gauge fields can be
conveniently implemented in the proper time formalism by identifying the
equivalent of a ``covariant derivative''. This captures some of the geometric
notion of the gauge field as a connection. The proper time equation is also
generalized so that the gauge invariances associated with higher spin massive
modes can be made manifest, at the free level, using loop variables. Some
explicit examples are worked out illustrating these ideas.


  This work pursues a circle of Lie-theoretic ideas involving Hessenberg
varieties, Poisson geometry, and wonderful compactifications. In more detail,
one may associate a symplectic Hamiltonian $G$-variety
$\mu:G\times\mathcal{S}\longrightarrow\mathfrak{g}$ to each complex semisimple
Lie algebra $\mathfrak{g}$ with adjoint group $G$ and fixed Kostant section
$\mathcal{S}\subseteq\mathfrak{g}$. This variety is one of Bielawski's
hyperk\"ahler slices, and it is central to Moore and Tachikawa's work on
topological quantum field theories. It also bears a close relation to two log
symplectic Hamiltonian $G$-varieties
$\overline{\mu}_{\mathcal{S}}:\overline{G\times\mathcal{S}}\longrightarrow\mathfrak{g}$
and $\nu:\mathrm{Hess}\longrightarrow\mathfrak{g}$. The former is a Poisson
transversal in the log cotangent bundle of the wonderful compactification
$\overline{G}$, while the latter is the standard family of Hessenberg
varieties. Each of $\overline{\mu}$ and $\nu$ is known to be a fibrewise
compactification of $\mu$.
  We exploit the theory of Poisson slices to relate the fibrewise
compactifications mentioned above. Our main result is a canonical
$G$-equivariant bimeromorphism
$\mathrm{Hess}\cong\overline{G\times\mathcal{S}}$ of varieties over
$\mathfrak{g}$. This bimeromorphism is shown to be a Hamiltonian $G$-variety
isomorphism in codimension one, and to be compatible with a Poisson isomorphism
obtained by B\u{a}libanu. We also show our bimeromorphism to be a
biholomorphism if $\mathfrak{g}=\mathfrak{sl}_2$, and we conjecture that this
is the case for arbitrary $\mathfrak{g}$. We conclude by discussing the
implications of our conjecture for Hessenberg varieties.