  The analysis of sentimental posts about software testing on Stack Overflow
reveals that motivation and commitment of developers to use software testing
methods is not only influenced by tools and technology. Rather, attitudes are
also influenced by socio-technical factors. No prior studies have attempted to
talk with Stack Overflow users about the sentimental posts that they write,
yet, this is crucial to understand their experiences of which their post is
only a fragment. As such, this study explores the precursors that make
developers write sentimental posts about software testing on Stack Overflow.
Through semi-structured interviews, we reconstruct the individual experiences
of Stack Overflow users leading to sentimental posts about testing. We use the
post as an anchor point to explore the events that lead to it and how users
moved on in the meantime. Using strategies from socio-technical grounded theory
(STGT), we derive hypotheses about the socio-technical factors that cause
sentiment towards software testing.


  The works of William Rowan Hamilton in Geometrical Optics are presented, with
emphasis on the Malus-Dupin theorem. According to that theorem, a family of
light rays depending on two parameters can be focused to a single point by an
optical instrument made of reflecting or refracting surfaces if and only if,
before entering the optical instrument, the family of rays is rectangular
(\emph{i.e.}, admits orthogonal surfaces). Moreover, that theorem states that a
rectangular system of rays remains rectangular after an arbitrary number of
reflections through, or refractions across, smooth surfaces of arbitrary shape.
The original proof of that theorem due to Hamilton is presented, along with
another proof founded in symplectic geometry. It was the proof of that theorem
which led Hamilton to introduce his \emph{characteristic function} in Optics,
then in Dynamics under the name \emph{action integral}


  We investigate the relationship between the diagonal of the Fremlin
projective tensor product of a Banach lattice $E$ with itself and the
2-concavification of $E$.


  Sketching is an important tool for dealing with high-dimensional vectors that
are sparse (or well-approximated by a sparse vector), especially useful in
distributed, parallel, and streaming settings. It is known that sketches can be
made differentially private by adding noise according to the sensitivity of the
sketch, and this has been used in private analytics and federated learning
settings. The post-processing property of differential privacy implies that all
estimates computed from the sketch can be released within the given privacy
budget.
  In this paper we consider the classical CountSketch, made differentially
private with the Gaussian mechanism, and give an improved analysis of its
estimation error. Perhaps surprisingly, the privacy-utility trade-off is
essentially the best one could hope for, independent of the number of
repetitions in CountSketch: The error is almost identical to the error from
non-private CountSketch plus the noise needed to make the vector private in the
original, high-dimensional domain.


  A backward computation method has been developed to accelerate modelling of
the critical state magnetization current in a staggered-array bulk
high-temperature superconducting (HTS) undulator. The key concept is as
follows: i) a large magnetization current is first generated on the surface of
the HTS bulks after rapid field-cooling (FC) magnetization; ii) the
magnetization current then relaxes inwards step-by-step obeying the critical
state model; iii) after tens of backward iterations the magnetization current
reaches a steady state. The simulation results show excellent agreement with
the H-formulation method for both the electromagnetic and
electromagnetic-mechanical coupled analyses, but with significantly faster
computation speed. Solving the FEA model with 1.8 million degrees of freedom
(DOFs), the backward computation method takes less than 1.4 hours, an order of
magnitude or higher faster than other state-of-the-art numerical methods.
Finally, the models are used to investigate the influence of the mechanical
stress on the distribution of the critical state magnetization current and the
undulator field along the central axis.


  Entangled states, such as the Bell and GHZ states, are generated from
separable states using matrices known to satisfy the Yang-Baxter equation and
its generalization. This remarkable fact hints at the possibility of using
braiding operators as quantum entanglers, and is part of a larger speculated
connection between topological and quantum entanglement. We push the analysis
of this connection forward, by showing that supersymmetry algebras can be used
to construct large families of solutions of the spectral parameter-dependent
generalized Yang-Baxter equation. We present a number of explicit examples and
outline a general algorithm for arbitrary numbers of qubits. The operators we
obtain produce, in turn, all the entangled states in a multi-qubit system
classified by the Stochastic Local Operations and Classical Communication
protocol introduced in quantum information theory.


  Polymer nanocomposite materials based on metallic nanowires are widely
investigated as transparent and flexible electrodes or as stretchable
conductors and dielectrics for biosensing. Here we show that Scanning
Dielectric Microscopy (SDM) can map the depth distribution of metallic
nanowires within the nanocomposites in a non-destructive way. This is achieved
by a quantitative analysis of sub-surface electrostatic force microscopy
measurements with finite-element numerical calculations. As an application we
determined the three-dimensional spatial distribution of around 50 nm diameter
silver nanowires in 100 - 250 nm thick gelatin films. The characterization is
done both under dry ambient conditions, where gelatin shows a relatively low
dielectric constant, epsilon around 5, and under humid ambient conditions,
where its dielectric constant increases up to epsilon around 14. The present
results show that SDM can be a valuable non-destructive subsurface
characterization technique for nanowire-based nanocomposite materials, which
can contribute to the optimization of these materials for applications in
fields such as wearable electronics, solar cell technologies or printable
electronics.


  GitHub is the largest source code repository in the world. It provides a
git-based source code management platform and also many features inspired by
social networks. For example, GitHub users can show appreciation to projects by
adding stars to them. Therefore, the number of stars of a repository is a
direct measure of its popularity. In this paper, we use multiple linear
regressions to predict the number of stars of GitHub repositories. These
predictions are useful both to repository owners and clients, who usually want
to know how their projects are performing in a competitive open source
development market. In a large-scale analysis, we show that the proposed models
start to provide accurate predictions after being trained with the number of
stars received in the last six months. Furthermore, specific models---generated
using data from repositories that share the same growth trends---are
recommended for repositories with slow growth and/or for repositories with less
stars. Finally, we evaluate the ability to predict not the number of stars of a
repository but its rank among the GitHub repositories. We found a very strong
correlation between predicted and real rankings (Spearman's rho greater than
0.95).


  The regularization of propagators by means of a complex metric is considered.
(The paper is an English translation of the first of two articles in Russian
published by the author in 1987-88: V.D. Ivashchuk, Regularization by
{\epsilon}-metric. I, Izvestiya Akademii Nauk Moldavskoy SSR, Ser.
Fiziko-tekhnicheskih i matematicheskih nauk, No 3, p. 8-17 (1987) [in Russian]
.)


  We present a first principle approach to obtain analytical predictions for
spherically-averaged cosmic densities in the mildly non-linear regime that go
well beyond what is usually achieved by standard perturbation theory. A large
deviation principle allows us to compute the leading-order cumulants of average
densities in concentric cells. In this symmetry, the spherical collapse model
leads to cumulant generating functions that are robust for finite variances and
free of critical points when logarithmic density transformations are
implemented. They yield in turn accurate density probability distribution
functions (PDFs) from a straightforward saddle-point approximation valid for
all density values. Based on this easy-to-implement modification, explicit
analytic formulas for the evaluation of the one- and two-cell PDF are provided.
The theoretical predictions obtained for the PDFs are accurate to a few percent
compared to the numerical integration, regardless of the density under
consideration and in excellent agreement with N-body simulations for a wide
range of densities. This formalism should prove valuable for accurately probing
the quasi-linear scales of low redshift surveys for arbitrary primordial power
spectra.


  Phase field theory is widely used to model multi-phase flows. A drop can
shrink or grow spontaneously due to the redistribution of interface and bulk
energies to minimize the system energy. In this paper, the spontaneous
behaviour of a drop on a flat surface is investigated. It is found that there
exists a critical radius dependent on the contact angle, the domain size and
the interface width, below which the droplet will eventually disappear. In
particular, the critical radius can be very large when the contact angle is
hydrophilic. The theoretical prediction of the critical radius is verified
numerically by simulating a drop on a surface with various contact angles, the
domain sizes and the interface widths.


  The connection between halo gas acquisition through the circumgalactic medium
(CGM) and galaxy star formation has long been studied. In this series of two
papers, we put this interplay within the context of the galaxy environment on
large scales (several hundreds of kpc), which, to a certain degree, maps out
various paths for galaxy interactions. We use the IllustrisTNG-100 simulation
to demonstrate that the large-scale environment modulates the circumgalactic
gas angular momentum, resulting in either enhanced (Paper I) or suppressed
(Paper II) star formation inside a galaxy. In this paper (Paper I), we show
that the large-scale environment around a star-forming galaxy is often
responsible for triggering new episodes of star formation. Such an episodic
star formation pattern is well synced with a pulsating motion of the
circumgalactic gas, which, on the one hand receives angular momentum
modulations from the large-scale environment, yielding in-spiralling gas to
fuel the star-forming reservoir, while, on the other hand, is affected by the
feedback activities from the galaxy centre. As a result, a present-day
star-forming galaxy may have gone through several cycles of star-forming and
quiescent phases during its evolutionary history, with the circumgalactic gas
carrying out a synchronized cadence of "breathing in and out" motions out to
$\sim 100$ kpc.


  One of the leading university goals is to provide the students with the
necessary skills for better functioning in their future studies. Gaining and
developing skills, both technical and soft skills, are the critical building
blocks for a successful career. The traditional teaching process, which
includes delivering lectures and conducting exams, emphasizes the upliftment of
technical knowledge rather than building self-esteem and enhancing skills
development among students. Development of non-technical skills like
self-esteem, life-long learning among students is vital for a successful
career. This paper targets to achieve the objective of identifying ways to
empower students with non-technical skills along with technical skills. The
approach adopted in this research work is to transform the delivery of a
faculty-wide course from teaching to coaching. One salient difference between
teaching and coaching is to move students motivation away from grades towards
life-long learning. Thus, university students maximize skills through coaching
like course structure, course delivery, course assessment, and student
involvement. As a case study, the proposed approach was successfully tested and
validated on a course taught in the Faculty of Computing and Information
Technology (FCIT) at King Abdulaziz University (KAU). The outcome of this case
study reveals that there is substantial potential towards enhancement of
self-responsibility. In the future, this approach can be extended for other
courses that aim to develop skills such as English language courses, computer,
and communication skills courses in the preparatory/foundation year.


  Graph data management (also called NoSQL) has revealed beneficial
characteristics in terms of flexibility and scalability by differently
balancing between query expressivity and schema flexibility. This peculiar
advantage has resulted into an unforeseen race of developing new task-specific
graph systems, query languages and data models, such as property graphs,
key-value, wide column, resource description framework (RDF), etc. Present-day
graph query languages are focused towards flexible graph pattern matching (aka
sub-graph matching), whereas graph computing frameworks aim towards providing
fast parallel (distributed) execution of instructions. The consequence of this
rapid growth in the variety of graph-based data management systems has resulted
in a lack of standardization. Gremlin, a graph traversal language, and machine
provides a common platform for supporting any graph computing system (such as
an OLTP graph database or OLAP graph processors). We present a formalization of
graph pattern matching for Gremlin queries. We also study, discuss and
consolidate various existing graph algebra operators into an integrated graph
algebra.


  In this contribution we study the onset of chaos via type-II intermittency
within the framework of Horizontal Visibility graph theory. We construct graphs
associated to time series generated by an iterated map close to a
Neimark-Sacker bifurcation and study, both numerically and analytically, their
main topological properties. We find well defined equivalences between the main
statistical properties of intermittent series (scaling of laminar trends and
Lyapunov exponent) and those of the resulting graphs, and accordingly construct
a graph theoretical description of type-II intermittency. We finally recast
this theory into a graph-theoretical renormalization group framework, and show
that the fixed point structure of RG flow diagram separates regular, critical
and chaotic dynamics.


  We study rational agents with different perception capabilities in strategic
games. We focus on a class of one-shot limited-perception games. These games
extend simultaneous-move normal-form games by presenting each player with an
individualized perception of all players' payoff functions. The accuracy of a
player's perception is determined by the player's capability level. Capability
levels are countable and totally ordered, with a higher level corresponding to
a more accurate perception. We study the rational behavior of players in these
games and formalize relevant equilibria conditions. In contrast to equilibria
in conventional bimatrix games, which can be represented by a pair of mixed
strategies, in our limited perception games a higher-order response function
captures how the lower-capability player uses their (less accurate) perception
of the payoff function to reason about the (more accurate) possible perceptions
of the higher-capability opponent. This response function characterizes, for
each possible perception of the higher-capability player (from the perspective
of the lower-capability player), the best response of the higher capability
player for that perception. Since the domain of the response function can be
exponentially large or even infinite, finding one equilibrium may be
computationally intractable or even undecidable. Nevertheless, we show that for
any $\epsilon$, there exists an $\epsilon$-equilibrium with a compact,
tractable representation whose size is independent of the size of the response
function's domain. We further identify classes of zero-sum limited-perception
games in which finding an equilibrium becomes a (typically tractable) nonsmooth
convex optimization problem.


  Cued Speech (CS) is a visual coding tool to encode spoken languages at the
phonetic level, which combines lip-reading and hand gestures to effectively
assist communication among people with hearing impairments. The Automatic CS
Recognition (ACSR) task aims to recognize CS videos into linguistic texts,
which involves both lips and hands as two distinct modalities conveying
complementary information. However, the traditional centralized training
approach poses potential privacy risks due to the use of facial and gesture
videos in CS data. To address this issue, we propose a new Federated Cued
Speech Recognition (FedCSR) framework to train an ACSR model over the
decentralized CS data without sharing private information. In particular, a
mutual knowledge distillation method is proposed to maintain cross-modal
semantic consistency of the Non-IID CS data, which ensures learning a unified
feature space for both linguistic and visual information. On the server side, a
globally shared linguistic model is trained to capture the long-term
dependencies in the text sentences, which is aligned with the visual
information from the local clients via visual-to-linguistic distillation. On
the client side, the visual model of each client is trained with its own local
data, assisted by linguistic-to-visual distillation treating the linguistic
model as the teacher. To the best of our knowledge, this is the first approach
to consider the federated ACSR task for privacy protection. Experimental
results on the Chinese CS dataset with multiple cuers demonstrate that our
approach outperforms both mainstream federated learning baselines and existing
centralized state-of-the-art ACSR methods, achieving 9.7% performance
improvement for character error rate (CER) and 15.0% for word error rate (WER).


  Since the birth of Bitcoin in 2009, cryptocurrencies have emerged to become a
global phenomenon and an important decentralized financial asset. Due to this
decentralization, the value of these digital currencies against fiat currencies
is highly volatile over time. Therefore, forecasting the crypto-fiat currency
exchange rate is an extremely challenging task. For reliable forecasting, this
paper proposes a multimodal AdaBoost-LSTM ensemble approach that employs all
modalities which derive price fluctuation such as social media sentiments,
search volumes, blockchain information, and trading data. To better support
investment decision making, the approach forecasts also the fluctuation
distribution. The conducted extensive experiments demonstrated the
effectiveness of relying on multimodalities instead of only trading data.
Further experiments demonstrate the outperformance of the proposed approach
compared to existing tools and methods with a 19.29% improvement.


  The Variation After Projection approach is applied for the first time to the
pairing hamiltonian to describe the thermodynamics of small systems with fixed
particle number. The minimization of the free energy is made by a direct
diagonalization of the entropy. The Variation After Projection applied at
finite temperature provides a perfect reproduction of the exact canonical
properties of odd or even systems from very low to high temperature.


  We present a classical analysis on the issue of vector superluminality in the
decoupling limit ghost-free massive gravity with a Minkowski reference metric.
We show explicitly in the Lorenz gauge that the theory is free of superluminal
vector excitations around a nontrivial solution at the cubic order in the
fields. In the same gauge, we demonstrate that superluminal vector modes arise
at the quartic order and compute some superluminal propagating solutions. We
then generalize our findings to all orders in a gauge-independent way. We check
the physical consistency of the vector superluminalities, arguing that they are
not physically detectable in the perturbation theory but could be trusted
classically in the strong coupling region. Nevertheless, these
superluminalities involve only low frequency group and phase velocities and are
unable to determine the acausality of the theory.


  Dynamic Adaptive Streaming over HTTP (DASH) is a video streaming technique
largely used. One key point is the adaptation mechanism which resides at the
client's side. This mechanism impacts greatly on the overall Quality of
Experience (QoE) of the video streaming. In this paper, we propose a new
adaptation algorithm for DASH, namely SSIM Based Adaptation (SBA). This
mechanism is user-experience driven: it uses the Structural Similarity Index
Measurement (SSIM) as main video perceptual quality indicator; moreover, the
adaptation is based on a joint consideration of SSIM indicator and the physical
resources (buffer occupancy, bandwidth) in order to minimize the buffer
starvation (rebuffering) and video quality instability, as well as to maximize
the overall video quality (through SSIM). To evaluate the performance of our
proposal, we carried out trace-driven emulation with real traffic traces
(captured in real mobile network). Comparisons with some representative
algorithms (BBA, FESTIVE, OSMF) through major QoE metrics show that our
adaptation algorithm SBA achieves an efficient adaptation minimizing both the
rebuffering and instability, whereas the displayed video is maintained at a
high level of bitrate.


  Capacity of entanglement (CoE), an information-theoretic measure of
entanglement, defined as the variance of modular Hamiltonian, is known to
capture the deviation from the maximal entanglement. We derive an exact
expression for the average eigenstate CoE in fermionic Gaussian states as a
finite series, valid for arbitrary bi-partition of the total system. Further,
we consider the complex SYK$_2$ model in the thermodynamic limit and we obtain
a closed-form expression of average CoE. In this limit, the variance of the
average CoE becomes independent of the system size. Moreover, when the
subsystem size is half of the total system, the leading volume-law coefficient
approaches a value of $\pi^{2}/8 - 1$. We identify this as a distinguishing
feature between integrable and quantum-chaotic systems. We confirm our
analytical results by numerical computations.


  In this theoretical study we analyze contrast transfer of weak-phase objects
in a transmission electron microscope, which is equipped with an aberration
corrector (Cs-corrector) in the imaging lens system and a physical phase plate
in the back focal plane of the objective lens. For a phase shift of pi/2
between scattered and unscattered electrons induced by a physical phase plate,
the sine-type phase contrast transfer function is converted into a cosine-type
function. Optimal imaging conditions could theoretically be achieved if the
phase shifts caused by the objective lens defocus and lens aberrations would be
equal zero. In reality this situation is difficult to realize because of
residual aberrations and varying, non-zero local defocus values, which in
general result from an uneven sample surface topography. We explore the
conditions - i.e. range of Cs-values and defocus - for most favourable contrast
transfer as a function of the information limit, which is only limited by the
effect of partial coherence of the electron wave in Cs-corrected transmission
electron microscopes. Under high-resolution operation conditions we find that a
physical phase plate improves strongly low- and medium-resolution object
contrast, while improving tolerance to defocus and Cs-variations, compared to a
microscope without a phase plate.


  The electric and magnetic polarizations as well as the electric and magnetic
susceptibilities of the Hubbard pair-cluster embedded in the external fields
were studied by the exact method. Based on the grand canonical ensemble for
open system, the numerical calculations were performed for the electron
concentration corresponding to the half-filling case. It has been found that
the electric and magnetic properties are strictly interrelated, what
constitutes a manifestation of a magnetoelectric effect, and the detailed
explanation of such behaviour was given. In particular, near the ground state
where the transitions are induced by the external fields, discontinuous changes
of the studied quantities have been found. They have been associated with the
occurrence of the singlet-triplet transitions. An anomalous behaviour of the
electric and magnetic polarizations as a function of the temperature, occurring
below the critical magnetic field, was illustrated. In the presence of the
competing electric and magnetic fields, the influence of Coulombic repulsion on
the studied properties was discussed.


  We derive a theory that describes homogeneous nucleation of grain boundary
(GB) phases. Our analysis takes account of the energy resulting from the GB
phase junction, the line defect separating two different GB structures, which
is necessarily a dislocation as well as an elastic line force due to the jump
in GB stresses. The theory provides analytic forms for the elastic interactions
and the core energy of the GB phase junction that, along with the change in GB
energy, determine the nucleation barrier. We apply the resulting nucleation
model to simulations of GB phase transformations in tungsten. Our theory
explains why under certain conditions GBs cannot spontaneously change their
structure even to a lower energy state.


  In recent work we formulated a new set of electrodynamic equations for
superconductors as an alternative to the conventional London equations,
compatible with the prediction of the theory of hole superconductivity that
superconductors expel negative charge from the interior towards the surface.
Charge expulsion results in a macroscopically inhomogeneous charge distribution
and an electric field in the interior, and because of this a spin current is
expected to exist. Furthermore, we have recently shown that a dynamical
explanation of the Meissner effect in superconductors leads to the prediction
that a spontaneous spin current exists near the surface of superconductors. In
this paper we extend the electrodynamic equations proposed earlier for the
charge density and charge current to describe also the space and time
dependence of the spin density and spin current. This allows us to determine
the magnitude of the expelled negative charge and interior electric field as
well as of the spin current in terms of other measurable properties of
superconductors. We also provide a 'geometric' interpretation of the difference
between type I and type II superconductors, discuss the relationship between
our model and Slater's seminal work on superconductivity, and discuss the
magnitude of the expected novel effects for elemental and other
superconductors.


  Spatial intermittency in decaying kinetic Alfven wave turbulence is
investigated to determine if it produces non Gaussian density fluctuations in
the interstellar medium. Non Gaussian density fluctuations have been inferred
from pulsar scintillation scaling. Kinetic Alfven wave turbulence characterizes
density evolution in magnetic turbulence at scales near the ion gyroradius. It
is shown that intense localized current filaments in the tail of an initial
Gaussian probability distribution function possess a sheared magnetic field
that strongly refracts the random kinetic Alfven waves responsible for
turbulent decorrelation. The refraction localizes turbulence to the filament
periphery, hence it avoids mixing by the turbulence. As the turbulence decays
these long-lived filaments create a non Gaussian tail. A condition related to
the shear of the filament field determines which fluctuations become coherent
and which decay as random fluctuations. The refraction also creates coherent
structures in electron density. These structures are not localized. Their
spatial envelope maps into a probability distribution that decays as density to
the power -3. The spatial envelope of density yields a Levy distribution in the
density gradient.


  We investigate the $\tau$-quantizations and Cohen's class distributions of a
suitable class of trace-class operators, called Feichtinger's operators, and
show that it is a convenient substitute for the class of Schwartz operators.
Many well-known concepts and results for functions in time-frequency analysis
have an operator-analog in our setting, e.g. that Cohen's classes are
convolutions of Wigner functions with distributions or characterization of the
class of Schwartz operators as an intersection of weighted variants of the
class of Feichtinger operators.


  We present an analysis of the substructure revealed by 407 RR Lyraes in Sloan
Digital Sky Survey (SDSS) Stripe 82. Period estimates are determined to high
accuracy using a string-length method. A subset of 178 RR Lyraes with
spectrally derived metallicities are employed to derive
metallicity-period-amplitude relations, which are then used to find
metallicities and distances for the entire sample. The RR Lyraes lie between 5
and 115 kpc from the Galactic center. They are divided into subsets of 316 RRab
types and 91 RRc types based on their period, colour and metallicity. The
density distribution is not smooth, but dominated by clumps and substructure.
Samples of 55 and 237 RR Lyraes associated with the Sagittarius Stream and the
Hercules-Aquila Cloud respectively are identified. Hence, ~ 70 % of the RR
Lyraes in Stripe 82 belong to known substructure. There is a sharp break in the
density distribution at Galactocentric radii of 40 kpc, reflecting the fact
that the dominant substructure in Stripe 82 - the Hercules-Aquila Cloud and the
Sagittarius Stream - lies within 40 kpc. In fact, almost 60 % of all the RR
Lyraes in Stripe 82 are associated with the Hercules-Aquila Cloud alone, which
emphasises its pre-eminence. Additionally, evidence of a new and distant
substructure - the Pisces Overdensity - is found, consisting of 28 faint RR
Lyraes centered on Galactic coordinates (80 deg, -55 deg) and with distances of
~ 80 kpc. The total stellar mass in the Pisces Overdensity is ~10000 solar
masses and its metallicity is [Fe/H] ~ -1.5.


A random graph of free groups contains a surface subgroup


  We wish to compute the gradient of an expectation over a finite or countably
infinite sample space having $K \leq \infty$ categories. When $K$ is indeed
infinite, or finite but very large, the relevant summation is intractable.
Accordingly, various stochastic gradient estimators have been proposed. In this
paper, we describe a technique that can be applied to reduce the variance of
any such estimator, without changing its bias---in particular, unbiasedness is
retained. We show that our technique is an instance of Rao-Blackwellization,
and we demonstrate the improvement it yields on a semi-supervised
classification problem and a pixel attention task.


  Atomistic simulations were carried out to analyze the interaction between $<
a>$ basal dislocations and precipitates in Mg-Al alloys and the associated
strengthening mechanisms.


  This paper reports a study of the experimental signatures of hierarchical
sectors beyond the Standard Model characterized by a flavor-violating heavy
vector and a set of light pseudo-Goldstone bosons $a_{1,2}$, spanning a large
range of lifetimes. The non-minimal scalar spectrum triggers novel $B$ decays
into multiple leptons that would have escaped the reach of current searches.
Novel displaced vertex analyses at LHCb are therefore discussed to probe the
hierarchical new physics, extending the scope of the tracking system of the
detector. Additionally, the reach of the proposed CODEX-b experiment is studied
as well. By exploiting the use of tracks only reconstructed in subsystems of
the detector at the high-level LHCb trigger, ${\mathcal{B}(B_s^0\to a_1 a_2) <
10^{-8}}$ and ${\mathcal{B}(B^+\to K^+ a_1 a_2) < 10^{-9}}$ could be reached in
the muon channel across seven orders of magnitude in the lifetime of the
Goldstone bosons. Correspondingly, heavy-light particle couplings of order
$\lesssim 1$ could be tested, potentially ruling out composite Higgs scenarios
where the heavy and light sectors couple strongly.


  A powerful method to measure the mass profile of a galaxy is through the
velocities of tracer particles distributed through its halo. Transforming this
kind of data accurately to a mass profile M(r), however, is not a trivial
problem. In particular, limited or incomplete data may substantially affect the
analysis. In this paper we develop a Bayesian method to deal with incomplete
data effectively; we have a hybrid-Gibbs sampler that treats the unknown
velocity components of tracers as parameters in the model. We explore the
effectiveness of our model using simulated data, and then apply our method to
the Milky Way using velocity and position data from globular clusters and dwarf
galaxies. We find that in general, missing velocity components have little
effect on the total mass estimate. However, the results are quite sensitive to
the outer globular cluster Pal 3. Using a basic Hernquist model with an
isotropic velocity dispersion, we obtain credible regions for the cumulative
mass profile M(r) of the Milky Way, and provide estimates for the model
parameters with 95 percent Bayesian credible intervals. The mass contained
within 260 kpc is 1.37x10^12 solar masses, with a 95 percent credible interval
of (1.27,1.51)x10^12 solar masses. The Hernquist parameters for the total mass
and scale radius are 1.55 (+0.18/-0.13)x10^12 solar masses and 16.9 (+4.8/-4.1)
kpc, where the uncertainties span the 95 percent credible intervals. The code
we developed for this work, Galactic Mass Estimator (GME), will be available as
an open source package in the R Project for Statistical Computing.


  Kronecker product covariance structure provides an efficient way to modeling
the inter-correlations of matrix-variate data. In this paper, we propose
testing statistics for Kronecker product covariance matrix based on linear
spectral statistics of renormalized sample covariance matrices. Central limit
theorem is proved for the linear spectral statistics with explicit formulas for
mean and covariance functions, which fills the gap in the literature. We then
theoretically justify that the proposed testing statistics have well-controlled
sizes and strong powers. To facilitate practical usefulness, we further propose
a bootstrap resampling algorithm to approximate the limiting distributions of
associated linear spectral statistics. Consistency of the bootstrap procedure
is guaranteed under mild conditions. A more general model which allows the
existence of noises will also be discussed. In the simulations, the empirical
sizes of the proposed testing procedure and its bootstrapped version are close
to corresponding theoretical values, while the powers converge to one quickly
as the dimension and sample size grow.


  The elastocaloric effect in the vicinity of the martensitic transition of a
Cu-Zn-Al has been studied by inducing the transition by strain or stress
measurements. While transition trajectories show significant differences, the
entropy change associated with the whole transformation (\DeltaSt) is
coincident in both kind of experiments since entropy production is small
compared to \DeltaSt. The values agree with estimations based on the Clausius-
Clapeyron equation. The possibility of using these materials for mechanical
refrigeration is also discussed.


  Although about 40% of the soft X-ray background emission in 0.4 to 1 keV
range has extragalactic origins and thus is totally blocked by the Galactic
absorption in midplane directions, it decreases at most by about 20 % in
midplane. Suzaku observation of the direction, (l, b) = (235, 0), showed an
OVII Kalpha emission intensity comparable with that of the MBM-12 on cloud
Suzaku observation, but revealed a narrow bump peaked at ~ 0.9 keV. The latter
component is partly filling the decrease of the extragalactic component in
midplane. The feature can be well represented by a thin thermal emission with a
temperature of about 0.8 keV. Because of the high pressure implied for
spatially extended hot gas, the emission is likely a sum of unresolved faint
sources. We consider a large fraction of the emission originates from faint dM
stars. We constructed a model spectrum for spatially unresolved dM stars that
consistently explains the observed spectrum and the surface brightness. The
model also suggests that the emission from dM stars decreases very rapidly with
increasing b, and thus that it cannot compensate entirely the decrease of the
extragalactic component at b ~ 2 - 10 deg.


  In magnetic crystals, despite the explicit breaking of time-reversal
symmetry, two equilibrium states related by time reversal are always
energetically degenerate. In ferromagnets such time-reversal degeneracy can be
manifested by hysteresis loops in the magnetic field dependence of the
magnetization and, if metallic, in the anomalous Hall effect. Importantly, both
quantities simply change signs but not their absolute sizes under time
reversal, which follows from their fundamental definitions. Our integral
experimental and theoretical study shows that in the metallic kagome spin ice
HoAgGe subject to finite magnetic fields parallel to the kagome plane, an
emergent time-reversal-like degeneracy appears between magnetic states that
have the same energy and net magnetization, but different sizes of the
anomalous Hall effect. These degeneracies are unraveled by finite hysteresis in
the field-dependent anomalous Hall effect contrasted with the vanishing
hysteresis in the magnetization, which appears only at low-temperatures T$<$4K
when the kagome spin ice is fully ordered into $\sqrt{3}$$\times$$\sqrt{3}$
state. By explicitly determining the degenerate states and calculating the
corresponding physical properties using a tight-binding model, we nailed down
the time-reversal-like operation that transforms these degenerate states into
each other. The operation is related to the nontrivial distortion of the kagome
lattice in HoAgGe and is effective only because of the richness of degenerate
states unique to kagome spin ice. Our work points to the powerful role of the
anomalous Hall effect to diagnose hidden symmetries in frustrated spin systems.


  We study the robustness of the bucket brigade quantum random access memory
model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100,
160501 (2008)]. Due to a result of Regev and Schiff [ICALP '08 pp. 773], we
show that for a class of error models the error rate per gate in the bucket
brigade quantum memory has to be of order $o(2^{-n/2})$ (where $N=2^n$ is the
size of the memory) whenever the memory is used as an oracle for the quantum
searching problem. We conjecture that this is the case for any realistic error
model that will be encountered in practice, and that for algorithms with
super-polynomially many oracle queries the error rate must be
super-polynomially small, which further motivates the need for quantum error
correction. By contrast, for algorithms such as matrix inversion [Phys. Rev.
Lett. 103, 150502 (2009)] or quantum machine learning [Phys. Rev. Lett. 113,
130503 (2014)] that only require a polynomial number of queries, the error rate
only needs to be polynomially small and quantum error correction may not be
required. We introduce a circuit model for the quantum bucket brigade
architecture and argue that quantum error correction for the circuit causes the
quantum bucket brigade architecture to lose its primary advantage of a small
number of "active" gates, since all components have to be actively error
corrected.


  Radio frequency data in astronomy enable scientists to analyze astrophysical
phenomena. However, these data can be corrupted by radio frequency interference
(RFI) that limits the observation of underlying natural processes. In this
study, we extend recent developments in deep learning algorithms to astronomy
data. We remove RFI from time-frequency spectrograms containing auroral
kilometric radiation (AKR), a coherent radio emission originating from the
Earth's auroral zones that is used to study astrophysical plasmas. We propose a
Denoising Autoencoder for Auroral Radio Emissions (DAARE) trained with
synthetic spectrograms to denoise AKR signals collected at the South Pole
Station. DAARE achieves 42.2 peak signal-to-noise ratio (PSNR) and 0.981
structural similarity (SSIM) on synthesized AKR observations, improving PSNR by
3.9 and SSIM by 0.064 compared to state-of-the-art filtering and denoising
networks. Qualitative comparisons demonstrate DAARE's capability to effectively
remove RFI from real AKR observations, despite being trained completely on a
dataset of simulated AKR. The framework for simulating AKR, training DAARE, and
employing DAARE can be accessed at github.com/Cylumn/daare.


  We used coherent light scattering in a multi-speckle detection scheme to
investigate the mesoscale dynamics in aqueous foam. Time-resolved correlation
of the scattered speckle intensities reveals the details of foam dynamics
during aging. We introduce Temporal Contrast Analysis, a novel statistical tool
that can be effective in characterizing structural rearrangements. Using
Temporal Contrast Analysis we were able to detect two distinct dynamical
components present during foam aging: spontaneous and intermittent,
avalanche-like events and continuous, flow-like rearrangements in the foam
structure. We were able to measure these contributions separately from the
intrinsic statistical noise contribution, and thereby independently analyze the
decay of each dynamical component during foam aging process.


  Curiosity is one of the main motives in many of the natural creatures with
measurable levels of intelligence for exploration and, as a result, more
efficient learning. It makes it possible for humans and many animals to explore
efficiently by searching for being in states that make them surprised with the
goal of learning more about what they do not know. As a result, while being
curious, they learn better. In the machine learning literature, curiosity is
mostly combined with reinforcement learning-based algorithms as an intrinsic
reward. This work proposes an algorithm based on the drive of curiosity for
autonomous learning to control by generating proper motor speeds from odometry
data. The quadcopter controlled by our proposed algorithm can pass through
obstacles while controlling the Yaw direction of the quad-copter toward the
desired location. To achieve that, we also propose a new curiosity approach
based on prediction error. We ran tests using on-policy, off-policy, on-policy
plus curiosity, and the proposed algorithm and visualized the effect of
curiosity in evolving exploration patterns. Results show the capability of the
proposed algorithm to learn optimal policy and maximize reward where other
algorithms fail to do so.


  All global symmetries are expected to be explicitly broken by quantum
gravitational effects, and yet may play an important role in Particle Physics
and Cosmology. As such, any evidence for a well-preserved global symmetry would
give insight into an important feature of gravity. We argue that a recently
reported $2.4\sigma$ detection of cosmic birefringence in the Cosmic Microwave
Background could be the first observational indication of a well-preserved
(although spontaneously broken) global symmetry in nature. A compelling
solution to explain this measurement is a very light pseudoscalar field that
interacts with electromagnetism. In order for gravitational effects not to lead
to large corrections to the mass of this scalar field, we show that the
breaking of global symmetries by gravity should be bounded above. Finally, we
highlight that any bound of this type would have clear implications for the
construction of theories of quantum gravity, as well as for many particle
physics scenarios.


  We show that the inductive limit of a certain inductive system of
quasi-cocommutative C$^{*}$-bialgebras is not quasi-cocommutative. This implies
that the category of quasi-cocommutative C$^{*}$-bialgebras is not closed with
respect to the inductive limit.


  The porous titanium nickelide is very popular in various industries due to
unique combination of physical and mechanical properties such as shape memory
effect, high corrosion resistance, and biocompatibility. The non-equilibrium
molecular dynamics simulation was applied to study the influence of porosity
degree on mechanical properties of porous amorphous titanium nickelide at
uniaxial tension, uniaxial compression, and uniform shear. We have found that
the porous amorphous alloy is characterized by a relatively large value of
Young's modulus in comparison to its crystalline analogue. It has been found
that the system with a percolated network of pores exhibits improved elastic
characteristics associated with resistance to tensile and shear. The system
contained isolated spherical pores is more resistant to compression and less
resistant to tensile and shear. These results can be applied to develop and
improve the methods for making amorphous metal foams.


  Remote control vehicles require the transmission of large amounts of data,
and video is one of the most important sources for the driver. To ensure
reliable video transmission, the encoded video stream is transmitted
simultaneously over multiple channels. However, this solution incurs a high
transmission cost due to the wireless channel's unreliable and random bit loss
characteristics. To address this issue, it is necessary to use more efficient
video encoding methods that can make the video stream robust to noise. In this
paper, we propose a low-complexity, low-latency 2-channel Multiple Description
Coding (MDC) solution with an adaptive Instantaneous Decoder Refresh (IDR)
frame period, which is compatible with the HEVC standard. This method shows
better resistance to high packet loss rates with lower complexity.


  Measure-theoretic slow entropy is a more refined invariant than the classical
measure-theoretic entropy to characterize the complexity of dynamical systems
with subexponential growth rates of distinguishable orbit types. In this paper
we prove flexibility results for the values of upper and lower polynomial slow
entropy of rigid transformations as well as maps admitting a good cyclic
approximation. Moreover, we show that there cannot exist a general upper bound
on the lower measure-theoretic slow entropy for systems of finite rank.


  We study the global existence and stability of surface diffusion flow (the
normal velocity is given by the Laplacian of the mean curvature) of smooth
boundaries of subsets of the $n$--dimensional flat torus. More precisely, we
show that if a smooth set is ``close enough'' to a strictly stable critical set
for the Area functional under a volume constraint, then the surface diffusion
flow of its boundary hypersurface exists for all time and asymptotically
converges to the boundary of a ``translated'' of the critical set. This result
was obtained in dimension $n=3$ by Acerbi, Fusco, Julin and Morini (extending
previous results for spheres of Escher, Mayer and Simonett and Elliott and
Garcke in dimension $n=2$). Our work generalizes such conclusion to any
dimension $n\in\mathbb N$. For sake of clarity, we show all the details in
dimension $n=4$ and we list the necessary modifications to the quantities
involved in the proof in the general $n$--dimensional case, in the last
section.


  The fermionic determinant of a lattice Dirac operator that obeys the
Ginsparg-Wilson relation factorizes into two factors that are complex conjugate
of each other. Each factor is naturally associated with a single chiral fermion
and can be realized as a overlap of two many body vacua.


  Recently, a layered ferroelectric CuInP2Se6 was shown to exhibit domain walls
with locally enhanced piezoresponse - a striking departure from the
observations of nominally zero piezoresponse in most ferroelectrics. Although
it was proposed that such "bright" domain walls are phase-boundaries between
ferri- and antiferroelectrically ordered regions of the materials, the physical
mechanisms behind the existence and response of these boundaries remain to be
understood. Here, using Landau-Ginzburg-Devonshire phenomenology combined with
four sub-lattices model, we describe quantitatively the bright-contrast and
dark-contrast domain boundaries between the antiferroelectric, ferroelectric or
ferrielectric long-range ordered phases in a layered
ferroelectric-antiferroelectric ferroics, such as CuInP2(S1-ySey)6


  Deepfakes pose severe threats of visual misinformation to our society. One
representative deepfake application is face manipulation that modifies a
victim's facial attributes in an image, e.g., changing her age or hair color.
The state-of-the-art face manipulation techniques rely on Generative
Adversarial Networks (GANs). In this paper, we propose the first defense
system, namely UnGANable, against GAN-inversion-based face manipulation. In
specific, UnGANable focuses on defending GAN inversion, an essential step for
face manipulation. Its core technique is to search for alternative images
(called cloaked images) around the original images (called target images) in
image space. When posted online, these cloaked images can jeopardize the GAN
inversion process. We consider two state-of-the-art inversion techniques
including optimization-based inversion and hybrid inversion, and design five
different defenses under five scenarios depending on the defender's background
knowledge. Extensive experiments on four popular GAN models trained on two
benchmark face datasets show that UnGANable achieves remarkable effectiveness
and utility performance, and outperforms multiple baseline methods. We further
investigate four adaptive adversaries to bypass UnGANable and show that some of
them are slightly effective.


  Within thunderstorms electrons can gain energies of up to hundred(s) of MeV.
These electrons can create X-rays and gamma-rays as Bremsstrahlung when they
collide with air molecules. Here we calculate the distribution of angles
between incident electrons and emitted photons as a function of electron and
photon energy. We derive these doubly differential cross-sections by
integrating analytically over the triply differential cross-sections derived by
Bethe and Heitler; this is appropriate for light atoms like nitrogen and oxygen
(Z=7,8) if the energy of incident and emitted electron is larger than 1 keV. We
compare our results with the approximations and cross section used by other
authors. We also discuss some simplifying limit cases, and we derive some
simple approximation for the most probable scattering angle. We also provide
cross sections for the production of electron positron pairs from energetic
photons when they interact with air molecules. This process is related to the
Bremsstrahlung process by some physical symmetry. Therefore the results above
can be transferred to predictions on the angles between incident photon and
emitted positron, again as a function of photon and positron energy. We present
the distribution of angles and again a simple approximation for the most
probable scattering angle. Our results are given as analytical expressions as
well as in the form of a C++ code that can be directly be implemented into
Monte Carlo codes.


  We consider a model where the strong magnetic fields of magnetars arise from
a high baryon density, magnetized core. In this framework magnetars are
distinguished from pulsars by their higher masses and central density. For
magnetars, as core densities exceed a threshold, the strong interaction induces
a phase transition to a neutral pion condensate that aligns all magnetic
moments. The core magnetic field is initially shielded by the ambient high
conductivity plasma. With time the shielding currents dissipate transporting
the core field out, first to the crust and then breaking through the crust to
the surface of the star. Recent observations provide strong support for this
model which accounts for several properties of magnetars and also enables us to
identify new magnetars.


  In the broad line region of AGN, acceleration occurs naturally when a cloud
condenses out of the hot confining medium due to the increase in line opacity
as the cloud cools. However, acceleration by radiation pressure is not very
efficient when the flux is time-independent, unless the flow is
one-dimensional. Here we explore how acceleration is affected by a time-varying
flux, as AGN are known to be highly variable. If the period of flux
oscillations is longer than the thermal timescale, we expect the gas to cool
during the low flux state, and therefore line opacity should quickly increase.
The cloud will receive a small kick due to the increased radiation force. We
perform hydrodynamical simulations using Athena to confirm this effect and
quantify its importance. We find that despite the flow becoming turbulent in 2D
due to hydrodynamic instabilities, a 20% modulation of the flux leads to a net
increase in acceleration --- by more than a factor of 2 --- in both 1D and 2D.
We show that this is sufficient to produce the observed line widths, although
we only consider optically thin clouds. We discuss the implications of our
results for photoionization modeling and reverberation mapping.


  Mendelian randomization (MR) is a popular instrumental variable (IV)
approach, in which one or several genetic markers serve as IVs that can
sometimes be leveraged to recover valid inferences about a given
exposure-outcome causal association subject to unmeasured confounding. A key IV
identification condition known as the exclusion restriction states that the IV
cannot have a direct effect on the outcome which is not mediated by the
exposure in view. In MR studies, such an assumption requires an unrealistic
level of prior knowledge about the mechanism by which genetic markers causally
affect the outcome. As a result, possible violation of the exclusion
restriction can seldom be ruled out in practice. To address this concern, we
introduce a new class of IV estimators which are robust to violation of the
exclusion restriction under data generating mechanisms commonly assumed in MR
literature. The proposed approach named "MR G-Estimation under No Interaction
with Unmeasured Selection" (MR GENIUS) improves on Robins' G-estimation by
making it robust to both additive unmeasured confounding and violation of the
exclusion restriction assumption. In certain key settings, MR GENIUS reduces to
the estimator of Lewbel (2012) which is widely used in econometrics but appears
largely unappreciated in MR literature. More generally, MR GENIUS generalizes
Lewbel's estimator to several key practical MR settings, including
multiplicative causal models for binary outcome, multiplicative and odds ratio
exposure models, case control study design and censored survival outcomes.


  We prove that the spin-boson system is ergodic, for arbitrary strengths of
the coupling between the spin and the boson bath, provided the spin tunneling
matrix element is small enough.


  We study the locally analytic vectors in the completed cohomology of modular
curves and determine the eigenvectors of a rational Borel subalgebra of
$\mathfrak{gl}_2(\mathbb{Q}_p)$. As applications, we prove a classicality
result for overconvergent eigenforms of weight one and give a new proof of the
Fontaine-Mazur conjecture in the irregular case under some mild hypotheses. For
an overconvergent eigenform of weight $k$, we show its corresponding Galois
representation has Hodge-Tate-Sen weights $0,k-1$ and prove a converse result.


  In this paper we describe algorithms for computing the BWT and for building
(compressed) indexes in external memory. The innovative feature of our
algorithms is that they are lightweight in the sense that, for an input of size
$n$, they use only ${n}$ bits of disk working space while all previous
approaches use $\Th{n \log n}$ bits of disk working space. Moreover, our
algorithms access disk data only via sequential scans, thus they take full
advantage of modern disk features that make sequential disk accesses much
faster than random accesses.
  We also present a scan-based algorithm for inverting the BWT that uses
$\Th{n}$ bits of working space, and a lightweight {\em internal-memory}
algorithm for computing the BWT which is the fastest in the literature when the
available working space is $\os{n}$ bits.
  Finally, we prove {\em lower} bounds on the complexity of computing and
inverting the BWT via sequential scans in terms of the classic product:
internal-memory space $\times$ number of passes over the disk data.


  In this article we describe recent progress in the computational many-body
theory of metal surfaces, and focus on current techniques beyond the
local-density approximation of density-functional theory. We overview various
applications to ground and excited states. We discuss the exchange-correlation
hole, the surface energy, and the work function of jellium surfaces, as
obtained within the random-phase approximation, a time-dependent
density-functional approach, and quantum Monte Carlo methods. We also present a
survey of recent quasiparticle calculations of unoccupied states at both
jellium and real surfaces.


  We describe Chandra, HST, and radio observations that reveal a radio-quiet
but magnetospherically active neutron star in the error circle of the
high-energy gamma-ray source 3EG J1835+5918, the brightest of the unidentified
EGRET sources at high Galactic latitude. A Chandra ACIS-S spectrum of the
ultrasoft X-ray source RX J1836.2+5925, suggested by Mirabal & Halpern as the
neutron star counterpart of 3EG J1835+5918, requires two components: a
blackbody of T~3x10^5 K and a hard tail that can be parameterized as a power
law of photon index Gamma~2. An upper limit of d < 800 pc can be derived from
the blackbody fit under an assumption of R = 10 km. Deep optical imaging with
the HST STIS CCD failed to detect this source to a limit of V > 28.5, thus
f_X/f_V > 6000 and d > 250 pc assuming the X-ray fitted temperature for the
full surface. Repeated observations with the 76 m Lovell telescope at Jodrell
Bank place an upper limit of < 0.1 mJy on the flux density at 1400 MHz for a
pulsar with P > 0.1 s, and < 0.25 mJy for a ~10 ms pulsar at the location of RX
J1836.2+5925. All of this evidence points to an older, possibly more distant
version of the highly efficient gamma-ray pulsar Geminga, as the origin of the
gamma-rays from 3EG J1835+5918.


  Quantum entanglement is known as a unique quantum feature that cannot be
obtained by classical physics. Over the last several decades, however, such an
understanding on quantum entanglement might have confined us in a limited world
of weird quantum mechanics. Unlike a single photon, a definite phase relation
between paired photons is the key to understanding quantum features. Recently,
an intuitive approach to the otherwise mysterious quantum features has emerged
and shined a light on coherence manipulations of product-basis superposition
via selective measurements. Here, a coherence manipulation is presented to
excite polarization-path correlation using Poisson-distributed coherent photons
for a classically excited joint-phase relation of independent local parameters.
For this, linear optics is used for the preparation of the polarization-basis
randomness, and a gated heterodyne detection technique is adopted for the
selective measurement of polarization bases. As a result, the nonlocal quantum
feature is now coherently understood in a deterministic way.


  Electron transfer with changing occupation in the 4f subshell poses a
considerable challenge for quantitative predictions in quantum chemistry. Using
the example of cerium oxide, we identify the main deficiencies of common
parameter-dependent one-electron approaches, such as density functional theory
(DFT) with a Hubbard correction, or hybrid functionals. As a response, we
present the first benchmark of ab initio many-electron theory for electron
transfer energies and lattice parameters under periodic boundary conditions. We
show that the direct random phase approximation clearly outperforms all DFT
variations. From this foundation, we, then, systematically improve even
further. Periodic second-order M{\o}ller-Plesset perturbation theory meanwhile
manages to recover standard hybrid functional values. Using these approaches to
eliminate parameter bias allows for highly accurate benchmarks of strongly
correlated materials, the reliable assessment of various density functionals,
and functional fitting via machine-learning.


  We compute the pion light-cone wave function and the pion quark distribution
amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars
regularization method and as a result the distribution amplitude satisfies
proper normalization and crossing properties. In the chiral limit we obtain the
simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and
<k_perp^2> = -M <ubar u> / f_pi^2 for the second moment of the pion light-cone
wave function, where M is the constituent quark mass and f_pi is the pion decay
constant. After the QCD Gegenbauer evolution of the pion distribution amplitude
good end-point behavior is recovered, and a satisfactory agreement with the
analysis of the experimental data from CLEO is achieved. This allows us to
determine the momentum scale corresponding to our model calculation, which is
close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis
of the pion parton distribution function. The value of <k_perp^2> is, after the
QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear
integral relation between the pion distribution amplitude and the parton
distribution function of the pion, which holds at the leading-order QCD
evolution.


  Multi-particle correlation observables in the Relativistic Heavy Ion Collider
small system scan are computed in a framework that contains both initial state
momentum anisotropies from the Color Glass Condensate effective theory and
final state hydrodynamic evolution. The initial state is computed using the
IP-Glasma model and coupled to viscous relativistic hydrodynamic simulations,
which are followed by microscopic hadronic transport. All parameters of the
calculation were previously constrained using experimental data on Au+Au
collisions at the same center of mass energy. We find that the qualitative
features of the experimental data, such as the system and centrality dependence
of the charged hadron momentum anisotropy, can only be reproduced when final
state interactions are present. On the other hand, we also demonstrate that the
details of the initial state are crucially important for the quantitative
description of observables in the studied small systems, as neglecting the
initial transverse flow profile or the initial shear stress tensor, which
contain information on the momentum anisotropy from the Color Glass Condensate,
has dramatic effects on the produced final state anisotropy. We further show
that the initial state momentum anisotropy is correlated with the observed
elliptic flow in all small systems, with the effect increasing with decreasing
multiplicity. We identify the precise measurement of $v_2$ in d+Au and Au+Au
collisions at RHIC energy at the same multiplicity as a means to reveal effects
of the initial state momentum anisotropy.


  We consider a fully-decentralized scenario in which no central trusted entity
exists and all clients are honest-but-curious. The state-of-the-art approaches
to this problem often rely on cryptographic protocols, such as multiparty
computation (MPC), that require mapping real-valued data to a discrete
alphabet, specifically a finite field. These approaches, however, can result in
substantial accuracy losses due to computation overflows. To address this
issue, we propose A-MPC, a private analog MPC protocol that performs all
computations in the analog domain. We characterize the privacy of individual
datasets in terms of $(\epsilon, \delta)$-local differential privacy, where the
privacy of a single record in each client's dataset is guaranteed against other
participants. In particular, we characterize the required noise variance in the
Gaussian mechanism in terms of the required $(\epsilon,\delta)$-local
differential privacy parameters by solving an optimization problem.
Furthermore, compared with existing decentralized protocols, A-MPC keeps the
privacy of individual datasets against the collusion of all other participants,
thereby, in a notably significant improvement, increasing the maximum number of
colluding clients tolerated in the protocol by a factor of three compared with
the state-of-the-art collaborative learning protocols. Our experiments
illustrate that the accuracy of the proposed $(\epsilon,\delta)$-locally
differential private logistic regression and linear regression models trained
in a fully-decentralized fashion using A-MPC closely follows that of a
centralized one performed by a single trusted entity.


  Galactic gas-gas collisions involving a turbulent multiphase ISM share common
ISM properties: dense extraplanar gas visible in CO, large linewidths (>= 50
km/s), strong mid-infrared H_2 line emission, low star formation activity, and
strong radio continuum emission. Gas-gas collisions can occur in the form of
ICM ram pressure stripping, galaxy head-on collisions, compression of the
intragroup gas and/or galaxy ISM by an intruder galaxy which flies through the
galaxy group at a high velocity, or external gas accretion on an existing gas
torus in a galactic center. We suggest that the common theme of all these
gas-gas interactions is adiabatic compression of the ISM leading to an increase
of the turbulent velocity dispersion of the gas. The turbulent gas clouds are
then overpressured and star formation is quenched. Within this scenario we
developed a model for turbulent clumpy gas disks where the energy to drive
turbulence is supplied by external infall or the gain of potential energy by
radial gas accretion within the disk. The cloud size is determined by the size
of a C-type shock propagating in dense molecular clouds with a low ionization
fraction at a given velocity dispersion. We give expressions for the expected
volume and area filling factors, mass, density, column density, and velocity
dispersion of the clouds. The latter is based on scaling relations of
intermittent turbulence whose open parameters are estimated for the CND in the
Galactic Center. The properties of the model gas clouds and the external mass
accretion rate necessary for the quenching of the star formation rate due to
adiabatic compression are consistent with those derived from high-resolution
H_2 line observations. Based on these findings, a scenario for the evolution of
gas tori in galactic centers is proposed and the implications for star
formation in the Galactic Center are discussed.


  We consider a triple-quantum-dot (TQD) system composed by an interacting
quantum dot connected to two effectively non-interacting dots, which in turn
are both connected in parallel to metallic leads. As we show, this system can
be mapped onto a single-impurity Anderson model with a non-trivial density of
states. The TQD's transport properties are investigated under a continuous
tuning of the non-interacting dots' energy-levels, employing the Numerical
Renormalization Group technique. Interference between single and many-particle
resonances splits the Kondo peak, fulfilling a generalized Friedel sum rule. In
addition, a particular configuration in which one of the non-interacting dots
is held out of resonance with the leads allows to access a pseudogap regime
where a Kosterlitz-Thouless type quantum-phase-transition (QPT) occur,
separating the Kondo and non-Kondo behavior. Within this same configuration,
the TQD exhibits traces of the Fano-Kondo effect, which is in turn, strongly
affected by the QPT. Signatures of all these phenomena are neatly displayed by
the calculated linear conductance.


  On the basis of the principle that topological quantum phases arise from the
scattering around space-time defects in higher dimensional unification, a
geometric model is presented that associates with each quantum phase an element
of a transformation group.


  For the duration of the Fermi Gamma-Ray Space Telescope's mission,
approximately one-third of the point sources detected have been noted as
"unassociated," meaning that they seem to have no known counterpart at any
other wavelength/frequency. This mysterious part of the gamma-ray sky is
perhaps one of the largest unknowns in current astronomical pursuits, and as
such has been probed extensively by various techniques at various frequencies.
Radio frequencies have been perhaps one of the most fruitful, producing a large
fraction of the identified and associated Active Galactic Nuclei (AGN) and
pulsars noted in each update of the point source catalogs. Here we present a
catalog of 7432 radio counterpart candidates for unassociated gamma-ray fields
in the 2nd Data Release of the 4th Fermi Point Source Catalog (4FGL-DR2). A
description of the catalog and source types is provided followed by a
discussion that demonstrates how the results of this work will aid new
associations and identifications. As part of this work, we also present a first
catalog derived from "quicklook" images of the Very Large Array Sky Survey
(VLASS).


  We study the cooling-heating phase transition of the charged accelerating
anti-de Sitter black hole in extended phase space, and investigate the critical
behavior of this black hole in extended phase space. By calculating the
thermodynamic quantities and state equation, we found that the charged
accelerating AdS black hole as thermodynamic system is similar to the van der
Waals system. The inversion temperature of this black hole is obtained, and
cooling-heating and isenthalpic curves are plotted in T-P plane. Our results
indicate that the inversion temperature for a given pressure increases with e,
and the acceleration parameter has the opposite effect, which the
cooling-heating curves decreases gradually with the the increases of a. We also
analyse the influence of acceleration parameter on isenthalpic curves, implying
that the phase transition point decreases with the increase of acceleration
factor under constant pressure.


  Cooperative game theory aims to study how to divide a joint value created by
a set of players. These games are often studied through the characteristic
function form with transferable utility, which represents the value obtainable
by each coalition. In the presence of externalities, there are many ways to
define this value. Various models that account for different levels of player
cooperation and the influence of external players on coalition value have been
studied. Although there are different approaches, typically, the optimistic and
pessimistic approaches provide sufficient insights into strategic interactions.
This paper clarifies the interpretation of these approaches by providing a
unified framework. We show that making sure that no coalition receives more
than their (optimistic) upper bounds is always at least as difficult as
guaranteeing their (pessimistic) lower bounds. We also show that if
externalities are negative, providing these guarantees is always feasible.
Then, we explore applications and show how our findings can be applied to
derive results from the existing literature.


  Turbulence in the restricted nonlinear (RNL) dynamics is analyzed and
compared with DNS of Poiseuille turbulence at $R=1650$. The structures are
obtained by POD analysis of the two components of the flow partition used in
RNL dynamics: the streamwise-mean flow and fluctuations. POD analysis of the
streamwise-mean flow indicates that the dominant POD modes, in both DNS and
RNL, are roll-streaks harmonic in the spanwise. However, we conclude that these
POD modes do not occur in isolation but rather are Fourier components of a
coherent roll-streak structure. POD analysis of the fluctuations in DNS and RNL
reveals similar complex structures consisting in part of oblique waves
collocated with the streak. The origin of these structures is identified by
their correspondence to POD modes predicted using a stochastic turbulence model
(STM). These predicted POD modes are dominated by the optimally growing
structures on the streak, which the STM predicts correctly to be of sinuous
oblique wave structure. This close correspondence between the roll-streak
structure and the associated fluctuations in DNS, RNL and the STM implies that
the self-sustaining mechanism operating in DNS is essentially the same as that
in RNL, which has been previously associated with optimal perturbation growth
on the streak.


  We calculate the semiclassical magnetoresistivity $\rho_{xx}(B)$ of
non-interacting fermions in two dimensions moving in a weak and smoothly
varying random potential or random magnetic field. We demonstrate that in a
broad range of magnetic fields the non-Markovian character of the transport
leads to a strong positive magnetoresistance. The effect is especially
pronounced in the case of a random magnetic field where $\rho_{xx}(B)$ becomes
parametrically much larger than its B=0 value.


  The aim of the present comment is to provoke the performance of simple
additional measurements at Tc which, after a professional experimental data
processing, will reveal an important quantitative information concerning the GL
parameters and applicability of the GL theory for high-Tc superconductors in
general. Confirmation of this would be crucial for the further studies of the
fluctuation phenomena in superconductors.


  In this paper we give two realizations of the restricted Kostka polynomials
for $\sl_2$. Firstly we identify the restricted Kostka polynomials with a
characters of the zero homology of the current algebra with a coefficients in a
certain modules. As a corollary we reobtain the alternating sum formula.
Secondly we show that the restricted Kostka polynomials are a
$q$-multiplicities of the decomposition of the certain integrable
$\hat{\sl}_2$-modules to the irreducible components. This allows to write a
kind of fermionic formula for the Virasoro unitary models.


  The de Broglie-Bohm pilot wave interpretation of quantum mechanics is shown
to provide a consistent explanation for a single relativistic particle (more
accurately, a single particle process since pair production is addressed). This
is accomplished by incorporating the Feynman-Stueckelberg interpretation of
anti-matter. The lack of conserved probability and existence of negative energy
solutions is studied through this interpretation. We discuss the resolution of
Klein's original paradox through the pilot wave interpretation, and similarly
analyze the potential barrier problem. Simulations are presented for a wave
packet incident on potential steps & barriers of various heights.


  A major driver of quantum-simulator technology is the prospect of probing
high-energy phenomena in synthetic quantum matter setups at a high level of
control and tunability. Here, we propose an experimentally feasible realization
of a large-scale $2+1$D $\mathrm{U}(1)$ gauge theory with dynamical matter and
gauge fields in a cold-atom quantum simulator with spinless bosons. We present
the full mapping of the corresponding Gauss's law onto the bosonic
computational basis. We then show that the target gauge theory can be
faithfully realized and stabilized by an emergent gauge protection term in a
two-dimensional single-species Bose--Hubbard optical Lieb superlattice with two
spatial periods along either direction, thereby requiring only moderate
experimental resources already available in current cold-atom setups. Using
infinite matrix product states, we calculate numerical benchmarks for adiabatic
sweeps and global quench dynamics that further confirm the fidelity of the
mapping. Our work brings quantum simulators of gauge theories a significant
step forward in terms of investigating particle physics in higher spatial
dimensions, and is readily implementable in existing cold-atom platforms.


  Solar wind measurements carried out by NASA's Wind spacecraft before, during
and after the passing of an interplanetary coronal mass ejection (ICME)
detected on 12-14 September 2014 have been used in order to examine several
properties of magnetohydrodynamic (MHD) turbulence. Spectral indices and
flatness scaling exponents of magnetic field, velocity and proton density
measurements were obtained, and provided a standard description of the
characteristics of turbulence within different sub-regions of the ICME and its
surroundings. This analysis was followed by the validation of the third-order
moment scaling law for isotropic, incompressible MHD turbulence in the same
sub-regions, which confirmed the fully developed nature of turbulence in the
ICME plasma. The energy transfer rate was also estimated in each ICME
sub-region and in the surrounding solar wind. An exceptionally high value was
found within the ICME sheath, accompanied by enhanced intermittency, possibly
related to the powerful energy injection associated with the arrival of the
ICME.


  Ann likes oranges much more than apples; Bob likes apples much more than
oranges. Tomorrow they will receive one fruit that will be an orange or an
apple with equal probability. Giving one half to each agent is fair for each
realization of the fruit. However, agreeing that whatever fruit appears will go
to the agent who likes it more gives a higher expected utility to each agent
and is fair in the average sense: in expectation, each agent prefers his
allocation to the equal division of the fruit, i.e., he gets a fair share.
  We turn this familiar observation into an economic design problem: upon
drawing a random object (the fruit), we learn the realized utility of each
agent and can compare it to the mean of his distribution of utilities; no other
statistical information about the distribution is available. We fully
characterize the division rules using only this sparse information in the most
efficient possible way, while giving everyone a fair share. Although the
probability distribution of individual utilities is arbitrary and mostly
unknown to the manager, these rules perform in the same range as the best rule
when the manager has full access to this distribution.


  Multi-messenger high-energy astrophysics has currently achieved the potential
to unravel the origin of cosmic rays and how sources accelerate them, their
relation to the diffuse radiation in the extra-galactic space, and their role
to forge their galaxies of origin while they wander in their magnetic fields
for millions of years. Neutrino astronomy produced its major scientific
milestone with the discovery by IceCube of a diffuse flux at energies above
60~TeV with intensity comparable to a predicted upper limit to the flux from
extra-galactic sources of ultra-high energy cosmic rays. More recent results
provide the first strong evidence of a standalone neutrino source and a highly
probable coincidence of a neutrino alert with gamma rays. These results of
IceCube indicate that neutrino astronomy can complement photon astronomy also
providing insights into opaque sources of high-energy radiation. Starburst
galaxies and jetted black holes in active galaxies are favored candidates to
explain the diffuse cosmic neutrino background. Additionally, gamma-ray bursts
remain an intriguing mystery now enriched by joint observations of gamma-rays
and gravitational waves.
  The galactic diffuse flux, produced by cosmic ray interactions on the
interstellar matter of our galaxy and peaking at lower energies, is within the
reach of neutrino detectors. Together with the measured galactic gamma-ray flux
up to PeV energies, they will shed light on the knee region of cosmic rays and
the possible existence of dark matter in the Galactic plane. In the future,
more work will be done in IceCube and deep sea and lake neutrino telescopes to
use further low-energy cascades for cosmic source searches thanks to improved
descriptions of detection media and deep learning methods.


  A \itbf{cover} of a string $x = x[1..n]$ is a proper substring $u$ of $x$
such that $x$ can be constructed from possibly overlapping instances of $u$. A
recent paper \cite{FIKPPST13} relaxes this definition --- an \itbf{enhanced
cover} $u$ of $x$ is a border of $x$ (that is, a proper prefix that is also a
suffix) that covers a {\it maximum} number of positions in $x$ (not necessarily
all) --- and proposes efficient algorithms for the computation of enhanced
covers. These algorithms depend on the prior computation of the \itbf{border
array} $\beta[1..n]$, where $\beta[i]$ is the length of the longest border of
$x[1..i]$, $1 \le i \le n$. In this paper, we first show how to compute
enhanced covers using instead the \itbf{prefix table}: an array $\pi[1..n]$
such that $\pi[i]$ is the length of the longest substring of $x$ beginning at
position $i$ that matches a prefix of $x$. Unlike the border array, the prefix
table is robust: its properties hold also for \itbf{indeterminate strings} ---
that is, strings defined on {\it subsets} of the alphabet $\Sigma$ rather than
individual elements of $\Sigma$. Thus, our algorithms, in addition to being
faster in practice and more space-efficient than those of \cite{FIKPPST13},
allow us to easily extend the computation of enhanced covers to indeterminate
strings. Both for regular and indeterminate strings, our algorithms execute in
expected linear time. Along the way we establish an important theoretical
result: that the expected maximum length of any border of any prefix of a
regular string $x$ is approximately 1.64 for binary alphabets, less for larger
ones.


  A study of two dE/dSph members of the nearby M 81 group of galaxies, KDG 61
and UGC 5442 = KDG 64, has been made. Direct Hubble Space Telescope (HST)
Advanced Camera for Surveys (ACS) images and integrated-light spectra of 6 m
telescope of Special Astrophysical Observatory of Russian Academy of Sciences
have been used for quantitative star formation history analysis. The
spectroscopic and colour-magnitude diagrams analysis gives consistent results.
These galaxies appear to be dominated by an old population (12-14 Gyr) of low
metallicity ([Fe/H]~-1.5). Stars of ages about 1 to 4 Gyr have been detected in
both galaxies. The later population shows marginal metal enrichment. We do not
detect any significant radial gradients in age or metallicity in these
galaxies. Our radial velocity measurement suggests that the HII knot on the
line-of-sight of KDG 61 is not gravitationally attached to the galaxy.


  Modern scientific problems are often multi-disciplinary and require
integration of computer models from different disciplines, each with distinct
functional complexities, programming environments, and computation times.
Linked Gaussian process (LGP) emulation tackles this challenge through a
divide-and-conquer strategy that integrates Gaussian process emulators of the
individual computer models in a network. However, the required stationarity of
the component Gaussian process emulators within the LGP framework limits its
applicability in many real-world applications. In this work, we conceptualize a
network of computer models as a deep Gaussian process with partial exposure of
its hidden layers. We develop a method for inference for these partially
exposed deep networks that retains a key strength of the LGP framework, whereby
each model can be emulated separately using a DGP and then linked together. We
show in both synthetic and empirical examples that our linked deep Gaussian
process emulators exhibit significantly better predictive performance than
standard LGP emulators in terms of accuracy and uncertainty quantification.
They also outperform single DGPs fitted to the network as a whole because they
are able to integrate information from the partially exposed hidden layers. Our
methods are implemented in an R package $\texttt{dgpsi}$ that is freely
available on CRAN.


  We consider the excitation of radial and non-radial oscillations in low-mass
B stars by the iron-bump opacity mechanism. The results are significant for the
interpretation of pulsations in subdwarf B stars, helium-rich subdwarfs and
extreme helium stars, including the EC14026 and PG1716 variables. We
demonstrate that, for radial oscillations, the driving mechanism becomes
effective by increasing the contrast between the iron-bump opacity and the
opacity from other sources. The location of the iron-bump instability boundary
depends on the mean molecular weight in the envelope and also on the radial
order of the oscillation. A bluer instability boundary is provided by
increasing the iron abundance alone, explaining the observed EC14026 variables,
and by higher radial order oscillations. We show that the coolest EC14026
variables may vary in the fundamental radial mode, but the hottest variables
must be of higher radial order. In considering non-radial oscillations, we
demonstrate that g-modes of high radial order and low spherical degree (l<4)
may be excited in some blue horizontal branch stars with near-normal
composition (Z=0.02). Additional iron enhancement extends the g-mode
instability zone to higher effective temperatures and also creates a p-mode
instability zone. With sufficient iron, the p-mode and g-mode instability zones
overlap, allowing a small region where the EC14026 and PG1716-type variability
can be excited simultaneously. However its location is roughly 5000 K too low
compared with the observed boundary between EC14026 and PG1716 variables.


  In this paper, we investigate how much of the numerical artefacts introduced
by finite system size and choice of boundary conditions can be removed by
finite size scaling, for strongly-correlated systems with quasi-long-range
order. Starting from the exact ground-state wave functions of hardcore bosons
and spinless fermions with infinite nearest-neighbor repulsion on finite
periodic chains and finite open chains, we compute the two-point,
density-density, and pair-pair correlation functions, and fit these to various
asymptotic power laws. Comparing the finite-periodic-chain and finite-openchain
correlations with their infinite-chain counterparts, we find reasonable
agreement among them for the power-law amplitudes and exponents, but poor
agreement for the phase shifts. More importantly, for chain lengths on the
order of 100, we find our finite-open-chain calculation overestimates some
infinite-chain exponents (as did a recent density-matrix renormalization-group
(DMRG) calculation on finite smooth chains), whereas our finite-periodic-chain
calculation underestimates these exponents. We attribute this systematic
difference to the different choice of boundary conditions. Eventually, both
finite-chain exponents approach the infinite-chain limit: by a chain length of
1000 for periodic chains, and > 2000 for open chains. There is, howwever, a
misleading apparent finite size scaling convergence at shorter chain lengths,
for both our finite-chain exponents, as well as the finite-smooth-chain
exponents. Implications of this observation are discussed.


  The Brattelli diagram associated with a given bicolored Dynkin-Coxeter graph
of type $A_n$ determines planar fractal sets obtained by infinite dissections
of a given triangle. All triangles appearing in the dissection process have
angles that are multiples of $\pi/ (n+1).$ There are usually several possible
infinite dissections compatible with a given $n$ but a given one makes use of
$n/2$ triangle types if $n$ is even. Jones algebra with index $[ 4 \ \cos^2{\pi
\over n+1}]^{-1}$ (values of the discrete range) act naturally on vector spaces
associated with those fractal sets. Triangles of a given type are always
congruent at each step of the dissection process. In the particular case $n=4$,
there are isometric and the whole structure lead, after proper inflation, to
aperiodic Penrose tilings. The ``tilings'' associated with other values of the
index are discussed and shown to be encoded by equivalence classes of infinite
sequences (with appropriate constraints) using $n/2$ digits (if $n$ is even)
and generalizing the Fibonacci numbers.


  It is shown that the dual to the linear programming problem that arises in
constraint-based models of metabolism can be given a thermodynamic
interpretation in which the shadow prices are chemical potential analogues, and
the objective is to minimise free energy consumption given a free energy drain
corresponding to growth. The interpretation is distinct from conventional
non-equilibrium thermodynamics, although it does satisfy a minimum entropy
production principle. It can be used to motivate extensions of constraint-based
modelling, for example to microbial ecosystems.


  For every two-dimensional torus $T^2$ and every $k\in \mathbb{N}$, $k\ge 3$,
we construct a conformal Willmore immersion $f:T^2\to \mathbb{R}^4$ with
exactly one point of density $k$ and Willmore energy $4\pi k$. Moreover, we
show that the energy value $8\pi$ cannot be attained by such an immersion.
Additionally, we characterize the branched double covers $T^2\to S^2 \times
\{0\}$ as the only branched conformal immersions, up to M\"obius
transformations of $\mathbb{R}^4$, from a torus into $\mathbb{R}^4$ with at
least one branch point and Willmore energy $8\pi$. Using a perturbation
argument in order to regularize a branched double cover, we finally show that
the infimum of the Willmore energy in every conformal class of tori is less
than or equal to $8\pi$.


  The recent advancement of deep learning techniques has made great progress on
hyperspectral image super-resolution (HSI-SR). Yet the development of
unsupervised deep networks remains challenging for this task. To this end, we
propose a novel coupled unmixing network with a cross-attention mechanism,
CUCaNet for short, to enhance the spatial resolution of HSI by means of
higher-spatial-resolution multispectral image (MSI). Inspired by coupled
spectral unmixing, a two-stream convolutional autoencoder framework is taken as
backbone to jointly decompose MS and HS data into a spectrally meaningful basis
and corresponding coefficients. CUCaNet is capable of adaptively learning
spectral and spatial response functions from HS-MS correspondences by enforcing
reasonable consistency assumptions on the networks. Moreover, a cross-attention
module is devised to yield more effective spatial-spectral information transfer
in networks. Extensive experiments are conducted on three widely-used HS-MS
datasets in comparison with state-of-the-art HSI-SR models, demonstrating the
superiority of the CUCaNet in the HSI-SR application. Furthermore, the codes
and datasets will be available at:
https://github.com/danfenghong/ECCV2020_CUCaNet.


  We analyse equilibrium phases in a multi-type lattice Widom-Rowlinson model
with (i) four particle types, (ii) varying exclusion diameters between
different particle types and (iii) large values of fugacity. Contrary to an
expectation, it is not the most "aggressive" species, with largest diameters,
which dominates the equilibrium measure, but the "most tolerant" one, which has
smallest exclusion diameters. Results of numerical simulations are presented,
showing densities of species in equilibrium phases and confirming the
theoretical picture.


  In literature, there are two different definitions of elliptic divisibility
sequences. The first one says that a sequence of integers $\{h_n\}_{n\geq 0}$
is an elliptic divisibility sequence if it verifies the recurrence relation
$h_{m+n}h_{m-n}h_{r}^2=h_{m+r}h_{m-r}h_{n}^2-h_{n+r}h_{n-r}h_{m}^2$ for every
natural number $m\geq n\geq r$. The second definition says that a sequence of
integers $\{\beta_n\}_{n\geq 0}$ is an elliptic divisibility sequence if it is
the sequence of the square roots (chosen with an appropriate sign) of the
denominators of the abscissas of the iterates of a point on a rational elliptic
curve. It is well-known that the two sequences are not equivalent. Hence, given
a sequence of the denominators $\{\beta_n\}_{n\geq 0}$, in general does not
hold
$\beta_{m+n}\beta_{m-n}\beta_{r}^2=\beta_{m+r}\beta_{m-r}\beta_{n}^2-\beta_{n+r}\beta_{n-r}\beta_{m}^2$
for $m\geq n\geq r$. We will prove that the recurrence relation above holds for
$\{\beta_n\}_{n\geq 0}$ under some conditions on the indexes $m$, $n$, and $r$.


  We study the $K$-armed contextual dueling bandit problem, a sequential
decision making setting in which the learner uses contextual information to
make two decisions, but only observes \emph{preference-based feedback}
suggesting that one decision was better than the other. We focus on the regret
minimization problem under realizability, where the feedback is generated by a
pairwise preference matrix that is well-specified by a given function class
$\mathcal F$. We provide a new algorithm that achieves the optimal regret rate
for a new notion of best response regret, which is a strictly stronger
performance measure than those considered in prior works. The algorithm is also
computationally efficient, running in polynomial time assuming access to an
online oracle for square loss regression over $\mathcal F$. This resolves an
open problem of Dud\'ik et al. [2015] on oracle efficient, regret-optimal
algorithms for contextual dueling bandits.


  We consider a dynamical approach to game in extensive forms. By restricting
the convertibility relation over strategy profiles, we obtain a semi-potential
(in the sense of Kukushkin), and we show that in finite games the corresponding
restriction of better-response dynamics will converge to a Nash equilibrium in
quadratic (finite) time. Convergence happens on a per-player basis, and even in
the presence of players with cyclic preferences, the players with acyclic
preferences will stabilize. Thus, we obtain a candidate notion for rationality
in the presence of irrational agents. Moreover, the restriction of
convertibility can be justified by a conservative updating of beliefs about the
other players strategies.
  For infinite games in extensive form we can retain convergence to a Nash
equilibrium (in some sense), if the preferences are given by continuous payoff
functions; or obtain a transfinite convergence if the outcome sets of the game
are $\Delta^0_2$-sets.


  In this paper, we prove two results. First, there is a family of sequences of
embedded quarters of the hyperbolic plane such that any sequence converges to a
limit which is an end of the hyperbolic plane. Second, there is no algorithm
which would allow us to check whether two given ends are equal or not.


  We perform a detailed comparison of the IRAS PSCz and 1.2-Jy spherical
harmonic coefficients of the density and velocity fields in redshift space. The
monopole terms predicted from the two surveys show some differences. The
mismatch between the velocity monopoles arises from faint sources and
disappears when extracting a PSCz subsample of galaxies with fluxes larger than
1.2 Jy. The analysis of PSCz dipole moments confirms the same inconsistencies
found by Davis, Nusser and Willick (1996) between the IRAS 1.2-Jy gravity field
and MARK III peculiar velocities. We conclude that shot-noise, which is greatly
reduced in our PSCz gravity field, cannot be responsible for the observed
mismatch.


  Despite the undeniable progress in visual recognition tasks fueled by deep
neural networks, there exists recent evidence showing that these models are
poorly calibrated, resulting in over-confident predictions. The standard
practices of minimizing the cross entropy loss during training promote the
predicted softmax probabilities to match the one-hot label assignments.
Nevertheless, this yields a pre-softmax activation of the correct class that is
significantly larger than the remaining activations, which exacerbates the
miscalibration problem. Recent observations from the classification literature
suggest that loss functions that embed implicit or explicit maximization of the
entropy of predictions yield state-of-the-art calibration performances. Despite
these findings, the impact of these losses in the relevant task of calibrating
medical image segmentation networks remains unexplored. In this work, we
provide a unifying constrained-optimization perspective of current
state-of-the-art calibration losses. Specifically, these losses could be viewed
as approximations of a linear penalty (or a Lagrangian term) imposing equality
constraints on logit distances. This points to an important limitation of such
underlying equality constraints, whose ensuing gradients constantly push
towards a non-informative solution, which might prevent from reaching the best
compromise between the discriminative performance and calibration of the model
during gradient-based optimization. Following our observations, we propose a
simple and flexible generalization based on inequality constraints, which
imposes a controllable margin on logit distances. Comprehensive experiments on
a variety of public medical image segmentation benchmarks demonstrate that our
method sets novel state-of-the-art results on these tasks in terms of network
calibration, whereas the discriminative performance is also improved.


  We present the algebraic foundations of the symmetric Zassenhaus algorithm
and some of its variants. These algorithms have proven effective in devising
higher-order methods for solving the time-dependent Schr\"{o}dinger equation in
the semiclassical regime. We find that the favourable properties of these
methods derive directly from the structural properties of a Z2-graded Lie
algebra. Commutators in this Lie algebra can be simplified explicitly, leading
to commutator-free methods. Their other structural properties are crucial in
proving unitarity, stability, convergence, error bounds and quadratic costs of
Zassenhaus based methods. These algebraic structures have also found
applications in Magnus expansion based methods for time-varying potentials
where they allow significantly milder constraints for convergence and lead to
highly effective schemes. The algebraic foundations laid out in this work pave
the way for extending higher-order Zassenhaus and Magnus schemes to other
equations of quantum mechanics.