  Functional magnetic resonance imaging (fMRI) is a notoriously noisy
measurement of brain activity because of the large variations between
individuals, signals marred by environmental differences during collection, and
spatiotemporal averaging required by the measurement resolution. In addition,
the data is extremely high dimensional, with the space of the activity
typically having much lower intrinsic dimension. In order to understand the
connection between stimuli of interest and brain activity, and analyze
differences and commonalities between subjects, it becomes important to learn a
meaningful embedding of the data that denoises, and reveals its intrinsic
structure. Specifically, we assume that while noise varies significantly
between individuals, true responses to stimuli will share common,
low-dimensional features between subjects which are jointly discoverable.
Similar approaches have been exploited previously but they have mainly used
linear methods such as PCA and shared response modeling (SRM). In contrast, we
propose a neural network called MRMD-AE (manifold-regularized multiple decoder,
autoencoder), that learns a common embedding from multiple subjects in an
experiment while retaining the ability to decode to individual raw fMRI
signals. We show that our learned common space represents an extensible
manifold (where new points not seen during training can be mapped), improves
the classification accuracy of stimulus features of unseen timepoints, as well
as improves cross-subject translation of fMRI signals. We believe this
framework can be used for many downstream applications such as guided
brain-computer interface (BCI) training in the future.


  We present a multipartite entanglement measure for $N$-qudit pure states,
using the norm of the correlation tensor which occurs in the Bloch
representation of the state. We compute this measure for important class of
$N$-qutrit pure states, namely general GHZ states. We prove that this measure
possesses almost all the properties expected of a good entanglement measure,
including monotonicity. Finally, we extend this measure to $N$-qudit mixed
states via convex roof construction and establish its various properties,
including its monotonicity.


  We investigate a quantum quench from a critical to an exceptional point. The
initial state, prepared in the ground state of a critical hermitian system, is
time evolved with a non-hermitian SSH model, tuned to its exceptional point.
The single particle density matrix exhibits supersonic modes and multiple light
cones, characteristic to non-hermitian time evolution. These propagate with
integer multiples of the original Fermi velocity. In the long time limit, the
fermionic Green's function decays spatially as $1/x^2$, in sharp contrast to
the usual $1/x$ decay of non-interacting fermions. The entanglement entropy is
understood as if all these supersonic modes arise from independent
quasiparticles (though they do not), traveling with the corresponding
supersonic light cone velocity. The entropy production rate decreases with time
and develops plateaus during the time evolution, signaling the distinct
velocities in the propagation of non-local quantum correlations. At late times,
the entanglement entropy saturates to a finite value, satisfying a volume law.


  The dynamics of symmetry breaking responsible for lifting the degeneracy of
the Landau levels in the integer quantum Hall effect in graphene is studied in
a low-energy model with the Coulomb interaction. The gap equation for Dirac
quasiparticles is analyzed for both the lowest and higher Landau levels, taking
into account the Landau levels mixing. It is shown that the characteristic
feature of the long-range Coulomb interaction is the decrease of the gap
parameters with increasing the Landau level index $n$ ("running" gaps). The
renormalization (running) of the Fermi velocity as a function of $n$ is also
studied. The solutions of the gap equation reproduce correctly the
experimentally observed integer quantum Hall plateaus in graphene in strong
magnetic fields.


  The work is devoted to investigation of the collective behavior of the
regular rectangular lattices of the NiFe nanoparticles caused by the
dipole-dipole interaction between them. The samples was prepared by the method
of the electron lithography and consist of about 100000 particles of
approximately 50 nm size. The magnetization curves were investigated by the
Hall magnetometry for the different orientation of the external magnetic field
at 4.2K and 77K. The results points on the collective behavior of the system.
The observed peculiarities we connect with the quasi-one-dimensional behavior
of the system and the formation of the solitons in the system.


  We study randomized gossip-based processes in dynamic networks that are
motivated by discovery processes in large-scale distributed networks like
peer-to-peer or social networks.
  A well-studied problem in peer-to-peer networks is the resource discovery
problem. There, the goal for nodes (hosts with IP addresses) is to discover the
IP addresses of all other hosts. In social networks, nodes (people) discover
new nodes through exchanging contacts with their neighbors (friends). In both
cases the discovery of new nodes changes the underlying network - new edges are
added to the network - and the process continues in the changed network.
Rigorously analyzing such dynamic (stochastic) processes with a continuously
self-changing topology remains a challenging problem with obvious applications.
  This paper studies and analyzes two natural gossip-based discovery processes.
In the push process, each node repeatedly chooses two random neighbors and puts
them in contact (i.e., "pushes" their mutual information to each other). In the
pull discovery process, each node repeatedly requests or "pulls" a random
contact from a random neighbor. Both processes are lightweight, local, and
naturally robust due to their randomization.
  Our main result is an almost-tight analysis of the time taken for these two
randomized processes to converge. We show that in any undirected n-node graph
both processes take O(n log^2 n) rounds to connect every node to all other
nodes with high probability, whereas Omega(n log n) is a lower bound. In the
directed case we give an O(n^2 log n) upper bound and an Omega(n^2) lower bound
for strongly connected directed graphs. A key technical challenge that we
overcome is the analysis of a randomized process that itself results in a
constantly changing network which leads to complicated dependencies in every
round.


  We report the discovery of quiescent emission from molecular hydrogen gas
located in the circumstellar disks of six pre-main sequence stars, including
two weak-line T Tauri stars (TTS), and one Herbig AeBe star, in the Chamaeleon
I star forming region. For two of these stars, we also place upper limits on
the 2->1 S(1)/1->0 S(1) line ratios of 0.4 and 0.5. Of the 11 pre-main sequence
sources now known to be sources of quiescent near-infrared hydrogen emission,
four possess transitional disks, which suggests that detectable levels of H$_2$
emission and the presence of inner disk holes are correlated. These H$_2$
detections demonstrate that these inner holes are not completely devoid of gas,
in agreement with the presence of observable accretion signatures for all four
of these stars and the recent detections of [Ne II] emission from three of
them. The overlap in [Ne II] and H$_2$ detections hints at a possible
correlation between these two features and suggests a shared excitation
mechanism of high energy photons. Our models, combined with the kinematic
information from the H$_2$ lines, locate the bulk of the emitting gas at a few
tens of AU from the stars. We also find a correlation between H$_2$ detections
and those targets which possess the largest H$\alpha$ equivalent widths,
suggesting a link between accretion activity and quiescent H$_2$ emission. We
conclude that quiescent H$_2$ emission from relatively hot gas within the disks
of TTS is most likely related to on-going accretion activity, the production of
UV photons and/or X-rays, and the evolutionary status of the dust grain
populations in the inner disks.


  The geometrical, electronic, and magnetic properties of twisted zigzag-edged
graphene nanoribbons (ZGNRs) and novel graphene M\"obius strips (GMS) are
systematically investigated using first-principles density functional
calculations. The structures of ZGNRs and GMS are optimized, and their
stabilities are examined. The molecular energy levels and the spin polarized
density of states are calculated. It is found that for twisted ZGNRs, the
atomic bonding energy decreases quadratically with the increase of the twisted
angle, and the HOMO-LUMO gap are varying in a sine-like behavior with the
twisted angle. The calculated spin densities reveal that the ZGNRs and GMS have
antiferromagnetic ground states, which persist during the twisting. The spin
flips on the zigzag edges of GMS are observed at some positions.


  By utilizing quantum mechanical effects, such as superposition and
entanglement, quantum metrology promises higher precision than the classical
strategies. It is, however, practically challenging to realize the quantum
advantages. This is mainly due to the difficulties in engineering non-classical
probe state and performing nontrivial measurement in practise, particularly
with a large number of particles. Here we propose a scalable scheme with a
symmetrical variational quantum circuit which, same as the Loschmidt echo,
consists of a forward and a backward evolution. We show that in this scheme the
quantum Fisher information, which quantifies the precision limit, can be
efficiently obtained from a measurement signal of the Loschmidt echo. We
experimentally implement the scheme on an ensemble of 10-spin quantum processor
and successfully achieves a precision near the theoretical limit which
outperforms the standard quantum limit with 12.4 dB. The scheme can be
efficiently implemented on various noisy intermediate-scale quantum devices
which provides a promising routine to demonstrate quantum advantages.


  This paper considers the problem of sampling and reconstruction of a
continuous-time sparse signal without assuming the knowledge of the sampling
instants or the sampling rate. This topic has its roots in the problem of
recovering multiple echoes of light from its low-pass filtered and
auto-correlated, time-domain measurements. Our work is closely related to the
topic of sparse phase retrieval and in this context, we discuss the advantage
of phase-free measurements. While this problem is ill-posed, cues based on
physical constraints allow for its appropriate regularization. We validate our
theory with experiments based on customized, optical time-of-flight imaging
sensors. What singles out our approach is that our sensing method allows for
temporal phase retrieval as opposed to the usual case of spatial phase
retrieval. Preliminary experiments and results demonstrate a compelling
capability of our phase-retrieval based imaging device.


  The general intractability of the constraint satisfaction problem has
motivated the study of restrictions on this problem that permit polynomial-time
solvability. One major line of work has focused on structural restrictions,
which arise from restricting the interaction among constraint scopes. In this
paper, we engage in a mathematical investigation of generalized hypertree
width, a structural measure that has up to recently eluded study. We obtain a
number of computational results, including a simple proof of the tractability
of CSP instances having bounded generalized hypertree width.


  In this work, we consider the economics of the interaction between Mobile
Virtual Network Operators (MVNOs) and Mobile Network Operators (MNOs). We
investigate the incentives of an MNO for offering some of her resources to an
MVNO instead of using the resources for her own. We formulate the problem as a
sequential game. We consider a market with one MNO and one MVNO, and a
continuum of undecided end-users. We assume that EUs have different preferences
for the MNO and the MVNO. These preferences can be because of the differences
in the service they are offering or the reluctance of an EU to buy her plan
from one of them. We assume that the preferences also depend on the investment
level the MNO and the MVNO. We show that there exists a unique interior SPNE,
i.e. the SPNE by which both SPs receive a positive mass of EUs, and
characterize it. We also consider a benchmark case in which the MNO and the
MVNO do not cooperate, characterize the unique SPNE of this case, and compare
the results of our model to the benchmark case to assess the incentive of the
MNO to invest in her infrastructure and to offer it to the MVNO.


  Optical Character Recognition has been a challenging field in the advent of
digital computers. It is needed where information is to be readable both to
humans and machines. The process of OCR is composed of a set of pre and post
processing steps that decide the level of accuracy of recognition. This paper
deals with one of the pre-processing steps involved in the OCR process i.e.
Skew (Slant) Detection and Correction. The proposed algorithm implemented for
skew-detection is termed as the COG (Centre of Gravity) method and for that of
skew-correction is Sub-Pixel Shifting method. The algorithm has been kept
simple and optimized for efficient skew-detection and correction. The
performance analysis of the algorithm after testing has been aptly
demonstrated.


  When a missing-data mechanism is NMAR or non-ignorable, missingness is itself
vital information and it must be taken into the likelihood, which, however,
needs to introduce additional parameters to be estimated. The incompleteness of
the data and introduction of more parameters can cause the identification
problem. When a response variable is binary, it becomes a more serious problem
because of less information of bi- nary data, however, there are no methods to
briefly verify whether a mode is identified or not. Therefore, we provide a new
necessary and sufficient condition to easily check model identifiability when
analyzing binary data with non-ignorable missing by condi- tional models. This
condition can give us what condition is needed for a model to have
identifiability as well as make easily check the identifiability of a model.


  Let $f\colon X\to X$, $X=[0,1)$, be an ergodic IET (interval exchange
transformation) relative to the Lebesgue measure on $X$. Denote by $f_t\colon
X_t\to X_t$ the IET obtained by inducing $f$ to the subinterval $X=[0,t)$,
$0<t<1$. We show that \[ \{0<t<1\mid f_{t} \text{is weakly mixing}\} \] is a
residual subset of $X$ of full Lebesgue measure. The result is proved by
establishing a generic Diophantine sufficient condition on $t$ for $f_{t}$ to
be weakly mixing.


  Coronal mass ejections (CMEs) are one of the primary manifestations of solar
activity and can drive severe space weather effects. Therefore, it is vital to
work towards being able to predict their occurrence. However, many aspects of
CME formation and eruption remain unclear, including whether magnetic flux
ropes are present before the onset of eruption and the key mechanisms that
cause CMEs to occur. In this work, the pre-eruptive coronal configuration of an
active region that produced an interplanetary CME with a clear magnetic flux
rope structure at 1 AU is studied. A forward-S sigmoid appears in
extreme-ultraviolet (EUV) data two hours before the onset of the eruption
(SOL2012-06-14), which is interpreted as a signature of a right-handed flux
rope that formed prior to the eruption. Flare ribbons and EUV dimmings are used
to infer the locations of the flux rope footpoints. These locations, together
with observations of the global magnetic flux distribution, indicate that an
interaction between newly emerged magnetic flux and pre-existing sunspot field
in the days prior to the eruption may have enabled the coronal flux rope to
form via tether-cutting-like reconnection. Composition analysis suggests that
the flux rope had a coronal plasma composition, supporting our interpretation
that the flux rope formed via magnetic reconnection in the corona. Once formed,
the flux rope remained stable for 2 hours before erupting as a CME.


  Generalized dilaton gravity in 2d is the most general consistent deformation
of the Jackiw-Teitelboim model that maintains local Lorentz invariance. The
action is generically not power-counting renormalizable, thus going beyond the
class of models typically studied. Nevertheless, all these models are exactly
soluble. We focus on a subclass of dilaton scale invariant models. Within this
subclass, we identify a 3-parameter family of models that describe black holes
asymptoting to AdS2 in the UV and to dS2 in the IR. Since these models could be
interesting for holography, we address thermodynamics and boundary issues,
including boundary charges, asymptotic symmetries and holographic
renormalization.


  This paper deals with the quasi-Armendariz ring in general setting. We
generalize the notions of quasi-Armendariz and $\alpha$-skew Armendariz ring to
quasi $\alpha$-Armendariz and quasi $\alpha$-skew Armendariz ring and
investigate their properties. We also consider the quasi Armendariz properties
of Laurent type rings.


  Using the language of twisted skew-commutative algebras, we define
\emph{secondary representation stability}, a stability pattern in the {\it
unstable} homology of spaces that are representation stable in the sense of
Church, Ellenberg, and Farb. We show that the rational homology of
configuration spaces of ordered points in noncompact manifolds satisfies
secondary representation stability. While representation stability for the
homology of configuration spaces involves stabilizing by introducing a point
``near infinity,'' secondary representation stability involves stabilizing by
introducing a pair of orbiting points -- an operation that relates homology
groups in different homological degrees. This result can be thought of as a
representation-theoretic analogue of \emph{secondary homological stability} in
the sense of Galatius, Kupers, and Randal-Williams. In the course of the proof
we establish some additional results: we give a new characterization of the
homology of the complex of injective words, and we give a new proof of integral
representation stability for configuration spaces of noncompact manifolds,
extending previous results to nonorientable manifolds.


  Planning for the development of a 3rd generation global gravitational-wave
detector array is a multifaceted and complex effort that will necessarily need
a high level of community input. Interfacing to extant and new stakeholders in
the broader scientific constituencies is necessary to keep them aware of the
activities taking place in the ground-based gravitational-wave community and
receive input to inform and evolve the planning. In this report, we present the
approaches GWIC and gravitational-wave collaborations and projects should
consider taking to engage with broader community.
  This report is the fifth in a six part series of reports by the GWIC 3G
Subcommittee: i) Expanding the Reach of Gravitational Wave Observatories to the
Edge of the Universe, ii) The Next Generation Global Gravitational Wave
Observatory: The Science Book, iii) 3G R&D: R&D for the Next Generation of
Ground-based Gravitational Wave Detectors, iv) Gravitational Wave Data
Analysis: Computing Challenges in the 3G Era, v) Future Ground-based
Gravitational-wave Observatories: Synergies with Other Scientific Communities
(this report), and vi) An Exploration of Possible Governance Models for the
Future Global Gravitational-Wave Observatory Network.


  An equi-isoclinic tight fusion frame (EITFF) is a type of Grassmannian code,
being a sequence of subspaces of a finite-dimensional Hilbert space of a given
dimension with the property that the smallest spectral distance between any
pair of them is as large as possible. EITFFs arise in compressed sensing,
yielding dictionaries with minimal block coherence. Their existence remains
poorly characterized. Most known EITFFs have parameters that match those of one
that arose from an equiangular tight frame (ETF) in a rudimentary,
direct-sum-based way. In this paper, we construct new infinite families of
non-"tensor-sized" EITFFs in a way that generalizes the one previously known
infinite family of them as well as the celebrated equivalence between harmonic
ETFs and difference sets for finite abelian groups. In particular, we construct
EITFFs consisting of $Q$ planes in $\mathbb{C}^Q$ for each prime power $Q\geq
4$, of $Q-1$ planes in $\mathbb{C}^Q$ for each odd prime power $Q$, and of $11$
three-dimensional subspaces in $\mathbb{R}^{11}$. The key idea is that every
harmonic EITFF -- one that is the orbit of a single subspace under the action
of a unitary representation of a finite abelian group -- arises from a smaller
tight fusion frame with a nicely behaved "Fourier transform." Our particular
constructions of harmonic EITFFs exploit the properties of Gauss sums over
finite fields.


  We consider alternative inflationary cosmologies in massive gravity with
degenerate reference metrics and study the feasibilities of the emergent
universe scenario, bouncing and cyclic universes. We focus on the construction
of the Einstein static universe, classes of exact solutions of bouncing and
cyclic universes in degenerate massive gravity. We further study the
stabilities of the Einstein static universe against both homogeneous and
inhomogeneous scalar perturbations and give the parameters region for a stable
Einstein static universe.


  Protecting privacy during inference with deep neural networks is possible by
adding noise to the activations in the last layers prior to the final
classifiers or other task-specific layers. The activations in such layers are
known as "features" (or, less commonly, as "embeddings" or "feature
embeddings"). The added noise helps prevent reconstruction of the inputs from
the noisy features. Lower bounding the variance of every possible unbiased
estimator of the inputs quantifies the confidentiality arising from such added
noise. Convenient, computationally tractable bounds are available from classic
inequalities of Hammersley and of Chapman and Robbins -- the HCR bounds.
Numerical experiments indicate that the HCR bounds are on the precipice of
being effectual for small neural nets with the data sets, "MNIST" and
"CIFAR-10," which contain 10 classes each for image classification. The HCR
bounds appear to be insufficient on their own to guarantee confidentiality of
the inputs to inference with standard deep neural nets, "ResNet-18" and
"Swin-T," pre-trained on the data set, "ImageNet-1000," which contains 1000
classes. Supplementing the addition of noise to features with other methods for
providing confidentiality may be warranted in the case of ImageNet. In all
cases, the results reported here limit consideration to amounts of added noise
that incur little degradation in the accuracy of classification from the noisy
features. Thus, the added noise enhances confidentiality without much reduction
in the accuracy on the task of image classification.


  We discuss the shape resonance in the superconducting gaps of a two band
superconductor by tuning the chemical potential at a Lifshitz transition for
Femi surface neck collapsing and for spot appearing. The high temperature
superconducting scenario for complex matter shows the coexistence of a first
BCS condensate made of Cooper pairs in the first band and a second boson-like
condensate made of bosons like bipolarons, in the second band where the
chemical potential is tuned near a Lifshitz transition. The interband coupling
controls the shape resonance in the pair exchange between the two condensates.
We discuss the particular BCS-Bose crossover that occurs at the shape resonance
tuning the Lifshitz parameter (the energy difference between the chemical
potential and the Lifshitz topological transition) like tuning the external
magnetic field for the Feshbach resonances in ultracold gases. This
superconducting phase provides a particular case of topological
superconductivity with multiple condensates of different winding numbers


  The work of Avestimehr et al. '07 has recently proposed a deterministic model
for wireless networks and characterized the unicast capacity C of such networks
as the minimum rank of the adjacency matrices describing all possible
source-destination cuts. Amaudruz & Fragouli first proposed a polynomial-time
algorithm for finding the unicast capacity of a linear deterministic wireless
network in their 2009 paper. In this work, we improve upon Amaudruz &
Fragouli's work and further reduce the computational complexity of the
algorithm by fully exploring the useful combinatorial features intrinsic in the
problem. Our improvement applies generally with any size of finite fields
associated with the channel model. Comparing with other algorithms on solving
the same problem, our improved algorithm is very competitive in terms of
complexity.


  As primary anchors of the distance scale, Cepheid stars play a crucial role
in our understanding of the distance scale of the Universe because of their
period-luminosity relation. Determining precise and consistent parameters
(radius, temperature, color excess, and projection factor) of Cepheid pulsating
stars is therefore very important. With the high-precision parallaxes delivered
by the early third Gaia data release, we aim to derive various parameters of
Cepheid stars in order to calibrate the period-luminosity and period-radius
relations and to investigate the relation of period to p-factor. We applied an
implementation of the parallax-of-pulsation method through the algorithm called
Spectro-Photo-Interferometry of Pulsating Stars, which combines all types of
available data for a variable star in a global modeling of its pulsation. We
present the SPIPS modeling of a sample of 63 Galactic Cepheids. Adopting Gaia
EDR3 parallaxes as an input associated with the best available dataset, we
derive consistent values of parameters for these stars such as the radius,
multiband apparent magnitudes, effective temperatures, color excesses, period
changes, Fourier parameters, and the projection factor. We then derive new
calibrations of the period-luminosity and period-radius relations. After
investigating the dependences of the p-factor on the parameters of the stars,
we find a high dispersion of its values and no evidence of its correlation with
the period or with any other parameters. Statistically, the p-factor has an
average value of p=1.26$\pm$0.07, but with an unsatisfactory agreement. In
absence of any clear correlation between the p-factor and other quantities, the
best agreement is obtained under the assumption that the p-factor can take any
value in a band with a width of 0.15. This result highlights the need for a
further examination of the physics behind the p-factor.


  The effect of spin-orbit interaction on persistent currents in mesoscopic
Hubbard rings threaded by an Aharonov-Bohm flux is investigated putting stress
on the orbital magnetism. The non-perturbative treatment of the spin-orbit
interaction developed by Meir {\em et al.} is combined with the Bethe ansatz
solution to deal with this problem exactly. We find that the interplay of
spin-orbit interaction and electron-electron interaction plays a crucial role,
bringing about some new effects on the orbital magnetism.


  In this paper, we present a set of photometric observations in 15 colors of
stars in the Landolt covered by the system range from 300 nm to 1000 nm. Visual
magnitudes of the stars being studied in the field are from 10th to 20th mag.
The observational methodology and the data reduction procedures are described.
The relationships between the BATC intermediate-band system and the Landolt
UBVRI broad band system are obtained. A catalogue of the photometry has been
produced which contains the SEDs of 3613 stars. The electronic form of this
catalogue can be accessed at the CDS via anonymous ftp to cdsarc.u-strasbg.fr.


  We investigate schemes for quantum secret sharing and quantum dense coding
via tripartite entangled states. We present a scheme for sharing classical
information via entanglement swapping using two tripartite entangled GHZ
states. In order to throw light upon the security affairs of the quantum dense
coding protocol, we also suggest a secure quantum dense coding scheme via W
state in analogy with the theory of sharing information among involved users.


  We present a strong lensing analysis on the massive cluster Abell 370 (A370;
z = 0.375), using a combination of deep multi-band Hubble Space Telescope (HST)
imaging and Multi-Unit Spectroscopic Explorer (MUSE) spectroscopy. From only
two hours of MUSE data, we are able to measure 120 redshifts in the Southern
BCG area, including several multiply-imaged lens systems. In total, we increase
the number of multiply-imaged systems with a secure redshift from 4 to 15, nine
of which are newly discovered. Of these, eight are located at z > 3, greatly
extending the redshift range of spectroscopically-confirmed systems over
previous work. Using these systems as constraints, we update a parametric lens
model of A370, probing the mass distribution from cluster to galaxy scales.
Overall, we find that a model with only two cluster- scale dark matter halos
(one for each BCG) does a poor job of fitting these new image constraints.
Instead, two additional mass clumps -- a central "bar" of mass located between
the BCGs, and another clump located within a "crown" of galaxies in the
Northern part of the cluster field -- provide significant improvements to the
fit. Additional physical evidence suggests these clumps are indeed real
features of the system, but with relatively few image constraints in the crown
region, this claim is difficult to evaluate from a modeling perspective.
Additional MUSE observations of A370 covering the entire strong-lensing region
will greatly help these efforts, further improving our understanding of this
intriguing cluster.


  The necessary and sufficient conditions for the equivalence of arbitrary
n-qubit pure quantum states under Local Unitary (LU) operations derived in [B.
Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different
LU-equivalence classes of up to five-qubit states. Due to this classification
new parameters characterizing multipartite entanglement are found and their
physical interpretation is given. Moreover, the method is used to derive
examples of two n-qubit states (with n>2 arbitrary) which have the properties
that all the entropies of any subsystem coincide, however, the states are
neither LU-equivalent nor can be mapped into each other by general local
operations and classical communication.


  Text simplification (TS) can be viewed as monolingual translation task,
translating between text variations within a single language. Recent neural TS
models draw on insights from neural machine translation to learn lexical
simplification and content reduction using encoder-decoder model. But different
from neural machine translation, we cannot obtain enough ordinary and
simplified sentence pairs for TS, which are expensive and time-consuming to
build. Target-side simplified sentences plays an important role in boosting
fluency for statistical TS, and we investigate the use of simplified sentences
to train, with no changes to the network architecture. We propose to pair
simple training sentence with a synthetic ordinary sentence via
back-translation, and treating this synthetic data as additional training data.
We train encoder-decoder model using synthetic sentence pairs and original
sentence pairs, which can obtain substantial improvements on the available
WikiLarge data and WikiSmall data compared with the state-of-the-art methods.


  The classical Kuramoto model is studied in the setting of an infinite horizon
mean field game. The system is shown to exhibit both synchronization and phase
transition. Incoherence below a critical value of the interaction parameter is
demonstrated by the stability of the uniform distribution. Above this value,
the game bifurcates and develops self-organizing time homogeneous Nash
equilibria. As interactions become stronger, these stationary solutions become
fully synchronized. Results are proved by an amalgam of techniques from
nonlinear partial differential equations, viscosity solutions, stochastic
optimal control and stochastic processes.


  Identification of dynamics underlying biochemical pathways of interest in
oncology is a primary goal in current systems biology. Understanding structures
and interactions that govern the evolution of such systems is believed to be a
cornerstone in this research. Systems theory and systems identification theory
are primary resources for this task since they both provide a self consistent
framework for modelling and manipulating models of dynamical systems that are
best suited for the problem under investigation. We address herein the issue of
obtaining an informative dataset ZN to be used as starting point for
identification of EGFR pathway dynamics. In order to match experimental
identifiability criteria we propose a theoretical framework for input stimulus
design based on dynamical properties of the system under investigation. A
feasible optofluidic design has been designed on the basis of the spectral
properties of the driving inputs that maximize information content after the
theoretical studies.


  With the wide applications of algorithmic trading, it has become critical for
traders to build a winning trading algorithm to beat the market. However, due
to the lack of efficient tools, traders mainly rely on their memory to manually
compare the algorithm instances of a trading algorithm and further select the
best trading algorithm instance for the real trading deployment. We work
closely with industry practitioners to discover and consolidate user
requirements and develop an interactive visual analytics system for trading
algorithm optimization. Structured expert interviews are conducted to
evaluateTradAOand a representative case study is documented for illustrating
the system effectiveness. To the best of our knowledge, previous financial data
visual analyses have mainly aimed to assist investment managers in investment
portfolio analysis but have neglected the need of traders in developing trading
algorithms for portfolio execution.TradAOis the first visual analytics system
that assists users in comprehensively exploring the performances of a trading
algorithm with different parameter settings.


  The nucleosynthesis of heavy neutron-deficient nuclei in a stellar photon
bath at the temperatures relevant for the astrophysical gamma process was
investigated. In order to derive (gamma,n) cross sections and reaction rates,
the stellar photon bath was simulated by the superposition of several
bremsstrahlung spectra with different endpoint energies. As a first test for
this method, the (gamma,n) reaction rates of the platinum isotopes 190Pt,
192Pt, and 198Pt were derived. The results are compared to other experimental
data and theoretical calculations.


  State representation learning, or the ability to capture latent generative
factors of an environment, is crucial for building intelligent agents that can
perform a wide variety of tasks. Learning such representations without
supervision from rewards is a challenging open problem. We introduce a method
that learns state representations by maximizing mutual information across
spatially and temporally distinct features of a neural encoder of the
observations. We also introduce a new benchmark based on Atari 2600 games where
we evaluate representations based on how well they capture the ground truth
state variables. We believe this new framework for evaluating representation
learning models will be crucial for future representation learning research.
Finally, we compare our technique with other state-of-the-art generative and
contrastive representation learning methods. The code associated with this work
is available at https://github.com/mila-iqia/atari-representation-learning


  In this paper we prove that polynomials $F(x_1, \cdots, x_n) \in
\mathbb{Z}[x_1, \cdots, x_n]$ of degree $d \geq 3$, satisfying certain
hypotheses, take on the expected density of $(d-1)$-free values. This extends
the authors' earlier result where a different method implied the similar
statement for polynomials of degree $d\geq 5$.


  We study the problem of Distributionally Robust Constrained RL (DRC-RL),
where the goal is to maximize the expected reward subject to environmental
distribution shifts and constraints. This setting captures situations where
training and testing environments differ, and policies must satisfy constraints
motivated by safety or limited budgets. Despite significant progress toward
algorithm design for the separate problems of distributionally robust RL and
constrained RL, there do not yet exist algorithms with end-to-end convergence
guarantees for DRC-RL. We develop an algorithmic framework based on strong
duality that enables the first efficient and provable solution in a class of
environmental uncertainties. Further, our framework exposes an inherent
structure of DRC-RL that arises from the combination of distributional
robustness and constraints, which prevents a popular class of iterative methods
from tractably solving DRC-RL, despite such frameworks being applicable for
each of distributionally robust RL and constrained RL individually. Finally, we
conduct experiments on a car racing benchmark to evaluate the effectiveness of
the proposed algorithm.


  This paper focuses on learning a model of system dynamics online while
satisfying safety constraints. Our objective is to avoid offline system
identification or hand-specified models and allow a system to safely and
autonomously estimate and adapt its own model during operation. Given streaming
observations of the system state, we use Bayesian learning to obtain a
distribution over the system dynamics. Specifically, we propose a new matrix
variate Gaussian process (MVGP) regression approach with an efficient
covariance factorization to learn the drift and input gain terms of a nonlinear
control-affine system. The MVGP distribution is then used to optimize the
system behavior and ensure safety with high probability, by specifying control
Lyapunov function (CLF) and control barrier function (CBF) chance constraints.
We show that a safe control policy can be synthesized for systems with
arbitrary relative degree and probabilistic CLF-CBF constraints by solving a
second order cone program (SOCP). Finally, we extend our design to a
self-triggering formulation, adaptively determining the time at which a new
control input needs to be applied in order to guarantee safety.


  Understanding the contents of multimodal documents is essential to accurately
extract relevant evidence and use it for reasoning. Existing document
understanding models tend to generate answers with a single word or phrase
directly, ignoring the source document's evidence and lacking interpretability.
In this work, we address the lack of step-wise capabilities through data
augmentation and extension. Specifically, We use Multi-modal Large Language
Models (MLLMs), which have strong visual understanding and reasoning abilities,
as data generators to generate step-wise question-and-answer pairs for document
images and use a high-performance LLM as the error detector to filter out noisy
data. This step-wise data generation pipeline is implemented using both
template-based and few-shot methods. We then use the generated high-quality
data to train a humanized document understanding and reasoning model,
specifically designed to solve complex questions that require reasoning or
multi-hop question answering, dubbed DocAssistant. Experimental results
demonstrate the effectiveness and application value of step-wise generation,
showing a 5 improvement on InfoVQA with complex layouts and a 7 improvement on
ChartQA with complex reasoning, compared to directly generated answers. We hope
our work highlights the potential of synthetic data and encourages further
exploration of multi-modal document reasoning capabilities.


  Open heavy flavor and quarkonium are unique probes of the hot-dense medium
produced in heavy-ion collisions. Their production in p+p collisions also
provide important test of QCD. In this paper, we review the selected results on
open heavy flavor and quarkonium in p+p and heavy-ion collisions achieved at
RHIC. Physics implications are also discussed.


  We outline the construction of compatible B-splines on 3D surfaces that
satisfy the continuity requirements for electromagnetic scattering analysis
with the boundary element method (method of moments). Our approach makes use of
Non-Uniform Rational B-splines to represent model geometry and compatible
B-splines to approximate the surface current, and adopts the isogeometric
concept in which the basis for analysis is taken directly from CAD (geometry)
data. The approach allows for high-order approximations and crucially provides
a direct link with CAD data structures that allows for efficient design
workflows. After outlining the construction of div- and curl-conforming
B-splines defined over 3D surfaces we describe their use with the electric and
magnetic field integral equations using a Galerkin formulation. We use B\'ezier
extraction to accelerate the computation of NURBS and B-spline terms and employ
H-matrices to provide accelerated computations and memory reduction for the
dense matrices that result from the boundary integral discretization. The
method is verified using the well known Mie scattering problem posed over a
perfectly electrically conducting sphere and the classic NASA almond problem.
Finally, we demonstrate the ability of the approach to handle models with
complex geometry directly from CAD without mesh generation.


  The optical properties of particularly the tungsten-based transition-metal
dichalcogenides are strongly influenced by the presence of dark excitons.
Recently, theoretical predictions as well as indirect experimental insights
have shown that two different dark excitons exist within the light cone. While
one is completely dark, the other one is only dipole forbidden out-of-plane,
hence referred to as grey exciton. Here, we present angle-resolved
spectroscopic data of a high-quality hexagonal-BN-encapsulated WSe2 monolayer
with which we directly obtain the radiation pattern of this grey exciton that
deviates from that of the bright exciton and other exciton complexes obtained
at cryogenic temperatures.


  The exact formulae for spectra of equilibrium diffusion in a fixed bistable
piecewise linear potential and in a randomly flipping monostable potential are
derived. Our results are valid for arbitrary intensity of driving white
Gaussian noise and arbitrary parameters of potential profiles. We find: (i) an
exponentially rapid narrowing of the spectrum with increasing height of the
potential barrier, for fixed bistable potential; (ii) a nonlinear phenomenon,
which manifests in the narrowing of the spectrum with increasing mean rate of
flippings, and (iii) a nonmonotonic behaviour of the spectrum at zero
frequency, as a function of the mean rate of switchings, for randomly switching
potential. The last feature is a new characterization of resonant activation
phenomenon.


  To explore whether a flat-band system can accommodate superconductivity, we
consider repulsively interacting fermions on the diamond chain, a simplest
quasi-one-dimensional system that contains a flat band. Exact diagonalization
and the density-matrix renormalization group (DMRG) are used to show that we
have a significant binding energy of a Cooper pair with a long-tailed pair-pair
correlation in real space when the total band filling is slightly below $1/3$,
where the dispersive band interacts with the flat band that is empty but close
to $E_F$. Pairs selectively formed across the outer sites of the diamond chain
are responsible for the pairing correlation. At exactly $1/3$-filling an
insulating phase emerges, where the entanglement spectrum indicates the
particles on the outer sites are highly entangled and topological. These come
from a peculiarity of the flat band in which "Wannier orbits" are not
orthogonalizable.


  This work deals with the time evolution of the Hamming distance density for
the public goods game. We consider distinct possibilities for this game, which
are exactly described by a function called $q$-exponential, that represents a
deformation of the usual exponential function parametrized by $q$, suggesting
that the system belongs to the class of weakly-chaotic systems when $q < 1$.
These possibilities are related to the amount of players allowed in each game.


  Communication networks are becoming increasingly complex towards 6G. Manual
management is no longer an option for network operators. Network automation has
been widely discussed in the networking community, and it is a sensible means
to manage the complex communication network. Deep learning models developed to
enable network automation for given operation practices have the limitations of
1) lack of explainability and 2) inapplicable across different networks and/or
network settings. To tackle the above issues, in this article we propose a new
knowledge-powered framework that provides a human-understandable explainable
artificial intelligence (XAI) agent for network automation. A case study of
path selection is developed to demonstrate the feasibility of the proposed
framework. Research on network automation is still in its infancy. Therefore,
at the end of this article, we provide a list of challenges and open issues
that can guide further research in this important area.


  Tandem or Van de Graaff accelerator with an energy of 3-MeV is typically used
for PIXE analysis. In this study, the beam line design used in PIXE analysis
was used to increase the production of isotopes instead of the typical
low-energy accelerator from a 13-MeV cyclotron. For PIXE analysis, the proton
beam should be focused at the target through the use of a nozzle after
degrading the proton beam energy from 13-MeV to 3-MeV using an energy degrader.
Previous studies have been conducted to determine the most appropriate material
and thickness of the energy degrader. Based on the energy distribution of the
degraded proton beam and the neutron occurrence rate at the degrader an
aluminum nozzle of X thickness was determined to be the most appropriate nozzle
construction. Neutrons are created by the collision of 3-MeV protons into the
nozzle after passage through energy degrader. In addition, a sufficient
intensity of proton beam is required for non-destructive analysis of PIXE.
Therefore, in order to optimize nozzle design, it is necessary to consider the
number of neutrons which arise from the collision of protons inside the nozzle,
as well as the track direction of the generated secondary neutrons, with the
primary aim of ensuring a sufficient number of protons passing through the
nozzle as a direct beam. A number of laboratories are currently conducting
research related to the design of nozzles used in accelerator fields, mostly
relating to medical fields. In this paper, a comparative analysis was carried
out for two typical nozzle shapes in order to minimize losses of protons and
generation of secondary neutrons. The neutron occurrence rate and the number of
protons after passing through the nozzle were analyzed using a Particle and
Heavy Ion Transport code System (PHITS) program, in order to identify the
nozzle which generated the strongest proton beam.


  A prominent example of a topologically ordered system is Kitaev's quantum
double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular
includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from
the point of view of local quantum physics. In particular, we will review how
in the abelian case, one can do a Doplicher-Haag-Roberts analysis to study the
different superselection sectors of the model. In this way one finds that the
charges are in one-to-one correspondence with the representations of
$\mathcal{D}(G)$, and that they are in fact anyons. Interchanging two of such
anyons gives a non-trivial phase, not just a possible sign change. The case of
non-abelian groups $G$ is more complicated. We outline how one could use
amplimorphisms, that is, morphisms $A \to M_n(A)$ to study the superselection
structure in that case. Finally, we give a brief overview of applications of
topologically ordered systems to the field of quantum computation.


  We consider unoriented strings in the supersymmetric SL(2,R)/U(1) coset,
which describes the two-dimensional Euclidean black hole, and its mirror dual
N=2 Liouville theory. We analyze the orientifolds of these theories from
several complementary points of view: the parity symmetries of the worldsheet
actions, descent from known AdS_3 parities, and the modular bootstrap method
(in some cases we can also check our results against known constraints coming
from the conformal bootstrap method). Our analysis extends previous work on
orientifolds in Liouville theory, the AdS_3 and SU(2) WZW models and minimal
models. Compared to these cases, we find that the orientifolds of the two
dimensional Euclidean black hole exhibit new intriguing features. Our results
are relevant for the study of orientifolds in the neighborhood of NS5-branes
and for the engineering of four-dimensional chiral gauge theories and gauge
theories with SO and Sp gauge groups with suitable configurations of D-branes
and orientifolds. As an illustration, we discuss an example related to a
configuration of D4-branes and O4-planes in the presence of two parallel
fivebranes.


  We analyze a metal-dielectric structure composed of a silicon nanoparticle
coupled to a stack of split-ring resonators, and reveal the possibility of
optically-induced antiferromagnetic response of such a hybrid meta-molecule
with a staggered pattern of the induced magnetization. We show that a hybrid
metamaterial created by a periodic lattice of the meta-molecules supports
antiferromagnetic modes with a checker-board pattern and the propagation of
spin waves, opening new ways for manipulating artificial antiferromagnetism at
high frequencies with low-loss materials.


  We analyze parity-violating nucleon-nucleon scattering at energies
E<m_\pi^2/M using the effective field theory appropriate for this regime. The
minimal Lagrangian for short-range parity-violating NN interactions is written
in an operator basis that encodes the five partial-wave transitions that
dominate at these energies. We calculate the leading-order relationships
between parity-violating NN asymmetries and the coefficients in the Lagrangian
and also discuss the size of sub-leading corrections. We conclude with a
discussion of further observables needed to completely determine the
leading-order Lagrangian.


  Molecular clouds are essentially made up of atomic and molecular hydrogen,
which in spite of being the simplest molecule in the ISM plays a key role in
the chemical evolution of molecular clouds. Since its formation time is very
long, the H2 molecules can be transported by the turbulent motions within the
cloud toward low density and warm regions, where its enhanced abundance can
boost the abundances of molecules with high endothermicities. We present high
resolution simulations where we include the evolution of the molecular gas
under the effect of the dynamics, and we analyze its impact on the abundance of
CH+.


  Deep neural networks (DNNs) have achieved great success in various
applications due to their strong expressive power. However, recent studies have
shown that DNNs are vulnerable to adversarial examples which are manipulated
instances targeting to mislead DNNs to make incorrect predictions. Currently,
most such adversarial examples try to guarantee "subtle perturbation" by
limiting the $L_p$ norm of the perturbation. In this paper, we aim to explore
the impact of semantic manipulation on DNNs predictions by manipulating the
semantic attributes of images and generate "unrestricted adversarial examples".
  In particular, we propose an algorithm \emph{SemanticAdv} which leverages
disentangled semantic factors to generate adversarial perturbation by altering
controlled semantic attributes to fool the learner towards various
"adversarial" targets. We conduct extensive experiments to show that the
semantic based adversarial examples can not only fool different learning tasks
such as face verification and landmark detection, but also achieve high
targeted attack success rate against \emph{real-world black-box} services such
as Azure face verification service based on transferability.
  To further demonstrate the applicability of \emph{SemanticAdv} beyond face
recognition domain, we also generate semantic perturbations on street-view
images. Such adversarial examples with controlled semantic manipulation can
shed light on further understanding about vulnerabilities of DNNs as well as
potential defensive approaches.


  In this contribution we propose a novel steganographic method based on
several orthogonal polynomials and their combinations. The steganographic
algorithm embeds a secrete message at the first eight coefficients of high
frequency image. Moreover, this embedding method uses the Beta chaotic map to
determine the order of the blocks where the secret bits will be inserted. In
addition, from a 128-bit private key and the steps of a cryptography algorithm
according to the Advanced Encryption Standard (AES) to generate the key
expansion, the proposed method generates a key expansion of 2560 bits, with the
purpose to permute the first eight coefficients of high frequency before the
insertion. The insertion takes eventually place at the first eight high
frequency coefficients in the transformed orthogonal moments domain. Before the
insertion of the message the image undergoes a series of transformations. After
the insertion the inverse transformations are applied to the original
transformations in reverse order. The experimental work on the validation of
the algorithm consists of the calculation of the Peak Signal-to-Noise Ratio
(PSNR), the Universal Image Quality Index (UIQI), the Image Fidelity (IF), and
the Relative Entropy (RE), comparing the same characteristics for the cover and
stego image. The proposed algorithm improves the level of imperceptibility and
security analyzed through the PSNR and RE values, respectively.


  Statistical disclosure limitation (SDL) methods aim to provide analysts
general access to a data set while limiting the risk of disclosure of
individual records. Many methods in the existing literature are aimed only at
the case of univariate distributions, but the multivariate case is crucial,
since most statistical analyses are multivariate in nature. Yet preserving the
multivariate structure of the data can be challenging, especially when both
continuous and categorical variables are present. Here we present a new SDL
method that automatically attains the correct multivariate structure,
regardless of whether the data are continuous, categorical or mixed. In
addition, operational methods for assessing data quality and risk will be
explored.


  The BRIght Target Explorer (BRITE) Constellation is the first nanosatellite
mission applied to astrophysical research. Five satellites in low-Earth orbits
perform precise optical two-colour photometry of the brightest stars in the
night sky. BRITE is naturally well suited for variability studies of hot stars.
This contribution describes the basic outline of the mission and some initial
problems that needed to be overcome. Some information on BRITE data products,
how to access them, and how to join their scientific exploration is provided.
Finally, a brief summary of the first scientific results obtained by BRITE is
given.


  The main goal of this paper is to introduce the notion of twisted partial
action of groupoids. We generalize the theorem about the existence of an
enveloping action, also known as the globalization theorem, and show that the
crossed products of the twisted partial action and of its associated twisted
global action are Morita equivalent. Finally, we generalize the concepts of
partial projective representation and partial Schur multiplier for a groupoid,
and we show the interaction between groupoid partial projective representions
and groupoid twisted partial actions.


  Framing bias plays a significant role in exacerbating political polarization
by distorting the perception of actual events. Media outlets with divergent
political stances often use polarized language in their reporting of the same
event. We propose a new loss function that encourages the model to minimize the
polarity difference between the polarized input articles to reduce framing
bias. Specifically, our loss is designed to jointly optimize the model to map
polarity ends bidirectionally. Our experimental results demonstrate that
incorporating the proposed polarity minimization loss leads to a substantial
reduction in framing bias when compared to a BART-based multi-document
summarization model. Notably, we find that the effectiveness of this approach
is most pronounced when the model is trained to minimize the polarity loss
associated with informational framing bias (i.e., skewed selection of
information to report).


  Fundamental results concerning the dynamics of abelian group codes
(behaviors) and their duals are developed. Duals of sequence spaces over
locally compact abelian groups may be defined via Pontryagin duality; dual
group codes are orthogonal subgroups of dual sequence spaces. The dual of a
complete code or system is finite, and the dual of a Laurent code or system is
(anti-)Laurent. If C and C^\perp are dual codes, then the state spaces of C act
as the character groups of the state spaces of C^\perp. The controllability
properties of C are the observability properties of C^\perp. In particular, C
is (strongly) controllable if and only if C^\perp is (strongly) observable, and
the controller memory of C is the observer memory of C^\perp. The controller
granules of C act as the character groups of the observer granules of C^\perp.
Examples of minimal observer-form encoder and syndrome-former constructions are
given. Finally, every observer granule of C is an "end-around" controller
granule of C.


  For treatment of the layers below the crust of a neutron star it is useful to
employ a relativistic model involving three independently moving constituents,
representing superfluid neutrons, superfluid protons, and degenerate negatively
charged leptons. A Kalb Ramond type formulation is used here to develop such a
model for the specific purpose of application at the semi macroscopic level
characterised by lengthscales that are long compared with the separation
between the highly localised and densely packed proton vortices of the
Abrikosov type lattice that carries the main part of the magnetic flux, but
that are short compared with the separation between the neutron vortices.


  The VAT-model (virtual address translation model) extends the EM-model
(external memory model) and takes the cost of address translation in virtual
memories into account. In this model, the cost of a single memory access may be
logarithmic in the largest address used. We show that the VAT-cost of
cache-oblivious algorithms is only by a constant factor larger than their
EM-cost; this requires a somewhat more stringent tall cache assumption as for
the EM-model.


  In this paper, we investigate resource allocation design for unmanned aerial
vehicle (UAV)-enabled communication systems, where a UAV is dispatched to
provide communications to multiple user nodes. Our objective is to maximize the
communication system throughput by jointly optimizing the subcarrier allocation
policy and the trajectory of the UAV, while taking into account the minimum
required data rate for each user node, no-fly zones (NFZs), the maximum UAV
cruising speed, and initial/final UAV locations. The design is formulated as a
mixed integer non-convex optimization problem which is generally intractable.
Subsequently, a computationally-efficient iterative algorithm is proposed to
obtain a locally optimal solution. Simulation results illustrate that the
performance of the proposed iterative algorithm approaches closely to that of
the system without NFZ. In addition, the proposed algorithm can achieve a
significant throughput gain compared to various benchmark schemes.


  In this work, by investigating the low temperature behaviour of a scalar
field around a cosmic string, and assuming stable thermodynamic equilibrium, it
is shown that the coupling parameter of the field with curvature must be
restricted to a certain range of values whose bounds are determined by the
deficit angle of the associated conical geometry.


  In this we briefly cover the covariant approach to describe inertial forces
in general relativity and in particular look at the behaviour of the cumulative
drag index for stationary Kerr geometry.


  We give the solution of certain parabolic evolution problems (time-depending
perturbations of the heat equation for the harmonic oscillator) as explicit
integrals on the Wiener space.


  Already for bivariate tropical polynomials, factorization is an NP-Complete
problem. In this paper, we give an efficient algorithm for factorization and
rational factorization of a rich class of tropical polynomials in $n$
variables. Special families of these polynomials have appeared in economics,
discrete convex analysis, and combinatorics. Our theorems rely on an intrinsic
characterization of regular mixed subdivisions of integral polytopes, and lead
to many open problems of interest in discrete geometry.


  In this paper, we introduce a topology on the set of isomorphism classes of
finitely generated modules over an associative algebra. Then we focus on the
relative topology on the set of isomorphism classes of maximal Cohen--Macaulay
modules over a Cohen--Macaulay local ring. We discuss the irreducible
components over certain hypersurfaces.


  We give a negative solution to the problem of the $L^p$-maximal regularity on
various classes of Banach spaces including $L^q$-spaces with $1<q \neq
2<+\infty$.


  We present, discuss and generalize an elegant geometrical proof of the law of
cosines, due to Al Cuoco.


  How much does a single image reveal about the environment it was taken in? In
this paper, we investigate how much of that information can be retrieved from a
foreground object, combined with the background (i.e. the visible part of the
environment). Assuming it is not perfectly diffuse, the foreground object acts
as a complexly shaped and far-from-perfect mirror. An additional challenge is
that its appearance confounds the light coming from the environment with the
unknown materials it is made of. We propose a learning-based approach to
predict the environment from multiple reflectance maps that are computed from
approximate surface normals. The proposed method allows us to jointly model the
statistics of environments and material properties. We train our system from
synthesized training data, but demonstrate its applicability to real-world
data. Interestingly, our analysis shows that the information obtained from
objects made out of multiple materials often is complementary and leads to
better performance.


  Let $X$ be an $n$-point subset of a Euclidean space and $0 < a < 1$. The
classical theorem of Schoenberg implies that the snowflake space $X^a$ can be
isometrically embedded into Euclidean space. In the paper we show that points
in the image of such an embedding always are in general position. As
application we prove the analogue of Schoenberg's result for quotients of
Euclidean spaces by finite groups.


  We analyse the aging dynamics of the one-dimensional Fredrickson-Andersen
(FA) model in the nonequilibrium regime following a low temperature quench.
Relaxation then effectively proceeds via diffusion limited pair coagulation
(DLPC) of mobility excitations. By employing a familiar stochastic similarity
transformation, we map exact results from the free fermion case of diffusion
limited pair annihilation to DLPC. Crucially, we are able to adapt the mapping
technique to averages involving multiple time quantities. This relies on
knowledge of the explicit form of the evolution operators involved. Exact
results are obtained for two-time correlation and response functions in the
free fermion DLPC process. The corresponding long-time scaling forms apply to a
wider class of DLPC processes, including the FA model. We are thus able to
exactly characterise the violations of the fluctuation-dissipation theorem
(FDT) in the aging regime of the FA model. We find nontrivial scaling forms for
the fluctuation-dissipation ratio (FDR) X = X(tw/t), but with a negative
asymptotic value X = -3*pi/(6*pi - 16) = -3.307. While this prevents a
thermodynamic interpretation in terms of an effective temperature, it is a
direct consequence of probing FDT with observables that couple to activated
dynamics. The existence of negative FDRs should therefore be a widespread
feature in non mean-field systems.


  Except for a limited number of cases, a complete classification of the
Diophantine sets of polynomial rings and fields of rational functions seems out
of reach at present. We contribute to this problem by proving that several
natural sets and relations over these structures are not Diophantine.


  We present a quantum adiabatic algorithm for a set of quantum
2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability
(2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is
similar to that of a Heisenberg chain. All the solutions of the given Q2SAT
problem span the subspace of the degenerate ground states. The Hamiltonian is
adiabatically evolved so that the system stays in the degenerate subspace. Our
numerical results suggest that the time complexity of our algorithm is
$O(n^{3.9})$ for yielding non-trivial solutions for problems with the number of
clauses $m=dn(n-1)/2\ (d\lesssim 0.1)$. We discuss the advantages of our
algorithm over the known quantum and classical algorithms.


  Advances in the technologies of networking, wireless communication and
trimness of computers lead to the rapid development in mobile communication
infrastructure, and have drastically changed information processing on mobile
devices. Users carrying portable devices can freely move around, while still
connected to the network. This provides flexibility in accessing information
anywhere at any time. For improving more flexibility on mobile device, the new
challenges in designing software systems for mobile networks include location
and mobility management, channel allocation, power saving and security. In this
paper, we are proposing intelligent software tool for software design on mobile
devices to fulfill the new challenges on mobile location and mobility
management. In this study, the proposed Business Process Redesign (BPR) concept
is aims at an extension of the capabilities of an existing, widely used process
modeling tool in industry with 'Intelligent' capabilities to suggest favorable
alternatives to an existing software workflow design for improving
flexibilities on mobile devices.


  Theoretical estimates of the convergence rate of many well-known
gradient-type optimization methods are based on quadratic interpolation,
provided that the Lipschitz condition for the gradient is satisfied. In this
article we obtain a possibility of constructing an analogue of such
interpolation in the class of locally Lipschitz quasi-convex functionals with
the special conditions of non-smoothness (Lipshitz-continuous subgradient)
introduced in this paper. As an application, estimates are obtained for the
rate of convergence of the previously proposed adaptive mirror descent method
for the problems of minimizing a quasi-convex locally Lipschitz functional with
several convex functional constraints.


  We study the effect of a time-delayed feedback within a generic model for a
saddle-node bifurcation on a limit cycle. Without delay the only attractor
below this global bifurcation is a stable node. Delay renders the phase space
infinite-dimensional and creates multistability of periodic orbits and the
fixed point. Homoclinic bifurcations, period-doubling and saddle-node
bifurcations of limit cycles are found in accordance with Shilnikov's theorems.


  In this paper we consider the achievable rate region of the Gaussian Multiple
Access Channel (MAC) when suboptimal transmission schemes are employed.
Focusing on the two-user MAC and assuming uncoded Pulse Amplitude Modulation
(PAM), we derive a rate region that is a pentagon, and propose a strategy with
which it can be achieved. We also compare the region with outer bounds and with
orthogonal transmission.


  In massive multiple-input multiple-output (MIMO) systems, acquisition of the
channel state information at the transmitter side (CSIT) is crucial. In this
paper, a practical CSIT estimation scheme is proposed for frequency division
duplexing (FDD) massive MIMO systems. Specifically, each received pilot symbol
is first quantized to one bit per dimension at the receiver side and then the
quantized bits are fed back to the transmitter. A joint one-bit compressed
sensing algorithm is implemented at the transmitter to recover the channel
matrices. The algorithm leverages the hidden joint sparsity structure in the
user channel matrices to minimize the training and feedback overhead, which is
considered to be a major challenge for FDD systems. Moreover, the one-bit
compressed sensing algorithm accurately recovers the channel directions for
beamforming. The one-bit feedback mechanism can be implemented in practical
systems using the uplink control channel. Simulation results show that the
proposed scheme nearly achieves the maximum output signal-to-noise-ratio for
beamforming based on the estimated CSIT.


  We present lattice Monte Carlo calculations of fermion-dimer scattering in
the limit of zero-range interactions using the adiabatic projection method. The
adiabatic projection method uses a set of initial cluster states and Euclidean
time projection to give a systematically improvable description of the
low-lying scattering cluster states in a finite volume. We use L\"uscher's
finite-volume relations to determine the s-wave, p-wave, and d-wave phase
shifts. For comparison, we also compute exact lattice results using Lanczos
iteration and continuum results using the Skorniakov-Ter-Martirosian equation.
For our Monte Carlo calculations we use a new lattice algorithm called impurity
lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which
incorporates elements of both worldline and auxiliary-field Monte Carlo
simulations.


  Given a topological property $\mathcal{P}$, a space $X$ is called
star-$\mathcal{P}$ if for any open cover $\mathcal{U}$ of the space $X$, there
exists a set $Y\subseteq X$ with property $\mathcal{P}$ such that
$St(Y,\mathcal{U})=X$; the set $Y$ is called a star kernel of the cover
$\mathcal{U}$. In this paper, we introduce and study spaces with star kernel
Menger, that is, star Menger spaces. Some examples are given to show the
relationship with some other related properties studied previously, and the
behaviour of the star Menger property with respect to subspaces, products,
continuous images and preimages are investigated. Additionally, some comments
on the star selection theory are given. Particularly, some questions posed by
Song within this theory are addressed. Finally, several new properties are
introduced as well as some general questions on them are posed.


  Having in mind their potential quantum physical applications, we classify all
geometric hyperplanes of the near hexagon that is a direct product of a line of
size three and the generalized quadrangle of order two. There are eight
different kinds of them, totalling to 1023 = 2^{10} - 1 = |PG(9, 2)|, and they
form two distinct families intricately related with the points and lines of the
Veldkamp space of the quadrangle in question.


  This paper characterizes when an $m \times n$ rectangle, where $m$ and $n$
are integers, can be tiled (exactly packed) by squares where each has an
integer side length of at least 2. In particular, we prove that tiling is
always possible when both $m$ and $n$ are sufficiently large (at least 10).
When one dimension $m$ is small, the behavior is eventually periodic in $n$
with period 1, 2, or 3. When both dimensions $m,n$ are small, the behavior is
determined computationally by an exhaustive search.


  In this article we present numerical results of conduction in a disordered
quasi-1D wire in the possible presence of magnetic impurities. Our analysis
leads us to the study of universal properties in different conduction regimes
such as the localized and metallic ones. In particular, we analyse the
cross-over between universality classes occurring when the strength of magnetic
disorder is increased. For this purpose, we use a numerical Landauer approach,
and derive the scattering matrix of the wire from electron's Green's function.


  Owing to a renewed interest in flat space higher spin gauge theories, in this
note we provide further details and clarifications on the results presented in
arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality
properties. Focusing, for simplicity, on quartic amplitudes with one of the
external legs having non-zero integer spin (which can be considered as a
prototype for Weinberg-type arguments), we review the appearance of $1/\Box$
non-localities. In particular, we emphasise that it appears to be not possible
to eliminate all of the aforementioned non-localities with a judicious choice
of coupling constants and spectrum. We also discuss the light-cone gauge fixing
in $d=4$, and argue that the non-local obstruction discussed in the covariant
language cannot be avoided using light-cone gauge formalism.


  Optical photometry, spectroscopy and XMM-Newton ultraviolet and X-ray
observations with full phase coverage are used for an in-depth study of WXLMi,
a system formerly termed as a low-accretion rate polar. We find a constant low
mass accretion rate, M_dot ~ 1.5e-13 M_sun/yr, a peculiar accretion geometry
with one spot not being accessible via Roche-lobe overflow, a low temperature
of the white dwarf, Teff < 8000 K and the secondary likely being Roche-lobe
underfilling. All this lends further support to the changed view on WXLMi and
related systems as detached binaries, i.e. magnetic post-common envelope
binaries without significant Roche-lobe overflow in the past. The transfer rate
determined here is compatible with accretion from a stellar wind. We use
cyclotron spectroscopy to determine the accretion geometry and to constrain the
plasma temperatures. Both, cyclotron spectroscopy and X-ray plasma diagnostics
reveal low plasma temperatures below 3 keV on both accretion spots. For the low
m_dot, high B plasma at the accretion spots in WXLMi, cyclotron cooling is
dominating thermal plasma radiation in the optical. Optical spectroscopy and
X-ray timing reveal atmospheric, chromospheric and coronal activity at the
saturation level on the dM4.5 secondary star.


  In communication restricted environments, a multi-robot system can be
deployed to either: i) maintain constant communication but potentially
sacrifice operational efficiency due to proximity constraints or ii) allow
disconnections to increase environmental coverage efficiency, challenges on
how, when, and where to reconnect (rendezvous problem). In this work we tackle
the latter problem and notice that most state-of-the-art methods assume that
robots will be able to execute a predetermined plan; however system failures
and changes in environmental conditions can cause the robots to deviate from
the plan with cascading effects across the multi-robot system. This paper
proposes a coordinated epistemic prediction and planning framework to achieve
consensus without communicating for exploration and coverage, task discovery
and completion, and rendezvous applications. Dynamic epistemic logic is the
principal component implemented to allow robots to propagate belief states and
empathize with other agents. Propagation of belief states and subsequent
coverage of the environment is achieved via a frontier-based method within an
artificial physics-based framework. The proposed framework is validated with
both simulations and experiments with unmanned ground vehicles in various
cluttered environments.


  The determination of the missing $U_{e3}$ element (magnitude and phase) of
the PMNS neutrino mixing matrix is possible via the detection of $\numu\to\nue$
oscillations at a baseline $L$ and energy $E$ given by the atmospheric
observations, corresponding to a mass squared difference $E/L \sim \Delta
m^2\simeq 2.5\times 10^{-3} eV^2$. While the current optimization of the CNGS
beam provides limited sensitivity to this reaction, we discuss in this document
the physics potential of an intensity upgraded and energy re-optimized CNGS
neutrino beam coupled to an off-axis detector. We show that improvements in
sensitivity to $\theta_{13}$ compared to that of T2K and NoVA are possible with
a next generation large liquid Argon TPC detector located at an off-axis
position (position rather distant from LNGS, possibly at shallow depth). We
also address the possibility to discover CP-violation and disentangle the mass
hierarchy via matter effects. The considered intensity enhancement of the CERN
SPS has strong synergies with the upgrade/replacement of the elements of its
injector chain (Linac, PSB, PS) and the refurbishing of its own elements,
envisioned for an optimal and/or upgraded LHC luminosity programme.


  The extreme versatility of two-dimensional van der Waals (vdW) materials
derives from their ability to exhibit new electronic properties when assembled
in proximity with dissimilar crystals. For example, although graphene is
inherently non-magnetic, recent work has reported a magnetic proximity effect
in graphene interfaced with magnetic substrates, potentially enabling a pathway
towards achieving a high-temperature quantum anomalous Hall effect. Here, we
investigate heterostructures of graphene and chromium trihalide magnetic
insulators (CrI$_3$, CrBr$_3$, and CrCl$_3$). Surprisingly, we are unable to
detect a magnetic exchange field in the graphene, but instead discover
proximity effects featuring unprecedented gate-tunability. The graphene becomes
highly hole-doped due to charge transfer from the neighboring magnetic
insulator, and further exhibits a variety of atypical transport features. These
include highly extended quantum Hall plateaus, abrupt reversals in the Landau
level filling sequence, and hysteresis over at least days-long time scales. In
the case of CrI$_3$, we are able to completely suppress the charge transfer and
all attendant atypical transport effects by gating. The charge transfer can
additionally be altered in a first-order phase transition upon switching the
magnetic states of the nearest CrI$_3$ layers. Our results provide a roadmap
for exploiting the magnetic proximity effect in graphene, and motivate further
experiments with other magnetic insulators.


  We present a higher index theorem for a certain class of etale
one-dimensional complex-analytic groupoids. The novelty is the use of the local
anomaly formula established in a previous paper, which represents the bivariant
Chern character of a quasihomomorphism as the chiral anomaly associated to a
renormalized non-commutative chiral field theory. In the present situation the
geometry is non-metric and the corresponding field theory can be renormalized
in a purely conformal way, by exploiting the complex-analytic structure of the
groupoid only. The index formula is automatically localized at the automorphism
subset of the groupoid and involves a cap-product with the sum of two different
cyclic cocycles over the groupoid algebra. The first cocycle is a trace
involving a generalization of the Lefschetz numbers to higher-order fixed
points. The second cocycle is a non-commutative Todd class, constructed from
the modular automorphism group of the algebra.


  We prove Nielsen realisation for finite subgroups of the groups of untwisted
outer automorphisms of RAAGs in the following sense: given any graph $\Gamma$,
and any finite group $G\leqslant \mathrm{U}^0(A_\Gamma) \leqslant
\mathrm{Out}^0(A_\Gamma)$, we find a non-positively curved cube complex with
fundamental group $A_\Gamma$ on which $G$ acts by isometries, realising the
action on $A_\Gamma$.


  The Ramsey Choice principle for families of $n$-element sets, denoted
$\mathrm{RC}_n$, states that every infinite set $X$ has an infinite subset
$Y\subseteq X$ with a choice function on $[Y]^n := \{z\subseteq Y : |z| = n\}$.
We investigate for which positive integers $m$ and $n$ the implication
$\mathrm{RC}_m \Rightarrow \mathrm{RC}_n$ is provable in ZF. It will turn out
that beside the trivial implications $\mathrm{RC}_m \Rightarrow \mathrm{RC}_m$,
under the assumption that every odd integer $n>5$ is the sum of three primes
(known as ternary Goldbach conjecture), the only non-trivial implication which
is provable in ZF is $\mathrm{RC}_2 \Rightarrow \mathrm{RC}_4$.


  The nonrelativistic reduction of the self-consistent covariant density
functional theory is realized for the first time with the similarity
renormalization group (SRG) method. The reduced nonrelativistic Hamiltonian and
densities are calculated by solving the corresponding flow equations with a
novel expansion in terms of the inverse of the Dirac effective mass. The
efficiency and accuracy of this newly proposed framework have been demonstrated
for several typical spherical nuclei. It is found that the exact solutions of
the total energies, traces of vector and scalar densities, and the
root-mean-square radii are reproduced quite well for all nuclei. This allows
one to directly compare and bridge the relativistic and nonrelativistic nuclear
energy density functional theories in the future.


  We report the Pockels electro-optic properties of ZrO2 and HfO2 orthorhombic
Pbc21 and rhombohedral R3m ferroelectric phases, and we compare them to the
well-known LiNbO3 Pockels material from density functional theory calculations
using the CRYSTAL suite of programs. Specifically, three essential processes
are explicitly investigated: The electronic, the ionic (or vibrational), and
the piezoelectric contributions. Our calculations reveal that the ionic part
coming from the low frequency phonon modes contributes the most to the
electro-optic coefficients of rhombohedral LiNbO3 and of orthorhombic ZrO2 and
HfO2. While these low-frequency modes show zero contribution to Pockels
coefficients for the rhombohedral phase of the latter compounds.


  The foundation for the theory of correlation functions of exactly solvable
models is determinant representation. Determinant representation permit to
describe correlation functions by classical completely integrable differential
equations [Barough, McCoy, Wu]. In this paper we show that determinant
represents works not only for free fermionic models. We obtained determinant
representation for the correlation function $<\psi(0,0)\psi^\dagger(x,t)>$ of
the quantum nonlinear Schr\"odinger equation, out of free fermionic point. In
the forthcoming publications we shall derive completely integrable equation and
asymptotic for the quantum correlation function of this model of interacting
fermions.


  By adding a large inductance in a dc-SQUID phase qubit loop, one decouples
the junctions' dynamics and creates a superconducting artificial atom with two
internal degrees of freedom. In addition to the usual symmetric plasma mode
({\it s}-mode) which gives rise to the phase qubit, an anti-symmetric mode
({\it a}-mode) appears. These two modes can be described by two anharmonic
oscillators with eigenstates $\ket{n_{s}}$ and $\ket{n_{a}}$ for the {\it s}
and {\it a}-mode, respectively. We show that a strong nonlinear coupling
between the modes leads to a large energy splitting between states
$\ket{0_{s},1_{a}}$ and $\ket{2_{s},0_{a}}$. Finally, coherent frequency
conversion is observed via free oscillations between the states
$\ket{0_{s},1_{a}}$ and $\ket{2_{s},0_{a}}$.


  The prompt production of the charm baryon $\rm \Lambda_{c}^{+}$ and the $\rm
\Lambda_{c}^{+}/\mathrm {D^0}$ production ratios were measured at midrapidity
with the ALICE detector in pp and p-Pb collisions at $\sqrt{s_\mathrm{NN}} =
5.02$TeV. These new measurements show a clear decrease of the $\rm
\Lambda_{c}^{+}/\mathrm {D^0}$ ratio with increasing transverse momentum
($p_{\rm T}$) in both collision systems in the range $2<p_{\rm T}<12$ GeV/$c$,
exhibiting similarities with the light-flavour baryon-to-meson ratios ${\rm
p}/\pi$ and $\Lambda/\mathrm {K^0_S}$. At low $p_{\rm T}$, predictions that
include additional colour-reconnection mechanisms beyond the leading-colour
approximation; assume the existence of additional higher-mass charm-baryon
states; or include hadronisation via coalescence can describe the data, while
predictions driven by charm-quark fragmentation processes measured in $\mathrm
{e^+e^-}$ and $\mathrm {e^-p}$ collisions significantly underestimate the data.
The results presented in this letter provide significant evidence that the
established assumption of universality (colliding-system independence) of
parton-to-hadron fragmentation is not sufficient to describe charm-baryon
production in hadronic collisions at LHC energies.


  Following the discovery of spiral structure in IC3328 (Jerjen et al.~2000),
we present further evidence that a sizable fraction of bright early-type dwarfs
in the Virgo cluster are genuine disk galaxies, or are hosting a disk
component. Among a sample of 23 nucleated dwarf ellipticals and dS0s observed
with the Very Large Telescope in $B$ and $R$, we found another four systems
exhibiting non-axisymmetric structures, such as a bar and/or spiral arms,
indicative of a disk (IC0783, IC3349, NGC4431, IC3468). Particularly remarkable
are the two-armed spiral pattern in IC0783 and the bar and trailing arms in
NGC4431. For both galaxies the disk nature has recently been confirmed by a
rotation velocity measurement (Simien & Prugniel 2002). Our photometric search
is based on a Fourier decomposition method and a specific version of unsharp
masking. Some ``early-type'' dwarfs in the Virgo cluster seem to be former
late-type galaxies which were transformed to early-type morphology, e.g. by
``harassment'', during their infall to the cluster, while maintaining part of
their disk structure.


  Reconfigurable intelligent surface (RIS) assisted millimeter-wave (mmWave)
communication systems relying on hybrid beamforming structures are capable of
achieving high spectral efficiency at a low hardware complexity and low power
consumption. In this paper, we propose an RIS-assisted mmWave point-to-point
system relying on dynamically configured sub-array connected hybrid beamforming
structures. More explicitly, an energy-efficient analog beamformer relying on
twin-resolution phase shifters is proposed. Then, we conceive a successive
interference cancelation (SIC) based method for jointly designing the hybrid
beamforming matrix of the base station (BS) and the passive beamforming matrix
of the RIS. Specifically, the associated bandwidth-efficiency maximization
problem is transformed into a series of sub-problems, where the sub-array of
phase shifters and RIS elements are jointly optimized for maximizing each
sub-array's rate. Furthermore, a greedy method is proposed for determining the
phase shifter configuration of each sub-array. We then propose to update the
RIS elements relying on a complex circle manifold (CCM)-based method. The
proposed dynamic sub-connected structure as well as the proposed joint hybrid
and passive beamforming method strikes an attractive trade-off between the
bandwidth efficiency and power consumption. Our simulation results demonstrate
the superiority of the proposed method compared to its traditional
counterparts.


  We propose a novel approach for detecting change points in high-dimensional
linear regression models. Unlike previous research that relied on strict
Gaussian/sub-Gaussian error assumptions and had prior knowledge of change
points, we propose a tail-adaptive method for change point detection and
estimation. We use a weighted combination of composite quantile and least
squared losses to build a new loss function, allowing us to leverage
information from both conditional means and quantiles. For change point
testing, we develop a family of individual testing statistics with different
weights to account for unknown tail structures. These individual tests are
further aggregated to construct a powerful tail-adaptive test for sparse
regression coefficient changes. For change point estimation, we propose a
family of argmax-based individual estimators. We provide theoretical
justifications for the validity of these tests and change point estimators.
Additionally, we introduce a new algorithm for detecting multiple change points
in a tail-adaptive manner using the wild binary segmentation. Extensive
numerical results show the effectiveness of our method. Lastly, an R package
called ``TailAdaptiveCpt" is developed to implement our algorithms.


  In [5] we investigated the response of vacuum energy to a gravitational field
by considering a Casimir apparatus in a weak gravitational field. Our approach
was based on a conjecture involving the interpretation of spacetime as a
refractive medium and its effect on vacuum energy composed of virtual massless
scalar particles. There it was shown how the case of virtual photons as the
constituents of vacuum could be inferred from that of the massless scalar
field. Here we explicitly show how the same conjecture applies to the
electromagnetic vacuum composed of virtual photons. Specifically we show that
the boundary conditions imposed on the components of the vector field,
decomposed into two scalar fields, result in the same frequency shift for
photons. Using the same decomposition and employing our conjecture, we also
calculate the electromagnetic energy density for the Casimir apparatus in a
weak gravitational field.


  Electrical and thermal transport properties of Cu-deficient kuramite
Cu3-xSnS4 (CTS) was examined as a possible earth-abundant thermoelectric
material. Crystallographic structure of CTS was characterized by partial
disorder between Cu and Sn. In contrast to semiconducting electrical transport
of related compounds, such as Cu2ZnSnS4 and Cu3SbS4, metallic conduction with
an electrical resistivity of 0.4 mohmcm and a carrier concentration of 3 \times
10^21 cm-3 was observed at 300 K. Lattice thermal conductivity was calculated
at 2.6 Wm^-1K^-1, which was probably reduced by Cu-deficiency and or partial
cation disorder. Density functional theory calculation indicates valence band
was composed of hybridization between Cu 3d orbitals and S 3p orbitals.


  The inferred value of the relic density from cosmological observations has
reached a precision that is akin to that of the LEP precision measurements.
This level of precision calls for the evaluation of the annihilation cross
sections of dark matter that goes beyond tree-level calculations as currently
implemented in all codes for the computation of the relic density. In
supersymmetry radiative corrections are known to be large and thus must be
implemented. Full one-loop radiative corrections for many annihilation
processes have been performed. It is important to investigate whether the bulk
of these corrections can be parameterised through an improved Born
approximation that can be implemented as a selection of form factors to a
tree-level code. This paper is a second in a series that addresses this issue.
After having provided these form factors for the annihilation of the
neutralinos into fermions, which cover the case of a bino-like LSP (Lightest
Supersymmetric Particle), we turn our attention here to a higgsino-like dark
matter candidate through its annihilation into $ZZ$. We also investigate the
cases of a mixed LSP. In all cases we compare the performance of the form
factor approach with the result of a full one-loop correction. We also study
the issue of the renormalisation scheme dependence. An illustration of the
phenomenon of non decoupling of the heavy sfermions that takes place for the
annihilation of the lightest neutralino into $ZZ$ is also presented.


  The demiclosedness principle is one of the key tools in nonlinear analysis
and fixed point theory. In this note, this principle is extended and made more
flexible by two mutually orthogonal affine subspaces. Versions for finitely
many (firmly) nonexpansive operators are presented. As an application, a simple
proof of the weak convergence of the Douglas-Rachford splitting algorithm is
provided.


  We prove fractional Leibniz rules and related commutator estimates in the
settings of weighted and variable Lebesgue spaces. Our main tools are uniform
weighted estimates for sequences of square-function-type operators and a
bilinear extrapolation theorem. We also give applications of the extrapolation
theorem to the boundedness on variable Lebesgue spaces of certain bilinear
multiplier operators and singular integrals.


  If planetesimal formation is an efficient process, as suggested by several
models involving gravitational collapse of pebble clouds, then, before long, a
significant part of the primordial dust mass should be absorbed in many km
sized objects. A good understanding of the total amount of solids in the disk
around a young star is crucial for planet formation theory. But as the mass of
particles above the mm size cannot be assessed observationally, one must ask
how much mass is hidden in bigger objects. We perform 0-d local simulations to
study how the planetesimal to dust and pebble ratio is evolving in time and to
develop an understanding of the potentially existing mass in planetesimals for
a certain amount of dust and pebbles at a given disk age. We perform a
parameter study based on a model considering dust growth, planetesimal
formation and collisional fragmentation of planetesimals, while neglecting
radial transport processes. While at early times, dust is the dominant solid
particle species, there is a phase during which planetesimals make up a
significant portion of the total mass starting at approximately $10^4 - 10^6$
yr. The time of this phase and the maximal total planetesimal mass strongly
depend on the distance to the star $R$, the initial disk mass, and the
efficiency of planetesimal formation $\epsilon$. After approximately $10^6$ yr,
our model predicts planetesimal collisions to dominate, which resupplies small
particles. In our model, planetesimals form fast and everywhere in the disk.
For a given $\epsilon$, we were able to relate the dust content and mass of a
given disk to its planetesimal content, providing us with some helpful basic
intuition about mass distribution of solids and its dependence on underlying
physical processes.


  We study the $\mathrm{Out}(F_n)$-action on the second bounded cohomology
$H^2_b(F_n, \mathbb{R})$, focusing on the countable-dimensional dense invariant
subspace given by Brooks quasimorphisms. We show that this subspace has no
finite-dimensional invariant subspaces, in particular no fixpoints, partially
answering a question of Mikl\'{o}s Ab\'{e}rt. To this end we introduce a notion
of speed of an element $g\in \mathrm{Out}(F_n)$, which measures the asymptotic
growth rate of bounded cohomology classes under repeated application of $g$.


  Mass-loss rates and terminal wind velocities are key parameters that
determine the kinetic wind energy and momenta of massive stars. Furthermore,
accurate mass-loss rates determine the mass and rotational velocity evolution
of mass stars, and their fates as neutron stars and black holes in function of
metallicity (Z). Here we update our Monte Carlo mass-loss Recipe with new
dynamically-consistent computations of the terminal wind velocity -- as a
function of Z. These predictions are particularly timely as the HST ULLYSES
project will observe ultraviolet spectra with blue-shifted P Cygni lines of
hundreds of massive stars in the low-Z Large and Small Magellanic Clouds, as
well as sub-SMC metallicity hosts. Around 35 000 K, we uncover a weak-wind
"dip" and we present diagnostics to investigate its physics with ULLYSES and
X-Shooter data. We discuss how the dip may provide important information on
wind-driving physics, and how this is of key relevance towards finding a new
gold-standard for OB star mass-loss rates. For B supergiants below the Fe IV to
III bi-stability jump, the terminal velocity is found to be independent of Z
and M, while the mass-loss rate still varies as $\dot{M} \propto Z^{0.85}$. For
O-type stars above the bi-stability jump we find a terminal-velocity dependence
of $v_{\infty} \propto Z^{0.19}$ and the Z-dependence of the mass-loss rate is
found to be as shallow as $\dot{M} \propto Z^{0.42}$, implying that to
reproduce the `heavy' black holes from LIGO/VIRGO, the `low Z' requirement
becomes even more stringent than was previously anticipated.


  We provide a simple analytical solution of the Friedmann equations for a
universe made of stiff matter, dust matter, and dark energy. A stiff matter era
is present in the cosmological model of Zel'dovich (1972) where the primordial
universe is assumed to be made of a cold gas of baryons. It also occurs in
certain cosmological models where dark matter is made of relativistic
self-gravitating Bose-Einstein condensates (BECs). When the energy density of
the stiff matter is positive, the primordial universe is singular. It starts
from a state with a vanishing scale factor and an infinite density. We consider
the possibility that the energy density of the stiff matter is negative
(anti-stiff matter). This happens, for example, when the BECs have an
attractive self-interaction. In that case, the primordial universe is
non-singular. It starts from a state in which the scale factor is finite and
the energy density is equal to zero. For the sake of generality, we consider a
cosmological constant of arbitrary sign. When the cosmological constant is
positive, the universe asymptotically reaches a de Sitter phase where the scale
factor increases exponentially rapidly. This can account for the accelerating
expansion of the universe that we observe at present. When the cosmological
constant is negative (anti-de Sitter), the evolution of the universe is cyclic.
Therefore, depending on the sign of the energy density of the stiff matter and
of the dark energy, we obtain singular and non-singular expanding or cyclic
universes.