  Context: The details of how galaxies have evolved are imprinted in their star
formation history, chemical enrichment and morpho-kinematic structure.
Parameters behind these can be measured by combining photometric techniques
with modelling. However, there are uncertainties from the ambiguity of colour
and magnitude and the effects of interstellar reddening.
  Aims: In this paper we present a detailed reddening map of the central 30
Doradus region of the Large Magellanic Cloud; for community use and to test the
methods used. The reddening, a measurement of dust extinction, acts as a tracer
of the interstellar medium (ISM).
  Methods: Near infrared photometry of red clump stars are used to measure
reddening as extinction is the main cause of their colour and magnitude
variance. The star formation history is used to convert colour to reddening
values which are subsequently converted to visual extinction.
  Results: Presented is a dust map for the 30 Doradus field. This map samples a
region of 1x1.5 deg, containing ~1.5x10^5 red clump stars which probe reddening
up to AV=6 mag. We compare our map with maps from the literature, including
optical extinction maps and radio, mid- and far-infrared maps of atomic
hydrogen and dust emission. Through estimation of column density we locate
molecular clouds.
  Conclusions: This new reddening map shows correlation with equivalent maps in
the literature, validating the method of red clump star selection. We make our
reddening map available for community use. In terms of ISM the red clump stars
appear to be more affected by the cooler dust measured by 70 micron emission
because there is stronger correlation between increasing emission and
extinction due to red clump stars not being located near hot stars that would
heat the dust. The transition from atomic hydrogen to molecular hydrogen occurs
between densities of NH=4x10^21 to 6x10^21 cm^-2.


  FeCrAs displays an unusual electrical response that is neither metallic in
character nor divergent at low temperatures, as expected for an insulating
response, and therefore it has been termed a "nonmetal-metal". We carried out
neutron scattering experiments on powder and single crystal samples to study
the magnetic dynamics and critical fluctuations in FeCrAs. Magnetic neutron
diffraction measurements find Cr3+ magnetic order setting in at 115 K with the
mean-field critical exponent. Neutron spectroscopy, however, observes gapless
stiff magnetic fluctuations emanating from magnetic positions with propagation
wave vector q_0=(1/3,1/3), which persists up to at least 80 meV. The magnetism
in FeCrAs therefore displays a response which resembles that of itinerant
magnets at high energy transfers, such as chromium alloys. We suggest that the
presence of stiff high-energy spin fluctuations is the origin of the unusual
temperature dependence of the resistivity.


  In this paper we aim to find the stationary stochastic viscosity solutions of
a parabolic type SPDEs through the infinite horizon backward doubly stochastic
differential equations (BDSDEs). For this, we study the existence, uniqueness
and regularity of solutions of the corresponding infinite horizon BDSDEs as
well as the "perfection procedure" applied to the solutions of BDSDEs. At last
the "perfect" stationary stochastic viscosity solutions of SPDEs constructed by
solutions of corresponding BDSDEs are obtained.


  We focus on an unloading problem, typical of the logistics sector, modeled as
a sequential pick-and-place task. In this type of task, modern machine learning
techniques have shown to work better than classic systems since they are more
adaptable to stochasticity and better able to cope with large uncertainties.
More specifically, supervised and imitation learning have achieved outstanding
results in this regard, with the shortcoming of requiring some form of
supervision which is not always obtainable for all settings. On the other hand,
reinforcement learning (RL) requires much milder form of supervision but still
remains impracticable due to its inefficiency. In this paper, we propose and
theoretically motivate a novel Unsupervised Reward Shaping algorithm from
expert's observations which relaxes the level of supervision required by the
agent and works on improving RL performance in our task.


  We explore the possibility of adding complex absorbing potential at the
boundaries when solving the one-dimensional real-time Schr\"odinger evolution
on a grid using a quantum computer with a fully quantum algorithm described on
a $n$ qubit register. Due to the complex potential, the evolution mixes real-
and imaginary-time propagation and the wave function can potentially be
continuously absorbed during the time propagation. We use the dilation quantum
algorithm to treat the imaginary-time evolution in parallel to the real-time
propagation. This method has the advantage of using only one reservoir qubit at
a time, that is measured with a certain success probability to implement the
desired imaginary-time evolution. We propose a specific prescription for the
dilation method where the success probability is directly linked to the
physical norm of the continuously absorbed state evolving on the mesh. We
expect that the proposed prescription will have the advantage of keeping a high
probability of success in most physical situations. Applications of the method
are made on one-dimensional wave functions evolving on a mesh. Results obtained
on a quantum computer identify with those obtained on a classical computer. We
finally give a detailed discussion on the complexity of implementing the
dilation matrix. Due to the local nature of the potential, for $n$ qubits, the
dilation matrix only requires $2^n$ CNOT and $2^n$ unitary rotation for each
time step, whereas it would require of the order of $4^{n+1}$ C-NOT gates to
implement it using the best-known algorithm for general unitary matrices.


  The transition between distinct phases of matter is characterized by the
nature of fluctuations near the critical point. We demonstrate that noise
spectroscopy can not only diagnose the presence of a phase transition, but can
also determine fundamental properties of its criticality. In particular, by
analyzing a scaling collapse of the decoherence profile, one can directly
extract the critical exponents of the transition and identify its universality
class. Our approach naturally captures the presence of conservation laws and
distinguishes between classical and quantum phase transitions. In the context
of quantum magnetism, our proposal complements existing techniques and provides
a novel toolset optimized for interrogating two-dimensional magnetic materials.


  Non-commutative differential geometry allows a scalar field to be regarded as
a gauge connection, albeit on a discrete space. We explain how the underlying
gauge principle corresponds to the independence of physics on the choice of
vacuum state, should it be non-unique. A consequence is that Yang-Mills-Higgs
theory can be reformulated as a generalised Yang-Mills gauge theory on
Euclidean space with a $Z_2$ internal structure. By extending the Hodge star
operation to this non-commutative space, we are able to define the notion of
self-duality of the gauge curvature form in arbitrary dimensions. It turns out
that BPS monopoles, critically coupled vortices, and kinks are all self-dual
solutions in their respective dimensions. We then prove, within this unified
formalism, that static soliton solutions to the Yang-Mills-Higgs system exist
only in one, two and three spatial dimensions.


  Perhaps the most widely used form of code documentation is function header
comments. We performed a large-scale survey of 367 developers to catalog their
expectations from such documentation and to chronicle actual practice.
Paradoxically, we found that developers appreciate the value of header comments
and estimate that they are worth the investment in time, but nevertheless they
tend not to write such documentation in their own code. Reasons for not writing
header comments vary from the belief that code should be self-documenting to
concern that documentation will not be kept up-to-date. A possible outcome of
this situation is that developers may evade requirements to write documentation
by using templates to generate worthless comments that do not provide any real
information. We define a simple metric for information-less documentation based
on its similarity to the function signature. Applying this to 21,140 files in
GitHub Python projects shows that most functions are undocumented, but when
header comments are written they typically do contain additional information
beyond the function signature.


  We introduce the category of b-analytic manifolds, a natural tool to define
constructible sheaves and functions up to infinity. We study with some details
the operations on these objects and also recall the Radon transform for
constructible functions.


  The role of neutrinos in big bang nucleosynthesis is reviewed. Neutrino
oscillations in the early universe both in resonance and non-resonance case are
briefly discussed. BBN and supernova limits on heavy sterile neutrinos with the
mass in 10-100 MeV range are presented and compared with direct experimental
bounds.


  Map makers have long searched for a way to construct cartograms -- maps in
which the sizes of geographic regions such as countries or provinces appear in
proportion to their population or some other analogous property. Such maps are
invaluable for the representation of census results, election returns, disease
incidence, and many other kinds of human data. Unfortunately, in order to scale
regions and still have them fit together, one is normally forced to distort the
regions' shapes, potentially resulting in maps that are difficult to read. Many
methods for making cartograms have been proposed, some of them extremely
complex, but all suffer either from this lack of readability or from other
pathologies, like overlapping regions or strong dependence on the choice of
coordinate axes. Here we present a new technique based on ideas borrowed from
elementary physics that suffers none of these drawbacks. Our method is
conceptually simple and produces useful, elegant, and easily readable maps. We
illustrate the method with applications to the results of the 2000 US
presidential election, lung cancer cases in the State of New York, and the
geographical distribution of stories appearing in the news.


  Transductive Few-Shot learning has gained increased attention nowadays
considering the cost of data annotations along with the increased accuracy
provided by unlabelled samples in the domain of few shot. Especially in
Few-Shot Classification (FSC), recent works explore the feature distributions
aiming at maximizing likelihoods or posteriors with respect to the unknown
parameters. Following this vein, and considering the parallel between FSC and
clustering, we seek for better taking into account the uncertainty in
estimation due to lack of data, as well as better statistical properties of the
clusters associated with each class. Therefore in this paper we propose a new
clustering method based on Variational Bayesian inference, further improved by
Adaptive Dimension Reduction based on Probabilistic Linear Discriminant
Analysis. Our proposed method significantly improves accuracy in the realistic
unbalanced transductive setting on various Few-Shot benchmarks when applied to
features used in previous studies, with a gain of up to $6\%$ in accuracy. In
addition, when applied to balanced setting, we obtain very competitive results
without making use of the class-balance artefact which is disputable for
practical use cases. We also provide the performance of our method on a high
performing pretrained backbone, with the reported results further surpassing
the current state-of-the-art accuracy, suggesting the genericity of the
proposed method.


  In this paper, we obtain new results on the weak and strong consistency of
the maximum and integrated conditional likelihood estimators for the community
detection problem in the Stochastic Block Model with k communities. In
particular, we show that maximum conditional likelihood achieves the optimal
known threshold for exact recovery in the logarithmic degree regime. For the
integrated conditional likelihood, we obtain a sub-optimal constant in the same
regime. Both methods are shown to be weakly consistent in the divergent degree
regime. These results confirm the optimality of maximum likelihood on the task
of community detection, something that has remained as an open problem until
now.


  A theorem of alternatives provides a reduction of validity in a substructural
logic to validity in its multiplicative fragment. Notable examples include a
theorem of Arnon Avron that reduces the validity of a disjunction of
multiplicative formulas in the R-mingle logic RM to the validity of a linear
combination of these formulas, and Gordan's theorem for solutions of linear
systems over the real numbers, that yields an analogous reduction for validity
in Abelian logic A. In this paper, general conditions are provided for
axiomatic extensions of involutive uninorm logic without additive constants to
admit a theorem of alternatives. It is also shown that a theorem of
alternatives for a logic can be used to establish (uniform) deductive
interpolation and completeness with respect to a class of dense totally ordered
residuated lattices.


  We consider flux lines in presence of a dense square array of columnar
defects, with insulating core and radius of the order of the coherence length.
The properties of the phase transition from the flux line regime to the
localized superconducting state are determined here. We show that the localized
superconducting state is a new vortex state because of the counterclockwise and
of the clockwise supercurrent flows found around each defect. We propose here a
general operator to count the vorticity of any cavity inside a superconductor
and give a new method to obtain the reversible magnetization of superconductors
with multiply connected geometries.


  Societal debates and political outcomes are subject to news and social media
influences, which are in turn subject to commercial and other forces. Local
press are in decline, creating a ``news gap''. Research shows a contrary
relationship between UK regions' economic dependence on EU membership and their
voting in the 2016 UK EU membership referendum, raising questions about local
awareness. We draw on a corpus of Twitter data which has been annotated for
user location and Brexit vote intent, allowing us to investigate how location,
topics of concern and Brexit stance are related. We compare this with a large
corpus of articles from local and national news outlets, as well as survey
data, finding evidence of a distinctly different focus in local reporting.
National press focused more on terrorism and immigration than local press in
most areas. Some Twitter users focused on immigration. Local press focused on
trade, unemployment, local politics and agriculture. We find that remain voters
shared interests more in keeping with local press on a per-region basis.


  We study the generation of small neutrino masses in an extra-dimensional
model, where right-handed neutrinos are allowed to propagate in the extra
dimension, while the Standard Model particles are confined to a brane.
Motivated by the fact that extra-dimensional models are non-renormalizable, we
truncate the Kaluza-Klein towers at a maximal extra-dimensional momentum. The
structure of the bulk Majorana mass term, motivated by the Sherk-Schwarz
mechanism, implies that the right-handed Kaluza-Klein neutrinos pair to form
Dirac neutrinos, except for a number of unpaired Majorana neutrinos at the top
of each tower. These heavy Majorana neutrinos are the only sources of lepton
number breaking in the model, and similarly to the type-I seesaw mechanism,
they naturally generate small masses for the left-handed neutrinos. The lower
Kaluza-Klein modes mix with the light neutrinos, and the mixing effects are not
suppressed with respect to the light-neutrino masses. Compared to conventional
fermionic seesaw models, such mixing can be more significant. We study the
signals of this model at the Large Hadron Collider, and find that the current
low-energy bounds on the non-unitarity of the leptonic mixing matrix are strong
enough to exclude an observation.


  We defined sufficient conditions for designing Ding-Helleseth sequences with
arbitrary period and high linear complexity for generalized cyclotomies. Also
we discuss the method of computing the linear complexity of Ding-Helleseth
sequences in the general case.


  Diagnosing hematological malignancies requires identification and
classification of white blood cells in peripheral blood smears. Domain shifts
caused by different lab procedures, staining, illumination, and microscope
settings hamper the re-usability of recently developed machine learning methods
on data collected from different sites. Here, we propose a cross-domain adapted
autoencoder to extract features in an unsupervised manner on three different
datasets of single white blood cells scanned from peripheral blood smears. The
autoencoder is based on an R-CNN architecture allowing it to focus on the
relevant white blood cell and eliminate artifacts in the image. To evaluate the
quality of the extracted features we use a simple random forest to classify
single cells. We show that thanks to the rich features extracted by the
autoencoder trained on only one of the datasets, the random forest classifier
performs satisfactorily on the unseen datasets, and outperforms published
oracle networks in the cross-domain task. Our results suggest the possibility
of employing this unsupervised approach in more complicated diagnosis and
prognosis tasks without the need to add expensive expert labels to unseen data.


  Deep neural networks have been shown to be very successful at learning
feature hierarchies in supervised learning tasks. Generative models, on the
other hand, have benefited less from hierarchical models with multiple layers
of latent variables. In this paper, we prove that hierarchical latent variable
models do not take advantage of the hierarchical structure when trained with
existing variational methods, and provide some limitations on the kind of
features existing models can learn. Finally we propose an alternative
architecture that do not suffer from these limitations. Our model is able to
learn highly interpretable and disentangled hierarchical features on several
natural image datasets with no task specific regularization or prior knowledge.


  There have recently been significant advances in the problem of unsupervised
object-centric representation learning and its application to downstream tasks.
The latest works support the argument that employing disentangled object
representations in image-based object-centric reinforcement learning tasks
facilitates policy learning. We propose a novel object-centric reinforcement
learning algorithm combining actor-critic and model-based approaches to utilize
these representations effectively. In our approach, we use a transformer
encoder to extract object representations and graph neural networks to
approximate the dynamics of an environment. The proposed method fills a
research gap in developing efficient object-centric world models for
reinforcement learning settings that can be used for environments with discrete
or continuous action spaces. Our algorithm performs better in a visually
complex 3D robotic environment and a 2D environment with compositional
structure than the state-of-the-art model-free actor-critic algorithm built
upon transformer architecture and the state-of-the-art monolithic model-based
algorithm.


  In goal-reaching reinforcement learning (RL), the optimal value function has
a particular geometry, called quasimetric structure. This paper introduces
Quasimetric Reinforcement Learning (QRL), a new RL method that utilizes
quasimetric models to learn optimal value functions. Distinct from prior
approaches, the QRL objective is specifically designed for quasimetrics, and
provides strong theoretical recovery guarantees. Empirically, we conduct
thorough analyses on a discretized MountainCar environment, identifying
properties of QRL and its advantages over alternatives. On offline and online
goal-reaching benchmarks, QRL also demonstrates improved sample efficiency and
performance, across both state-based and image-based observations.


  The commutative Hopf monoid of set compositions is a fundamental Hopf monoid
internal to vector species, having undecorated bosonic Fock space the
combinatorial Hopf algebra of quasisymmetric functions. We construct a
geometric realization of this Hopf monoid over the adjoint of the
(essentialized) braid hyperplane arrangement, which identifies the monomial
basis with signed characteristic functions of the interiors of permutohedral
tangent cones. We show that the indecomposable quotient Lie coalgebra is
obtained by restricting functions to chambers of the adjoint arrangement, i.e.
by quotienting out the higher codimensions. The resulting functions are
characterized by the Steinmann relations of axiomatic quantum field theory,
demonstrating an equivalence between the Steinmann relations, tangent cones to
(generalized) permutohedra, and having algebraic structure internal to species.
Our results give a new interpretation of a construction appearing in the
mathematically rigorous formulation of renormalization by Epstein-Glaser,
called causal perturbation theory. In particular, we show that operator
products of time-ordered products correspond to the H-basis of the
cocommutative Hopf monoid of set compositions, and generalized retarded
products correspond to a spanning set of its primitive part Lie algebra.


  We argue using simple models that all successful practical uses of
probabilities originate in quantum fluctuations in the microscopic physical
world around us, often propagated to macroscopic scales. Thus we claim there is
no physically verified fully classical theory of probability. We comment on the
general implications of this view, and specifically question the application of
classical probability theory to cosmology in cases where key questions are
known to have no quantum answer. We argue that the ideas developed here may
offer a way out of the notorious measure problems of eternal inflation.


  As low as possible radioactive contamination of a detector plays a crucial
role to improve sensitivity of a double beta decay experiment. The radioactive
contamination of a sample of $^{116}$CdWO$_4$ crystal scintillator by thorium
was reduced by a factor $\approx 10$, down to the level 0.01 mBq/kg
($^{228}$Th), by exploiting the recrystallization procedure. The total alpha
activity of uranium and thorium daughters was reduced by a factor $\approx 3$,
down to 1.6 mBq/kg. No change in the specific activity (the total $\alpha$
activity and $^{228}$Th) was observed in a sample of ZnWO$_4$ crystal produced
by recrystallization after removing $\approx 0.4$ mm surface layer of the
crystal.


  The field of reinforcement learning can be split into model-based and
model-free methods. Here, we unify these approaches by casting model-free
policy optimisation as amortised variational inference, and model-based
planning as iterative variational inference, within a `control as hybrid
inference' (CHI) framework. We present an implementation of CHI which naturally
mediates the balance between iterative and amortised inference. Using a
didactic experiment, we demonstrate that the proposed algorithm operates in a
model-based manner at the onset of learning, before converging to a model-free
algorithm once sufficient data have been collected. We verify the scalability
of our algorithm on a continuous control benchmark, demonstrating that it
outperforms strong model-free and model-based baselines. CHI thus provides a
principled framework for harnessing the sample efficiency of model-based
planning while retaining the asymptotic performance of model-free policy
optimisation.


  We study Fayet-Iliopoulos (FI) terms of 5-dimensional supersymmetric $U(1)$
gauge theory compactified on $S^1/Z_2$. In this model, loop diagrams including
matter hypermultiplets and brane chiral multiplets induce FI-terms localized at
the fixed points. Localized FI-terms lead instabilities of bulk modes. The form
of the induced FI-terms strictly depends on wave function profiles of matter
multiplets. It is a non-trivial question whether the vacuum of 1-loop corrected
potential is stable under radiative corrections. We investigate this issue and
it is found that the stable configuration is obtained when the bulk zero modes
shield the brane charge completely.


  An algorithm implemented in an open-source python library was developed for
building periodic coincidence site lattice (CSL) grain boundary models in a
universal fashion. The software framework aims to generate tilt and twist grain
boundaries from cubic and tetragonal crystals for ab-initio and classical
atomistic simulation. This framework has two useful features: i) it can
calculate all the CSL matrices for generating CSL from a given Sigma ({\Sigma})
value and rotation axis, allowing the users to build the specific CSL and grain
boundary models; ii) it provides a convenient command line tool to enable
high-throughput generation of tilt and twist grain boundaries by assigning an
input crystal structure, {\Sigma} value, rotation axis, and grain boundary
plane. The developed algorithm in the open-source python library is expected to
facilitate studies of grain boundary in materials science. The software
framework is available on the website: aimsgb.org.


  We present a carefully selected sample of short gamma-ray bursts (SGRBs)
observed by the Swift satellite up to June 2013. Inspired by the criteria we
used to build a similar sample of bright long GRBs (the BAT6 sample), we
selected SGRBs with favorable observing conditions for the redshift
determination on ground, ending up with a sample of 36 events, almost half of
which with a redshift measure. The redshift completeness increases up to about
70% (with an average redshift value of z = 0.85) by restricting to those events
that are bright in the 15-150 keV Swift Burst Alert Telescope energy band. Such
flux-limited sample minimizes any redshift-related selection effects, and can
provide a robust base for the study of the energetics, redshift distribution
and environment of the Swift bright population of SGRBs. For all the events of
the sample we derived the prompt and afterglow emission in both the observer
and (when possible) rest frame and tested the consistency with the correlations
valid for long GRBs. The redshift and intrinsic X-ray absorbing column density
distributions we obtain are consistent with the scenario of SGRBs originated by
the coalescence of compact objects in primordial binaries, with a possible
minor contribution (~10%-25%) of binaries formed by dynamical capture (or
experiencing large natal kicks). This sample is expected to significantly
increase with further years of Swift activity.


  The authors present a visual instrument developed as part of the creation of
the artwork Learning to See. The artwork explores bias in artificial neural
networks and provides mechanisms for the manipulation of specifically trained
for real-world representations. The exploration of these representations acts
as a metaphor for the process of developing a visual understanding and/or
visual vocabulary of the world. These representations can be explored and
manipulated in real time, and have been produced in such a way so as to reflect
specific creative perspectives that call into question the relationship between
how both artificial neural networks and humans may construct meaning.


  Motivated by the new higher D-supergravity solutions on intersecting
attractors obtained by Ferrara et al. in [Phys.Rev.D79:065031-2009], we focus
in this paper on 8D maximal supergravity with moduli space
[SL(3,R)/SO(3)]x[SL(2,R)/SO(2)] and study explicitly the attractor mechanism
for various configurations of extremal black p- branes (anti-branes) with the
typical near horizon geometries AdS_{p+2}xS^{m}xT^{6-p-m} and p=0,1,2,3,4;
2<=m<=6. Interpretations in terms of wrapped M2 and M5 branes of the 11D
M-theory on 3-torus are also given.
  Keywords: 8D supergravity, black p-branes, attractor mechanism, M-theory.


  In many atmospheric and earth sciences, it is of interest to identify
dominant spatial patterns of variation based on data observed at $p$ locations
and $n$ time points with the possibility that $p>n$. While principal component
analysis (PCA) is commonly applied to find the dominant patterns, the
eigenimages produced from PCA may exhibit patterns that are too noisy to be
physically meaningful when $p$ is large relative to $n$. To obtain more precise
estimates of eigenimages, we propose a regularization approach incorporating
smoothness and sparseness of eigenimages, while accounting for their
orthogonality. Our method allows data taken at irregularly spaced or sparse
locations. In addition, the resulting optimization problem can be solved using
the alternating direction method of multipliers, which is easy to implement,
and applicable to a large spatial dataset. Furthermore, the estimated
eigenfunctions provide a natural basis for representing the underlying spatial
process in a spatial random-effects model, from which spatial covariance
function estimation and spatial prediction can be efficiently performed using a
regularized fixed-rank kriging method. Finally, the effectiveness of the
proposed method is demonstrated by several numerical examples


  Multilingual machine translation models can benefit from synergy between
different language pairs, but also suffer from interference. While there is a
growing number of sophisticated methods that aim to eliminate interference, our
understanding of interference as a phenomenon is still limited. This work
identifies the main factors that contribute to interference in multilingual
machine translation. Through systematic experimentation, we find that
interference (or synergy) are primarily determined by model size, data size,
and the proportion of each language pair within the total dataset. We observe
that substantial interference occurs mainly when the model is very small with
respect to the available training data, and that using standard transformer
configurations with less than one billion parameters largely alleviates
interference and promotes synergy. Moreover, we show that tuning the sampling
temperature to control the proportion of each language pair in the data is key
to balancing the amount of interference between low and high resource language
pairs effectively, and can lead to superior performance overall.


  An account is given on the first studies on the physics of ammonia, focusing
on the infrared spectra of that molecule. Relevant contributions from several
authors, in the years until 1932, are pointed out, discussing also an unknown
study by E.Majorana on this topic.


  We study autoequivalences of the derived category of coherent sheaves of a
variety arising from a variation of GIT quotient. We show that these
automorphisms are spherical twists, and describe how they result from mutations
of semiorthogonal decompositions. Beyond the GIT setting, we show that all
spherical twist autoequivalences of a dg-category can be obtained from mutation
in this manner.
  Motivated by a prediction from mirror symmetry, we refine the recent notion
of "grade restriction rules" in equivariant derived categories. We produce
additional derived autoequivalences of a GIT quotient and propose an
interpretation in terms of monodromy of the quantum connection. We generalize
this observation by proving a criterion under which a spherical twist
autoequivalence factors into a composition of other spherical twists.


  We present solutions for the velocity field and mass-loss rates for 2D
axisymmetric outflows, as well as for the case of mass accretion through the
use of the Lambert W-function. For the case of a rotating radiation-driven wind
the velocity field is obtained analytically using a parameterised description
of the line acceleration that only depends on radius r at any given latitude
$\theta$. The line acceleration g(r) is obtained from Monte-Carlo multi-line
radiative transfer calculations. The critical/sonic point of our equation of
motion varies with latitude $\theta$. Furthermore, an approximate analytical
solution for the supersonic flow of a rotating wind is derived, which is found
to closely resemble the exact solution. For the simultaneous solution of the
mass-loss rate and velocity field, we use the iterative method of our 1D method
extended to the non-spherical 2D case. We apply the new theoretical expressions
with our iterative method to the stellar wind from a differentially rotating 40
$M_{sun}$ O5-V main sequence star as well as to a 60 $M_{sun}$ O-giant star,
and we compare our results to previous studies that are extensions of the
Castor et al. (1975, ApJ, 195, 157) CAK formalism. Next, we account for the
effects of oblateness and gravity darkening. Our numerical results predict an
equatorial decrease of the mass-loss rate, which would imply that
(surface-averaged) total mass-loss rates are lower than for the spherical 1D
case, in contradiction to the Maeder & Meynet (2000, A&A, 361, 159) formalism
that is oftentimes employed in stellar evolution calculations for rotating
massive stars. To clarify the situation in nature we discuss observational
tests to constrain the shapes of large-scale 2D stellar winds.


  With densification of nodes in cellular networks, free space optic (FSO)
connections are becoming an appealing low cost and high rate alternative to
copper and fiber as the backhaul solution for wireless communication systems.
To ensure a reliable cellular backhaul, provisions for redundant, disjoint
paths between the nodes must be made in the design phase. This paper aims at
finding a cost-effective solution to upgrade the cellular backhaul with
pre-deployed optical fibers using FSO links and mirror components. Since the
quality of the FSO links depends on several factors, such as transmission
distance, power, and weather conditions, we adopt an elaborate formulation to
calculate link reliability. We present a novel integer linear programming model
to approach optimal FSO backhaul design, guaranteeing $K$-disjoint paths
connecting each node pair. Next, we derive a column generation method to a
path-oriented mathematical formulation. Applying the method in a sequential
manner enables high computational scalability. We use realistic scenarios to
demonstrate our approaches efficiently provide optimal or near-optimal
solutions, and thereby allow for accurately dealing with the trade-off between
cost and reliability.


  We study the post-inflationary dynamics of the Standard Model Higgs and a
real singlet scalar $s$, coupled together through a renormalizable coupling
$\lambda_{sh}h^2s^2$, in a $Z_2$ symmetric model that may explain the observed
dark matter abundance and/or the origin of baryon asymmetry. The initial values
for the Higgs and $s$ condensates are given by inflationary fluctuations, and
we follow their dissipation and relaxation to the low energy vacua. We find
that both the lowest order perturbative and the non-perturbative decays are
blocked by thermal effects and large background fields and that the condensates
decay by two-loop thermal effects. Assuming instant reheating at $T=10^{16}$
GeV, the characteristic temperature for the Higgs condensate thermalization is
found to be $T_h \sim 10^{14}$ GeV, whereas $s$ thermalizes typically around
$T_s \sim 10^{6}$ GeV. By that time, the amplitude of the singlet is driven
very close to the vacuum value by the expansion of the universe, unless the
portal coupling takes a value $\lambda_{sh}\lesssim 10^{-7}$ and the singlet
$s$ never thermalizes. With these values of the coupling, it is possible to
slowly produce a sizeable fraction of the observed dark matter abundance via
singlet condensate fragmentation and thermal Higgs scattering. Physics also
below the electroweak scale can therefore be affected by the non-vacuum initial
conditions generated by inflation.


  We present a minimal model of a doped Mott insulator that simultaneously
supports antiferromagnetic stripes and d-wave superconductivity. We explore the
implications for the global phase diagram of the superconducting cuprates. At
the unrestricted mean-field level, the various phases of the cuprates,
including weak and strong pseudogap phases, and two different types of
superconductivity in the underdoped and the overdoped regimes, find a natural
interpretation. We argue that on the underdoped side, the superconductor is
intrinsically inhomogeneous -- striped coexistence of of superconductivity and
magnetism -- and global phase coherence is achieved through Josephson-like
coupling of the superconducting stripes. On the overdoped side, the state is
overall homogeneous and the superconductivity is of the classical BCS type.


  Motivated by the data from Super-Kamiokande and elsewhere indicating
oscillations of atmospheric and solar neutrinos, we study
charged-lepton-flavour violation, in particular the radiative decays mu -> e
gamma and tau -> mu gamma, but also commenting on mu -> 3e and tau -> 3 mu/e
decays, as well as mu - e conversion on nuclei. We first show how the
renormalization group may be used to calculate flavour-violating soft
supersymmetry-breaking masses for charged sleptons and sneutrinos in models
with universal input parameters. Subsequently, we classify possible patterns of
lepton-flavour violation in the context of phenomenological neutrino mass
textures that accommodate the Super-Kamiokande data, giving examples based on
Abelian flavour symmetries. Then we calculate in these examples rates for mu ->
e gamma and tau ->mu gamma, which may be close to the present experimental
upper limits, and show how they may distinguish between the different generic
mixing patterns. The rates are promisingly large when the soft
supersymmetry-breaking mass parameters are chosen to be consistent with the
cosmological relic-density constraints. In addition, we discuss mu -> e
conversion on Titanium, which may also be accessible to future experiments.


  Modern experiments on neutron and allowed nuclear $\beta$ decay search for
new semileptonic interactions, beyond the ``left-handed'' electroweak force. We
show that ongoing and planned $\beta$-decay experiments, with isotopes at rest
and in flight, can be exploited as sensitive tests of Lorentz invariance. The
variety of correlations that involve the nuclear spin, the direction of the
emitted $\beta$ particle, and the recoil direction of the daughter nucleus
allow for relatively simple experiments that give direct bounds on Lorentz
violation. The pertinent observables are decay-rate asymmetries and their
dependence on sidereal time. We discuss the potential of several asymmetries
that together cover a large part of the parameter space for Lorentz violation
in the gauge sector. High counting statistics is required.


  A two-level quantum system can absorb or emit not more than one photon at a
time. Using this fundamental property, we demonstrate how a superconducting
quantum system strongly coupled to a transmission line can be used as a sensor
of the photon flux. We propose four methods of sensing the photon flux and
analyse them for the absolute calibration of power by measuring spectra of
scattered radiation from the two-level system. This type of sensor can be tuned
to operate in a wide frequency range, and does not disturb the propagating
waves when not in use. Using a two-level system as a power sensor enables a
range of applications in quantum technologies, here in particular applied to
calibrate the attenuation of transmission lines inside dilution refrigerators.


  We examine the transition from trivial to non-trivial phases in a
Su-Schrieffer-Heeger model subjected to disorder in a quasi-periodic
environment. We analytically determine the phase boundary, and characterize the
localization of normal modes using their inverse participation ratio. We
compute energy-dependent mobility edges and provide evidence for the emergence
of a topological Anderson insulator within specific parameter ranges. Whereas
the phase transition boundary is affected by the quasi-periodic modulation, the
topologically insulating Anderson phase is stable with respect to the chiral
disorder in a quasi-periodic setup. Additionally, our results also uncover a
re-entrant topological phase transition from non-trivial to trivial phases for
certain values of quasi-periodic modulation with fixed chiral disorder.


  Modern optical communication systems transmit multiple frequency channels,
each operating very close to its theoretical limit. The total bandwidth can
reach 10THz limited by the optical amplifiers. Maximizing spectral efficiency,
the throughput per bandwidth is thus crucial. Replacing independent lasers with
an optical frequency comb can enable very dense packing by overcoming relative
drifts. However, to date, interference from non-ideal spectral shaping prevents
exploiting the full potential of frequency combs. Here, we demonstrate
comb-enabled multi-channel digital signal processing, which overcomes these
limitations. Each channel is detected using an independent coherent receiver
and processed at two samples-per-symbol. By accounting for the unique comb
stability and exploiting aliasing in the design of the dynamic equalizer, we
show that the optimal spectral shape changes, resulting in a higher signal to
noise ratio that pushes the optimal symbol rate towards and even \emph{above}
the channel spacing, resulting in the first example of frequency-domain
super-Nyquist transmission with multi-channel detection for optical systems.
The scheme is verified both in back-to-back configuration and in single span
transmission of a 21 channel superchannel originating from a 25GHz-spaced
frequency comb. By jointly processing 3 wavelength channels at a time, we
achieve spectral efficiency beyond what is possible with independent channels.
At the same time, one significantly relaxes the hardware requirements on
digital-to-analog resolution and bandwidth, and well as filter tap numbers. Our
results show that comb-enabled multi-channel processing can overcome the
limitations of classical dense wavelength division multiplexing systems by
enabling tighter spacing to reach the ultimate spectral efficiency in optical
communications.


  Hydrodynamic and magnetohydrodynamic numerical studies of a mechanically
forced two-vortex flow inside a sphere are reported. The simulations are
performed in the intermediate regime between the laminar flow and developed
turbulence where a hydrodynamic instability is found to generate internal waves
with a characteristic m=2 zonal wave number. It is shown that this
time-periodic flow acts as a dynamo although snapshots of the flow as well as
the mean flow are not dynamos. The magnetic fields' growth rate exhibits
resonance effects depending on the wave frequency. Furthermore, a cyclic
self-killing and self-recovering dynamo based on the relative alignment of the
velocity and magnetic fields is presented. The phenomena are explained in terms
of a mixing of non-orthogonal eigenstates of the time dependent linear operator
of the magnetic induction equation. The potential relevance of this mechanism
to dynamo experiments is discussed.


  A fundamental task in phase retrieval is to recover an unknown signal $\vx\in
\Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \;
i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models
(PAMs) which have non-convex and quadratic-type loss function. When the
measurements $ \va_i \in \Rn$ are Gaussian random vectors and the number of
measurements $m\ge Cn$, we rigorously prove that the PAMs admit no spurious
local minimizers with high probability, i.e., the target solution $ \vx$ is the
unique global minimizer (up to a global phase) and the loss function has a
negative directional curvature around each saddle point. Thanks to the
well-tamed benign geometric landscape, one can employ the vanilla gradient
descent method to locate the global minimizer $\vx$ (up to a global phase)
without spectral initialization. We carry out extensive numerical experiments
to show that the gradient descent algorithm with random initialization
outperforms state-of-the-art algorithms with spectral initialization in
empirical success rate and convergence speed.


  A one parameter expression for the single ionization cross-section of atoms
by electron impact is presented. Using this expression, the agreement obtained
with available experimental data for 45 elements (from ionization threshold up
to 200 eV ionizing electron energy) is shown to be comparable with (or better
than) that achieved using other multi-parameter approaches. We suggest that the
single parameter used here is associated with the effective reduction in the
number of equivalent electrons within a given shell accessible for ionization
by electron impact. We attribute this reduction effect to intra-shell shadowing
of part of the shell electrons by other electrons of the same shell. For atoms
with 2s^2p^i (i = 3,4,5,6) outer shell configurations we suggest also an
intershell shadowing effect. Finally, we discuss the possibility of a
meaningful contribution of inner shell ionization to the single ionization
cross-section due to various post-collision interactions. These interactions
may be responsible for decreasing the formation probability of doubly charged
ions.


  A systematic study of magnetic properties of Ni2+xMn1-xGa (0 \le x \le 0.19)
Heusler alloys undergoing structural martensite-austenite transformations while
in ferromagnetic state has been performed. From measurements of spontaneous
magnetization, Ms(T), jumps \Delta M at structural phase transitions were
determined. Virtual Curie temperatures of the martensite were estimated from
the comparison of magnetization in martensitic and austenitic phases. Both
saturation magnetic moments in ferromagnetic state and effective magnetic
moments in paramagnetic state of Mn and Ni atoms were estimated and the
influence of delocalization effects on magnetism in these alloys was discussed.
The experimental results obtained show that the shift of martensitic transition
temperature depends weakly on composition. The values of this shift are in good
correspondence with Clapeyron-Clausius formalism taking into account the
experimental data on latent heat at martensite-austenite transformations.


  We are performing a survey of the Galactic Center region with the BeppoSAX
satellite. Several known point sources are visible (including one at the
position of SgrA*), as well as newly discovered sources and diffuse emission.
Here we report the preliminary results of the on-going analysis of both the
point sources and the diffuse X-ray emission.


  Longitudinal imaging forms an essential component in the management and
follow-up of many medical conditions. The presence of lesion changes on serial
imaging can have significant impact on clinical decision making, highlighting
the important role for automated change detection. Lesion changes can represent
anomalies in serial imaging, which implies a limited availability of
annotations and a wide variety of possible changes that need to be considered.
Hence, we introduce a new unsupervised anomaly detection and localisation
method trained exclusively with serial images that do not contain any lesion
changes. Our training automatically synthesises lesion changes in serial
images, introducing detection and localisation pseudo-labels that are used to
self-supervise the training of our model. Given the rarity of these lesion
changes in the synthesised images, we train the model with the imbalance robust
focal Tversky loss. When compared to supervised models trained on different
datasets, our method shows competitive performance in the detection and
localisation of new demyelinating lesions on longitudinal magnetic resonance
imaging in multiple sclerosis patients. Code for the models will be made
available on GitHub.


  Fermionic superfluidity with a nontrivial Cooper-pairing, beyond the
conventional Bardeen-Cooper-Schrieffer state, is a captivating field of study
in quantum many-body systems. In particular, the search for superconducting
states with finite-momentum pairs has long been a challenge, but establishing
its existence has long suffered from the lack of an appropriate probe to reveal
its momentum. Recently, it has been proposed that the nonreciprocal {\cred
electron} transport is the most {\cred powerful} probe for the finite-momentum
pairs, {\cred because it directly couples} to the supercurrents. Here we reveal
such a pairing state by the non-reciprocal transport on tricolor superlattices
with strong spin-orbit coupling combined with broken inversion-symmetry
consisting of atomically thin $d$-wave superconductor CeCoIn$_5$. We find that
while the second-harmonic resistance exhibits a distinct dip anomaly at the
low-temperature ($T$)/high-magnetic field ($H$) corner in the $HT$-plane for
${\bm H}$ applied to the antinodal direction of the $d$-wave gap, such an
anomaly is absent for ${\bm H}$ along the nodal direction. By meticulously
isolating extrinsic effects due to vortex dynamics, we reveal the presence of a
non-reciprocal response originating from intrinsic superconducting properties
characterized by finite-momentum pairs. We attribute the high-field state to
the helical superconducting state, wherein the phase of the order parameter is
spontaneously spatially modulated.


  We provide an efficient algorithm to generate random samples from the bounded
kth order statistic in a sample of independent, but not necessarily identically
distributed, random variables. The bounds can be upper or lower bounds and need
only hold on the kth order statistic. Furthermore, we require access to the
inverse CDF for each statistic in the ordered sample. The algorithm is slightly
slower than rejection sampling when the density of the bounded statistic is
large, however, it is significantly faster when the bounded density becomes
sparse. We provide a practical example and a simulation that shows the
superiority of this method for sparse regions arising from tight boundary
conditions and/or over regions of low probability density.


  In the combinatorics of finite finite Coxeter groups, there is a simple
formula giving the number of maximal chains of noncrossing partitions. It is a
reinterpretation of a result by Deligne which is due to Chapoton, and the goal
of this article is to refine the formula. First, we prove a one-parameter
generalization, by the considering enumeration of noncrossing chains where we
put a weight on some relations. Second, we consider an equivalence relation on
noncrossing chains coming from the natural action of the group on set
partitions, and we show that each equivalence class has a simple generating
function. Using this we recover Postnikov's hook length formula in type A and
obtain a variant in type B.


  We consider propagation of gravitational radiation in a magnetized
multicomponent plasma. It is shown that large density perturbations can be
generated, even for small deviations from flat space, provided the cyclotron
frequency is much larger than the plasma frequency. Furthermore, the induced
density gradients can generate frequency conversion of electromagnetic
radiation, which may give rise to indirect observational effect of the
gravitational waves.


  To exploit a given physical system for quantum information processing, it is
critical to understand the different types of noise affecting quantum control.
Distinguishing coherent and incoherent errors is extremely useful as they can
be reduced in different ways. Coherent errors are generally easier to reduce at
the hardware level, e.g. by improving calibration, whereas some sources of
incoherent errors, e.g. T2* processes, can be reduced by engineering robust
pulses. In this work, we illustrate how purity benchmarking and randomized
benchmarking can be used together to distinguish between coherent and
incoherent errors and to quantify the reduction in both of them due to using
optimal control pulses and accounting for the transfer function in an electron
spin resonance system. We also prove that purity benchmarking provides bounds
on the optimal fidelity and diamond norm that can be achieved by correcting the
coherent errors through improving calibration.


  We present SQUID susceptibility data on Zn and Ni substituted
YBa_{2}Cu_{3}O_{6+x}. Cross-checks with NMR yield an unprecedented accuracy in
the estimate of the magnetic susceptibility associated with the substituants,
from the underdoped to the lightly overdoped case. This allows us to determine
the Weiss temperature \theta for YBCO: its value is very small for all hole
dopings n_h. Since in conventional metals, the Kondo temperature,
$T_{K}<\theta$, magnetic screening effects would not be expected for $T\gg
\theta$; in contrast, increasing n_h produces a reduction of the small moment
induced by Zn^{2+} and a nearly constant effective moment for Ni^{2+}
corresponding to a spin 1/2 rather than to a spin 1.


  For $\Gamma$ a cocompact or cofinite Fuchsian group, we study the lattice
point problem on the Riemann surface $\Gamma\backslash\mathbb{H}$. The main
asymptotic for the counting of the orbit $\Gamma z$ inside a circle of radius
$r$ centered at $z$ grows like $c e^r$. Phillips and Rudnick studied
$\Omega$-results for the error term and mean results in $r$ for the normalized
error term. We investigate the normalized error term in the natural parameter
$X=2 \cosh r$ and prove $\Omega_{\pm}$-results for the orbit $\Gamma w$ and
circle centered at $z$, even for $z \neq w$.


  We develop an accurate nanoelectronic modeling approach for realistic
three-dimensional topological insulator nanostructures and investigate their
low-energy surface-state spectrum. Starting from the commonly considered
four-band $\boldsymbol{\mathrm{k\cdot p}}$ bulk model Hamiltonian for the
Bi$_2$Se$_3$ family of topological insulators, we derive new parameter sets for
Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$. We consider a fitting strategy
applied to \emph{ab initio} band structures around the $\Gamma$ point that
ensures a quantitatively accurate description of the low-energy bulk and
surface states, while avoiding the appearance of unphysical low-energy states
at higher momenta, something that is not guaranteed by the commonly considered
perturbative approach. We analyze the effects that arise in the low-energy
spectrum of topological surface states due to band anisotropy and electron-hole
asymmetry, yielding Dirac surface states that naturally localize on different
side facets. In the thin-film limit, when surface states hybridize through the
bulk, we resort to a thin-film model and derive thickness-dependent model
parameters from \emph{ab initio} calculations that show good agreement with
experimentally resolved band structures, unlike the bulk model that neglects
relevant many-body effects in this regime. Our versatile modeling approach
offers a reliable starting point for accurate simulations of realistic
topological material-based nanoelectronic devices.


  The ABCD matrix is one of the essential mathematical instruments in optics.
It is the two-by-two representation of the group Sp(2), which is applicable to
many branches of physics, including squeezed states of light, special
relativity and coupled oscillators. It is pointed out that the shear
representation is oriented to binary logic which may be friendly to computer
applications. While this is a future possibility, it is known that para-axial
lens optics is based on the shear representation of the Sp(2) group. It is
pointed out that the most general form of the ABCD matrix can be written in
terms of six shear matrices, which correspond to lens and translation matrices.
The parameter for each shear matrix is computed in terms of the three
independent parameters of the ABCD matrix.


  Emergence of new types of services has led to various traffic and diverse
delay requirements in fifth generation (5G) wireless networks. Meeting diverse
delay requirements is one of the most critical goals for the design of 5G
wireless networks. Though the delay of point-to-point communications has been
well investigated, the delay of multi-point to multi-point communications has
not been thoroughly studied since it is a complicated function of all links in
the network. In this work, we propose a novel tractable approach to analyze the
delay in the heterogenous cellular networks with spatio-temporal random arrival
of traffic. Specifically, we propose the notion of \emph{delay outage} and
evaluated the effect of different scheduling policies on the delay performance.
Our numerical analysis reveals that offloading policy based on cell range
expansion greatly reduces the macrocell traffic while bringing a small amount
of growth for the picocell traffic. Our results also show that the delay
performance of round-robin scheduling outperforms first in first out scheduling
for heavy traffic, and it is reversed for light traffic. In summary, this
analytical framework provides an understanding and a rule-of-thumb for the
practical deployment of 5G systems where delay requirement is increasingly
becoming a key concern.


  Penetration Testing is a methodology for assessing network security, by
generating and executing possible attacks. Doing so automatically allows for
regular and systematic testing. A key question then is how to automatically
generate the attacks. A natural way to address this issue is as an attack
planning problem. In this thesis, we are concerned with the specific context of
regular automated pentesting, and use the term "attack planning" in that sense.
The following three research directions are investigated.
  First, we introduce a conceptual model of computer network attacks, based on
an analysis of the penetration testing practices. We study how this attack
model can be represented in the PDDL language. Then we describe an
implementation that integrates a classical planner with a penetration testing
tool. This allows us to automatically generate attack paths for real world
pentesting scenarios, and to validate these attacks by executing them.
  Secondly, we present efficient probabilistic planning algorithms,
specifically designed for this problem, that achieve industrial-scale runtime
performance (able to solve scenarios with several hundred hosts and exploits).
These algorithms take into account the probability of success of the actions
and their expected cost (for example in terms of execution time, or network
traffic generated).
  Finally, we take a different direction: instead of trying to improve the
efficiency of the solutions developed, we focus on improving the model of the
attacker. We model the attack planning problem in terms of partially observable
Markov decision processes (POMDP). This grounds penetration testing in a
well-researched formalism. POMDPs allow the modelling of information gathering
as an integral part of the problem, thus providing for the first time a means
to intelligently mix scanning actions with actual exploits.


  Identifying locations of occupants is beneficial to energy management in
buildings. A key observation in indoor environment is that distinct functional
areas are typically controlled by separate HVAC and lighting systems and room
level localization is sufficient to provide a powerful tool for energy usage
reduction by occupancy-based actuation of the building facilities. Based upon
this observation, this paper focuses on identifying the room where a person or
a mobile device is physically present. Existing room localization methods,
however, require special infrastructure to annotate rooms.
  SoundLoc is a room-level localization system that exploits the intrinsic
acoustic properties of individual rooms and obviates the needs for
infrastructures. As we show in the study, rooms' acoustic properties can be
characterized by Room Impulse Response (RIR). Nevertheless, obtaining precise
RIRs is a time-consuming and expensive process. The main contributions of our
work are the following. First, a cost-effective RIR measurement system is
implemented and the Noise Adaptive Extraction of Reverberation (NAER) algorithm
is developed to estimate room acoustic parameters in noisy conditions. Second,
a comprehensive physical and statistical analysis of features extracted from
RIRs is performed. Also, SoundLoc is evaluated using the dataset consisting of
ten (10) different rooms. The overall accuracy of 97.8% achieved demonstrates
the potential to be integrated into automatic mapping of building space.


  Quantum reduced loop gravity is designed to consistently study symmetry
reduced systems within the loop quantum gravity framework. In particular, it
bridges the gap between the effective cosmological models of loop quantum
cosmology and the full theory, addressing the dynamics before the
minisuperspace reduction. This mostly preserves the graph structure and SU(2)
quantum numbers. In this article, we study the phenomenological consequences of
the isotropic sector of the theory, the so-called emergent bouncing universe
model. In particular, the parameter space is scanned and we show that the
number of inflationary e-folds is almost always higher than the observational
lower-bound. We also compute the primordial tensor power spectrum and study its
sensitivity upon the fundamental parameters used in the model.


  We present two concepts of deformable mirror to compensate for first order
optical aberrations. Deformation systems are designed using both elasticity
theory and Finite Element Analysis in order to minimize the number of
actuators. Starting from instrument specifications, we explain the methodology
to design dedicated deformable mirrors. The work presented here leads to
correcting devices optimized for specific functions. The Variable Off-Axis
paraboLA concept is a 3-actuators, 3-modes system able to generate
independently Focus, Astigmatism and Coma. The Correcting Optimized Mirror with
a Single Actuator is a 1-actuator system able to generate a given combination
of optical aberrations.


  The inner few hundred parsecs of our galaxy provide a laboratory for the
study of the production and propagation of energetic particles.
Very-high-energy gamma-rays provide an effective probe of these processes and,
especially when combined with data from other wave-bands, gamma-rays
observations are a powerful diagnostic tool. Within this central region, data
from the H.E.S.S. instrument have revealed three discrete sources of
very-high-energy gamma-rays and diffuse emission correlated with the
distribution of molecular material. Here I provide an overview of these recent
results from H.E.S.S.


  Rapid advances in deep learning have led to paradigm shifts in a number of
fields, from medical image analysis to autonomous systems. These advances,
however, have resulted in digital neural networks with large computational
requirements, resulting in high energy consumption and limitations in real-time
decision making when computation resources are limited. Here, we demonstrate a
meta-optic based neural network accelerator that can off-load computationally
expensive convolution operations into high-speed and low-power optics. In this
architecture, metasurfaces enable both spatial multiplexing and additional
information channels, such as polarization, in object classification.
End-to-end design is used to co-optimize the optical and digital systems
resulting in a robust classifier that achieves 95% accurate classification of
handwriting digits and 94% accuracy in classifying both the digit and its
polarization state. This approach could enable compact, high-speed, and
low-power image and information processing systems for a wide range of
applications in machine-vision and artificial intelligence.


  From economics point of view, we investigate a new optimal control problem
driven by a stochastic differential equation with a multi-time states cost
functional. By constructing a series of first-order adjoint equations, we
establish the stochastic maximum principle and sufficient optimality conditions
for this new optimal control problem. A constraints problem also be studied. In
the end, we develop a near optimal control problem for a general cost
functional.


  This paper introduces prime holdout problems, a problem class related to the
Collatz conjecture. After applying a linear function, instead of removing a
finite set of prime factors, a holdout problem specifies a set of primes to be
retained. A proof that all positive integers converge to 1 is given for both a
finite and an infinite holdout problem. It is conjectured that finite holdout
problems cannot diverge for any starting value, which has implications for
divergent sequences in the Collatz conjecture.


  Lu-Minguzzi-Ohta have introduced the notion of a lower $N$-weighted Ricci
curvature bound with $\varepsilon$-range, and derived several comparison
geometric estimates from a Laplacian comparison theorem for weighted Laplacian.
The aim of this paper is to investigate various rigidity phenomena for the
equality case of their comparison geometric results. We will obtain rigidity
results concerning the Laplacian comparison theorem, diameter comparisons, and
volume comparisons. We also generalize their works for non-symmetric Laplacian
induced from vector field potential.


  In this paper, we consider the problem of minimizing the completion delay for
instantly decodable network coding (IDNC), in wireless multicast and broadcast
scenarios. We are interested in this class of network coding due to its
numerous benefits, such as low decoding delay, low coding and decoding
complexities and simple receiver requirements. We first extend the IDNC graph,
which represents all feasible IDNC coding opportunities, to efficiently operate
in both multicast and broadcast scenarios. We then formulate the minimum
completion delay problem for IDNC as a stochastic shortest path (SSP) problem.
Although finding the optimal policy using SSP is intractable, we use this
formulation to draw the theoretical guidelines for the policies that can
efficiently reduce the completion delay in IDNC. Based on these guidelines, we
design a maximum weight clique selection algorithm, which can efficiently
reduce the IDNC completion delay in polynomial time. We also design a quadratic
time heuristic clique selection algorithm, which can operate in real-time
applications. Simulation results show that our proposed algorithms efficiently
reduce the IDNC completion delay compared to the random and maximum-rate
algorithms, and almost achieve the global optimal completion delay performance
over all network codes in broadcast scenarios.


  Triad resonances for gravity waves propagating in opposite direction with
respect to uniform current are introduced. They are produced by multivalued and
anisotropic dispersion and occur even in deep water. In contrast, existing
literature suggests non-degenerate deep water triads require inhomogeneity or
capillary effects. In this sense, the new resonances are a first of their kind.
Analytical conditions for the existence of resonance may be reduced to
universal constants. Solution of a three-wave interaction model, adapted to the
wave-current problem, shows regimes wherein the dominant direction, speed and
strength of resonant energy transfer differs between wavenumber scales. This
suggests uniform current is a fundamental source of spatial inhomogeneity. The
new resonances significantly modify the picture of nonlinear interactions in
wave-current fields. Since the resonances are quadratic, they will also
dominate well known quartet interactions.


  Coronal-Line Forest Active Galactic Nuclei (CLiF AGN) are remarkable in the
sense that they have a rich spectrum of dozens of coronal emission lines (e.g.
[FeVII], [FeX] and [NeV]) in their spectra. Rose, Elvis & Tadhunter (2015)
suggest that the inner obscuring torus wall is the most likely location of the
coronal line region in CLiF AGN, and the unusual strength of the forbidden high
ionization lines is due to a specific AGN-torus inclination angle. Here we test
this suggestion using mid-IR colours (4.6$\mu$m-22$\mu$m) from the Wide-Field
Infrared Survey Explorer (WISE) for the CLiF AGN. We use the Fischer et al.
(2014) result that showed that as the AGN-torus inclination becomes more face
on, the Spitzer 5.5$\mu$m to 30$\mu$m colours become bluer. We show that the
[W2-W4] colours for the CLiF AGN ($\langle$[W2-W4]$\rangle$ = 5.92$\pm$0.12)
are intermediate between SDSS type 1 ($\langle$[W2-W4]$\rangle$ =
5.22$\pm$0.01) and type 2 AGN ($\langle$[W2-W4]$\rangle$ = 6.35$\pm$0.03). This
implies that the AGN-torus inclinations for the CLiF AGN are indeed
intermediate, supporting the work of Rose, Elvis \& Tadhunter (2015). The
confirmed relation between CLiF AGN and their viewing angle shows that CLiF AGN
may be useful for our understanding of AGN unification.


  We introduce in non-coordinate presentation the notions of a quantum algebra
and of a quantum module over such an algebra. Then we give the definition of a
projective quantum module and of a free quantum module, the latter as a
particular case of the notion of a free object in a rigged category. (Here we
say "quantum" instead of frequently used protean adjective "operator"). After
this we discuss the general connection between projectivity and freeness. Then
we show that for a Banach quantum algebra A and a Banach quantum space E the
Banach quantum A-module $A\widehat\otimes_{op}E$ is free, where "
$\widehat\otimes_{op}$ " denotes the operator-projective tensor product of
Banach quantum spaces. This is used in the proof of the following theorem: all
closed left ideals in a separable C*-algebra, endowed with the standard
quantization, are projective left quantum modules over this algebra.


  A square of a path on $k$ vertices is a directed path $x_1\ldots x_k$, where
$x_i$ is directed to $x_{i+2}$, for every $i\in \{1,\ldots, k-1\}$. Recently,
Yuster showed that any tournament on $n$ vertices contains a square of a path
of length at least $n^{0.295}$. In this short note, we improve this bound. More
precisely, we show that for every $\varepsilon>0$, there exists
$c_{\varepsilon}>0$ such that any tournament on $n$ vertices contains a square
of a path on at least $c_{\varepsilon}n^{1-\varepsilon}$ vertices.


  We propose a general method by which a spin-$S$ is decomposed into spins less
than $S$. We have obtain the exact mapping between spin $S=\frac{p^{M}-1}{2}$
and a cluster of $M$ spins $\sigma=\frac{p-1}{2}$. We have discuss the possible
applications of such transformations. In particular we have show how a general
$d+1$ dimensional spin-$\frac{p-1}{2}$ model with general interactions can be
reduced to $d$-dimensional spin-$S$ model with $S=\frac{p^{M}-1}{2}$.


  The magnetic phase diagram $T_c(P)$ of the weak itinerant helimagnetic
compound MnSi is reviewed upon a Nuclear Magnetic Resonance (NMR) experiment.
We present a systematic study on the evolution of the NMR spin echo signal at
$T=1.4$ K of the non-magnetic silicone sites, $^{29}$Si, up to 17.8 kbar. The
pressure effect is interpreted as a weak variation of the local electronic spin
polarization and the coexistence of magnetic and non magnetic Mn atoms under
pressure. From the volume dependence of $f_0$ ($P$), we show notably that a
local magnetic order remains above the critical pressure of $P_c=14.8$ kbar.


  We develop a local version of Huisken-Stampacchia iteration, using it to
obtain local versions of a host of important sharp curvature pinching estimates
for mean curvature flow. The local estimates we obtain do not depend on the
quality of noncollapsing of the solution and the method adopted applies in a
host of other settings.


  Recently, machine learning algorithms have been used remarkably to study the
equilibrium phase transitions, however there are only a few works have been
done using this technique in the nonequilibrium phase transitions. In this
work, we use the supervised learning with the convolutional neural network
(CNN) algorithm and unsupervised learning with the density-based spatial
clustering of applications with noise (DBSCAN) algorithm to study the
nonequilibrium phase transition in two models. We use CNN and DBSCAN in order
to determine the critical points for directed bond percolation (bond DP) model
and Domany-Kinzel cellular automaton (DK) model. Both models have been proven
to have a nonequilibrium phase transition belongs to the directed percolation
(DP) universality class. In the case of supervised learning we train CNN using
the images which are generated from Monte Carlo simulations of directed bond
percolation. We use that trained CNN in studding the phase transition for the
two models. In the case of unsupervised learning, we train DBSCAN using the raw
data of Monte Carlo simulations. In this case, we retrain DBSCAN at each time
we change the model or lattice size. Our results from both algorithms show
that, even for a very small values of lattice size, machine can predict the
critical points accurately for both models. Finally, we mention to that, the
value of the critical point we find here for bond DP model using CNN or DBSCAN
is exactly the same value that has been found using transfer learning with a
domain adversarial neural network (DANN) algorithm.


  The indistinguishability of successively generated photons from a single
quantum emitter is most commonly measured using two-photon interference at a
beam splitter. Whilst for sources excited in the pulsed regime the measured
bunching of photons reflects the full wavepacket indistinguishability of the
emitted photons, for continuous wave (cw) excitation the inevitable dependence
on detector timing resolution and driving strength obscures the underlying
photon interference process. Here we derive a method to extract the photon
indistinguishability from cw measurements by considering the relevant
correlation functions. The equivalence of both methods is experimentally
verified through comparison of cw and pulsed excitation of an archetypal source
of photons, a single molecule.


  We prove bounds on the saturation degrees of homogeneous ideals (and their
powers) defining smooth complex projective varieties. For example, we show that
a classical statement due to Macualay for zero-dimensional complete
intersection ideals holds for any smooth variety. For curves, we bound the
saturation degree of powers in terms of the regularity.


  The sequence $\{\,_2\phi_1(q^{-k},q^{b+1};\,q^{-\overline{b}-k+1};\, q,
q^{-\overline{b}+1/2} z)\}_{k \geq 0}$ of basic hypergeometric polynomials is
known to be orthogonal on the unit circle with respect to the weight function
$|(q^{1/2}e^{i\theta};\,q)_{\infty}/(q^{b+1/2}e^{i\theta};\,q)_{\infty}|^2$.
This result, where one must take the parameters $q$ and $b$ to be $0 < q < 1$
and $\Re(b) > -1/2$, is due to P.I. Pastro \cite{Pastro-1985}. In the present
manuscript we deal with the orthogonal polynomials $\hat{\Phi}_{n}(b;.)$ and
$\check{\Phi}_{n}(b;.)$ on the unit circle with respect to the two parametric
families of weight functions $\hat{\omega}(b; \theta) =
|(e^{i\theta};\,q)_{\infty}/(q^{b}e^{i\theta};\,q)_{\infty}|^2$ and
$\check{\omega}(b;\theta) =
|(qe^{i\theta};\,q)_{\infty}/(q^{b}e^{i\theta};\,q)_{\infty}|^2$, where $0 < q
< 1$ and $\Re(b) > 0$. With the use of the basic hypergeometric polynomials $
_2\phi_1(q^{-k},q^{b};\,q^{-\overline{b}-k+1};\, q, q^{-\overline{b}+1} z)$, $k
\geq 0$, which have zeros on the unit circle when $\Re(b) > 0$, simple
expressions for the (monic) polynomials $\hat{\Phi}_{n}(b;.)$ and
$\check{\Phi}_{n}(b;.)$, their norms, the associated Verblunsky coefficients
and also the respective Szeg\H{o} functions are found.


  We develop a theory describing the dynamics of quantum kicked rotators
(modelling cold atoms in a pulsed optical field) which are subjected to
combined amplitude and timing noise generated by a renewal process (acting as
an engineered reservoir). For waiting-time distributions of variable exponent
(L\'evy noise), we demonstrate the existence of a regime of nonexponential loss
of phase coherence. In this regime, the momentum dynamics is subdiffusive,
which also manifests itself in a non-Gaussian limiting distribution and a
fractional power-law decay of the inverse participation ratio. The purity
initially decays with a stretched exponential which is followed by two regimes
of power-law decay with different exponents. The averaged logarithm of the
fidelity probes the sprinkling distribution of the renewal process. These
analytical results are confirmed by numerical computations on quantum kicked
rotators subjected to noise events generated by a Yule-Simon distribution.


  Water shows intriguing thermodynamic and dynamic anomalies in the supercooled
liquid state. One possible explanation of the origin of these anomalies lies in
the existence of a metastable liquid-liquid phase transition (LLPT) between two
(high and low density) forms of water. While the anomalies are observed in
experiments on bulk and confined water and by computer simulation studies of
water-like models, the existence of a LLPT in water is still debated.
Unambiguous experimental proof of the existence of a LLPT in bulk supercooled
water is hampered by fast ice nucleation which is a precursor of the
hypothesized LLPT. Moreover, the hypothesized LLPT, being metastable, in
principle cannot exist in the thermodynamic limit (infinite size, infinite
time). Therefore, computer simulations of water models are crucial for
exploring the possibility of the metastable LLPT and the nature of the
anomalies. In this work, we present new simulation results in the NVT ensemble
for one of the most accurate classical molecular models of water, TIP4P/2005.
To describe the computed properties and explore the possibility of a LLPT we
have applied two-structure thermodynamics, viewing water as a non-ideal mixture
of two interconvertible local structures ("states"). The results suggest the
presence of a liquid-liquid critical point and a LLPT in this model for the
simulated length and time scales. We have compared the behavior of TIP4P/2005
with other popular water-like models, namely mW and ST2, and with real water,
all of which are well described by two-state thermodynamics. In view of the
current debate involving different studies of TIP4P/2005, we discuss
consequences of metastability and finite size in observing the liquid-liquid
separation. We also address the relationship between the phenomenological order
parameter of two-structure thermodynamics and the microscopic nature of the
low-density structure.


  The magnitude of a graph is one of a family of cardinality-like invariants
extending across mathematics; it is a cousin to Euler characteristic and
geometric measure. Among its cardinality-like properties are multiplicativity
with respect to cartesian product and an inclusion-exclusion formula for the
magnitude of a union. Formally, the magnitude of a graph is both a rational
function over Q and a power series over Z. It shares features with one of the
most important of all graph invariants, the Tutte polynomial; for instance,
magnitude is invariant under Whitney twists when the points of identification
are adjacent. Nevertheless, the magnitude of a graph is not determined by its
Tutte polynomial, nor even by its cycle matroid, and it therefore carries
information that they do not.


  A mechanism responsible for the directed transport and molecular separation
in a symmetric channel is proposed. We found that under the action of spatial
harmonic oscillations of the channel, the system exhibits a directed transport
in either direction, presenting multiple current reversals as the amplitude
and/or frequency of the oscillations are varied. The particles of different
masses may be forced to move with different velocities in the same or in the
opposite directions by properly adjusting driving parameters. The directed
transport can be produced in both directions even in the absence of thermal
noise, the latter can speed up or slow down the transport depending on the
system parameters.


  Ceramics are easy to break, and very few generic mechanisms are available for
improving their mechanical properties, e.g., the 1975-discovered anti-fracture
mechanism is strictly limited to zirconia and hafnia. Here we report a general
mechanism for achieving high plasticity through liquefaction of ceramics. We
further disclose the general material design strategies to achieve this
difficult task through entropy-boosted amorphous ceramics (EBACs), enabling
fracture-resistant properties that can withstand severe plastic deformation
(e.g., over 95%, deformed to a thickness of a few nanometers) while maintaining
high hardness and reduced modulus. The findings reported here open a new route
to ductile ceramics and many applications.


  We have mapped the physics of a system of semi-flexible inextensible polymers
onto a complex Ginzburg-Landau field theory using techniques of functional
integration. It is shown in the limit of low number density of monomers in a
melt of semi-flexible, inextensible polymers, kept apart by an excluded volume
interaction, the radius of gyration scales as N^{nu}, where N is the chain
length, and nu = 1, in contrast to the value of nu ~ 0.6 for flexible polymer
melts. Using Renormalization Group arguments, we show that the system exhibits
an infra-red stable fixed point which can be identified as the transition to
the entangled state. Experiments to test these calculations are suggested.


  We comment on article by Yi Zhang , Hanna Terletska, Ka-Ming Tam, Yang Wang,
Markus Eisenbach, Liviu Chioncel, and Mark Jarrell [Phys. Rev. B {\bf 100},
054205 (2019)]\cite{Zhang} in which to study substitution disordered systems,
they presented an embedding scheme for the locally self-consistent method. Here
we show that their methods is a truncated case of our super-cell approximation,
achieved by neglecting super-cell wave vectors dependence on self-energy
$\Sigma_{sc}({\bf K}_{n},E)$ and replacing them by a local on-site self-energy,
$\Sigma_{sc}({\bf K}_{n},E)=\Sigma_{sc}(L,L,E)$ in our
articles\cite{Moradian01, Moradian02, Moradian03}. Also their real and k-space
self-energies in the limit of the number of super-cell sites, $N_{c}$,
approaching the number of lattice sites, N, do not recover exact self-energies
$\Sigma(l, l', E)$ and $\Sigma({\bf k}, E)$. For highlighting advantages of our
methods with respect to other approximations such as dynamical cluster
approximation (DCA)\cite{Jarrell} in capturing electron localization, we apply
our real space super-cell approximation (SCA), and super-cell local self-energy
approximation (SCLSA) to one and two dimensional substitution disorder alloy
systems. Our electron localization probability calculations for these systems
determine non zero values that indicate electrons localization.


  The standard way to generate many-body quantum correlations is via a
dynamical protocol: an initial product state is transformed by interactions
that generate non-classical correlations at later times. Here, we show that
many-body Bell correlations are inherently present in the eigenstates of a
variety of spin-1/2 chains. In particular, we show that the eigenstates and
thermal states of the collective Lipkin-Meshkov-Glick model possess many-body
Bell correlations. We demonstrate that the Bell correlations can take on
quantized values that change discontinuously with variations in the total
magnetization. Finally, we show that these many-body Bell correlations persist
even in the presence of both diagonal and off-diagonal disorder.


  Large number of ReLU and MAC operations of Deep neural networks make them
ill-suited for latency and compute-efficient private inference. In this paper,
we present a model optimization method that allows a model to learn to be
shallow. In particular, we leverage the ReLU sensitivity of a convolutional
block to remove a ReLU layer and merge its succeeding and preceding convolution
layers to a shallow block. Unlike existing ReLU reduction methods, our joint
reduction method can yield models with improved reduction of both ReLUs and
linear operations by up to 1.73x and 1.47x, respectively, evaluated with
ResNet18 on CIFAR-100 without any significant accuracy-drop.


  Let $R$ be a commutative noetherian ring with a dualizing complex. By recent
work of Iyengar and Krause, the difference between the category of acyclic
complexes and its subcategory of totally acyclic complexes measures how far $R$
is from being Gorenstein. In particular, $R$ is Gorenstein if and only if every
acyclic complex is totally acyclic.
  In this note we exhibit a specific acyclic complex with the property that it
is totally acyclic if and only if $R$ is Gorenstein.


  The nonlinear force-free field (NLFFF) model is often used to describe the
solar coronal magnetic field, however a series of earlier studies revealed
difficulties in the numerical solution of the model in application to
photospheric boundary data. We investigate the sensitivity of the modeling to
the spatial resolution of the boundary data, by applying multiple codes that
numerically solve the NLFFF model to a sequence of vector magnetogram data at
different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active
Region 10978 on 2007 December 13. We analyze the resulting energies and
relative magnetic helicities, employ a Helmholtz decomposition to characterize
divergence errors, and quantify changes made by the codes to the vector
magnetogram boundary data in order to be compatible with the force-free model.
This study shows that NLFFF modeling results depend quantitatively on the
spatial resolution of the input boundary data, and that using more highly
resolved boundary data yields more self-consistent results. The free energies
of the resulting solutions generally trend higher with increasing resolution,
while relative magnetic helicity values vary significantly between resolutions
for all methods. All methods require changing the horizontal components, and
for some methods also the vertical components, of the vector magnetogram
boundary field in excess of nominal uncertainties in the data. The solutions
produced by the various methods are significantly different at each resolution
level. We continue to recommend verifying agreement between the modeled field
lines and corresponding coronal loop images before any NLFFF model is used in a
scientific setting.


  We prove a cabling formula for the concordance invariant $\nu^+$, defined by
the author and Hom. This gives rise to a simple and effective 4-ball genus
bound for many cable knots.


  We investigate the prospect of stop squark search at Tevatron RUN-II in
mSUGRA motivated as well as unconstrained supersymmetric models, when the
lighter stop squark turns out to be the next lightest supersymmetric particle
(NLSP). In this case the decay into a 4-body final state consisting of a b
quark, the lightest neutralino and two light fermions may compete with the much
publicized loop induced two body decay into a charm quark and the lightest
neutralino. We systematically study the parameter space in mSUGRA where the
lighter stop squark turns out to be the NLSP and calculate the branching ratios
of the competing channels in both models. Our results show that the four body
decay may indeed be the main discovery channel particularly in the low tan
$\beta$ scenarios. We discuss the detectability of stop squark pairs in the
4-body decay channel leading to one lepton with 2 or more jets accompanied by a
large amount of missing energy. We also studied the corresponding background
processes and the kinematic cuts required to suppress them using parton level
Monte Carlo simulations. We have commented upon with illustrative examples, the
required revision of the existing mass limits of the stop NLSP assumed to decay
solely into the loop induced 2-body channel in the presence of the competing
4-body decay.


  Let N be a complete Riemannian manifold of dimension n+1 whose Riemannian
metric g is conformally equivalent to a metric with non-negative Ricci
curvature. The normalized Steklov eigenvalues of a bounded domain in N are
bounded above in terms of the isoperimetric ratio of the domain. Consequently,
the normalized Steklov eigenvalues of a bounded domain in Euclidean space,
hyperbolic space or a standard hemisphere are uniformly bounded above. On a
compact surface with boundary, the normalized Steklov eigenvalues are uniformly
bounded above in terms of the genus. We also obtain a relationship between the
Steklov eigenvalues of a domain and the eigenvalues of the Laplace-Beltrami
operator on its bounding hypersurface.


  In this letter we consider the distinctive phenomenology of supersymmetric
models in which the scale of SUSY breaking is very low, \sqrt{F}= O(TeV),
focusing on the Higgs sector and the process of electroweak breaking. Using an
effective Lagrangian description of the interactions between the observable
fields and the SUSY breaking sector, it is shown how the conventional MSSM
picture can be substantially modified. For instance, the Higgs potential has
non-negligible SUSY breaking quartic couplings that can modify completely the
pattern of electroweak breaking and the Higgs spectrum with respect to that of
conventional MSSM-like models.


  In this paper, we prove that any simple $\{C_3,C_5\}$-free non-empty
connected graph $G$ with LLY curvature bounded below by $\kappa>0$ has the
order at most $2^{\frac{2}{\kappa}}$. This upper bound is achieved if and only
if $G$ is a hypercube $Q_d$ and $\kappa=\frac{2}{d}$ for some integer $d\geq
1$.


  We present a physical interpretation of the doubling of the algebra, which is
the basic ingredient of the noncommutative spectral geometry, developed by
Connes and collaborators as an approach to unification. We discuss its
connection to dissipation and to the gauge structure of the theory. We then
argue, following 't Hooft's conjecture, that noncommutative spectral geometry
classical construction carries implicit in its feature of the doubling of the
algebra the seeds of quantization.


  In this paper, we investigate the Hermite spectral method (HSM) to
numerically solve the forward Kolmogorov equation (FKE). A useful guideline of
choosing the scaling factor of the generalized Hermite functions is given in
this paper. It greatly improves the resolution of HSM. The convergence rate of
HSM to FKE is analyzed in the suitable function space and has been verified by
the numerical simulation. As an important application and our primary
motivation to study the HSM to FKE, we work on the implementation of the
nonlinear filtering (NLF) problem with a real-time algorithm developed in [17].
The HSM to FKE is served as the off-line computation in this algorithm. The
translating factor of the generalized Hermite functions and the moving-window
technique are introduced to deal with the drifting of the posterior conditional
density function of the states in the on-line experiments. Two numerical
experiments of NLF problems are carried out to illustrate the feasibility of
our algorithm. Moreover, our algorithm surpasses the particle filter as a
real-time solver to NLF.


  This work introduces the first toolkit around path-norms that fully
encompasses general DAG ReLU networks with biases, skip connections and any
operation based on the extraction of order statistics: max pooling, GroupSort
etc. This toolkit notably allows us to establish generalization bounds for
modern neural networks that are not only the most widely applicable path-norm
based ones, but also recover or beat the sharpest known bounds of this type.
These extended path-norms further enjoy the usual benefits of path-norms: ease
of computation, invariance under the symmetries of the network, and improved
sharpness on layered fully-connected networks compared to the product of
operator norms, another complexity measure most commonly used.
  The versatility of the toolkit and its ease of implementation allow us to
challenge the concrete promises of path-norm-based generalization bounds, by
numerically evaluating the sharpest known bounds for ResNets on ImageNet.


  A hybrid evolutionary algorithm with importance sampling method is proposed
for multi-dimensional optimization problems in this paper. In order to make use
of the information provided in the search process, a set of visited solutions
is selected to give scores for intervals in each dimension, and they are
updated as algorithm proceeds. Those intervals with higher scores are regarded
as good intervals, which are used to estimate the joint distribution of optimal
solutions through an interaction between the pool of good genetics, which are
the individuals with smaller fitness values. And the sampling probabilities for
good genetics are determined through an interaction between those estimated
good intervals. It is a cross validation mechanism which determines the
sampling probabilities for good intervals and genetics, and the resulted
probabilities are used to design crossover, mutation and other stochastic
operators with importance sampling method. As the selection of genetics and
intervals is not directly dependent on the values of fitness, the resulted
offsprings may avoid the trap of local optima. And a purely random EA is also
combined into the proposed algorithm to maintain the diversity of population.
30 benchmark test functions are used to evaluate the performance of the
proposed algorithm, and it is found that the proposed hybrid algorithm is an
efficient algorithm for multi-dimensional optimization problems considered in
this paper.


  We propose a model-independent approach for the search of charged long-lived
particles produced in ultraperipheral collisions at the LHC. The main idea is
to improve event reconstruction at ATLAS and CMS with the help of their forward
detectors. Detection of both scattered protons in forward detectors allows
complete recovery of event kinematics. Though this requirement reduces the
number of events, it greatly suppresses the background, including the large
background from the pile-up.


  Consider a branching random walk on $\mathbb{R}$, with offspring distribution
Z and nonnegative displacement distribution W. We say that explosion occurs if
an infinite number of particles may be found within a finite distance of the
origin. In this paper, we investigate this phenomenon when the offspring
distribution Z is heavy-tailed. Under an appropriate condition, we are able to
characterize the pairs (Z, W) for which explosion occurs, by demonstrating the
equivalence of explosion with a seemingly much weaker event: that the sum over
generations of the minimum displacement in each generation is finite.
Furthermore, we demonstrate that our condition on the tail is best possible for
this equivalence to occur. We also investigate, under additional smoothness
assumptions, the behavior of $M_n$, the position of the particle in generation
n closest to the origin, when explosion does not occur (and hence
$\lim_{n\rightarrow\infty}M_n=\infty$).


  We consider the pairing of electrons and holes due to their Coulomb
attraction in two parallel, independently gated graphene layers, separated by a
barrier. At weak coupling, there exist the BCS-like pair-condensed state.
Despite the fact that electrons and holes behave like massless Dirac fermions,
the problem of BCS-like electron-hole pairing in graphene bilayer turns out to
be rather similar to that in usual coupled semiconductor quantum wells. The
distinctions are due to Berry phase of electronic wave functions and different
screening properties. We estimate values of the gap in one-particle excitation
spectrum for different interlayer distances and carrier concentrations.
Influence of disorder is discussed. At large enough dielectric susceptibility
of surrounding medium, the weak coupling regime holds even at arbitrarily small
carrier concentrations. Localized electron-hole pairs are absent in graphene,
thus the behavior of the system versus coupling strength is cardinally
different from usual BCS-BEC crossover.


  We determine the isomorphism classes of semisimple Hopf algebras of dimension
60 which are simple as Hopf algebras.


  We investigate the accretion flows onto the supermassive binary black holes
(SMBBHs) from the circumbinary disk with the equal mass, eccentric binary on
the subparsec scale, using Smoothed Particle Hydrodynamics (SPH) code. We find
that the material can be supplied from circumbinary disk, which leads to the
formation of two accretion disks around the SMBBHs. The mass accretion rates
significantly modulate with the binary orbital motion. These could provide the
observable diagnosis of the existence of the supermassive binary black holes
(e.g. OJ287) on the subparsec scale in merged galactic nuclei.


  This paper introduces almost partitionable sets to generalize the known
concept of partitionable sets. These notions provide a unified frame to
construct $\mathbb{Z}$-cyclic patterned starter whist tournaments and cyclic
balanced sampling plans excluding contiguous units. The existences of
partitionable sets and almost partitionable sets are investigated. As an
application, a large number of optical orthogonal codes achieving the Johnson
bound or the Johnson bound minus one are constructed.


  The continued logarithm algorithm was introduced by Gosper around 1978, and
recently studied by Borwein, Calkin, Lindstrom, and Mattingly. In this note I
show that the continued logarithm algorithm terminates in at most 2 log_2 p +
O(1) steps on input a rational number p/q >= 1. Furthermore, this bound is
tight, up to an additive constant.