  We study the existence of maximizers for a one-parameter family of Strichartz
inequalities on the torus. In general maximizing sequences can fail to be
precompact in $L^2(\mathbb T)$, and maximizers can fail to exist. We provide a
sufficient condition for precompactness of maximizing sequences (after
translation in Fourier space), and verify the existence of maximizers for a
range of values of the parameter. Maximizers for the Strichartz inequalities
correspond to stable, periodic (in space and time) solutions of a model
equation for optical pulses in a dispersion-managed fiber.


  Nodland and Ralston (astro-ph/9704196) claim evidence for a
wavelength-independent cosmic birefringence. Although it has been shown
(astro-ph/9704247, astro-ph/9704263) that the data analysed did not support
this conclusion, the possibility of such an effect remains interesting. Here I
present a much more accurate test using high-resolution radio images of distant
radio galaxies and quasars. A preliminary application sets an upper limit about
thirty times lower than the original claim.


  Cross-language learning allows us to use training data from one language to
build models for a different language. Many approaches to bilingual learning
require that we have word-level alignment of sentences from parallel corpora.
In this work we explore the use of autoencoder-based methods for cross-language
learning of vectorial word representations that are aligned between two
languages, while not relying on word-level alignments. We show that by simply
learning to reconstruct the bag-of-words representations of aligned sentences,
within and between languages, we can in fact learn high-quality representations
and do without word alignments. Since training autoencoders on word
observations presents certain computational issues, we propose and compare
different variations adapted to this setting. We also propose an explicit
correlation maximizing regularizer that leads to significant improvement in the
performance. We empirically investigate the success of our approach on the
problem of cross-language test classification, where a classifier trained on a
given language (e.g., English) must learn to generalize to a different language
(e.g., German). These experiments demonstrate that our approaches are
competitive with the state-of-the-art, achieving up to 10-14 percentage point
improvements over the best reported results on this task.


  Existing 3D extensions to the standard model show that flux-rope footpoints
are surrounded by curved-shaped QSL-footprints that can be related with
hook-shaped flare-ribbons. We build upon this finding and further address the
joint questions of their time-evolution, and of the formation of flare loops at
the ends of flaring PILs of the erupting bipole, which are both relevant for
flare understanding in general and for ICME studies in particular. We calculate
QSLs and relevant field lines in an MHD simulation of a torus-unstable
flux-rope. The evolving QSL footprints are used to define the outer edge of the
flux rope at different times, and to identify and characterize new 3D
reconnection geometries and sequences that occur above the ends of the flaring
PIL. We also analyse flare-ribbons as observed in EUV by SDO/AIA and IRIS
during two X-class flares. The flux-rope footpoints are drifting during the
eruption, which is unexpected due to line-tying. This drifting is due to a
series of coronal reconnections that erode the flux rope on one side and
enlarge it on the other side. Other changes in the flux-rope footpoint-area are
due to multiple reconnections of individual field lines whose topology can
evolve sequentially from arcade to flux rope and finally to flare loop. These
are associated with deformations and displacements of QSL footprints, which
resemble those of the studied flare ribbons. Our model predicts continuous
deformations and a drifting of ICME flux-rope footpoints whose areas are
surrounded by equally-evolving hooked-shaped flare-ribbons, as well as the
formation of flare loops at the ends of flaring PILs which originate from the
flux-rope itself, both of which being due to purely three-dimensional
reconnection geometries. The observed evolution of flare-ribbons in two events
supports the model, but more observations are required to test all its
predictions.


  For each $s\in\{2,4\}$, the generating function of $R_s(n)$, the number of
partitions of $n$ into odd parts or congruent to $0$, $\pm s\pmod {10}$, arises
naturally in regime III of Rodney Baxter's solution of the hard-hexagon model
of statistical mechanics. For each $s\in\{1,3\}$, the generating function of
$R^*_s(n)$, the number of partitions of $n$ into parts not congruent to $0$,
$\pm s\pmod {10}$ and $10-2s \pmod {20}$, arises naturally in regime IV of
Rodney Baxter's solution of the hard-hexagon model of statistical mechanics. In
this paper, we investigate the parity of $R_s(n)$ and $R^*_s(n)$, providing new
parity results involving sums of partition numbers $p(n)$ and squares in
arithmetic progressions.


  T-odd correlations of polarizations and momenta provide a promising testing
ground for new physics beyond the standard model. We estimate the contribution
of the minimal supersymmetric extension of the standard model to two such
observables: in the production of $t\bar{t}$, we look for a term proportional
to \mbox{${\bf J}_t \cdot ({\bf p}_q \times {\bf p}_{t})$}-where {\bf J}$_t$ is
the polarization of the $t$ quark and {\bf p} $_{q,t}$ are the momenta of the
initial and final particles-and find that it is of the order of $10^{-1} \times
(\alpha_s/\pi)$. In the production of $W^+W^-$, we look for a term proportional
to \mbox{${\bf E}_W \cdot ({\bf p}_q \times {\bf p}_{W})({\bf p}_q \cdot {\bf
E}_W)$}-where {\bf E}$_W$ is the transverse polarization of W- to find that it
can be as large as $10^{-1} \times (\alpha_w/\pi)$.


  The Mathisson-Papapetrou-Dixon (MPD) equations, providing the "pole-dipole"
description of spinning test particles in general relativity, have to be
supplemented by a condition specifying the worldline that will represent the
history of the studied body. It has long been thought that the Mathisson-Pirani
(MP) spin condition -- unlike other major choices made in the literature --
does not yield an explicit momentum-velocity relation. We derive here the
desired (and very simple) relation and show that it is in fact equivalent to
the MP condition. We clarify the apparent paradox between the existence of such
a definite relation and the known fact that the MP condition is degenerate
(does not specify a unique worldline), thus shedding light on some conflicting
statements made in the literature. We then show how, for a given body, this
spin condition yields infinitely many possible representative worldlines, and
derive a detailed method how to switch between them in a curved spacetime. The
MP condition is a convenient choice in situations when it is easy to recognize
its "non-helical" solution, as exemplified here by bodies in circular orbits
and in radial fall in the Schwarzschild spacetime.


  In a previous paper (Phase Transitions, 80(9), 987, 2007) we discussed the
smectic and nematic textures of some mesomorphic oxadiazole compounds with
terminal Cl-substituent. Optical microscope investigations showed a very
interesting behaviour of smectic and nematic phases; the smectic phase has
fan-shaped and toric textures and the nematic phase has spherulitic domains,
which disappear as the sample is further heated, the texture changing into a
smooth one. Here, we investigate four oxadiazole compounds with the same
structure but terminal Br-substituent. The behaviour of the smectic and nematic
phases is like that observed in the compounds with Cl. The focus of the paper
is on the growth of toric domains from the nematic melt and on the role of
defects in the domain structure.


  In this contribution, we exploit machine learning techniques to evaluate
whether and how close firms are to becoming successful exporters. First, we
train and test various algorithms using financial information on both exporters
and non-exporters in France in 2010-2018. Thus, we show that we are able to
predict the distance of non-exporters from export status. In particular, we
find that a Bayesian Additive Regression Tree with Missingness In Attributes
(BART-MIA) performs better than other techniques with an accuracy of up to
0.90. Predictions are robust to changes in definitions of exporters and in the
presence of discontinuous exporting activity. Eventually, we discuss how our
exporting scores can be helpful for trade promotion, trade credit, and
assessing aggregate trade potential. For example, back-of-the-envelope
estimates show that a representative firm with just below-average exporting
scores needs up to 44% more cash resources and up to 2.5 times more capital to
get to foreign markets.


  The security of a cryptographic key that is generated by communication
through a noisy quantum channel relies on the ability to distill a shorter
secure key sequence from a longer insecure one. We show that -- for protocols
that use quantum channels of any dimension and completely characterize them by
state tomography -- the noise threshold for classical advantage distillation is
substantially lower than the threshold for quantum entanglement distillation
because the eavesdropper can perform powerful coherent attacks. The earlier
claims that the two noise thresholds are identical, which were based on
analyzing incoherent attacks only, are therefore invalid.


  Increasing agricultural productivity is a gradual process with significant
time lags between research and development (R&D) investment and the resulting
gains. We estimate the response of US agricultural Total Factor Productivity
(TFP) to both R&D investment and weather, and quantify the public R&D spending
required to offset the emerging impacts of climate change. We find that
offsetting the climate-induced productivity slowdown by 2050 alone requires a
sustained public R&D spending growth of 5.2-7.8% per year over 2021-2050. This
amounts to an additional $208-$434B investment over this period. These are
substantial requirements comparable to the public R&D spending growth that
followed the two World Wars.


  We show that the longitudinal current-voltage characteristics of
superconductors in mixed state have the general form of extended power law.
Isotherms simulated from this nonlinear equation fit the experimental I-V data
of Strachan et al. [ Phys. Rev. Lett. {\bf 87}, 067007 (2001)]. We determine
the average pinning force in the flux creep and strong pinning regime and
discuss both the puzzling scaling behavior $\rho_{xy}\propto\rho_{xx}^\beta$
and a recently found new scaling relationship of nonlinear Hall resistivity
$\rho_{xy}(T)$.


  The discovery of postquantum nonlocality, i.e., the existence of nonlocal
correlations that are stronger than any quantum correlations but nevertheless
consistent with the no-signaling principle, has deepened our understanding of
the foundations of quantum theory. In this work, we investigate whether the
phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum
nonlocality, can also be generalized beyond quantum theory. While postquantum
steering does not exist in the bipartite case, we prove its existence in the
case of three observers. Importantly, we show that postquantum steering is a
genuinely new phenomenon, fundamentally different from postquantum nonlocality.
Our results provide new insight into the nonlocal correlations of multipartite
quantum systems.


  SModelS is an automatized tool enabling the fast interpretation of simplified
model results from the LHC within any model of new physics respecting a
$\mathbb{Z}_2$ symmetry. In this contribution, we report on two important
updates of SModelS during 2020: the extension of the SModelS' database with 13
ATLAS and 10 CMS analyses, including 5 ATLAS and 1 CMS analyses at full Run~2
luminosity, and the ability to use full likelihoods now provided by ATLAS in
the form of pyhf JSON files. Moreover, we briefly explain how to use SModelS
and give an overview of ongoing developments.


  This course aims to introduce the student to random matrix models for
decoherence and fidelity decay. They present a very powerful alternate
approach, that emphasizes the disordered character of many environments and
uncontrollable perturbations/couplings. The inherent integrability of such
models makes analytic studies possible. We limit our considerations to linear
response treatment, as high fidelity and small decoherence are the backbone of
quantum information processes. For fidelity decay, where experimental results
are available, a comparison with experiments shows excellent agreement with
random matrix theory predictions.


  We present $N$-body simulations which are fully compatible with general
relativity, with dark energy consistently included at both the background and
perturbation level. We test our approach for dark energy parameterised as both
a fluid, and using the parameterised post-Friedmann (PPF) formalism. In most
cases, dark energy is very smooth relative to dark matter so that its leading
effect on structure formation is the change to the background expansion rate.
This can be easily incorporated into Newtonian $N$-body simulations by changing
the Friedmann equation. However, dark energy perturbations and relativistic
corrections can lead to differences relative to Newtonian $N$-body simulations
at the tens of percent level for scales $k < (10^{-3} \unicode{x2013}
10^{-2})\,\mathrm{Mpc}^{-1}$, and given the accuracy of upcoming large scale
structure surveys such effects must be included. In this paper we will study
both effects in detail and highlight the conditions under which they are
important. We also show that our $N$-body simulations exactly reproduce the
results of the Boltzmann solver CLASS for all scales which remain linear.


  We review time-dependent multiconfiguration self-consistent-field (TD-MCSCF)
method and time-dependent optimized coupled-cluster (TD-OCC) method for
first-principles simulations of high-field phenomena such as tunneling
ionization and high-order harmonic generation in atoms and molecules irradiated
by a strong laser field. These methods provide a flexible and systematically
improvable description of the multielectron dynamics by expressing the
all-electron wavefunction by configuration interaction expansion or
coupled-cluster expansion, using time-dependent one-electron orbital functions.
The time-dependent variational principle plays a key role to derive these
methods satisfying gauge invariance and Ehrenfest theorem. The
real-time/real-space implementation with an absorbing boundary condition
enables the simulation of high-field processes involving multiple excitation
and ionization. We present a detailed, comprehensive discussion of such
features of TD-MCSCF and TD-OCC methods.


  The modern formulation of exclusive reactions within Quantum Chromodynamics
is reviewed, the emphasis being placed on the pivotal ideas and methods
pertaining to perturbative and non-perturbative topics. Specific problems,
related to scale locality, infrared safety, gluonic radiative corrections
(Sudakov effects), and the role of hadronic size effects (intrinsic transverse
momentum), are studied. These issues are more precisely analyzed in terms of
the essential mechanisms of momentum transfer to a hadron while remaining
intact. Different factorization schemes are considered and the conceptual
lacunas are pointed out. The quite technical subject of renormalization-group
evolution is given a detailed account. By combining analytical and numerical
algorithms, the one-gluon exchange nucleon evolution equation is diagonalized
and next-to-leading eigenfunctions are calculated in terms of Appell
polynomials. The corresponding anomalous dimensions of trilinear quark
operators are found to form a degenerate system whose envelope shows
logarithmic large-order behavior. Selected applications of this framework are
presented, focusing on the helicity-conserving elastic form factors of the pion
and the nucleon. The theoretical constraints imposed by QCD sum rules on the
moments of nucleon distribution amplitudes are used to determine a whole
spectrum of optional solutions. They organize themselves along an ``orbit''
characterized by a striking scaling relation between the form-factor ratio
$R=|G_{\rm M}^{\rm n}|/G_{\rm M}^{\rm p}$ and the projection coefficient
$B_{4}$ on to the corresponding eigensolution. The main reasons for the failure
of the present theoretical predictions to match the experimental data are
discussed and workable explanations are sketched.


  Conventional feature selection algorithms applied to Pseudo Time-Series (PTS)
data, which consists of observations arranged in sequential order without
adhering to a conventional temporal dimension, often exhibit impractical
computational complexities with high dimensional data. To address this
challenge, we introduce a Deep Learning (DL)-based feature selection algorithm:
Feature Selection through Discrete Relaxation (FSDR), tailored for PTS data.
Unlike the existing feature selection algorithms, FSDR learns the important
features as model parameters using discrete relaxation, which refers to the
process of approximating a discrete optimisation problem with a continuous one.
FSDR is capable of accommodating a high number of feature dimensions, a
capability beyond the reach of existing DL-based or traditional methods.
Through testing on a hyperspectral dataset (i.e., a type of PTS data), our
experimental results demonstrate that FSDR outperforms three commonly used
feature selection algorithms, taking into account a balance among execution
time, $R^2$, and $RMSE$.


  In this work, we studied time-reversal-breaking topological phases as a
result of the interplay between antiferromagnetism and inverted band structures
in thin films of antiferromagnetic double perovskite transition-metal
Sr$_2$FeOsO$_6$. By combining the first-principles calculations and analytical
models, we demonstrate that the quantum anomalous Hall phase and chiral
topological superconducting phase can be realized in this system. We find that
to achieve time-reversal-breaking topological phases in antiferromagnetic
materials, it is essential to break the combined symmetry of time reversal and
inversion, which generally exists in antiferromagnetic structures. As a result,
we can utilize an external electric gate voltage to induce the phase transition
between topological phases and trivial phases, thus providing an electrically
controllable topological platform for the future transport experiments.


  The CMS pixel barrel system will consist of three layers built of about 800
modules. One module contains 66560 readout channels and the full pixel barrel
system about 48 million channels. It is mandatory to test each channel for
functionality, noise level, trimming mechanism, and bump bonding quality.
Different methods to determine the bump bonding yield with electrical
measurements have been developed. Measurements of several operational
parameters are also included in the qualification procedure. Among them are
pixel noise, gains and pedestals. Test and qualification procedures of the
pixel barrel modules are described and some results are presented.


  Wide black hole binaries (wide-BBHs; $\geqslant 10^3$ AU) in the field can be
perturbed by random stellar flybys that excite their eccentricities. Once a
wide binary is driven to a sufficiently small pericenter approach,
gravitational wave (GW) emission becomes significant, and the binary inspirals
and merges. In our previous study, using simplified models for wide-BBHs, we
found that successive flybys lead to significant merger fractions of wide-BBHs
in less than Hubble time, making the flyby perturbation mechanism a relevant
contributor to the production rate of GW-sources. However, the exact rates and
detailed properties of the resulting GW sources depend on the wide binary
progenitors. In this paper we use detailed population synthesis models for the
initial wide-BBH population, considering several populations corresponding to
different natal-kick models and metallicities, and then follow the wide-BBHs
evolution due to flyby perturbations and GW-emission. We show that the
cumulative effect of flybys is conductive for the production of GW sources in
non-negligible rates of $1-20$ Gpc$^{-3}$ yr$^{-1}$, which are sensitive to the
natal kicks model. Such rates are relevant to the observationally inferred
rate. Our models, now derived from detailed population of binaries, provide the
detailed properties of the produced GW-sources, including mass-functions and
delay times. The GW mergers are circularized when enter the aLIGO band; have a
preference for high velocity dispersion host galaxies (in particular
ellipticals); have a relatively uniform delay-time distribution; and likely
have mildly correlated (less than isolated evolution channels and more than
dynamical channels) prograde spin-spin and spin-orbits.


  Where the response variable in a big data set is consistent with the variable
of interest for small area estimation, the big data by itself can provide the
estimates for small areas. These estimates are often subject to the coverage
and measurement error bias inherited from the big data. However, if a
probability survey of the same variable of interest is available, the survey
data can be used as a training data set to develop an algorithm to impute for
the data missed by the big data and adjust for measurement errors. In this
paper, we outline a methodology for such imputations based on an kNN algorithm
calibrated to an asymptotically design-unbiased estimate of the national total
and illustrate the use of a training data set to estimate the imputation bias
and the fixed - asymptotic bootstrap to estimate the variance of the small area
hybrid estimator. We illustrate the methodology of this paper using a public
use data set and use it to compare the accuracy and precision of our hybrid
estimator with the Fay-Harriot (FH) estimator. Finally, we also examine
numerically the accuracy and precision of the FH estimator when the auxiliary
variables used in the linking models are subject to under-coverage errors.


  We compute new chemical profiles for the core and envelope of white dwarfs
appropriate for pulsational studies of ZZ Ceti stars. These profiles are
extracted from the complete evolution of progenitor stars, evolved through the
main sequence and the thermally-pulsing asymptotic giant branch (AGB) stages,
and from time-dependent element diffusion during white dwarf evolution. We
discuss the importance of the initial-final mass relationship for the white
dwarf carbon-oxygen composition. In particular, we find that the central oxygen
abundance may be underestimated by about 15% if the white dwarf mass is assumed
to be the hydrogen-free core mass before the first thermal pulse. We also
discuss the importance for the chemical profiles expected in the outermost
layers of ZZ Ceti stars of the computation of the thermally-pulsing AGB phase
and of the phase in which element diffusion is relevant. We find a strong
dependence of the outer layer chemical stratification on the stellar mass. In
particular, in the less massive models, the double-layered structure in the
helium layer built up during the thermally-pulsing AGB phase is not removed by
diffusion by the time the ZZ Ceti stage is reached. Finally, we perform
adiabatic pulsation calculations and discuss the implications of our new
chemical profiles for the pulsational properties of ZZ Ceti stars. We find that
the whole $g-$mode period spectrum and the mode-trapping properties of these
pulsating white dwarfs as derived from our new chemical profiles are
substantially different from those based on chemical profiles widely used in
existing asteroseismological studies. Thus, we expect the asteroseismological
models derived from our chemical profiles to be significantly different from
those found thus far.


  The emission angle distribution of projectile fragments (PFs) and the
temperature of PFs emission source for fragmentation of $^{56}$Fe on
polyethylene, carbon and aluminum targets at the highest energy of 496 A MeV
are investigated using CR-39 plastic nuclear track detector. It is found that
the averaged emission angle of PFs increases with the decrease of PF charge for
the same target, and no obvious dependence of angular distribution on the mass
of target nucleus is found for the same PF. The cumulated squared transverse
momentum distribution of PF can be well represented by a single Rayleigh
distribution, the temperature of PFs emission source is extracted from the
distribution, which is about 1.0-8.0 MeV and do not depend on the mass of
target for PF with charge of 9<=Z<=25.


  We discuss the problem of determining the dimension of self-similar sets and
measures on $\mathbf{R}$. We focus on the developments of the last four years.
At the end of the paper, we survey recent results about other aspects of
self-similar measures including their Fourier decay and absolute continuity.


  The virial theorem prescribes the ratio of the globally-averaged equatorial
to vertical velocity dispersion of a tracer population in spherical and
flattened dark haloes. This gives sequences of physical models in the plane of
global anisotropy and flattening. The tracer may have any density, though there
are particularly simple results for power-laws and exponentials. We prove the
flattening theorem: for a spheroidally stratified tracer density with axis
ratio q in a dark density potential with axis ratio g, the ratio of globally
averaged equatorial to vertical velocity dispersion depends only on q/g. As the
stellar halo density and velocity dispersion of the Milky Way are accessible to
observations, this provides a new method for measuring the flattening of the
dark matter. If the kinematics of the local halo subdwarfs are representative,
then the Milky Way's dark halo is oblate with a flattening in the potential of
g ~ 0.85, corresponding to a flattening in the dark matter density of ~ 0.7.
The fractional pressure excess for power-law populations is roughly
proportional to both the ellipticity and the fall-off exponent. Given the same
pressure excess, if the density profile of one stellar population declines more
quickly than that of another, then it must be rounder. This implies that the
dual halo structure claimed by Carollo et al. (2007) for the Galaxy, a flatter
inner halo and a rounder outer halo, is inconsistent with the virial theorem.
For the thick disc, we provide formulae for the virial sequences of
double-exponential discs in logarithmic and Navarro-Frenk-White (NFW) haloes.
There are good matches to the observational data on the flattening and
anisotropy of the thick disc if the thin disc is exponential with a short
scalelength ~ 2.6 kpc and normalisation of 56 solar masses per square parsec,
together with a logarithmic dark halo.


  Differential dependencies (DDs) capture the relationships between data
columns of relations. They are more general than functional dependencies (FDs)
and and the difference is that DDs are defined on the distances between values
of two tuples, not directly on the values. Because of this difference, the
algorithms for discovering FDs from data find only special DDs, not all DDs and
therefore are not applicable to DD discovery. In this paper, we propose an
algorithm to discover DDs from data following the way of fixing the left hand
side of a candidate DD to determine the right hand side. We also show some
properties of DDs and conduct a comprehensive analysis on how sampling affects
the DDs discovered from data.


  Inelastic and diffractive production of J/psi mesons at HERA is reviewed. The
data on inelastic photoproduction are described well within errors by the
Colour Singlet Model in next-to-leading order. A search for colour octet
processes predicted within the NRQCD/factorisation approach is conducted in
many regions of phase space. No unambiguous evidence has been found to date.
Diffractive elastic production of J/psi mesons has been measured in the limit
of photoproduction up to the highest photon proton center of mass energies. The
increase of the cross section is described by pQCD models. At larger Q^2, the W
dependence is found to be similar to that observed in photoproduction. First
analyses of data at high t yield a powerlike dependence on |t|. A LO BFKL
calculation gives a good description of the data.


  The wave functions of a quantum isotropic harmonic oscillator in N-space
modified by barriers at the coordinate hyperplanes can be expressed in terms of
certain generalized spherical harmonics. These are associated with a
product-type weight function on the sphere. Their analysis is carried out by
means of differential-difference operators. The symmetries of this system
involve the Weyl group of type B, generated by permutations and changes of sign
of the coordinates. A new basis for symmetric functions as well as an explicit
transition matrix to the monomial basis is constructed. This basis leads to a
basis for invariant spherical harmonics. The determinant of the Gram matrix for
the basis in the natural inner product over the sphere is evaluated, and there
is a formula for the evaluation of the basis elements at (1,1,...,1). When the
underlying parameter is specialized to zero, the basis consists of ordinary
spherical harmonics with cube group symmetry, as used for wave functions of
electrons in crystals. The harmonic oscillator can also be considered as a
degenerate interaction-free spin Calogero model.


  The joint detection of gravitational waves and electromagnetic radiation from
the binary neutron star (BNS) merger GW170817 has provided unprecedented
insight into a wide range of physical processes: heavy element synthesis via
the $r$-process; the production of relativistic ejecta; the equation of state
of neutron stars and the nature of the merger remnant; the binary coalescence
timescale; and a measurement of the Hubble constant via the "standard siren"
technique. In detail, all of these results depend on the distance to the host
galaxy of the merger event, NGC4993. In this paper we measure the surface
brightness fluctuation (SBF) distance to NGC4993 in the F110W and F160W
passbands of the Wide Field Camera 3 Infrared Channel on the Hubble Space
Telescope (HST). For the preferred F110W passband we derive a distance modulus
of $m{-}M=33.05\pm0.08\pm0.10$ mag, or a linear distance $d=40.7\pm1.4\pm1.9$
Mpc (random and systematic errors, respectively); a virtually identical result
is obtained from the F160W data. This is the most precise distance to NGC4993
available to date. Combining our distance measurement with the corrected
recession velocity of NGC4993 implies a Hubble constant $H_0=71.9\pm
7.1~km~s^{-1}~Mpc^{-1}$. A comparison of our result to the GW-inferred value of
$H_0$ indicates a binary orbital inclination of $i\,{\gtrsim}\,137~\deg$. The
SBF technique can be applied to early-type host galaxies of BNS mergers to
${\sim\,}100$ Mpc with HST and possibly as far as ${\sim\,}300$ Mpc with the
James Webb Space Telescope, thereby helping to break the inherent
distance-inclination degeneracy of the GW signals at distances where many
future BNS mergers are likely to be detected.


  In machine learning, training data often capture the behaviour of multiple
subgroups of some underlying human population. When the amounts of training
data for the subgroups are not controlled carefully, under-representation bias
arises. We introduce two natural notions of subgroup fairness and instantaneous
fairness to address such under-representation bias in time-series forecasting
problems. In particular, we consider the subgroup-fair and instant-fair
learning of a linear dynamical system (LDS) from multiple trajectories of
varying lengths, and the associated forecasting problems. We provide globally
convergent methods for the learning problems using hierarchies of
convexifications of non-commutative polynomial optimisation problems. Our
empirical results on a biased data set motivated by insurance applications and
the well-known COMPAS data set demonstrate both the beneficial impact of
fairness considerations on statistical performance and encouraging effects of
exploiting sparsity on run time.


  The target of our study is to approximate numerically and, in some particular
physically relevant cases, also analytically, the residence time of particles
undergoing an asymmetric simple exclusion dynamics on a stripe. The source of
asymmetry is twofold: (i) the choice of boundary conditions (different
reservoir levels) and (ii) the strong anisotropy from a nonlinear drift with
prescribed directionality. We focus on the effect of the choice of anisotropy
in the flux on the asymptotic behavior of the residence time with respect to
the length of the stripe. The topic is relevant for situations occurring in
pedestrian flows or biological transport in crowded environments, where lateral
displacements of the particles occur predominantly affecting therefore in an
essentially way the efficiency of the overall transport mechanism.


  Ions of the same charge inside confining potentials can form crystalline
structures which can be controlled by means of the ions density and of the
external trap parameters. In particular, a linear chain of trapped ions
exhibits a transition to a zigzag equilibrium configuration, which is
controlled by the strength of the transverse confinement. Studying this phase
transition in the quantum regime is a challenging problem, even when employing
numerical methods to simulate microscopically quantum many-body systems. Here
we present a compact analytical treatment to map the original long-range
problem into a short-range quantum field theory on a lattice. We provide a
complete numerical architecture, based on Density Matrix Renormalization Group,
to address the effective quantum phi-four model. This technique is instrumental
in giving a complete characterization of the phase diagram, as well as pinpoint
the universality class of the criticality.


  The Landauer-B\"uttiker formalism provides a simple and insightful way for
investigating many phenomena in mesoscopic physics. By this approach we derive
general formulas for the energy properties and apply them to the basic setups.
Of particular interest are the noise properties. We show that energy current
fluctuations can be induced by zero-point fluctuations and we discuss the
implications of this result.


  A common assumption in financial engineering is that the market price for any
derivative coincides with an objectively defined risk-neutral price - a
plausible assumption only if traders collectively possess objective knowledge
about the price dynamics of the underlying security over short time scales.
Here we assume that traders have an objective knowledge about the underlying
security's price trajectories only for large time scales. We show that
avoidance of arbitrage that is still feasible uniquely determines the prices of
options with large expiration times, and we derive limit theorems useful for
estimation of model parameters and present-value analysis of derivative
portfolios.


  The production of light (anti-)(hyper-)nuclei in heavy-ion collisions at the
LHC is considered in the framework of the Saha equation, making use of the
analogy between the evolution of the early universe after the Big Bang and that
of "Little Bangs" created in the lab. Assuming that disintegration and
regeneration reactions involving light nuclei proceed in relative chemical
equilibrium after the chemical freeze-out of hadrons, their abundances are
determined through the famous cosmological Saha equation of primordial
nucleosynthesis and show no exponential dependence on the temperature typical
for the thermal model. A quantitative analysis, performed using the hadron
resonance gas model in partial chemical equilibrium, shows agreement with
experimental data of the ALICE collaboration on d, $^3$He, $^3_\Lambda$H, and
$^4$He yields for a very broad range of temperatures at $T \lesssim 155$ MeV.
The presented picture is supported by the observed suppression of resonance
yields in central Pb-Pb collisions at the LHC.


  In this paper, we introduce 3-dimensional $L-$summing method, which is a
rearrangement of the summation $\sum A_{abc}$ with $1\leq a,b,c\leq n$.
Applying this method on some special arrays, we obtain some identities on the
Riemann zeta function and digamma function. Also, we give a Maple program for
this method to obtain identities with input various arrays and out put
identities concerning some elementary functions and hypergeometric functions.
Finally, we introduce a further generalization of $L-$summing method in higher
dimension spaces.


  An analytical solution is derived for the bifurcations of an elastic disc
that is constrained on the boundary with an isoperimetric Cosserat coating. The
latter is treated as an elastic circular rod, either perfectly or partially
bonded (with a slip interface in the latter case) and is subjected to three
different types of uniformly distributed radial loads (including hydrostatic
pressure). The proposed solution technique employs complex potentials to treat
the disc's interior and incremental Lagrangian equations to describe the
prestressed elastic rod modelling the coating. The bifurcations of the disc
occur with modes characterized by different circumferential wavenumbers,
ranging between ovalization and high-order waviness, as a function of the ratio
between the elastic stiffness of the disc and the bending stiffness of its
coating. The presented results find applications in various fields, such as
coated fibres, mechanical rollers, and the growth and morphogenesis of plants
and fruits.


  Objects that float at the interface between a liquid and a gas interact
because of interfacial deformation and the effect of gravity. We highlight the
crucial role of buoyancy in this interaction, which, for small particles,
prevails over the capillary suction that is often assumed to be the dominant
effect. We emphasize this point using a simple classroom demonstration, and
then derive the physical conditions leading to mutual attraction or repulsion.
We also quantify the force of interaction in some particular instances and
present a simple dynamical model of this interaction. The results obtained from
this model are then validated by comparison to experimental results for the
mutual attraction of two identical spherical particles. We conclude by looking
at some of the applications of the effect that can be found in the natural and
manmade worlds.


  This paper describes a tool suite for the ACL2 programming language which
incorporates certain ideas from the Hindley-Milner paradigm of functional
programming (as exemplified in popular languages like ML and Haskell),
including a "typed" style of programming with the ability to define polymorphic
types. These ideas are introduced via macros into the language of ACL2, taking
advantage of ACL2's guard-checking mechanism to perform type checking on both
function definitions and theorems. Finally, we discuss how these macros were
used to implement features of Specware, a software specification and
implementation system.


  We propose an end-to-end solution, from watermark feature generation to
metric design, for effectively demoting watermarked images surfed by a real
world image search engine. We use a few fundamental techniques to obtain
effective watermark features of images in the image search index, and utilize
the signals in a commercial search engine to improve the image search quality.
We collect a diverse and large set (about 1M) of images with human labels
indicating whether the image contains visible watermark. We train a few deep
convolutional neural networks to extract watermark information from the raw
images. The deep CNN classifiers we trained can achieve high accuracy on the
watermark test data set. We also analyze the images based on their domains to
get watermark information from a domain-based watermark classifier. We design a
new novel hybrid metric which includes the relevance, image attractiveness and
watermark information all together. We demonstrate that using these watermark
signals together with the new metric in image search ranker can significantly
demote the watermarked images during the online image ranking.


  Rector neutrinos have been a tool to investigate neutrino properties for more
than 60 years. The reactor neutrino flux was measured throughout 80s-90s. In
the 2000s, reactor neutrino oscillations at large baselines were observed by
the KamLAND experiment and later in 2012 at short baselines by the Daya Bay,
Double Chooz and RENO experiments. Reactor neutrino experiments have
significantly contributed to our current knowledge of oscillation parameters.
The detector technology has been majorly improved over decades and we have
entered era of precise measurements. The recent absolute measurement reactor
neutrino flux and spectral shape revealed deviations from the prediction model,
known as reactor antineutrino flux and spectrum shape anomalies. In this
article, we review the latest development in short baseline reactor experiments
and we discuss observed anomalies.


  We propose using the Wasserstein loss for training in inverse problems. In
particular, we consider a learned primal-dual reconstruction scheme for
ill-posed inverse problems using the Wasserstein distance as loss function in
the learning. This is motivated by miss-alignments in training data, which when
using standard mean squared error loss could severely degrade reconstruction
quality. We prove that training with the Wasserstein loss gives a
reconstruction operator that correctly compensates for miss-alignments in
certain cases, whereas training with the mean squared error gives a smeared
reconstruction. Moreover, we demonstrate these effects by training a
reconstruction algorithm using both mean squared error and optimal transport
loss for a problem in computerized tomography.


  Let $v(k, \lambda)$ be the maximum number of vertices of a connected
$k$-regular graph with second largest eigenvalue at most $\lambda$. The
Alon-Boppana Theorem implies that $v(k, \lambda)$ is finite when $k >
\frac{\lambda^2 + 4}{4}$. In this paper, we show that for fixed $\lambda
\geq1$, there exists a constant $C(\lambda)$ such that $2k+2 \leq v(k, \lambda)
\leq 2k + C(\lambda)$ when $k > \frac{\lambda^2 + 4}{4}$.


  Past Suzaku, XMM and NuSTAR observations of the nearby (z=0.0323) bright
Seyfert 2 galaxy MCG-03-58-007 revealed the presence of two deep and
blue-shifted Fe K-shell absorption line profiles. These could be explained with
the presence of two phases of a highly ionized, high column density accretion
disk wind outflowing with $v_{out1}\sim -0.1c$ and $v_{out2}\sim -0.2c$. Here
we present two new observations of MCG-03-58-007: one was carried out in 2016
with Chandra and one in 2018 with Swift. Both caught MCG-03-58-007 in a
brighter state ($F_{\mathrm{2-10\,keV}}\sim 4\times 10^{-12}$ erg cm$^{-2}$
s$^{-1}$) confirming the presence of the fast disk wind. The multi-epoch
observations of MCG-03-58-007 covering the period from 2010 to 2018 were then
analysed. These data show that the lower velocity component outflowing with
$v_{out1}\sim -0.072\pm 0.002c$ is persistent and detected in all the
observations, although it is variable in column density in the range
$N_\rm{H}\sim 3-8 \times 10^{23}$cm$^{-2}$. In the 2016 Swift observation we
detected again the second faster component outflowing with $v_{out2}\sim
-0.2c$, with a column density ($N_\rm{H}=7.0^{+5.6}_{-4.1}\times
10^{23}$cm$^{-2}$), similar to that seen during the Suzaku observation. However
during the Chandra observation two years earlier, this zone was not present
($N_\rm{H}<1.5\times 10^{23}$cm$^{-2}$), suggesting that this faster zone is
intermittent. Overall the multi-epochs observations show that the disk wind in
MCG-03-58-007 is not only powerful, but also extremely variable, hence placing
MCG-03-58-007 among unique disk winds such as the one seen in the famous QSO
PDS456. One of the main results of this investigation is the consideration that
these winds could be extremely variable, sometime appearing and sometime
disappearing; thus to reach solid and firm conclusions about their energetics
multiple observations are mandatory.


  Being able to characterise objects at low frequencies, but above the limiting
frequency of the eddy current approximation of the Maxwell system, is important
for improving current metal detection technologies. Importantly, the upper
frequency limit of the eddy current model depends on the object topology and on
its materials, with the maximum frequency being much smaller for certain
geometries compared to others of the same size and materials. Additionally, the
eddy current model breaks down at much smaller frequencies for highly magnetic
conducting materials compared to non-permeable objects (with similar
conductivities, sizes and shapes) and, hence, characterising small magnetic
objects made of permeable materials using the eddy current at typical
frequencies of operation for a metal detector is not always possible. To
address this, we derive a new asymptotic expansion for permeable highly
conducting objects that is valid for small objects and holds for frequencies
just beyond the eddy current limit. The leading order term we derive leads to
new forms of object characterisations in terms of polarizability tensor object
descriptions where the coefficients can be obtained from solving vectorial
transmission problems. We expect these new characterisations to be important
when considering objects at greater stand-off distance from the coils, which is
important for safety critical applications, such as the identification of
landmines, unexploded ordnance and concealed weapons. We also expect our
results to be important when characterising artefacts of archaeological and
forensic significance at greater depths than the eddy current model allows and
to have further applications parking sensors and improving the detection of
hidden, out-of-sight, metallic objects.


  In this research, we discuss the intermittent traveling salesman problem
(ITSP), which extends the traditional traveling salesman problem (TSP) by
imposing temperature restrictions on each node. These additional constraints
limit the maximum allowable visit time per node, and result in multiple visits
for each node which cannot be serviced in a single visit. We discuss three
different temperature increase and decrease functions, namely a linear, a
quadratic and an exponential function. To solve the problem, we consider three
different solution representations as part of a metaheuristic approach. We
argue that in case of similar temperature increase and decrease profiles, it is
always beneficial to apply a greedy approach, i.e. to process as much as
possible given the current node temperature.


  Zero-shot Chinese character recognition has attracted rising attention in
recent years. Existing methods for this problem are mainly based on either
certain low-level stroke-based decomposition or medium-level radical-based
decomposition. Considering that the stroke- and radical-level decompositions
can provide different levels of information, we propose an effective zero-shot
Chinese character recognition method by combining them. The proposed method
consists of a training stage and an inference stage. In the training stage, we
adopt two similar encoder-decoder models to yield the estimates of stroke and
radical encodings, which together with the true encodings are then used to
formalize the associated stroke and radical losses for training. A similarity
loss is introduced to regularize stroke and radical encoders to yield features
of the same characters with high correlation. In the inference stage, two key
modules, i.e., the stroke screening module (SSM) and feature matching module
(FMM) are introduced to tackle the deterministic and confusing cases
respectively. In particular, we introduce an effective stroke rectification
scheme in FMM to enlarge the candidate set of characters for final inference.
Numerous experiments over three benchmark datasets covering the handwritten,
printed artistic and street view scenarios are conducted to demonstrate the
effectiveness of the proposed method. Numerical results show that the proposed
method outperforms the state-of-the-art methods in both character and radical
zero-shot settings, and maintains competitive performance in the traditional
seen character setting.


  We prove duality relations for two interacting particle systems: the
$q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the
asymmetric simple exclusion process (ASEP). Expectations of the duality
functionals correspond to certain joint moments of particle locations or
integrated currents, respectively. Duality implies that they solve systems of
ODEs. These systems are integrable and for particular step and half-stationary
initial data we use a nested contour integral ansatz to provide explicit
formulas for the systems' solutions, and hence also the moments. We form
Laplace transform-like generating functions of these moments and via residue
calculus we compute two different types of Fredholm determinant formulas for
such generating functions. For ASEP, the first type of formula is new and
readily lends itself to asymptotic analysis (as necessary to reprove GUE
Tracy--Widom distribution fluctuations for ASEP), while the second type of
formula is recognizable as closely related to Tracy and Widom's ASEP formula
[Comm. Math. Phys. 279 (2008) 815--844, J. Stat. Phys. 132 (2008) 291--300,
Comm. Math. Phys. 290 (2009) 129--154, J. Stat. Phys. 140 (2010) 619--634]. For
$q$-TASEP, both formulas coincide with those computed via Borodin and Corwin's
Macdonald processes [Probab. Theory Related Fields (2014) 158 225--400]. Both
$q$-TASEP and ASEP have limit transitions to the free energy of the continuum
directed polymer, the logarithm of the solution of the stochastic heat equation
or the Hopf--Cole solution to the Kardar--Parisi--Zhang equation. Thus,
$q$-TASEP and ASEP are integrable discretizations of these continuum objects;
the systems of ODEs associated to their dualities are deformed discrete quantum
delta Bose gases; and the procedure through which we pass from expectations of
their duality functionals to characterizing generating functions is a rigorous
version of the replica trick in physics.


  We theoretically investigate the development of unconventional
superconductivity in the Sb(111) thin film when its Fermi level is tuned to
near type-II Van Hove singularities (VHS), which locate at non-time-reversal
invariant momenta. Via patch renormalization group analysis, we show that the
leading instability is a chiral p + ip-wave superconducting order. The origin
of such pairing relies on the hexagonal structure of the VHS and strong
spin-orbit coupling, resulting in the anisotropy of the electron-electron
scattering to provide an attractive channel. Our study hence suggests that
superconducting Sb thin films originated from VHS physics may host Majorana
zero modes in the magnetic vortices and provides another application
perspective to such material.


  The problem of deciding whether one point in a program is data dependent upon
another is fundamental to program analysis and has been widely studied. In this
paper we consider this problem at the abstraction level of program schemas in
which computations occur in the Herbrand domain of terms and predicate symbols,
which represent arbitrary predicate functions, are allowed. Given a vertex l in
the flowchart of a schema S having only equality (variable copying) assignments
and variables v,w, we show that it is PSPACE-hard to decide whether there
exists an execution of a program defined by S in which v holds the initial
value of w at at least one occurrence of l on the path of execution, with
membership in PSPACE holding provided there is a constant upper bound on the
arity of any predicate in S. We also consider the `dual' problem in which v is
required to hold the initial value of w at every occurrence of l, for which the
analogous results hold. Additionally, the former problem for programs with
non-deterministic branching (in effect, free schemas) in which assignments with
functions are allowed is proved to be polynomial-time decidable provided a
constant upper bound is placed upon the number of occurrences of the
concurrency operator in the schemas being considered. This result is promising
since many concurrent systems have a relatively small number of threads
(concurrent processes), especially when compared with the number of statements
they have.


  We prove different forms of the Nullstellensatz for difference fields and
absolutely flat simple difference rings, called pseudofields. A difference ring
is a ring on which an arbitrary group is acting by means of ring automorphisms.


  Since beginning of Grid computing, scheduling of dependent tasks application
has attracted attention of researchers due to NP-Complete nature of the
problem. In Grid environment, scheduling is deciding about assignment of tasks
to available resources. Scheduling in Grid is challenging when the tasks have
dependencies and resources are heterogeneous. The main objective in scheduling
of dependent tasks is minimizing make-span. Due to NP-complete nature of
scheduling problem, exact solutions cannot generate schedule efficiently.
Therefore, researchers apply heuristic or random search techniques to get
optimal or near to optimal solution of such problems. In this paper, we show
how Genetic Algorithm can be used to solve dependent task scheduling problem.
We describe how initial population can be generated using random assignment and
height based approaches. We also present design of crossover and mutation
operators to enable scheduling of dependent tasks application without violating
dependency constraints. For implementation of GA based scheduling, we explore
and analyze SimGrid and GridSim simulation toolkits. From results, we found
that SimGrid is suitable, as it has support of SimDag API for DAG applications.
We found that GA based approach can generate schedule for dependent tasks
application in reasonable time while trying to minimize make-span.


  Human emotions are often not expressed directly, but regulated according to
internal processes and social display rules. For affective computing systems,
an understanding of how users regulate their emotions can be highly useful, for
example to provide feedback in job interview training, or in psychotherapeutic
scenarios. However, at present no method to automatically classify different
emotion regulation strategies in a cross-user scenario exists. At the same
time, recent studies showed that instruction-tuned Large Language Models (LLMs)
can reach impressive performance across a variety of affect recognition tasks
such as categorical emotion recognition or sentiment analysis. While these
results are promising, it remains unclear to what extent the representational
power of LLMs can be utilized in the more subtle task of classifying users'
internal emotion regulation strategy. To close this gap, we make use of the
recently introduced \textsc{Deep} corpus for modeling the social display of the
emotion shame, where each point in time is annotated with one of seven
different emotion regulation classes. We fine-tune Llama2-7B as well as the
recently introduced Gemma model using Low-rank Optimization on prompts
generated from different sources of information on the \textsc{Deep} corpus.
These include verbal and nonverbal behavior, person factors, as well as the
results of an in-depth interview after the interaction. Our results show, that
a fine-tuned Llama2-7B LLM is able to classify the utilized emotion regulation
strategy with high accuracy (0.84) without needing access to data from
post-interaction interviews. This represents a significant improvement over
previous approaches based on Bayesian Networks and highlights the importance of
modeling verbal behavior in emotion regulation.


  We present the flare occurrence rates and starspot evolution for GJ 1245 A
and B, two active M5 stars, based on nine months of Kepler short cadence
observations, and four years of nearly continuous long cadence observations.
The A component is separated from the B component by 7 arcseconds, and the
stars are not resolved in the Kepler pipeline processing due to Kepler's large
plate scale of 4 arcseconds/pixel. Analyzing the target pixel data, we have
generated separate light curves for components A and B using the PyKE pixel
response function modeling procedures, and note the effects of CCD saturation
and non-linear response to high energy flares. In our sample, GJ 1245A and B
exhibit an average of 3.0 and 2.6 flares per day, respectively. We introduce a
new metric, $L_{fl}/L_{\mathrm{Kp}}$, to compare the flare rates between stars,
and discuss this in the context of GJ 1245 A and B. Both stars exhibit starspot
features that evolve on long time scales, with the slower rotating B component
showing evidence of differential rotation. Intriguingly, the angular separation
between the A and B component photocenters decreases during the four years of
observations in a manner consistent with a shift in the position of the A
photocenter due to the orbit of its unseen M8 companion (GJ 1245C), which is
$\sim$94% less bright. Among the most detailed photometric studies of fully
convective M dwarfs in a multiple system, these results provide an important
constraint on stellar age-rotation-activity models.


  The purpose of this paper is to provide further understanding into the
structure of the sequential allocation ("stochastic multi-armed bandit", or
MAB) problem by establishing probability one finite horizon bounds and
convergence rates for the sample (or "pseudo") regret associated with two
simple classes of allocation policies $\pi$.
  For any slowly increasing function $g$, subject to mild regularity
constraints, we construct two policies (the $g$-Forcing, and the $g$-Inflated
Sample Mean) that achieve a measure of regret of order $ O(g(n))$ almost surely
as $n \to \infty$, bound from above and below. Additionally, almost sure upper
and lower bounds on the remainder term are established. In the constructions
herein, the function $g$ effectively controls the "exploration" of the
classical "exploration/exploitation" tradeoff.


  Sleep staging plays an important role on the diagnosis of sleep disorders. In
general, experts classify sleep stages manually based on polysomnography (PSG),
which is quite time-consuming. Meanwhile, the acquisition process of multiple
signals is much complex, which can affect the subject's sleep. Therefore, the
use of single-channel electroencephalogram (EEG) for automatic sleep staging
has become a popular research topic. In the literature, a large number of sleep
staging methods based on single-channel EEG have been proposed with promising
results and achieve the preliminary automation of sleep staging. However, the
performance for most of these methods in the N1 stage do not satisfy the needs
of the diagnosis. In this paper, we propose a deep learning model multi scale
dual attention network(MSDAN) based on raw EEG, which utilizes multi-scale
convolution to extract features in different waveforms contained in the EEG
signal, connects channel attention and spatial attention mechanisms in series
to filter and highlight key information, and uses soft thresholding to remove
redundant information. Experiments were conducted using two datasets with
5-fold cross-validation and hold-out validation method. The final average
accuracy, overall accuracy, macro F1 score and Cohen's Kappa coefficient of the
model reach 96.70%, 91.74%, 0.8231 and 0.8723 on the Sleep-EDF dataset, 96.14%,
90.35%, 0.7945 and 0.8284 on the Sleep-EDFx dataset. Significantly, our model
performed superiorly in the N1 stage, with F1 scores of 54.41% and 52.79% on
the two datasets respectively. The results show the superiority of our network
over the existing methods, reaching a new state-of-the-art. In particular, the
proposed method achieves excellent results in the N1 sleep stage compared to
other methods.


  This paper presents a novel compact delay model of Ovonic Threshold Switch
(OTS) devices that works efficiently for circuit simulations. The internal
state variable of the two terminal devices is estimated using a delay system
that uses a few electrical components related to a suggested equivalent circuit
of the device. Finally, we tested the proposed model against measured data from
devices fabricated by Western Digital Research.


  In this paper I present several novel, efficient, algorithmic techniques for
solving some multidimensional geometric data management and analysis problems.
The techniques are based on several data structures from computational geometry
(e.g. segment tree and range tree) and on the well-known sweep-line method.


  Based on new near-infrared spectroscopic data from the instrument EMIR on the
10.4 m Gran Telescopio Canarias (GTC) we report the presence of an ionized and
warm molecular outflow in the luminous type-2 quasar J150904.22+043441.8 (z =
0.1118). The ionized outflow is faster than its molecular counterpart, although
the outflow sizes that we derive for them are consistent within the errors
(1.34$\pm$0.18 kpc and 1.46$\pm$0.20 kpc respectively). We use these radii, the
broad emission-line luminosities and in the case of the ionized outflow, the
density calculated from the trans-auroral [OII] and [SII] lines, to derive mass
outflow rates and kinetic coupling efficiencies. Whilst the ionized and warm
molecular outflows represent a small fraction of the AGN power ($\leq$0.033%
and 0.0001% of L$_{bol}$ respectively), the total molecular outflow, whose mass
is estimated from an assumed warm-to-cold gas mass ratio of 6$\times10^{-5}$,
has a kinetic coupling efficiency of $\sim$1.7%L$_{bol}$. Despite the large
uncertainty, this molecular outflow represents a significant fraction of
L$_{bol}$ and it could potentially have a significant impact on the host
galaxy. In addition, the quasar spectrum reveals bright and patchy narrow
Pa$\alpha$ emission extending out to 4 arcsec (8 kpc) South-East and North-West
from the active nucleus.


  Although the expectation maximisation (EM) algorithm was introduced in 1970,
it remains somewhat inaccessible to machine learning practitioners due to its
obscure notation, terse proofs and lack of concrete links to modern machine
learning techniques like autoencoded variational Bayes. This has resulted in
gaps in the AI literature concerning the meaning of such concepts like "latent
variables" and "variational lower bound," which are frequently used but often
not clearly explained. The roots of these ideas lie in the EM algorithm. We
first give a tutorial presentation of the EM algorithm for estimating the
parameters of a $K$-component mixture density. The Gaussian mixture case is
presented in detail using $K$-ary scalar hidden (or latent) variables rather
than the more traditional binary valued $K$-dimenional vectors. This
presentation is motivated by mixture modelling from the target tracking
literature. In a similar style to Bishop's 2009 book, we present variational
Bayesian inference as a generalised EM algorithm stemming from the variational
(or evidential) lower bound, as well as the technique of mean field
approximation (or product density transform). We continue the evolution from EM
to variational autoencoders, developed by Kingma & Welling in 2014. In so
doing, we establish clear links between the EM algorithm and its variational
counterparts, hence clarifying the meaning of "latent variables." We provide a
detailed coverage of the "reparametrisation trick" and focus on how the AEVB
differs from conventional variational Bayesian inference. Throughout the
tutorial, consistent notational conventions are used. This unifies the
narrative and clarifies the concepts. Some numerical examples are given to
further illustrate the algorithms.


  Alan Weinstein remarked that, working in the framework of diffeology, a
construction from Noncommutative Differential Geometry might provide the
non-trivial representations required for the geometric quantisation of a
symplectic structure which is not integral. In this note we show that the
construction we gave with P. Antonini does indeed provide non-trivial
representations.


  Reconstructing hadron spectral functions through Euclidean correlation
functions are of the important missions in lattice QCD calculations. However,
in a K\"allen--Lehmann(KL) spectral representation, the reconstruction is
observed to be ill-posed in practice. It is usually ascribed to the fewer
observation points compared to the number of points in the spectral function.
In this paper, by solving the eigenvalue problem of continuous KL convolution,
we show analytically that the ill-posedness of the inversion is fundamental and
it exists even for continuous correlation functions. We discussed how to
introduce regulators to alleviate the predicament, in which include the
Artificial Neural Networks(ANNs) representations recently proposed by the
Authors in~[Phys. Rev. D 106 (2022) L051502]. The uniqueness of solutions using
ANNs representations is manifested analytically and validated numerically.
Reconstructed spectral functions using different regularization schemes are
also demonstrated, together with their eigen-mode decomposition. We observe
that components with large eigenvalues can be reliably reconstructed by all
methods, whereas those with low eigenvalues need to be constrained by
regulators.


  We study the massless Klein-Gordon equation in the background of the most
general rotating dyonic AdS black hole in gauged $\mathcal{N}=2$, $U(1)^{2}$
gauged supergravity in $D=4$, given by Chow and Comp\`{e}re [Phys. Rev.
D\textbf{89} (2014) 065003]. The angular part of the separable wave equation is
of the Heun type, while the radial part is a Fuchsian equation with five
regular singularities. The radial equation is further analyzed and written in a
specific form, that reveals the pole structure of the horizon equation, whose
residua are expressed in terms of the surface gravities and angular velocities
associated with respective horizons. The near-horizon (near-)extremal limits of
the solution are also studied, where the expected hidden conformal symmetry is
revealed. Furthermore, we present the retarded Green's functions for these
limiting cases. We also comment on the generality of the charge-dependent parts
of the metric parameters and address some further examples of limiting cases.


  The spreadsheet application is among the most widely used computing tools in
modern society. It provides excellent usability and usefulness, and it easily
enables a non-programmer to perform programming-like tasks in a visual tabular
"pen and paper" approach. However, spreadsheets are mostly limited to
bookkeeping-like applications due to their mono-directional data flow. This
paper shows how the spreadsheet computing paradigm is extended to break this
limitation for solving constraint satisfaction problems. We present an enhanced
spreadsheet system where finite-domain constraint solving is well supported in
a visual environment. Furthermore, a spreadsheet-specific constraint language
is constructed for general users to specify constraints among data cells in a
declarative and scalable way. The new spreadsheet system significantly
simplifies the development of many constraint-based applications using a visual
tabular interface. Examples are given to illustrate the usability and
usefulness of the extended spreadsheet paradigm.
  KEYWORDS: Spreadsheet computing, Finite-domain constraint satisfaction,
Constraint logic programming


  We investigate the behavior of the kinetic and the exchange energy densities
near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we
derive analytical expressions near the nucleus, for single shells, as well as
in the semiclassical limit of large non-relativistic neutral atoms. We show
that a model based on the helium iso-electronic series is very accurate, as
also confirmed by numerical calculations on real atoms up to two thousands
electrons. Based on this model, we propose non-local density-dependent
ingredients that are suitable for the description of the kinetic and exchange
energy densities in the region close to the nucleus. These non-local
ingredients are invariant under the uniform scaling of the density, and they
can be used in the construction of non-local exchange-correlation and kinetic
functionals.


  Using scanning tunneling microscopy (STM), low energy electron diffraction
(LEED), and density functional theory (DFT), we demonstrate the formation of
quasicrystalline gallium adlayer on icosahedral ($i$)-Al-Pd-Mn. Quasiperiodic
motifs are evident in the STM topography images, including the Ga white flower
(GaWF) and $\tau$ inflated GaWF ($\tau$-GaWF), where $\tau$ is the golden mean.
A larger and more complicated ring motif is also identified, comprised of a
bright center and an outer ring of pentagons. The fast Fourier transform of the
STM images exhibits distinct quasiperiodic spots, thereby establishing
quasiperiodicity on a length scale of $\sim$350 nm. Based on our DFT
calculations, the preferred adsorption sites of Ga on i-Al-Pd-Mn are determined
to be either the Mn atoms at the center of the Penrose P1 tile or the vertices
of the P1 tile containing Pd atoms at the center of a cluster of 5 Al atoms
(5-Al). The GaWF motif is modeled by an inner 6 atom Ga cluster (6-Ga) around
the central Mn atom and an outer ring of 5 Ga atoms adsorbed at the centers of
the 5-Al clusters, both having pentagonal symmetry. The $\tau$-GaWF motif is
modeled by the 6-Ga arranged on the $\tau$-P1 tiling, while the ring motif is
modeled by Ga atoms adsorbed at the center of 5-Al clusters above a Pd atom.
The side lengths and diameters of the GaWF, $\tau$-GaWF, and the ring motifs
are $\tau$ scaled and show excellent agreement with the DFT-based models. An
additional indication of the quasiperiodic characteristics of the Ga monolayer
is the 5-fold LEED patterns that were detected throughout the entire range of
beam energy that was measured.


  The effect of changes in plasma parameters, that are characteristic near or
at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths
are analysed by means of drift-Alfven turbulence computations. Scalings by
density gradient length, collisionality, plasma beta, and by an imposed shear
flow are considered. It is found that strongly sheared flows lead to the
appearence of long-range correlations in electrostatic potential fluctuations
parallel and perpendicular to the magnetic field.


  Cancer cells evolve through random somatic mutations. "Beneficial" mutations
which disrupt key pathways (e.g. cell cycle regulation) are subject to natural
selection. Multiple mutations may lead to the same "beneficial" effect, in
which case there is no selective advantage to having more than one of these
mutations. Hence we are interested in finding sets of genes whose mutations are
approximately mutually exclusive (anti-co-occurring) within the TCGA Pancancer
dataset. In principle, finding the best set is NP Hard. Nevertheless, we will
show how a new Mutation anti-co-OCcurrence Algorithm (MOCA) provides an
effective greedy search and testing algorithm with guaranteed control of the
familywise error rate or false discovery rate, by combining some
under-appreciated ideas from frequentist hypothesis testing. These ideas
include: (a) A novel exact conditional test for the tendency of multiple sets
to have a large/small union/intersection, which generalises Fisher's exact test
of 2x2 tables. (b) Randomised hypothesis tests for discrete distributions. (c)
Stouffer's method for combining p-values. (d) Weighted multiple hypothesis
testing. A new approach to setting a-priori weights which generates additional
implicit hypothesis tests is suggested, and allows us to preserve almost all
statistical power when testing pairs despite introducing a combinatorially
large number of additional hypotheses.


  A kinetic-rate equation approach in a thermally expanding medium is employed
to calculate the evolution of charmonium and bottomonium distributions in
heavy-ion collisions. The equilibrium properties of the quarkonia are taken
from in-medium spectral functions which are schematically constrained by
euclidean correlators from lattice QCD. The initial conditions for the rate
equation (heavy-flavor cross sections, nuclear absorption) and the thermal
evolution are constrained by data as available. After fixing two free
parameters to describe charmonium data at SPS and RHIC, the predictions for LHC
are discussed in light of recent data.


  In this paper, we will define $a$-deformed Laguerre operators $L_{a,\alpha}$
and $a$-deformed Laguerre holomorphic semigroups on
$L^2\left(\left(0,\infty\right),d\mu_{a,\alpha}\right)$. Then we give a
spherical harmonic expansion, which reduces to the Bochner-type identity when
taking the boundary value $z=\frac{\pi i}2$, of the $(k,a)$-generalized
Laguerre semigroup introduced by S. Ben Sa\"id, T. Kobayashi and B. \O rsted.
And then we prove a Hardy inequality for fractional powers of the $a$-deformed
Dunkl harmonic oscillator
$\triangle_{k,a}:=\left|x\right|^{2-a}\triangle_k-\left|x\right|^a$ using this
expansion. When $a=2$, the fractional Hardy inequality reduces to that of
Dunkl--Hermite operators given by \'O. Ciaurri, L. Roncal and S. Thangavelu.
The operators $L_{a,\alpha}$ also give a tangible characterization of the
radial part of the $(k,a)$-generalized Laguerre semigroup on each $k$-spherical
component $\mathcal H_k^m\left(\mathbb{R}^N\right)$ for
$\lambda_{k,a,m}:=\frac{2m+2\left\langle k\right\rangle+N-2}a\geq -1/2$ defined
via decomposition of unitary representation.


  For free-field theories associated with BRST first-quantized gauge systems,
we identify generalized auxiliary fields and pure gauge variables already at
the first-quantized level as the fields associated with algebraically
contractible pairs for the BRST operator. Locality of the field theory is taken
into account by separating the space--time degrees of freedom from the internal
ones. A standard extension of the first-quantized system, originally developed
to study quantization on curved manifolds, is used here for the construction of
a first-order parent field theory that has a remarkable property: by
elimination of generalized auxiliary fields, it can be reduced both to the
field theory corresponding to the original system and to its unfolded
formulation. As an application, we consider the free higher-spin gauge theories
of Fronsdal.


  Though deep neural networks have achieved state-of-the-art performance in
visual classification, recent studies have shown that they are all vulnerable
to the attack of adversarial examples. Small and often imperceptible
perturbations to the input images are sufficient to fool the most powerful deep
neural networks. Various defense methods have been proposed to address this
issue. However, they either require knowledge on the process of generating
adversarial examples, or are not robust against new attacks specifically
designed to penetrate the existing defense. In this work, we introduce
key-based network, a new detection-based defense mechanism to distinguish
adversarial examples from normal ones based on error correcting output codes,
using the binary code vectors produced by multiple binary classifiers applied
to randomly chosen label-sets as signatures to match normal images and reject
adversarial examples. In contrast to existing defense methods, the proposed
method does not require knowledge of the process for generating adversarial
examples and can be applied to defend against different types of attacks. For
the practical black-box and gray-box scenarios, where the attacker does not
know the encoding scheme, we show empirically that key-based network can
effectively detect adversarial examples generated by several state-of-the-art
attacks.


  The distribution of isoscalar monopole strength in the neutron-even
112-124Sn-isotopes has been computed using a relativistic
random-phase-approximation approach. The accurately-calibrated model used here
(``FSUGold'') has been successful in reproducing both ground-state observables
as well as collective excitations - including the giant monopole resonance
(GMR) in 90Zr, 144Sm, and 208Pb. Yet this same model significantly
overestimates the GMR energies in the Sn isotopes. It is argued that the
question of ``Why is Tin so soft?'' becomes an important challenge to the field
and one that should be answered without sacrificing the success already
achieved by several theoretical models.


  We report a systematic study of the $c$ lattice parameter in the
Na$_{x}$CoO$_{2}$ phases versus Na content $x>0.5$, in which sodium always
displays ordered arrangements. This allows us to single out the first phase
which exhibits an AF magnetic order at a N\'eel temperature $T_{N}=$22 K which
is found to occur for $x\approx 0.77(1)$. Pure samples of this phase have been
studied both as aligned powders and single crystals. They exhibit identical
$^{23}$Na NMR spectra in which three sets of Na sites could be fully resolved,
and are found to display $T$ dependencies of their NMR shifts which scale with
each other. This allows us to establish that the $T$ variation of the shifts is
due to the paramagnetism of the Co sites with formal charge state larger than
3$^{+}$. The existence of a sodium site with axial charge symmetry and the
intensity ratio between the sets of $^{23}$Na lines permits us to reveal that
the 2D structure of the Na order corresponds to 10 Na sites on top of a 13 Co
sites unit cell, that is with $x=10/13\approx 0.77$. This structure fits with
that determined from local density calculations and involves triangles of 3 Na
sites located on top of Co sites (so called Na1 sites). The associated ordering
of the Na vacancies is quite distinct from that found for $x<0.75$.


  This papers consists of two parts. The first is a critical review of prior
art on adversarial learning, identifying some significant limitations of
previous works. The second part is an experimental study considering
adversarial active learning and an investigation of the efficacy of a mixed
sample selection strategy for combating an adversary who attempts to disrupt
the classifier learning.


  Using generalized Konishi anomaly equations, it is known that one can
express, in a large class of supersymmetric gauge theories, all the chiral
operators expectation values in terms of a finite number of a priori arbitrary
constants. We show that these constants are fully determined by the requirement
of gauge invariance and an additional anomaly equation. The constraints so
obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa
quantum glueball superpotential, with all terms (including the
Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill
non-trivial gaps in existing derivations of the mass gap and confinement
properties in super Yang-Mills theories.


  The conductance of thin films with diffusive surface scattering was solved
semi-classically by Fuchs and Sondheimer. However, when the intrinsic electron
mean free path is very large or infinite their conductance diverges. In this
letter a simple diffraction picture is presented. It yields a conductance which
corresponds to a limiting mean free path. PACS: 73.50.-h, 73.50.Bk, 73.23.-b,
73.25.+i, B146


  Biological systems, including human beings, have the innate ability to
perform complex tasks in versatile and agile manner. Researchers in
sensorimotor control have tried to understand and formally define this innate
property. The idea, supported by several experimental findings, that biological
systems are able to combine and adapt basic units of motion into complex tasks
finally lead to the formulation of the motor primitives theory. In this
respect, Dynamic Movement Primitives (DMPs) represent an elegant mathematical
formulation of the motor primitives as stable dynamical systems, and are well
suited to generate motor commands for artificial systems like robots. In the
last decades, DMPs have inspired researchers in different robotic fields
including imitation and reinforcement learning, optimal control,physical
interaction, and human-robot co-working, resulting a considerable amount of
published papers. The goal of this tutorial survey is two-fold. On one side, we
present the existing DMPs formulations in rigorous mathematical terms,and
discuss advantages and limitations of each approach as well as practical
implementation details. In the tutorial vein, we also search for existing
implementations of presented approaches and release several others. On the
other side, we provide a systematic and comprehensive review of existing
literature and categorize state of the art work on DMP. The paper concludes
with a discussion on the limitations of DMPs and an outline of possible
research directions.


  The current energy transition promotes the convergence of operation between
the power and natural gas systems. In that direction, it becomes paramount to
improve the modeling of non-convex natural gas flow dynamics within the
coordinated power and gas dispatch. In this work, we propose a
neural-network-constrained optimization method which includes a regression
model of the Weymouth equation, based on supervised machine learning. The
Weymouth equation links gas flow to inlet and outlet pressures for each
pipeline via a quadratic equality, which is captured by a neural network. The
latter is encoded via a tractable mixed-integer linear program into the set of
constraints. In addition, our proposed framework is capable of considering
bidirectionality without having recourse to complex and potentially inaccurate
convexification approaches. We further enhance our model by introducing a
reformulation of the activation function, which improves the computational
efficiency. An extensive numerical study based on the real-life Belgian power
and gas systems shows that the proposed methodology yields promising results in
terms of accuracy and tractability.


  The Sturm-Liouville boundary value problem (SLBVP) stands as a fundamental
cornerstone in the realm of mathematical analysis and physical modeling. Also
known as the Sturm-Liouville problem (SLP), this paper explores the intricacies
of this classical problem, particularly the relationship between its canonical
and Liouville normal (Schr\"odinger) forms. While the conversion from canonical
to Schr\"odinger form using Liouville's transformation is well-known in the
literature, the inverse transformation seems to be neglected. Our study
attempts to fill this gap by investigating the inverse of Liouville's
transformation, that is, given any SLP in the Schr\"odinger form with some
invariant function, we seek the SLP in its canonical form. By examining closely
the second Paine-de Hoog-Anderson (PdHA) problem, we argue that retrieving the
SLP to its canonical form can be notoriously difficult and even impossible to
achieve in its exact form. Finding the inverse relationship between the two
independent variables seems to be the main obstacle. We confirm this claim by
considering four different scenarios depending on the potential and density
functions that appear in the corresponding invariant function. In the second
PdHA problem, this invariant function takes a reciprocal quadratic binomial
form. In some cases, the inverse Liouville's transformation produces an exact
expression for the SLP in its canonical form. In other situations, however,
while an exact canonical form is not possible to obtain, we have successfully
derived the SLP in its canonical form asymptotically.


  We study Superconductor/Ferromagnet/Superconductor junctions with CuNi, PtNi,
or Ni interlayers. Remarkably, we observe that supercurrents through Ni can be
significantly larger than through diluted alloys. The phenomenon is attributed
to the dirtiness of disordered alloys leading to a short coherence length
despite a small exchange energy. To the contrary, pure Ni is clean resulting in
a coherence length as long as in a normal metal. Analysis of temperature
dependencies of critical currents reveals a crossover from short (dirty) to
long (clean) range proximity effects in Pt1-xNix with increasing Ni
concentration. Our results point out that structural properties of a
ferromagnet play a crucial role for the proximity effect and indicate that
conventional strong-but-clean ferromagnets can be advantageously used in
superconducting spintronic devices.


  In multi-messenger astronomy, rapid investigation of interesting transients
is imperative. As an observatory with a 4$\pi$ steradian field of view and
$\sim$99\% uptime, the IceCube Neutrino Observatory is a unique facility to
follow up transients, and to provide valuable insight for other observatories
and inform their observing decisions. Since 2016, IceCube has been using
low-latency data to rapidly respond to interesting astrophysical events
reported by the multi-messenger observational community. Here, we describe the
pipeline used to perform these follow up analyses and provide a summary of the
58 analyses performed as of July 2020. We find no significant signal in the
first 58 analyses performed. The pipeline has helped inform various
electromagnetic observing strategies, and has constrained neutrino emission
from potential hadronic cosmic accelerators.


  We introduce a model for the randomization of complex networks with geometric
structure. The geometric randomization (GR) model assumes a homogeneous
distribution of the nodes in an underlying similarity space and uses rewirings
of the links to find configurations that maximize a connection probability akin
to that of the $\mathbb{S}^1$ or $\mathbb{H}^2$ geometric network models.
However, GR preserves the original degree sequence, as in the configuration
model, thus eliminating the fluctuations of the degree cutoff. Moreover, the
model does not require the explicit estimation of hidden degree variables,
which restricts the number of free parameters to one, controlling the level of
clustering in the rewired network. We illustrate the potential of GR as a null
model by investigating the effects on modularity that derive from the
flattening of geometric communities in both real and synthetic networks. As a
result, we find that for real networks the geometric and topological
communities are consistent, while for the randomized counterparts, the
topological communities detected are attributable to structural constraints
induced by the underlying geometric architecture.


  We consider those Gaussian Unitary Ensembles where the eigenvalues have
prescribed multiplicities, and obtain joint probability density for the
eigenvalues. In the simplest case where there is only one multiple eigenvalue
t, this leads to orthogonal polynomials with the Hermite weight perturbed by a
factor that has a multiple zero at t. We show through a pair of ladder
operators, that the diagonal recurrence coefficients satisfy a particular
Painleve IV equation for any real multiplicity. If the multiplicity is even
they are expressed in terms of the generalized Hermite polynomials, with t as
the independent variable.


  In this letter we propose a scheme to build up high coherent solid-state
quantum bit (qubit) from two coupled quantum dots. Quantum information is
stored in electron-hole pair state with the electron and hole locating in
different dots, and universal quantum gates involving any pair of qubits are
realized by effective coupling interaction via virtually exchanging cavity
photons.


  Time-resolved near-infrared absorption spectroscopy of single non-repeatable
transient events is performed at high spectral resolution with a dual-comb
interferometer using a continuous-wave laser followed by a single electro-optic
amplitude modulator. By sharing high-speed electrical/optical components, our
spectrometer greatly simplifies the implementation of dual-comb spectroscopy
and it offers a high mutual coherence time, measured up to 50-s, without any
active stabilization system and/or data processing. The time resolution, which
can be reconfigured a posteriori, is as short 100 microseconds in our
experimental demonstration. For a span of 36 GHz, the mean signal-to-noise
ratio of 80, at 100-MHz spectral resolution and 100-microsecond measurement
time, enables the precise determination of the parameters of rovibrational
lines, including intensity or concentration.


  We present a study of excited charm-strange baryon states produced in
$e^+e^-$ annihilations at or near a center-of-mass energy of
$10.58\mathrm{Ge\kern -0.1em V}$, in a data sample with an integrated
luminosity of $384 fb^{-1}$ recorded with the BABAR detector at the PEP-II
$e^+e^-$ storage rings at the Stanford Linear Accelerator Center. We study
strong decays of charm-strange baryons to $\Lambda_c^+K^0_{\scriptscriptstyle
S}$, $\Lambda_c^+K^-$, $\Lambda_c^+K^-\pi^+$,
$\Lambda_c^+K^0_{\scriptscriptstyle S}\pi^-$,
$\Lambda_c^+K^0_{\scriptscriptstyle S}\pi^-\pi^+$, and
$\Lambda_c^+K^-\pi^+\pi^-$. This study confirms the existence of the states
$\Xi_c(2980)^+$, $\Xi_c(3077)^+$, and $\Xi_c(3077)^0$, with a more accurate
determination of the $\Xi_c(2980)^+$ mass and width. We also present evidence
for two new states, $\Xi_c(3055)^+$ and $\Xi_c(3123)^+$, decaying through the
intermediate resonant modes $\Sigma_c(2455)^{++}K^-$ and
$\Sigma_c(2520)^{++}K^-$, respectively. For each of these baryons, we measure
the yield in each final state, determine the statistical significance, and
calculate the product of the production cross-section and branching fractions.
We also measure the masses and widths of these excited charm-strange baryons.


  General relativity is supported by great experimental evidence. Yet there is
a lot of interest in precisely setting its limits with on going and future
experiments. A question to answer is about the validity of the Strong
Equivalence Principle. Ground experiments and Lunar Laser Ranging have provided
the best upper limit on the Nordtvedt parameter $\sigma[\eta]=4.4\times
10^{-4}$. With the future planetary mission BepiColombo, this parameter will be
further improved by at least an order of magnitude. In this paper we envisage
yet another possible testing environment with spacecraft ranging towards the
nearby Sun-Earth collinear Lagrangian points. Neglecting errors in planetary
masses and ephemerides, we forecast $\sigma[\eta]=6.4\,(2.0)\times10^{-4}$ (5
yr integration time) via ranging towards $L_1$ in a realistic (optimistic)
scenario depending on current (future) range capabilities and knowledge of the
Earth's ephemerides. A combined measurement, $L_1$+$L_2$, gives instead
$4.8\,(1.7)\times10^{-4}$. In the optimistic scenario a single measurement of
one year would be enough to reach $\approx3\times10^{-4}$. All figures are
comparable with Lunar Laser Ranging, but worse than BepiColombo. Performances
could be much improved if data were integrated over time and over the number of
satellites flying around either of the two Lagrangian points. We point out that
some systematics (gravitational perturbations of other planets or figure
effects) are much more in control compared to other experiments. We do not
advocate a specific mission to constrain the Strong Equivalence Principle, but
we do suggest analysing ranging data of present and future spacecrafts flying
around $L_1$/$L_2$ (one key mission is, for instance, LISA Pathfinder). This
spacecraft ranging would be a new and complementary probe to constrain the
Strong Equivalence Principle in space.


  In the presence of Rashba-Dresselhaus coupling, strong spin-orbit
interactions in liquid crystal optical cavities result in a distinctive
spin-split entangled dispersion. Spin coherence between such modes give rise to
an optical persistent-spin-helix. In this letter, we introduce optical gain in
such a system, by dispersing a molecular dye in a liquid-crystal microcavity.
We demonstrate both lasing in the Rashba-Dresselhaus regime and the emergence
of an optical persistent spin helix.


  Generative Adversarial Network (GAN) and its variants serve as a perfect
representation of the data generation model, providing researchers with a large
amount of high-quality generated data. They illustrate a promising direction
for research with limited data availability. When GAN learns the semantic-rich
data distribution from a dataset, the density of the generated distribution
tends to concentrate on the training data. Due to the gradient parameters of
the deep neural network contain the data distribution of the training samples,
they can easily remember the training samples. When GAN is applied to private
or sensitive data, for instance, patient medical records, as private
information may be leakage. To address this issue, we propose a
Privacy-preserving Generative Adversarial Network (PPGAN) model, in which we
achieve differential privacy in GANs by adding well-designed noise to the
gradient during the model learning procedure. Besides, we introduced the
Moments Accountant strategy in the PPGAN training process to improve the
stability and compatibility of the model by controlling privacy loss. We also
give a mathematical proof of the differential privacy discriminator. Through
extensive case studies of the benchmark datasets, we demonstrate that PPGAN can
generate high-quality synthetic data while retaining the required data
available under a reasonable privacy budget.


  In our quantum mechanics courses, measurement is usually taught in passing,
as an ad-hoc procedure involving the ugly collapse of the wave function. No
wonder we search for more satisfying alternatives to the Copenhagen
interpretation. But this overlooks the fact that the approach fits very well
with modern measurement theory with its notions of the conditioned state and
quantum trajectory. In addition, what we know of as the Copenhagen
interpretation is a later 1950's development and some of the earlier pioneers
like Bohr did not talk of wave function collapse. In fact, if one takes these
earlier ideas and mixes them with later insights of decoherence, a much more
satisfying version of Copenhagen quantum mechanics emerges, one for which the
collapse of the wave function is seen to be a harmless book keeping device.
Along the way, we explain why chaotic systems lead to wave functions that
spread out quickly on macroscopic scales implying that Schrodinger cat states
are the norm rather than curiosities generated in physicists' laboratories. We
then describe how the conditioned state of a quantum system depends crucially
on how the system is monitored illustrating this with the example of a decaying
atom monitored with a time of arrival photon detector, leading to Bohr's
quantum jumps. On the other hand, other kinds of detection lead to much
smoother behaviour, providing yet another example of complementarity. Finally
we explain how classical behaviour emerges, including classical mechanics but
also thermodynamics.


  We study two variations of the Gyarfas--Lehel conjecture on the minimum
number of monochromatic components needed to cover an edge-coloured complete
bipartite graph. Specifically, we show the following. - For p>> (\log
n/n)^{1/2}, w.h.p.~every 2-colouring of the random bipartite graph G~ G(n,n,p)
admits a cover of all but O(1/p) vertices of G using at most three
vertex-disjoint monochromatic components. - For every 2-colouring of a
bipartite graph G with parts of size n and minimum degree (13/16+o(1))n, the
vertices of G can be covered using at most three vertex-disjoint monochromatic
components.


  We study the emission of Hawking radiation in the form of scalar fields from
a (4+n)-dimensional, rotating black hole on the brane. We perform a numerical
analysis to solve both the radial and angular parts of the scalar field
equation, and derive exact results for the radial wavefunction and angular
eigenvalues, respectively. We then determine the Hawking radiation energy
emission rate, and find that, as the angular momentum increases, it is
suppressed in the low-energy regime but enhanced in the intermediate and
high-energy regimes. Our results agree with previous analytical studies,
derived in the low-angular momentum and low-energy approximation, and
generalize them to include angular momentum and energy regimes that were until
now unexplored. We also investigate the energy amplification due to
super-radiance and we find that, in the presence of extra dimensions, the
effect is significantly enhanced.


  We study algebro-geometric properties of determinantal loci of (n+1)th
symmetric matrices and also their double covers for even ranks. Their
singularities, Fano indices and birational geometries are studied in general.
The double covers of symmetric determinantal loci of rank four are studied with
special interest by noting their relation to the Hilbert schemes of conics on
Grassmannians.


  Large-scale three dimensional molecular dynamics simulations of hopper flow
are presented. The flow rate of the system is controlled by the width of the
aperture at the bottom. As the steady-state flow rate is reduced, the force
distribution $P(f)$ changes only slightly, while there is a large change in the
impulse distribution $P(i)$. In both cases, the distributions show an increase
in small forces or impulses as the systems approach jamming, the opposite of
that seen in previous Lennard-Jones simulations. This occurs dynamically as
well for a hopper that transitions from a flowing to a jammed state over time.
The final jammed $P(f)$ is quite distinct from a poured packing $P(f)$ in the
same geometry. The change in $P(i)$ is a much stronger indicator of the
approach to jamming. The formation of a peak or plateau in $P(f)$ at the
average force is not a general feature of the approach to jamming.