  We propose two different seesaw models namely, type I and inverse seesaw to
realise light Dirac neutrinos within the framework of $A_4$ discrete flavour
symmetry. The additional fields and their transformations under the flavour
symmetries are chosen in such a way that naturally predicts the hierarchies of
different elements of the seesaw mass matrices in these two types of seesaw
mechanisms. For generic choices of flavon alignments, both the models predict
normal hierarchical light neutrino masses with the atmospheric mixing angle in
the lower octant. Apart from predicting interesting correlations between
different neutrino parameters as well as between neutrino and model parameters,
the model also predicts the leptonic Dirac CP phase to lie in a specific range
-$\pi/3$ to $\pi/3$. While the type I seesaw model predicts smaller values of
absolute neutrino mass, the inverse seesaw predictions for the absolute
neutrino masses can saturate the cosmological upper bound on sum of absolute
neutrino masses for certain choices of model parameters.


  Privacy concerns are considered one of the main challenges in smart cities as
sharing sensitive data brings threatening problems to people's lives. Federated
learning has emerged as an effective technique to avoid privacy infringement as
well as increase the utilization of the data. However, there is a scarcity in
the amount of labeled data and an abundance of unlabeled data collected in
smart cities, hence there is a need to use semi-supervised learning. We propose
a semi-supervised federated learning method called FedSem that exploits
unlabeled data. The algorithm is divided into two phases where the first phase
trains a global model based on the labeled data. In the second phase, we use
semi-supervised learning based on the pseudo labeling technique to improve the
model. We conducted several experiments using traffic signs dataset to show
that FedSem can improve accuracy up to 8% by utilizing the unlabeled data in
the learning process.


  A decade ago, it was shown that a wide class of scalar-tensor theories can
pass very restrictive weak field tests of gravity and yet exhibit
non-perturbative strong field deviations away from General Relativity. This
phenomenon was called `Spontaneous Scalarization' and causes the (Einstein
frame) scalar field inside a neutron star to rapidly become inhomogeneous once
the star's mass increases above some critical value. For a star whose mass is
below the threshold, the field is instead nearly uniform (a state which
minimises the star's energy) and the configuration is similar to the General
Relativity one. Here, we show that the spontaneous scalarization phenomenon is
linked to another strong field effect: a spontaneous violation of the weak
energy condition.


  We study the long time behavior of small solutions of semi-linear dispersive
Hamiltonian partial differential equations on confined domains. Provided that
the system enjoys a new non-resonance condition and a strong enough energy
estimate, we prove that its low super-actions are almost preserved for very
long times. Roughly speaking, it means that, to exchange energy, modes have to
oscillate at the same frequency. Contrary to the previous existing results, we
do not require the solutions to be especially smooth. They only have to live in
the energy space. We apply our result to nonlinear Klein-Gordon equations in
dimension d = 1 and nonlinear Schr{\"o}dinger equations in dimension d $\le$ 2.


  The Morgan-Morgan-Finney (MMF) model is a widely used semi-physically based
soil erosion model that has been tested and validated in various land use types
and climatic regions. The latest version of the model, the modified MMF (MMMF)
model, improved its conceptual physical representations through several
modifications of the original model. However, the MMMF model has three
problematic parts to be corrected: 1) the effective rainfall equation, 2) the
interflow equation, and 3) the improperly normalized C-factor of the transport
capacity equation. In this commentary, we identify and correct the problematic
parts of the MMMF model, which should result in more accurate estimations of
runoff and soil erosion rates.


  The Mini-EUSO telescope is the first space-based detector of the JEM-EUSO
program. It was launched for the International Space Station on August
22$^{nd}$, 2019 to observe from the ISS orbit ($\sim$420 km altitude) various
phenomena occurring in the Earth's atmosphere through a UV-transparent window
located in the Russian Zvezda Module. The dimension of the window defines and
constrains the dimension of the optics, based on a set of two Fresnel lenses of
25 cm diameter each, almost two orders of magnitude smaller than the system
foreseen for a larger space-based detector, like the original JEM-EUSO detector
or the future POEMMA. As a consequence, the energy threshold of Mini-EUSO is
very high, above $10^{21} $eV. Nevertheless, a series of events that resemble
the shape and the time duration of EAS-induced events have been detected in
Mini-EUSO data. This contribution presents the most interesting cases, showing
that the vast majority of the EAS-like events can be traced back to ground
sources repeatedly flashing and triggered many times by Mini-EUSO. Some
non-repeated EAS-like events are also present. In these cases, it is possible
to exclude their cosmic origin through the comparison with simulated events.
Since it is clear that those events can not be originated by a UHECR, we
decided to rename them "Short Light Transients" or SLTs. Finally, it was
possible to associate some of the SLTs with atmospheric activity. This analysis
confirms the validity of the JEM-EUSO detection principle and shows that it is
possible for a space-based detector to distinguish between events induced by
UHECRs and events with a different origin.


  We introduce a high performance differential dilatometer based on an
all-fiber Michelson interferometer at cryogenic temperature with $10^{-10}$
resolution in $\delta L/L$. It resolve the linear thermal expansion coefficient
by measuring the oscillating changes of sample thickness and sample temperature
with the interferometer and in-situ thermometer, respectively. By measuring the
linear thermal expansion coefficient $\alpha$ near the antiferromagnetic
transition region of BaFe$_2$As$_2$ as a demonstration, we show our dilatometer
is able to measure thin samples with sub-pm-level length change resolution and
mK-level temperature resolution. Despite there is residual background thermal
expansion of a few nm/K in measurement result, our new dilatometer is sitll a
powerful tool for study of phase transition in condensed matter physics,
especially significant advantages in fragile materials with sub-100$\mu$m
thickness and being integrated with multiple synchronous measurements and
tuning thanks to the extremely high resolution and contactless nature. The
prototype design of this setup can be further improved in many aspects for
specific applications.


  We establish Sobolev type inequalities in the noncommutative settings by
generalizing monotone metrics in the space of quantum states, such as
matrix-valued Beckner inequalities. We also discuss examples such as random
transpositions and Bernoulli-Laplace models.


  Selfish mining is a well known vulnerability in blockchains exploited by
miners to steal block rewards. In this paper, we explore a new form of selfish
mining attack that guarantees high rewards with low cost. We show the
feasibility of this attack facilitated by recent developments in blockchain
technology opening new attack avenues. By outlining the limitations of existing
countermeasures, we highlight a need for new defense strategies to counter this
attack, and leverage key system parameters in blockchain applications to
propose an algorithm that enforces fair mining. We use the expected transaction
confirmation height and block publishing height to detect selfish mining
behavior and develop a network-wide defense mechanism to disincentivize selfish
miners. Our design involves a simple modifications to transactions' data
structure in order to obtain a "truth state" used to catch the selfish miners
and prevent honest miners from losing block rewards.


  Jet vetoes are a prominent part of the signal selection in various analyses
at the LHC. We discuss jet vetoes for which the transverse momentum of a jet is
weighted by a smooth function of the jet rapidity. With a suitable choice of
the rapidity-weighting function, such jet-veto variables can be factorized and
resummed allowing for precise theory predictions. They thus provide a
complementary way to divide phase space into exclusive jet bins. In particular,
they provide a natural and theoretically clean way to implement a tight veto on
central jets with the veto constraint getting looser for jets at increasingly
forward rapidities. We mainly focus our discussion on the 0-jet case in
color-singlet processes, using Higgs production through gluon fusion as a
concrete example. For one of our jet-veto variables we compare the resummed
theory prediction at NLL'+NLO with the recent differential cross section
measurement by the ATLAS experiment in the $H\to\gamma\gamma$ channel, finding
good agreement. We also propose that these jet-veto variables can be measured
and tested against theory predictions in other SM processes, such as Drell-Yan,
diphoton, and weak diboson production.


  We present a complete and independent set of dimension-7 operators in the low
energy effective field theory (LEFT) where the dynamical degrees of freedom are
the standard model five quarks and all of the neutral and charged leptons. All
operators are non-Hermitian and are classified according to their baryon
($\Delta B$) and lepton ($\Delta L$) numbers violated. Including
Hermitian-conjugated operators, there are in total $3168$, $750$, $588$, $712$
operators with $(\Delta B,\Delta L)=(0,0)$, $(0,\pm 2)$, $(\pm 1,\mp 1)$, $(\pm
1,\pm 1)$ respectively. We perform the tree-level matching with the standard
model effective field theory (SMEFT) up to dimension-7 (dim-7) operators in
both LEFT and SMEFT. As a phenomenological application we study the effective
neutrino-photon interactions due to dim-7 lepton number violating operators
that are induced and much enhanced at one loop from dim-6 operators that in
turn are matched from dim-7 SMEFT operators. We compare the cross sections of
various neutrino-photon scattering with their counterparts in the standard
model and highlight the new features. Finally we illustrate how these effective
interactions could arise from ultraviolet completion.


  We discuss a dynamical mechanism of pion production from disoriented chiral
condensates (DCC). It leads to an explosive production of pions via the
parametric amplification mechanism, which is similar to the reheating mechanism
in inflationary cosmology. Classically, it is related with the instability in
the solutions of the Mathieu equation and we explore the quantum aspects of the
mechanism. We show that nonlinearlities and back reactions can be ignorable for
sufficiently long time under the small amplitude approximations of background
$\sigma$ oscillations, which may be appropriate for the late stage of
nonequilibrium phase transition. It allows us to obtain an explicit quantum
state of the produced pions and $\sigma$, the squeezed state of BCS type.
Single particle distributions and two-pion correlation functions are computed
within these approximations. The results obtained illuminate the characteristic
features of multi-pion states produced through the parametric amplification
mechanism. In particular, two-pion correlations of various charge combinations
contain back-to-back correlations which cannot be masked by the identical
particle interference effect.


  The Goldberg conjecture states that a compact almost K\"ahler, Einstein
manifold must be K\"ahler. The analogue of this conjecture in $G_2$-geometry
says that an Einstein closed $G_2$-structure on a compact manifold must be
torsion-free, and this was proven to be true by Cleyton-Ivanov and Bryant. In
this paper, we remove the compactness assumption and prove the $G_2$-Goldberg
conjecture for noncompact manifolds. In general, we prove that there is no
closed $G_2$-structure on a noncompact manifold whose metric is complete and
has Ricci curvature pinched sufficiently close to a negative constant. We also
find restrictions on the lengths of geodesics when the metric is incomplete.


  We develop a method for estimating the instantaneous lift coefficient on a
rapidly pitching airfoil that uses a small number of pressure sensors and a
measurement of the angle of attack. The approach assimilates four surface
pressure measurements with a modified nonlinear state space model
(Goman-Khrabrov model) through a Kalman filter. The error of lift coefficient
estimates based only on a weighted-sum of the measured pressures are found to
be noisy and biased, which leads to inaccurate estimates. The estimate is
improved by including the predictive model in an conventional Kalman filter.
The Goman-Khrabrov model is shown to be a linear parameter-varying system and
can therefore be used in the Kalman filter without the need for linearization.
Additional improvement is realized by modifying the algorithm to provide more
accurate estimate of the lift coefficient. The improved Kalman filtering
approach results in a bias-free lift coefficient estimate that is more precise
than either the pressure-based estimate or the Goman-Khrabrov model on their
own. The new method will enable performance enhancements in aerodynamic systems
whose performance relies on lift.


  We define analytic indices which involve the eta form and the analytic
torsion form. We show that these indices are independent of the geometric
choices made in their definitions, and hence are topological in nature.


  The international PEN collaboration aims to obtain the branching ratio for
the pion electronic decay $\pi^+ \to e^+\nu_e(\gamma)$, aka $\pi_{e2}$, to a
relative precision of $5\times 10^{-4}$ or better. The PEN apparatus comprises
a number of detection systems, all contributing vital information to the PEN
event reconstruction. This paper discusses the design, performance, and Monte
Carlo simulation of the mini time projection chamber (mTPC) used for pion,
muon, and positron beam particle tracking. We also review the use of the
extracted trajectory coordinates in the analysis, in particular in constructing
observables critical for discriminating background processes, and in maximizing
the fiducial volume of the target in which decay event vertices can be accepted
for branching ratio extraction without introducing bias.


  We present broad band R and narrow band H_alpha emission line images of a
sample of optically selected starburst galaxies from the Markarian lists. The
emission line morphology is studied and global properties like luminosities,
equivalent widths and star formation rates are derived. The radial distribution
of H_alpha flux and the EW are determined using concentric aperture photometry
on the emission line and the continuum images. H_alpha flux is generally found
to peak in the nuclear region and fall off outwards. The EW is found to peak
off-center in most of the cases implying that though the intensity of emission
is maximum at the nucleus, the star formation activity relative to the
underlying continuum often peaks away from the center in Markarian starburst
galaxies.


  Conventional imitation learning assumes access to the actions of
demonstrators, but these motor signals are often non-observable in naturalistic
settings. Additionally, sequential decision-making behaviors in these settings
can deviate from the assumptions of a standard Markov Decision Process (MDP).
To address these challenges, we explore deep generative modeling of state-only
sequences with non-Markov Decision Process (nMDP), where the policy is an
energy-based prior in the latent space of the state transition generator. We
develop maximum likelihood estimation to achieve model-based imitation, which
involves short-run MCMC sampling from the prior and importance sampling for the
posterior. The learned model enables \textit{decision-making as inference}:
model-free policy execution is equivalent to prior sampling, model-based
planning is posterior sampling initialized from the policy. We demonstrate the
efficacy of the proposed method in a prototypical path planning task with
non-Markovian constraints and show that the learned model exhibits strong
performances in challenging domains from the MuJoCo suite.


  For Gaussian Spin Glasses in low dimensions, we introduce a simple Strong
Disorder renormalization procedure at zero temperature. In each disordered
sample, the difference between the ground states associated to Periodic and
Anti-Periodic boundary conditions defines a system-size Domain Wall. The
numerical study in dimensions $d=2$ (up to sizes $2048^2$) and $d=3$ (up to
sizes $128^3$) yields fractal Domain Walls of dimensions $d_s(d=2) \simeq 1.27$
and $d_s(d=3) \simeq 2.55$ respectively.


  I review the theoretical motivation for the axion and present an update of
the experimental status of axion searches. I finally comment on some aspects of
the physics of axion-like particles.


  Dirac materials have unique transport properties, partly due to the presence
of surface states. A new type of Dirac materials, protected by non-symmorphic
symmetries was recently proposed by Young and Kane [1]. By breaking of time
reversal or inversion symmetry one can split the Dirac cones into Weyl nodes.
The later are characterized by local Chern numbers, that makes them
two-dimensional analogs of Weyl semimetals. We find that the formation of the
Weyl nodes is accompanied by an emergence of one-dimensional surface states,
similar to Fermi arcs in Weyl semimetals and edge states in two-dimensional
graphene. We explore these states for a quasi-one-dimensional non-symmorphic
ribbon. The type and strength of applied deformation control the location and
Weyl nodes and their composition. This determines the properties of emerging
edge states. The sensitivity of these edge states to the external deformations
makes non-symmorphic materials potentially useful as a new type of
electromechanical sensors.


  Invariance in duality transformation, the self-dual property, has important
applications in electromagnetic engineering. In the present paper, the problem
of most general linear and local boundary conditions with self-dual property is
studied. Expressing the boundary conditions in terms of a generalized impedance
dyadic, the self-dual boundaries fall in two sets depending on symmetry or
antisymmetry of the impedance dyadic. Previously known cases are found to
appear as special cases of the general theory. Plane-wave reflection from
boundaries defined by each of the two cases of self-dual conditions are
analyzed and waves matched to the corresponding boundaries are determined. As a
numerical example, reflection from a special case, the self-dual EH boundary,
is computed for two planes of incidence.


  In this paper, we study a parameterized Douglas-Rachford splitting method for
a class of nonconvex optimization problem. A new merit function is constructed
to establish the convergence of the whole sequence generated by the
parameterized Douglas-Rachford splitting method. We then apply the
parameterized Douglas-Rachford splitting method to three important classes of
nonconvex optimization problems arising in data science: sparsity constrained
least squares problem, feasibility problem and low rank matrix completion.
Numerical results validate the effectiveness of the parameterized
Douglas-Rachford splitting method compared with some other classical methods.


  Our extraction of the pion-nucleon coupling constant from \pi p elastic
scattering data is outlined. A partial wave analysis (T_{\pi} < 2100 MeV) is
performed simultaneously with a fixed-t dispersion relation analysis (T_{\pi} <
800 MeV). The \pi NN coupling constant g^2/4\pi is searched to find the best
fit. The result 13.73 \pm 0.01 \pm 0.07 (first error statistical, second
systematic) is found to be insensitive to database changes and Coulomb barrier
corrections. This value satisfies important elements of low energy QCD like the
Goldberger-Treiman discrepancy, the Dashen-Weinstein sum rule, and chiral
perturbation theory predictions of threshold pion photoproduction.


  Transformers have supplanted recurrent models in a large number of NLP tasks.
However, the differences in their abilities to model different syntactic
properties remain largely unknown. Past works suggest that LSTMs generalize
very well on regular languages and have close connections with counter
languages. In this work, we systematically study the ability of Transformers to
model such languages as well as the role of its individual components in doing
so. We first provide a construction of Transformers for a subclass of counter
languages, including well-studied languages such as n-ary Boolean Expressions,
Dyck-1, and its generalizations. In experiments, we find that Transformers do
well on this subclass, and their learned mechanism strongly correlates with our
construction. Perhaps surprisingly, in contrast to LSTMs, Transformers do well
only on a subset of regular languages with degrading performance as we make
languages more complex according to a well-known measure of complexity. Our
analysis also provides insights on the role of self-attention mechanism in
modeling certain behaviors and the influence of positional encoding schemes on
the learning and generalization abilities of the model.


  In this paper, we describe the relationship between the Perron root and
eigenvectors of an irreducible subshift of finite type with the correlation
between the forbidden words in the subshift. In particular, we derive an
expression for the Perron eigenvectors of the associated adjacency matrix. As
an application, we obtain the Perron eigenvectors for irreducible $(0,1)$
matrices which are adjacency matrices for directed graphs. Moreover, we derive
an alternate definition of the Parry measure in ergodic theory on an
irreducible subshift of finite type.


  I study the technique of Algebraic Bethe Ansatz for solving integrable models
and show how it works in detail on the simplest example of spin 1/2 XXX
magnetic chain. Several other models are treated more superficially, only the
specific details are given. Several parameters, appearing in these
generalizations: spin $s$, anisotropy parameter $\ga$, shift $\om$ in the
alternating chain, allow to include in our treatment most known examples of
soliton theory, including relativistic model of Quantum Field Theory.


  Since the discovery of adversarial examples - the ability to fool modern CNN
classifiers with tiny perturbations of the input, there has been much
discussion whether they are a "bug" that is specific to current neural
architectures and training methods or an inevitable "feature" of high
dimensional geometry. In this paper, we argue for examining adversarial
examples from the perspective of Bayes-Optimal classification. We construct
realistic image datasets for which the Bayes-Optimal classifier can be
efficiently computed and derive analytic conditions on the distributions under
which these classifiers are provably robust against any adversarial attack even
in high dimensions. Our results show that even when these "gold standard"
optimal classifiers are robust, CNNs trained on the same datasets consistently
learn a vulnerable classifier, indicating that adversarial examples are often
an avoidable "bug". We further show that RBF SVMs trained on the same data
consistently learn a robust classifier. The same trend is observed in
experiments with real images in different datasets.


  We review the current understanding of the upper atmospheres of Uranus and
Neptune, and explore the upcoming opportunities available to study these
exciting planets. The ice giants are the least understood planets in the solar
system, having been only visited by a single spacecraft, in 1986 and 1989,
respectively. The upper atmosphere plays a critical role in connecting the
atmosphere to the forces and processes contained within the magnetic field. For
example, auroral current systems can drive charged particles into the
atmosphere, heating it by way of Joule heating. Ground-based observations of
H$_3^+$ provides a powerful remote diagnostic of the physical properties and
processes that occur within the upper atmosphere, and a rich data set exists
for Uranus. These observations span almost three decades and have revealed that
the upper atmosphere has continuously cooled between 1992 and 2018 at about 8
K/year, from $\sim$750 K to $\sim$500 K. The reason for this trend remain
unclear, but could be related to seasonally driven changes in the Joule heating
rates due to the tilted and offset magnetic field, or could be related to
changing vertical distributions of hydrocarbons. H$_3^+$ has not yet been
detected at Neptune, but this discovery provides low-hanging fruit for upcoming
facilities such as the James Webb Space Telescope (JWST) and the next
generation of 30 metre telescopes. Detecting H$_3^+$ at Neptune would enable
the characterisation of its upper atmosphere for the first time since 1989. To
fully understand the ice giants we need dedicated orbital missions, in the same
way the Cassini spacecraft explored Saturn. Only by combining in-situ
observations of the magnetic field with in-orbit remote sensing can we get the
complete picture of how energy moves between the atmosphere and the magnetic
field.


  The fundamental vacuum state of quantum fields, related to Minkowski space,
produces divergent fluctuations that must be suppressed in order to bring
reality to the description of physical systems. As a consequence, negative
vacuum expectation values of classically positive-defined quantities can
appear. This has been addressed in the literature as subvacuum phenomenon. Here
it is investigated how a scalar charged test particle is affected by the vacuum
fluctuations of a massive scalar field in D+1 spacetime when the background
evolves from empty space to a thermal bath, and also when a perfectly
reflecting boundary is included. It is shown that when the particle is brought
into a thermal bath it gains an amount of energy by means of positive
dispersions of its velocity components. The magnitude of this effect is
dependent on the temperature and also on the field mass. However, when a
reflecting wall is inserted, dispersions can be positive or negative, showing
that subvacuum effect happens even in a finite temperature environment.
Furthermore, a remarkable result is that temperature can even improve negative
velocity fluctuations. The magnitude of the residual effects depends on the
switching interval of time the system takes to evolve between two states.


  We provide integral formulae for the ADM mass of asymptotically flat
hypersurfaces in Riemannian manifolds with a certain warped product structure
in a neighborhood of infinity, thus extending Lam's recent results on Euclidean
graphs to this broader context. As applications we exhibit, in any dimension,
new classes of manifolds for which versions of the Positive Mass and Riemannian
Penrose inequalities hold and discuss a notion of quasi-local mass in this
setting. The proof explores a novel connection between the co-vector defining
the ADM mass of a hypersurface as above and the Newton tensor associated to its
shape operator, which takes place in the presence of an ambient Killing field.


  The brightest blazars detected by the Fermi Gamma-ray Space Telescope Large
Area Telescope (Fermi/LAT) show significant breaks in their spectra at a few
GeV. The sharpness and the position of the breaks can be well reproduced by
absorption of $\gamma$-rays via photon--photon pair production on He ii and H i
Lyman recombination continua (LyC) produced in the broad-line region (BLR).
Using 138 weeks of LAT observations of the brightest GeV blazar 3C 454.3 we
find a power-law dependence of the peak energy on flux and discover
anti-correlation between flux and the column density of the He ii LyC which is
responsible for absorption of the >2.5 GeV photons in this object. The strength
and the variability of the absorption implies the location of the gamma-ray
emitting zone close to the boundary of the high-ionization part of the BLR and
moving away from the black hole when the flux increases. A combination of the
GeV breaks with the detection of a few powerful blazars in the TeV range puts
strong constraints on the BLR size. Additional spectral breaks at ~100 and ~400
GeV due to absorption by the Balmer and Paschen lines could be detected by the
Cherenkov Telescope Array.


  Recently we have considered supertwistor reformulation of the D=4 N=1,2
superstring action that comprises Newman-Penrose dyad components and is
classically equivalent to the Green-Schwarz one. It was shown that in the
covariant kappa-symmetry gauge the supertwistor representation of the string
action simplifies. Here we analyze its Hamiltonian formulation, classify the
constraints on the phase-space variables, and find the covariant set of
generators of the gauge symmetries. Quantum symmetries of the supertwistor
representation of the string action are examined applying the world-sheet CFT
technique. Considered are various generalizations of the model from the
perspective of their possible relation to known twistor superstring models.


  We furnish a supersymmetric extension of the Standard Model with a flavour
discrete symmetry $A_5$ under which the lepton fields transform as an
irreducible triplet. Additional (`flavon') superfields are used to break $A_5$
into a $\mathbb{Z}_2 \times \mathbb{Z}_2$ subgroup in the charged-lepton sector
and another $\mathbb{Z}_2$ subgroup in the neutrino sector. The first column of
the resulting lepton mixing matrix is predicted and has entries which are
related to the golden ratio. Using the observed $\theta_{13}$ as input, our
model predicts a solar mixing angle $\theta_{12}$ in very good agreement with
experiment; it also predicts a correlation between the atmospheric mixing angle
$\theta_{23}$ and the $CP$-violating Dirac phase $\delta$.


  We explore the relations among quadratic modules, 2-crossed modules, crossed
squares and simplicial groups with Moore complex of length 2.


  We completed observations with the Effelsberg 100-m radio telescope to
measure the polarised emission from a complete sample of Compact Steep-Spectrum
sources. We observed the sources at four different frequencies. We complemented
these measurements with polarisation parameters at 1.4 GHz derived from the
NVSS. Previous single dish measurements were taken from the catalogue of Tabara
and Inoue. The depolarisation index DP was computed for four pairs of
frequencies. A drop in the fractional polarisation appeared in the radio
emission when observing at frequencies below about 2 GHz. Rotation measures
were derived for about 25% of the sources in the sample. The values range from
about -20 rad/m**2} found for 3C138 to 3900 rad/m**2 in 3C119. In all cases,
the lambda**2 law is closely followed. The presence of a foreground screen as
predicted by the Tribble model or with ``partial coverage'' as defined by
ourselves can explain the polarimetric behaviour of the CSS sources detected in
polarisation by the present observations. Indication of repolarisation at lower
frequencies was found for some sources. A case of possible variability in the
fractional polarisation is also suggested. The most unexpected result was found
for the distribution of the fractional polarisations versus the linear sizes of
the sources. Our results appear to disagree with the findings of Cotton and
collaborators and Fanti and collaborators for the B3-VLA sample of CSS sources,
the so-called ``Cotton effect''. This apparent contradiction may, however, be
caused by the large contamination of the sample by quasars with respect to the
B3-VLA.


  Realistic fluid-solid interaction potentials are essential in description of
confined fluids especially in the case of geometric heterogeneous surfaces.
Correlated random field is considered as a model of random surface with high
geometric roughness. We provide the general theory of effective coarse-grained
fluid-solid potential by proper averaging of the free energy of fluid molecules
which interact with the solid media. This procedure is largely based on the
theory of random processes. We apply first passage time probability problem and
assume the local Markov properties of random surfaces. General expression of
effective fluid-solid potential is obtained. In the case of small surface
irregularities analytical approximation for effective potential is proposed.
Both amorphous materials with large surface roughness and crystalline solids
with several types of fcc lattices are considered. It is shown that the wider
the lattice spacing in terms of molecular diameter of the fluid, the more
obtained potentials differ from classical ones. A comparison with published
Monte-Carlo simulations shows good qualitative agreement with the theory
predictions. The work provides a promising approach to explore how the random
geometric heterogeneity affects on thermodynamic properties of the fluids.


  This article is concerned with the derivation and the mathematical study of a
new mean-field model for the description of interacting electrons in crystals
with local defects. We work with a reduced Hartree-Fock model, obtained from
the usual Hartree-Fock model by neglecting the exchange term. First, we recall
the definition of the self-consistent Fermi sea of the perfect crystal, which
is obtained as a minimizer of some periodic problem, as was shown by Catto, Le
Bris and Lions. We also prove some of its properties which were not mentioned
before. Then, we define and study in details a nonlinear model for the
electrons of the crystal in the presence of a defect. We use formal analogies
between the Fermi sea of a perturbed crystal and the Dirac sea in Quantum
Electrodynamics in the presence of an external electrostatic field. The latter
was recently studied by Hainzl, Lewin, S\'er\'e and Solovej, based on ideas
from Chaix and Iracane. This enables us to define the ground state of the
self-consistent Fermi sea in the presence of a defect. We end the paper by
proving that our model is in fact the thermodynamic limit of the so-called
supercell model, widely used in numerical simulations.


  As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra
of type A_1 is introduced. Explicit realization of the new quantum TKK algebra
is constructed with the help of twisted quantum vertex operators over a Fock
space.


  In the last two decades, several classes of codes are introduced to protect
the copyrighted digital data. They have important applications in the scenarios
like digital fingerprinting and broadcast encryption schemes. In this paper we
will discuss three important classes of such codes, namely, frameproof codes,
parent-identifying codes and traceability codes.
  Firstly, suppose $N(t)$ is the minimal integer such that there exists a
binary $t$-frameproof code of length $N$ with cardinality larger than $N$, we
prove that $N(t)\ge\frac{15+\sqrt{33}}{24} (t-2)^2$, which is a great
improvement of the previously known bound $N(t)\ge\binom{t+1}{2}$. Moreover, we
find that the determination of $N(t)$ is closely related to a conjecture of
Erd\H{o}s, Frankl and F\"uredi posed in the 1980's, which implies the
conjectured value $N(t)=t^2+o(t^2)$. Secondly, we derive a new upper bound for
parent-identifying codes, which is superior than all previously known bounds.
Thirdly, we present an upper bound for 3-traceability codes, which shows that a
$q$-ary 3-traceability code of length $N$ can have at most $cq^{\lceil
N/9\rceil}$ codewords, where $c$ is a constant only related to the code length
$N$. It is the first meaningful upper bound for 3-traceability codes and our
result supports a conjecture of Blackburn et al. posed in 2010.


  A significant portion of research on distributed ledgers has focused on
circumventing the limitations of leader-based blockchains mainly in terms of
scalability, decentralization and power consumption. Leaderless architectures
based on directed acyclic graphs (DAGs) avoid many of these limitations
altogether, but their increased flexibility and performance comes at the cost
of increased design complexity, so their potential has remained largely
unexplored. Management of write access to these ledgers presents a major
challenge because ledger updates may be made in parallel, hence transactions
cannot simply be serialised and prioritised according to token fees paid to
validators. In this work, we propose an access control scheme for leaderless
DAG-based ledgers which is based on consuming credits rather than paying fees
in the base token. We outline a general model for this new approach and provide
some simulation results showing promising performance boosts.


  Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.


  We consider a class of fully nonlinear integro-differential operators where
the nonlocal integral has two components: the non-degenerate one corresponds to
the $\alpha$-stable operator and the second one (possibly degenerate)
corresponds to a class of \textit{lower order} L\'evy measures. Such operators
do not have a global scaling property. We establish H\"{o}lder regularity,
Harnack inequality and boundary Harnack property of solutions of these
operators.


  For given graphs $G_1, G_2,\ldots, G_n$ and any integer $j$, the size of the
multipartite Ramsey number $m_j(G_1, G_2,\ldots, G_n)$ is the smallest positive
integer $t$ such that any $n$-coloring of the edges of $K_{j\times t}$ contains
a monochromatic copy of $G_i$ in color $i$ for some $i$, $1 \leq i \leq n$,
where $K_{j\times t}$ denotes the complete multipartite graph having $j$
classes with $t$ vertices per each class. In this paper we compute the size of
the multipartite Ramsey number $m_j(K_{1,2}, P_4, nK_2)$ for any $j,n\geq 2$
and $m_j(nK_2,C_7)$, for any $j\leq4$ and $n\geq 2$.


  We show that measuring the $\cos 2\phi $ angular dependence in unpolarized
Drell-Yan processes with $\pi^-$ beams colliding on proton and deuteron targets
can determine the ratio of the Boer-Mulders functions for $d$ and $u$ quarks
inside the proton $h_1^{\perp,d}/h_1^{\perp,u}$, which is still lack of
theoretical constraint. The comparison of the $\cos 2 \phi$ asymmetries
measured in unpolarized $\pi^- p$ and $\pi^- D$ Drell-Yan processes, which are
accessible at CERN by the COMPASS collaboration, can help to discriminate
whether $h_1^\perp$ effects or QCD vacuum effects are preferred by data.


  In this semi-expository paper, we first explain key notions from current
quantum information theory and criteria for them in a coherent way. These
include separability/entanglement, Schmidt numbers of bi-partite states and
block-positivity, together with various kinds of positive maps between matrix
algebras like entanglement breaking maps, $k$-superpositive maps, completely
positive maps, $k$-positive maps. We will begin with concrete examples of
elementary positive maps given by $x\mapsto s^*xs$, and use Choi matrices and
duality to explain all the notions mentioned above. We also show that the Choi
matrix can be defined free from coordinates. The above notions of positive maps
give rise to mapping cones, whose dual cones are characterized in terms of
compositions or tensor products of linear maps. Through the discussion, we
exhibit an identity which connects tensor products and compositions of linear
maps between matrix algebras through the Choi matrices. Using this identity, we
show that the description of the dual cone with tensor products is possible
only when the involving cones are mapping cones, and recover various known
criteria with ampliation for the notions mentioned above. As another
applications of the identity, we construct various mapping cones arising from
ampliation and factorization, and provide several equivalent statements to PPT
(positive partial transpose) square conjecture in terms of tensor products.


  An implementation of a harmonic injection pulse width modulation
frequency-modulated triangular carrier (HIPWM-FMTC) control strategy applied to
a multilevel power inverter feeding an asynchronous motor is presented. The aim
was to justify the reduction in acoustic noise emitted by the machine compared
with other strategies in the technical literature. In addition, we checked how
the THD at the inverter output was reduced compared to the other control
techniques used as a reference. The proposed strategy is based on frequency
modulation of the triangular carrier. The main advantage of the proposed method
is that only one control parameter is required for modifying the electrical
spectrum. Therefore, the mechanical natural frequencies and spatial harmonics
of the machine can be avoided, and acoustic noise can be reduced. The
effectiveness of the technique was demonstrated after laboratory validation by
comparing the acoustic results for a 1 kW motor. The results obtained from the
laboratory tests are presented and compared with those of other acoustic
measurements using different PWM strategies.


  We present rest-frame optical spectroscopic observations of 24 Hot
Dust-Obscured Galaxies (Hot DOGs) at redshifts 1.7-4.6 with KECK/NIRES. Our
targets are selected based on their extreme red colors to be the highest
luminosity sources from the WISE infrared survey. In 20 sources with
well-detected emission we fit the key [O III], H$\beta$, H$\alpha$, [N II], and
[S II] diagnostic lines to constrain physical conditions. Of the 17 targets
with a clear detection of the [O III]$\rm \lambda$5007A emission line, 15
display broad blueshifted and asymmetric line profiles, with widths ranging
from 1000 to 8000 $\rm km\ s^{-1}$ and blueshifts up to 3000 $\rm km\ s^{-1}$.
These kinematics provide strong evidence for the presence of massive ionized
outflows of up to $8000\ \rm M_\odot\ yr^{-1}$, with a median of $150\ \rm
M_\odot\ yr^{-1}$. As many as eight sources show optical emission line ratios
consistent with vigorous star formation. Balmer line star-formation rates,
uncorrected for reddening, range from 30--1300 $\rm M_\odot\ yr^{-1}$, with a
median of $50\ \rm M_\odot\ yr^{-1}$. Estimates of the SFR from SED fitting of
mid and far-infrared photometry suggest significantly higher values. We
estimate the central black hole masses to be of order $10^{8-10}\rm\ M_\odot$,
assuming the present-day $\rm M_{BH}-\sigma_*$ relation. The bolometric
luminosities and the estimated masses of the central black holes of these
galaxies suggest that many of the AGN-dominated Hot DOGs are accreting at or
above their Eddington limit. The combination of ongoing star formation, massive
outflows, and high Eddington ratios suggest Hot DOGs are a transitional phase
in galaxy evolution.


  The critical behavior of a model with N-vector complex order parameter and
three quartic coupling constants that describes phase transitions in
unconventional superconductors, helical magnets, stacked triangular
antiferromagnets, superfluid helium-3, and zero-temperature transitions in
fully frustrated Josephson-junction arrays is studied within the field-
theoretical renormalization-group approach in three dimensions. To obtain
qualitatively and quantitatively correct results perturbative expansions for
\beta-functions and critical exponents are calculated up to three-loop order
and resummed by means of the generalized Pade-Borel procedure. Fixed-point
coordinates, critical exponent values, RG flows, etc. are found for the
physically interesting cases N = 2 and N = 3. Marginal values of N at which the
topology of the flow diagram changes are determined as well. In most cases the
systems mentioned are shown to undergo fluctuation-driven first-order phase
transitions. Continuous transitions are allowed in hexagonal d-wave
superconductors, in planar helical magnets (into sinusoidal linearly-polarized
phase), and in triangular antiferromagnets (into simple unfrustrated ordered
states) with critical exponents \gamma = 1.336, \nu = 0.677, \alpha = -0.030,
\beta = 0.347, \eta = 0.026, which are hardly believed to be experimentally
distinguishable from those of the 3D XY model. The chiral fixed point of RG
equations is found to exist and possess some domain of attraction provided N >
3. Thus, magnets with Heisenberg (N = 3) and XY-like (N = 2) spins should not
demonstrate chiral critical behavior with unusual critical exponents; they can
approach the chiral state only via first-order phase transitions.


  We discuss the thermal pressures ($n_H T$) in predominantly cold, neutral
interstellar gas in the Magellanic Clouds, derived from analyses of the
fine-structure excitation of neutral carbon, as seen in high-resolution
HST/STIS spectra of seven diverse sight lines in the LMC and SMC. Detailed fits
to the line profiles of the absorption from C I, C I*, and C I** yield
consistent column densities for the 3--6 C I multiplets detected in each sight
line. In the LMC and SMC, $N$(C I$_{\rm tot}$) is consistent with Galactic
trends versus $N$(Na I) and $N$(CH), but is slightly lower versus $N$(K I) and
$N$(H$_2$). As for $N$(Na I) and $N$(K I), $N$(C I$_{\rm tot}$) is generally
significantly lower, for a given $N$(H$_{\rm tot}$), in the LMC and
(especially) in the SMC, compared to the local Galactic relationship. For the
LMC and SMC components with well determined column densities for C I, C I*, and
C I**, the derived thermal pressures are typically factors of a few higher than
the values found for most cold, neutral clouds in the Galactic ISM. Such
differences are consistent with the predictions of models for clouds in systems
(like the LMC and SMC) that are characterized by lower metallicities, lower
dust-to-gas ratios, and enhanced radiation fields -- where higher pressures are
required for stable cold, neutral clouds. The pressures may be further enhanced
by energetic activity (e.g., due to stellar winds, star formation, and/or
supernova remnants) in several of the regions probed by these sight lines.
Comparisons are made with the C I observed in some quasar absorption-line
systems.


  Marker-less monocular 3D human motion capture (MoCap) with scene interactions
is a challenging research topic relevant for extended reality, robotics and
virtual avatar generation. Due to the inherent depth ambiguity of monocular
settings, 3D motions captured with existing methods often contain severe
artefacts such as incorrect body-scene inter-penetrations, jitter and body
floating. To tackle these issues, we propose HULC, a new approach for 3D human
MoCap which is aware of the scene geometry. HULC estimates 3D poses and dense
body-environment surface contacts for improved 3D localisations, as well as the
absolute scale of the subject. Furthermore, we introduce a 3D pose trajectory
optimisation based on a novel pose manifold sampling that resolves erroneous
body-environment inter-penetrations. Although the proposed method requires less
structured inputs compared to existing scene-aware monocular MoCap algorithms,
it produces more physically-plausible poses: HULC significantly and
consistently outperforms the existing approaches in various experiments and on
different metrics. Project page: https://vcai.mpi-inf.mpg.de/projects/HULC/.


  We develop a behavioral theory for the untyped call-by-value lambda calculus
extended with the delimited-control operators shift and reset. For this
calculus, we discuss the possible observable behaviors and we define an
applicative bisimilarity that characterizes contextual equivalence. We then
compare the applicative bisimilarity and the CPS equivalence, a relation on
terms often used in studies of control operators. In the process, we illustrate
how bisimilarity can be used to prove equivalence of terms with
delimited-control effects.


  AM CVn systems are a rare type of cataclysmic variable star consisting of a w
hite dwarf accreting material from a low-mass, hydrogen-poor donor star. These
helium-rich systems usually have orbital periods that are less than 65 minutes
an d are predicted to be sources of gravitational waves. We have analyzed the
catalogued X-ray data from the Chandra, XMM-Newton, and the Neil Gehrels Swift
Observatory (hereafter referred to as 'Swift') to investigate the relationship
between X-ray luminosity and the orbital period of AM CVn systems. We find that
the high accretion-rate systems which are likely to have optically thick
boundary laye rs are sub-luminous in X-rays relative to theoretical model
predictions for the boundary layer luminosity, while the longer orbital period,
lower bolometric luminosity systems match fairly well to the model predictions,
with the exception of an overluminous system which has already been suggested
to show magnetic accretion.


  We prove that for a class of zero-sum differential games with incomplete
information on both sides, the value admits a probabilistic representation as
the value of a zero-sum stochastic differential game with complete information,
where both players control a continuous martingale. A similar representation as
a control problem over discontinuous martingales was known for games with
incomplete information on one side (see Cardaliaguet-Rainer [8]), and our
result is a continuous-time analog of the so called splitting-game introduced
in Laraki [20] and Sorin [27] in order to analyze discrete-time models. It was
proved by Cardaliaguet [4, 5] that the value of the games we consider is the
unique solution of some Hamilton-Jacobi equation with convexity constraints.
Our result provides therefore a new probabilistic representation for solutions
of Hamilton-Jacobi equations with convexity constraints as values of stochastic
differential games with unbounded control spaces and unbounded volatility.


  The study of young star cluster (YSC) systems, preferentially in starburst
and merging galaxies, has seen great interest in the recent past, as it
provides important input to models of star formation. However, even some basic
properties (like the luminosity function [LF]) of YSC systems are still under
debate. Here we study the photometric properties of the YSC system in the
nearest major merger system, the Antennae galaxies. We find evidence for the
existence of a statistically significant turnover in the LF.


  Despite sophisticated phishing email detection systems, and training and
awareness programs, humans continue to be tricked by phishing emails. In an
attempt to better understand why phishing email attacks still work and how best
to mitigate them, we have carried out an empirical study to investigate
people's thought processes when reading their emails. We used a scenario-based
role-play "think aloud" method and follow-up interviews to collect data from 19
participants. The experiment was conducted using a simulated web email client,
and real phishing and legitimate emails adapted to the given scenario. The
analysis of the collected data has enabled us to identify eleven factors that
influence people's response decisions to both phishing and legitimate emails.
Furthermore, based on the user study findings, we discuss novel insights into
flaws in the general email decision-making behaviors that could make people
susceptible to phishing attacks.


  In this article we provide the noncommutative Sprott models. We demonstrate,
that effectively, each of them is described by system of three complex,
ordinary and nonlinear differential equations. Apart of that, we find for such
modified models the corresponding (noncommutative) jerk dynamics as well as we
study numerically as an example, the deformed Sprott-A system.


  In the recently-published paper "Gold Nanobipyramid-Enhanced Hydrogen Sensing
with Plasmon Red Shifts Reaching 140 nm at 2 vol% Hydrogen Concentration" by
Yip et al.,[1] the authors claimed that the tuning of catalytic activities of
the synthesized Au nanobipyramids(NBP)@Pd nanostructures was mainly due to the
electronic effect. Here, we show that this claim is unsupported and an
important reference was mis-cited in this commented publication.


  A sterile neutrino in the $3+1$ scheme, where the sterile accounts for
neutrino anomalies not explained solely by the weak active neutrinos, arises as
a natural source for the breaking of the $\mu-\tau$ symmetry suggested by
oscillation neutrino data. We explore the predictions for the Dirac CP phases
in this scenario, with and without sterile neutrino decay, and show that
current limits on $\delta_{CP}$ suggest a normal hierarchy and a lightest
neutrino scale below 0.1~eV as the most plausible explanation for that, when
Majorana phases are null. Other Dirac phases turn out to be non zero as well.


  In the present paper, we study the upper and lower bounds for the number of
facets of symmetric edge polytopes of connected graphs conjectured by Braun and
Bruegge. In particular, we show that their conjecture is true for any graph
that is the join of two graphs (equivalently, for any connected graph whose
complement graph is not connected). It is known that any symmetric edge
polytope is a centrally symmetric reflexive polytope. Hence our results give a
partial answer to Nill's conjecture: the number of facets of a $d$-dimensional
reflexive polytope is at most $6^{d/2}$.


  We introduce transverse momentum dependent parton distribution functions
(TMDs) for gluons with definite rank. The rank refers to the azimuthal
dependence corresponding to the tensorial structure in transverse momenta
multiplying universal functions only depending on $x$ and $p_T^2$. In this way
only a finite number of functions of definite rank remains for a target with
the maximal rank depending on its spin. Gauge links, required for color gauge
invariance, enter in the explicit description of the matrix elements
corresponding to these TMDs and account for their process dependence. In this
way a general gauge link dependent function is expressed in the universal set,
where all process (i.e. gauge link) dependence is isolated in gluonic pole
factors multiplying the universal TMDs of definite rank.


  Pricing exotic multi-asset path-dependent options requires extensive Monte
Carlo simulations. In the recent years the interest to the Quasi-monte Carlo
technique has been renewed and several results have been proposed in order to
improve its efficiency with the notion of effective dimension. To this aim,
Imai and Tan introduced a general variance reduction technique in order to
minimize the nominal dimension of the Monte Carlo method. Taking into account
these advantages, we investigate this approach in detail in order to make it
faster from the computational point of view. Indeed, we realize the linear
transformation decomposition relying on a fast ad hoc QR decomposition that
considerably reduces the computational burden. This setting makes the linear
transformation method even more convenient from the computational point of
view. We implement a high-dimensional (2500) Quasi-Monte Carlo simulation
combined with the linear transformation in order to price Asian basket options
with same set of parameters published by Imai and Tan. For the simulation of
the high-dimensional random sample, we use a 50-dimensional scrambled Sobol
sequence for the first 50 components, determined by the linear transformation
method, and pad the remaining ones out by the Latin Hypercube Sampling. The aim
of this numerical setting is to investigate the accuracy of the estimation by
giving a higher convergence rate only to those components selected by the
linear transformation technique. We launch our simulation experiment also using
the standard Cholesky and the principal component decomposition methods with
pseudo-random and Latin Hypercube sampling generators. Finally, we compare our
results and computational times, with those presented in Imai and Tan.


  Understanding electronic properties of sub-stoichiometric phases of titanium
oxide such as Magn\'eli phase Ti4O7 is crucial in designing and modeling
resistive switching devices. Here we present our study on Magn\'eli phase Ti4O7
together with rutile TiO2 and Ti2O3 using density functional theory methods
with atomic-orbital-based self-interaction correction (ASIC). We predict a new
antiferromagnetic ground state in the low temperature phase (or LT phase), and
we explain energy difference with a competing antiferromagnetic state using a
Heisenberg model. The predicted energy ordering of these states in the LT phase
is calculated to be robust in a wide range of modeled isotropic strain. We have
also investigated the dependence of the electronic structures of the Ti-O
phases on stoichiometry. The splitting of titanium t2g orbitals is enhanced
with increasing oxygen deficiency as Ti-O is reduced. The electronic properties
of all these phases can be reasonably well described by applying ASIC with a
standard value for transition metal oxides of the empirical parameter {\alpha}
of 0.5 representing the magnitude of the applied self-interaction correction.


  Efficient and robust policy transfer remains a key challenge for
reinforcement learning to become viable for real-wold robotics. Policy transfer
through warm initialization, imitation, or interacting over a large set of
agents with randomized instances, have been commonly applied to solve a variety
of Reinforcement Learning tasks. However, this seems far from how skill
transfer happens in the biological world: Humans and animals are able to
quickly adapt the learned behaviors between similar tasks and learn new skills
when presented with new situations. Here we seek to answer the question: Will
learning to combine adaptation and exploration lead to a more efficient
transfer of policies between domains? We introduce a principled mechanism that
can "Adapt-to-Learn", that is adapt the source policy to learn to solve a
target task with significant transition differences and uncertainties. We show
that the presented method learns to seamlessly combine learning from adaptation
and exploration and leads to a robust policy transfer algorithm with
significantly reduced sample complexity in transferring skills between related
tasks.


  Application of the Ramsey Infinite Theorem to the variational principles of
physics is discussed. According to the Ramsey Infinite Theorem,there exists the
infinite, monochromatic chain of the pathways (clique), which are completely
built from actual or virtual paths, connecting the intermediate states of the
system.


  We have provided a fractional generalization of the Poisson renewal processes
by replacing the first time derivative in the relaxation equation of the
survival probability by a fractional derivative of order $\alpha ~(0 < \alpha
\leq 1)$. A generalized Laplacian model associated with the Mittag-Leffler
distribution is examined. We also discuss some properties of this new model and
its relevance to time series. Distribution of gliding sums, regression
behaviors and sample path properties are studied. Finally we introduce the
$q$-Mittag-Leffler process associated with the $q$-Mittag-Leffler distribution.


  The dependence on volume fraction $\varphi$ of the Flory-Huggins
$\chi_{\mathrm{wp}}\left(\varphi\right)$ describing the free energy of mixing
of polymers in water is obtained by exploiting the connection of
$\chi_{\mathrm{wp}}\left(\varphi\right)$ to the chemical potential of the
water, for which quasi-chemical theory is satisfactory. We test this
theoretical approach with simulation data for aqueous solutions of capped PEO
oligomers. For CH$_3$(CH$_2$-O-CH$_2$)$_m$CH$_3$ ($m$=11),
$\chi_{\mathrm{wp}}\left(\varphi\right)$ depends strongly on $\varphi$,
consistent with experiment. These results identify coexisting water-rich and
water-poor solutions at $T$ = 300K and $p$ = 1atm. Direct observation of the
coexistence of these two solutions on simulation time scales supports that
prediction for the system studied. This approach directly provides the osmotic
pressures. The osmotic second virial coefficient for these chains is positive,
reflecting repulsive interactions between the chains in the water, a good
solvent for these chains.


  Magnetic dc susceptibility ($\chi$) and electron spin resonance (ESR)
measurements in the paramagnetic regime, are presented. We found a Curie-Weiss
(CW) behavior for $\chi$(T) with a ferromagnetic $\Theta = 446(5)$ K and
$\mu_{eff} = 4.72(9) \mu_{B}/f.u.$, this being lower than that expected for
either $Fe^{3+}(5.9\mu_{B})$ or $Fe^{2+}(4.9\mu_{B})$ ions. The ESR g-factor $g
= 2.01(2)$, is associated with $Fe^{3+}$. We obtained an excellent description
of the experiments in terms of two interacting sublattices: the localized
$Fe^{3+}$ ($3d^{5}$) cores and the delocalized electrons. The coupled equations
were solved in a mean-field approximation, assuming for the itinerant electrons
a bare susceptibility independent on $T$. We obtained $\chi_{e}^{0} = 3.7$
$10^{-4}$ emu/mol. We show that the reduction of $\mu_{eff}$ for $Fe^{3+}$
arises from the strong antiferromagnetic (AFM) interaction between the two
sublattices. At variance with classical ferrimagnets, we found that $\Theta$ is
ferromagnetic. Within the same model, we show that the ESR spectrum can be
described by Bloch-Hasegawa type equations. Bottleneck is evidenced by the
absence of a $g$-shift. Surprisingly, as observed in CMR manganites, no
narrowing effects of the ESR linewidth is detected in spite of the presence of
the strong magnetic coupling. These results provide evidence that the magnetic
order in $Sr_{2}FeMoO_{6}$ does not originates in superexchange interactions,
but from a novel mechanism recently proposed for double perovskites.


  Collecting genomics data across multiple heterogeneous populations (e.g.,
across different cancer types) has the potential to improve our understanding
of disease. Despite sequencing advances, though, resources often remain a
constraint when gathering data. So it would be useful for experimental design
if experimenters with access to a pilot study could predict the number of new
variants they might expect to find in a follow-up study: both the number of new
variants shared between the populations and the total across the populations.
While many authors have developed prediction methods for the single-population
case, we show that these predictions can fare poorly across multiple
populations that are heterogeneous. We prove that, surprisingly, a natural
extension of a state-of-the-art single-population predictor to multiple
populations fails for fundamental reasons. We provide the first predictor for
the number of new shared variants and new total variants that can handle
heterogeneity in multiple populations. We show that our proposed method works
well empirically using real cancer and population genetics data.


  This paper studies the design of an optimal privacyaware estimator of a
public random variable based on noisy measurements which contain private
information. The public random variable carries non-private information,
however, its estimate will be correlated with the private information due to
the estimation process. It is assumed that the estimate of the public random
variable is revealed to an untrusted party. The objective is to design an
estimator for the public random variable such that the leakage of the private
information, via the estimation process, is kept below a certain level. The
privacy metric is defined as the discrete conditional entropy of the private
random variable, which carries the private information, given the output of the
estimator. A binary loss function is considered for the estimation of the
public random variable. It is shown that the optimal privacy-aware estimator is
the solution of a (possibly infinite-dimensional) convex optimization problem.
We next study the optimal perfect privacy estimator which ensures that the
estimate of the public random variable is independent of the private
information. A necessary and sufficient condition is derived which guarantees
that an estimator satisfies the perfect privacy requirement. It is shown that
the optimal perfect privacy estimator is the solution of a linear optimization
problem. A sufficient condition for the existence of the optimal perfect
privacy estimator is derived when the estimator has access to discretized
measurements of sensors.


  Thanks to the high quality data of space missions, the detection of mixed
modes has become possible in numerous stars. In this work, we investigate how
the mixing character of dipolar mixed modes changes with stellar evolution, as
well as with frequency within each stellar model. This is achieved by
monitoring the variations in the coupling strength and the period spacing of
dipolar mixed modes in red-giant models. These parameters are measured by
fitting the asymptotic expansion of mixed modes to the model frequencies of a
grid of red-giant models with masses between 1.0 and 2.0 $M_\odot$ and three
different chemical abundances. The coupling strength and the period spacing
decrease with stellar evolution. We find that the slopes of their decreasing
trends depend on the radial order of the pressure mode component. A
non-negligible increase of the coupling strength with frequency by up to around
40\% is found in the observable frequency range for a set of red-giant models.
On the contrary, no significant changes of the period spacing with frequency
are found. The changes in the mixing character of the modes are in most cases
affected by the model mass and metallicity. Buoyancy glitches also have an
impact on the mixing character. Significant fluctuations in the estimated
coupling strength and period spacing are found for models approaching the
luminosity bump, if the glitch impact of the frequencies is not considered in
the applied asymptotic expansion.


  Using the Salpeter criterion and known results from solid state physics,the
Debye temperature of a solid in equilibrium with a Debye-Huckel plasma was
calculated.This result could have interesting applications in studies of
various kinds of interstellar clouds.


  The consideration of dynamics of relativistic beams/particles is based on
variational approach to rational (in dynamical variables) approximation for
equations of motions. It allows to control contribution from each scale of
underlying multiscales and represent solutions via exact nonlinear eigenmodes
expansions. Our approach is based on methods provided possibility to work with
well-localized bases in phase space and good convergence properties of the
corresponding expansions.


  In this paper, we derive a new linear convergence rate for the gradient
method with fixed step lengths for non-convex smooth optimization problems
satisfying the Polyak-Lojasiewicz (PL) inequality. We establish that the PL
inequality is a necessary and sufficient condition for linear convergence to
the optimal value for this class of problems. We list some related classes of
functions for which the gradient method may enjoy linear convergence rate.
Moreover, we investigate their relationship with the PL inequality.


  The von Mises-Fisher family is a parametric family of distributions on the
surface of the unit ball, summarised by a concentration parameter and a mean
direction. As a quasi-Bayesian prior, the von Mises-Fisher distribution is a
convenient and parsimonious choice when parameter spaces are isomorphic to the
hypersphere (e.g., maximum score estimation in semi-parametric discrete choice,
estimation of single-index treatment assignment rules via empirical welfare
maximisation, under-identifying linear simultaneous equation models). Despite a
long history of application, measures of statistical divergence have not been
analytically characterised for von Mises-Fisher distributions. This paper
provides analytical expressions for the $f$-divergence of a von Mises-Fisher
distribution from another, distinct, von Mises-Fisher distribution in
$\mathbb{R}^p$ and the uniform distribution over the hypersphere. This paper
also collect several other results pertaining to the von Mises-Fisher family of
distributions, and characterises the limiting behaviour of the measures of
divergence that we consider.


  The annihilation parameters of positrons with electrons in different shells
of Argon, Iron and Copper atoms are calculated below the positronium (Ps)
formation thresholds. Quite accurate ab initio calculations of the bound state
wavefunctions of Argon, Iron and Copper orbitals are obtained from Cowan
computer code. A least-squares variational method (LSVM) is used for
determining the wavefunction of the positrons. The program is employed for
calculating the s-wave partial cross sections of positrons scattered by Iron
and Copper atoms. Our results of the effective charge are compared with
available experimental and theoretical ones. --


  We propose a novel scheme for enhancing the quality factor of coupled
resonators optical waveguides (CROWs) when operating near a degenerate band
edge (DBE). A DBE is a four-mode exceptional point of degeneracy (EPD)
occurring when four Bloch eigenmodes coalesce providing a resonance condition
with a giant enhancement in fields. We report an unprecedented scaling law of
quality factor of CROWs when operating at the DBE, even in the presence of
losses and structural perturbations. Remarkably, the Q factor of the proposed
CROW can be engineered to exceed that of a single ring resonator having a
diameter equal to the CROW length, hence having an overall strong area
reduction. The findings reported in this letter are critical for enhancing
fields amplitudes to giant levels and the Q factor of ring resonators and are
very beneficial for various applications including four wave mixing, Q
switching, lasers, and highly sensitive sensors.


  We compute the index of the real Cauchy-Riemann operator defined in FJRW
theory in case of the smooth metric. For the cylindrical metric, we study the
relation between the index of the linearized operator of Witten map and weights
in weighted Sobolev space.


  A comprehensive temporal analysis has been performed on the 319 brightest
GRBs with T90>2s from the BATSE current catalog. The rise times, fall times,
full-widths at half maximum (FWHM), pulse amplitudes and pulse areas were
measured and the frequency distributions are presented here. The distribution
of time intervals between pulses is not random but compatible with a lognormal
distribution when allowance was made for the 64 ms time resolution and a small
excess (5%) of long duration intervals that is often referred to as a
Pareto-Levy tail. A range of correlations are presented on pulse and burst
properties. The rise and fall times, FWHM and area of the pulses are highly
correlated with each other. The time intervals between pulses and pulse
amplitudes of neighbouring pulses are correlated with each other. It was also
found that the number of pulses, N, in GRBs is strongly correlated with the
fluence and the duration and that can explain the well known correlation
between duration and fluence. The GRBs were sorted into three catagories based
on N i.e. 3<=N<=12, 13<=N<=24, N>=25. The properties of pulses before and after
the stongest pulse were compared for the three catagories of bursts. This
analysis revealed that the GRBs with large numbers of pulses have narrower and
faster pulses and also larger fluences, longer durations and higher hardness
ratios than the GRBs with smaller numbers of pulses.


  The P-matrix approach for the determination of the orbit spaces of compact
linear groups enabled to determine all orbit spaces of compact coregular linear
groups with up to 4 basic polynomial invariants and, more recently, all orbit
spaces of compact non-coregular linear groups with up to 3 basic invariants.
This approach does not involve the knowledge of the group structure of the
single groups but it is very general, so after the determination of the orbit
spaces one has to determine the corresponding groups. In this article it is
reviewed the main ideas underlying the P-matrix approach and it is reported the
list of linear irreducible finite groups and of linear compact simple Lie
groups, with up to 4 basic invariants, together with their orbit spaces. Some
general properties of orbit spaces of coregular groups are also discussed. This
article will deal only with the mathematical aspect, however one must keep in
mind that the stratification of the orbit spaces represents the possible
schemes of symmetry breaking and that the phase transitions appear when the
minimum of an invariant potential function shifts from one stratum to another,
so the exact knowledge of the orbit spaces and their stratifications might be
useful to single out some yet hidden properties of phase transitions.


  Langmuir monolayers are modeled as systems of short chains, which are
confined to a planar surface at one end, but free to move within the plane. The
phase behavior is calculated in a mean field approximation, which combines the
self consistent field method with elements of classical density functional
theory. It is shown that phases with tilt order are unstable in systems of
stiff chains, but can be stabilized by chain conformational entropy in systems
of sufficiently flexible chains. The chain entropy is also responsible for the
appearance of an additional untilted phase, the liquid expanded phase. The
region of stability of the different phases is discussed, and their microscopic
structure is analyzed in some detail.


  Optical spectral weight transfer associated with the onset of
superconductivity at high energy scales compared with the superconducting gap
has been observed in several systems such as high-$T_c$ cuprates. While there
are still debates on the origin of this phenomenon, a consensus is that it is
due to strong correlation effects beyond the BCS theory. Here we show that
there is another route to a nonzero spectral weight transfer based on the
quantum geometry of the conduction band in multiband systems. We discuss
applying this idea to the cuprates and twisted multilayer graphene.


  The frequency distinguishability of two single photons was successfully
erased using single photon frequency up-conversion. A frequency non-degenerate
photon pair generated via spontaneous four-wave mixing in a dispersion shifted
fiber was used to emulate two telecom-band single photons that were in the same
temporal mode but in different frequency modes. The frequencies of these
photons were converted to the same frequency by using the sum frequency
generation process in periodically poled lithium niobate waveguides, while
maintaining their temporal indistinguishability. As a result, the two converted
photons exhibited a non-classical dip in a Hong-Ou-Mandel quantum interference
experiment. The present scheme will add flexibility to networking quantum
information systems that use photons with various wavelengths.


  The action of the idempotent deformations on finite groups is discussed. This
action is described in terms of the homological properties of groups. The
orbits of finite simple groups are determined.


  We introduce the isoperimetric loss as a regularization criterion for
learning the map from a visual representation to a semantic embedding, to be
used to transfer knowledge to unknown classes in a zero-shot learning setting.
We use a pre-trained deep neural network model as a visual representation of
image data, a Word2Vec embedding of class labels, and linear maps between the
visual and semantic embedding spaces. However, the spaces themselves are not
linear, and we postulate the sample embedding to be populated by noisy samples
near otherwise smooth manifolds. We exploit the graph structure defined by the
sample points to regularize the estimates of the manifolds by inferring the
graph connectivity using a generalization of the isoperimetric inequalities
from Riemannian geometry to graphs. Surprisingly, this regularization alone,
paired with the simplest baseline model, outperforms the state-of-the-art among
fully automated methods in zero-shot learning benchmarks such as AwA and CUB.
This improvement is achieved solely by learning the structure of the underlying
spaces by imposing regularity.


  The standard model of particle physics is analyzed for the case of a Higgs
potential not favoring spontaneous electroweak symmetry breaking to gain
insight into the physics of the standard model. Electroweak breaking still
takes place, and quarks and leptons still acquire masses but through bosonic
technicolor. This ``other'' phase of the standard model exhibits interesting
phenomena.


  This text develops a homotopy theory of 2-categories analogous to
Grothendieck's homotopy theory of categories developed in "Pursuing Stacks". We
define the notion of "basic localizer of 2-Cat", 2-categorical generalization
of Grothendieck's notion of basic localizer, and we show that the homotopy
theories of $Cat$ and 2-$Cat$ are equivalent in a remarkably strong sense:
there is an isomorphism, compatible with localization, between the ordered
classes of basic localizers of $Cat$ and 2-$Cat$. It follows that weak homotopy
equivalences in 2-$Cat$ can be characterised in an internal way, without
mentioning topological spaces or simplicial sets.


  Maximally recoverable local reconstruction codes (MR LRCs for short) have
received great attention in the last few years. Various constructions have been
proposed in literatures. The main focus of this topic is to construct MR LRCs
over small fields. An $(N=nr,r,h,\Gd)$-MR LRC is a linear code over finite
field $\F_\ell$ of length $N$, whose codeword symbols are partitioned into $n$
local groups each of size $r$. Each local group can repair any $\Gd$ erasure
errors and there are further $h$ global parity checks to provide fault
tolerance from more global erasure patterns.
  MR LRCs deployed in practice have a small number of global parities such as
$h=O(1)$. In this parameter setting, all previous constructions require the
field size $\ell =\Omega_h (N^{h-1-o(1)})$. It remains challenging to improve
this bound. In this paper, via subspace direct sum systems, we present a
construction of MR LRC with the field size $\ell= O(N^{h-2+\frac1{h-1}-o(1)})$.
In particular, for the most interesting cases where $h=2,3$, we improve
previous constructions by either reducing field size or removing constraints.
In addition, we also offer some constructions of MR LRCs for larger global
parity $h$ that have field size incomparable with known upper bounds. The main
techniques used in this paper is through subspace direct sum systems that we
introduce. Interestingly, subspace direct sum systems are actually equivalent
to $\F_q$-linear codes over extension fields. Based on various constructions of
subspace direct sum systems, we are able to construct several classes of MR
LRCs.


  We study the free resolutions of some Artin Gorenstein algebras of Hilbert
function $(1,4,k,k,4,1)$ and we prove that all such algebras have the Strong
Lefschetz property if they have the Weak Lefschetz property. In the case $k=4$
we prove that the Hilbert function alone fixes the betti table. For higher $k$
stronger conditions on the algebras are needed to fix the betti table. In
particular, if the algebra is a complete intersection or if it is defined by an
equigenerated ideal then the betti table is unique.


  In this paper, we investigate a radio frequency (RF) lens-embedded massive
multiple-input multiple-output (MIMO) system and evaluate the system
performance of limited feedback by utilizing a technique for generating a
suitable codebook for the system. We fabricate an RF lens that operates on a 77
GHz (mmWave) band. Experimental results show a proper value of amplitude gain
and an appropriate focusing property. In addition, using a simple numerical
technique--beam propagation method (BPM)--we estimate the power profile of the
RF lens and verify its accordance with experimental results. We also design a
codebook--multi-variance codebook quantization (MVCQ)--for limited feedback by
considering the characteristics of the RF lens antenna for massive MIMO
systems. Numerical results confirm that the proposed system shows significant
performance enhancement over a conventional massive MIMO system without an RF
lens.


  Updated data of the 153 Galactic globular clusters are used to readdress
fundamental parameters of the Milky Way. We build a reduced sample,
decontaminated of the clusters younger than 10Gyr, those with retrograde orbits
and/or evidence of relation to dwarf galaxies. The 33 metal-rich globular
clusters of the reduced sample extend basically to the Solar circle and
distribute over a region with projected axial-ratios typical of an oblate
spheroidal, $\rm\Delta x:\Delta y:\Delta z\approx1.0:0.9:0.4$. The 81
metal-poor globular clusters span a nearly spherical region of axial-ratios
$\approx1.0:1.0:0.8$ extending from the central parts to the outer halo. A new
estimate of the Sun's distance to the Galactic center is provided, $\rm
R_O=7.2\pm0.3 kpc$. The metal-rich and metal-poor radial-density distributions
flatten for $\rm R_{GC}\leq2 kpc$ and are well represented both by a power-law
with a core-like term and S\'ersic's law; at large distances they fall off as
$\rm\sim R^{-3.9}$. Both metallicity components appear to have a common origin,
which is different from that of the dark matter halo. Structural similarities
of the metal-rich and metal-poor radial distributions with the stellar halo are
consistent with a scenario where part of the reduced sample was formed in the
primordial collapse, and part was accreted in an early period of merging. This
applies to the bulge as well, suggesting an early merger affecting the central
parts of the Galaxy. We estimate that the present globular cluster population
corresponds to $\rm\leq23\pm6%$ of the original one. The fact that the
volume-density radial distributions of the metal-rich and metal-poor globular
clusters of the reduced sample follow both a core-like power-law and S\'ersic's
law indicates that we are dealing with spheroidal subsystems in all scales.


  A verification method for distributed systems based on decoupling forward and
backward behaviour is proposed. This method uses an event structure based
algorithm that, given a CCS process, constructs its causal compression relative
to a choice of observable actions. Verifying the original process equipped with
distributed backtracking on non-observable actions, is equivalent to verifying
its relative compression which in general is much smaller. We call this method
Declarative Concurrent Programming (DCP). DCP technique compares well with
direct bisimulation based methods. Benchmarks for the classic dining
philosophers problem show that causal compression is rather efficient both
time- and space-wise. State of the art verification tools can successfully
handle more than 15 agents, whereas they can handle no more than 5 following
the traditional direct method; an altogether spectacular improvement, since in
this example the specification size is exponential in the number of agents.


  The effect of a nearby $\gamma$-ray burst (GRB) on the preplanetary solar
nebula is considered. The intense irradiation by x-rays and $\gamma$-rays would
have caused dust balls to become molten in a matter of seconds, cooling more
slowly to form chondrules. The role of iron is crucial in this process because
it was the major absorber of x-rays between 7 keV and 30 keV. In this scenario,
chondrules formed at the same time across the side of the nebula toward the GRB
source. At least 27 Earth masses (M$\oplus$) could have been produced in the
nebula with well mixed gas and dust of solar composition, increasing to 100
M$\oplus$ with only moderate depletion of nebular gases. The chondrules
combined to form meteorites and possibly the terrestrial planets, the cores of
the giant planets and chondrules in comets. Assuming GRBs are linked to massive
stars like supernovae, the probability of a GRB within 100 pc which could form
chondrules is about 10$^{-3}$ and the same small probability may apply to other
planetary systems being akin to our solar system. A GRB in a nearby galaxy will
reveal protoplanetary disks by delayed transient infrared emission from the
chondrule formation process. We suggest that a GRB was first detected about 4.5
Gyrs ago and its signature was written in stone and preserved by the chondrules
in meteorites.


  Understanding the factors driving innovation in energy technologies is of
critical importance to mitigating climate change and addressing other
energy-related global challenges. Low levels of innovation, measured in terms
of energy patent filings, were noted in the 1980s and 90s as an issue of
concern and were attributed to low investment in public and private research
and development (R&D). Here we build a comprehensive global database of energy
patents covering the period 1970-2009 which is unique in its temporal and
geographical scope. Analysis of the data reveals a recent, marked departure
from historical trends. A sharp increase in rates of patenting has occurred
over the last decade, particularly in renewable technologies, despite continued
low levels of R&D funding. To solve the puzzle of fast innovation despite
modest R&D increases we develop a model that explains the nonlinear response
observed in the empirical data of technological innovation to various types of
investment. The model reveals a regular relationship between patents, R&D
funding, and growing markets across technologies, and accurately predicts
patenting rates at different stages of technological maturity and market
development. We show quantitatively how growing markets have formed a vital
complement to public R&D in driving innovative activity; these two forms of
investment have each leveraged the effect of the other in driving patenting
trends over long periods of time.


  In this work we consider a combined theoretical framework comprised by $F(R)$
gravity and a kinetic scalar field. The kinetic energy of the scalar field
dominates over its potential for all cosmic times, and the kinetic scalar
potential is chosen to be small and non-trivial. In this case, we show that the
primordial gravitational wave energy spectrum of vacuum $F(R)$ gravity is
significantly enhanced and can be detectable in future interferometers. The
kinetic scalar thus affects significantly the inflationary era, since it
extends its duration, but also has an overall amplifying effect on the energy
spectrum of pure $F(R)$ gravity primordial gravitational waves. The form of the
signal is characteristic for all these theories, since it is basically flat and
should be detectable from all future gravitational wave experiments for a wide
range of frequencies, unless some unknown damping factor occurs due to some
unknown physical process.


  Compared to other body-centered cubic (bcc) transition metals Nb has been the
subject of fewer compression studies and there are still aspects of its phase
diagram which are unclear. Here, we report a combined theoretical and
experimental study of Nb under high pressure and temperature. We present the
results of static laser-heated diamond anvil cell experiments up to 120 GPa
using synchrotron-based fast x-ray diffraction combined with ab initio quantum
molecular dynamics simulations. The melting curve of Nb is determined, and
evidence for a solid-solid phase transformation in Nb with increasing
temperature is found. The high-temperature phase of Nb is orthorhombic Pnma.
The bcc-Pnma transition is clearly seen in the experimental data on the Nb
principal Hugoniot. The bcc-Pnma coexistence observed in our experiments is
explained. Agreement between the measured and calculated melting curves is very
good except at 40-60 GPa where three experimental points lie below the
theoretical melting curve by 250 K (or 7%); a possible explanation is given.


  Neural architecture search (NAS) aims to automate architecture engineering in
neural networks. This often requires a high computational overhead to evaluate
a number of candidate networks from the set of all possible networks in the
search space during the search. Prediction of the networks' performance can
alleviate this high computational overhead by mitigating the need for
evaluating every candidate network. Developing such a predictor typically
requires a large number of evaluated architectures which may be difficult to
obtain. We address this challenge by proposing a novel evolutionary-based NAS
strategy, Predictor-assisted E-NAS (PRE-NAS), which can perform well even with
an extremely small number of evaluated architectures. PRE-NAS leverages new
evolutionary search strategies and integrates high-fidelity weight inheritance
over generations. Unlike one-shot strategies, which may suffer from bias in the
evaluation due to weight sharing, offspring candidates in PRE-NAS are
topologically homogeneous, which circumvents bias and leads to more accurate
predictions. Extensive experiments on NAS-Bench-201 and DARTS search spaces
show that PRE-NAS can outperform state-of-the-art NAS methods. With only a
single GPU searching for 0.6 days, competitive architecture can be found by
PRE-NAS which achieves 2.40% and 24% test error rates on CIFAR-10 and ImageNet
respectively.


  In this paper, we consider inverse scattering and inverse boundary value
problems at sufficiently large and fixed energy for the multidimensional
relativistic and nonrelativistic Newton equations in a static external
electromagnetic field $(V,B)$, $V\in C^2,$ $B\in C^1$ in classical mechanics.
Developing the approach going back to Gerver-Nadirashvili 1983's work on an
inverse problem of mechanics, we obtain, in particular, theorems of uniqueness.


  Let ${\mathbb F}$ be an arbitrary field. We consider a commutative,
non-associative, $4$-dimensional algebra ${\mathfrak M}$ of the rock, the paper
and the scissors with unit over ${\mathbb F}$ and we prove that the image over
${\mathfrak M}$ of every non-associative multilinear polynomial over ${\mathbb
F}$ is a vector space. The same question we consider for two subalgebras: an
algebra of the rock, the paper and the scissors without unit, and an algebra of
trace zero elements with zero scalar part. Moreover in this paper we consider
the questions of possible evaluations of homogeneous polynomials on these
algebras.


  To describe and analyze the dynamics of Self-Organized Criticality (SOC)
systems, a four-state continuous-time Markov model is proposed in this paper.
Different to computer simulation or numeric experimental approaches commonly
employed for explaining the power law in SOC, in this paper, based on this
Markov model, using E.T.Jayness' Maximum Entropy method, we have derived a
mathematical proof on the power law distribution for the size of these events.
Both this Makov model and the mathematical proof on power law present a new
angle on the universality of power law distributions, they also show that the
scale free property exists not necessary only in SOC system, but in a class of
dynamical systems which can be modelled by the proposed Markov model.


  This posting announces public availability of version 1.2 of the DiskFit
software package developed by the authors, which may be used to fit simple
non-axisymmetric models either to images or to velocity fields of disk
galaxies. Here we give an outline of the capability of the code and provide the
link to downloading executables, the source code, and a comprehensive on-line
manual. We argue that in important respects the code is superior to rotcur for
fitting kinematic maps and to galfit for fitting multi-component models to
photometric images.


  Magnetic properties of a single vacancy in graphene is a relevant and still
much discussed problem. The experimental results point to a clearly detectable
magnetic defect state at the Fermi energy, while calculations based on density
functional theory (DFT) yield widely varying results for the magnetic moment,
in the range of $\mu=1.04-2.0$ $\mu_{B}$. We present a multi-tool \textit{ab
initio} theoretical study of the same defect, using two simulation protocols
for a defect in a crystal (cluster and periodic boundary conditions) and
different DFT functionals - bare and hybrid DFT, mixing a fraction of
Hartree-Fock exchange (XC). Our main conclusions are two-fold: First, we find
that due to the $\pi$-character of the Fermi-energy states of graphene,
inclusion of XC is crucial and for a single isolated vacancy we can predict an
integer magnetic moment $\mu=2\mu_{B}$. Second, we find that due to the
specific symmetry of the graphene lattice, periodic arrays of single vacancies
may provide interesting diffuse spin-spin interactions.


  Motivated by time-sensitive e-service applications, we consider the design of
effective policies in a Markovian model for the dynamic control of both
admission and routing of a single class of real-time transactions to multiple
heterogeneous clusters of web servers, each having its own queue and server
pool. Transactions come with response-time deadlines, staying until completion
if the latter are missed. Per job rejection and deadline-miss penalties are
incurred. Since computing an optimal policy is intractable, we aim to design
near optimal heuristic policies that are tractable for large-scale systems.
Four policies are developed: the static optimal Bernoulli-splitting (BS)
policy, and three index policies, based respectively on individually optimal
(IO) actions, one-step policy improvement (PI), and restless bandit (RB)
indexation. A computational study demonstrates that PI is the best of such
policies, being consistently near optimal. In the pure-routing case, both the
PI and RB policies are nearly optimal.


  The recently proposed optimization algorithm for deep neural networks
Sharpness Aware Minimization (SAM) suggests perturbing parameters before
gradient calculation by a gradient ascent step to guide the optimization into
parameter space regions of flat loss. While significant generalization
improvements and thus reduction of overfitting could be demonstrated, the
computational costs are doubled due to the additionally needed gradient
calculation, making SAM unfeasible in case of limited computationally
capacities. Motivated by Nesterov Accelerated Gradient (NAG) we propose
Momentum-SAM (MSAM), which perturbs parameters in the direction of the
accumulated momentum vector to achieve low sharpness without significant
computational overhead or memory demands over SGD or Adam. We evaluate MSAM in
detail and reveal insights on separable mechanisms of NAG, SAM and MSAM
regarding training optimization and generalization. Code is available at
https://github.com/MarlonBecker/MSAM.


  We complete the Wilf classification of signed patterns of length 5 for both
signed permutations and signed involutions. New general equivalences of
patterns are given which prove Jaggard's conjectures concerning involutions in
the symmetric group avoiding certain patterns of length 5 and 6. In this way,
we also complete the Wilf classification of S_5, S_6, and S_7 for both
permutations and involutions.


  The decreasing enumeration of the points of a Poisson random measure whose
mean measure has finite survival function on the positive half-axis can be
represented as a non-increasing function of the jump times of a standard
Poisson process. This observation allows to generalize the essential idea from
a well-known exact simulation algorithm for arbitrary extreme-value copulas to
copulas of a more general family of max-infinitely divisible distributions,
with reciprocal Archimedean copulas being a particular example.


  We discuss the BPS configurations of IIB strings in the 7-brane background
from M-theory viewpoint. We first obtain the hyperkahler geometry background of
M-theory expected from the 7-brane solutions of the type IIB supergravity. We
choose the appropriate complex structures of the background geometries and
embed a membrane of M-theory holomorphically to obtain a BPS string
configuration. The recently discussed BPS string configurations such as
3-string junctions and string networks in the flat background are generalized
to the cases with the 7-brane backgrounds. The property of the BPS string
configurations in the 7-brane backgrounds is in agreement with the previously
known results from the IIB string viewpoint.


  We present limits for the compactification scale in the theory of Large Extra
Dimensions (LED) proposed by Arkani-Hamed, Dimopoulos, and Dvali. We use 11
months of data from the Fermi Large Area Telescope (Fermi-LAT) to set gamma ray
flux limits for 6 gamma-ray faint neutron stars (NS). To set limits on LED we
use the model of Hannestad and Raffelt (HR) that calculates the Kaluza-Klein
(KK) graviton production in supernova cores and the large fraction subsequently
gravitationally bound around the resulting NS. The predicted decay of the bound
KK gravitons to {\gamma}{\gamma} should contribute to the flux from NSs.
Considering 2 to 7 extra dimensions of the same size in the context of the HR
model, we use Monte Carlo techniques to calculate the expected differential
flux of gamma-rays arising from these KK gravitons, including the effects of
the age of the NS, graviton orbit, and absorption of gamma-rays in the
magnetosphere of the NS. We compare our Monte Carlo-based differential flux to
the experimental differential flux using maximum likelihood techniques to
obtain our limits on LED. Our limits are more restrictive than past EGRET-based
optimistic limits that do not include these important corrections.
Additionally, our limits are more stringent than LHC based limits for 3 or
fewer LED, and comparable for 4 LED. We conclude that if the effective Planck
scale is around a TeV, then for 2 or 3 LED the compactification topology must
be more complicated than a torus.