  Multi-agent reinforcement learning (MARL) is a powerful technology to
construct interactive artificial intelligent systems in various applications
such as multi-robot control and self-driving cars. Unlike supervised model or
single-agent reinforcement learning, which actively exploits network pruning,
it is obscure that how pruning will work in multi-agent reinforcement learning
with its cooperative and interactive characteristics. \par In this paper, we
present a real-time sparse training acceleration system named LearningGroup,
which adopts network pruning on the training of MARL for the first time with an
algorithm/architecture co-design approach. We create sparsity using a weight
grouping algorithm and propose on-chip sparse data encoding loop (OSEL) that
enables fast encoding with efficient implementation. Based on the OSEL's
encoding format, LearningGroup performs efficient weight compression and
computation workload allocation to multiple cores, where each core handles
multiple sparse rows of the weight matrix simultaneously with vector processing
units. As a result, LearningGroup system minimizes the cycle time and memory
footprint for sparse data generation up to 5.72x and 6.81x. Its FPGA
accelerator shows 257.40-3629.48 GFLOPS throughput and 7.10-100.12 GFLOPS/W
energy efficiency for various conditions in MARL, which are 7.13x higher and
12.43x more energy efficient than Nvidia Titan RTX GPU, thanks to the fully
on-chip training and highly optimized dataflow/data format provided by FPGA.
Most importantly, the accelerator shows speedup up to 12.52x for processing
sparse data over the dense case, which is the highest among state-of-the-art
sparse training accelerators.


  In \cite{elgindi2022regular}, a family of singular steady states near the
Bahouri-Chemin patch was introduced. In this paper, we obtain the optimal
regularity and convergence of the singular steady states contruced in
\cite{elgindi2022regular} to the Bahouri-Chemin patch. We first derive a
boundary Harnack principle, and then obtain the optimal convergence results
using the singular integral representation based on Green's function.


  Let E/K be an elliptic curve with complex multiplication and let $K^{ab}$ be
the Abelian closure of $K$. We prove in this article that there exists a
constant $c(E/K)$ such that : for all point $P\in E(\bar{K})-E_{tors}$, we have
\[\hat{h}(P)\geq\frac{c(E/K)}{D}(\frac{\log \log 5D}{\log 2D})^{13},\] where
$D=[K^{ab}(P):K^{ab}]$. This result extends to the case of elliptic curve s
with complex multiplication the previous resultof Amoroso-Zannier \cite{AZ} on
the analogous problem on the multiplicative group $\mathbb{G}_m$, and
generalizes to the case of extensions of degree D the result of Baker
\cite{baker} on the lower bound of the N\'eron-Tate height of the points
defined over an Abelian extension of an elliptic curve with complex
multiplication. This result also enables us to simplify the proof of a theorem
of Viada \cite{viada}.


  One of the concepts of Relativity theory that challenges conventional
intuition the most is time dilation and length contraction. Usual approaches
for describing relativistic effects in quantum systems merely postulate the
consequences of these effects as physical constraints. Here, we propose to
rebuild Special Relativity from quantum mechanical considerations. This is done
by dropping one of its fundamental postulates: the universality of the speed of
light. Lorentz transformations are obtained by a quantum mechanism. We use the
fact that quantum states depend on the Galilean reference frame where they are
defined. In other words, quantum states outside an observer's Galilean
reference frame are distorted. Then, we show in a theorem the existence of
time-dependent observables that are sensible to this distortion in such a way
that their expectation value is a Lorentz-covariant function of time. We then
postulate this mechanism as the source of the phenomena of Special Relativity.
As a corollary of the main theorem, we show the existence of a Lorentz
covariant momentum and mass operators which yield the relativistic momentum and
mass. In this theory, the fundamental limit of the speed of light imposes a
transparency condition for faster-than-light particles: they are allowed but
they are not observable. The transparency effect could explain dark matter in a
more general theory following this quantum formalism.


  With an aim to include the contribution of surface tension in the action of
the boundary, we define the tangential pressure in terms of surface tension and
Normal curvature in a more naturally geometric way. First, we show that the
negative tangential pressure is independent of the four-velocity of a very thin
hyper-surface. Second, we relate the 3-pressure of a surface layer to the
normal curvature and the surface tension. Third, we relate the surface tension
to the energy of the surface layer. Four, we show that the delta like energy
flows across the hyper-surface will be zero for such a representation of
intrinsic 3-pressure. Five, for the weak field approximation and for static
spherically symmetric configuration, we deduce the classical Kelvin's relation.
Six, we write a modified action for the boundary having contributions both from
surface tension and normal curvature of the surface layer. Also we propose a
method to find the physical action assuming a reference background, where the
background is not flat.


  This work presents a novel reconfigurable architecture for Low Latency Graph
Neural Network (LL-GNN) designs for particle detectors, delivering
unprecedented low latency performance. Incorporating FPGA-based GNNs into
particle detectors presents a unique challenge since it requires
sub-microsecond latency to deploy the networks for online event selection with
a data rate of hundreds of terabytes per second in the Level-1 triggers at the
CERN Large Hadron Collider experiments. This paper proposes a novel
outer-product based matrix multiplication approach, which is enhanced by
exploiting the structured adjacency matrix and a column-major data layout.
Moreover, a fusion step is introduced to further reduce the end-to-end design
latency by eliminating unnecessary boundaries. Furthermore, a GNN-specific
algorithm-hardware co-design approach is presented which not only finds a
design with a much better latency but also finds a high accuracy design under
given latency constraints. To facilitate this, a customizable template for this
low latency GNN hardware architecture has been designed and open-sourced, which
enables the generation of low-latency FPGA designs with efficient resource
utilization using a high-level synthesis tool. Evaluation results show that our
FPGA implementation is up to 9.0 times faster and achieves up to 13.1 times
higher power efficiency than a GPU implementation. Compared to the previous
FPGA implementations, this work achieves 6.51 to 16.7 times lower latency.
Moreover, the latency of our FPGA design is sufficiently low to enable
deployment of GNNs in a sub-microsecond, real-time collider trigger system,
enabling it to benefit from improved accuracy. The proposed LL-GNN design
advances the next generation of trigger systems by enabling sophisticated
algorithms to process experimental data efficiently.


  We study configurations of $n$ points and $n$ lines that form
$\Theta(n^{4/3})$ incidences, when the point set is a Cartesian product. We
prove structural properties of such configurations, such that there exist many
families of parallel lines or many families of concurrent lines. We show that
the line slopes have multiplicative structure or that many sets of
$y$-intercepts have additive structure. We introduce the first infinite family
of configurations with $\Theta(n^{4/3})$ incidences. We also derive a new
variant of a different structural point-line result of Elekes.
  Our techniques are based on the concept of line energy. Recently, Rudnev and
Shkredov introduced this energy and showed how it is connected to point-line
incidences. We also prove that their bound is tight up to sub-polynomial
factors.


  The solar activity in Cycle 23--24 shows differences from the previous cycles
that were observed with modern instruments, e.g. long cycle duration and a
small number of sunspots. To appreciate the anomalies further, we investigated
the prominence eruptions and disappearances observed with the Nobeyama
Radioheliograph during over 20 years. Consequently, we found that the
occurrence of the prominence activities in the northern hemisphere is normal
because the period of the number variation is 11 years and the migration of the
producing region of the prominence activities traces the migration of 11 years
ago. On the other hand, the migration in the southern hemisphere significantly
differs from that in the northern hemisphere and the previous cycles. The
prominence activities occurred over -50 degrees latitude in spite of the late
decay phase of Cycle 23, and the number of the prominence activities in the
higher latitude region (over -65 degrees) is very small even near the solar
maximum of Cycle 24. The results suggest that the anomalies of the global
magnetic field distribution started at the solar maximum of Cycle 23.
Comparison of the butterfly diagram of the prominence activities with the
magnetic butterfly diagram indicates that the timing of "the rush to the pole"
and the polar magnetic field closely relates to the unusual migration.
Considering that the rush to the pole is made of the sunspots, the hemispheric
asymmetry of the sunspots and the strength of the polar magnetic fields are
essential for understanding the anomalies of the prominence activities.


  Mathematical modelers have long known of a "rule of thumb" referred to as the
Linear Chain Trick (LCT; aka the Gamma Chain Trick): a technique used to
construct mean field ODE models from continuous-time stochastic state
transition models where the time an individual spends in a given state (i.e.,
the dwell time) is Erlang distributed (i.e., gamma distributed with integer
shape parameter). Despite the LCT's widespread use, we lack general theory to
facilitate the easy application of this technique, especially for complex
models. This has forced modelers to choose between constructing ODE models
using heuristics with oversimplified dwell time assumptions, using time
consuming derivations from first principles, or to instead use non-ODE models
(like integro-differential equations or delay differential equations) which can
be cumbersome to derive and analyze. Here, we provide analytical results that
enable modelers to more efficiently construct ODE models using the LCT or
related extensions. Specifically, we 1) provide novel extensions of the LCT to
various scenarios found in applications; 2) provide formulations of the LCT and
it's extensions that bypass the need to derive ODEs from integral or stochastic
model equations; and 3) introduce a novel Generalized Linear Chain Trick (GLCT)
framework that extends the LCT to a much broader family of distributions,
including the flexible phase-type distributions which can approximate
distributions on $\mathbb{R}^+$ and be fit to data. These results give modelers
more flexibility to incorporate appropriate dwell time assumptions into mean
field ODEs, including conditional dwell time distributions, and these results
help clarify connections between individual-level stochastic model assumptions
and the structure of corresponding mean field ODEs.


  In this paper we give bounds for the first eigenvalue of the conformal
Laplacian and the Yamabe invariant of a compact Riemannian manifold, by using
conditions on the Ricci curvature and the diameter and deduce certain
conditions on the manifold to be conformal to a sphere.


  A description of complete normal varieties with lower dimensional torus
action has been given by Altmann, Hausen, and Suess, generalizing the theory of
toric varieties. Considering the case where the acting torus T has codimension
one, we describe T-invariant Weil and Cartier divisors and provide formulae for
calculating global sections, intersection numbers, and Euler characteristics.
As an application, we use divisors on these so-called T-varieties to define new
evaluation codes called T-codes. We find estimates on their minimum distance
using intersection theory. This generalizes the theory of toric codes and
combines it with AG codes on curves. As the simplest application of our general
techniques we look at codes on ruled surfaces coming from decomposable vector
bundles. Already this construction gives codes that are better than the related
product code. Further examples show that we can improve these codes by
constructing more sophisticated T-varieties. These results suggest to look
further for good codes on T-varieties.


  S-nitrosylation, the covalent addition of NO to the thiol side chain of
cysteine, is an important post-transitional modification (PTM) that can affect
the function of proteins. As such, PTMs extend and diversify protein functions
and thus characterizing consequences of PTM at a molecular level is of great
interest. Although PTMs can be detected through various direct/indirect
methods, they lack the capabilities to investigate the modifications at the
molecular level. In the present work local and global structural dynamics,
their correlation, the hydration structure, and the infrared spectroscopy for
WT and S-nitrosylated Kirsten rat sarcoma virus (KRAS) and Hemoglobin (Hb) are
characterized from molecular dynamics simulations. It is found that for KRAS
attaching NO to Cys118 rigidifies the protein in the Switch-I region which has
functional implications, whereas for Hb nitrosylation at Cys93 at the $\beta_1$
chain increases the flexibility of secondary structural motives for Hb in its
T$_{0}$ and R$_{4}$ conformational substates. Solvent water access decreased by
40\% after nitrosylation in KRAS, similar to Hb for which, however, local
hydration of the R$_4$NO state is yet lower than for T$_0$NO. Finally,
S-nitrosylation leads to detectable peaks for NO stretch, however, congested IR
region will make experimental detection of these bands difficult.


  We investigate the groundstate properties of a recently proposed model for a
topological Kondo insulator in one dimension (i.e., the $p$-wave
Kondo-Heisenberg lattice model) by means of the Density Matrix Renormalization
Group method. The non-standard Kondo interaction in this model is different
from the usual (i.e., local) Kondo interaction in that the localized spins
couple to the "$p$-wave" spin density of conduction electrons, inducing a
topologically non-trivial insulating groundstate. Based on the analysis of the
charge- and spin-excitation gaps, the string order parameter, and the spin
profile in the groundstate, we show that, at half-filling and low energies, the
system is in the Haldane phase and hosts topologically protected spin-1/2
end-states. Beyond its intrinsic interest as a useful "toy-model" to understand
the effects of strong correlations on topological insulators, we show that the
$p$-wave Kondo-Heisenberg model can be implemented in $p-$band optical lattices
loaded with ultra-cold Fermi gases.


  Long Short-Term Memory (LSTM) Recurrent Neural networks (RNNs) rely on gating
signals, each driven by a function of a weighted sum of at least 3 components:
(i) one of an adaptive weight matrix multiplied by the incoming external input
vector sequence, (ii) one adaptive weight matrix multiplied by the previous
memory/state vector, and (iii) one adaptive bias vector. In effect, they
augment the simple Recurrent Neural Networks (sRNNs) structure with the
addition of a "memory cell" and the incorporation of at most 3 gating signals.
  The standard LSTM structure and components encompass redundancy and overly
increased parameterization. In this paper, we systemically introduce variants
of the LSTM RNNs, referred to as SLIM LSTMs. These variants express
aggressively reduced parameterizations to achieve computational saving and/or
speedup in (training) performance---while necessarily retaining (validation
accuracy) performance comparable to the standard LSTM RNN.


  This paper has been withdrawn due to submission of subsequent versions as a
new preprint


  We have fabricated PbTiO$_{3}$/SrRuO$_{3}$ superlattices with ultra-thin
SrRuO$_{3}$ layers. Due to the superlattice geometry, the samples show a large
anisotropy in their electrical resistivity, which can be controlled by changing
the thickness of the PbTiO$_{3}$ layers. Therefore, along the ferroelectric
direction, SrRuO$_{3}$ layers can act as dielectric, rather than metallic,
elements. We show that, by reducing the concentration of PbTiO$_{3}$, an
increasingly important effect of polarization asymmetry due to compositional
inversion symmetry breaking occurs. The results are significant as they
represent a new class of ferroelectric superlattices, with a rich and complex
phase diagram. By expanding our set of materials we are able to introduce new
behaviors that can only occur when one of the materials is not a perovskite
titanate. Here, compositional inversion symmetry breaking in bi-color
superlattices, due to the combined variation of A and B site ions within the
superlattice, is demonstrated using a combination of experimental measurements
and first principles density functional theory.


  Compositional barrier functions are proposed in this paper to systematically
compose multiple objectives for teams of mobile robots. The objectives are
first encoded as barrier functions, and then composed using AND and OR logical
operators. The advantage of this approach is that compositional barrier
functions can provably guarantee the simultaneous satisfaction of all composed
objectives. The compositional barrier functions are applied to the example of
ensuring collision avoidance and static/dynamical graph connectivity of teams
of mobile robots. The resulting composite safety and connectivity barrier
certificates are verified experimentally on a team of four mobile robots.


  We present a tight inequality to test the dynamical nature of spacetime. A
general-relativistic violation of that inequality certifies change of
curvature, in the same sense as a quantum-mechanical violation of a Bell
inequality certifies a source of entanglement. The inequality arises from a
minimal generalization of the Bell setup. It represents a limit on the winning
chance of a collaborative multi-agent game played on the M\"obius graph. A long
version of this Letter including other games and how these games certify the
dynamical character of the celebrated quantum switch is accessible as
arXiv:2309.15752 [gr-qc].


  We present a high scale method to produce few layer graphene (FLG) based on
the mechanical exfoliation of graphite and compare the obtained FLG with the
one reported earlier arising from pencil lead ablation. Several things are
modified and improved in the new approach. The purification and the ablation
set_up are simplified, and the morphology of the FLG is modified and improved
in view of some applications. The morphology dependent properties of FLGs, lead
FLG and graphite FLG, are investigated as conductive layers and in
nanocomposites. Newly obtained FLG has higher aspect ratio (high lateral size
vs. thickness,higher 2D aspect) which is reflected by an enhanced
transparency_conductivity features of the layer (film) and an elongation at
break behavior in the polymer composites. On the contrary, the nanocomposite
containing lead FLG shows for instance excellent gas barrier properties due to
the multistep structure of lead FLG flakes. Such structure exhibits less 2D and
more 3D character, which can be highly suitable for applications where the
presence of active, reactive edges is beneficial ( in catalysis or
supercapacitors electrodes). Nuclear reaction analysis is employed to
investigate the morphology of graphite FLG film.


  For certain affine galoisian coverings whose automorphims are affine
transformations, we give a method to compute the group of affine
transformations of the base manifold. We use the fact that, in this case, the
base manifold inherits a linear connection so that the projection is an affine
map. Then we extend this latter result to homogeneous manifolds. More
specifically, we give necessary conditions so that a homogeneous $G$-space
admits an invariant linear connection induced from a left invariant linear
connection on $G$ (the reductive case is treated separately), and we show that
if the connection is bi-invariant the natural projection is an affine map.
Moreover we prove that, given an affine homogeneous space $G/H$, affine
transformations of $G$ commuting with the $G$-action determine affine
transformations of $G/H$. The reciprocal is true when $H$ is discrete. As an
application, we exhibit the group of affine transformations of the orientable
flat affine surfaces.


  We have proposed a novel numerical method to calculate accurately the
physical quantities of the ground state with the tensor-network wave function
in two dimensions. We determine the tensor network wavefunction by a projection
approach which applies iteratively the Trotter-Suzuki decomposition of the
projection operator and the singular value decomposition of matrix. The norm of
the wavefunction and the expectation value of a physical observable are
evaluated by a coarse grain renormalization group approach. Our method allows a
tensor-network wavefunction with a high bond degree of freedom (such as D=8) to
be handled accurately and efficiently in the thermodynamic limit. For the
Heisenberg model on a honeycomb lattice, our results for the ground state
energy and the staggered magnetization agree well with those obtained by the
quantum Monte Carlo and other approaches.


  Turbulence is ubiquitous in molecular clouds (MCs), but its origin is still
unclear because MCs are usually assumed to live longer than the turbulence
dissipation time. Interstellar medium (ISM) turbulence is likely driven by SN
explosions, but it has never been demonstrated that SN explosions can establish
and maintain a turbulent cascade inside MCs consistent with the observations.
In this work, we carry out a simulation of SN-driven turbulence in a volume of
(250 pc)$^3$, specifically designed to test if SN driving alone can be
responsible for the observed turbulence inside MCs. We find that SN driving
establishes a velocity scaling consistent with the usual scaling laws of
supersonic turbulence, suggesting that previous idealized simulations of MC
turbulence, driven with a random, large-scale volume force, were correctly
adopted as appropriate models for MC turbulence, despite the artificial
driving. We also find that the same scaling laws extend to the interior of MCs,
and that the velocity-size relation of the MCs selected from our simulation is
consistent with that of MCs from the Outer-Galaxy Survey, the largest MC sample
available. The mass-size relation and the mass and size probability
distributions also compare successfully with those of the Outer Galaxy Survey.
Finally, we show that MC turbulence is super-Alfv\'{e}nic with respect to both
the mean and rms magnetic-field strength. We conclude that MC structure and
dynamics are the natural result of SN-driven turbulence.


  In this paper, we investigate the relation between a $q$-matroid and its
associated matroid called the projectivization matroid. The latter arises by
projectivizing the groundspace of the $q$-matroid and considering the
projective space as the groundset of the associated matroid on which is defined
a rank function compatible with that of the $q$-matroid. We show that the
projectivization map is a functor from categories of $q$-matroids to categories
of matroids, which allows to prove new results about maps of $q$-matroids. We
furthermore show the characteristic polynomial of a $q$-matroid is equal to
that of the projectivization matroid. We use this relation to establish a
recursive formula for the characteristic polynomial of a $q$-matroid in terms
of the characteristic polynomial of its minors. Finally we use the
projectivization matroid to prove a $q$-analogue of the critical theorem in
terms of $\mathbb{F}_{q^m}$-linear rank metric codes and $q$-matroids.


  The paper studies randomness extraction from sources with bounded
independence and the issue of independence amplification of sources, using the
framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is
${\rm dep}(x,y) = \max\{C(x) - C(x \mid y), C(y) - C(y\mid x)\}$, where
$C(\cdot)$ denotes the Kolmogorov complexity. It is shown that there exists a
computable Kolmogorov extractor $f$ such that, for any two $n$-bit strings with
complexity $s(n)$ and dependency $\alpha(n)$, it outputs a string of length
$s(n)$ with complexity $s(n)- \alpha(n)$ conditioned by any one of the input
strings. It is proven that the above are the optimal parameters a Kolmogorov
extractor can achieve. It is shown that independence amplification cannot be
effectively realized. Specifically, if (after excluding a trivial case) there
exist computable functions $f_1$ and $f_2$ such that ${\rm dep}(f_1(x,y),
f_2(x,y)) \leq \beta(n)$ for all $n$-bit strings $x$ and $y$ with ${\rm
dep}(x,y) \leq \alpha(n)$, then $\beta(n) \geq \alpha(n) - O(\log n)$.


  We study the time-sliced thawed Gaussian propagation method, which was
recently proposed for solving the time-dependent Schr\"odinger equation. We
introduce a triplet of quadrature-based analysis, synthesis and
re-initialization operators to give a rigorous mathematical formulation of the
method. Further, we derive combined error bounds for the discretization of the
wave packet transform and the time-propagation of the thawed Gaussian basis
functions. Numerical experiments in 1D illustrate the theoretical results.


  One reports computational study revealing a set of general requirements,
fulfilling of which would allow employing changes in ambient conditions to
regulate accomplishing the collective outcome of emerging active network
patterns in an ensemble of a moderate number of finite discrete systems. The
patterns within all these component systems emerge out of random expansion
process governed by certain local rule. The systems modeled are of the same
type but different in details, finite discrete spatial domains of the expansion
within the systems are equivalent regular hexagonal arrays. The way in which
elements of a component system function in the local information transmission
allows dividing them into two classes. One class is represented by
zero-dimensional entities coupled into pairs identified at the array sites
being nearest neighbors. The pairs preserve their orientation in the space
while experiencing conditional hopping to positions close by and transferring
certain information portions. Messenger particles hopping to signal the pairs
for the conditional jumping constitute the other class. Contribution from the
hopping pairs results in finite size effects being specific feature of
accomplishing the mean expected network pattern representing the collective
outcome. It is shown how manifestations of the finite size effects allow using
changes in parameters of the model ambient conditions of the ensemble evolution
to regulate accomplishing the collective outcome representation.


  There are a number of localic separation axioms which are roughly analogous
to the $T_1$-axiom from classical topology. For instance, besides the
well-known subfitness and fitness, there are also Rosicky-Smarda's
$T_1$-locales, totally unordered locales and, more categorically, the recently
introduced $\mathcal{F}$-separated locales (i.e., those with a fitted diagonal)
- a property strictly weaker than fitness.
  It has recently been shown that the strong Hausdorff property and
$\mathcal{F}$-separatedness are in a certain sense dual to each other. In this
paper, we provide further instances of this duality - e.g., we introduce a new
first-order separation property which is to $\mathcal{F}$-separatedness as the
Johnstone-Sun-shu-Hao-Paseka-Smarda conservative Hausdorff axiom is to the
strong Hausdorff property, and which can be of independent interest. Using
this, we tie up the loose ends of the theory by establishing all the possible
implications between these properties and other $T_1$-type axioms occurring in
the literature. In particular, we show that the strong Hausdorff property does
not imply $\mathcal{F}$-separatedness, a question which remained open and shows
a remarkable difference with its counterpart in the category of topological
spaces.


  Measurements of inclusive jet production are performed in $pp$ and Pb+Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV with the ATLAS detector at the
LHC, corresponding to integrated luminosities of 4.0 $\mathrm{pb}^{-1}$ and
0.14 $\mathrm{nb}^{-1}$, respectively. The jets are identified with the
anti-$k_t$ algorithm with $R=0.4$, and the spectra are measured over the
kinematic range of jet transverse momentum $32 < p_{\mathrm{T}} < 500$ GeV, and
absolute rapidity $|y| < 2.1$ and as a function of collision centrality. The
nuclear modification factor, $R_{\mathrm{AA}}$, is evaluated and jets are found
to be suppressed by approximately a factor of two in central collisions
compared to $pp$ collisions. The $R_{\mathrm{AA}}$ shows a slight increase with
$p_{\mathrm{T}}$ and no significant variation with rapidity.


  Modifying characters of a piece of text to their visual similar ones often
ap-pear in spam in order to fool inspection systems and other conditions, which
we regard as a kind of adversarial attack to neural models. We pro-pose a way
of generating such visual text attack and show that the attacked text are
readable by humans but mislead a neural classifier greatly. We ap-ply a
vision-based model and adversarial training to defense the attack without
losing the ability to understand normal text. Our results also show that visual
attack is extremely sophisticated and diverse, more work needs to be done to
solve this.


  This paper describes the performance of XMM-Newton for serendipitous surveys
and summarises the scope and potential of the XMM-Newton Serendipitous Survey.
The role of the Survey Science Centre (SSC) in the XMM-Newton project is
outlined. The SSC's follow-up and identification programme for the XMM-Newton
serendipitous survey is described together with the presentation of some of the
first results.


  Considering the hypothesis of mixing of three active neutrinos with, at
least, one sterile neutrino, we report on a simple $4\times 4$ texture whose $
3 \times 3 $ part arises from the popular bimaximal texture for three active
neutrinos $ \nu_e, \nu_\mu, \nu_\tau $, where $ c_{12} = 1/\sqrt{2} = s_{12}$,
$ c_{23} = 1/\sqrt{2} = s_{23}$ and $ s_{13} = 0$. Such a $3\times 3 $
bimaximal texture is perturbed through a rotation in the 14 plane, where $\nu_4
$ is the extra neutrino mass state induced by the sterile neutrino $\nu_s $
which becomes responsible for the LSND effect. Then, with $m^2_1\simeq m^2_2$
we predict that $\sin^2 2\theta_{\rm atm} = {1/2}(1+ c^2_{14}) \sim 0.99$ and
$\sin^2 2\theta_{\rm LSND} = {1/2}s^4_{14} \sim 4.5\times10^{-4}$, and in
addition $ \Delta m^2_{\rm atm} = \Delta m^2_{32}$ and $ \Delta m^2_{\rm LSND}
= |\Delta m^2_{41}|$, where $c^2_{14} = \sin^2 2\theta_{\rm sol} \sim 0.97$ and
$\Delta m^2_{21} = \Delta m^2_{\rm sol} \sim 10^{-7} {\rm eV}^2$ if {\it e.g.}
the LOW solar solution is applied. In this four-neutrino texture with $m^2_1
\simeq m^2_2 $ the sum rule $\sin^2 2 \theta_{\rm sol} + {1/2}\sin^2 2
\theta_{\rm Chooz} + \sin^2 2 \theta_{\rm LSND} = 1$ holds in the two-flavor
approximation (for each of three cases), leaving room for the LSND effect,
depending on the magnitude of Chooz effect that, not observed so far, leads (at
present) to the upper bound $\sin^2 2\theta_{\rm LSND}\stackrel{<}{\sim}
1.3\times10^{-3}$ and the lower bound $\sin^2 2\theta_{\rm sol}
\stackrel{>}{\sim} 0.95$. At the end a four-neutrino seesaw mechanism is
sketched.


  Measurement-based quantum computation (MQC) is a leading paradigm for
building a quantum computer. Cluster states being used in this context act as
one-way quantum computers. Here, we consider Z-states as a type of highly
entangled states like cluster states, which can be used for one-way or
measurement based quantum computation. We define Z-state basis as a set of
orthonormal states which are as equally entangled as the cluster states. We
design new quantum circuits to non-destructively discriminate these highly
entangled Z-states. The proposed quantum circuits can be generalized for
N-qubit quantum system. We confirm the preservation of Z-states after the
performance of the circuit by quantum state tomography process.


  This document reports (in French) some achievements performed in the frame of
computational fluid dynamics applied to aerospace applications. Different
physical issues have been tacled out during several studies focusing on
turbulent jets, single phase approach of cryogenic sprays for rocket engines,
flows around complex geometries, and hypersonic entry. For each of the
different application studied a chapter detailed the related issues and the
approach developed. At the end an appraisal for the different topic
investigated is done, and potential directions for future activities proposed.
This document gives also the state-of-the-art for different aerospace
applications in the mid- 2000.


  The Large Scale Structure (LSS) in the galaxy distribution is investigated
using the Sloan Digital Sky Survey Early Data Release (SDSS EDR). Using the
Minimal Spanning Tree technique we have extracted sets of filaments, of
wall-like structures, of galaxy groups, and of rich clusters from this unique
sample. The physical properties of these structures were then measured and
compared with the expectations from Zel'dovich' theory.
  The measured characteristics of galaxy walls were found to be consistent with
those for a spatially flat $\Lambda$CDM cosmological model with
$\Omega_m\approx$ 0.3 and $\Omega_\Lambda \approx$ 0.7, and for Gaussian
initial perturbations with a Harrison -- Zel'dovich power spectrum.
Furthermore, we found that the mass functions of groups and of unrelaxed
structure elements generally fit well with the expectations from Zel'dovich'
theory, although there was some discrepancy for lower mass groups which may be
due to incompleteness in the selected sample of groups. We also note that both
groups and rich clusters tend to prefer the environments of walls, which tend
to be of higher density, rather than the environments of filaments, which tend
to be of lower density.
  Finally, we note evidence of systematic differences in the properties of the
LSS between the Northern Galactic Cap stripe and the Southern Galactic Cap
stripe -- in particular, in the physical properties of the walls, their spatial
distribution, and the relative numbers of clusters embedded in walls. Because
the mean separation of walls is $\approx$ 60 -- 70$h^{-1}$ Mpc, each stripe
only intersects a few tens of walls. Thus, small number statistics and cosmic
variance are the likely drivers of these systematic differences.


  An external magnetic field has been applied in laterally coupled dots (QDs)
and we have studied the QD properties related to charge decoherence. The
significance of the applied magnetic field to the suppression of
electron-phonon relaxation and dephasing rates has been explored. The coupled
QDs have been studied by varing the magnetic field and the interdot distance as
other system parameters. Our numerical results show that the electron
scattering rates are strongly dependent on the applied external magnetic field
and the details of the double QD configuration.


  Recently, it has been observed that the Noether-Gaillard-Zumino (NGZ)
identity holds order by order in $\alpha'$ expansion in nonlinear
electrodynamics theories as Born-Infeld (BI) and Bossard-Nicolai (BN). The
nonlinear electrodynamics theory that couples to an axion field is invariant
under the $SL(2,R)$ duality in all orders of $\alpha'$ expansion in the
Einstein frame. In this paper we show that there are the $SL(2,R)$ invariant
forms of the energy momentum tensors of axion-nonlinear electrodynamics
theories in the Einstein frame. These $SL(2,R)$ invariant structures appear in
the energy momentum tensors of BI and BN theories at all orders of $\alpha'$
expansion. The $SL(2,R)$ symmetry appears in the BI and BN Lagrangians as a
multiplication of Maxwell Lagrangian and a series of $SL(2,R)$ invariant
structures.


  Currently proposed architectures for long-distance quantum communication rely
on networks of quantum processors connected by optical communications channels
[1,2]. The key resource for such networks is the entanglement of matter-based
quantum systems with quantum optical fields for information transmission. The
optical interaction bandwidth of these material systems is a tiny fraction of
that available for optical communication, and the temporal shape of the quantum
optical output pulse is often poorly suited for long-distance transmission.
Here we demonstrate that nonlinear mixing of a quantum light pulse with a
spectrally tailored classical field can compress the quantum pulse by more than
a factor of 100 and flexibly reshape its temporal waveform, while preserving
all quantum properties, including entanglement. Waveform conversion can be used
with heralded arrays of quantum light emitters to enable quantum communication
at the full data rate of optical telecommunications.


  We consider outlier-robust and sparse estimation of linear regression
coefficients, when the covariates and the noises are contaminated by
adversarial outliers and noises are sampled from a heavy-tailed distribution.
Our results present sharper error bounds under weaker assumptions than prior
studies that share similar interests with this study. Our analysis relies on
some sharp concentration inequalities resulting from generic chaining.


  We propose a field theory model for dark energy and dark matter in
interaction. Comparing the classical solutions of the field equations with the
observations of the CMB shift parameter, BAO, lookback time and Gold supernovae
sample, we observe a possible interaction between dark sectors with energy
decay from dark energy into dark matter. The observed interaction provides an
alleviation to the coincidence problem.


  We obtain exact moving and stationary, spatially periodic and localized
solutions of a generalized discrete nonlinear Schr\"odinger equation. More
specifically, we find two different moving periodic wave solutions and a
localized moving pulse solution. We also address the problem of finding exact
stationary solutions and, for a particular case of the model when stationary
solutions can be expressed through the Jacobi elliptic functions, we present a
two-point map from which all possible stationary solutions can be found.
Numerically we demonstrate the generic stability of the stationary pulse
solutions and also the robustness of moving pulses in long-term dynamics.


  An important contribution to the thermoelectric and spin-caloric transport
properties in magnetic materials at elevated temperatures is the formation of a
spin-disordered state due to local moment fluctuations. This effect has not
been largely investigated so far. We focus on various magnetic nanostructures
of CrTe in the form of thin layers or nanowires embedded in ZnTe matrix,
motivated by the miniaturization of spintronics devices and by recent
suggestions that magnetic nanostructures can lead to extraordinary
thermoelectric effects due to quantum confinement. The electronic structure of
the studied systems is calculated within the multiple scattering screened
Korringa-Kohn-Rostoker Green function (KKR-GF) framework. The Monte Carlo
method is used to simulate the magnetization in the temperature induced spin
disorder. The transport properties are evaluated from the transmission
probability obtained using the Baranger-Stone approach within the KKR-GF
framework. We find qualitative and quantitative changes in the thermoelectric
and spin-caloric coefficients when spin-disorder is included in the
calculation. Furthermore, we show that substitutional impurities in CrTe
nanowires could considerably enhance the Seebeck coefficient and the
thermoelectric figure of merit.


  We analyse the photometric and spectroscopic properties of four galaxies in
the epoch of reionisation (EoR) within the SMACS 0723 JWST Early Release
Observations field. Given the known spectroscopic redshifts of these sources,
we investigated the accuracy with which photometric redshifts can be derived
using NIRCam photometry alone, finding that F115W imaging is essential to
distinguish between z~8 galaxies with high equivalent width (EW) [O III]
{\lambda}5007 emission and z~10 Balmer break galaxies. We find that all four
sources exhibit strong (\geq 0.6 mag) F356W-F444W colours, which sit at the
extreme end of theoretical predictions from numerical simulations. We find that
these galaxies deviate (by roughly 0.5 dex) from the local correlation between
[O III] {\lambda}5007/H\beta and [Ne III] {\lambda}3869/[O II], which is
consistent with the predictions from simulations of high-redshift galaxies
having elevated line excitation ratios. We measure the [O III] {\lambda}5007
rest-frame equivalent widths both directly from the spectroscopy, and
indirectly as inferred from the strong F356W-F444W colours, finding large [O
III] {\lambda}5007 EWs of 225-1740 {\AA}. The [O III] {\lambda}5007 and H\beta
EWs are consistent with those seen in extreme, intensely star-forming dwarf
galaxies in the local Universe. Our structural analysis indicates that these
galaxies are resolved, exhibiting irregular shapes with bright clumps. In line
with the predictions from the FLARES hydrodynamic simulations, such intense
star formation and extreme nebular conditions are likely the norm, rather than
the exception, in the EoR.


  Using parton density functions (PDFs) with threshold-resummation improvement,
we consistently calculate higgsino/gaugino and slepton pair production at
next-to-leading order and next-to-leading logarithmic accuracy at the LHC. The
smaller PDF uncertainty of the global PDF sets is exploited with a
factorisation method, which also avoids complications arising in the refitting
of threshold-resummation improved PDF replicas in Mellin space. We explicitly
take into account the reduction of the scale uncertainty due to the
resummation. We show that the resummation contributions in the PDF fits
partially compensate the cross section enhancements induced by those in the
partonic matrix elements.


  We study confining strings in ${\cal{N}}=1$ supersymmetric $SU(N_c)$
Yang-Mills theory in the semiclassical regime on $\mathbb{R}^{1,2} \times
\mathbb{S}^1$. Static quarks are expected to be confined by double strings
composed of two domain walls - which are lines in $\mathbb{R}^2$ - rather than
by a single flux tube. Each domain wall carries part of the quarks'
chromoelectric flux. We numerically study this mechanism and find that
double-string confinement holds for strings of all $N$-alities, except for
those between fundamental quarks. We show that, for $N_c \ge 5$, the two domain
walls confining unit $N$-ality quarks attract and form non-BPS bound states,
collapsing to a single flux line. We determine the $N$-ality dependence of the
string tensions for $2 \le N_c \le 10$. Compared to known scaling laws, we find
a weaker, almost flat $N$-ality dependence, which is qualitatively explained by
the properties of BPS domain walls. We also quantitatively study the behavior
of confining strings upon increasing the $\mathbb{S}^1$ size by including the
effect of virtual "$W$-bosons" and show that the qualitative features of
double-string confinement persist.


  This paper studies multiuser immersive communications networks in which
different user equipment may demand various extended reality (XR) services. In
such heterogeneous networks, time-frequency resource allocation needs to be
more adaptive since XR services are usually multi-modal and latency-sensitive.
To this end, we develop a scalable time-frequency resource allocation method
based on multi-numerology and mini-slot. To appropriately determining the
discrete parameters of multi-numerology and mini-slot for multiuser immersive
communications, the proposed method first presents a novel flexible
time-frequency resource block configuration, then it leverages the deep
reinforcement learning to maximize the total quality-of-experience (QoE) under
different users' QoE constraints. The results confirm the efficiency and
scalability of the proposed time-frequency resource allocation method.


  Tactile sensing on human feet is crucial for motion control, however, has not
been explored in robotic counterparts. This work is dedicated to endowing
tactile sensing to legged robot's feet and showing that a single-legged robot
can be stabilized with only tactile sensing signals from its foot. We propose a
robot leg with a novel vision-based tactile sensing foot system and implement a
processing algorithm to extract contact information for feedback control in
stabilizing tasks. A pipeline to convert images of the foot skin into
high-level contact information using a deep learning framework is presented.
The leg was quantitatively evaluated in a stabilization task on a tilting
surface to show that the tactile foot was able to estimate both the surface
tilting angle and the foot poses. Feasibility and effectiveness of the tactile
system were investigated qualitatively in comparison with conventional
single-legged robotic systems using inertia measurement units (IMU).
Experiments demonstrate the capability of vision-based tactile sensors in
assisting legged robots to maintain stability on unknown terrains and the
potential for regulating more complex motions for humanoid robots.


  This is a brief, non-exhaustive review of Fast Radio Burst (FRB), a new
category of radio transients originating from extragalactic distances. We
discuss the key observational properties known so far and the scientific
applications of FRBs. We summarize the FRB-related research in the French
astrophysics community, and conclude by sharing some insights to the future of
FRB science.


  We investigate the utility of an algorithm for translation lexicon
acquisition (SABLE), used previously on a very large corpus to acquire general
translation lexicons, when that algorithm is applied to a much smaller corpus
to produce candidates for domain-specific translation lexicons.


  Network seeding for efficient information diffusion over time-varying
graphs~(TVGs) is a challenging task with many real-world applications. There
are several ways to model this spatio-temporal influence maximization problem,
but the ultimate goal is to determine the best moment for a node to start the
diffusion process. In this context, we propose Spatio-Temporal Influence
Maximization~(STIM), a model trained with Reinforcement Learning and Graph
Embedding over a set of artificial TVGs that is capable of learning the
temporal behavior and connectivity pattern of each node, allowing it to predict
the best moment to start a diffusion through the TVG. We also develop a special
set of artificial TVGs used for training that simulate a stochastic diffusion
process in TVGs, showing that the STIM network can learn an efficient policy
even over a non-deterministic environment. STIM is also evaluated with a
real-world TVG, where it also manages to efficiently propagate information
through the nodes. Finally, we also show that the STIM model has a time
complexity of $O(|E|)$. STIM, therefore, presents a novel approach for
efficient information diffusion in TVGs, being highly versatile, where one can
change the goal of the model by simply changing the adopted reward function.


  We present a detailed description of the recently proposed numerical
renormalization group method for models of quantum impurities coupled to a
bosonic bath. Specifically, the method is applied to the spin-boson model, both
in the Ohmic and sub-Ohmic cases. We present various results for static as well
as dynamic quantities and discuss details of the numerical implementation,
e.g., the discretization of a bosonic bath with arbitrary continuous spectral
density, the suitable choice of a finite basis in the bosonic Hilbert space,
and questions of convergence w.r.t. truncation parameters. The method is shown
to provide high-accuracy data over the whole range of model parameters and
temperatures, which are in agreement with exact results and other numerical
data from the literature.


  Image light source transfer (LLST), as the most challenging task in the
domain of image relighting, has attracted extensive attention in recent years.
In the latest research, LLST is decomposed three sub-tasks: scene reconversion,
shadow estimation, and image re-rendering, which provides a new paradigm for
image relighting. However, many problems for scene reconversion and shadow
estimation tasks, including uncalibrated feature information and poor semantic
information, are still unresolved, thereby resulting in insufficient feature
representation. In this paper, we propose novel down-sampling feature
self-calibrated block (DFSB) and up-sampling feature self-calibrated block
(UFSB) as the basic blocks of feature encoder and decoder to calibrate feature
representation iteratively because the LLST is similar to the recalibration of
image light source. In addition, we fuse the multi-scale features of the
decoder in scene reconversion task to further explore and exploit more semantic
information, thereby providing more accurate primary scene structure for image
re-rendering. Experimental results in the VIDIT dataset show that the proposed
approach significantly improves the performance for LLST.


  Architecture, size, and shape of glands are most important patterns used by
pathologists for assessment of cancer malignancy in prostate histopathological
tissue slides. Varying structures of glands along with cumbersome manual
observations may result in subjective and inconsistent assessment. Cribriform
gland with irregular border is an important feature in Gleason pattern 4. We
propose using deep neural networks for cribriform pattern classification in
prostate histopathological images. $163708$ Hematoxylin and Eosin (H\&E)
stained images were extracted from histopathologic tissue slides of $19$
patients with prostate cancer and annotated for cribriform patterns. Our
automated image classification system analyses the H\&E images to classify them
as either `Cribriform' or `Non-cribriform'. Our system uses various deep
learning approaches and hand-crafted image pixel intensity-based features. We
present our results for cribriform pattern detection across various parameters
and configuration allowed by our system. The combination of fine-tuned deep
learning models outperformed the state-of-art nuclei feature based methods. Our
image classification system achieved the testing accuracy of $85.93~\pm~7.54$
(cross-validated) and $88.04~\pm~5.63$ ( additional unseen test set) across
three folds. In this paper, we present an annotated cribriform dataset along
with analysis of deep learning models and hand-crafted features for cribriform
pattern detection in prostate histopathological images.


  Isolated, short dispersed pulses of radio emission of unknown origin have
been reported and there is strong interest in wide-field, sensitive searches
for such events. To achieve high sensitivity, large collecting area is needed
and dispersion due to the interstellar medium should be removed. To survey a
large part of the sky in reasonable time, a telescope that forms multiple
simultaneous beams is desirable. We have developed a novel FPGA-based transient
search engine that is suitable for these circumstances. It accepts
short-integration-time spectral power measurements from each beam of the
telescope, performs incoherent de-dispersion simultaneously for each of a wide
range of dispersion measure (DM) values, and automatically searches the
de-dispersed time series for pulse-like events. If the telescope provides
buffering of the raw voltage samples of each beam, then our system can provide
trigger signals to allow data in those buffers to be saved when a tentative
detection occurs; this can be done with a latency of tens of ms, and only the
buffers for beams with detections need to be saved. In one version of our
implementation, intended for the ASKAP array of 36 antennas (currently under
construction in Australia), 36 beams are simultaneously de-dispersed for 448
different DMs with an integration time of 1.0 ms. In the absence of such a
multi-beam telescope, we have built a second version that handles up to 6 beams
at 0.1 ms integration time and 512 DMs. We have deployed and tested this at a
34-m antenna of the Deep Space Network in Goldstone, California. A third
version that processes up to 6 beams at an integration time of 2.0 ms and 1,024
DMs has been built and deployed at the Murchison Widefield Array telescope.


  The chiton Acanthopleura granulata uses aragonitic lenses embedded in its
shell to focus light onto photoreceptors. Because aragonite is biaxially
birefringent, the microstructure of the lens greatly impacts the optical
performance. In addition, the chiton lives in the intertidal, so lenses
experience two environments with different refractive indices: air and water.
Using EBSD, we find that the lens is polycrystalline and contains curved grain
boundaries. A combination of large, twinned grains and nanotwins ensure that
the aragonitic <001> axis is consistent across the lens. However, the
orientation of the <001> axis relative to the shell varies between lenses. Ray
tracing simulations predict the optical performance of lenses of various
microstructures in wet and dry environments. Though twinning helps to limit
birefringence-induced aberrations, variations in the orientation of the <001>
axis between lenses lead to variations in focal lengths between lenses and
cause image doubling in some lenses. As such, the birefringence of aragonite
does not help the lens to transmit focused images in both air and water.


  The contribution of gravitational neutrino oscillations to the solar neutrino
problem is studied by constructing the Dirac Hamiltonian and calculating the
corresponding dynamical phase in the vicinity of the Sun in a non-Riemann
background Kerr space-time with torsion and non-metricity. We show that certain
components of non-metricity and the axial as well as non-axial components of
torsion may contribute to neutrino oscillations. We also note that the rotation
of the Sun may cause a suppression of transitions among neutrinos. However, the
observed solar neutrino deficit could not be explained by any of these effects
because they are of the order of Planck scales.


  We compare the five major sources of corporate Credit Default Swap prices:
GFI, Fenics, Reuters, CMA, and Markit, using the most liquid single name 5-year
CDS in the iTraxx and CDX indexes from 2004 to 2010. Deviations from the common
trend among prices in the different databases are not random but are explained
by idiosyncratic factors, financing costs, global risk, and other trading
factors. The CMA quotes lead the price discovery process. Moreover, we find
that there is not a full agreement among databases in the results of the price
discovery analysis between stock and CDS returns.


  In this work, we calibrate the relationship between Halpha emission and M
dwarf ages. We compile a sample of 892 M dwarfs with Halpha equivalent width
(HaEW) measurements from the literature that are either co-moving with a white
dwarf of known age (21 stars) or in a known young association (871 stars). In
this sample we identify 7 M dwarfs that are new candidate members of known
associations. By dividing the stars into active and inactive categories
according to their HaEW and spectral type (SpT), we find that the fraction of
active dwarfs decreases with increasing age, and the form of the decline
depends on SpT. Using the compiled sample of age-calibrators we find that HaEW
and fractional Halpha luminosity (LHaLbol) decrease with increasing age. HaEW
for SpT<M7 decreases gradually up until ~1Gyr. For older ages, we found only
two early M dwarfs which are both inactive and seem to continue the gradual
decrease. We also found 14 mid-type out of which 11 are inactive and present a
significant decrease of HaEW, suggesting that the magnetic activity decreases
rapidly after ~1Gyr. We fit LHaLbol versus age with a broken power-law and find
an index of -0.11+0.02-0.01 for ages <~776Myr. The index becomes much steeper
at older ages however a lack of field age-calibrators leaves this part of the
relation far less constrained. Finally, from repeated independent measurements
for the same stars we find that 94% of these has a level of HaEW variability
<=5A at young ages (<1Gyr).


  The NVOs core data mining and archive federation activities are heavily
dependent on the underlying data pipeline software necessary to translate the
raw data into scientifically relevant source detections. The data pipeline
software dictates: the raw data storage and retrieval mechanisms, the meaning
and format of the fields in the source catalogs, and the ability of the NVO
users to re-analyze raw data for their own purposes. Increasing the performance
of the core data pipeline software so that it can address the needs of current
and future high data rate surveys is an important activity that should be
addressed in concert with the development of the NVO.


  Multistable non-equilibrium systems are abundant outcomes of nonlinear
dynamics with feedback but still relatively little is known about what
determines the stability of the steady states and their switching rates in
terms of entropy and entropy production. Here, we will link fluctuation
theorems for the entropy production along trajectories with the action
obtainable from the Freidlin--Wentzell theorem to elucidate the thermodynamics
of switching between states in the large volume limit of multistable systems.
We find that the entropy production at steady state plays no role, but the
entropy production during switching is key. Steady-state entropy and diffusive
noise strength can be neglected in this limit. The relevance to biology,
ecological, and climate models is apparent.


  In this paper, we establish uniform asymptotic certainty bands for the
conditional cumulative distribution function. To this aim, we give exact rate
of strong uniform consistency for the local linear estimator of this function.
The corollaries of this result are the asymptotic certainty bands for the
quantiles and the regression function. We illustrate our results with
simulations and an application on fetopathologic data.


  We propose a model that accounts for budding behavior of domains in lipid
bilayers, where each of the bilayer leaflets has a coupling between its local
curvature and local lipid composition. The compositional asymmetry between the
two monolayers leads to an overall spontaneous curvature. The membrane
free-energy contains three contributions: bending energy, line tension, and a
Landau free-energy for a lateral phase separation. Within a mean-field
treatment, we obtain various phase diagrams which contain fully-budded, dimpled
and flat states. In particular, for some range of membrane parameters, the
phase diagrams exhibit a tricritical behavior as well as three-phase
coexistence region. The global phase diagrams can be divided into three types
and are analyzed in terms of the curvature-composition coupling parameter and
domain size.


  This work is dedicated to the study of the Moebius invariant class of
constrained Willmore surfaces and its symmetries. We define a spectral
deformation by the action of a loop of flat metric connections; Baecklund
transformations, by applying a dressing action; and, in 4-space, Darboux
transformations, based on the solution of a Riccati equation. We establish a
permutability between spectral deformation and Baecklund transformation and
prove that non-trivial Darboux transformation of constrained Willmore surfaces
in 4-space can be obtained as a particular case of Baecklund transformation.
All these transformations corresponding to the zero multiplier preserve the
class of Willmore surfaces. We verify that, for special choices of parameters,
both spectral deformation and Baecklund transformation preserve the class of
constrained Willmore surfaces admitting a conserved quantity, and, in
particular, the class of CMC surfaces in 3-dimensional space-form.


  We extend the refined G-structure classification of supersymmetric solutions
of eleven dimensional supergravity. We derive necessary and sufficient
conditions for the existence of an arbitrary number of Killing spinors whose
common isotropy group contains a compact factor acting irreducibly in eight
spatial dimensions and which embeds in
$(Spin(7)\ltimes\mathbb{R}^8)\times\mathbb{R}$. We use these conditions to
explicitly derive the general local bosonic solution of the Killing spinor
equation admitting an N=4 SU(4) structure embedding in a
$(Spin(7)\ltimes\mathbb{R}^8)\times\mathbb{R}$ structure, up to an
eight-manifold of SU(4) holonomy. Subject to very mild assumptions on the form
of the metric, we explicitly derive the general local bosonic solutions of the
Killing spinor equation for N=6 Sp(2) structures and N=8 $SU(2)\times SU(2)$
structures embedding in a $(Spin(7)\ltimes\mathbb{R}^8)\times\mathbb{R}$
structure, again up to eight-manifolds of special holonomy. We construct
several other classes of explicit solutions, including some for which the
preferred local structure group defined by the Killing spinors does not
correspond to any holonomy group in eleven dimensions. We also give a detailed
geometrical characterisation of all supersymmetric spacetimes in eleven
dimensions admitting G-structures with structure groups of the form
$(G\ltimes\mathbb{R}^8)\times\mathbb{R}$.


  A variety of theoretically-sound policy gradient algorithms exist for the
on-policy setting due to the policy gradient theorem, which provides a
simplified form for the gradient. The off-policy setting, however, has been
less clear due to the existence of multiple objectives and the lack of an
explicit off-policy policy gradient theorem. In this work, we unify these
objectives into one off-policy objective, and provide a policy gradient theorem
for this unified objective. The derivation involves emphatic weightings and
interest functions. We show multiple strategies to approximate the gradients,
in an algorithm called Actor Critic with Emphatic weightings (ACE). We prove in
a counterexample that previous (semi-gradient) off-policy actor-critic
methods--particularly Off-Policy Actor-Critic (OffPAC) and Deterministic Policy
Gradient (DPG)--converge to the wrong solution whereas ACE finds the optimal
solution. We also highlight why these semi-gradient approaches can still
perform well in practice, suggesting strategies for variance reduction in ACE.
We empirically study several variants of ACE on two classic control
environments and an image-based environment designed to illustrate the
tradeoffs made by each gradient approximation. We find that by approximating
the emphatic weightings directly, ACE performs as well as or better than OffPAC
in all settings tested.


  In this article we derive rigorously amplitude equations for stochastic PDEs
with quadratic nonlinearities, under the assumption that the noise acts only on
the stable modes and for an appropriate scaling between the distance from
bifurcation and the strength of the noise. We show that, due to the presence of
two distinct timescales in our system, the noise (which acts only on the fast
modes) gets transmitted to the slow modes and, as a result, the amplitude
equation contains both additive and multiplicative noise.
  As an application we study the case of the one dimensional Burgers equation
forced by additive noise in the orthogonal subspace to its dominant modes. The
theory developed in the present article thus allows to explain theoretically
some recent numerical observations from [Rob03].


  The Casimir densities are investigated for a massive spinor field in de
Sitter spacetime with an arbitrary number of toroidally compactified spatial
dimensions. The vacuum expectation value of the energy-momentum tensor is
presented in the form of the sum of corresponding quantity in the
uncompactified de Sitter spacetime and the part induced by the non-trivial
topology. The latter is finite and the renormalization is needed for the first
part only. The asymptotic behavior of the topological term is investigated in
the early and late stages of the cosmological expansion. When the comoving
lengths of the compactified dimensions are much smaller than the de Sitter
curvature radius, to the leading order the topological part coincides with the
corresponding quantity for a massless fermionic field and is conformally
related to the corresponding flat spacetime result with the same topology. In
this limit the topological term dominates the uncompactified de Sitter part and
the back-reaction effects should be taken into account. In the opposite limit,
for a massive field the asymptotic behavior of the topological part is damping
oscillatory.


  We give an alternate proof of Schnyder's Theorem, that the incidence poset of
a graph $G$ has dimension at most three if and only if $G$ is planar.


  In this paper we present a comprehensive analysis of the inclusive heavy
quark photoproduction in $pp$, $pPb$ and $PbPb$ collisions at Run 2 LHC
energies using the Color Dipole formalism. The rapidity distributions and total
cross sections for the charm and bottom production are estimated considering
the more recent phenomenological models for the dipole - proton scattering
amplitude, which are based on the Color Glass Condensate formalism and are able
to describe the inclusive and exclusive $ep$ HERA data. Moreover, we present,
by the first time, the predictions for the transverse momentum distributions of
the $D$ and $B$ mesons produced in the photon -- induced interactions.


  We report an unexpectedly strong and complex chemical bonding of rare-gas
atoms to neutral gold clusters. The bonding features are consistently
reproduced at different levels of approximation within density-functional
theory and beyond: from GGA, through hybrid and double-hybrid functionals, up
to renormalized second-order perturbation theory. The main finding is that the
adsorption of Ar, Kr, and Xe reduces electron-electron repulsion within gold
dimer, causing strengthening of the Au-Au bond. Differently from the dimer, the
rare-gas adsorption effects on the gold trimer's geometry and vibrational
frequencies are mainly due to electron occupation of the trimer's lowest
unoccupied molecular orbital. For the trimer, the theoretical results are also
consistent with far-infrared multiple photon dissociation experiments.


  Federated learning (FL) is typically performed in a synchronous parallel
manner, where the involvement of a slow client delays a training iteration.
Current FL systems employ a participant selection strategy to select fast
clients with quality data in each iteration. However, this is not always
possible in practice, and the selection strategy often has to navigate an
unpleasant trade-off between the speed and the data quality of clients.
  In this paper, we present Pisces, an asynchronous FL system with intelligent
participant selection and model aggregation for accelerated training. To avoid
incurring excessive resource cost and stale training computation, Pisces uses a
novel scoring mechanism to identify suitable clients to participate in a
training iteration. It also adapts the pace of model aggregation to dynamically
bound the progress gap between the selected clients and the server, with a
provable convergence guarantee in a smooth non-convex setting. We have
implemented Pisces in an open-source FL platform called Plato, and evaluated
its performance in large-scale experiments with popular vision and language
models. Pisces outperforms the state-of-the-art synchronous and asynchronous
schemes, accelerating the time-to-accuracy by up to 2.0x and 1.9x,
respectively.


  In this paper we propose an estimator of spot covariance matrix which ensure
symmetric positive semi-definite estimations. The proposed estimator relies on
a suitable modification of the Fourier covariance estimator in Malliavin and
Mancino (2009) and it is consistent for suitable choices of the weighting
kernel. The accuracy and the ability of the estimator to produce positive
semi-definite covariance matrices is evaluated with an extensive numerical
study, in comparison with the competitors present in the literature. The
results of the simulation study are confirmed under many scenarios, that
consider the dimensionality of the problem, the asynchronicity of data and the
presence of several specification of market microstructure noise.


  We focus on multi-domain Neural Machine Translation, with the goal of
developing efficient models which can handle data from various domains seen
during training and are robust to domains unseen during training. We
hypothesize that Sparse Mixture-of-Experts (SMoE) models are a good fit for
this task, as they enable efficient model scaling, which helps to accommodate a
variety of multi-domain data, and allow flexible sharing of parameters between
domains, potentially enabling knowledge transfer between similar domains and
limiting negative transfer. We conduct a series of experiments aimed at
validating the utility of SMoE for the multi-domain scenario, and find that a
straightforward width scaling of Transformer is a simpler and surprisingly more
efficient approach in practice, and reaches the same performance level as SMoE.
We also search for a better recipe for robustness of multi-domain systems,
highlighting the importance of mixing-in a generic domain, i.e. Paracrawl, and
introducing a simple technique, domain randomization.


  We perform, in a manifestly $SO(n-1,1)$ [$SO(n)$] covariant fashion, the
Hamiltonian analysis of general relativity in $n$ dimensions written as a
constrained $BF$ theory. We solve the constraint on the $B$ field in a way
naturally adapted to the foliation of the spacetime that avoids explicitly the
introduction of the vielbein. This leads to a form of the action involving a
presymplectic structure, which is reduced by doing a suitable parametrization
of the connection and then, after integrating out some auxiliary fields, the
Hamiltonian form involving only first-class constraints is obtained.


  It is usually hard for a learning system to predict correctly on rare events
that never occur in the training data, and there is no exception for
segmentation algorithms. Meanwhile, manual inspection of each case to locate
the failures becomes infeasible due to the trend of large data scale and
limited human resource. Therefore, we build an alarm system that will set off
alerts when the segmentation result is possibly unsatisfactory, assuming no
corresponding ground truth mask is provided. One plausible solution is to
project the segmentation results into a low dimensional feature space; then
learn classifiers/regressors to predict their qualities. Motivated by this, in
this paper, we learn a feature space using the shape information which is a
strong prior shared among different datasets and robust to the appearance
variation of input data.The shape feature is captured using a Variational
Auto-Encoder (VAE) network that trained with only the ground truth masks.
During testing, the segmentation results with bad shapes shall not fit the
shape prior well, resulting in large loss values. Thus, the VAE is able to
evaluate the quality of segmentation result on unseen data, without using
ground truth. Finally, we learn a regressor in the one-dimensional feature
space to predict the qualities of segmentation results. Our alarm system is
evaluated on several recent state-of-art segmentation algorithms for 3D medical
segmentation tasks. Compared with other standard quality assessment methods,
our system consistently provides more reliable prediction on the qualities of
segmentation results.


  In this paper, we use the linear deterministic approximation model to study a
two user multiple access channel mutually interfering with a point to point
link, which represents a basic setup of a cellular system. We derive outer
bounds on the achievable sum rate and construct coding schemes achieving the
outer bounds. For a large parameter range, the sum capacity is identical to the
sum capacity of the interference channel obtained by silencing the weaker user
in the multiple access channel. For other interference configurations, the sum
rate can be increased using interference alignment, which exploits the channel
gain difference of the users in the multiple access channel. From these
results, lower bounds on the generalized degrees of freedom for the Gaussian
counterpart are derived.


  Quantum dots realized in InAs are versatile systems to study the effect of
spin-orbit interaction on the spin coherence, as well as the possibility to
manipulate single spins using an electric field. We present transport
measurements on quantum dots realized in InAs nanowires. Lithographically
defined top-gates are used to locally deplete the nanowire and to form
tunneling barriers. By using three gates, we can form either single quantum
dots, or two quantum dots in series along the nanowire. Measurements of the
stability diagrams for both cases show that this method is suitable for
producing high quality quantum dots in InAs.


  The largest geomagnetic storm so far in the solar cycle 24 was produced by a
fast coronal mass ejection (CME) originating on 2015 March 15. It was an
initially west-oriented CME and expected to only cause a weak geomagnetic
disturbance. Why did this CME finally cause such a large geomagnetic storm? We
try to find some clues by investigating its propagation from the Sun to 1 AU.
First, we reconstruct the CME's kinematic properties in the corona from the
SOHO and SDO imaging data with the aid of the graduated cylindrical shell (GCS)
model. It is suggested that the CME propagated to the west
$\sim$$33^\circ$$\pm$$10^\circ$ away from the Sun-Earth line with a speed of
about 817 km s$^{-1}$ before leaving the field of view of the SOHO/LASCO C3
camera. A magnetic cloud (MC) corresponding to this CME was measured in-situ by
the Wind spacecraft two days later. By applying two MC reconstruction methods,
we infer the configuration of the MC as well as some kinematic information,
which implies that the CME possibly experienced an eastward deflection on its
way to 1 AU. However, due to the lack of observations from the STEREO
spacecraft, the CME's kinematic evolution in interplanetary space is not clear.
In order to fill this gap, we utilize numerical MHD simulation, drag-based CME
propagation model (DBM) and the model for CME deflection in interplanetary
space (DIPS) to recover the propagation process, especially the trajectory, of
the CME from $30 R_S$ to 1 AU. It is suggested that the trajectory of the CME
was deflected toward the Earth by about $12^\circ$, consistent with the
implication from the MC reconstruction at 1 AU. This eastward deflection
probably contributed to the CME's unexpected geoeffectiveness by pushing the
center of the initially west-oriented CME closer to the Earth.


  We study the effect of crystal field anisotropy in the underscreened $S=1$
Kondo lattice model. Starting from the two orbital Anderson lattice model and
including a local anisotropy term, we show, through Schrieffer-Wolff
transformation, that local anisotropy is equivalent to an anisotropic Kondo
interaction ($J_{\parallel} \neq{J_{\perp}}$). The competition and coexistence
between ferromagnetism and Kondo effect in this effective model is studied
within a generalized mean-field approximation. Several regimes are obtained,
depending on the parameters, exhibiting or not coexistence of magnetic order
and Kondo effect. Particularly, we show that a re-entrant Kondo phase at low
temperature can be obtained. We are also able to describe phases where the
Kondo temperature is smaller than the Curie temperature ($T_K<T_C$). We propose
that some aspects of uranium and neptunium compounds that present coexistence
of Kondo effect and ferromagnetism, can be understood within this model.


  In this paper we design and prove correct a fully dynamic distributed
algorithm for maintaining an approximate Steiner tree that connects via a
minimum-weight spanning tree a subset of nodes of a network (referred as
Steiner members or Steiner group) . Steiner trees are good candidates to
efficiently implement communication primitives such as publish/subscribe or
multicast, essential building blocks for the new emergent networks (e.g. P2P,
sensor or adhoc networks). The cost of the solution returned by our algorithm
is at most $\log |S|$ times the cost of an optimal solution, where $S$ is the
group of members. Our algorithm improves over existing solutions in several
ways. First, it tolerates the dynamism of both the group members and the
network. Next, our algorithm is self-stabilizing, that is, it copes with nodes
memory corruption. Last but not least, our algorithm is
\emph{superstabilizing}. That is, while converging to a correct configuration
(i.e., a Steiner tree) after a modification of the network, it keeps offering
the Steiner tree service during the stabilization time to all members that have
not been affected by this modification.


  We have examined the effect of the decoherence in the Ekert91 quantum
cryptographic protocol. In order to explore this issue we have introduced two
major decoherences, the depolarizing channel and the generalized amplitude
damping, between the singlet source and one of the legitimate users. It is
shown that the depolarizing channel disentangles the quantum channel more
easily than the generalized amplitude damping. This fact indicates that the
Ekert protocol is more robust to the generalized amplitude damping. We also
have computed the Bell inequality to check the robustness or weakness of the
Ekert91 protocol. Computation of the Bell inequality also confirms the
robustness of the Ekert91 protocol to the generalized amplitude damping
compared to the depolarizing channel.


  In this paper we give a Casimir Invariant for the Symmetric group $S_n$.
Furthermore we obtain and present, for the first time in the literature,
explicit formulas for the matrices of the standard representation in terms of
the matrices of the permutation representation.


  Control modular addition is a core arithmetic function, and we must consider
the computational cost for actual quantum computers to realize efficient
implementation. To achieve a low computational cost in a control modular adder,
we focus on minimizing KQ, defined by the product of the number of qubits and
the depth of the circuit. In this paper, we construct an efficient control
modular adder with small KQ by using relative-phase Toffoli gates in two major
types of quantum computers: Fault-Tolerant Quantum Computers (FTQ) on the
Logical layer and Noisy Intermediate-Scale Quantum Computers (NISQ). We give a
more efficient construction compared to Van Meter and Itoh's, based on a
carry-lookahead adder. In FTQ, $T$ gates incur heavy cost due to distillation,
which fabricates ancilla for running $T$ gates with high accuracy but consumes
a lot of specially prepared ancilla qubits and a lot of time. Thus, we must
reduce the number of $T$ gates. We propose a new control modular adder that
uses only 20% of the number of $T$ gates of the original. Moreover, when we
take distillation into consideration, we find that we minimize $\text{KQ}_{T}$
(the product of the number of qubits and $T$-depth) by running $\Theta\left(n /
\sqrt{\log n} \right)$ $T$ gates simultaneously. In NISQ, CNOT gates are the
major error source. We propose a new control modular adder that uses only 35%
of the number of CNOT gates of the original. Moreover, we show that the
$\text{KQ}_{\text{CX}}$ (the product of the number of qubits and CNOT-depth) of
our circuit is 38% of the original. Thus, we realize an efficient control
modular adder, improving prospects for the efficient execution of arithmetic in
quantum computers.


  Let $(M^m,g_M)$ be a closed, connected manifold with positive scalar
curvature and $(T^k,g)$ some flat $k$-Torus of unit volume. By a result of F.
Dobarro and E. Lami Dozo, there exists a unique $f: M \rightarrow
\mathbf{R}_{>0}$ such that the warped product $M\times_f T^k$ has constant
scalar curvature and unit volume. We study the Yamabe equation on these spaces.
We use techniques from bifurcation theory, along with spectral theory for
warped products, to prove multiplicity results for the Yamabe problem.


  The classical Minkowski problem for convex bodies has deeply influenced the
development of differential geometry. During the past several decades, abundant
mathematical theories have been developed for studying the solutions of the
Minkowski problem, however, the numerical solution of this problem has been
largely left behind, with only few methods available to achieve that goal. In
this article, focusing on the two-dimensional Minkowski problem with Dirichlet
boundary conditions, we introduce two solution methods, both based on
operator-splitting. One of these two methods deals directly with the Dirichlet
condition, while the other method uses an approximation of this Dirichlet
condition. This relaxation of the Dirichlet condition makes this second method
better suited than the first one to treat those situations where the Minkowski
and the Dirichlet condition are not compatible. Both methods are
generalizations of the solution method for the canonical Monge-Amp\`{e}re
equation discussed by Glowinski et al. (Journal of Scientific Computing, 79(1),
1-47, 2019); as such they take advantage of a divergence formulation of the
Minkowski problem, well-suited to a mixed finite element approximation, and to
the the time-discretization via an operator-splitting scheme, of an associated
initial value problem. Our methodology can be easily implemented on convex
domains of rather general shape (with curved boundaries, possibly). The
numerical experiments we performed validate both methods and show that if one
uses continuous piecewise affine finite element approximations of the smooth
solution of the Minkowski problem and of its three second order derivatives,
these two methods provide nearly second order accuracy for the $L^2$ and
$L^{\infty}$ error. One can extend easily the methods discussed in this
article, to address the solution of three-dimensional Minkowski problem.


  Dry-snow slab avalanches are considered to be the most difficult to predict,
yet the deadliest avalanche types. The release of snow slab avalanches starts
with a initial failure in a weak layer that may propagate across the slope
until the slab fractures and slides. The evaluation of crack propagation area
is a primary concern for avalanche forecasters. The purpose of this study is to
test the hypothesis that the heterogeneity of snowpack properties is one of the
primary factors that may potentially stop dynamic crack propagation. To test
this assumption, we use a depth-averaged Material Point Method (DA-MPM) for
efficient elasto-plastic modeling of snow slab avalanches. Our analysis
includes scenarios involving i) pure-elastic slabs and ii) elasto-plastic
slabs. In the first scenario, we report a significant decrease in slab tensile
stress with increasing crack speed compared to quasi-static theory. In
addition, we quantify the effect of weak layer heterogeneity and softening
fracture energy on the crack stopping mechanism. In the second scenario, we
analyse the interplay between weak layer heterogeneity and slab tensile
fracture and quantify their combined effect on crack arrest. Results are
interpreted through a scaling law relating the crack arrest distance to two
dimensionless numbers related to weak layer strength variability and slab
tensile fracture. Furthermore, the proposed model is applied to field campaigns
in which spatial variations of weak layer shear strength were measured.
Finally, DA-MPM simulations are performed on three-dimensional terrain with
spatial variations revealing interesting release patterns. This research and
the proposed methods can not only enhance our comprehension of the factors
influencing avalanche release sizes,and possibly, the design of new mitigation
measures for avalanche start zones.


  We formulate the locally supersymmetric E$_{7(7)}$ exceptional field theory
in a $(4+56|32)$ dimensional superspace, corresponding to a 4D $N\!=\!8$
"external" superspace augmented with an "internal" 56-dimensional space. This
entails the unification of external diffeomorphisms and local supersymmetry
transformations into superdiffeomorphisms. The solutions to the superspace
Bianchi identities lead to on-shell duality equations for the $p$-form field
strengths for $p\leq 4$. The reduction to component fields provides a complete
description of the on-shell supersymmetric theory. As an application of our
results, we perform a generalized Scherk-Schwarz reduction and obtain the
superspace formulation of maximal gauged supergravity in four dimensions
parametrized by an embedding tensor.


  The trade-off between regret and computational cost is a fundamental problem
for online kernel regression, and previous algorithms worked on the trade-off
can not keep optimal regret bounds at a sublinear computational complexity. In
this paper, we propose two new algorithms, AOGD-ALD and NONS-ALD, which can
keep nearly optimal regret bounds at a sublinear computational complexity, and
give sufficient conditions under which our algorithms work. Both algorithms
dynamically maintain a group of nearly orthogonal basis used to approximate the
kernel mapping, and keep nearly optimal regret bounds by controlling the
approximate error. The number of basis depends on the approximate error and the
decay rate of eigenvalues of the kernel matrix. If the eigenvalues decay
exponentially, then AOGD-ALD and NONS-ALD separately achieves a regret of
$O(\sqrt{L(f)})$ and $O(\mathrm{d}_{\mathrm{eff}}(\mu)\ln{T})$ at a
computational complexity in $O(\ln^2{T})$. If the eigenvalues decay
polynomially with degree $p\geq 1$, then our algorithms keep the same regret
bounds at a computational complexity in $o(T)$ in the case of $p>4$ and $p\geq
10$, respectively. $L(f)$ is the cumulative losses of $f$ and
$\mathrm{d}_{\mathrm{eff}}(\mu)$ is the effective dimension of the problem. The
two regret bounds are nearly optimal and are not comparable.


  Recent measurements of deuterium abundances from QSO absorption spectra show
two conflicting numbers, which differ by an order of magnitude. Allowing the
neutrino degeneracy together with gravitational constant variation at the epoch
of primordial nucleosynthesis, the implication of these observations on the
^6Li, ^9Be and ^11B abundances will be discussed. Within the permitted ranges
consistent with D, ^4He and ^7Li, we observe the strong \eta dependence of ^11B
as in SBBN but no significant dependence of ^6Li and ^9Be on the baryon number
density is observed. The predictions of ^6Li and ^9Be for low and high
deuterium differ by an order of magnitude and predictions for ^11B differ by
several orders of magnitude at most and vary with \eta.


  Large Language Models (LLMs) have been found to have difficulty knowing they
do not possess certain knowledge and tend to provide specious answers in such
cases. Retrieval Augmentation (RA) has been extensively studied to mitigate
LLMs' hallucinations. However, due to the extra overhead and unassured quality
of retrieval, it may not be optimal to conduct RA all the time. A
straightforward idea is to only conduct retrieval when LLMs are uncertain about
a question. This motivates us to enhance the LLMs' ability to perceive their
knowledge boundaries to help RA. In this paper, we first quantitatively measure
LLMs' such ability and confirm their overconfidence. Then, we study how LLMs'
certainty about a question correlates with their dependence on external
retrieved information. We propose several methods to enhance LLMs' perception
of knowledge boundaries and show that they are effective in reducing
overconfidence. Additionally, equipped with these methods, LLMs can achieve
comparable or even better performance of RA with much fewer retrieval calls.


  In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are
scrambled sets. Suppose that a group $G$ acts geometrically (i.e. properly and
cocompactly by isometries) on a CAT(0) space $X$. (Such group $G$ is called a
{\it CAT(0) group}.) Then the group $G$ acts by homeomorphisms on the boundary
$\partial X$ of $X$ and we can define a metric $d_{\partial X}$ on the boundary
$\partial X$. The boundary $\partial X$ is called a {\it scrambled set} if for
any $\alpha,\beta\in\partial X$ with $\alpha\neq\beta$, (1)
$\limsup\{d_{\partial X}(g\alpha,g\beta) | g\in G\}>0$ and (2)
$\liminf\{d_{\partial X}(g\alpha,g\beta) | g\in G\}=0$. We investigate when are
boundaries of CAT(0) groups (and Coxeter groups) scrambled sets.


  What is the impact of COVID-19 on South Africa? This paper envisages
assisting researchers and decision-makers in battling the COVID-19 pandemic
focusing on South Africa. This paper focuses on the spread of the disease by
applying heatmap retrieval of hotspot areas and spatial analysis is carried out
using the Moran index. For capturing spatial autocorrelation between the
provinces of South Africa, the adjacent, as well as the geographical distance
measures, are used as a weight matrix for both absolute and relative counts.
Furthermore, generalized logistic growth curve modeling is used for the
prediction of the COVID-19 spread. We expect this data-driven modeling to
provide some insights into hotspot identification and timeous action
controlling the spread of the virus.


  Using integral transforms to the end of lines detection in images with
complex background, makes the detection a hard task needing additional
processing to manage the detection. As an integral transform, the Scale Space
Radon Transform (SSRT) suffers from such drawbacks, even with its great
abilities for thick lines detection. In this work, we propose a method to
address this issue for automatic detection of thick linear structures in gray
scale and binary images using the SSRT, whatever the image background content.
This method involves the calculated Hessian orientations of the investigated
image while computing its SSRT, in such a way that linear structures are
emphasized in the SSRT space. As a consequence, the subsequent maxima detection
in the SSRT space is done on a modified transform space freed from unwanted
parts and, consequently, from irrelevant peaks that usually drown the peaks
representing lines. Besides, highlighting the linear structure in the SSRT
space permitting, thus, to efficiently detect lines of different thickness in
synthetic and real images, the experiments show also the method robustness
against noise and complex background.


  The transition from a non-equilibrium state to an equilibrium state is
characterized not only by the disappearance of the entropy production, but
mainly by the disappearance of the organized currents, due to the gradients
present in a non-equilibrium system. Their disappearance is necessary to obtain
maximum entropy in the equilibrium state.


  The vertex expansion of the graph is a fundamental graph parameter. Given a
graph $G=(V,E)$ and a parameter $\delta \in (0,1/2]$, its $\delta$-Small-Set
Vertex Expansion (SSVE) is defined as \[ \min_{S : |S| = \delta |V|}
\frac{|{\partial^V(S)}|}{ \min \{ |S|, |S^c| \} } \] where $\partial^V(S)$ is
the vertex boundary of a set $S$. The SSVE~problem, in addition to being of
independent interest as a natural graph partitioning problem, is also of
interest due to its connections to the Strong Unique Games problem. We give a
randomized algorithm running in time $n^{{\sf poly}(1/\delta)}$, which outputs
a set $S$ of size $\Theta(\delta n)$, having vertex expansion at most \[
\max\left(O(\sqrt{\phi^* \log d \log (1/\delta)}) ,
\tilde{O}(d\log^2(1/\delta)) \cdot \phi^* \right), \] where $d$ is the largest
vertex degree of the graph, and $\phi^*$ is the optimal $\delta$-SSVE. The
previous best-known guarantees for this were the bi-criteria bounds of
$\tilde{O}(1/\delta)\sqrt{\phi^* \log d}$ and $\tilde{O}(1/\delta)\phi^*
\sqrt{\log n}$ due to Louis-Makarychev [TOC'16].
  Our algorithm uses the basic SDP relaxation of the problem augmented with
${\rm poly}(1/\delta)$ rounds of the Lasserre/SoS hierarchy. Our rounding
algorithm is a combination of the rounding algorithms of Raghavendra-Tan
[SODA'12] and Austrin-Benabbas-Georgiou [SODA'13]. A key component of our
analysis is novel Gaussian rounding lemma for hyperedges which might be of
independent interest.


  We report on the epitaxial strain-driven electronic and antiferromagnetic
modulations of a pseudospin-half square lattice realized in superlattices of
(SrIrO3)1/(SrTiO3)1. With increasing compressive strain, we find the
low-temperature insulating behavior to be strongly suppressed with a
corresponding systematic reduction of both the Neel temperature and the
staggered moment. However, despite such a suppression, the system remains
weakly insulating above the Neel transition. The emergence of metallicity is
observed under large compressive strain but only at temperatures far above the
N\'eel transition. These behaviors are characteristics of the Slater-Mott
crossover regime, providing a unique experimental model system of the spin-half
Hubbard Hamiltonian with a tunable intermediate coupling strength.


  Similar to linear spaces, many examples of quasilinear spaces have a notion
of multiplication of the elements. To characterising these examples, in the
present paper we generalize the notion of quasilinear spaces and introduce
quasi-algebras and normed quasi-algebras with the help of what was done in
constructing algebras. After examining some properties of these new spaces, we
introduce the concept of quasi-homomorphisms that is an instance of a
quasilinear operator. Moreover since the study of spaces with algebraic
structures cannot be completed without the study of spectrums, we define the
concept of quasi-spectrum on quasi-algebras as we expect it to be.


  This paper considers a general framework for the study of the existence of
quasi-variational and variational solutions to a class of nonlinear evolution
systems in convex sets of Banach spaces describing constraints on a linear
combination of partial derivatives of the solutions. The quasi-linear operators
are of monotone type, but are not required to be coercive for the existence of
weak solutions, which is obtained by a double penalisation/regularisation for
the approximation of the solutions. In the case of time-dependent convex sets
that are independent of the solution, we show also the uniqueness and the
continuous dependence of the strong solutions of the variational inequalities,
extending previous results to a more general framework.


  We show that the isomorphism class of a two-step solvable Lie poset
subalgebra of a semisimple Lie algebra is determined by its dimension. We
further establish that all such algebras are absolutely rigid.


  A deep understanding of the dynamics of the human nervous system requires the
simultaneous study of multiple spatiotemporal scales from the level of
neurotransmitters up to the level of human cultures. This is likely impossible
for technical and ethical reasons. Piecemeal analysis provides some
understanding of the dynamics at single levels, but this does not illuminate
the interactions between levels which are, at the very least, of great
importance clinically. It would be useful to have an accessible biological
system which could serve as a proxy for the nervous system and from which
useful insights might be obtained. Functional homologies between the nervous
system and collective intelligence systems, in particular social insect
colonies, are described. It is proposed that social insects colonies could
serve as functional proxies for nervous systems. Thus a multiscale study of
social insect colonies may provide insights into the dynamics of nervous
systems.


  As an alternative to the well-known methods of "chaining" and "bracketing"
that have been developed in the study of random fields, a new method, which is
based on a stochastic maximal inequality derived by using It\^o's formula and
on a new concept named strict countability, is presented. The main results are
some weak convergence theorems for sequences of separable random fields of
locally square-integrable martingales under the uniform topology with the help
also of entropy methods. As special cases, some new results for i.i.d. random
sequences, including a new Donsker theorem and a moment bound for suprema of
empirical processes indexed by classes of sets or functions, are obtained. An
application to statistical estimation in semiparametric models is presented
with an illustration to construct adaptive estimators in Cox's regression
model.


  The fragmentation of spin-orbit coupled spin-1 Bose gas with a weak
interaction in external harmonic trap is explored by both exact diagonalization
and mean-field theory. This fragmentation tendency, which originates from the
total angular momentum conservation, is affected obviously by the spin-orbit
coupling strength and the spin-dependent interaction. Strong spin-orbit
interaction raises the inverse participation ratio, which describes the number
of significantly occupied single-particle states. As the spin-dependent
interaction changes from anti-ferromagnetic to ferromagnetic, the peak values
in the inverse participation ratio become lower. Without the confinement of the
appointed total angular momentum, the condensate chooses a zero or finite total
angular momentum ground state, which is determined by both the interaction and
the spin-orbit coupling strength.