  Remote state monitoring over wireless is envisaged to play a pivotal role in
enabling beyond 5G applications ranging from remote drone control to remote
surgery. One key challenge is to identify the system dynamics that is
non-linear with a large dimensional state. To obviate this issue, in this
article we propose to train an autoencoder whose encoder and decoder are split
and stored at a state sensor and its remote observer, respectively. This
autoencoder not only decreases the remote monitoring payload size by reducing
the state representation dimension, but also learns the system dynamics by
lifting it via a Koopman operator, thereby allowing the observer to locally
predict future states after training convergence. Numerical results under a
non-linear cart-pole environment demonstrate that the proposed split learning
of a Koopman autoencoder can locally predict future states, and the prediction
accuracy increases with the representation dimension and transmission power.


  Starting from the requirement that a Lagrangian field theory be invariant
under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we
derive the BRST--anti-BRST analogue of the Batalin-Vilkovisky formalism. This
is done through standard Lagrangian gauge fixing respecting the extended BRST
symmetry. The solutions of the resulting Master Equation and the gauge-fixing
procedure for the quantum action can be brought into forms that coincide with
those obtained earlier on algebraic grounds by Batalin, Lavrov and Tyutin.


  A flow generator is described in which homogeneous axisymmetric turbulent air
flows with varying and fully controllable degrees of anisotropy, including the
much studied isotropic case, are generated by the combined agitations produced
by 32 acoustic mixers focusing at the center of the system. The axisymmetric
turbulence in a central volume of the size of the inertial scale is shown to
have negligible mean and shear. The Taylor Reynolds number is about 480.
  The influence of large scale anisotropy on the turbulence is examined from
three aspects, namely the velocity structure functions, the velocity
correlation functions, and the integral lengths. The directional dependence of
two different second order transverse structure functions, in which one of them
has separations stretched along the axis of symmetry of the turbulence and the
other one normal to it, is studied. It is shown that the inertial range scaling
exponents, determined using the extended-self-similarity procedure, and the
Kolmogorov constants of the two structure functions are unaffected by the
direction in which the structure functions are measured.
  Finally, it is found that, except in the isotropic case, the second order
transverse velocity correlation functions deviate from each other at the large
scale with increasing anisotropy. A self-similarity argument similar to one
found in the study of critical phenomena is proposed. It is shown that the
argument leads to a power-law relationship between the large scale velocity
fluctuation and the correlation length, with an exponent that depends on the
inertial range scaling exponent of the turbulence. The data collapse predicted
by the self-similarity hypothesis is verified. It is demonstrated that the
value of the power-law exponent is consistent with the value of the inertial
range scaling exponent.


  We report on a new method for tracking the phases of the orbital modulations
in very short-period, near-contact, and contact binary systems systems in order
to follow starspots. We apply this technique to Kepler light curves for 414
binary systems that were identified as having anticorrelated O-C curves for the
midtimes of the primary and secondary eclipses, or in the case of non-eclipsing
systems, their light-curve minima. This phase tracking approach extracts more
information about starspot and binary system behavior than may be easily
obtained from the O-C curves. We confirm the hypothesis of Tran et al. (2013)
that we can successfully follow the rotational motions of spots on the surfaces
of the stars in these binaries. In ~34% of the systems, the spot rotation is
retrograde as viewed in the frame rotating with the orbital motion, while ~13%
show significant prograde spot rotation. The remaining systems show either
little spot rotation or erratic behavior, or sometimes include intervals of
both types of behavior. We discuss the possibility that the relative motions of
spots are related to differential rotation of the stars. It is clear from this
study that the motions of the starspots in at least 50% of these short-period
binaries are not exactly synchronized with the orbits.


  The Euclid 6.2 project MOSES addressed quality issues in the development of
military KBS. A contribution to this project was to develop a computational
model of KBS that could be used to define and analyze aspects of KBS quality.
Since a key characteristic of KBS is search, a computational model based on
non-determinism was developed and used to express terms relating to quality.
This research report describes the approach.


  One of the most important problems in regression-based error model is
modeling the complex representation error caused by various corruptions and
environment changes in images. For example, in robust face recognition, images
are often affected by varying types and levels of corruptions, such as random
pixel corruptions, block occlusions, or disguises. However, existing works are
not robust enough to solve this problem due to they cannot model the complex
corrupted errors very well. In this paper, we address this problem by a unified
sparse weight learning and low-rank approximation regression model, which
enables the random noises and contiguous occlusions in images to be treated
simultaneously. For the random noise, we define a generalized correntropy (GC)
function to match the error distribution. For the structured error caused by
occlusions or disguises, we propose a GC function based rank approximation to
measure the rank of error matrices. Since the proposed objective function is
non-convex, an effective iterative optimization algorithm is developed to
achieve the optimal weight learning and low-rank approximation. Extensive
experimental results on three public face databases show that the proposed
model can fit the error distribution and structure very well, thus obtain
better recognition accuracies in comparison with the existing methods.


  This paper presents an overview of S2AEA (v2) (Strategic Alignment Assessment
based on Enterprise Architecture (version2)), a platform for modelling
enterprise architecture and for assessing strategic alignment based on internal
enterprise architecture metrics. The idea of the platform is based on the fact
that enterprise architecture provides a structure for business processes and
information systems that supports them. This structure can be used to measure
the degree of consistency between business strategies and information systems.
In that sense, this paper presents a platform illustrating the role of
enterprise architecture in the strategic alignment assessment. This assessment
can be used in auditing information systems. The platform is applied to assess
an e-government process.


  A Cosmic Muon Veto (CMV) detector using extruded scintillators is being
designed around the mini-Iron Calorimeter detector at the transit campus of the
India-based Neutrino Observatory at Madurai for measuring its efficiency at
shallow depth underground experiments. The scintillation signal is transmitted
through a Wavelength Shifting (WLS) fibre and readout by Hamamatsu
Silicon-Photomultipliers (SiPMs). A Light Emitting Diode (LED) system is
included on the front-end readout for in-situ calibration of the gain of each
SiPM. A characterization system was developed for the measurement of gain and
choice of the overvoltage (Vov) of SiPMs using LED as well as a cosmic muon
telescope. The Vov is obtained by studying the noise rate, the gain of the
SiPM, and the muon detection efficiency. In case of any malfunction of the LED
system during the operation, the SiPM can also be calibrated with the noise
data as well as using radioactive sources. This paper describes the basic
characteristics of the SiPM and the comparison of the calibration results using
all three methods, as well as the Vov of the SiPMs and muon selection criteria
for the veto detector.


  For four newly suggested microscopic equations of state of neutron star
matter, we construct equilibrium sequences of rapidly rotating neutron stars in
general relativity. The sequences are the normal and supramassive evolutionary
sequences of constant rest mass. We find that for these equations of state the
maximum (gravitational) mass rotating models occur (in central density and
rotation rate $\Omega$) before the maximum--$\Omega$ models. We calculate
equilibrium sequences for a constant value of $\Omega$ corresponding to the
most rapidly rotating pulsar PSR 1937+21. Also calculated is the radius of the
marginally stable orbit and its dependence on $\Omega$.


  We review the derivation of the Liouville action in 2DQG via the trace
anomaly and emphasize how a similar approach can be used to derive an effective
action describing the long wavelength dynamics of the conformal factor in 4D.
In 2D we describe how to make an explicit connection between dynamical
triangulations and this continuum theory, and present results which confirm the
equivalance of the two approaches. By reconstructing a lattice conformal mode
from DT simulations it should be possible to test this equivalence in 4D also.


  We show that there is a simple separable unital (non-nuclear) tracially AF
algebra $A$ which does not absorb the Jiang-Su algebra $\mathcal Z$
tensorially, i.e., $A \ncong A\otimes\mathcal Z$.


  Lower dimensional gravity has the potential of providing non-trivial and
valuable insight into some of the conceptual issues arising in four dimensional
relativistic gravitational analysis. The asymptotically anti-de Sitter (2+1)
dimensional spacetime described by Ba$\tilde{n}$ados, Teitelboim and Zanelli
(BTZ) which admits a black hole solution, has become a source of fascination
for theoretical physicists in recent years. By suitably choosing the form of
the mass function $m(r)$, we derive a new class of solutions for the interior
of an isotropic star corresponding to the exterior (2+1) asymptotically anti-de
Sitter BTZ spacetime. The solution obtained satisfies all the regularity
conditions and its simple analytical form helps us to study the physical
parameters of the configuration in a simple manner.


  Contagious processes, such as spread of infectious diseases, social
behaviors, or computer viruses, affect biological, social, and technological
systems. Epidemic models for large populations and finite populations on
networks have been used to understand and control both transient and
steady-state behaviors. Typically it is assumed that after recovery from an
infection, every agent will either return to its original susceptible state or
acquire full immunity to reinfection. We study the network SIRI
(Susceptible-Infected-Recovered-Infected) model, an epidemic model for the
spread of contagious processes on a network of heterogeneous agents that can
adapt their susceptibility to reinfection. The model generalizes existing
models to accommodate realistic conditions in which agents acquire partial or
compromised immunity after first exposure to an infection. We prove necessary
and sufficient conditions on model parameters and network structure that
distinguish four dynamic regimes: infection-free, epidemic, endemic, and
bistable. For the bistable regime, which is not accounted for in traditional
models, we show how there can be a rapid resurgent epidemic after what looks
like convergence to an infection-free population. We use the model and its
predictive capability to show how control strategies can be designed to
mitigate problematic contagious behaviors.


  We show the actual status of the project to implement the Astronomical
Observatory of the National University of Engineering (OAUNI), including its
first light. The OAUNI was installed with success at the site of the Huancayo
Observatory on the peruvian central Andes. At this time, we are finishing the
commissioning phase which includes the testing of all the instruments: optical
tube, robotic mount, CCD camera, filter wheel, remote access system, etc. The
first light gathered from a stellar field was very promissory. The next step
will be to start the scientific programs and to bring support to the
undergraduate courses in observational astronomy at the Faculty of Sciences of
UNI.


  The Infinitesimal Jackknife is a general method for estimating variances of
parametric models, and more recently also for some ensemble methods. In this
paper we extend the Infinitesimal Jackknife to estimate the covariance between
any two models. This can be used to quantify uncertainty for combinations of
models, or to construct test statistics for comparing different models or
ensembles of models fitted using the same training dataset. Specific examples
in this paper use boosted combinations of models like random forests and
M-estimators. We also investigate its application on neural networks and
ensembles of XGBoost models. We illustrate the efficacy of variance estimates
through extensive simulations and its application to the Beijing Housing data,
and demonstrate the theoretical consistency of the Infinitesimal Jackknife
covariance estimate.


  The natural alpha decay of 180W has been unambiguously detected for the first
time. The alpha peak is found in a (gamma,beta and neutron)-free background
spectrum. This has been achieved by the simultaneous measurement of phonon and
light signals with the CRESST cryogenic detectors. A half-life of T1/2 = (1.8
+- 0.2) x 10^18 y and an energy release of Q = (2516.4 +- 1.1 (stat.) +- 1.2
(sys.)) keV have been measured. New limits are also set on the half-lives of
the other naturally occurring tungsten isotopes.


  The discovery of planets in binaries is one the most interesting outcomes of
planetary research. With the growing number of discoveries has also grown the
interest on describing their formation, long-term evolution and potential
habitability. In this work we revisit the dynamics of planets in S-type binary
systems. For that purpose we develop explicit formulas for the secularized
octupolar Hamiltonian, coupled with general relativistic corrections and
non-conservative interactions. We implemented those formulas in an open-source
package \texttt{SecDev3B}, that can be used to reproduce our results or test
improved versions of the models. In order to test it, we study the long-term
dynamical evolution of S-type binary planets during the pre-main-sequence phase
of stellar evolution. During that phase, stellar radius significantly changes
in timescales similar to secular timescales. We hypothesize that when
close-encounters between the planet and its host star happens (e.g. via
Lidov-Kozai effect), particularities in the secular formalism plus changes in
stellar radius may alter significantly the dynamical evolution. We study the
well-known binary planet HD 80606b and found that an octupolar expansion of the
conservative Hamiltonian is required to properly predict its dynamical
evolution. We also apply the dynamical model, enriched with results coming from
stellar evolutionary models, to demonstrate that in S-type systems around
low-mass stars, with relative high inclinations ($\itot\ge 60^\circ$), moderate
eccentricities ($0.2\le e\le 0.4$) and planets located around 1 AU, the
evolution of stellar radius during the first few hundreds of Myr, alters
significantly the timescales of dynamical evolution.


  One of the most interesting tools that have recently entered the data science
toolbox is topological data analysis (TDA). With the explosion of available
data sizes and dimensions, identifying and extracting the underlying structure
of a given dataset is a fundamental challenge in data science, and TDA provides
a methodology for analyzing the shape of a dataset using tools and prospects
from algebraic topology. However, the computational complexity makes it quickly
infeasible to process large datasets, especially those with high dimensions.
Here, we introduce a preprocessing strategy called the Characteristic Lattice
Algorithm (CLA), which allows users to reduce the size of a given dataset as
desired while maintaining geometric and topological features in order to make
the computation of TDA feasible or to shorten its computation time. In
addition, we derive a stability theorem and an upper bound of the barcode
errors for CLA based on the bottleneck distance.


  We show that the ring of Siegel-Jacobi forms of fixed degree and of fixed or
bounded ratio between weight and index is not finitely generated. Our main tool
is the theory of toroidal b-divisors and their relation to convex geometry. As
a byproduct of our methods, we prove a conjecture of Kramer about the
representation of all Siegel-Jacobi forms as sections of certain line bundles
and we recover a formula due to Tai for the asymptotic dimension of the space
of Siegel-Jacobi forms of given ratio between weight and index.


  The flavor ratio of the atmospheric neutrino flux and its zenith angle
dependence have been studied in the multi-GeV energy range using an exposure of
25.5 kiloton-years of the Super-Kamiokande detector. By comparing the data to a
detailed Monte Carlo simulation, the ratio $(\mu/e)_{DATA}/(\mu/e)_{MC}$ was
measured to be $0.66\pm0.06(stat.)\pm0.08(sys.)$. In addition, a strong
distortion in the shape of the $\mu$-like event zenith angle distribution was
observed. The ratio of the number of upward to downward $\mu$-like events was
found to be 0.52$^{+0.07}_{-0.06}(stat.)\pm0.01(sys.)$, with an expected value
of $0.98\pm0.03(stat.)\pm0.02(sys.)$, while the same ratio for the $e$-like
events was consistent with unity.


  M-estimators offer simple robust alternatives to the maximum likelihood
estimator. Much of the robustness literature, however, has focused on the
problems of location, location-scale and regression estimation rather than on
estimation of general parameters. The density power divergence (DPD) and the
logarithmic density power divergence (LDPD) measures provide two classes of
competitive M-estimators (obtained from divergences) in general parametric
models which contain the MLE as a special case. In each of these families, the
robustness of the estimator is achieved through a density power down-weighting
of outlying observations. Both the families have proved to be very useful tools
in the area of robust inference. However, the relation and hierarchy between
the minimum distance estimators of the two families are yet to be
comprehensively studied or fully established. Given a particular set of real
data, how does one choose an optimal member from the union of these two classes
of divergences? In this paper, we present a generalized family of divergences
incorporating the above two classes; this family provides a smooth bridge
between the DPD and the LDPD measures. This family helps to clarify and settle
several longstanding issues in the relation between the important families of
DPD and LDPD, apart from being an important tool in different areas of
statistical inference in its own right.


  The standard $1-$equation model \ of turbulence was first derived by Prandtl
and has evolved to be a common method for practical flow simulations. Five
fundamental laws that any URANS model should satisfy are \[ \begin{array}
[c]{ccc} \textbf{1.} & \text{Time window:} & \begin{array} [c]{c}
\tau\downarrow 0\text{ implies }v_{\text{{\small URANS}}}\rightarrow
u_{\text{{\small NSE}}}\text{ \&}\\ \text{ }\tau\uparrow\text{implies
}\nu_{T}\uparrow \end{array} \\ \textbf{2.} & l(x)=0\ \text{at walls:} &
l(x)\rightarrow 0\text{ as }x\rightarrow walls,\\ \textbf{3.} & \text{ Bounded
energy:} & \sup_{t}\int\frac{1} {2}|v(x,t)|^{2}+k(x,t)dx<\infty\\ \textbf{4.} &
\begin{array} [c]{c} \text{Statistical }\\ \text{equilibrium:} \end{array} &
\lim\sup_{T\rightarrow\infty}\frac{1}{T}\int_{0}^{T}\varepsilon
_{\text{model}}(t)dt=\mathcal{O}\left( \frac{U^{3}}{L}\right) \\ \textbf{5.} &
\begin{array} [c]{c} \text{Backscatter}\\ \text{possible:} \end{array} &
\text{(without negative viscosities)} \end{array} \] This report proves that a
\textit{kinematic} specification of the model's turbulence lengthscale by \[
l(x,t)=\sqrt{2}k^{1/2}(x,t)\tau\text{ }, \] where $\tau$\ is the time filter
window, results in a $1-$equation model satisfying Conditions 1,2,3,4 without
model tweaks, adjustments or wall damping multipliers.


  We prove that for any closed, connected, oriented 3-manifold M, there exists
an infinite family of 2-fold branched covers of M that are hyperbolic
3-manifolds and surface bundles over the circle with arbitrarily large volume.


  Functional linear models are one of the most fundamental tools to assess the
relation between two random variables of a functional or scalar nature. This
contribution proposes a goodness-of-fit test for the functional linear model
with functional response that neatly adapts to functional/scalar
responses/predictors. In particular, the new goodness-of-fit test extends a
previous proposal for scalar response. The test statistic is based on a
convenient regularized estimator, is easy to compute, and is calibrated through
an efficient bootstrap resampling. A graphical diagnostic tool, useful to
visualize the deviations from the model, is introduced and illustrated with a
novel data application. The R package goffda implements the proposed methods
and allows for the reproducibility of the data application.


  General-relativistic stable spacetimes can be made unstable under the
presence of certain nonminimally coupled free scalar fields. In this paper, we
analyze the evolution of linear scalar-field perturbations in spherically
symmetric spacetimes and compare the classical stability analysis with a
recently discussed quantum field one. In particular, it is shown that vacuum
fluctuations lead to natural seeds for the unstable phase, whereas in the
classical framework the presence of such seeds in the initial conditions must
be assumed.


  Several tasks in machine learning are evaluated using non-differentiable
metrics such as mean average precision or Spearman correlation. However, their
non-differentiability prevents from using them as objective functions in a
learning framework. Surrogate and relaxation methods exist but tend to be
specific to a given metric.
  In the present work, we introduce a new method to learn approximations of
such non-differentiable objective functions. Our approach is based on a deep
architecture that approximates the sorting of arbitrary sets of scores. It is
trained virtually for free using synthetic data. This sorting deep (SoDeep) net
can then be combined in a plug-and-play manner with existing deep
architectures. We demonstrate the interest of our approach in three different
tasks that require ranking: Cross-modal text-image retrieval, multi-label image
classification and visual memorability ranking. Our approach yields very
competitive results on these three tasks, which validates the merit and the
flexibility of SoDeep as a proxy for sorting operation in ranking-based losses.


  Probability distributions can be read as simple expressions of information.
Each continuous probability distribution describes how information changes with
magnitude. Once one learns to read a probability distribution as a measurement
scale of information, opportunities arise to understand the processes that
generate the commonly observed patterns. Probability expressions may be parsed
into four components: the dissipation of all information, except the
preservation of average values, taken over the measurement scale that relates
changes in observed values to changes in information, and the transformation
from the underlying scale on which information dissipates to alternative scales
on which probability pattern may be expressed. Information invariances set the
commonly observed measurement scales and the relations between them. In
particular, a measurement scale for information is defined by its invariance to
specific transformations of underlying values into measurable outputs.
Essentially all common distributions can be understood within this simple
framework of information invariance and measurement scale.


  The GENIUS (\underline {Ge}rmanium in Liquid \underline {Ni}trogen \underline
{U}nderground \underline {S}etup) project has been proposed in 1997
\cite{KK-BEY97} as first third generation double beta decay project, with a
sensitivity aiming down to a level of an effective neutrino mass of $<m>\sim$
0.01 - 0.001 eV. Such sensitivity has been shown to be indispensable to solve
the question of the structure of the neutrino mass matrix which cannot be
solved by neutrino oscillation experiments alone \cite{KKPS}. It will allow
broad access also to many other topics of physics beyond the Standard Model of
particle physics at the multi-TeV scale. For search of cold dark matter GENIUS
will cover almost the full range of the parameter space of predictions of SUSY
for neutralinos as dark matter \cite{KK-Ram,Bed-KK2}. Finally, GENIUS has the
potential to be the first real-time detector for low-energy (pp and $^7{Be}$)
solar neutrinos \cite{Bau-KK,KKPropos99}. A GENIUS-Test Facility has just been
funded and will come into operation by end of 2001.


  Theoretical and empirical evidence indicates that the depth of neural
networks is crucial for their success. However, training becomes more difficult
as depth increases, and training of very deep networks remains an open problem.
Here we introduce a new architecture designed to overcome this. Our so-called
highway networks allow unimpeded information flow across many layers on
information highways. They are inspired by Long Short-Term Memory recurrent
networks and use adaptive gating units to regulate the information flow. Even
with hundreds of layers, highway networks can be trained directly through
simple gradient descent. This enables the study of extremely deep and efficient
architectures.


  We show that L\"uck's conjecture on torsion growth in homology implies that
two 3-manifolds have equal volume if the fundamental groups have the same set
of finite quotients.


  We report the detection of electron spin resonance (ESR) in individual dimers
of the stable free radical 2,2,6,6-tetramethyl-piperidine-1-oxyl (TEMPO). ESR
is measured by the current fluctuations in a scanning tunnelling microscope
(ESR-STM method). The multi-peak power spectra, distinct from macroscopic data,
are assigned to dimers having exchange and Dzyaloshinskii-Moriya interactions
in presence of spin-orbit coupling. These interactions are generated in our
model by interfering electronic tunneling pathways from tip to sample via the
dimer's two molecules. This is the first demonstration that tunneling via two
spins is a valid mechanism of the ESR-STM method.


  The operation of an interface dynamo (as has been suggested for the Sun and
other stars with convective envelopes) relies crucially upon the effective
transport of magnetic flux between two spatially disjoint generation regions.
In the simplest models communication between the two regions is achieved solely
by diffusion. Here we incorporate a highly simplified anisotropic transport
mechanism in order to model the net effect of flux conveyance by magnetic
pumping and by magnetic buoyancy. We investigate the influence of this
mechanism on the efficiency of kinematic dynamo action. It is found that the
effect of flux transport on the efficiency of the dynamo is dependent upon the
spatial profile of the transport. Typically, transport hinders the onset of
dynamo action and increases the frequency of the dynamo waves. However, in
certain cases there exists a preferred magnitude of transport for which dynamo
action is most efficient. Furthermore, we demonstrate the importance of the
imposition of boundary conditions in drawing conclusions on the role of
transport.


  Equationally compact subgroups of countable groups were introduced by
Banaschewski. For all known cases the orbit closure of such a subgroup is a
countable subset in the space of subgroups and has finite Cantor-Bendixson
rank. We show that there exists a finitely generated group $\Gamma$ such that
for any countable ordinal $\alpha$ we have an equationally compact subgroup
$H\subset \Gamma$ for which the Cantor-Bendixson rank of the orbit closure of
$H$ equals to $\alpha+2$. Then we give an explicite construction of continuum
many equationally compact subgroups of $\Gamma$ such that the associated
ergodic Bernoulli shift actions are pairwise weakly incomparable. We also
answer two questions on equational compactness posed by Prest and Rajani.


  Hybrid inflation, driven by a Fayet-Iliopoulos (FI) D term, is an intriguing
inflationary model. In its usual formulation, it however suffers from several
shortcomings. These pertain to the origin of the FI mass scale, the stability
of scalar fields during inflation, gravitational corrections in supergravity,
as well as to the latest constraints from the cosmic microwave background. We
demonstrate that these issues can be remedied if D-term inflation is realized
in the context of strongly coupled supersymmetric gauge theories. We suppose
that the D term is generated in consequence of dynamical supersymmetry
breaking. Moreover, we assume canonical kinetic terms in the Jordan frame as
well as an approximate shift symmetry along the inflaton direction. This
provides us with a unified picture of D-term inflation and high-scale
supersymmetry breaking. The D term may be associated with a gauged U(1)_B-L, so
that the end of inflation spontaneously breaks B-L in the visible sector.


  In 2015 Berezhiani & Khoury proposed a Superfluid Dark Matter (SFDM) model
where dark matter condenses and forms a superfluid on galactic scales. In the
superfluid state phonons interact with baryons, resulting in a behavior similar
to that of Modified Newtonian Dynamics (MOND). If one assumes that the DM
condensate rotates along with the galaxy, a grid of vortices should form
throughout the superfluid component if the rotation is fast enough. We aim to
investigate the size and impact of the vortices on surrounding baryons, and to
further investigate the parameter space of the model. We also look for a
possible vortex solution of the Lagrangian presented for the SFDM theory. We
first take a simple approach and investigate vortex properties in a constant
density DM halo, applying knowledge from condensed matter physics. We then use
the zero-temperature condensate density profile as a template to vary the DM
particle mass and the energy scale, $\Lambda$, of the SFDM model. Further, we
attempt to find a vortex solution of the theory by extracting the
Euler-Lagrange equation with respect to the modulus of the condensate
wavefunction from the full relativistic SFDM Lagrangian. For the constant
density approach we find that the vortices are on millimeter scale, and
separated by distances $\sim0.002\,\rm{AU}$. The parameter space of the model
is found to be substantial and a reduction in the DM particle mass leads to
larger vortices with a higher energy. However, none of the parameter
combinations explored here give both realistic values of $\Lambda$ and vortices
energetic enough to have an observational impact on the galaxy as a whole. The
vortex equation extracted from the Lagrangian of the model is unstable, and no
solution exhibiting the standard properties of a vortex solution is found.


  We explore the absorption and scattering properties of one dimensional
parity-time ($\mathcal{PT}$)-symmetric photonic crystal. In addition to the
familiar transmittance and reflectance, we give the definition of the
generalized absorptance to include the amplifying effect of the dielectric with
negative imaginary part of the permittivity, moreover, we present the
mathematical expressions of the transmittance, reflectances and absorptances
from both sides of this photonic crystal with N periods in terms of the
elements of the transfer matrix of the primitive cell. The complex band
structure of this photonic crystal is studied and the corresponding evolutions
of the exceptional points, $\mathcal{PT}$-exact phase and $\mathcal{PT}$-broken
phase are disclosed. Near the exceptional points, we find some singular
behaviors, the transmittance and reflectances from both sides are all greater
than one and even all reach large values at the same time, then the
corresponding absorptances from both sides are negative. In the band gap, the
transmittance is zero, the reflectance form one side can be very large, while
the reflectance from the other side is very small, we call this phenomenon
unidirectional weak visibility. We believe that these phenomena are very
beneficial for the design of the optical devices.


  In this paper we develop a new method to study Iwasawa theory and Eisenstein
families for unitary groups $\mathrm{U}(r,s)$ of general signature over a
totally real field $F$. As a consequence we prove that for a motive
corresponding to a regular algebraic cuspidal automorphic representation $\pi$
on $\mathrm{U}(r,s)_{/F}$ which is ordinary at $p$, twisted by a Hecke
character, if its Selmer group has rank $0$, then the corresponding central
$L$-value is nonzero. This generalizes a result of Skinner-Urban in their ICM
2006 report in the special case when $F=\mathbb{Q}$ and the motive is conjugate
self-dual. Along the way we also obtain $p$-adic functional equations for the
corresponding $p$-adic $L$-functions and $p$-adic families of Klingen
Eisenstein series. Our method does not involve computing Fourier-Jacobi
coefficients (as opposed to previous work which only work in low rank cases,
e.g. $\mathrm{U}(1,1)$, $\mathrm{U}(2,0)$ and $\mathrm{U}(1,0)$) whose
automorphic interpretation is unclear in general.


  We analyze the nonlinear transport properties of a bilayer exciton condensate
that is contacted by four metallic leads by calculating the full counting
statistics of electron transport for arbitrary system parameters. Despite its
formal similarity to a superconductor the transport properties of the exciton
condensate turn out to be completely different. We recover the generic features
of exciton condensates such as counterpropagating currents driven by excitonic
Andreev reflections and make predictions for nonlinear transconductance between
the layers as well as for the current (cross)correlations and generalized
Johnson-Nyquist relationships. Finally, we explore the possibility of
connecting another mesoscopic system (in our case a quantum point contact) to
the bottom layer of the exciton condensate and show how the excitonic Andreev
reflections can be used for transforming voltage at the nanoscale.


  In the spirit of geometric quantisation we consider representations of the
Heisenberg(--Weyl) group induced by hypercomplex characters of its centre. This
allows to gather under the same framework, called p-mechanics, the three
principal cases: quantum mechanics (elliptic character), hyperbolic mechanics
and classical mechanics (parabolic character). In each case we recover the
corresponding dynamic equation as well as rules for addition of probabilities.
Notably, we are able to obtain whole classical mechanics without any kind of
semiclassical limit h->0.
  Keywords: Heisenberg group, Kirillov's method of orbits, geometric
quantisation, quantum mechanics, classical mechanics, Planck constant, dual
numbers, double numbers, hypercomplex, jet spaces, hyperbolic mechanics,
interference, Segal--Bargmann representation, Schroedinger representation,
dynamics equation, harmonic and unharmonic oscillator, contextual probability


  In this review, the status of measurements of the matter density (Omega), the
vaccuum energy density or cosmological constant (Lambda), the Hubble constant
(H0), and ages of the oldest measured objects (t0) are summarized. Measurements
of the statistics of gravitational lenses and strong gravitational lensing are
discussed in the context of limits on Lambda. Three separate routes to the
Hubble constant are considered: the measurement of time delays in
multiply-imaged quasars, the Sunyaev-Zel'dovich effect in clusters, and
Cepheid-based extragalactic distances. Globular-cluster ages plus a new age
measurement based on radioactive dating of thorium in a metal-poor star are
briefly summarized. Many recent, independent dynamical measurements are
yielding a low value for the matter density (omega ~ 0.2 - 0.3). A wide range
of Hubble constant measurements appear to be converging in the range of 60-80
km/sec/Mpc. Particular attention is paid to sources of systematic error and the
assumptions that underlie many of the measurement methods.


  In recent years polymer translocation, i.e., transport of polymeric molecules
through nanometer-sized pores and channels embedded in membranes, has witnessed
strong advances. It is now possible to observe single-molecule polymer dynamics
during the motion through channels with unprecedented spatial and temporal
resolution. These striking experimental studies have stimulated many
theoretical developments. In this short theory-experiment review, we discuss
recent progress in this field with a strong focus on non-equilibrium aspects of
polymer dynamics during the translocation process.


  We study the evolution of the Kondo effect in heavy fermion compounds,
Yb(Fe$_{1-x}$Co$_{x}$)$_{2}$Zn$_{20}$ (0$\leqslant$ x $\leqslant$ 1), by means
of temperature-dependent electric resistivity and specific heat. The ground
state of YbFe$_2$Zn$_{20}$ can be well described by a Kondo model with
degeneracy $N$ = 8 and a $T_K\sim$30 K. In the presence of a very similar total
CEF splitting with YbFe$_2$Zn$_{20}$, the ground state of YbCo$_2$Zn$_{20}$ is
close to a Kondo state with degeneracy $N$ = 2 and a much lower $T_K\sim$ 2 K.
Upon Co substitution, the coherence temperature of YbFe$_2$Zn$_{20}$ is
suppressed, accompanied by an emerging Schottky-like feature in specific heat
associated with the thermal depopulation of CEF levels upon cooling. For
0.4$\lesssim$ x $\lesssim$ 0.9, the ground state remains roughly the same which
can be qualitatively understood by Kondo effect in the presence of CEF
splitting. There is no clear indication of Kondo coherence observable in
resistivity within this substitution range down to 500 mK. The coherence
re-appears at around x$\gtrsim$ 0.9 and the coherence temperature increases
with higher Co concentration levels.


  Apart from its debatable correctness, we examine the perturbative stability
of the recently proposed cosmology from quantum potential. We find that the
proposed quantum corrections invoke additional parameters which apparently
introduce perturbative instability to the Universe.


  We report on the development of a 10B conversion layer optimized for
ultra-cold neutron detection with silicon detectors. The efficiency of this
layer is high and roughly uniform over a large ultra-cold neutron velocity
range. The designed titanium-boron-nickel multilayer film was deposited on
silicon using a microwave plasma-assisted co-sputtering method (first, for test
purpose, on silicon wafers, then directly on the surface of a CCD sensor). The
obtained sensor was then tested using both cold and ultra-cold neutrons.


  In this paper, we study the single-item economic lot-sizing problem with
production cost functions that are piecewise linear. The lot-sizing problem
stands as a foundational cornerstone within the domain of lot-sizing problems.
It is also applicable to a variety of important production planning problems
which are special cases to it according to \cite{ou}. The problem becomes
intractable when $m$, the number of different breakpoints of the
production-cost function is variable as the problem was proven NP-hard by
\cite{Florian1980}. For a fixed $m$ an $O(T^{2m+3})$ time algorithm was given
by \cite{Koca2014} which was subsequently improved to $O(T^{m+2}\log(T))$ time
by \cite{ou} where $T$ is the number of periods in the planning
horizon.\newline We introduce a more efficient $O(T^{m+2})$ time algorithm for
this problem which improves upon the previous state-of-the-art algorithm by Ou
and which is derived using several novel algorithmic techniques that may be of
independent interest.


  (Abridged): The total populations of globular cluster systems (GCSs) are
discussed in terms of their connection to the efficiency of globular cluster
formation---the mass fraction of star-forming gas that was able to form bound
stellar clusters rather than isolated stars or unbound associations---in galaxy
halos. Observed variations in GCS specific frequencies (S_N=N_gc/L_gal), both
as a function of galactocentric radius in individual systems and globally
between entire galaxies, are reviewed in this light. It is argued that trends
in S_N do not reflect any real variation in the underlying efficiency of
cluster formation; rather, they result from ignoring the hot gas in many large
ellipticals. This claim is checked and confirmed in each of M87, M49, and NGC
1399, for which existing data are combined to show that the volume density
profile of globular clusters, rho_cl, is directly proportional to the sum of
(rho_gas+rho_stars) at large radii. The constant of proportionality is the same
in each case: epsilon=0.0026 +/- 0.0005 in the mean. This is identified with
the globular cluster formation efficiency. The implication that epsilon might
have had a universal value is supported by data on the GCSs of 97 early-type
galaxies, on the GCS of the Milky Way, and on the ongoing formation of open
clusters. These results have specific implications for some issues in GCS and
galaxy formation, and they should serve as a strong constraint on more general
theories of star and cluster formation.


  UKQCD's dynamical fermion project uses the Generalised Hybrid Monte-Carlo
(GHMC) algorithm to generate QCD gauge configurations for a non-perturbatively
O(a) improved Wilson action with two degenerate sea-quark flavours. We describe
our implementation of the algorithm on the Cray-T3E, concentrating on issues
arising from code verification and performance optimisation, such as parameter
tuning, reversibility, the effect of precision, the choice of matrix inverter
and the behaviour of different molecular dynamics integration schemes.


  In this work we consider fermionic zero modes in the external scalar and
electromagnetic field forming the vortex on a sphere. We find the
correspondence between the equations for the fermions in different dimensions,
find their explicit expressions through the vortex fields in case of massless
fermions, asymptotics near the poles in case of massive fermions and check the
number of the solutions by proving index theorem for the fermions on a sphere.
As a part of deriving the index, we write a detailed calculation of the Green
function of the Heat equation.


  The aim of this article is to generalize the notion of the cut locus and to
get the structure theorem for it. For this purpose, we first introduce a class
of 1-Lipschitz functions, each member of which is called an {\it almost
distance function}. Typical examples of an almost distance function are the
distance function from a point and the Busemann function on a complete
Riemannian manifold. The generalized notion of the cut locus in this paper is
called the {\it singular locus} of an almost distance function. The singular
locus consists of the upper one and the lower one. The upper singular locus
coincides with the cut locus of a point for the distance function from the
point, and the lower singular locus coincides with the set of all copoints of a
ray when the almost distance function is the Busman function of the ray.
Therefore, it is possible to treat the cut locus of a closed subset and the set
of copoints of a ray in a unified way by introducing the singular locus for the
almost distance function. In this article, we obtain the structure theorem
(Theorem B) for the singular locus of an almost distance function on a
2-dimensional Finsler manifold that contains both structure theorems ([S],
Theorem B) and [Sa,Theorem 2.13]) for the cut locus and the set of copoints of
a ray as a corollary.


  Understanding the elementary mechanism for the dissipation of vortex energy
in quantum liquids is one central issue in quantum hydrodynamics, such as
quantum turbulence in systems ranging from neutron stars to atomic condensates.
In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature,
besides the vortex drift-out process from the boundary, vortex-antivortex pair
can annihilate in the bulk, but controversy remains on the number of vortices
involved in the annihilation process. We find there exists a dynamical
transition from four-body to three-body vortex annihilation processes with the
time evolution in a boundary-less uniform quasi-2D BEC. Such dynamical
transition depends on the initial vortex pair density, and occurs when the
sound waves generated in the vortex annihilation process surpass a critical
energy. With the confinement along the third direction is relaxed in a quasi-2D
BEC, the critical sound wave energy decreases due to the 3D vortex line curve
and reconnection, shifting the dynamical transition to the early time. Our work
reveals an elementary mechanism for the dissipation of vortex energy that may
help understand exotic matter and dynamics in quantum liquids.


  Optical activation of material properties illustrates the potentials held by
tuning light-matter interactions with impacts ranging from basic science to
technological applications. Here, we demonstrate for the first time that
composite nanostructures providing nonlocal environments can be engineered to
optically trigger photoinduced charge transfer dynamic (CTD) modulations in the
solid state. The nanostructures herein explored lead to unprecedented
out-of-phase behaviour between charge separation and recombination dynamics,
along with linear CTD variations with the optical-field amplitude. Using
transient absorption spectroscopy, up to 270 % increase in charge separation
rate is obtained in organic semiconductor thin films. We provide evidences that
composite nanostructures allow for surface photovoltages to be created, which
kinetics vary with the composite architecture and last beyond optical pulse
temporal characteristics. Furthermore, by generalizing Marcus theory framework,
we explain why CTD modulations can only be unveiled when optic field effects
are enhanced by nonlocal image dipole interactions. Demonstrating that
composite nanostructures can be designed to use optical fields as CTD remote
actuators opens the path for their use in practical and original applications
ranging from photochemistry to optoelectronics.


  An infinitely smooth symmetric convex body $K\subset\mathbb R^d$ is called
$k$-separably integrable, $1\leq k<d$, if its $k$-dimensional isotropic volume
function $V_{K,H}(t)=\mathcal H^d(\{\boldsymbol x\in
K:\mathrm{dist}(\boldsymbol x,H^\perp)\leq t\})$ can be written as a finite sum
of products in which the dependence on $H\in\mathrm{Gr}(k,\mathbb R^d)$ and
$t\in\mathbb R$ is separated. In this paper, we will obtain a complete
classification of such bodies. Namely, we will prove that if $d-k$ is even,
then $K$ is an ellipsoid, and if $d-k$ is odd, then $K$ is a Euclidean ball.
This generalizes the recent classification of polynomially integrable convex
bodies in the symmetric case.


  Entanglement is an extraordinary feature of quantum mechanics. Sources of
entangled optical photons were essential to test the foundations of quantum
physics through violations of Bell's inequalities. More recently, entangled
many-body states have been realized via strong non-linear interactions in
microwave circuits with superconducting qubits. Here we demonstrate a
chip-scale source of entangled optical and microwave photonic qubits. Our
device platform integrates a piezo-optomechanical transducer with a
superconducting resonator which is robust under optical illumination. We drive
a photon-pair generation process and employ a dual-rail encoding intrinsic to
our system to prepare entangled states of microwave and optical photons. We
place a lower bound on the fidelity of the entangled state by measuring
microwave and optical photons in two orthogonal bases. This entanglement source
can directly interface telecom wavelength time-bin qubits and GHz frequency
superconducting qubits, two well-established platforms for quantum
communication and computation, respectively.


  The launch of the Hinode satellite has allowed unprecedented high resolution,
stable images of solar quiescent prominences to be taken over extended periods
of time.
  These new images led to the discovery of dark upflows that propagated from
the base of prominences developing highly turbulent profiles.
  As yet, how these flows are driven is not fully understood.
  To study the physics behind this phenomena we use 3-D magnetohydrodynamic
(MHD) simulations to investigate the nonlinear stability of the
Kippenhahn-Shl\"{u}ter prominence model to the magnetic Rayleigh-Taylor
instability.
  The model simulates the rise of a buoyant tube inside a quiescent prominence,
where the upper boundary between the tube and prominence model is perturbed to
excite the interchange of magnetic field lines.
  We found upflows of constant velocity (maximum found 6\,km\,s$^{-1}$) and a
maximum plume width $\approx 1500$\,km which propagate through a height of
approximately 6\,Mm in the no guide field case. The case with the strong guide
field (initially $B_y=2B_x$) results in a large plume that rises though the
prominence model at $\sim 5$\,km\,s$^{-1}$ with width $\sim 900$\,km (resulting
in width of 2400\,km when viewed along the axis of the prominence) reaching a
height of $\sim 3.1$\,Mm. In both cases nonlinear processes were important for
determining plume dynamics.


  Covariant loop gravity comes out of the canonical analysis of the Palatini
action and the use of the Dirac brackets arising from dealing with the second
class constraints (``simplicity'' constraints). Within this framework, we
underline a quantization ambiguity due to the existence of a family of possible
Lorentz connections. We show the existence of a Lorentz connection generalizing
the Ashtekar-Barbero connection and we loop-quantize the theory showing that it
leads to the usual SU(2) Loop Quantum Gravity and to the area spectrum given by
the SU(2) Casimir. This covariant point of view allows to analyze closely the
drawbacks of the SU(2) formalism: the quantization based on the (generalized)
Ashtekar-Barbero connection breaks time diffeomorphisms and physical outputs
depend non-trivially on the embedding of the canonical hypersurface into the
space-time manifold. On the other hand, there exists a true space-time
connection, transforming properly under all diffeomorphisms. We argue that it
is this connection that should be used in the definition of loop variables.
However, we are still not able to complete the quantization program for this
connection giving a full solution of the second class constraints at the
Hilbert space level. Nevertheless, we show how a canonical quantization of the
Dirac brackets at a finite number of points leads to the kinematical setting of
the Barrett-Crane model, with simple spin networks and an area spectrum given
by the SL(2,C) Casimir.


  This document contains a review on the quark model, prepared for lectures at
the Niccolo Cabeo School at Ferrara in May 2012. It includes some historical
aspects, the spectral properties of the 2-body and 3-body Schroedinger
operators applied to mesons and baryons, the link between meson and baryon
spectra, the role of flavour independence, and the speculations about stable or
metastable multiquarks. The analogies between few-charge systems and few-quark
bound states will be underlined.


  The transverse momentum (pt) dependence, the centrality dependence and the
rapidity dependence of the elliptic flow of thermal photons in Au+Au collisions
at $\sqrt{s_{NN}}=200$ GeV are predicted, based on a three-dimensional ideal
hydrodynamic description of the hot and dense matter. The elliptic flow
parameter $v_{2}$, i.e. the second Fourier coefficient of azimuthal
distribution, of thermal photons, first increases with $\pt$ and then decreases
for $\pt>$ 2 GeV/$c$, due to the weak transverse flow at the early stage. The
$\pt$-integrated $v_{2}$ first increases with centrality, reaches a maximum at
about 50% centrality, and decreases. The rapidity dependence of the elliptic
flow $v_{2}(y)$ of direct photons (mainly thermal photons) is very sensitive to
the initial energy density distribution along longitudinal direction, which
provides a useful tool to extract the realistic initial condition from
measurements.


  We propose a novel Riemannian manifold preconditioning approach for the
tensor completion problem with rank constraint. A novel Riemannian metric or
inner product is proposed that exploits the least-squares structure of the cost
function and takes into account the structured symmetry that exists in Tucker
decomposition. The specific metric allows to use the versatile framework of
Riemannian optimization on quotient manifolds to develop preconditioned
nonlinear conjugate gradient and stochastic gradient descent algorithms for
batch and online setups, respectively. Concrete matrix representations of
various optimization-related ingredients are listed. Numerical comparisons
suggest that our proposed algorithms robustly outperform state-of-the-art
algorithms across different synthetic and real-world datasets.


  We study properties of a class of spin singlet Mott states for arbitrary spin
S bosons on a lattice, with particle number per cite n=S/l+1, where l is a
positive integer. We show that such a singlet Mott state can be mapped to a
bosonic Laughlin wave function on the sphere with a finite number of particles
at filling {\nu}=1/2l. Spin, particle and hole excitations in the Mott state
are discussed, among which the hole excitation can be mapped to the quasi-hole
of the bosonic Laughlin wave function. We show that this singlet Mott state can
be realized in a cold atom system on optical lattice, and can be identified
using Bragg spectroscopy and Stern-Gerlach techniques. This class of singlet
Mott states may be generalized to simulate bosonic Laughlin states with filling
{\nu}=q/2l.


  In our recent paper W.S. Rossi, P. Frasca and F. Fagnani, "Average resistance
of toroidal graphs", SIAM Journal on Control and Optimization,
53(4):2541--2557, 2015, we studied how the average resistances of
$d$-dimensional toroidal grids depend on the graph topology and on the
dimension of the graph. Our results were based on the connection between
resistance and Laplacian eigenvalues. In this note, we contextualize our work
in the body of literature about random walks on graphs. Indeed, the average
effective resistance of the $d$-dimensional toroidal grid is proportional to
the mean hitting time of the simple random walk on that grid. If $d\geq3 $,
then the average resistance can be bounded uniformly in the number of nodes and
its value is of order $1/d$ for large $d$.


  With the relentless growth of the wind industry, there is an imperious need
to design automatic data-driven solutions for wind turbine maintenance. As
structural health monitoring mainly relies on visual inspections, the first
stage in any automatic solution is to identify the blade region on the image.
Thus, we propose a novel segmentation algorithm that strengthens the U-Net
results by a tailored loss, which pools the focal loss with a contiguity
regularization term. To attain top performing results, a set of additional
steps are proposed to ensure a reliable, generic, robust and efficient
algorithm. First, we leverage our prior knowledge on the images by filling the
holes enclosed by temporarily-classified blade pixels and by the image
boundaries. Subsequently, the mislead classified pixels are successfully
amended by training an on-the-fly random forest. Our algorithm demonstrates its
effectiveness reaching a non-trivial 97.39% of accuracy.


  We have derived a new photographic photometry and proper motions for 20000
stars with completeness to V = 18 in the direction of galactic center at the
intermediate latitude (l = 3 deg,b = 47 deg; alpha(1950)=15h 18m, delta(1950) =
+02deg 16') for a 15.5 sq deg field. The combination of four glass copies of
the Palomar Observatory Sky Survey (i.e. POSS 1402 E&O and POSS 1429 E&O) has
been used as a first epoch for proper motion determination. The random error of
the proper motions is approximately 0.''3/cen to V=17. The photometric accuracy
ranges between 0.07 to 0.10 in the V, B and U bands. We stress the importance
of the magnitude and color effects in astrometric surveys of field stars. Using
color-magnitude diagrams of a few cluster member stars, a new distance of
6.9+-0.5 kpc is derived for M5 and 20.3+-0.8 kpc for Pal 5 globular clusters.
This is in good agreement with other determinations. We have analyzed the
components of U+W and V galactic space motions resulting from the accurate
proper motions survey. No dependence with z distance is found in the asymmetric
drift of the thick disk population. New estimates of the parameters of the
velocity ellipsoid have been derived for the thin disk, thick disk and halo
populations of the Galaxy.


  Nonequilibria show currents that are maintained as the result of a steady
driving. We ask here what decides their direction. It is not only the second
law, or the positivity of the entropy production that decides; also
non-dissipative aspects often matter and sometimes completely decide.


  A global effort to redefine our International System of Units (SI) is
underway and the change to the new system is expected to occur in 2018. Within
the newly redefined SI, the present base units will still exist but be derived
from fixed numerical values of seven reference constants. More specifically,
the unit of mass, the kilogram, will be realized through a fixed value of the
Planck constant $h$. For instance, a watt balance can be used to realize the
kilogram unit of mass within a few parts in $10^8$. Such a balance has been
designed and constructed at the National Institute of Standards and Technology.
For educational outreach and to demonstrate the principle, we have constructed
a LEGO tabletop watt balance capable of measuring a gram size mass to 1 %
relative uncertainty. This article presents the design, construction, and
performance of the LEGO watt balance and its ability to determine $h$


  We present observations spanning 355 orbital phases of HAT-P-7 observed by
Kepler from May 2009 to March 2011 (Q1-9). We find a shallower secondary
eclipse depth than initially announced, consistent with a low optical albedo
and detection of nearly exclusively thermal emission, without a reflected light
component. We find an approximately 10 ppm perturbation to the average transit
light curve near phase -0.02 that we attribute to a temperature decrease on the
surface of the star, phased to the orbit of the planet. This cooler spot is
consistent with planet-induced gravity darkening, slightly lagging the
sub-planet position due to the finite response time of the stellar atmosphere.
The brightness temperature of HAT-P-7b in the Kepler bandpass is T_B = 2733 +/-
21 K and the amplitude of the deviation in stellar surface temperature due to
gravity darkening is approximately -0.18 K. The detection of the spot is not
statistically unequivocal due its small amplitude, though additional Kepler
observations should be able to verify the astrophysical nature of the anomaly.


  In this article, using the recent theory of noncommutative motives, we
compute the additive invariants of orbifolds (equipped with a sheaf of Azumaya
algebras) using solely "fixed-point data". As a consequence, we recover, in a
unified and conceptual way, the original results of Vistoli concerning
algebraic K-theory, of Baranovsky concerning cyclic homology, of the second
author with Polishchuk concerning Hochschild homology, and of Baranovsky-Petrov
and Caldararu-Arinkin (unpublished) concerning twisted Hochschild homology; in
the case of topological Hochschild homology and periodic topological cyclic
homology, the aforementioned computation is new in the literature. As an
application, we verify Grothendieck's standard conjectures of type C and D, as
well as Voevodsky's smash-nilpotence conjecture, in the case of
"low-dimensional" orbifolds. Finally, we establish a result of independent
interest concerning nilpotency in the Grothendieck ring of an orbifold.


  We give a class of domains for which Fridman invariant and injectivity radius
function coincide with respect to Carath\'eodory metric. We give explicit
expressions of the squeezing functions for these domains and investigate some
of their properties.


  We present radio observations of the magnetic chemically peculiar Bp star HR
Lup (HD 133880) at 647 and 277 MHz with the GMRT. At both frequencies the
source is not detected but we are able to determine upper limits to the
emission. The 647 MHz limits are particularly useful, with a 5\sigma\ value of
0.45 mJy. Also, no large enhancements of the emission were seen. The
non-detections, along with previously published higher frequency detections,
provide evidence that an optically thick gyrosynchrotron model is the correct
mechanism for the radio emission of HR Lup.


  By the theory of Eisenstein series, generating functions of various divisor
functions arise as modular forms. It is natural to ask whether further divisor
functions arise systematically in the theory of mock modular forms. We
establish, using the method of Zagier and Zwegers on holomorphic projection,
that this is indeed the case for certain (twisted) "small divisors" summatory
functions $\sigma_{\psi}^{\mathrm{sm}}(n)$. More precisely, in terms of the
weight 2 quasimodular Eisenstein series $E_2(\tau)$ and a generic Shimura theta
function $\theta_{\psi}(\tau)$, we show that there is a constant
$\alpha_{\psi}$ for which $$ \mathcal{E}^{+}_{\psi}(\tau):=
\alpha_{\psi}\cdot\frac{E_2(\tau)}{\theta_{\psi}(\tau)}+
\frac{1}{\theta_{\psi}(\tau)} \sum_{n=1}^\infty \sigma^{\mathrm{sm}}_\psi(n)q^n
$$ is a half integral weight (polar) mock modular form. These include
generating functions for combinatorial objects such as the Andrews
$spt$-function and the "consecutive parts" partition function. Finally, in
analogy with Serre's result that the weight $2$ Eisenstein series is a $p$-adic
modular form, we show that these forms possess canonical congruences with
modular forms.


  We summarize the R&D activities on a novel semitransparent microstrip sensor
to be used on laser-based alignment systems for silicon trackers. The new
sensor is used both for particle tracking and laser detection. The aim of this
research line is to increase the optical transmittance (T) of Silicon
microstrips detectors to infrared light, introducing minor modifications to the
sensor design still suitable for its industrial production. The optical
simulations used in the sensor design have been experimentally validated
against several patterned material samples. This activities have been carried
out in the context of SiLC collaboration for the next International Linear
Collider.


  The recent release of ChatGPT has gained huge attention and discussion
worldwide, with responsible AI being a key topic of discussion. How can we
ensure that AI systems, including ChatGPT, are developed and adopted in a
responsible way? To tackle the responsible AI challenges, various ethical
principles have been released by governments, organisations, and companies.
However, those principles are very abstract and not practical enough. Further,
significant efforts have been put on algorithm-level solutions that only
address a narrow set of principles, such as fairness and privacy. To fill the
gap, we adopt a pattern-oriented responsible AI engineering approach and build
a Responsible AI Pattern Catalogue to operationalise responsible AI from a
system perspective. In this article, we first summarise the major challenges in
operationalising responsible AI at scale and introduce how we use the
Responsible AI Pattern Catalogue to address those challenges. We then examine
the risks at each stage of the chatbot development process and recommend
pattern-driven mitigations to evaluate the the usefulness of the Responsible AI
Pattern Catalogue in a real-world setting.


  The paper presents an approach to the modelling of epistemic uncertainty in
Conjunction Data Messages (CDM) and the classification of conjunction events
according to the confidence in the probability of collision. The approach
proposed in this paper is based on the Dempster-Shafer Theory (DSt) of evidence
and starts from the assumption that the observed CDMs are drawn from a family
of unknown distributions. The Dvoretzky-Kiefer-Wolfowitz (DKW) inequality is
used to construct robust bounds on such a family of unknown distributions
starting from a time series of CDMs. A DSt structure is then derived from the
probability boxes constructed with DKW inequality. The DSt structure
encapsulates the uncertainty in the CDMs at every point along the time series
and allows the computation of the belief and plausibility in the realisation of
a given probability of collision. The methodology proposed in this paper is
tested on a number of real events and compared against existing practices in
the European and French Space Agencies. We will show that the classification
system proposed in this paper is more conservative than the approach taken by
the European Space Agency but provides an added quantification of uncertainty
in the probability of collision.


  In this work we consider the computational approximation of a unique
continuation problem for the Helmholtz equation using a stabilized finite
element method. First conditional stability estimates are derived for which,
under a convexity assumption on the geometry, the constants grow at most
linearly in the wave number. Then these estimates are used to obtain error
bounds for the finite element method that are explicit with respect to the wave
number. Some numerical illustrations are given.


  The multiplicity fluctuations are studied in the van der Waals excluded
volume hadron-resonance gas model. The calculations are done in the grand
canonical ensemble within the Boltzmann statistics approximation. The scaled
variances for positive, negative and all charged hadrons are calculated along
the chemical freeze-out line of nucleus-nucleus collisions at different
collision energies. The multiplicity fluctuations are found to be suppressed in
the van der Waals gas. The numerical calculations are presented for two values
of hard-core hadron radius, $r=0.3$ fm and 0.5 fm, as well as for the upper
limit of the excluded volume suppression effects.


  In this paper, we study a new cyclic sieving phenomenon on the set
$\mathsf{SST}_n(\lambda)$ of semistandard Young tableaux with the cyclic action
$\mathsf{c}$ arising from its $U_q(\mathfrak{sl}_n)$-crystal structure. We
prove that if $\lambda$ is a Young diagram with $\ell(\lambda) < n$ and $\gcd(
n, |\lambda| )=1$, then the triple $\left( \mathsf{SST}_n(\lambda), \mathsf{C},
q^{- \kappa(\lambda)} s_\lambda(1,q, \ldots, q^{n-1}) \right) $ exhibits the
cyclic sieving phenomenon, where $\mathsf{C}$ is the cyclic group generated by
$\mathsf{c}$. We further investigate a connection between $\mathsf{c}$ and the
promotion $\mathsf{pr}$ and show the bicyclic sieving phenomenon given by
$\mathsf{c}$ and $\mathsf{pr}^n$ for hook shape.


  In this paper, the new formalism of thermodynamic geometry proposed in [1] is
employed in investigating phase transition points and the critical behavior of
a Gauss Bonnet-AdS black hole in four dimensional spacetime. In this regard,
extrinsic and intrinsic curvatures of a certain kind of hypersurface immersed
in the thermodynamic manifold contain information about stability/instability
of heat capacities. We, therefore, calculate the intrinsic curvature of the
$Q$-zero hypersurface for a four-dimensional neutral Gauss Bonnet black hole
case in the extended phase space. Interestingly, intrinsic curvature can be
positive for small black holes at low temperature, which indicates a repulsive
interaction among black hole microstructures. This finding is in contrast with
the five-dimensional neutral Gauss Bonnet black hole with only dominant
attractive interaction between its microstructures.


  The manifestation of exceptional points in the scattering continuum of atomic
nucleus is studied using the real-energy continuum shell model. It is shown
that low-energy exceptional points appear for realistic values of coupling to
the continuum and, hence, could be accessible experimentally. Experimental
signatures are proposed which include the jump by $2\pi$ of the elastic
scattering phase shift and a salient energy dependence of cross-sections in the
vicinity of the exceptional point.


  Weyl fermions are shown to exist inside a parabolic band, where the kinetic
energy of carriers is given by the non-relativistic Schroedinger equation.
There are Fermi arcs as a direct consequence of the folding of a ring shaped
Fermi surface inside the first Brillouin zone. Our results stem from the
decomposition of the kinetic energy into the sum of the square of the Weyl
state, the coupling to the local magnetic field and the Rashba interaction. The
Weyl fermions break the time and reflection symmetries present in the kinetic
energy, thus allowing for the onset of a weak three-dimensional magnetic field
around the layer. This field brings topological stability to the current
carrying states through a Chern number. In the special limit that the Weyl
state becomes gapless this magnetic interaction is shown to be purely
attractive, thus suggesting the onset of a superconducting condensate of zero
helicity states.


  We develop a numerical approach to reconstruct the phase dynamics of driven
or coupled self-sustained oscillators. Employing a simple algorithm for
computation of the phase of a perturbed system, we construct numerically the
equation for the evolution of the phase. Our simulations demonstrate that the
description of the dynamics solely by phase variables can be valid for rather
strong coupling strengths and large deviations from the limit cycle. Coupling
functions depend crucially on the coupling and are generally non-decomposable
in phase response and forcing terms. We also discuss limitations of the
approach.


  The non-Gaussian cold spot detected in wavelet space in the WMAP 1-year data,
is detected again in the coadded WMAP 3-year data at the same position (b =
-57, l = 209) and size in the sky (around 10 degrees). The present analysis is
based on several statistical methods: kurtosis, maximum absolute temperature,
number of pixels below a given threshold, volume and Higher Criticism. All
these methods detect deviations from Gaussianity in the 3--year data set at a
slightly higher confidence level than in the WMAP 1-year data. These small
differences are mainly due to the new foreground reduction technique and not to
the reduction of the noise level, which is negligible at the scale of the spot.
In order to avoid "a posteriori" analyses, we recalculate for the WMAP 3-year
data the significance of the deviation in the kurtosis. The skewness and
kurtosis tests were the first tests performed with wavelets for the WMAP data.
We obtain that the probability of finding an at least as high deviation in
Gaussian simulations is 1.85%. The frequency dependence of the spot is shown to
be extremely flat. Galactic foreground emissions are not likely to be
responsible for the detected deviation from Gaussianity.


  Simulations using the fully kinetic neoclassical code XGCa were undertaken to
explore the impact of kinetic effects on scrape-off layer (SOL) physics in
DIII-D H-mode plasmas. XGCa is a total-f, gyrokinetic code which
self-consistently calculates the axisymmetric electrostatic potential and
plasma dynamics, and includes modules for Monte Carlo neutral transport.
  Previously presented XGCa results showed several noteworthy features,
including large variations of ion density and pressure along field lines in the
SOL, experimentally relevant levels of SOL parallel ion flow (Mach number~0.5),
skewed ion distributions near the sheath entrance leading to subsonic flow
there, and elevated sheath potentials [R.M. Churchill, Nucl. Mater. & Energy,
submitted].
  In this paper, we explore in detail the question of pressure balance in the
SOL, as it was observed in the simulation that there was a large deviation from
a simple total pressure balance (the sum of ion and electron static pressure
plus ion inertia). It will be shown that both the contributions from the ion
viscosity (driven by ion temperature anisotropy) and neutral source terms can
be substantial, and should be retained in the parallel momentum equation in the
SOL, but still falls short of accounting for the observed fluid pressure
imbalance in the XGCa simulation results.


  We apply optimal control theory (OCT) to the design of refocusing pulses
suitable for the CPMG sequence that are robust over a wide range of B0 and B1
offsets. We also introduce a model, based on recent progress in the analysis of
unitary dynamics in the field of quantum information processing (QIP), that
describes the multiple refocusing dynamics of the CPMG sequence as a dephasing
Pauli channel. This model provides a compact characterization of the
consequences and severity of residual pulse errors. We illustrate the methods
by considering a specific example of designing and analyzing broadband OCT
refocusing pulses of length 10 t180 that are constrained by the maximum
instantaneous pulse power. We show that with this refocusing pulse, the CPMG
sequence can refocus over 98% of magnetization for resonance offsets up to 3.2
times the maximum RF amplitude, even in the presence of +/- 10% RF
inhomogeneity.


  It has been previously shown (Phys. Rev. E 66, 066305, 2002) that a
non-rotating turbulent convection with nonuniform large-scale flows contributes
to the turbulent heat flux. As a result, the turbulent heat flux depends
explicitly not only on the gradients of the large-scale temperature, but it
also depends on the gradients of the large-scale velocity. This is because the
nonuniform large-scale flows produce anisotropic velocity fluctuations which
modify the turbulent heat flux. This effect causes an excitation of a
convective-wind instability and formation of large-scale semi-organised
coherent structures (large-scale convective cells). We perform mean-field
numerical simulations of shear-free convection which take into account the
modification of the turbulent heat flux by nonuniform large-scale flows. The
redistribution of the turbulent heat flux by the nonuniform large-scale motions
in turbulent convection plays a crucial role in the formation of the
large-scale semi-organised coherent structures. This effect results in a strong
reduction of the critical effective Rayleigh number (based on the eddy
viscosity and turbulent temperature diffusivity) required for the formation of
the large-scale convective cells. The convective-wind instability is excited
when the scale separation ratio between the height of the convective layer and
the integral turbulence scale is large. The level of the mean kinetic energy at
saturation increases with the scale separation ratio. Inside the large-scale
convective cells, there are local regions with the positive vertical gradient
of the potential temperature which implies that these regions are stably
stratified.


  Cryogenic environments benefit ion trapping experiments by offering lower
motional heating rates, collision energies, and an ultra-high vacuum (UHV)
environment for maintaining long ion chains for extended periods of time.
Mechanical vibrations caused by compressors in closed-cycle cryostats can
introduce relative motion between the ion and the wavefronts of lasers used to
manipulate the ions. Here, we present a novel ion trapping system where a
commercial low-vibration closed-cycle cryostat is used in a custom monolithic
enclosure. We measure mechanical vibrations of the sample stage using an
optical interferometer, and observe a root-mean-square relative displacement of
2.4 nm and a peak-to-peak displacement of 17 nm between free-space beams and
the trapping location. We packaged a surface ion trap in a cryo-package
assembly that enables easy handling, while creating a UHV environment for the
ions. The trap cryo-package contains activated carbon getter material for
enhanced sorption pumping near the trapping location, and source material for
ablation loading. Using $^{171}$Yb$^{+}$ as our ion we estimate the operating
pressure of the trap as a function of package temperature using phase
transitions of zig-zag ion chains as a probe. We measured the radial mode
heating rate of a single ion to be 13 quanta/s on average. The Ramsey coherence
measurements yield 330 ms coherence time for counter-propagating Raman carrier
transitions using a 355 nm mode-locked pulse laser, demonstrating the high
optical stability.


  We review two works arXiv:2006.04987 and arXiv:2201.03487 which study the
stochastic quantisation equations of Yang-Mills on two and three dimensional
Euclidean space with finite volume. The main result of these works is that one
can renormalise the 2D and 3D stochastic Yang-Mills heat flow so that the
dynamic becomes gauge covariant in law. Furthermore, there is a state space of
distributional $1$-forms $\mathcal{S}$ to which gauge equivalence $\sim$
extends and such that the renormalised stochastic Yang-Mills heat flow projects
to a Markov process on the quotient space of gauge orbits $\mathcal{S}/{\sim}$.
In this review, we give unified statements of the main results of these works,
highlight differences in the methods, and point out a number of open problems.


  Following our previous results, which provide evidence for the emergence of a
chiral p-wave triplet-pairing component in superconducting Nb upon the
adsorption of chiral molecules, we turned to investigate whether such an effect
can take place in a proximal superconductor consisting of metal on
superconductor bilayer. Note that in such proximity systems, correlated
electron-hole (Andreev) pairs exist in the normal metal rather than genuine
Cooper pairs. To that end, we used scanning tunneling spectroscopy (STS) on
thin Au films grown in-situ on NbN (a conventional s-wave superconductor)
before and after adsorbing helical chiral, alpha-helix polyalanine molecules.
The tunneling spectra measured on the pristine Au surface showed conventional
(s-wave like) proximity gaps. However, upon molecules adsorption the spectra
significantly changed, all exhibiting a zero-bias conductance peak embedded
inside a gap, indicating unconventional superconductivity. The peak reduced
with magnetic field but did not split, consistent with equal-spin
triplet-pairing p-wave symmetry. In contrast, adsorption of non-helical chiral
cysteine molecules did not yield any apparent change in the order parameter,
and the tunneling spectra exhibited only gaps free of in-gap structure.


  The recent discovery of a number of circumbinary planets lends a new tool to
astrophysicists seeking to understand how and where planet formation takes
place. Of the increasingly numerous circumbinary systems, Kepler-16 is arguably
the most dynamically interesting: it consists of a planet on an almost
perfectly circular orbit (e = 0.0069) around a moderately eccentric binary (e =
0.16). We present high-resolution 3D smoothed-particle hydrodynamics
simulations of a Kepler-16 analogue embedded in a circumbinary disc, and show
that the planet's eccentricity is damped by its interaction with the
protoplanetary disc. We use this to place a lower limit on the gas surface
density in the real disc through which Kepler-16b migrated of \Sigma_min ~ 10 g
cm^-2. This suggests that Kepler-16b, and other circumbinary planets, formed
and migrated in relatively massive discs. We argue that secular evolution of
circumbinary discs requires that these planets likely formed early on in the
lifetime of the disc and migrated inwards before the disc lost a significant
amount of its original mass.


  Recent results on the $B$ CP-violation parameter $\sin2\phi_1$, the
$B^0_d$-$\overline{B}^0_d$ mixing parameter $\Delta m_d$ and $B$-meson
lifetimes are reported. The results are based on 10.5 $fb^{-1}$ of data
collected with the Belle detector at KEKB. Using both semileptonic and hadronic
decay modes the neutral and charged $B$-meson lifetimes are measured to be
$\taubz=1.548\pm0.035 (\mathrm{stat.})$~ps and $\taubm=1.656\pm0.038
(\mathrm{stat.})$~ps. The oscillation frequency $\Delta m_d$ for
$B^0_d$-$\overline{B}^0_d$ mixing is measured to be $0.522\pm0.026
(\mathrm{stat.})$~ps$^{-1}$ using semileptonic modes and $0.527\pm0.032
(\mathrm{stat.})$~ps$^{-1}$ using hadronic modes. The above results are
preliminary. The time evolution of $B^0_d$ decays into $J/\psi K^0_S$,
$\psi(2S) K^0_S$, $\chi_{c1} K^0_S$, $\eta_{c} K^0_S$, $J/\psi K^0_L$ and
$J/\psi \pi^0$ modes are studied to obtain $\sin2\phi_1$. Using 282 fully
reconstructed events, $\sin2\phi_1$ is measured to be $$\sin
2\phi_1=0.58^{+0.32}_{-0.34} (\mathrm{stat.})^{+0.09}_{-0.10} (\mathrm{syst.}
).$$


  We discuss the structure of the Motzkin algebra $M_k(D)$ by introducing a
sequence of idempotents and the basic construction. We show that $\cup_{k\geq
1}M_k(D)$ admits a factor trace if and only if $D\in \{2\cos(\pi/n)+1|n\geq
3\}\cup [3,\infty)$ and higher commutants of these factors depend on $D$. Then
a family of irreducible bimodules over the factors are constructed. A tensor
category with $A_n$ fusion rule is obtained from these bimodules.


  The convex hull of several i.i.d. beta distributed random vectors in $\mathbb
R^d$ is called the random beta polytope. Recently, the expected values of their
intrinsic volumes, number of faces, normal and tangent angles and other
quantities have been calculated, explicitly and asymptotically. In this paper,
we aim to investigate the asymptotic behavior of the beta polytopes with
extremal intrinsic volumes. We suggest a conjecture and solve it in dimension
2. To this end, we obtain some general limit relation for a wide class of
$U$-$\max$ statistics whose kernels include the perimeter and the area of the
convex hull of the arguments.


  We provide guarantees for approximate Gaussian Process (GP) regression
resulting from two common low-rank kernel approximations: based on random
Fourier features, and based on truncating the kernel's Mercer expansion. In
particular, we bound the Kullback-Leibler divergence between an exact GP and
one resulting from one of the afore-described low-rank approximations to its
kernel, as well as between their corresponding predictive densities, and we
also bound the error between predictive mean vectors and between predictive
covariance matrices computed using the exact versus using the approximate GP.
We provide experiments on both simulated data and standard benchmarks to
evaluate the effectiveness of our theoretical bounds.


  Continuous and discrete time systems possessing strange non-chaotic
attractors are under investigation. It is demonstrated that unpredictable
trajectories exist in the dynamics. A recent numerical technique, the
sequential test, is utilized to show the presence of unpredictability.


  In deep learning theory, the covariance matrix of the representations serves
as a proxy to examine the network's trainability. Motivated by the success of
Transformers, we study the covariance matrix of a modified Softmax-based
attention model with skip connections in the proportional limit of
infinite-depth-and-width. We show that at initialization the limiting
distribution can be described by a stochastic differential equation (SDE)
indexed by the depth-to-width ratio. To achieve a well-defined stochastic
limit, the Transformer's attention mechanism is modified by centering the
Softmax output at identity, and scaling the Softmax logits by a width-dependent
temperature parameter. We examine the stability of the network through the
corresponding SDE, showing how the scale of both the drift and diffusion can be
elegantly controlled with the aid of residual connections. The existence of a
stable SDE implies that the covariance structure is well-behaved, even for very
large depth and width, thus preventing the notorious issues of rank degeneracy
in deep attention models. Finally, we show, through simulations, that the SDE
provides a surprisingly good description of the corresponding finite-size
model. We coin the name shaped Transformer for these architectural
modifications.


  In this work, we present an analytical solution for QCD$\otimes$QED coupled
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the
leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in
perturbative QCD using double Laplace transform. This technique is applied to
obtain the singlet, gluon and photon distribution functions and also the proton
structure function. We also obtain contribution of photon in proton at LO and
NLO at high energy and successfully compare the proton structure function with
HERA data \cite{12} and APFEL results \cite{7}. Some comparisons also have been
done for the singlet and gluon distribution functions with the MSTW
results\cite{9}. In addition, the contribution of photon distribution function
inside the proton has been compared with results of MRST \cite{11} and with the
contribution of sea quark distribution functions which obtained by MSTW
\cite{9} and CTEQ6M \cite{14}.


  We report synthesis, crystal structure and physical properties of a quinary
iron-arsenide fluoride KCa$_2$Fe$_4$As$_4$F$_2$. The new compound crystallizes
in a body-centered tetragonal lattice (with space group $I4/mmm$, $a$ =
3.8684(2) {\AA}, c = 31.007(1) {\AA}, and $Z$ = 2), which contains double
Fe$_2$As$_2$ conducting layers separated by insulating Ca$_2$F$_2$ layers. Our
measurements of electrical resistivity, dc magnetic susceptibility and heat
capacity demonstrate bulk superconductivity at 33 K in
KCa$_2$Fe$_4$As$_4$F$_2$.


  Large lithium molybdate (Li$_2$MoO$_4$) crystal boules were produced by using
the low thermal gradient Czochralski growth technique from deeply purified
molybdenum. A small sample from one of the boules was preliminary characterized
in terms of X-ray-induced and thermally-excited luminescence. A large
cylindrical crystalline element (with a size of $\oslash 40\times40$ mm) was
used to fabricate a scintillating bolometer, which was operated aboveground at
$\sim 15$ mK by using a pulse-tube cryostat housing a high-power dilution
refrigerator. The excellent detector performance in terms of energy resolution
and $\alpha$ background suppression along with preliminary positive indications
on the radiopurity of this material show the potentiality of Li$_2$MoO$_4$
scintillating bolometers for low-counting experiment to search for neutrinoless
double beta decay of $^{100}$Mo.


  We present high-frequency angle-dependent EPR data for crystals of
[NixZn1-x(hmp)(t-BuEtOH)Cl]4 (x = 1 and 0.02). The x = 1 complex behaves as a
single-molecule magnet at low temperatures, displaying hysteresis and
exceptionally fast magnetization tunneling. We show that this behavior is
related to a 4th-order transverse crystal-field interaction, which produces a
significant tunnel-splitting (~10 MHz) of the ground state of this S = 4
system. The magnitude of the 4th-order anisotropy, and the dominant axial term
(D), can be related to the single-ion interactions (Di and Ei) at the
individual NiII sites, as determined for the x = 0.02 crystals.


  Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et
al, 2015] values to evaluate some of the well-known cryptographically
significant spectra of Boolean functions, namely the Walsh spectrum, the
cross-correlation spectrum and the autocorrelation spectrum. We introduce the
existing 2-fold Forrelation formulation with bent duality based promise
problems as desirable instantiations. Next we concentrate on the $3$-fold
version through two approaches. First, we judiciously set-up some of the
functions in $3$-fold Forrelation, so that given an oracle access, one can
sample from the Walsh Spectrum of $f$. Using this, we obtain improved results
than what we obtain from the Deutsch-Jozsa algorithm, and in turn it has
implications in resiliency checking. Furthermore, we use similar idea to obtain
a technique in estimating the cross-correlation (and thus autocorrelation)
value at any point, improving upon the existing algorithms. Finally, we tweak
the quantum algorithm with superposition of linear functions to obtain a
cross-correlation sampling technique. To the best of our knowledge, this is the
first cross-correlation sampling algorithm with constant query complexity. This
also provides a strategy to check if two functions are uncorrelated of degree
$m$. We further modify this using Dicke states so that the time complexity
reduces, particularly for constant values of $m$.


  It is proved that the Halphen system of ordinary differential equations has
no non-trivial rational first integrals.


  The Aesthetics Assessment of Children's Paintings (AACP) is an important
branch of the image aesthetics assessment (IAA), playing a significant role in
children's education. This task presents unique challenges, such as limited
available data and the requirement for evaluation metrics from multiple
perspectives. However, previous approaches have relied on training large
datasets and subsequently providing an aesthetics score to the image, which is
not applicable to AACP. To solve this problem, we construct an aesthetics
assessment dataset of children's paintings and a model based on self-supervised
learning. 1) We build a novel dataset composed of two parts: the first part
contains more than 20k unlabeled images of children's paintings; the second
part contains 1.2k images of children's paintings, and each image contains
eight attributes labeled by multiple design experts. 2) We design a pipeline
that includes a feature extraction module, perception modules and a
disentangled evaluation module. 3) We conduct both qualitative and quantitative
experiments to compare our model's performance with five other methods using
the AACP dataset. Our experiments reveal that our method can accurately capture
aesthetic features and achieve state-of-the-art performance.


  We study the distribution of active, noninteracting particles over two bulk
states separated by a ratchet potential. By solving the steady-state
Smoluchowski equations in a flux-free setting, we show that the ratchet
potential affects the distribution of particles over the bulks, and thus exerts
an influence of infinitely long range. As we show, crucial for having such a
long-range influence is an external potential that is nonlinear. We
characterize how the difference in bulk densities depends on activity and on
the ratchet potential, and we identify power law dependencies on system
parameters in several limiting cases. While weakly active systems are often
understood in terms of an effective temperature, we present an analytical
solution that explicitly shows that this is not possible in the current
setting. Instead, we rationalize our results by a simple transition state
model, that presumes particles to cross the potential barrier by Arrhenius
rates modified for activity. While this model does not quantitatively describe
the difference in bulk densities for feasible parameter values, it does
reproduce - in its regime of applicability - the complete power law behavior
correctly.


  Cognitive radio (CR) is a key enabler realizing future networks to achieve
higher spectral efficiency by allowing spectrum sharing between different
wireless networks. It is important to explore whether spectrum access
opportunities are available, but conventional CR based on transmitter (TX)
sensing cannot be used to this end because the paired receiver (RX) may
experience different levels of interference, according to the extent of their
separation, blockages, and beam directions. To address this problem, this paper
proposes a novel form of medium access control (MAC) termed sense-and-predict
(SaP), whereby each secondary TX predicts the interference level at the RX
based on the sensed interference at the TX; this can be quantified in terms of
a spatial interference correlation between the two locations. Using stochastic
geometry, the spatial interference correlation can be expressed in the form of
a conditional coverage probability, such that the signal-to-interference ratio
(SIR) at the RX is no less than a predetermined threshold given the sensed
interference at the TX, defined as an opportunistic probability (OP). The
secondary TX randomly accesses the spectrum depending on OP. We optimize the
SaP framework to maximize the area spectral efficiencies (ASEs) of secondary
networks while guaranteeing the service quality of the primary networks.
Testbed experiments using USRP and MATLAB simulations show that SaP affords
higher ASEs compared with CR without prediction.


  With the support of cloud computing, large quantities of data collected from
various WSN applications can be managed efficiently. However, maintaining data
security and efficiency of data processing in cloud-WSN (C-WSN) are important
and challenging issues. In this paper, we present an efficient data outsourcing
scheme based on CP-ABE, which can not only guarantee secure data access, but
also reduce overall data processing time. In our proposed scheme, a large file
is divided into several data blocks by data owner (DO) firstly. Then, the data
blocks are encrypted and transferred to the cloud server in parallel. For data
receiver (DR), data decryption and data transmission is also processed in
parallel. In addition, data integrity can be checked by DR without any master
key components. The security analysis shows that the proposed scheme can meet
the security requirement of C-WSN. By performance evaluation, it shows that our
scheme can dramatically improve data processing efficiency compared to the
traditional CP-ABE method.


  In this paper, we study abstractive summarization for open-domain videos.
Unlike the traditional text news summarization, the goal is less to "compress"
text information but rather to provide a fluent textual summary of information
that has been collected and fused from different source modalities, in our case
video and audio transcripts (or text). We show how a multi-source
sequence-to-sequence model with hierarchical attention can integrate
information from different modalities into a coherent output, compare various
models trained with different modalities and present pilot experiments on the
How2 corpus of instructional videos. We also propose a new evaluation metric
(Content F1) for abstractive summarization task that measures semantic adequacy
rather than fluency of the summaries, which is covered by metrics like ROUGE
and BLEU.


  We discuss the gravitational lensing of neutrinos by astrophysical objects.
Unlike photons, neutrinos can cross a stellar core; as a result, the lens
quality improves. We also estimate the depletion of the neutrino flux after
crossing a massive object and the signal amplification expected. While Uranians
alone would benefit from this effect in the Sun, similar effects could be
considered for binary systems.


  Context: Outflows are an important part of the star formation process as both
the result of ongoing active accretion and one of the main sources of
mechanical feedback on small scales. Water is the ideal tracer of these effects
because it is present in high abundance in various parts of the protostar.
Method: We present \textit{Herschel} HIFI spectra of multiple water-transitions
towards 29 nearby Class 0/I protostars as part of the WISH Survey. These are
decomposed into different Gaussian components, with each related to one of
three parts of the protostellar system; quiescent envelope, cavity shock and
spot shocks in the jet and at the base of the outflow. We then constrain the
excitation conditions present in the two outflow-related components. Results:
Water emission is optically thick but effectively thin, with line ratios that
do not vary with velocity, in contrast to CO. The physical conditions of the
cavity and spot shocks are similar, with post-shock H$_{2}$ densities of order
10$^{5}-$10$^{8}$\,cm$^{-3}$ and H$_{2}$O column densities of order
10$^{16}-$10$^{18}$\,cm$^{-2}$. H$_{2}$O emission originates in compact
emitting regions: for the spot shocks these correspond to point sources with
radii of order 10-200\,AU, while for the cavity shocks these come from a thin
layer along the outflow cavity wall with thickness of order 1-30\,AU.
Conclusions: Water emission at the source position traces two distinct
kinematic components in the outflow; J shocks at the base of the outflow or in
the jet, and C shocks in a thin layer in the cavity wall. Class I sources have
similar excitation conditions to Class 0 sources, but generally smaller
line-widths and emitting region sizes. We suggest that it is the velocity of
the wind driving the outflow, rather than the decrease in envelope density or
mass, that is the cause of the decrease in H$_{2}$O intensity between Class 0
and I.


  We explore single and multi-loop conformal integrals, such as the ones
appearing in dual conformal theories in flat space. Using Mellin amplitudes, a
large class of higher loop integrals can be written as simple
integro-differential operators on star integrals: one-loop $n$-gon integrals in
$n$ dimensions. These are known to be given by volumes of hyperbolic simplices.
We explicitly compute the five-dimensional pentagon integral in full generality
using Schl\"afli's formula. Then, as a first step to understanding higher
loops, we use spline technology to construct explicitly the $6d$ hexagon and
$8d$ octagon integrals in two-dimensional kinematics. The fully massive hexagon
and octagon integrals are then related to the double box and triple box
integrals respectively. We comment on the classes of functions needed to
express these integrals in general kinematics, involving elliptic functions and
beyond.