  A numerical approach to disordered 2D superconductors described by BCS mean
field theory is outlined. The energy gap and the superfluid density at zero
temperature and the quasiparticle density of states are studied. The method
involves approximate self-consistent solutions of the Bogolubov-de$\,$Gennes
equations on finite square lattices. Where comparison is possible, the results
of standard analytic approaches to this problem are reproduced. Detailed
modeling of impurity effects is practical using this approach. The {\it range}
of the impurity potential is shown to be of {\it quantitative importance} in
the case of strong potential scatterers. We discuss the implications for
experiments, such as the rapid suppression of superconductivity by Zn doping in
Copper-Oxide superconductors.


  Edge Computing in 5G and Beyond is a promising solution for ultra-low latency
applications (e.g. Autonomous Vehicle, Augmented Reality, and Remote Surgery),
which have an extraordinarily low tolerance for the delay and require fast data
processing for a very high volume of data. The requirements of delay-sensitive
applications (e.g. Low latency, proximity, and Location/Context-awareness)
cannot be satisfied by Cloud Computing due to the high latency between User
Equipment and Cloud. Nevertheless, Edge Computing in 5G and beyond can promise
an ultra-high-speed caused by placing computation capabilities closer to
endpoint devices, whereas 5G encourages the speed rate that is 200 times faster
than 4G LTE-Advanced. This paper deeply investigates Edge Computing in 5G and
characterizes it based on the requirements of ultra-low latency applications.
As a contribution, we propose a hybrid architecture that takes advantage of
novel and sustainable technologies (e.g. D2D communication, Massive MIMO, SDN,
and NFV) and has major features such as scalability, reliability and ultra-low
latency support. The proposed architecture is evaluated based on an agent-based
simulation that demonstrates it can satisfy requirements and has the ability to
respond to high volume demands with low latency.


  Nowadays, as the ever-increasing demand for more powerful computing resources
continues, alternative advanced computing paradigms are under extensive
investigation. Significant effort has been made to deviate from conventional
Von Neumann architectures. In-memory computing has emerged in the field of
electronics as a possible solution to the infamous bottleneck between memory
and computing processors, which reduces the effective throughput of data. In
photonics, novel schemes attempt to collocate the computing processor and
memory in a single device. Photonics offers the flexibility of multiplexing
streams of data not only spatially and in time, but also in frequency or,
equivalently, in wavelength, which makes it highly suitable for parallel
computing. Here, we numerically show the use of time and wavelength division
multiplexing (WDM) to solve four independent tasks at the same time in a single
photonic chip, serving as a proof of concept for our proposal. The system is a
time-delay reservoir computing (TDRC) based on a microring resonator (MRR). The
addressed tasks cover different applications: Time-series prediction, waveform
signal classification, wireless channel equalization, and radar signal
prediction. The system is also tested for simultaneous computing of up to 10
instances of the same task, exhibiting excellent performance. The footprint of
the system is reduced by using time-division multiplexing of the nodes that act
as the neurons of the studied neural network scheme. WDM is used for the
parallelization of wavelength channels, each addressing a single task. By
adjusting the input power and frequency of each optical channel, we can achieve
levels of performance for each of the tasks that are comparable to those quoted
in state-of-the-art reports focusing on single-task operation...


  This paper proposes a novel neural-network-based adaptive hybrid-reflectance
three-dimensional (3-D) surface reconstruction model. The neural network
combines the diffuse and specular components into a hybrid model. The proposed
model considers the characteristics of each point and the variant albedo to
prevent the reconstructed surface from being distorted. The neural network
inputs are the pixel values of the two-dimensional images to be reconstructed.
The normal vectors of the surface can then be obtained from the output of the
neural network after supervised learning, where the illuminant direction does
not have to be known in advance. Finally, the obtained normal vectors can be
applied to integration method when reconstructing 3-D objects. Facial images
were used for training in the proposed approach


  We study non-isothermal diffusive transport of a weakly-soluble two-component
substance in a liquid-saturated porous medium being in contact with the
reservoir of this substance. Particular attention is given to the example case
of infiltration of nitrogen and oxygen from the atmosphere under the annual
temperature oscillation. The surface temperature of the porous medium
half-space oscillates in time, which results in a decaying solubility wave
propagating deep into the porous medium. In such a system, the zones of
saturated solution and nondissolved phase coexist with the zones of
undersaturated solution; these zones migrate with time. Moreover, the
solubility of a multicomponent substance depends on its composition, which
results in a much more intricate mathematical model of solubility as compared
to the single-component case. We describe the phenomenon of formation of a
near-surface bubbly horizon due to the temperature oscillation. An analytical
theory of the phenomenon is developed. For multicomponent solutions we report
the formation of diffusion boundary layer, which is not possible for
single-component solutions. We construct an analytical theory for this boundary
layer; in particular, we derive effective boundary conditions for the problem
of the diffusive transport beyond this layer.


  Chemical equilibrium has proven extremely useful to predict the chemical
composition of AGB atmospheres. Here we use a recently developed code and an
updated thermochemical database, including gaseous and condensed species
involving 34 elements, to compute the chemical equilibrium composition of AGB
atmospheres of M-, S-, and C-type stars. We include for the first time TixCy
clusters, with x = 1-4 and y = 1-4, and selected larger clusters ranging up to
Ti13C22, for which thermochemical data is obtained from quantum chemical
calculations. We find that in general chemical equilibrium reproduces well the
observed abundances of parent molecules in circumstellar envelopes of AGB
stars. There are however severe discrepancies, of various orders of magnitude,
for some parent molecules: HCN, CS, NH3, and SO2 in M-type stars, H2O and NH3
in S-type stars, and the hydrides H2O, NH3, SiH4, and PH3 in C-type stars.
Several molecules not yet observed in AGB atmospheres, like SiC5, SiNH, SiCl,
PS, HBO, and the metal-containing molecules MgS, CaS, CaOH, CaCl, CaF, ScO,
ZrO, VO, FeS, CoH, and NiS, are good candidates for detection with
observatories like ALMA. The first condensates predicted are carbon, TiC, and
SiC in C-rich atmospheres and Al2O3 in O-rich outflows. The most probable
gas-phase precursors of dust are acetylene, atomic carbon, and/or C3 for carbon
dust, SiC2 and Si2C for SiC dust, and atomic Al and AlOH, AlO, and Al2O for
Al2O3 dust. In the case of TiC dust, atomic Ti is probably the main supplier of
titanium. However, chemical equilibrium predicts that clusters like Ti8C12 and
Ti13C22 become the major reservoirs of titanium at the expense of atomic Ti in
the region where condensation of TiC is expected to occur, suggesting that the
assembly of large TixCy clusters could be related to the formation of the first
condensation nuclei of TiC.


  Massive multiple-input multiple-output (MIMO) is expected to play a central
role in future wireless systems. The deployment of large antenna arrays at the
base station and the mobile users offers multiplexing and beamforming gains
that boost system spectral efficiency. Unfortunately, the high cost and power
consumption of components like analog-to-digital converters makes assigning an
RF chain per antenna and applying typical fully digital precoding/combining
solutions difficult. In this paper, a novel architecture for massive MIMO
receivers, consisting of arrays of switches and constant (non-tunable) phase
shifters, is proposed. This architecture applies a quasi-coherent combining in
the RF domain to reduce the number of required RF chains. An algorithm that
designs the RF combining for this architecture is developed and analyzed.
Results show that the proposed massive MIMO combining model can achieve a
comparable performance to the fully-digital receiver architecture in
single-user and multi-user massive MIMO setups.


  The magnetohydrodynamics system consists of the Navier-Stokes and Maxwell's
equations, coupled through multiples of nonlinear terms. Such a system forced
by space-time white noise has been studied by physicists for decades, and the
rigorous proof of its solution theory has been recently established in Yamazaki
(2019, arXiv:1910.04820 [math.AP]) using the theory of paracontrolled
distributions and a technique of coupled renormalizations. When an equation is
well-posed, and it is approximated by replacing the differentiation operator by
reasonable discretization schemes with a parameter, it is widely believed that
a solution of the approximating equation should converge to the solution of the
original equation as the parameter approaches zero. We prove otherwise in the
case of the three-dimensional magnetohydrodynamics system forced by space-time
white noise. Specifically, it is proven that the limit of the solution to the
approximating system with an additional 32 drift terms solves the original
system. These 32 drift terms depend on the choice of approximations, can be
calculated explicitly in the process of renormalizations, and essentially
represent a spatial version of It$\hat{\mathrm{o}}$-Stratonovich correction
terms. In particular, the proof relies on the technique of coupled
renormalizations again, as well as taking advantage of the special structure of
the magnetohydrodynamics system on many occasions.


  We consider the problem of finding the matching map between two sets of $d$
dimensional vectors from noisy observations, where the second set contains
outliers. The matching map is then an injection, which can be consistently
estimated only if the vectors of the second set are well separated. The main
result shows that, in the high-dimensional setting, a detection region of
unknown injection can be characterized by the sets of vectors for which the
inlier-inlier distance is of order at least $d^{1/4}$ and the inlier-outlier
distance is of order at least $d^{1/2}$. These rates are achieved using the
estimated matching minimizing the sum of logarithms of distances between
matched pairs of points. We also prove lower bounds establishing optimality of
these rates. Finally, we report results of numerical experiments on both
synthetic and real world data that illustrate our theoretical results and
provide further insight into the properties of the estimators studied in this
work.


  The source of spin-wave resonance (SWR) in thin films of the ferromagnetic
semiconductor (Ga,Mn)As is still under debate: does SWR stem from the
\emph{surface} anisotropy (in which case the surface inhomogeneity (SI) model
would apply), or does it originate in the \emph{bulk} inhomogeneity of the
magnetic structure of the sample (and thus requires the use of the volume
inhomogeneity (VI) model)? This paper outlines the ground on which the
controversy arose and shows why in different conditions a resonance sample may
meet the assumptions of either the SI or the VI model. In our considerations we
refer to the SWR spectra measured by Furdyna's team [X. Liu \textit{et al.},
Physical Review B \textbf{75}, 195220 (2007)] in (Ga,Mn)As thin films in
different configurations of the static magnetic field $\vec{H}$ with respect to
the surface. We demonstrate that the observed configuration dependence of the
SWR spectrum of the studied material can be described with the use of the
surface pinning parameter.


  We study spherically symmetric solutions of a four-dimensional theory of
gravity with a topological action, which was constructed as a Yang-Mills theory
of the Poincar\'e group and can be considered a generalization to higher
dimensions of well-known two-dimensional models. We also discuss the
perturbative degrees of freedom and the properties of the theory under
conformal transformations.


  In this paper we determine, under some mild restrictions, the lattice of
submodules $\gL$ of a module $M$ all of whose composition factors have
multiplicity one. Such a lattice is distributive, and hence determined by its
poset of down-sets $P$. We define a directed Ext graph $\Ext_\gL$ of $\gL$ and
show that if $\Ext_\gL$ is acyclic, then $\Ext_\gL$ determines $P$. The result
applies to multiplicity free indecomposable modules for finite dimensional
algebras with acyclic Ext graph. It also applies to some deformed Verma modules
which arise in the Jantzen sum formula basic classical simple Lie superalgebras
in the deformed case.


  Fairness in algorithmic decision-making processes is attracting increasing
concern. When an algorithm is applied to human-related decision-making an
estimator solely optimizing its predictive power can learn biases on the
existing data, which motivates us the notion of fairness in machine learning.
while several different notions are studied in the literature, little studies
are done on how these notions affect the individuals. We demonstrate such a
comparison between several policies induced by well-known fairness criteria,
including the color-blind (CB), the demographic parity (DP), and the equalized
odds (EO). We show that the EO is the only criterion among them that removes
group-level disparity. Empirical studies on the social welfare and disparity of
these policies are conducted.


  We start by taking the analytical approach to discuss how the minimizer of
Yamabe functional provides constant scalar curvature and its relationship with
the Sobolev Space $W^{1,2}.$ Then, after demonstrating the importance of the
sphere $S^n$, with stereographic projection and dilation, we show that the
minimizer of Yamabe functional on standard sphere is obtained from a standard
round metric $\bar{g}$ by a conformal diffeomorphism, thus giving us the
constraint $\lambda (M) < \lambda(S^n),$ which leads us to the final theorem
that the Yamabe problem is solvable when $\lambda(M) < \lambda(S^n).$ For the
proof of this theorem, we adopt the approach of Concentration-Compactness.


  The spontaneous emergence of scale invariance, called self-organized
criticality (SOC), is often attributed to a second-order absorbing-state phase
transition (ASPT). Many real-world systems display SOC, yet extreme events are
often overrepresented, causing significant disruption, and are called dragon
kings (DK). We show analytically that the tradeoff between driving impulse and
dissipation rate can create DKs in a second-order ASPT. This establishes that
DKs exist in SOC systems, reveals a taxonomy of DKs, and shows that larger
dissipation and smoother driving lower risk of extreme events.


  There is a natural connection between the third homology of
$\textrm{SL}_2(A)$ and the refined Bloch group $\mathcal{RB}(A)$ of a
commutative ring $A$. In this article we investigate this connection and as the
main result we show that if $A$ is a universal $\textrm{GE}_2$-domain such that
$-1 \in A^{\times 2}$, then we have the exact sequence
$H_3(\textrm{SM}_2(A),\mathbb{Z}) \to H_3(\textrm{SL}_2(A),\mathbb{Z}) \to
\mathcal{RB}(A) \to 0$, where $\textrm{SM}_2(A)$ is the group of monomial
matrices in $\textrm{SL}_2(A)$. Moreover we show that $\mathcal{RP}_1(A)$, the
refined scissors congruence group of $A$, naturally is isomorph with the
relative homology group $H_3(\textrm{SL}_2(A), \textrm{SM}_2(A),\mathbb{Z})$.


  Topological defects form at cosmological phase transitions by the Kibble
mechanism. Cosmic strings and superstrings can lead to particularly interesting
astrophysical and cosmological consequences, but this study is is currently
limited by the availability of accurate numerical simulations, which in turn is
bottlenecked by hardware resources and computation time. Aiming to eliminate
this bottleneck, in recent work we introduced and validated a GPU-accelerated
evolution code for local Abelian-Higgs strings networks. While this leads to
significant gains in speed, it is still limited by the physical memory
available on a graphical accelerator. Here we report on a further step towards
our main goal, by implementing and validating a multiple GPU extension of the
earlier code, and further demonstrate its good scalability, both in terms of
strong and weak scaling. A $8192^3$ production run, using $4096$ GPUs, runs in
$33.2$ minutes of wall clock time on the Piz Daint supercomputer.


  The main aim of this article is to study and develop valuation theory for
Krasner hyperfields. In analogy with classical valuation theory for fields, we
generalise the formalism of valuation rings to describe equivalence of
valuations on hyperfields. After proving basic results and discussing several
examples, we focus on the valued hyperfields that Krasner originally defined in
1957. We find that these must have a particular additive structure which in
turns implies the existence of a valuation a'la Krasner. We note that given
such a valued hyperfield $(F,v)$, the valuation induced by its additive
structure does not have to be equivalent to $v$. We discuss the cases in which
it does.


  We describe a novel binary classification technique called Banded SVM
(B-SVM). In the standard C-SVM formulation of Cortes et al. (1995), the
decision rule is encouraged to lie in the interval [1, \infty]. The new B-SVM
objective function contains a penalty term that encourages the decision rule to
lie in a user specified range [\rho_1, \rho_2]. In addition to the standard set
of support vectors (SVs) near the class boundaries, B-SVM results in a second
set of SVs in the interior of each class.


  We investigate the dependence of the escape rate on the position of a hole
placed in uniformly hyperbolic systems admitting a finite Markov partition. We
derive an exact periodic orbit formula for finite size Markov holes which
differs from other periodic expansions in the literature and can account for
additional distortion to maps with piecewise constant expansion rate. Using
asymptotic expansions in powers of hole size we show that for systems conjugate
to the binary shift, the average escape rate is always larger than the
expectation based on the hole size. Moreover, we show that in the small hole
limit the difference between the two decays like a known constant times the
square of the hole size. Finally, we relate this problem to the random choice
of hole positions and we discuss possible extensions of our results to
non-Markov holes as well as applications to leaky dynamical networks.


  Although 3D shape matching and interpolation are highly interrelated, they
are often studied separately and applied sequentially to relate different 3D
shapes, thus resulting in sub-optimal performance. In this work we present a
unified framework to predict both point-wise correspondences and shape
interpolation between 3D shapes. To this end, we combine the deep functional
map framework with classical surface deformation models to map shapes in both
spectral and spatial domains. On the one hand, by incorporating spatial maps,
our method obtains more accurate and smooth point-wise correspondences compared
to previous functional map methods for shape matching. On the other hand, by
introducing spectral maps, our method gets rid of commonly used but
computationally expensive geodesic distance constraints that are only valid for
near-isometric shape deformations. Furthermore, we propose a novel test-time
adaptation scheme to capture both pose-dominant and shape-dominant
deformations. Using different challenging datasets, we demonstrate that our
method outperforms previous state-of-the-art methods for both shape matching
and interpolation, even compared to supervised approaches.


  Flexoelectricity describes the coupling between polarization and
strain/stress gradients in insulating crystals. In this paper, using the
Landau-Ginsburg-Devonshire phenomenological approach, we found that
flexoelectricity could increase the theoretical critical thickness in epitaxial
BaTiO3 thin films, below which the switchable spontaneous polarization
vanishes. This increase is remarkable in tensile films while trivial in
compressive films due to the electrostriction caused decrease of potential
barrier, which can be easily destroyed by the flexoelectricity, between the
ferroelectric state and the paraelectric state in tensile films. In addition,
the films are still in a uni-polar state even below the critical thickness due
to the flexoelectric effect.


  The study of off-equatorial orbits in razor-thin disks is still in its
beginnings. Contrary to what was presented in the literature in recent
publications, the vertical stability criterion for equatorial circular orbits
cannot be based on the vertical epicyclic frequency, because of the
discontinuity in the gravitational field on the equatorial plane. We present a
rigorous criterion for the vertical stability of circular orbits in systems
composed by a razor-thin disk surrounded by a smooth axially symmetric
distribution of matter, the latter representing additional structures such as
thick disk, bulge and (dark matter) halo. This criterion is satisfied once the
mass surface density of the thin disk is positive. Qualitative and quantitative
analyses of nearly equatorial orbits are presented. In particular, the analysis
of nearly equatorial orbits allows us to construct an approximate analytical
third integral of motion in this region of phase-space, which describes the
shape of these orbits in the meridional plane.


  We study "buried" active galactic nuclei (AGNs) almost fully covered by
circumnuclear material in ultra-/luminous infrared galaxies (U/LIRGs), which
show weak ionized lines from narrow line regions. Employing an indicator of [O
IV] 25.89-um or [Ne V] 14.32-um line to 12-um AGN luminosity ratio, we find 17
buried AGN candidates that are [O IV]-weak ($L_{\rm [O\,IV]}$/$L_{\rm 12,AGN}
\leq -$3.0) or [Ne V]-weak ($L_{\rm [Ne\,V]}$/$L_{\rm 12,AGN} \leq -$3.4) among
30 AGNs in local U/LIRGs. For the [O IV]-weak AGNs, we estimate their covering
fractions of Compton-thick (CT; $N_{\rm H} \geq 10^{24}$ cm$^{-2}$) material
with an X-ray clumpy torus model to be $f^{\rm (spec)}_{\rm CT} = 0.55\pm0.19$
on average. This value is consistent with the fraction of CT AGNs ($f^{\rm
(stat)}_{\rm CT} = 53\pm12$%) among the [O IV]-weak AGNs in U/LIRGs and much
larger than that in Swift/BAT AGNs ($23\pm6$%). The fraction of [O IV]-weak
AGNs increases from $27^{+13}_{-10}$% (early) to $66^{+10}_{-12}$% (late
mergers). Similar results are obtained with the [Ne V] line. The [O IV] or [Ne
V]-weak AGNs in late mergers show larger $N_{\rm H}$ and Eddington ratios
($\lambda_{\rm Edd}$) than those of the Swift/BAT AGNs, and the largest $N_{\rm
H}$ is $\gtrsim$10$^{25}$ cm$^{-2}$ at ${\log}\lambda_{\rm Edd} \sim -$1, close
to the effective Eddington limit for CT material. These suggest that (1) the
circumnuclear material in buried AGNs is regulated by the radiation force from
high-$\lambda_{\rm Edd}$ AGNs on the CT obscurers, and (2) their dense material
with large $f^{\rm (spec)}_{\rm CT}$ ($\sim 0.5 \pm 0.1$) in U/LIRGs is a
likely cause of a unique structure of buried AGNs, whose amount of material may
be maintained through merger-induced supply from their host galaxies.


  In the present work, we give a phenomenological theory of the monolayer
graphene where two worlds quantum and classical meet together and complete each
other in the most natural way. It appears that the graphene is the unique
material where this complementarity could be explained in an effective way due
to its exceptional band structure properties. We introduce the electron
mass-vortex representation and we define surface tension excitation states in
the monolayer graphene. By abstracting from the usual band energy dispersion we
calculate the band mass of the electrons at the Dirac point by introducing the
mathematical mass-dispersion relation. As a result, we obtain the Dirac energy
dispersion in monolayer graphene from the classical Newton law. Within the
semiclassical theory, we show the presence of the surface spin tension
vectorial field which, possibly, closely relates the surface tension and spin
tension states on the helical surface. We calculate the surface tension related
with the electron band mass-vortex formation at the Dirac's point and we
predict accurately the surface tension value related to the excitonic binding
at the Dirac point as being formed from the electron and hole band
mass-vortices. Moreover, we give the solution to a long-standing problem in the
spin group theory and we construct an example which shows, phenomenologically,
that the manifolds on $\rm S^{(6)}$ are not integrable. The principal reason
for this is attributed to the irreducibility of the spinorial group $\rm
Spin(6)^{\rm R}$ at the Dirac's point, due to the band mass formation via
gravitational field.


  Traditional myoelectric pattern recognition (MPR) systems excel within
controlled laboratory environments but they are interfered when confronted with
anomaly or novel motions not encountered during the training phase. Utilizing
metric ways to distinguish the target and novel motions based on extractors
compared to training set is a prevalent idea to alleviate such interference. An
innovative method for anomaly motion detection was proposed based on simplified
log-Euclidean distance (SLED) of symmetric positive definite manifolds. The
SLED enhances the discrimination between target and novel motions. Moreover, it
generates a more flexible shaping of motion boundaries to segregate target and
novel motions, therefore effectively detecting the novel ones. The proposed
method was evaluated using surface-electromyographic (sEMG) armband data
recorded while performing 6 target and 8 novel hand motions. Based on linear
discriminate analysis (LDA) and convolution prototype network (CPN) feature
extractors, the proposed method achieved accuracies of 89.7% and 93.9% in novel
motion detection respectively, while maintaining a target motion classification
accuracy of 90%, outperforming the existing ones with statistical significance
(p<0.05). This study provided a valuable solution for improving the robustness
of MPR systems against anomaly motion interference.


  Deploying complex deep learning models on edge devices is challenging because
they have substantial compute and memory resource requirements, whereas edge
devices' resource budget is limited. To solve this problem, extensive pruning
techniques have been proposed for compressing networks. Recent advances based
on the Lottery Ticket Hypothesis (LTH) show that iterative model pruning tends
to produce smaller and more accurate models. However, LTH research focuses on
unstructured pruning, which is hardware-inefficient and difficult to accelerate
on hardware platforms.
  In this paper, we investigate iterative pruning in the context of structured
pruning because structurally pruned models map well on commodity hardware. We
find that directly applying a structured weight-based pruning technique
iteratively, called iterative L1-norm based pruning (ILP), does not produce
accurate pruned models. To solve this problem, we propose two activation-based
pruning methods, Iterative Activation-based Pruning (IAP) and Adaptive
Iterative Activation-based Pruning (AIAP). We observe that, with only 1%
accuracy loss, IAP and AIAP achieve 7.75X and 15.88$X compression on LeNet-5,
and 1.25X and 1.71X compression on ResNet-50, whereas ILP achieves 4.77X and
1.13X, respectively.


  We introduce a class of probability measure-valued diffusions, coined
polynomial, of which the well-known Fleming--Viot process is a particular
example. The defining property of finite dimensional polynomial processes
considered by Cuchiero et al. (2012) and Filipovic and Larsson (2016) is
transferred to this infinite dimensional setting. This leads to a
representation of conditional marginal moments via a finite dimensional linear
PDE, whose spatial dimension corresponds to the degree of the moment. As a
result, the tractability of finite dimensional polynomial processes are
preserved in this setting. We also obtain a representation of the corresponding
extended generators, and prove well-posedness of the associated martingale
problems. In particular, uniqueness is obtained from the duality relationship
with the PDEs mentioned above.


  We study the effects of the uniaxial tensile strain and shear deformation as
well as their combinations on the electronic properties of single-layer black
phosphorene. The evolutions of the strain-dependent band gap are obtained using
the numerical calculations within the tight-binding (TB) model as well as the
first-principles (DFT) simulations and compared with previous findings. The
TB-model-based findings show that the band gap of the strain-free phosphorene
agrees with the experimental value and linearly depends on both stretching and
shearing: increases (decreases) as the stretching increases (decreases),
whereas gradually decreases with increasing the shear. A linear dependence is
less or more similar as compared to that obtained from the ab initio
simulations for shear strain, however disagrees with a non-monotonic behaviour
from the DFT-based calculations for tensile strain. Possible reasons for the
discrepancy are discussed. In case of a combined deformation, when both strain
types (tensile/compression + shear) are loaded simultaneously, their mutual
influence extends the realizable band gap range: from zero up to the values
respective to the wide-band-gap semiconductors. At a switched-on combined
strain, the semiconductor-semimetal phase transition in the phosphorene is
reachable at a weaker (strictly non-destructive) strain, which contributes to
progress in fundamental and breakthroughs.


  We define the space of functions of bounded variation ($BV$) on the graph.
Using the notion of divergence of flows on graphs, we show that the unit ball
of the dual space to $BV$ in the graph setting can be described as the image of
the unit ball of the space $\ell^{\infty}$ by the divergence operator. Based on
this result, we propose a new iterative algorithm to find the exact minimizer
for the total variation (TV) denoising problem on the graph. The proposed
algorithm is provable convergent and its performance on image denoising
examples is compared with the Split Bregman and Primal-Dual algorithms as
benchmarks for iterative methods and with BM3D as a benchmark for other
state-of-the-art denoising methods. The experimental results show highly
competitive empirical convergence rate and visual quality for the proposed
algorithm.


  Fiber lasers operating via Raman gain or based on rare-earth doped active
fibers are widely used as sources of CW radiation. However these lasers are
only quasi-CW: their intensity fluctuates strongly on short time-scales. Here
the framework of the complex Ginzburg-Landau equations, that are well known as
an efficient model of mode-locked fiber lasers, is applied for the description
of quasi-CW fiber lasers as well. The first ever vector model of a Raman fiber
laser describes the experimentally observed turbulent-like intensity dynamics,
as well as polarization rogue waves. Our results open debates about the common
underlying physics of operation of very different laser types - quasi-CW lasers
and passively mode-locked lasers.


  Photonic quantum computing is one of the leading approaches to universal
quantum computation. However, large-scale implementation of photonic quantum
computing has been hindered by its intrinsic difficulties, such as
probabilistic entangling gates for photonic qubits and lack of scalable ways to
build photonic circuits. Here we discuss how to overcome these limitations by
taking advantage of two key ideas which have recently emerged. One is a hybrid
qubit-continuous variable approach for realizing a deterministic universal gate
set for photonic qubits. The other is time-domain multiplexing technique to
perform arbitrarily large-scale quantum computing without changing the
configuration of photonic circuits. These ideas together will enable scalable
implementation of universal photonic quantum computers in which
hardware-efficient error correcting codes can be incorporated. Furthermore,
all-optical implementation of such systems can increase the operational
bandwidth beyond THz in principle, utimately enabling large-scale
fault-tolerant universal quantum computers with ultra-high operation frequency.


  Numerical studies of shock waves in large scale systems via kinetic
simulations with millions of particles are too computationally demanding to be
processed in serial. In this work we focus on optimizing the parallel
performance of a kinetic Monte Carlo code for astrophysical simulations such as
core-collapse supernovae. Our goal is to attain a flexible program that scales
well with the architecture of modern supercomputers. This approach requires a
hybrid model of programming that combines a message passing interface (MPI)
with a multithreading model (OpenMP) in C++. We report on our approach to
implement the hybrid design into the kinetic code and show first results which
demonstrate a significant gain in performance when many processors are applied.


  We use JWST NIRCam short wavelength photometry to capture a transit
lightcurve of the exoplanet HAT-P-14 b to assess performance as part of
instrument commissioning. The short wavelength precision is 152 ppm per 27
second integration as measured over the full time series compared to a
theoretical limit of 107 ppm, after corrections to spatially correlated 1/f
noise. Persistence effects from charge trapping are well fit by an exponential
function with short characteristic timescales, settling on the order of 5-15
minutes. The short wavelength defocused photometry is also uniquely well suited
to measure the realtime wavefront error of JWST. Analysis of the images and
reconstructed wavefront maps indicate that two different hexagonal primary
mirror segments exhibited "tilt events" where they changed orientation rapidly
in less than ~1.4 seconds. In some cases, the magnitude and timing of the flux
jumps caused by tilt events can be accurately predicted with a telescope model.
These tilt events can be sensed by simultaneous longer-wavelength NIRCam grism
spectral images alone in the form of changes to the point spread function,
diagnosed from the FWHM. They can also be sensed with the FGS instrument from
difference images. Tilt events possibly from sudden releases of stress in the
backplane structure behind the mirrors were expected during the commissioning
period because they were found in ground-based testing. Tilt events have shown
signs of decreasing in frequency but have not disappeared completely. The
detectors exhibit some minor (less than 1%) deviations from linear behavior in
the first few groups of each integration, potentially impacting absolute fluxes
and transit depths on bright targets where only a handful of groups are
possible. Overall, the noise is within 50% of the theoretical photon noise and
read noise. This bodes well for high precision time series measurements.


  Principal Component Analysis (PCA) is a widely used technique in machine
learning, data analysis and signal processing. With the increase in the size
and complexity of datasets, it has become important to develop low-space usage
algorithms for PCA. Streaming PCA has gained significant attention in recent
years, as it can handle large datasets efficiently. The kernel method, which is
commonly used in learning algorithms such as Support Vector Machines (SVMs),
has also been applied in PCA algorithms.
  We propose a streaming algorithm for Kernel PCA problems based on the
traditional scheme by Oja. Our algorithm addresses the challenge of reducing
the memory usage of PCA while maintaining its accuracy. We analyze the
performance of our algorithm by studying the conditions under which it
succeeds. Specifically, we show that, when the spectral ratio $R :=
\lambda_1/\lambda_2$ of the target covariance matrix is lower bounded by $C
\cdot \log n\cdot \log d$, the streaming PCA can be solved with $O(d)$ space
cost.
  Our proposed algorithm has several advantages over existing methods. First,
it is a streaming algorithm that can handle large datasets efficiently. Second,
it employs the kernel method, which allows it to capture complex nonlinear
relationships among data points. Third, it has a low-space usage, making it
suitable for applications where memory is limited.


  We present three-dimensional simulations of viscous dissipation of AGN
induced gas motions and waves in clusters of galaxies. These simulations are
motivated by recent detections of ripples in the Perseus and Virgo clusters.
Although the sound waves generated by buoyant bubbles decay with distance from
the cluster center, we show that these waves can contribute substantially to
offsetting the radiative cooling at distances significantly exceeding the
bubble size. The energy flux of the waves declines more steeply with radius
than the inverse-square law predicted by energy conservation, implying that
dissipation plays an important role in tapping the wave energy. We show that
such dispersing sound waves/weak shocks are detectable as ripples on
unsharp-masked X-ray cluster maps, and point out that the interfaces between
the intracluster medium and old bubbles are also clearly detectable in
unsharp-masked X-ray maps. This opens up the possibility of detecting fossil
bubbles that are difficult to detect in radio emission. This mode of heating is
consistent with other observational constraints, such as the presence of cool
rims around the bubbles and the absence of strong shocks. Thus, the mechanism
offers a way of heating clusters in a spatially distributed and gentle fashion.
We also discuss the energy transfer between the central AGN and the surrounding
medium. In our numerical experiments, we find that roughly 65 per cent of the
energy injected by the AGN is transferred to the intracluster medium and
approximately 25 percent of the injected energy is dissipated by viscous
effects and contributes to heating of the gas. The overall transfer of heat
from the AGN to the gas is comparable to the radiative cooling losses. The
simulations were performed with the FLASH adaptive mesh refinement code.


  This work presents a Monte Carlo study of the phase transition in the
perovskites La$_{0.7}$Sr$_{0.3}$Mn$_{0.7}^{3+}$Mn$_{0.3-x}^{4+}$Ti$_x$O$_3$
($x$= 0.1, 0.2, and 0.25). We take into accountnearest-neighbor (NN)
interactions between magnetic ions Mn$^{3+}$($S=2$) and Mn$^{4+}$($S=3/2$)
using a spin model describing a strong anisotropy on the $z$ axis. We have
calculated the uniform and staggered magnetizations as well as the
Edwards-Anderson order parameter as functions of temperature, with and without
an applied magnetic field. Fitting the experimental Curie temperature at $x=0$,
we estimated values of various exchange interactions in the system. The
dominant one is that between Mn$^{3+}$ and Mn$^{4+}$ which is at the origin of
the ferromagnetic ordering. Effects of the very small interaction $J\_2$
between NN Mn$^{3+}$ is analyzed: we show that it can cause an
antiferromagnetic phase above $T\_c$ which disappears at smaller $J\_2$ or at
Mn$^{3+}$ concentrations smaller than 0.55. Our results show a good agreement
with experiments on the magnetizations for substitution concentration $x=0.1$,
0.2 and 0.3. We also studied the applied-field effect on the magnetization and
our obtained results are compared with experiments performed at $x=10\%$.


  With the rapid increase of big data, distributed Machine Learning (ML) has
been widely applied in training large-scale models. Stochastic Gradient Descent
(SGD) is arguably the workhorse algorithm of ML. Distributed ML models trained
by SGD involve large amounts of gradient communication, which limits the
scalability of distributed ML. Thus, it is important to compress the gradients
for reducing communication. In this paper, we propose FastSGD, a Fast
compressed SGD framework for distributed ML. To achieve a high compression
ratio at a low cost, FastSGD represents the gradients as key-value pairs, and
compresses both the gradient keys and values in linear time complexity. For the
gradient value compression, FastSGD first uses a reciprocal mapper to transform
original values into reciprocal values, and then, it utilizes a logarithm
quantization to further reduce reciprocal values to small integers. Finally,
FastSGD filters reduced gradient integers by a given threshold. For the
gradient key compression, FastSGD provides an adaptive fine-grained delta
encoding method to store gradient keys with fewer bits. Extensive experiments
on practical ML models and datasets demonstrate that FastSGD achieves the
compression ratio up to 4 orders of magnitude, and accelerates the convergence
time up to 8x, compared with state-of-the-art methods.


  The concept of an objective spatial direction in special relativity is
investigated and theories assuming light-speed isotropy while accepting the
existence of a privileged spatial direction are classified. A natural
generalization of the proper time principle is introduced which makes it
possible to devise experimental tests of spatial isotropy. Several common
misunderstandings in the relativistic literature concerning the role of spatial
isotropy are clarified.


  The initial stage of a heavy ion collision is dominated by nonperturbatively
strong chromoelectric and -magnetic fields. The spatial Wilson loop provides a
gauge invariant observable to probe the dynamics of the longitudinal
chromomagnetic field. We discuss recent results from a real time lattice
calculation of the area-dependence of the expectation value of the spatial
Wilson loop. We show that at relatively early times after the collision, a
universal scaling as a function of the area emerges at large distances for very
different initial conditions, with a nontrivial critical exponent. A similar
behavior has earlier been seen in calculations of the gluon transverse momentum
spectrum, which becomes independent of the initial spectrum of gauge fields. We
also show the distribution of eigenvalues of the spatial Wilson loop and the
fluctuations of its real and imaginary parts.


  We present a multi-component structural analysis of the internal structure of
$1074$ high redshift massive galaxies at $1<z<3$ from the CANDELS HST Survey.
In particular we examine galaxies best-fit by two structural components, and
thus likely forming discs and bulges. We examine the stellar mass, star
formation rates, and colours of both the inner `bulge' and outer `disc'
components for these systems using SED information from the resolved ACS+WFC3
HST imaging. We find that the majority of both inner and outer components lie
in the star-forming region of UVJ space ($68$ and $90$ per cent respectively).
However, the inner portions, or the likely forming bulges, are dominated by
dusty star formation. Furthermore, we show that the outer components of these
systems have a higher star formation rate than their inner regions, and the
ratio of star formation rate between `disc' and `bulge' increases at lower
redshifts. Despite the higher star formation rate of the outer component, the
stellar mass ratio of inner to outer component remains constant through this
epoch. This suggests that there is mass transfer from the outer to inner
components for typical two component forming systems, thus building bulges from
disks. Finally, using Chandra data we find that the presence of an AGN is more
common in both $1$-component spheroid-like galaxies and $2$-component systems
($13\pm3$ and $11\pm2$ per cent) than in $1$-component disc-like galaxies
($3\pm1$ per cent), demonstrating that the formation of a central
inner-component likely triggers the formation of central massive black holes in
these galaxies.


  Be stars are surrounded by outflowing circumstellar matter structured in the
form of decretion discs. They are often members of binary systems, where it is
expected that the decretion disc interacts both radiatively and gravitationally
with the companion. In this work we study how various orbital (period, mass
ratio and eccentricity) and disc (viscosity) parameters affect the disc
structure in coplanar systems. We simulate such binaries with the use of a
smoothed particle hydrodynamics code. The main effects of the secondary on the
disc are its truncation and the accumulation of material inwards of truncation.
We find two cases with respect to the effects of eccentricity: (i) In circular
or nearly circular prograde orbits, the disc maintains a rotating, constant in
shape, configuration, which is locked to the orbital phase. The disc is smaller
in size, more elongated and more massive for low viscosity parameter, small
orbital separation and/or high mass ratio. (ii) Highly eccentric orbits are
more complex, with the disc structure and total mass strongly dependent on the
orbital phase and the distance to the secondary. We also study the effects of
binarity in the disc continuum emission. Since the infrared and radio SED are
sensitive to the disc size and density slope, the truncation and matter
accumulation result in considerable modifications in the emergent spectrum. We
conclude that binarity can serve as an explanation for the variability
exhibited in observations of Be stars, and that our model can be used to detect
invisible companions.


  The radial component of the motion of compact binary systems composed of
neutron stars and/or black holes on eccentric orbit is integrated. We consider
all type of perturbations that emerge up to second post-Newtonian order. These
perturbations are either of relativistic origin or are related to the spin,
mass quadrupole and magnetic dipole moments of the binary components. We derive
a generalized Kepler equation and investigate its domain of validity, in which
it properly describes the radial motion.


  We study the supersymmetric extension of the Faddeev model in four
dimensions. The Faddeev model contains three dimensional soliton solutions and
we are interested in how these solitons are affected by supersymmetry. We
consider both the N=1 and N=2 extensions and find that in neither case it is
possible to supersymmetrize the model without adding additional bosonic terms.
There are essentially two ways of constructing the supersymmetric theory, one
that will lead to a model which allows for solitons and another that gives a
model where solitons are excluded.
  The N=2 model is studied since extending supersymmetry is the natural way of
including topological charges in the algebra. A lower bound to the mass is
obtained by computing the central charge. The result is that it is possible to
have a non-trivial lower bound on the mass, this in principle allows for
massive solitons.


  We show how non-radial motions, originating in the outskirts of clusters of
galaxies, may reduce the discrepancy between the Cold Dark Matter (CDM)
predicted X-ray temperature distribution function of clusters of galaxies and
the observed one and also the discrepancy between the CDM predicted two-point
correlation function of clusters of galaxies and that observed. We compare Edge
et al. (1990) and Henry & Arnaud (1991) data with the distribution function of
X-ray temperature, calculated using Press- Schechter's (1974 - hereafter PS)
theory and Evrard's (1990) prescriptions for the mass-temperature relation and
taking account of the non-radial motions originating from the gravitational
interaction of the quadrupole moment of the protocluster with the tidal field
of the matter of the neighboring protostructures. We find that the model
produces a reasonable clusters temperature distribution. We compare the
two-point cluster correlation function which takes account of the non-radial
motions both with that obtained by Sutherland & Efstathiou (1991), from the
analysis of Huchra's et al. (1990) deep redshift survey, and with the data
points for the Automatic Plate Measuring (APM) clusters, computed by Efstathiou
et al. (1992a), showing that non-radial motions reduce the discrepancy between
the theoretical and the obsservational correlation function.


  We present a theoretical study of the ground state of a Bose-Einstein
condensate with repulsive inter-particle interactions in a double-well
potential, using a restricted variational principle. Within such an approach,
there is a transition from a single condensate to a fragmented condensate as
the strength of the central barrier of the potential is increased. We determine
the nature of this transition through approximate analytic as well as numerical
solutions of our model in the regime where the inter-particle interactions can
be treated perturbatively. The degree of fragmentation of the condensate is
characterized by the degrees of first-order and second-order spatial coherence
across the barrier.


  In this article we study the static polarization in ABC-stacked multilayer
graphene. Since the density of states diverges for these systems if the number
of layers exceeds three, screening effects are expected to be important. In the
random phase approximation, screening can be included through the polarization.
We derive an analytical integral expression for the polarization in both the
full-band model and an effective two-band model. Numerical evaluation of these
integrals are very time consuming in the full-band model. Hence, for
ABC-stacked trilayer graphene, we use the two-band model to calculate the low
momentum part of the polarization. The results for the two-band model are
universal, i.e. independent of doping. The high momentum part is linear and is
determined by calculating two points, such that we can determine the slope. For
ABC stacked trilayer graphene, the slope is given by three times the monolayer
value. We compare our results to previous ones in the literature and discuss
the similarities and discrepancies. Our results can be used to include
screening in ABC-stacked multilayer systems in a way that all the
characteristics of the polarization function are included. The numerical
results for the polarization of trilayer graphene are used to sketch the
screened potential.


  Despite the fact, a handful of scholars have endorsed the Internet of Things
(IoT) as an effective transformative tool for shifting traditional farming to
smart farming, relatively little study has addressed the enabling role of smart
agriculture in achieving sustainable agriculture and green climate. Researchers
are more focused on technological invention and model introduction rather than
discussing societal or global development goals. Sustainable development goals
(SDGs) designed by United Nations (UN), therefore demand discussions as SDGs
targets have a closer implication of technology. To fill this gap, in this
study a model of smart agriculture is developed and centring the model we
investigated how the model addresses SDGs targets. The investigation suggests
that smart agriculture supports targets mentioned in Goal 6, 7, 8, 9, 11 and 12
of SDG. This research is very important, both for developing and developed
nations since most of the nations are moving more towards industrialization and
aiming to achieve the SDG goals This research is expected to provide a path to
the IT practitioners, governments and developing agencies on how technological
intervention can provide a more sustainable agricultural world.


  In this paper, the Quantum Approximate Optimization Algorithm (QAOA) is
analyzed by leveraging symmetries inherent in problem Hamiltonians. We focus on
the generalized formulation of optimization problems defined on the sets of
$n$-element $d$-ary strings. Our main contribution encompasses dimension
reductions for the originally proposed QAOA. These reductions retain the same
problem Hamiltonian as the original QAOA but differ in terms of their mixer
Hamiltonian, and initial state. The vast QAOA space has a daunting dimension of
exponential scaling in $n$, where certain reduced QAOA spaces exhibit
dimensions governed by polynomial functions. This phenomenon is illustrated in
this paper, by providing partitions corresponding to polynomial dimensions of
the corresponding subspaces. As a result, each reduced QAOA partition
encapsulates unique classical solutions absent in others, allowing us to
establish a lower bound on the number of solutions to the initial optimization
problem. Our novel approach opens promising practical advantages in
accelerating the algorithm. Restricting the algorithm to Hilbert spaces of
smaller dimension may lead to significant acceleration of both quantum and
classical simulation of circuits and serve as a tool to cope with barren
plateaus problem.


  The usual setting for learning the structure and parameters of a graphical
model assumes the availability of independent samples produced from the
corresponding multivariate probability distribution. However, for many models
the mixing time of the respective Markov chain can be very large and i.i.d.
samples may not be obtained. We study the problem of reconstructing binary
graphical models from correlated samples produced by a dynamical process, which
is natural in many applications. We analyze the sample complexity of two
estimators that are based on the interaction screening objective and the
conditional likelihood loss. We observe that for samples coming from a
dynamical process far from equilibrium, the sample complexity reduces
exponentially compared to a dynamical process that mixes quickly.


  We update the indirect constraints on the Georgi-Machacek model from
$B$-physics and electroweak precision observables, including new constraints
from $b \to s \gamma$ and $B^0_s \to \mu^+ \mu^-$. We illustrate the effect of
these constraints on the couplings of the Standard Model-like Higgs boson by
performing scans using the most general scalar potential, subject to vacuum
stability and perturbativity constraints. We find that simultaneous
enhancements of all the Higgs production cross sections by up to 39\% are still
allowed after imposing these constraints. LHC rate measurements on the Higgs
pole could be blind to these enhancements if unobserved non-standard Higgs
decays are present.


  Periodogram methods are widely used for the estimation of power- and
cross-spectra, of which Welch's method is the most popular. Previous studies
have analyzed the variance of the power spectra estimates and developed
analytical probability functions, showing that the approach is unbiased when
applied to white-noise signals or in the limit of infinite window lengths.
However, no explicit expression for the estimation bias is available for more
complex signals when finite windows are used. In this study, we show that, for
finite window lengths, Welch's method is biased for all signals other than the
white-noise signal. A novel two-window approach that is unbiased when applied
to signals with bounded correlation lengths is proposed. Numerical experiments
are used to illustrate the advantages of the novel approach.


  We study the spin-wave excitations near the zigzag edge of graphene. It is
rather interesting that we obtain a single branch of relativistic ferromagnetic
magnon due to the presence of the open boundary. Note that magnons in
antiferomagnets appear in pairs, while the single brach magnon in ferromagnets
does not have relativistic dispersion. Thus, the magnon near the zigzag edge of
graphene is a hybrid of both, signaling its intrinsic property as a boundary
excitation that must be embedded in a higher dimensional bulk system.


  This research presents a new turbulence generation method based on stochastic
wavelets and tests its various properties in both homogeneous and inhomogeneous
turbulence. Turbulence field can be generated with less basis compared to
previous synthetic Fourier methods. Adaptive generation of inhomogeneous
turbulence is achieved by scale reduction algorithm and lead to smaller
computation cost. The generated turbulence shows good agreement with input data
and theoretical results.


  We report the first search for the $K_L \to \pi^0 \gamma$ decay, which is
forbidden by Lorentz invariance, using the data from 2016 to 2018 at the J-PARC
KOTO experiment. With a single event sensitivity of $(7.1\pm 0.3_{\rm stat.}
\pm 1.6_{\rm syst.})\times 10^{-8}$, no candidate event was observed in the
signal region. The upper limit on the branching fraction was set to be
$1.7\times 10^{-7}$ at the 90\% confidence level.


  We present a comprehensive black-hole event generator, BlackMax, which
simulates the experimental signatures of microscopic and Planckian black-hole
production and evolution at the LHC in the context of brane world models with
low-scale quantum gravity. The generator is based on phenomenologically
realistic models free of serious problems that plague low-scale gravity, thus
offering more realistic predictions for hadron-hadron colliders. The generator
includes all of the black-hole graybody factors known to date and incorporates
the effects of black-hole rotation, splitting between the fermions, non-zero
brane tension and black-hole recoil due to Hawking radiation (although not all
simultaneously).
  The generator can be interfaced with Herwig and Pythia.


  This work presents SeasoNet, a new large-scale multi-label land cover and
land use scene understanding dataset. It includes $1\,759\,830$ images from
Sentinel-2 tiles, with 12 spectral bands and patch sizes of up to $ 120 \
\mathrm{px} \times 120 \ \mathrm{px}$. Each image is annotated with large scale
pixel level labels from the German land cover model LBM-DE2018 with land cover
classes based on the CORINE Land Cover database (CLC) 2018 and a five times
smaller minimum mapping unit (MMU) than the original CLC maps. We provide pixel
synchronous examples from all four seasons, plus an additional snowy set. These
properties make SeasoNet the currently most versatile and biggest remote
sensing scene understanding dataset with possible applications ranging from
scene classification over land cover mapping to content-based cross season
image retrieval and self-supervised feature learning. We provide baseline
results by evaluating state-of-the-art deep networks on the new dataset in
scene classification and semantic segmentation scenarios.


  We prove a large deviations principle for the largest eigenvalue of a class
of biorthogonal and multiple orthogonal polynomial ensembles that includes a
matrix model of Lueck, Sommers and Zirnbauer for disordered bosons and
Angelesco ensembles. Moreover we consider matrix ensembles in mesoscopic
physics.


  We propose to consider the N=4,d=1 supermultiplet with $% (4,4,0) component
content as a ``root'' one. We elaborate a new reduction scheme from the
``root'' multiplet to supermultiplets with a smaller number of physical bosons.
Starting from the most general sigma-model type action for the ``root''
multiplet, we explicitly demonstrate that the actions for the rest of linear
and nonlinear N=4 supermultiplets can be easily obtained by reduction.
  Within the proposed reduction scheme there is a natural possibility to
introduce Fayet-Iliopoulos terms. In the reduced systems, such terms give rise
to potential terms, and in some cases also to terms describing the interaction
with a magnetic field.
  We demonstrate that known N=4 superconformal actions, together with their
possible interactions, appear as results of the reduction from a free action
for the ``root'' supermultiplet. As a byproduct, we also construct an N=4
supersymmetric action for the linear (3,4,1) supermultiplet, containing both an
interaction with a Dirac monopole and a harmonic oscillator-type potential,
generalized for arbitrary conformally flat metrics.


  Noncommutative geometry may be a starting point to a quantum gravity. We
study the influence of the spacetime noncommutative parameter on the strong
field gravitational lensing in the noncommutative Schwarzschild black-hole
spacetime and obtain the angular position and magnification of the relativistic
images. Supposing that the gravitational field of the supermassive central
object of the galaxy described by this metric, we estimate the numerical values
of the coefficients and observables for strong gravitational lensing. Comparing
to the Reissner-Norstr\"{om} black hole, we find that the influences of the
spacetime noncommutative parameter is similar to those of the charge, just
these influences are much smaller. This may offer a way to distinguish a
noncommutative black hole from a Reissner-Norstr\"{om} black hole, and may
probe the spacetime noncommutative constant $\vartheta$ \cite{foot} by the
astronomical instruments in the future.


  We discuss the performance characteristics of using the modification of the
tree code suggested by Barnes \citep{1990JCoPh..87..161B} in the context of the
TreePM code. The optimisation involves identifying groups of particles and
using only one tree walk to compute force for all the particles in the group.
This modification has been in use in our implementation of the TreePM code for
some time, and has also been used by others in codes that make use of tree
structures. In this paper, we present the first detailed study of the
performance characteristics of this optimisation. We show that the
modification, if tuned properly can speed up the TreePM code by a significant
amount. We also combine this modification with the use of individual time steps
and indicate how to combine these two schemes in an optimal fashion. We find
that the combination is at least a factor of two faster than the modified
TreePM without individual time steps. Overall performance is often faster by a
larger factor, as the scheme of groups optimises use of cache for large
simulations.


  We investigate an array of metal nanoparticles as a channel for nanophotonic
quantum communication and the generation of quantum plasmonic interference. We
consider the transfer of quantum states, including single-qubits as plasmonic
wavepackets, and highlight the necessity of a quantum mechanical description by
comparing the predictions of quantum theory with those of classical
electromagnetic theory. The effects of loss in the metal are included, thus
putting our investigation into a practical setting and enabling the
quantification of the performance of realistic nanoparticle arrays as plasmonic
quantum channels. We explore the interference of single plasmons, finding
nonlinear absorption effects associated with the quantum properties of the
plasmon excitations. This work highlights the benefits and drawbacks of using
nanophotonic periodic systems for quantum plasmonic applications, such as
quantum communication, and the generation of quantum interference.


  Superfluidity is an emergent quantum phenomenon which arises due to strong
interactions between elementary excitations in liquid helium. These excitations
have been probed with great success using techniques such as neutron and light
scattering. However measurements to-date have been limited, quite generally, to
average properties of bulk superfluid or the driven response far out of thermal
equilibrium. Here, we use cavity optomechanics to probe the thermodynamics of
superfluid excitations in real-time. Furthermore, strong light-matter
interactions allow both laser cooling and amplification of the thermal motion.
This provides a new tool to understand and control the microscopic behaviour of
superfluids, including phonon-phonon interactions, quantised vortices and
two-dimensional quantum phenomena such as the Berezinskii-Kosterlitz-Thouless
transition. The third sound modes studied here also offer a pathway towards
quantum optomechanics with thin superfluid films, including femtogram effective
masses, high mechanical quality factors, strong phonon-phonon and phonon-vortex
interactions, and self-assembly into complex geometries with sub-nanometre
feature size.


  Let $A_{1}$, $A_{2}$, $...$, $A_{k}$ be strictly positive operators on a
Hilbert space. This note is to show a sufficient condition of $A_{k}\geq
A_{k-1}\geq\geq A_{3}\geq A_{2}\geq A_{1}$, which extends the related result
before.


  In the present work, we report extensive GEANT4 simulations in order to study
the dependence of sensitivity of GAGG:Ce scintillation crystal based detector
on thickness of the crystal. All the simulations are made considering a
thermalised Am-Be neutron source. The simulations are validated, qualitatively
and quantitatively, by comparing the simulated energy spectra and sensitivity
values with those obtained from experimental measurements carried out using two
different thicknesses of the crystal from our own experiment (0.5mm and 3mm)
and validated with three other thicknesses (0.01mm, 0.1 mm and 1 mm) from
literature. In this study, we define sensitivity of GAGG:Ce as the ratio of
area under 77 keV sum peak to 45 keV peak. The present studies clearly confirm
that, while it requires about 0.1 mm thickness for the GAGG:Ce crystal to fully
absorb thermal neutrons, it requires about 3 mm to fully absorb the thermal
neutron induced events. Further, we propose an equation, that can be used to
estimate the thickness of the GAGG:Ce crystal directly from the observed
sensitivity of the GAGG:Ce crystal. This equation could be very useful for the
neutron imaging community for medical and space applications, as well as for
manufactures of cameras meant for nuclear security purposes.


  Ab initio calculations in bcc iron show that a <111> screw dislocation
induces a short-range dilatation field in addition to the Volterra elastic
field. This core field is modeled in anisotropic elastic theory using force
dipoles. The elastic modeling thus better reproduces the atom displacements
observed in ab initio calculations. Including this core field in the
computation of the elastic energy allows deriving a core energy which converges
faster with the cell size, thus leading to a result which does not depend on
the geometry of the dislocation array used for the simulation.


  The performance of Cherenkov instruments for the detection of very high
energy gamma rays is ultimately limited by the fluctuations in the development
of air showers. With particular emphasis on the angular resolution, the
ultimate performance limits are investigated on the basis of simulations.


  A field-theoretic formulation of the exponential-operator technique is
applied to a Hamiltonian eigenvalue problem in electrodynamics, quantized in
light-front coordinates. Specifically, we consider the dressed-electron state,
without positron contributions but with an unlimited number of photons, and
compute its anomalous magnetic moment. A simple perturbative solution
immediately yields the Schwinger result of alpha/2pi. The nonperturbative
solution, which requires numerical techniques, sums a subset of corrections to
all orders in alpha and incorporates additional physics.


  Consider a diffusion process X=(X_t), with t in [0,1], observed at discrete
times and high frequency, solution of a stochastic differential equation whose
drift and diffusion coefficients are assumed to be unknown. In this article, we
focus on the nonparametric esstimation of the diffusion coefficient. We propose
ridge estimators of the square of the diffusion coefficient from discrete
observations of X and that are obtained by minimization of the least squares
contrast. We prove that the estimators are consistent and derive rates of
convergence as the size of the sample paths tends to infinity, and the
discretization step of the time interval [0,1] tend to zero. The theoretical
results are completed with a numerical study over synthetic data.


  Many word clouds provide no semantics to the word placement, but use a random
layout optimized solely for aesthetic purposes. We propose a novel approach to
model word significance and word affinity within a document, and in comparison
to a large background corpus. We demonstrate its usefulness for generating more
meaningful word clouds as a visual summary of a given document. We then select
keywords based on their significance and construct the word cloud based on the
derived affinity. Based on a modified t-distributed stochastic neighbor
embedding (t-SNE), we generate a semantic word placement. For words that
cooccur significantly, we include edges, and cluster the words according to
their cooccurrence. For this we designed a scalable and memory-efficient
sketch-based approach usable on commodity hardware to aggregate the required
corpus statistics needed for normalization, and for identifying keywords as
well as significant cooccurences. We empirically validate our approch using a
large Wikipedia corpus.


  The singly charged $SU(2)_L$ singlet scalar, with its necessarily flavour
violating couplings to leptons, lends itself particularly well for an
explanation of the Cabibbo Angle Anomaly and of hints for lepton flavour
universality violation in $\tau \to \mu\bar \nu\nu$. In a setup addressing both
anomalies, we predict loop-induced effects in $\tau\to e\gamma$ and in $\tau
\to e\mu\mu$. A recast of ATLAS selectron and smuon searches allows us to
derive a coupling-independent lower limit of $\approx 200$ GeV on the mass of
the singly charged singlet scalar. At a future $e^+e^-$ collider, dark matter
mono-photon searches could provide a complementary set of bounds.


  Understanding individual customers' sensitivities to prices, promotions,
brands, and other marketing mix elements is fundamental to a wide swath of
marketing problems. An important but understudied aspect of this problem is the
dynamic nature of these sensitivities, which change over time and vary across
individuals. Prior work has developed methods for capturing such dynamic
heterogeneity within product categories, but neglected the possibility of
correlated dynamics across categories. In this work, we introduce a framework
to capture such correlated dynamics using a hierarchical dynamic factor model,
where individual preference parameters are influenced by common cross-category
dynamic latent factors, estimated through Bayesian nonparametric Gaussian
processes. We apply our model to grocery purchase data, and find that a
surprising degree of dynamic heterogeneity can be accounted for by only a few
global trends. We also characterize the patterns in how consumers'
sensitivities evolve across categories. Managerially, the proposed framework
not only enhances predictive accuracy by leveraging cross-category data, but
enables more precise estimation of quantities of interest, like price
elasticity.


  This paper considers the problem of conflict-free distribution of agents on a
circular periphery encompassing all agents. The two key elements of the
proposed policy include the construction of a set of convex layers (nested
convex polygons) using the initial positions of the agents, and a novel search
space region for each of the agents. The search space for an agent on a convex
layer is defined as the region enclosed between the lines passing through the
agent's position and normal to its supporting edges. Guaranteeing
collision-free paths, a goal assignment policy designates a unique goal
position within the search space of an agent. In contrast to the existing
literature, this work presents a one-shot, collision-free solution to the
circular distribution problem by utilizing only the initial positions of the
agents. Illustrative examples demonstrate the effectiveness of the proposed
policy.


  Several ways to accelerate the solution of 2D/3D linear min-max problems in
$n$ constraints are discussed. We also present an algorithm for solving such
problems in the 2D case, which is superior to CGAL's linear programming solver,
both in performance and in stability.


  Recent Leibniz scholarship has sought to gauge which foundational framework
provides the most successful account of the procedures of the Leibnizian
calculus (LC). While many scholars (e.g., Ishiguro, Levey) opt for a default
Weierstrassian framework, Arthur compares LC to a non-Archimedean framework SIA
(Smooth Infinitesimal Analysis) of Lawvere-Kock-Bell. We analyze Arthur's
comparison and find it rife with equivocations and misunderstandings on issues
including the non-punctiform nature of the continuum, infinite-sided polygons,
and the fictionality of infinitesimals. Rabouin and Arthur claim that Leibniz
considers infinities as contradictory, and that Leibniz' definition of
incomparables should be understood as nominal rather than as semantic. However,
such claims hinge upon a conflation of Leibnizian notions of bounded infinity
and unbounded infinity, a distinction emphasized by early Knobloch.
  The most faithful account of LC is arguably provided by Robinson's framework.
We exploit an axiomatic framework for infinitesimal analysis called SPOT
(conservative over ZF) to provide a formalisation of LC, including the
bounded/unbounded dichotomy, the assignable/inassignable dichotomy, the
generalized relation of equality up to negligible terms, and the law of
continuity.


  We analyze the utilization of publish-subscribe protocols in IoT and Fog
Computing and challenges around security configuration, performance, and
qualitative characteristics. Such problems with security configuration lead to
significant disruptions and high operation costs. Yet, These issues can be
prevented by selecting the appropriate transmission technology for each
configuration, considering the variations in sizing, installation, sensor
profile, distribution, security, networking, and locality. This work aims to
present a comparative qualitative and quantitative analysis around diverse
configurations, focusing on Smart Agriculture's scenario and specifically the
case of fish-farming. As result, we applied a data generation workbench to
create datasets of relevant research data and compared the results in terms of
performance, resource utilization, security, and resilience. Also, we provide a
qualitative analysis of use case scenarios for the quantitative data produced.
As a contribution, this robust analysis provides a blueprint to decision
support for Fog Computing engineers analyzing the best protocol to apply in
various configurations.


  The presence of moonlight is usually a limiting factor for imaging
atmospheric Cherenkov telescopes due to the high sensitivity of the camera
photomultiplier tubes (PMTs). In their standard configuration, the extra noise
limits the sensitivity of the experiment to gamma-ray signals and the higher
PMT currents also accelerates PMT aging. Since fall 2012, observations have
been carried out with VERITAS under bright moonlight (Moon illumination $>
35\%$), in two observing modes, by reducing the voltage applied to the PMTs and
with UV bandpass filters, which allow observations up to $\sim80\%$ Moon
illumination resulting in $29\%$ more observing time over the course of the
year. In this presentation, we provide details of these new observing modes and
their performance relative to the standard VERITAS observations.


  Untrimmed videos on social media or those captured by robots and surveillance
cameras are of varied aspect ratios. However, 3D CNNs usually require as input
a square-shaped video, whose spatial dimension is smaller than the original.
Random- or center-cropping may leave out the video's subject altogether. To
address this, we propose an unsupervised video cropping approach by shaping
this as a retargeting and video-to-video synthesis problem. The synthesized
video maintains a 1:1 aspect ratio, is smaller in size and is targeted at
video-subject(s) throughout the entire duration. First, action localization is
performed on each frame by identifying patches with homogeneous motion
patterns. Thus, a single salient patch is pinpointed per frame. But to avoid
viewpoint jitters and flickering, any inter-frame scale or position changes
among the patches should be performed gradually over time. This issue is
addressed with a polyBezier fitting in 3D space that passes through some chosen
pivot timestamps and whose shape is influenced by the in-between control
timestamps. To corroborate the effectiveness of the proposed method, we
evaluate the video classification task by comparing our dynamic cropping
technique with random cropping on three benchmark datasets, viz. UCF-101,
HMDB-51 and ActivityNet v1.3. The clip and top-1 accuracy for video
classification after our cropping, outperform 3D CNN performances for
same-sized random-crop inputs, also surpassing some larger random-crop sizes.


  In this paper, we study weakly unital dg categories as they were defined by
Kontsevich and Soibelman [KS, Sect.4]. We construct a cofibrantly generated
Quillen model structure on the category $\mathrm{Cat}_{\mathrm{dgwu}}(\Bbbk)$
of small weakly unital dg categories over a field $\Bbbk$. Our model structure
can be thought of as an extension of the model structure on the category
$\mathrm{Cat}_{\mathrm{dg}}(\Bbbk)$ of (strictly unital) small dg categories
over $\Bbbk$, due to Tabuada [Tab]. More precisely, we show that the imbedding
of $\mathrm{Cat}_{\mathrm{dg}}(\Bbbk)$ to $\mathrm{Cat}_{\mathrm{dgwu}}(\Bbbk)$
is a right adjoint of a Quillen pair of functors. We prove that this Quillen
pair is, in turn, a Quillen equivalence. In course of the proof, we study a
non-symmetric dg operad $\mathcal{O}$, governing the weakly unital dg
categories, which is encoded in the Kontsevich-Soibelman definition. We prove
that this dg operad is quasi-isomorphic to the operad $\mathrm{Assoc}_+$ of
unital associative algebras.


  Reconstruction of arithmetic circuits has been heavily studied in the past
few years and has connections to proving lower bounds and deterministic
identity testing. In this paper we present a polynomial time randomized
algorithm for reconstructing $\Sigma\Pi\Sigma(2)$ circuits over $\mathbb{F}$
($char(\mathbb{F})=0$), i.e. depth$-3$ circuits with fan-in $2$ at the top
addition gate and having coefficients from a field of characteristic $0$. The
algorithm needs only a blackbox query access to the polynomial $f \in
\mathbb{F}[x_1,\ldots, x_n]$ of degree $d$, computable by a
$\Sigma\Pi\Sigma(2)$ circuit $C$. In addition, we assume that "simple rank" of
this polynomial (essential number of variables after removing gcd of the two
multiplication gates) is bigger than a constant. Our algorithm runs in time
$poly(n, d)$ and returns an equivalent $\Sigma\Pi\Sigma(2)$ circuit(with high
probability). The problem of reconstructing $\Sigma\Pi\Sigma(2)$ circuits over
finite fields was first proposed by Shpilka in [24]. The generalization to
$\Sigma\Pi\Sigma(k)$ circuits, $k = O(1)$ (over finite fields) was addressed by
Karnin and Shpilka in [15]. The techniques in these previous involve iterating
over all objects of certain kinds over the ambient field and thus running time
depends on size of the field $\mathbb{F}$. Their reconstruction algorithm uses
lower bounds on the lengths of Linear Locally Decodable Codes with $2$ queries.
In our settings, such ideas immediately pose a problem and we need new ideas to
handle the case of the characteristic $0$ field $\mathbb{F}$. Our main
techniques are based on the use of Quantitative Syslvester Gallai Theorems from
the work of Barak et.al. [3] to find a small collection of subspaces to project
onto. The heart of our paper lies in subtle applications of Quantitative
Sylvester Gallai theorems to prove why projections w.r.t. these subspaces can
be glued.


  Double-exchange model interacting with adiabatic phonons is studied in the
presence of randomness by using the Monte-Carlo method and the systematic
size-scaling analysis. A bicritical behavior is found between the ferromagnetic
metal and the charge-ordered insulator. We find the distinct response to the
randomness between these two states, which agrees well with the experimental
results in the colossal magnetoresistance manganites.


  Recent trends in networking are proposing the use of Machine Learning (ML)
techniques for the control and operation of the network. In this context, ML
can be used as a computer network modeling technique to build models that
estimate the network performance. Indeed, network modeling is a central
technique to many networking functions, for instance in the field of
optimization, in which the model is used to search a configuration that
satisfies the target policy. In this paper, we aim to provide an answer to the
following question: Can neural networks accurately model the delay of a
computer network as a function of the input traffic? For this, we assume the
network as a black-box that has as input a traffic matrix and as output delays.
Then we train different neural networks models and evaluate its accuracy under
different fundamental network characteristics: topology, size, traffic
intensity and routing. With this, we aim to have a better understanding of
computer network modeling with neural nets and ultimately provide practical
guidelines on how such models need to be trained.


  We consider the strongly connected components (SCCs) of a uniform directed
graph on $n$ vertices with i.i.d. in- and out-degree pairs distributed as
$(D^-,D^+)$, with $\mathbb E[D^+]=\mathbb E[D^-]=\mu$. We condition on equal
total in- and out-degree. A phase transition for the emergence of a giant SCC
is known to occur at the critical value $\mathbb E[D^-D^+] = \mu$. We study the
model at this critical value and, additionally, require that $\mathbb
E[(D^-)^i(D^+)^j]<\infty$ for all $i+j\leq 3$, and for $(i,j)=(1,3)$ and
$(i,j)=(3,1)$. We show that, under these conditions, the SCCs ranked by
decreasing number of edges with distances rescaled by $n^{-1/3}$ converge in
distribution to a sequence of finite strongly connected directed multigraphs
with edge lengths, and that these are either $3$-regular or loops. The limit
objects lie in a $3$-parameter family, which contains the scaling limit of the
SCCs in the directed Erd\H{o}s-R\'enyi model at criticality as found by
Goldschmidt and Stephenson (2019). This is the first universality result for
the scaling limit of a critical directed graph model and the first quantitative
result on the directed configuration model at criticality. As a trivial
consequence, the largest SCCs at criticality contain $\Theta(n^{1/3})$ vertices
and edges in probability, and the diameter of the directed graph at criticality
is $\Omega(n^{1/3})$ in probability. We use a metric on the space of weighted
multigraphs in which two multigraphs are close if there are compatible
isomorphisms between their vertex and edge sets which roughly preserve the edge
lengths. We use the product topology on the sequence of multigraphs. Our method
of proof involves a depth-first exploration of the directed graph, resulting in
a spanning forest with additional identifications, of which we study the limit
under rescaling.


  A mutation loop of a valued quiver $Q$, is a combination of quiver
automorphisms (permutations of vertices and valuations) and mutations that
sends $Q$ to itself. In this article we study what we called \emph{global
mutations loops} which are sequences formed of mutations only that send each
quiver $Q'$ in the mutation class $[Q]$ to $\sigma (Q')$ for some permutation
$\sigma$. Based on the weight of $[Q]$ and the shape of $Q$, we identify which
quivers have mutations global loops and we provide them for each case.


  Quantum operations are used to describe the observed probability
distributions and conditional states of the measured system. In this paper, we
address the problem of their joint measurability (coexistence). We derive two
equivalent coexistence criteria. The two most common classes of operations -
Luders operations and conditional state preparators - are analyzed. It is shown
that Luders operations are coexistent only under very restrictive conditions,
when the associated effects are either proportional to each other, or disjoint.


  The semiclassical theory for billiards with mixed boundary conditions is
developed and explicit expressions for the smooth and the oscillatory parts of
the spectral density are derived. The parametric dependence of the spectrum on
the boundary condition is shown to be a very useful diagnostic tool in the
semiclassical analysis of the spectrum of billiards. It is also used to check
in detail some recently proposed parametric spectral statistics. The methods
are illustrated in the analysis of the spectrum of the Sinai billiard and its
parametric dependence on the boundary condition on the dispersing arc.


  Escherichia coli is a motile bacterium that moves up a chemoattractant
gradient by performing a biased random walk composed of alternating runs and
tumbles. This paper presents calculations of the chemotactic drift velocity vd
(the mean velocity up the chemoattractant gradient) of an E. coli cell
performing chemotaxis in a uniform, steady shear flow, with a weak
chemoattractant gradient at right angles to the flow. Extending earlier models,
a combined analytic and numerical approach is used to assess the effect of
several complications, namely (i) a cell cannot detect a chemoattractant
gradient directly but rather makes temporal comparisons of chemoattractant
concentration, (ii) the tumbles exhibit persistence of direction, meaning that
the swimming directions before and after a tumble are correlated, (iii) the
cell suffers random re-orientations due to rotational Brownian motion, and (iv)
the non-spherical shape of the cell affects the way that it is rotated by the
shear flow. These complications influence the dependence of vd on the shear
rate gamma. When they are all included, it is found that (a) shear disrupts
chemotaxis and shear rates beyond gamma = 2/second cause the cell to swim down
the chemoattractant gradient rather than up it, (b) in terms of maximising
drift velocity, persistence of direction is advantageous in a quiescent fluid
but disadvantageous in a shear flow, and (c) a more elongated body shape is
advantageous in performing chemotaxis in a strong shear flow.


  This paper is devoted to the problem of classification of ${\rm
AT4}(p,p+2,r)$-graphs. There is a unique ${\rm AT4}(p,p+2,r)$-graph with $p=2$,
namely, the distance-transitive Soicher graph with intersection array $\{56,
45, 16, 1;1, 8, 45, 56\}$, whose local graphs are isomorphic to the Gewirtz
graph. It is still unknown whether an ${\rm AT4}(p,p+2,r)$-graph with $p>2$
exists. The local graphs of each ${\rm AT4}(p,p+2,r)$-graph are strongly
regular with parameters $((p+2)(p^2+4p+2),p(p+3),p-2,p)$. In the present paper,
we find an upper bound for the prime spectrum of an automorphism group of a
strongly regular graph with such parameters, and we also obtain some
restrictions for the prime spectrum and the structure of an automorphism group
of an ${\rm AT4}(p,p+2,r)$-graph in case when $p$ is a prime power. As a
corollary, we show that there are no arc-transitive ${\rm AT4}(p,p+2,r)$-graphs
with $p\in \{11,17,27\}$.


  We show that a compact Kaehler manifold X is a complex torus if both the
continuous part and discrete part of some automorphism group G of X are
infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant
fibration. Some applications to dynamics are given.


  In a world, as complex and constantly changing as ours cloud computing is a
driving force for shaping the IT landscape and changing the way we do business.
Current trends show a world of people, things and services all digitally
interconnected via the Internet of Things (IoT). This applies in particular to
an industrial environment where smart devices and intelligent services pave the
way for smart factories and smart businesses. This paper investigates in a use
case driven study the potential of making use of smart devices to enable
direct, automated and voice-controlled smart businesses. Furthermore, the paper
presents an initial investigation on methodologies for measuring costs of cyber
security controls for cloud services.


  The construction of $r$-nets offers a powerful tool in computational and
metric geometry. We focus on high-dimensional spaces and present a new
randomized algorithm which efficiently computes approximate $r$-nets with
respect to Euclidean distance. For any fixed $\epsilon>0$, the approximation
factor is $1+\epsilon$ and the complexity is polynomial in the dimension and
subquadratic in the number of points. The algorithm succeeds with high
probability. More specifically, the best previously known LSH-based
construction of Eppstein et al.\ \cite{EHS15} is improved in terms of
complexity by reducing the dependence on $\epsilon$, provided that $\epsilon$
is sufficiently small. Our method does not require LSH but, instead, follows
Valiant's \cite{Val15} approach in designing a sequence of reductions of our
problem to other problems in different spaces, under Euclidean distance or
inner product, for which $r$-nets are computed efficiently and the error can be
controlled. Our result immediately implies efficient solutions to a number of
geometric problems in high dimension, such as finding the
$(1+\epsilon)$-approximate $k$th nearest neighbor distance in time subquadratic
in the size of the input.


  Understanding how electronic structure determines the reactivity of solid
surface, is a central topic of modern surface science. This is mostly commonly
done through some intermediate quantity termed descriptor. However, such
descriptors are very scarce for solid surface compared to for molecule, likely
due to their significantly more complex electronic structure (cf. molecules).
Here we elaborate on the theory of a concept dubbed "Fermi softness", which
distinguishes itself by enabling prediction of surface reactivity with spatial
as well as atomic resolution. Other pertinent concepts and descriptors are also
mentioned so as to make the treatment comprehensive.


  Quantum sensors based on the superposition of neutral atoms are promising for
sensing the nature of dark matter (DM). In this study, we utilize the
Stern-Gerlach (SG) interferometer configuration to seek a novel method for the
detection of detect axion-like particles (ALPs). Using an SG interferometer, we
create a spatial quantum superposition of neutral atoms such as $^{3}$He and
$^{87}$Rb. It is shown that the interaction of ALPs with this superposition
induces a relative phase between superposed quantum components. We use the
quantum Boltzmann equation (QBE) to introduce a first-principles analysis that
describes the temporal evolution of the sensing system. The QBE approach
employs quantum field theory (QFT) to highlight the role of the quantum nature
of the interactions with the quantum systems. The resulting exclusion area
demonstrates that our scheme allows for the exclusion of a range of ALP mass in
the range of $10^{-10}\leq m_{a}\leq 10^{2}\,\mathrm{eV}$ and ALP-atom coupling
constant in the range $10^{-13}\leq g_{ae}\leq 10^{0}$.


  Topological order of a topological phase of matter in two spacial dimensions
is encoded by a unitary modular (tensor) category (UMC). A group symmetry of
the topological phase induces a group symmetry of its corresponding UMC.
Gauging is a well-known theoretical tool to promote a global symmetry to a
local gauge symmetry. We give a mathematical formulation of gauging in terms of
higher category formalism. Roughly, given a UMC with a symmetry group $G$,
gauging is a 2-step process: first extend the UMC to a $G$-crossed braided
fusion category and then take the equivariantization of the resulting category.
Gauging can tell whether or not two enriched topological phases of matter are
different, and also provides a way to construct new UMCs out of old ones. We
derive a formula for the $H^4$-obstruction, prove some properties of gauging,
and carry out gauging for two concrete examples.


  Online class-incremental continual learning is a specific task of continual
learning. It aims to continuously learn new classes from data stream and the
samples of data stream are seen only once, which suffers from the catastrophic
forgetting issue, i.e., forgetting historical knowledge of old classes.
Existing replay-based methods effectively alleviate this issue by saving and
replaying part of old data in a proxy-based or contrastive-based replay manner.
Although these two replay manners are effective, the former would incline to
new classes due to class imbalance issues, and the latter is unstable and hard
to converge because of the limited number of samples. In this paper, we conduct
a comprehensive analysis of these two replay manners and find that they can be
complementary. Inspired by this finding, we propose a novel replay-based method
called proxy-based contrastive replay (PCR). The key operation is to replace
the contrastive samples of anchors with corresponding proxies in the
contrastive-based way. It alleviates the phenomenon of catastrophic forgetting
by effectively addressing the imbalance issue, as well as keeps a faster
convergence of the model. We conduct extensive experiments on three real-world
benchmark datasets, and empirical results consistently demonstrate the
superiority of PCR over various state-of-the-art methods.


  We consider an optimization problem with strongly convex objective and linear
inequalities constraints. To be able to deal with a large number of constraints
we provide a penalty reformulation of the problem. As penalty functions we use
a version of the one-sided Huber losses. The smoothness properties of these
functions allow us to choose time-varying penalty parameters in such a way that
the incremental procedure with the diminishing step-size converges to the exact
solution with the rate $O(1/{\sqrt k})$. To the best of our knowledge, we
present the first result on the convergence rate for the penalty-based gradient
method, in which the penalty parameters vary with time.


  Given an inner function $\theta$ on the unit disk, let
$K^p_\theta:=H^p\cap\theta\bar z\bar{H^p}$ be the associated star-invariant
subspace of the Hardy space $H^p$. Also, we put
$K_{*\theta}:=K^2_\theta\cap{\rm BMO}$. Assuming that $B=B_{\mathcal Z}$ is an
interpolating Blaschke product with zeros $\mathcal Z=\{z_j\}$, we
characterize, for a number of smoothness classes $X$, the sequences of values
$\mathcal W=\{w_j\}$ such that the interpolation problem $f\big|_{\mathcal
Z}=\mathcal W$ has a solution $f$ in $K^2_B\cap X$. Turning to the case of a
general inner function $\theta$, we further establish a non-duality relation
between $K^1_\theta$ and $K_{*\theta}$. Namely, we prove that the latter space
is properly contained in the dual of the former, unless $\theta$ is a finite
Blaschke product. From this we derive an amusing non-interpolation result for
functions in $K_{*B}$, with $B=B_{\mathcal Z}$ as above.


  The combination of learning methods with Model Predictive Control (MPC) has
attracted a significant amount of attention in the recent literature. The hope
of this combination is to reduce the reliance of MPC schemes on accurate
models, and to tap into the fast developing machine learning and reinforcement
learning tools to exploit the growing amount of data available for many
systems. In particular, the combination of reinforcement learning and MPC has
been proposed as a viable and theoretically justified approach to introduce
explainable, safe and stable policies in reinforcement learning. However, a
formal theory detailing how the safety and stability of an MPC-based policy can
be maintained through the parameter updates delivered by the learning tools is
still lacking. This paper addresses this gap. The theory is developed for the
generic Robust MPC case, and applied in simulation in the robust tube-based
linear MPC case, where the theory is fairly easy to deploy in practice. The
paper focuses on Reinforcement Learning as a learning tool, but it applies to
any learning method that updates the MPC parameters online.


  We present the discovery of a z=4.13 galaxy TN J1338-1942, the most distant
radio galaxy in the southern hemisphere known to date. The source was selected
from a sample of Ultra Steep Spectrum (USS; alpha < -1.3) radio sources using
the Texas and NVSS catalogs. The discovery spectrum, obtained with the ESO 3.6m
telescope, shows bright extended Ly-alpha emission. The radio source has a very
asymmetric morphology, suggesting a strong interaction with an inhomogeneous
surrounding medium.


  Optical seeing measurements carried out at Sierra Negra, the site of the
Large Millimeter Telescope, are reported. The site, one of the highest peaks of
Central Mexico, offers good coverage of Northern and Southern hemispheres and
we have undertaken several campaigns to investigate the astronomical potential
of the site in the optical. Here we report on our campaign aimed at
establishing the seeing quality of the site. We present data of the first three
campaigns of optical seeing monitoring covering from February 2000 to May 2002,
carried out with a Differential Image Motion Monitor. The results clearly
indicate a sub-arcsec seeing, better statistics during the dry season and no
dependence with the time of night. We find no dependence of our results with
the integration time used.


  A search is reported for a narrow vector resonance decaying to
quark-antiquark pairs in proton-proton collisions at sqrt(s) = 13 TeV,
collected with the CMS detector at the LHC. The data sample corresponds to an
integrated luminosity of 2.7 inverse femtobarns. The vector resonance is
produced at large transverse momenta, with its decay products merged into a
single jet. The resulting signature is a peak over background in the
distribution of the invariant mass of the jet. The results are interpreted in
the framework of a leptophobic vector resonance and no evidence is found for
such particles in the mass range of 100-300 GeV. Upper limits at 95% confidence
level on the production cross section are presented in a region of
mass-coupling phase space previously unexplored at the LHC. The region below
140 GeV has not been explored by any previous experiments.