  We consider multilevel low rank (MLR) matrices, defined as a row and column
permutation of a sum of matrices, each one a block diagonal refinement of the
previous one, with all blocks low rank given in factored form. MLR matrices
extend low rank matrices but share many of their properties, such as the total
storage required and complexity of matrix-vector multiplication. We address
three problems that arise in fitting a given matrix by an MLR matrix in the
Frobenius norm. The first problem is factor fitting, where we adjust the
factors of the MLR matrix. The second is rank allocation, where we choose the
ranks of the blocks in each level, subject to the total rank having a given
value, which preserves the total storage needed for the MLR matrix. The final
problem is to choose the hierarchical partition of rows and columns, along with
the ranks and factors. This paper is accompanied by an open source package that
implements the proposed methods.


  We used optical spectroscopy of the neutron star X-ray transient XTE
J2123-058 to measure the rotational broadening of the binary companion's
stellar absorption lines and determined that the companion's projected
rotational velocity is vsini = 121 (+21)(-29) km/s. This value is considerably
larger than the measurements of vsini obtained previously for three other
neutron star systems where the values are between 34 and 65 km/s. The larger
value is likely due to the combination of high binary inclination and short (6
hr) orbital period for XTE J2123-058. Along with previously measured
parameters, the rotational broadening measurement allowed us to determine the
binary parameters, including the ratio of the neutron star mass to the
companion mass, q = M_1/M_2 = 2.7 (+1.3)(-0.9), the neutron star mass, M_1 =
1.46 (+0.30)(-0.39) solar masses, and the companion mass, M_2 = 0.53
(+0.28)(-0.39) solar masses, assuming a Roche lobe filling companion
synchronously rotating with the binary orbit. These values are consistent with
a previous measurement where the H alpha emission line was used to determine
the semiamplitude of the neutron star's radial velocity curve (K_1). It is a
significant result that the two methods give consistent values. We also report
the first measurement of the XTE J2123-058 companion's radius. Assuming
synchronous rotation, we obtain R_2 = 0.62 (+0.11)(-0.15) solar radii, which is
in-line with that expected for a late K-type star on or close to the main
sequence. Finally, we report the first precise spectroscopic determination of
the binary orbital period (P_orb = 21442.3 +/- 1.8 seconds).


  This paper considers a class of nonparametric autoregressive models with
nonstationarity. We propose a nonparametric kernel test for the conditional
mean and then establish an asymptotic distribution of the proposed test. Both
the setting and the results differ from earlier work on nonparametric
autoregression with stationarity. In addition, we develop a new bootstrap
simulation scheme for the selection of a suitable bandwidth parameter involved
in the kernel test as well as the choice of a simulated critical value. The
finite-sample performance of the proposed test is assessed using one simulated
example and one real data example.


  In this paper we consider the inverse electromagnetic scattering for a cavity
surrounded by an inhomogeneous medium in three dimensions. The measurements are
scattered wave fields measured on some surface inside the cavity, where such
scattered wave fields are due to sources emitted on the same surface. We first
prove that the measurements uniquely determine the shape of the cavity, where
we make use of a boundary value problem called the exterior transmission
problem. We then complete the inverse scattering problem by designing the
linear sampling method to reconstruct the cavity. Numerical examples are
further provided to illustrate the viability of our algorithm.


  We review recent results on localization for discrete alloy-type models based
on the multiscale analysis and the fractional moment method, respectively. The
discrete alloy-type model is a family of Schr\"odinger operators $H_\omega = -
\Delta + V_\omega$ on $\ell^2 (\ZZ^d)$ where $\Delta$ is the discrete Laplacian
and $V_\omega$ the multiplication by the function $V_\omega (x) = \sum_{k \in
\ZZ^d} \omega_k u(x-k)$. Here $\omega_k$, $k \in \ZZ^d$, are i.i.d. random
variables and $u \in \ell^1 (\ZZ^d ; \RR)$ is a so-called single-site
potential. Since $u$ may change sign, certain properties of $H_\omega$ depend
in a non-monotone way on the random parameters $\omega_k$. This requires new
methods at certain stages of the localization proof.


  We apply the prescription proposed in hep-th/0307197 for non-abelian
expansion of S-matrix elements, to the S-matrix element of four tachyons and
one gauge field in superstring theory. We show that the leading order terms of
the expansion are in perfect agreement with the non-abelian generalization of
the tachyon DBI action in which the tachyon potential is $V(T)=1+\pi\alpha'
m^2T^2+\frac{1}{2!}(\pi\alpha' m^2T^2)^2+...$ where $m^2=-1/(2\alpha')$ is the
mass of tachyon. This calculation fixes the coefficient of $T^4$ in the
potential without on-shell ambiguity.


  It is shown that for the spin 1/2 anisotropic Heisenberg model the result for
the transition temperature is completely insensitive to the anisotropy within
the Onsager reaction field theory, which yields a vanishing T_c in two
dimensions, in total conflict with the expected finite T_c, increasing with
anisotropy. This establishes that the breakdown of the Onsager reaction field
theory in two dimensions is not limited to the Ising model, but actually
extends over the whole range of anisotropy. Therefore, for the isotropic case,
the results of vanishing T_c and exponential dependence of spin correlation
length should be seen as mere coincidence.


  Classification models for the multivariate time series have gained
significant importance in the research community, but not much research has
been done on generating adversarial samples for these models. Such samples of
adversaries could become a security concern. In this paper, we propose
transforming the existing adversarial transformation network (ATN) on a
distilled model to attack various multivariate time series classification
models. The proposed attack on the classification model utilizes a distilled
model as a surrogate that mimics the behavior of the attacked classical
multivariate time series classification models. The proposed methodology is
tested onto 1-Nearest Neighbor Dynamic Time Warping (1-NN DTW) and a Fully
Convolutional Network (FCN), all of which are trained on 18 University of East
Anglia (UEA) and University of California Riverside (UCR) datasets. We show
both models were susceptible to attacks on all 18 datasets. To the best of our
knowledge, adversarial attacks have only been conducted in the domain of
univariate time series and have not been conducted on multivariate time series.
such an attack on time series classification models has never been done before.
Additionally, we recommend future researchers that develop time series
classification models to incorporating adversarial data samples into their
training data sets to improve resilience on adversarial samples and to consider
model robustness as an evaluative metric.


  The photometer section of SPIRE is one of the key instruments on board of
Herschel. Its legacy depends very much on how well the scanmap observations
that it carried out during the Herschel mission can be converted to high
quality maps. In order to have a comprehensive assessment on the current status
of SPIRE map-making, as well as to provide guidance for future development of
the SPIRE scan-map data reduction pipeline, we carried out a test campaign on
SPIRE map-making. In this report, we present results of the tests in this
campaign.


  Analogous to the light-shining-through-wall setup proposed for axion-like
particle searches, a pair of resonant cavities have been considered to search
for an extra U(1) massive gauge boson, called a hidden photon, which mediates
the interactions in the hidden sector. We propose a new cavity configuration,
consisting of a cylindrical emitter surrounded by a hollow cylindrical detector
to remarkably improve experimental sensitivity to hidden photon signals in the
$\mu$eV mass range. An extensive study was conducted to find the optimal cavity
geometry and resonant mode, which yields the best performance. In addition, a
feasible application of superconducting RF technology was explored. We found
the integration of these potential improvements will enhance the sensitivity to
the effective kinetic mixing parameter between the hidden photon and the
Standard Model photon by multiple orders of magnitude.


  Given a join semilattice $S$ with a minimum $\hat{0}$, the quarks (also
called atoms in order theory) are the elements that cover $\hat{0}$, and for
each $x \in S \setminus \{\hat{0}\}$ a factorization (into quarks) of $x$ is a
minimal set of quarks whose join is $x$. If every element $x \in S \setminus
\{\hat{0}\}$ has a factorization, then $S$ is called factorizable. If for each
$x \in S \setminus \{\hat{0}\}$, any two factorizations of $x$ have equal
(resp., distinct) size, then we say that $S$ is half-factorial (resp.,
length-factorial). Let $B_\mathbb{N}$ be the Boolean lattice consisting of all
finite subsets of $\mathbb{N}$ under intersections and unions. Here we study
factorizations into quarks in join subsemilattices of $B_\mathbb{N}$, focused
on the notions of half-factoriality and length-factoriality. We also consider
the unique factorization property, which is the most special and relevant type
of half-factoriality, and the elasticity, which is an arithmetic statistic that
measures the deviation from half-factoriality.


  We show that the combined effect of photon emission and Coulomb interactions
may drive an exciton-polariton system towards a dynamical coherent state, even
without phonon thermalization or any other relaxation mechanism. Exact
diagonalization results for a finite system (a multilevel quantum dot
interacting with the lowest energy photon mode of a microcavity) are presented
in support to this statement.


  We construct infinitely many pairwise non-diffeomorphic smooth structures on
a definite $4$-manifold with non-cyclic fundamental group $\mathbb{Z}/2\times
\mathbb{Z}/2$.


  Internal microscopic symmetry of a many body system leads to global
constraints. We obtain explicit forms of the global macroscopic condition
assuring that at the microscopic level the evolution respects the overall
symmetry.


  We extend the notion of quantum reading to the case where the information to
be retrieved, which is encoded into a set of quantum channels, is of quantum
nature. We use two qubit unitaries describing the system environment
interaction, with the initial environment state determining the system's input
output channel and hence the encoded information. The performance of the most
relevant two-qubit unitaries is determined with two different approaches: i)
one-shot quantum capacity of the channel arising between environment and
system's output; ii) estimation of parameters characterizing the initial
quantum state of the environment. The obtained results are mostly in
(qualitative) agreement, with some distinguishing features that include the
CNOT unitary.


  The Higgs mode corresponds to the collective motion of particles due to the
vibrations of an invisible field. It plays a fundamental role for our
understanding of both low and high energy physics, giving elementary particles
their mass and leading to collective modes in condensed matter and nuclear
systems. The Higgs mode has been observed in a limited number of table-top
systems, where it however is characterised by a short lifetime due to decay
into a continuum of modes. A major goal which has remained elusive so far, is
therefore to realise a long-lived Higgs mode in a controllable system. Here, we
show how an undamped Higgs mode can be observed unambiguously in a Fermi gas in
a two-dimensional trap, close to a quantum phase transition between a normal
and a superfluid phase. We develop a first-principles theory of the pairing and
the associated collective modes, which is quantitatively reliable when the
pairing energy is much smaller than the trap level spacing, yet simple enough
to allow the derivation of analytical results. The theory includes the trapping
potential exactly, which is demonstrated to stabilize the Higgs mode by making
its decay channels discrete. Our results show how atoms in micro-traps can
unravel properties of a long-lived Higgs mode, including the role of
confinement and finite size effects.


  We establish a general transference principle for the irrationality measure
of points with $\mathbb{Q}$-linearly independent coordinates in
$\mathbb{R}^{n+1}$, for any given integer $n\geq 1$. On this basis, we recover
an important inequality of Marnat and Moshchevitin which describes the spectrum
of the pairs of ordinary and uniform exponents of rational approximation to
those points. For points whose pair of exponents are close to the boundary in
the sense that they almost realize the equality, we provide additional
information about the corresponding sequence of best rational approximations.
We conclude with an application.


  As the globally increasing population drives rapid urbanisation in various
parts of the world, there is a great need to deliberate on the future of the
cities worth living. In particular, as modern smart cities embrace more and
more data-driven artificial intelligence services, it is worth remembering that
technology can facilitate prosperity, wellbeing, urban livability, or social
justice, but only when it has the right analog complements (such as
well-thought out policies, mature institutions, responsible governance); and
the ultimate objective of these smart cities is to facilitate and enhance human
welfare and social flourishing. Researchers have shown that various
technological business models and features can in fact contribute to social
problems such as extremism, polarization, misinformation, and Internet
addiction. In the light of these observations, addressing the philosophical and
ethical questions involved in ensuring the security, safety, and
interpretability of such AI algorithms that will form the technological bedrock
of future cities assumes paramount importance. Globally there are calls for
technology to be made more humane and human-centered. In this paper, we analyze
and explore key challenges including security, robustness, interpretability,
and ethical (data and algorithmic) challenges to a successful deployment of AI
in human-centric applications, with a particular emphasis on the convergence of
these concepts/challenges. We provide a detailed review of existing literature
on these key challenges and analyze how one of these challenges may lead to
others or help in solving other challenges. The paper also advises on the
current limitations, pitfalls, and future directions of research in these
domains, and how it can fill the current gaps and lead to better solutions. We
believe such rigorous analysis will provide a baseline for future research in
the domain.


  The co-evolution of host galaxies and the active black holes which reside in
their centre is one of the most important topics in modern observational
cosmology. Here we present a study of the properties of obscured Active
Galactic Nuclei (AGN) detected in the CDFS 1Ms observation and their host
galaxies. We limited the analysis to the MUSIC area, for which deep K-band
observations obtained with ISAAC@VLT are available, ensuring accurate
identifications of the counterparts of the X-ray sources as well as reliable
determination of photometric redshifts and galaxy parameters, such as stellar
masses and star formation rates. In particular, we: 1) refined the
X-ray/infrared/optical association of 179 sources in the MUSIC area detected in
the Chandra observation; 2) studied the host galaxies observed and rest frame
colors and properties. We found that X-ray selected (L_X>10^{42} erg s^{-1})
AGN show Spitzer colors consistent with both AGN and starburst dominated
infrared continuum; the latter would not have been selected as AGN from
infrared diagnostics. The host galaxies of X-ray selected obscured AGN are all
massive (M_*>10^{10} M_sun) and, in 50% of the cases, are also actively forming
stars (1/SSFR<t_{Hubble}) in dusty environments. The median L/LEdd value of the
active nucleus is between 2% and 10% depending on the assumed M_{BH}/M_{*}
ratio. Finally, we found that the X-ray selected AGN fraction increases with
the stellar mass up to a value of ~30% at z>1 and M_*>3x10^{11} M_sun, a
fraction significantly higher than in the local Universe for AGN of similar
luminosities.


  The first experimental evidence is presented of the topological insulator
state in PbBi$_{2}$Te$_{4}$. A single surface Dirac cone is observed by
angle-resolved photoemission spectroscopy (ARPES) with synchrotron radiation.
Topological invariants $\mathbb{Z}_2$ are calculated from the {\it ab initio}
band structure to be 1; (111). The observed two-dimensional iso-energy contours
in the bulk energy gap are found to be the largest among the known
three-dimensional topological insulators. This opens a pathway to achieving a
sufficiently large spin current density in future spintronic devices.


  In their study of a quartic integral, Boros and Moll discovered a special
class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers
and Paule proved the conjecture of Moll that these polynomials are log-concave.
In this paper, we show that the Boros-Moll polynomials possess the ratio
monotone property which implies the log-concavity and the spiral property. We
conclude with a conjecture which is stronger than Moll's conjecture on the
$\infty$-log-concavity.


  Sharp Trudinger-Moser inequalities on the first order Sobolev spaces and
their analogous Adams inequalities on high order Sobolev spaces play an
important role in geometric analysis, partial differential equations and other
branches of modern mathematics. Such geometric inequalities have been studied
extensively by many authors in recent years and there is a vast literature.
There are two types of such optimal inequalities: critical and subcritical
sharp inequalities, both are with best constants. Critical sharp inequalities
are under the restriction of the full Sobolev norms for the functions under
consideration, while the subcritical inequalities are under the restriction of
the partial Sobolev norms for the functions under consideration. There are
subtle differences between these two type of inequalities. Surprisingly, we
prove in this paper that these critical and subcritical Trudinger-Moser and
Adams inequalities are actually equivalent. Moreover, we also establish the
asymptotic behavior of the supremum for the subcritical Trudinger-Moser and
Adams inequalities on the entire Euclidean spaces (Theorem 1.1 and Theorem 1.3)
and provide a precise relationship between the supremums for the critical and
subcritical Trudinger-Moser and Adams inequalities (Theorem 1.2 and Theorem
1.4).


  The high energy consumption of electronic data processors, together with
physical challenges limiting their further improvement, has triggered intensive
interest in alternative computation paradigms. Here we focus on network-based
biocomputation (NBC), a massively parallel approach that benefits from the
energy efficiency of biological agents, such as molecular motors or bacteria,
and their availability in large numbers. We analyse and define the fundamental
requirements that need to be fulfilled to scale up NBC computers to become a
viable technology that can solve large NP-complete problem instances faster or
with less energy consumption than electronic computers. Our work can serve as a
guide for further efforts to contribute to elements of future NBC devices, and
as the theoretical basis for a detailed NBC roadmap.


  According to the topological design theory and method of parallel mechanism
(PM) based on position and orientation characteristic (POC) equations, this
paper studied a 3-DOF translational PM that has three advantages, i.e., (i) it
consists of three fixed actuated prismatic joints, (ii) the PM has analytic
solutions to the direct and inverse kinematic problems, and (iii) the PM is of
partial motion decoupling property. Firstly, the main topological
characteristics, such as the POC, degree of freedom and coupling degree were
calculated for kinematic modeling. Thanks to these properties, the direct and
inverse kinematic problems can be readily solved. Further, the conditions of
the singular configurations of the PM were analyzed which corresponds to its
partial motion decoupling property.


  Supersymmetric theories generally have new flavor and CP violation sources in
the squark and slepton mass matrices. They will contribute to the lepton flavor
violation processes, such as $\mu \to e \gamma$, which can be probed far below
the current bound with an intense muon source at the front end of the muon
collider. In addition, if sleptons can be produced at the muon collider, the
flavor violation can occur at their production and decay, allowing us to probe
the flavor mixing structure directly. Asymmetry between numbers of $\mu^+ e^-$
and $e^+ \mu^-$ events will be a sign for CP violation in supersymmetric flavor
mixing.


  In this work we study the production of $\Sigma$ and $\Lambda$ hyperons in
strangeness changing $\Delta S = -1$ charged current interactions of muon
antineutrinos on nuclear targets. At the nucleon level, besides quasielastic
scattering we consider the inelastic mechanism in which a pion is produced
alongside the hyperon. Its relevance for antineutrinos with energies below 2
GeV is conveyed in integrated and differential cross sections. We observe that
the distributions on the angle between the hyperon and the final lepton are
clearly different for quasielastic and inelastic processes. Hyperon final state
interactions, modeled with an intranuclear cascade, lead to a significant
transfer from primary produced $\Sigma$'s into final $\Lambda$'s. They also
cause considerable energy loss, which is apparent in hyperon energy
distributions. We have investigated $\Lambda$ production off ${}^{40}$Ar in the
conditions of the recently reported MicroBooNE measurement. We find that the
$\Lambda \pi$ contribution, dominated by $\Sigma^*(1385)$ excitation, accounts
for about one third of the cross section.


  The magnetization curve of the ferrofluid EMG909 is measured. It can
adequately be described by a superposition of four Langevin terms. The
effective dipole strength of the magnetic particles in this fluid is
subsequently obtained by a graphical rectification of the magnetization curve
based on the inverse Langevin function. The method yields the arithmetic and
the harmonic mean of the magnetic moment distribution function, and a guess for
the geometric mean and the relative standard deviation. It has the advantage
that it does not require a prejudiced guess of the distribution function of the
poly-disperse suspension of magnetic particles.


  We present a characterization of the completeness of the field of real
numbers in the form of a \emph{collection of ten equivalent statements}
borrowed from algebra, real analysis, general topology and non-standard
analysis. We also discuss the completeness of non-Archimedean fields and
present several examples of such fields. As an application we exploit one of
our results to argue that the Leibniz infinitesimal calculus in the
$18^\textrm{th}$ century was already a rigorous branch of mathematics -- at
least much more rigorous than most contemporary mathematicians prefer to
believe. By advocating our particular historical point of view, we hope to
provoke a discussion on the importance of mathematical rigor in mathematics and
science in general. We believe that our article will be of interest for those
readers who teach courses on abstract algebra, real analysis, general topology,
logic and the history of mathematics.


  Modern theories of the hydrophobic effect highlight its dependence on length
scale, emphasizing in particular the importance of interfaces that emerge in
the vicinity of sizable hydrophobes. We recently showed that a faithful
treatment of such nanoscale interfaces requires careful attention to the
statistics of capillary waves, with significant quantitative implications for
the calculation of solvation thermodynamics. Here we show that a coarse-grained
lattice model in the spirit of those pioneered by Chandler and coworkers, when
informed by this understanding, can capture a broad range of hydrophobic
behaviors with striking accuracy. Specifically, we calculate probability
distributions for microscopic density fluctuations that agree very well with
results of atomistic simulations, even many standard deviations from the mean,
and even for probe volumes in highly heterogeneous environments. This accuracy
is achieved without adjustment of free parameters, as the model is fully
specified by well-known properties of liquid water. As illustrative examples of
its utility, we characterize the free energy profile for a solute crossing the
air-water interface, and compute the thermodynamic cost of evacuating the space
between extended nanoscale surfaces. Together, these calculations suggest that
a highly reduced model for aqueous solvation can serve as the basis for
efficient multiscale modeling of spatial organization driven by hydrophobic and
interfacial forces.


  We report on the observation of spatially asymmetric turbulent structures
with a long radial correlation length in the core of high-collisionality H-mode
plasmas on DIII-D tokamak. These turbulent structures develop from shorter
wavelength turbulence and have a radially elongated structure. The envelope of
turbulence spans a broad radial range in the mid-radius region, leading to
streamer-like transport events. The underlying turbulence is featured by
intermittency, long-term memory effect, and the characteristic spectrum of
self-organized criticality. The amplitude and the radial scale increase
substantially when the shearing rate of the mean flow is reduced below the
turbulent scattering rate. The enhanced LRRC transport events are accompanied
by apparent degradation of normalized energy confinement time. These findings
constitute the first experimental observation of long-radial-range turbulent
transport events in high-collisionality H-mode plasmas, and demonstrate the
role of mean shear flows in the formation and propagation of turbulence with
long-radial-range correlation.


  Myocardial infarction (MI) is a scientific term that refers to heart attack.
In this study, we infer highly relevant second harmonic generation (SHG) cues
from collagen fibers exhibiting highly non-centrosymmetric assembly together
with two-photon excited cellular autofluorescence in infarcted mouse heart to
quantitatively probe fibrosis, especially targeted at an early stage after MI.
We present a robust one-shot machine learning algorithm that enables
determination of 2D assembly of collagen with high spatial resolution along
with its structural arrangement in heart tissues post-MI with spectral
specificity and sensitivity. Detection, evaluation, and precise quantification
of fibrosis extent at early stage would guide one to develop treatment
therapies that may prevent further progression and determine heart transplant
needs for patient survival.


  We construct certain metrics on the Sierpinski carpet via a class of
self-similar weight functions. Using these metrics and by applying known
results, we obtain the two-sided sub-Gaussian heat kernel estimates of time
change of the standard diffusion on the Sierpinski carpet with respect to
self-similar measures. This proves a conjecture by Kigami.


  We have numerically implemented a perturbation series for the scattered
electromagnetic fields above rough surfaces, due to Greffet, allowing us to
evaluate the local density of states to second order in the surface profile
function. We present typical results for thermal near fields of surfaces with
regular nanostructures, investigating the relative magnitude of the
contributions appearing in successive orders. The method is then employed for
estimating the resolution limit of an idealized Near-Field Scanning Thermal
Microscope (NSThM).


  In this paper, we present Multi-scale Feature Aggregation Conformer
(MFA-Conformer), an easy-to-implement, simple but effective backbone for
automatic speaker verification based on the Convolution-augmented Transformer
(Conformer). The architecture of the MFA-Conformer is inspired by recent
stateof-the-art models in speech recognition and speaker verification. Firstly,
we introduce a convolution subsampling layer to decrease the computational cost
of the model. Secondly, we adopt Conformer blocks which combine Transformers
and convolution neural networks (CNNs) to capture global and local features
effectively. Finally, the output feature maps from all Conformer blocks are
concatenated to aggregate multi-scale representations before final pooling. We
evaluate the MFA-Conformer on the widely used benchmarks. The best system
obtains 0.64%, 1.29% and 1.63% EER on VoxCeleb1-O, SITW.Dev, and SITW.Eval set,
respectively. MFA-Conformer significantly outperforms the popular ECAPA-TDNN
systems in both recognition performance and inference speed. Last but not the
least, the ablation studies clearly demonstrate that the combination of global
and local feature learning can lead to robust and accurate speaker embedding
extraction. We have also released the code for future comparison.


  Implicit neural representations (INR) have been recently proposed as deep
learning (DL) based solutions for image compression. An image can be compressed
by training an INR model with fewer weights than the number of image pixels to
map the coordinates of the image to corresponding pixel values. While
traditional training approaches for INRs are based on enforcing pixel-wise
image consistency, we propose to further improve image quality by using a new
structural regularizer. We present structural regularization for INR
compression (SINCO) as a novel INR method for image compression. SINCO imposes
structural consistency of the compressed images to the groundtruth by using a
segmentation network to penalize the discrepancy of segmentation masks
predicted from compressed images. We validate SINCO on brain MRI images by
showing that it can achieve better performance than some recent INR methods.


  We analyze theoretically and experimentally the influence of current noise on
the longitudinal mode hopping dynamics of a bulk semiconductor laser. It is
shown that the mean residence times on each mode have different sensitivity to
external noise added to the bias current. In particular, an increase of the
noise level enhances the residence time on the longitudinal mode that dominates
at low current, evidencing the multiplicative nature of the stochastic process.
A two-mode rate equation model for semiconductor laser is able to reproduce the
experimental findings. Under a suitable separation of the involved time scales,
the model can be reduced to a 1D bistable potential system with a
multiplicative stochastic term related to the current noise strength. The
reduced model clarifies the influence of the different noise sources on the
hopping dynamics.


  The phase transition between galaxies and quasars is often identified with
the rare population of hyper-luminous, hot dust-obscured galaxies. Galaxy
formation models predict these systems to grow via mergers, that can deliver
large amounts of gas toward their centers, induce intense bursts of star
formation and feed their supermassive black holes. Here we report the detection
of 24 galaxies emitting Lyman-alpha emission on projected physical scales of
about 400 kpc around the hyper-luminous hot dust-obscured galaxy W0410-0913, at
redshift z = 3.631, using Very Large Telescope observations. While this
indicates that W0410-0913 evolves in a very dense environment, we do not find
clear signs of mergers that could sustain its growth. Data suggest that if
mergers occurred, as models expect, these would involve less massive
satellites, with only a moderate impact on the internal interstellar medium of
W0410-0913, which is sustained by a rotationally-supported fast-rotating
molecular disk, as Atacama Large Millimeter Array observations suggest.


  The paper presents a measurement of the Standard Model Higgs Boson decaying
to $b$-quark pairs in the vector boson fusion (VBF) production mode. A sample
corresponding to 126 fb$^{-1}$ of $\sqrt{s} =$ 13 TeV proton-proton collision
data, collected with the ATLAS experiment at the Large Hadron Collider, is
analyzed utilizing an adversarial neural network for event classification. The
signal strength, defined as the ratio of the measured signal yield to that
predicted by the Standard Model for VBF Higgs production, is measured to be
$0.95^{+0.38}_{-0.36}$, corresponding to an observed (expected) significance of
2.6 (2.8) standard deviations from the background only hypothesis. The results
are additionally combined with an analysis of Higgs bosons decaying to
$b$-quarks, produced via VBF in association with a photon.


  By means of a semiclassical analysis we show that the trace anomaly does not
affect the cosmological constant. We calculate the evolution of the Hubble
parameter in quasi de Sitter spacetime, where the Hubble parameter varies
slowly in time, and in FLRW spacetimes. We show dynamically that a Universe
consisting of matter with a constant equation of state, a cosmological constant
and the quantum trace anomaly evolves either to the classical de Sitter
attractor or to a quantum trace anomaly driven one. There is no dynamical
effect that influences the effective value of the cosmological constant.


  We present a spectroscopic investigation into the vibrational and
optoelectronic properties of WS2 domes in the 0-0.65 GPa range. The pressure
evolution of the system morphology, deduced by the combined analysis of Raman
and photoluminescence spectra, revealed a significant variation in the dome's
aspect ratio. The modification of the dome shape caused major changes in the
mechanical properties of the system resulting in a sizable increase of the
out-of-plane compressive strain while keeping the in-plane tensile strain
unchanged. The variation of the strain gradients drives a non-linear behavior
in both the exciton energy and radiative recombination intensity, interpreted
as the consequence of a hybridization mechanism between the electronic states
of two distinct minima in the conduction band. Our results indicate that
pressure and strain can be efficiently combined in low dimensional systems with
unconventional morphology to obtain modulations of the electronic band
structure not achievable in planar crystals.


  A generic extension $L[x]$ of $L$ by a real $x$ is defined, in which the
$\mathsf E_0$-class of $x$ is a lightface $\Pi^1_2$ set containing no
ordinal-definable reals.


  We study theoretically the distributions of charge and spin polarization of a
topological insulator ribbon, with a realistic rectangular cross section. Due
to constriction in two lateral directions, the surface states discretize into a
series of subbands inside of the bulk band gap. The charge and spin
distribution show interesting characters which are different from an ideal
topological surface state. The effect of merging of four different surface
states into the new one as an entity are analyzed. Optical conductivity and
dynamical spin susceptibility of the ribbon are studied. Different from a
single ideal surface, the optical response and dynamical spin susceptibility of
a ribbon do not have a clear correspondence. The dynamical spin susceptibility
could be used to identify the more adequate model for Bi$_2$Se$_3$.


  Just-in-time arrival in the maritime industry is a key concept for the
reduction of Greenhouse gas emissions and cost-cutting, with the aim to reach
the industrywide overall climate goals set by the International Maritime
Organization (IMO) for 2030. In this note, we propose a mathematical
formulation which allows for an implementation on quantum computers.


  Definition modeling is an important task in advanced natural language
applications such as understanding and conversation. Since its introduction, it
focus on generating one definition for a target word or phrase in a given
context, which we refer to as Single Definition Modeling (SDM). However, this
approach does not adequately model the correlations and patterns among
different contexts and definitions of words. In addition, the creation of a
training dataset for SDM requires significant human expertise and effort. In
this paper, we carefully design a new task called Multiple Definition Modeling
(MDM) that pool together all contexts and definition of target words. We
demonstrate the ease of creating a model as well as multiple training sets
automatically. % In the experiments, we demonstrate and analyze the benefits of
MDM, including improving SDM's performance by using MDM as the pretraining task
and its comparable performance in the zero-shot setting.


  In recent years, efficient optimization algorithms for Nonlinear Model
Predictive Control (NMPC) have been proposed, that significantly reduce the
on-line computational time. In particular, direct multiple shooting and
Sequential Quadratic Programming (SQP) are used to efficiently solve Nonlinear
Programming (NLP) problems arising from continuous-time NMPC applications. One
of the computationally demanding steps for on-line optimization is the
computation of sensitivities of the nonlinear dynamics at every sampling
instant, especially for systems of large dimensions, strong stiffness, and when
using long prediction horizons. In this paper, within the algorithmic framework
of the Real-Time Iteration (RTI) scheme based on multiple shooting, an inexact
sensitivity updating scheme is proposed, that performs a partial update of the
Jacobian of the constraints in the NLP. Such update is triggered by using a
Curvature-like Measure of Nonlinearity (CMoN), so that only sensitivities
exhibiting highly nonlinear behaviour are updated, thus adapting to system
operating conditions and possibly reducing the computational burden. An
advanced tuning strategy for the updating scheme is provided to automatically
determine the number of sensitivities being updated, with a guaranteed bounded
error on the Quadratic Programming (QP) solution. Numerical and control
performance of the scheme is evaluated by means of two simulation examples
performed on a dedicated implementation. Local convergence analysis is also
presented and a tunable convergence rate is proven, when applied to the SQP
method.


  Instabilities and long term shifts in seasons, whether induced by natural
drivers or human activities, pose great disruptive threats to ecological,
agricultural, and social systems. Here, we propose, measure, and explore two
fundamental markers of location-sensitive seasonal variations: the Summer and
Winter Teletherms---the on-average annual dates of the hottest and coldest days
of the year. We analyse daily temperature extremes recorded at 1218 stations
across the contiguous United States from 1853--2012, and observe large regional
variation with the Summer Teletherm falling up to 90 days after the Summer
Solstice, and 50 days for the Winter Teletherm after the Winter Solstice. We
show that Teletherm temporal dynamics are substantive with clear and in some
cases dramatic shifts reflective of system bifurcations. We also compare
recorded daily temperature extremes with output from two regional climate
models finding considerable though relatively unbiased error. Our work
demonstrates that Teletherms are an intuitive, powerful, and statistically
sound measure of local climate change, and that they pose detailed, stringent
challenges for future theoretical and computational models.


  Let $Z(F)$ be the number of solutions of a random $k$-satisfiability formula
$F$ with $n$ variables and clause density $\alpha$. Assume that the probability
that $F$ is unsatisfiable is $O(1/\log(n)^{1+\e})$ for $\e>0$. We show that
(possibly excluding a countable set of `exceptional' $\alpha$'s) the number of
solutions concentrate in the logarithmic scale, i.e., there exists a non-random
function $\phi(\alpha)$ such that, for any $\delta>0$, $(1/n)\log Z(F)\in
[\phi-\delta,\phi+\delta]$ with high probability. In particular, the assumption
holds for all $\alpha<1$, which proves the above concentration claim in the
whole satisfiability regime of random $2$-SAT. We also extend these results to
a broad class of constraint satisfaction problems. The proof is based on an
interpolation technique from spin-glass theory, and on an application of
Friedgut's theorem on sharp thresholds for graph properties.


  NGC 1851 is an intriguing Galactic globular cluster, with multiple stellar
evolutionary sequences, light and heavy element abundance variations and
indications of a surrounding stellar halo. We present the first results of a
spectroscopic study of red giant stars within and outside of the tidal radius
of this cluster. Our results identify nine probable new cluster members (inside
the tidal radius) with heliocentric radial velocities consistent with that of
NGC 1851. We also identify, based on their radial velocities, four probable
extratidal cluster halo stars at distances up to ~3.1 times the tidal radius,
which are supportive of previous findings that NGC 1851 is surrounded by an
extended stellar halo. Proper motions were available for 12 of these 13 stars
and all are consistent with that of NGC 1851. Apart from the cluster members
and cluster halo stars, our observed radial velocity distribution agrees with
the expected distribution from a Besancon disk/N-body stellar halo Milky Way
model generated by the Galaxia code, suggesting that no other structures at
different radial velocities are present in our field. The metallicities of
these stars are estimated using equivalent width measurements of the near
infrared calcium triplet absorption lines and are found, within the limitations
of this method, to be consistent with that of NGC 1851. In addition we recover
110 red giant cluster members from previous studies based on their radial
velocities and identify three stars with unusually high radial velocities.


  Hypergraphs provide a natural representation for many real world datasets. We
propose a novel framework, HNHN, for hypergraph representation learning. HNHN
is a hypergraph convolution network with nonlinear activation functions applied
to both hypernodes and hyperedges, combined with a normalization scheme that
can flexibly adjust the importance of high-cardinality hyperedges and
high-degree vertices depending on the dataset. We demonstrate improved
performance of HNHN in both classification accuracy and speed on real world
datasets when compared to state of the art methods.


  Running deep neural network (DNN) inference on mobile devices, i.e., mobile
inference, has become a growing trend, making inference less dependent on
network connections and keeping private data locally. The prior studies on
optimizing DNNs for mobile inference typically focus on the metric of average
inference latency, thus implicitly assuming that mobile inference exhibits
little latency variability. In this note, we conduct a preliminary measurement
study on the latency variability of DNNs for mobile inference. We show that the
inference latency variability can become quite significant in the presence of
CPU resource contention. More interestingly, unlike the common belief that the
relative performance superiority of DNNs on one device can carry over to
another device and/or another level of resource contention, we highlight that a
DNN model with a better latency performance than another model can become
outperformed by the other model when resource contention be more severe or
running on another device. Thus, when optimizing DNN models for mobile
inference, only measuring the average latency may not be adequate; instead,
latency variability under various conditions should be accounted for, including
but not limited to different devices and different levels of CPU resource
contention considered in this note.


  Let $(Y, d)$ be a Gromov-Hausdorff limit of $n$-dimensional closed shrinking
K\"ahler-Ricci solitons with uniformly bounded volumes and Futaki invariants.
We prove that off a closed subset of codimension at least 4, Y is a smooth
manifold satisfying a shrinking K\"ahler-Ricci soliton equation. A similar
convergence result for K\"ahler-Ricci flow of positive first Chern class is
also obtained.


  Given the present distribution of mass tracing objects in an expanding
universe, we develop and test a fast method for recovering their past orbits
using the least action principle. In this method, termed FAM for Fast Action
Minimization, the orbits are expanded in a set of orthogonal time-base
functions satisfying the appropriate boundary conditions at the initial and
final times. The conjugate gradient method is applied to locate the extremum of
the action in the space of the expansion coefficients of the orbits. The
TREECODE gravity solver routine is used for computing the gravitational fields
appearing in the action and its gradients. The time integration of the
Lagrangian is done using Gaussian quadratures. FAM allows us to increase the
number of galaxies used in previous numerical action principle implementations
by more than one order of magnitude. For example, orbits for the $\sim 15,000$
IRAS PSC$z$ galaxies can be recovered in $\sim 12,000$ CPU seconds on a 400MHz
DEC-Alpha machine. FAM can recover the present peculiar velocities of particles
and the initial fluctuations field. It successfully recovers the flow field
down to clusters scales, where deviations of the flow from the Zel'dovich
solution are significant. We also show how to recover orbits from the present
distribution of objects as in redshift space by direct minimization of a
modified action, without iterating the solution between real and redshift
spaces.


  Limits are imposed upon the possible rate of change of extra spatial
dimensions in a decrumpling model Universe with time variable spatial
dimensions (TVSD) by considering the time variation of (1+3)-dimensional
Newton's constant. Previous studies on the time variation of (1+3)-dimensional
Newton's constant in TVSD theory had not been included the effects of the
volume of the extra dimensions and the effects of the surface area of the unit
sphere in D-space dimensions. Our main result is that the absolute value of the
present rate of change of spatial dimensions to be less than about
10^{-14}yr^{-1}. Our results would appear to provide a prima facie case for
ruling the TVSD model out. We show that based on observational bounds on the
present-day variation of Newton's constant, one would have to conclude that the
spatial dimension of the Universe when the Universe was at the Planck scale to
be less than or equal to 3.09. If the dimension of space when the Universe was
at the Planck scale is constrained to be fractional and very close to 3, then
the whole edifice of TVSD model loses credibility.


  Phase evolution in (Ag1-xLix)NbO3 (ALN) solid solution was investigated by
X-ray diffraction technique, dielectric and polarization measurements. It is
shown that small substitution of Ag with Li gives rise to an
orthorhombic-rhombohedral structural transformation in ABO3-perovskite silver
niobate at room temperature. Structural refinements indicate that both A- and
B-site displacements contribute to the spontaneous polarization of the
ferroelectric phase with symmetry R3c. Increasing Li-concentration enhances the
ferroelectric rhombohedral distortion, resulting in the increase of the
para-ferroelectric phase transition temperature and the polarization of the
solid solutions.


  We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard
model analogous to the time-dependent Hartree-Fock (HF) method. The formalism
incorporates ground state correlations of the random phase approximation (RPA)
type beyond the GA. Static quantities like ground state energy and double
occupancy are in excellent agreement with exact results in one dimension up to
moderate coupling and in two dimensions for all couplings. We find a
substantial improvement over traditional GA and HF+RPA treatments. Dynamical
correlation functions can be easily computed and are also substantially better
than HF+RPA ones and obey well behaved sum rules.


  The invisibility graph $I(X)$ of a set $X \subseteq \mathbb{R}^d$ is a
(possibly infinite) graph whose vertices are the points of $X$ and two vertices
are connected by an edge if and only if the straight-line segment connecting
the two corresponding points is not fully contained in $X$. We consider the
following three parameters of a set $X$: the clique number $\omega(I(X))$, the
chromatic number $\chi(I(X))$ and the convexity number $\gamma(X)$, which is
the minimum number of convex subsets of $X$ that cover $X$. We settle a
conjecture of Matou\v{s}ek and Valtr claiming that for every planar set $X$,
$\gamma(X)$ can be bounded in terms of $\chi(I(X))$. As a part of the proof we
show that a disc with $n$ one-point holes near its boundary has $\chi(I(X)) \ge
\log\log(n)$ but $\omega(I(X))=3$. We also find sets $X$ in $\mathbb{R}^5$ with
$\chi(X)=2$, but $\gamma(X)$ arbitrarily large.


  Working within the path-integral framework we first establish a duality
between the partion functions of two $U(1)$ gauge theories with a theta term in
$d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$
dimensions we arrive to the partition function of a $U(1)$ gauge theory coupled
to a scalar field with an action that exhibits a Dirac monopole solution. A
subsequent reduction to $d=2$ dimensions leads to the partition function of a
theory in which the gauge field decouples from two scalars which have
non-trivial vortex-like solutions. Finally this $d=2$ partition function can be
related to the bosonized version of the two-dimensional QED$_2$ (Schwinger)
model.


  In this survey article, given a smooth closed manifold M we study the space
of Riemannian metrics of positive scalar curvature on M. A long-standing
question is: when is this space non-empty (i.e. when does M admit a metric of
positive scalar curvature)? More generally: what is the topology of this space?
For example, what are its homotopy groups?
  Higher index theory of the Dirac operator is the basic tool to address these
questions. This has seen tremendous development in recent years, and in this
survey we will discuss some of the most pertinent examples.
  In particular, we will show how advancements of large scale index theory
(also called coarse index theory) give rise to new types of obstructions, and
provide the tools for a systematic study of the existence and classification
problem via the K-theory of C*-algebras. This is part of a program "mapping the
topology of positive scalar curvature to analysis".
  In addition, we will show how advanced surgery theory and smoothing theory
can be used to construct the first elements of infinite order in the k-th
homotopy groups of the space of metrics of positive scalar curvature for
arbitrarily large k. Moreover, these examples are the first ones which remain
non-trivial in the moduli space of such metrics.


  Equilibrium aspects of molecular recognition of rigid biomolecules are
investigated using coarse-grained lattice models. The analysis is carried out
in two stages. First an ensemble of probe molecules is designed with respect to
the target biomolecule. The recognition ability of the probe ensemble is then
investigated by calculating the free energy of association. The influence of
cooperative and anti-cooperative effects accompanying the association of the
target and probe molecules is studied. Numerical findings are presented and
compared to analytical results which can be obtained in the limit of dominating
cooperativity and in the mean-field formulation of the models.


  We present a compositional embedding framework that infers not just a single
class per input image, but a set of classes, in the setting of one-shot
learning. Specifically, we propose and evaluate several novel models consisting
of (1) an embedding function f trained jointly with a "composition" function g
that computes set union operations between the classes encoded in two embedding
vectors; and (2) embedding f trained jointly with a "query" function h that
computes whether the classes encoded in one embedding subsume the classes
encoded in another embedding. In contrast to prior work, these models must both
perceive the classes associated with the input examples and encode the
relationships between different class label sets, and they are trained using
only weak one-shot supervision consisting of the label-set relationships among
training examples. Experiments on the OmniGlot, Open Images, and COCO datasets
show that the proposed compositional embedding models outperform existing
embedding methods. Our compositional embedding models have applications to
multi-label object recognition for both one-shot and supervised learning.


  We propose to use a new platform - ultracold polar molecules - for quantum
computing with switchable interactions. The on/off switch is accomplished by
selective excitation of one of the "0" or "1" qubits - long-lived molecular
states - to an "excited" molecular state with a considerably different dipole
moment. We describe various schemes based on this switching of dipolar
interactions where the selective excitation between ground and excited states
is accomplished via optical, micro-wave, or electric fields. We also generalize
the schemes to take advantage of the dipole blockade mechanism when dipolar
interactions are very strong. These schemes can be realized in several recently
proposed architectures.


  We undertook a search for new dwarf galaxies in the Leo-I group using the
data from the DECaLS digital sky survey. Five new presumed members of this
group have been found in a wide vicinity of ${\rm M}\,105 ({\rm NGC}\,3379$).
Currently, the group has a population of $83$ galaxies, $33$ of which have
measured radial velocities. More than half of the group members belong to early
types with no signs of ongoing star formation. About a quarter of the galaxies
are outside the group's virial radius, $R_v = 385$~kpc. The presence of
multiple systems with a size of about 15~kpc is evident in the group, but there
are no noticeable global flat or filamentary substructures. The luminosity
function of the group looks to be deficient in galaxies with absolute
magnitudes in the interval $M_B = [-18, -15]$ mag. The ${\rm M}\,105$ group is
characterized by a radial velocity dispersion of $136$~km~s$^{-1}$, orbital
mass estimate $(5.76\pm1.32)\times 10^{12}~M_{\odot}$, and the total
mass-to-K-band-luminosity ratio $(17.8\pm4.1) M_\odot/L_\odot$. The neighboring
group of galaxies around ${\rm M}\,66 ({\rm NGC}\,3627$) has a similar virial
radius, $390$~kpc, velocity dispersion, $135$~km~s$^{-1}$, and total
mass-to-luminosity ratio, $(15.6\pm3.9) M_\odot/L_\odot$. Both groups in the
Leo constellation are approaching the Local Group with a velocity of about
100~km~s$^{-1}$. In the background of the ${\rm M}\,105$ group, we noted a
group of 6 galaxies with an unusually low virial mass-to-luminosity ratio,
$M_T/L_K = (4.1\pm2.2) M_\odot/L_\odot$.


  In the physically non viscous fluid dynamics, "shock capturing" methods adopt
either an artificial viscosity contribution or an appropriate Riemann solver
algorithm. These techniques are necessary to solve the strictly hyperbolic
Euler equations if flow discontinuities (the Riemann problem) must be solved. A
necessary dissipation is normally used in such cases. An explicit artificial
viscosity contribution is normally adopted to smooth out spurious heating and
to treat transport phenomena. Such a treatment of inviscid flows is also widely
adopted in the Smooth Particle Hydrodynamics (SPH) finite volume free
Lagrangian scheme. In other cases, the intrinsic dissipation of Godunov - type
methods is implicitly useful. Instead "shock tracking" methods normally use the
Rankine - Hugoniot jump conditions to solve such problem. A simple, effective
solution of the Riemann problem in inviscid ideal gases is here proposed, based
on an empirical reformulation of the equation of state (EoS) in the Euler
equations in fluid dynamics, whose limit for a motionless gas coincides with
the classical EoS of ideal gases. The application of such effective solution of
the Riemann problem excludes any dependence, in the transport phenomena, on
particle resolution length $h$ in non viscous SPH flows. Results on 1D shock
tube tests are here shown.


  Non-Gaussianity inducing operations are studied in the recent past from
different perspectives. Here, we study the role of photon addition, a
non-Gaussianity inducing operation, in the enhancement of nonclassicality in a
finite dimensional quantum state, namely hypergeometric state with the help of
some quantifiers and measures of nonclassicality. We observed that measures to
characterize the quality of single photon source and anticlassicality lead to
the similar conclusion, i.e., to obtain the desired quantum features one has to
choose all the state parameters such that average photon numbers remains low.
Wigner logarithmic negativity of the photon added hypergeometric state and
concurrence of the two-mode entangled state generated at the output of a
beamsplitter from this state show that nonclassicality can be enhanced by
increasing the state parameter and photon number addition but decreasing the
dimension of the state. In principle, decreasing the dimension of the state is
analogous to holeburning and is thus expected to increase nonclassicality.
Further, the variation of Wigner function not only qualitatively illustrates
the same features as observed quantitatively through concurrence potential and
Wigner logarithimic negativity, but illustrate non-Gaussianity of the quantum
state as well.


  We consider a simple Newtonian model of a steady accretion disk around a
black hole. The model is based on height-integrated hydrodynamic equations,
alpha-viscosity, and a pseudo-Newtonian potential that results in an innermost
stable circular orbit (ISCO) that closely approximates the one predicted by GR.
We find that the hydrodynamic models exhibit increasing deviations from the
standard disk model of Shakura & Sunyaev as disk thickness H/R or the value of
alpha increases. The latter is an analytical model in which the viscous torque
is assumed to vanish at the ISCO. We consider the implications of the results
for attempts to estimate black hole spin by using the standard disk model to
fit continuum spectra of black hole accretion disks. We find that the error in
the spin estimate is quite modest so long as H/R < 0.1 and alpha < 0.2. At
worst the error in the estimated value of the spin parameter is 0.1 for a
non-spinning black hole; the error is much less for a rapidly spinning hole. We
also consider the density and disk thickness contrast between the gas in the
disk and that inside the ISCO. The contrast needs to be large if black hole
spin is to be successfully estimated by fitting the relativistically-broadened
X-ray line profile of fluorescent iron emission from reflection off an
accretion disk. In our hydrodynamic models, the contrast in density and
thickness is low when H/R>0.1, sugesting that the iron line technique may be
most reliable in extemely thin disks. We caution that these results have been
obtained with a viscous hydrodynamic model and need to be confirmed with MHD
simulations of radiatively cooled thin disks.


  We study fair resource allocation when the resources contain a mixture of
divisible and indivisible goods, focusing on the well-studied fairness notion
of maximin share fairness (MMS). With only indivisible goods, a full MMS
allocation may not exist, but a constant multiplicative approximate allocation
always does. We analyze how the MMS approximation guarantee would be affected
when the resources to be allocated also contain divisible goods. In particular,
we show that the worst-case MMS approximation guarantee with mixed goods is no
worse than that with only indivisible goods. However, there exist problem
instances to which adding some divisible resources would strictly decrease the
MMS approximation ratio of the instance. On the algorithmic front, we propose a
constructive algorithm that will always produce an $\alpha$-MMS allocation for
any number of agents, where $\alpha$ takes values between $1/2$ and $1$ and is
a monotone increasing function determined by how agents value the divisible
goods relative to their MMS values.


  Recently Gizon, Duvall and Schou (2002) suggested that supergranulation has a
wave-like component. In this paper I show that the same phenomenon can be
observed using surface Doppler shift data, thereby confirming their
observations. I am also able to measure the dispersion relation to lower
wavenumbers and to extend the results for rotation and meridional flows beyond
+/-70 degrees latitude.


  Recently, in a study the X-ray flaring activity of Sgr A* with Chandra and
XMM-Newton public observations from 1999 to 2014 and 2014 Swift data, it has
been argued that the "bright and very bright" flaring rate raised from 2014
Aug. 31. Thanks to 482ks of observations performed in 2015 with Chandra,
XMM-Newton and Swift, we test the significance of this rise of flaring rate and
determine the threshold of unabsorbed flare flux or fluence leading to any
flaring-rate change. The mean unabsorbed fluxes of the 107 flares detected in
the 1999-2015 observations are consistently computed from the extracted spectra
and calibration files, assuming the same spectral parameters. We construct the
observed flare fluxes and durations distribution for the XMM-Newton and Chandra
flares and correct it from the detection biases to estimate the intrinsic
distribution from which we determine the average flare detection efficiency for
each observation. We apply the BB algorithm on the flare arrival times
corrected from the corresponding efficiency. We confirm a constant overall
flaring rate in 1999-2015 and a rise in the flaring rate for the most
luminous/energetic flares from 2014 Aug. 31 (4 months after the passage of the
DSO/G2 close to Sgr A*). We also identify a decay of the flaring rate for the
less luminous and less energetic flares from 2013 Aug. and Nov., respectively
(10 and 7 months before the pericenter of the DSO/G2). The decay of the faint
flaring rate is difficult to explain by the tidal disruption of the DSO/G2,
whose stellar nature is now well established, since it occurred well before its
pericenter. Moreover, a mass transfer from the DSO/G2 to Sgr A* is not required
to produce the rise in the bright flaring rate since the energy saved by the
decay of the number of faint flares during a long time period may be later
released by several bright flares during a shorter time period. (abridged)


  Biological materials exhibit complex structure-property relationships which
are only beginning to be elucidated. Understanding the underlying physical
mechanisms of the structure-property relationships is the key to designing
bioinspired materials. The eggshell is an excellent example because many design
trade-offs are well balanced by its seemingly simple but highly evolved
structures. The first design trade-off: to break an eggshell, the internal
breaking load needed is much lower than the external breaking load. The reason
is that the dome-shaped structure leads to a special stress distribution which
inhibits the propagation of the first crack. The second design trade-off: the
eggshell is tough during the incubation but weakened at the time of hatching.
The membrane of the eggshell significantly improves the toughness by bridging
the primary crack and creating more secondary cracks. Moreover, the moisture
content-controlled property of the membrane makes the toughness of the eggshell
tunable. The third design trade-off: the eggshell must be thick enough to
withstand the external forces, but the supply of the building material calcium
is limited. The proposed three-index model indicates that the driving force in
the evolution of eggshell thickness could be the balance between the protection
and nutrient consumption to maximize survivability. The general methodologies
presented here hold great potential for the development of eggshell-inspired
structural materials that can be used in sports safety applications and the
packaging industry.


  This paper provides a collection of mathematical and computational tools for
the study of robustness in nonlinear gene regulatory networks, represented by
time- and state-discrete dynamical systems taking on multiple states. The focus
is on networks governed by nested canalizing functions (NCFs), first introduced
in the Boolean context by S. Kauffman. After giving a general definition of
NCFs we analyze the class of such functions. We derive a formula for the
normalized average $c$-sensitivities of multistate NCFs, which enables the
calculation of the Derrida plot, a popular measure of network stability. We
also provide a unique canonical parametrized polynomial form of NCFs. This form
has several consequences. We can easily generate NCFs for varying parameter
choices, and derive a closed form formula for the number of such functions in a
given number of variables, as well as an asymptotic formula. Finally, we
compute the number of equivalence classes of NCFs under permutation of
variables. Together, the results of the paper represent a useful mathematical
framework for the study of NCFs and their dynamic networks.


  Information technology (IT) companies implement multi-dimensional policy
plans that include procedures, sub-plans, and instructions to outline their
business scopes, targets, and communications. This work outlined the IT policy
implementation plan designed by an imaginary company with a random name called
Northcentral Cloud Consulting Firm (NCCF), containing proposed IT policies,
milestones and roadmaps, control framework, stakeholder responsibilities,
knowledge transfer plan, and leadership roles. As NCCF's major customers seek
data-driven solutions in cloud computing, the NCCF IT policy plan provides
various data policies, including security and proper usage of machine learning
services. The plan offers a detailed roadmap of its financial, geographical,
and reputational expansion within three years. The IT policy plan also
compromises an IT risk management, contingency, and emergency communication
plan, mainly for protecting data and business continuity. Stakeholder
responsibilities are incorporated into the IT policy plan, as NCCF considers
any engagement with its customers as a collaborative effort in which both
parties have and share several responsibilities.


  To achieve mass, power, and cost reduction, there is a trend to reduce the
volume of many instruments aboard spacecraft, especially for small spacecraft
(cubesats or nanosats) with very limited mass, volume and power budgets. With
the current trend of miniaturizing spacecraft instruments one could naturally
ask if is there a physical limit to this process for star sensors. This paper
shows that there is a fundamental limit on star sensor accuracy, which depends
on stellar distribution, star sensor dimensions and exposure time. An estimate
of such limit is given for our location in the galaxy.


  Storytelling plays a central role in human socializing and entertainment.
However, much of the research on automatic storytelling generation assumes that
stories will be generated by an agent without any human interaction. In this
paper, we introduce the task of collaborative storytelling, where an artificial
intelligence agent and a person collaborate to create a unique story by taking
turns adding to it. We present a collaborative storytelling system which works
with a human storyteller to create a story by generating new utterances based
on the story so far. We constructed the storytelling system by tuning a
publicly-available large scale language model on a dataset of writing prompts
and their accompanying fictional works. We identify generating sufficiently
human-like utterances to be an important technical issue and propose a
sample-and-rank approach to improve utterance quality. Quantitative evaluation
shows that our approach outperforms a baseline, and we present qualitative
evaluation of our system's capabilities.


  We focus on uncertainties in supernova measurements, in particular of
individual magnitudes and redshifts, to review to what extent supernovae
measurements of the expansion history of the universe are likely to allow us to
constrain a possibly redshift-dependent equation of state of dark energy,
$w(z)$. focus in particular on the central question of how well one might rule
out the possibility of a cosmological constant $w=-1$. We argue that it is
unlikely that we will be able to significantly reduce the uncertainty in the
determination of $w$ beyond its present bounds, without significant
improvements in our ability to measure the cosmic distance scale as a function
of redshift. Thus, unless the dark energy significantly deviates from $w(z)=-1$
at some redshift, very stringent control of the statistical and systematic
errors will be necessary to have a realistic hope of empirically distinguishing
exotic dark energy from a cosmological constant.


  Let X be a n-dimensional (smooth) intersection of two quadrics, and let T*X
be its cotangent bundle. We show that the algebra of symmetric tensors on X is
a polynomial algebra in n variables. The corresponding map F: T*X -- > C^n is a
Lagrangian fibration, which admits an explicit geometric description; its
general fiber is a Zariski open subset of an abelian variety, quotient of a
hyperelliptic Jacobian by a 2-torsion subgroup. For n = 3 F is the Hitchin
fibration of the moduli space of rank 2 bundles with fixed determinant on a
curve of genus 2.


  In superconductors that lack inversion symmetry, a supercurrent flow can lead
to nondissipative magnetoelectric effects. We offer a straightforward formalism
to obtain a supercurrent-induced magnetization in superconductors with broken
inversion symmetry, which may have orbital, layer, sublattice, or valley
degrees of freedom, multiband noncentrosymmetric superconductors. The
nondissipative magnetoelectric effect may find applications in fabricating
quantum computation platforms or efficient superconducting spintronic devices.
We explore how the current-induced magnetization can be employed to create and
manipulate Majorana zero modes in a simple hybrid structure.


  A suitable notion of weak solution to infinite-dimensional rate-independent
systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The
key feature of such notion is that the energy dissipated at jump
discontinuities takes both into account inertial and viscous effects. Under a
general set of assumptions it is shown that IBV solutions arise as vanishing
inertia and viscosity limits of second order dynamic evolutions as well as of
the corresponding time-incremental approximations. Relevant examples coming
from applications, such as Allen-Cahn type evolutions and Kelvin-Voigt models
in linearized elasticity, are considered.


  Tensor network states and methods have erupted in recent years. Originally
developed in the context of condensed matter physics and based on
renormalization group ideas, tensor networks lived a revival thanks to quantum
information theory and the understanding of entanglement in quantum many-body
systems. Moreover, it has been not-so-long realized that tensor network states
play a key role in other scientific disciplines, such as quantum gravity and
artificial intelligence. In this context, here we provide an overview of basic
concepts and key developments in the field. In particular, we briefly discuss
the most important tensor network structures and algorithms, together with a
sketch on advances related to global and gauge symmetries, fermions,
topological order, classification of phases, entanglement Hamiltonians,
AdS/CFT, artificial intelligence, the 2d Hubbard model, 2d quantum
antiferromagnets, conformal field theory, quantum chemistry, disordered
systems, and many-body localization.


  We analyze the problem of comparing unitary transformations. The task is to
decide, with minimal resources and maximal reliability, whether two given
unitary transformations are identical or different. It is possible to make such
comparisons without obtaining any information about the individual
transformations. Different comparison strategies are presented and compared
with respect to their efficiency. With an interferometric setup, it is possible
to compare two unitary transforms using only one test particle. Another
strategy makes use of a two-particle singlet state. This strategy is more
efficient than using a non-entangled two-particle test state, thus
demonstrating the benefit of entanglement. Generalisations to higher
dimensional transforms and to more than two transformations are made.


  In this memory we made the design of an indexing model for Arabic language
and adapting standards for describing learning resources used (the LOM and
their application profiles) with learning conditions such as levels education
of students, their levels of understanding...the pedagogical context with
taking into account the repre-sentative elements of the text, text's
length,...in particular, we highlight the specificity of the Arabic language
which is a complex language, characterized by its flexion, its voyellation and
its agglutination.


  Generalization to out-of-distribution data has been a problem for Visual
Question Answering (VQA) models. To measure generalization to novel questions,
we propose to separate them into "skills" and "concepts". "Skills" are visual
tasks, such as counting or attribute recognition, and are applied to "concepts"
mentioned in the question, such as objects and people. VQA methods should be
able to compose skills and concepts in novel ways, regardless of whether the
specific composition has been seen in training, yet we demonstrate that
existing models have much to improve upon towards handling new compositions. We
present a novel method for learning to compose skills and concepts that
separates these two factors implicitly within a model by learning grounded
concept representations and disentangling the encoding of skills from that of
concepts. We enforce these properties with a novel contrastive learning
procedure that does not rely on external annotations and can be learned from
unlabeled image-question pairs. Experiments demonstrate the effectiveness of
our approach for improving compositional and grounding performance.


  The low-temperature state of the quantum spin liquid candidate
$\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ emerges via an anomaly at
$T^{*}\sim6$ K. Although signatures of this anomaly have been revealed in
various quantities, its origin has remained unclear. Here we report inelastic
neutron scattering measurements on single crystals of
$\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, aiming at studying phonon
renormalization effects at $T^{*}$. A drastic change was observed in the phonon
damping across $T^{*}$ for a breathing mode of BEDT-TTF dimers at $E=4.7$ meV.
The abrupt change in the phonon damping is attributed to a phase transition
into a valence bond solid state based on an effective model describing the
spin-charge coupling in this dimer-Mott system.


  In a recent article S. Gharibian
[\href{http://dx.doi.org/10.1103/PhysRevA.86.042106}{Phys. Rev. A {\bf 86},
042106 (2012)}] has conjectured that no two qubit separable state of rank
greater than two could be maximally non classical (defined to be those which
have normalized geometric discord $1/4$) and asked for an analytic proof. In
this work we prove analytically that among the subclass of $X$ states, there is
a unique (up to local unitary equivalence) maximal separable state of rank two.
Partial progress has been made towards the general problem and some necessary
conditions have been derived.


  Deep hashing methods have shown great retrieval accuracy and efficiency in
large-scale image retrieval. How to optimize discrete hash bits is always the
focus in deep hashing methods. A common strategy in these methods is to adopt
an activation function, e.g. $\operatorname{sigmoid}(\cdot)$ or
$\operatorname{tanh}(\cdot)$, and minimize a quantization loss to approximate
discrete values. However, this paradigm may make more and more hash bits stuck
into the wrong saturated area of the activation functions and never escaped. We
call this problem "Dead Bits Problem~(DBP)". Besides, the existing quantization
loss will aggravate DBP as well. In this paper, we propose a simple but
effective gradient amplifier which acts before activation functions to
alleviate DBP. Moreover, we devise an error-aware quantization loss to further
alleviate DBP. It avoids the negative effect of quantization loss based on the
similarity between two images. The proposed gradient amplifier and error-aware
quantization loss are compatible with a variety of deep hashing methods.
Experimental results on three datasets demonstrate the efficiency of the
proposed gradient amplifier and the error-aware quantization loss.


  The quantum Hall system is known to have two mutually dual Chern-Simons
descriptions, one associated with the hydrodynamics of the electron fluid, and
another associated with the statistics. Recently, Susskind has made the claim
that the hydrodynamic Chern-Simons theory should be considered to have a
non-commutative gauge symmetry. The statistical Chern-Simons theory has a
perturbative momentum expansion. In this paper, we study this perturbation
theory and show that the effective action, although commutative at leading
order, is non-commutative. This conclusion is arrived at through a careful
study of the three-point function of Chern-Simons gauge fields. The
non-commutative gauge symmetry of this system is thus a quantum symmetry, which
we show can only be fully realized only through the inclusion of all orders in
perturbation theory. We discuss the duality between the two non-commutative
descriptions.


  We analyze efficiency of excitation energy transfer in photosynthetic
complexes in transient and stationary setting. In the transient setting the
absorption process is modeled as an individual event resulting in a subsequent
relaxation dynamics. In the stationary setting the absorption is a continuous
stationary process, leading to the nonequilibrium steady state. We show that,
as far as the efficiency is concerned, both settings can be considered to be
the same, as they result in almost identical efficiency. We also show that
non-Markovianity has no effect on the resulting efficiency, i.e., corresponding
Markovian dynamics results in identical efficiency. Even more, if one maps
dynamics to appropriate classical rate equations, the same efficiency as in
quantum case is obtained.


  We study mixed local and nonlocal elliptic equation with a variable
coefficient $\rho$. Under suitable assumptions on the behaviour at infinity of
$\rho$, we obtain uniqueness of solutions belonging to certain weighted Lebsgue
spaces, with a weight depending on the coefficient $\rho$. The hypothesis on
$\rho$ is optimal; indeed, when it fails we get nonuniqueness of solutions. We
also investigate the parabolic counterpart of such equation.


  The majority of machine learning methods can be regarded as the minimization
of an unavailable risk function. To optimize the latter, given samples provided
in a streaming fashion, we define a general stochastic Newton algorithm and its
weighted average version. In several use cases, both implementations will be
shown not to require the inversion of a Hessian estimate at each iteration, but
a direct update of the estimate of the inverse Hessian instead will be favored.
This generalizes a trick introduced in [2] for the specific case of logistic
regression, by directly updating the estimate of the inverse Hessian. Under
mild assumptions such as local strong convexity at the optimum, we establish
almost sure convergences and rates of convergence of the algorithms, as well as
central limit theorems for the constructed parameter estimates. The unified
framework considered in this paper covers the case of linear, logistic or
softmax regressions to name a few. Numerical experiments on simulated data give
the empirical evidence of the pertinence of the proposed methods, which
outperform popular competitors particularly in case of bad initializa-tions.


  In this paper, we compose a new task for deep argumentative structure
analysis that goes beyond shallow discourse structure analysis. The idea is
that argumentative relations can reasonably be represented with a small set of
predefined patterns. For example, using value judgment and bipolar causality,
we can explain a support relation between two argumentative segments as
follows: Segment 1 states that something is good, and Segment 2 states that it
is good because it promotes something good when it happens. We are motivated by
the following questions: (i) how do we formulate the task?, (ii) can a
reasonable pattern set be created?, and (iii) do the patterns work? To examine
the task feasibility, we conduct a three-stage, detailed annotation study using
357 argumentative relations from the argumentative microtext corpus, a small,
but highly reliable corpus. We report the coverage of explanations captured by
our patterns on a test set composed of 270 relations. Our coverage result of
74.6% indicates that argumentative relations can reasonably be explained by our
small pattern set. Our agreement result of 85.9% shows that a reasonable
inter-annotator agreement can be achieved. To assist with future work in
computational argumentation, the annotated corpus is made publicly available.


  We present a new solution to the problem of classifying Type Ia supernovae
from their light curves alone given a spectroscopically confirmed but biased
training set, circumventing the need to obtain an observationally expensive
unbiased training set. We use Gaussian processes (GPs) to model the
supernovae's (SN) light curves, and demonstrate that the choice of covariance
function has only a small influence on the GPs ability to accurately classify
SNe. We extend and improve the approach of Richards et al (2012} -- a diffusion
map combined with a random forest classifier -- to deal specifically with the
case of biassed training sets. We propose a novel method, called STACCATO
(SynThetically Augmented Light Curve ClassificATiOn') that synthetically
augments a biased training set by generating additional training data from the
fitted GPs. Key to the success of the method is the partitioning of the
observations into subgroups based on their propensity score of being included
in the training set. Using simulated light curve data, we show that STACCATO
increases performance, as measured by the area under the Receiver Operating
Characteristic curve (AUC), from 0.93 to 0.96, close to the AUC of 0.977
obtained using the 'gold standard' of an unbiased training set and
significantly improving on the previous best result of 0.88. STACCATO also
increases the true positive rate for SNIa classification by up to a factor of
50 for high-redshift/low brightness SNe.


  We consider the following novel variation on a classical avoidance problem
from combinatorics on words: instead of avoiding repetitions in all factors of
a word, we avoid repetitions in all factors where each individual factor is
considered as a "circular word", i.e., the end of the word wraps around to the
beginning. We determine the best possible avoidance exponent for alphabet size
2 and 3, and provide a lower bound for larger alphabets.


  Efficient Human Epithelial-2 (HEp-2) cell image classification can facilitate
the diagnosis of many autoimmune diseases. This paper presents an automatic
framework for this classification task, by utilizing the deep convolutional
neural networks (CNNs) which have recently attracted intensive attention in
visual recognition. This paper elaborates the important components of this
framework, discusses multiple key factors that impact the efficiency of
training a deep CNN, and systematically compares this framework with the
well-established image classification models in the literature. Experiments on
benchmark datasets show that i) the proposed framework can effectively
outperform existing models by properly applying data augmentation; ii) our
CNN-based framework demonstrates excellent adaptability across different
datasets, which is highly desirable for classification under varying laboratory
settings. Our system is ranked high in the cell image classification
competition hosted by ICPR 2014.


  We study structural properties of Wiener-Lebesgue spaces with respect to a
slowly varying metrics and certain Lebesgue parameters. For $p\in (0,1]$, we
deduce Schatten-$p$ properties for pseudo-differential operators whose symbols,
together with their derivatives, obey suitable Wiener-Lebesgue-boundedness
conditions. Especially, we perform such investigations for the Weyl-H\"ormander
calculus. Finally, we apply our results to global-type SG and Shubin
pseudo-differential operators.


  We show that the N\'eel states of two-dimensional antiferromagnets have low
energy vector boson excitations in the vicinity of deconfined quantum critical
points. We compute the universal damping of these excitations arising from
spin-wave emission. Detection of such a vector boson will demonstrate the
existence of emergent topological gauge excitations in a quantum spin system.


  Within the context of linear elasticity we show that a two-terminal network
of springs and masses, can respond exactly the same as a normal spring, but
with a frequency dependent spring constant. As a consequence a network of such
springs can have a frequency dependent effective elasticity tensor but zero
effective mass density. The internal masses influence the elasticity tensor,
but do not contribute to the effective mass density at any frequency.


  We review the passage from the supermembrane to matrix theory via a
consistent truncation following a non-commutative deformation in light-cone
gauge. Some indications are given that there should exist a generalisation of
non-commutativity involving a three-index theta on the membrane, and we discuss
some possible ways of investigating the corresponding algebraic structure.


  We examine the double copy structure of anyons in gauge theory and gravity.
Using on-shell amplitude techniques, we construct little group covariant
spinor-helicity variables describing massive particles with spin, which
together with locality and unitarity enables us to derive the long-range
tree-level scattering amplitudes involving anyons. We discover that classical
gauge theory anyon solutions double copy to their gravitational counterparts in
a non-trivial manner. Interestingly, we show that the massless double copy
captures the topological structure of curved spacetime in three dimensions by
introducing a non-trivial mixing of the topological graviton and the dilaton.
Finally, we show that the celebrated Aharonov-Bohm phase can be derived
directly from the constructed on-shell amplitude and that it too enjoys a
simple double copy to its gravitational counterpart.


  Semileptonic decay processes of $\Xi_c \to \Xi\ell\nu_\ell$ are studied by
light-cone QCD sum rules in this paper. The six form factors of $\Xi_c \to \Xi$
semileptonic transition matrix elements are calculated by this method with the
light-cone distribution amplitudes of $\Xi$ baryon up to twist six. With the
six form factors, the absolute branching ratios of $\Xi_c^0 \to \Xi^- \ell^+
\nu_\ell$ and $\Xi_c^+ \to \Xi^0 \ell^+ \nu_\ell$ are calculated by the
helicity amplitudes formalism of semileptonic differential decay widths. The
ratios of absolute branching ratios of electron and muon final states processes
give the proof of lepton flavor universality. Our results are in accordance
with the recent experimental and theoretical reports.


  A fully conservative sharp-interface method is developed for multiphase flows
with phase change. The coupling between two phases is implemented via
introducing the interfacial fluxes, which are obtained by solving a general
Riemann problem with phase change. A novel four-wave model is proposed to
obtain an approximate Riemann solution, which simplifies the eight-dimensional
roo-finding procedure in the exact solver to a sole iteration of the mass flux.
Unlike in the previous research, the jump conditions of all waves are imposed
strictly in the present approximate Riemann solver so that conservation is
guaranteed. Different choices of the fluid states used in the phase change
model are compared, and we have shown that the adjacent states of phase
interface should be used to ensure numerical consistency. To the authors'
knowledge, it has not been reported before in the open literature. With good
agreements, various numerical examples are considered to validate the present
method by comparing the results against the exact solutions or the previous
simulations.


  Community structure is one of the key properties of real-world complex
networks. It plays a crucial role in their behaviors and topology. While an
important work has been done on the issue of community detection, very little
attention has been devoted to the analysis of the community structure. In this
paper, we present an extensive investigation of the overlapping community
network deduced from a large-scale co-authorship network. The nodes of the
overlapping community network represent the functional communities of the
co-authorship network, and the links account for the fact that communities
share some nodes in the co-authorship network. The comparative evaluation of
the topological properties of these two networks shows that they share similar
topological properties. These results are very interesting. Indeed, the network
of communities seems to be a good representative of the original co-authorship
network. With its smaller size, it may be more practical in order to realize
various analyses that cannot be performed easily in large-scale real-world
networks.


  HARPS and it Kepler results indicate that half of solar-type stars host
planets with periods P<100 d and masses M < 30 M_E. These super Earth systems
are compact and dynamically cold. Here we investigate the stability of the
super Earth system around the K-dwarf HD40307. It could host up to six planets,
with one in the habitable zone. We analyse the system's stability using
numerical simulations from initial conditions within the observational
uncertainties. The most stable solution deviates 3.1 sigma from the published
value, with planets e and f not in resonance and planets b and c apsidally
aligned. We study the habitability of the outer planet through the
yearly-averaged insolation and black-body temperature at the pole. Both undergo
large variations because of its high eccentricity and are much more intense
than on Earth. The insolation variations are precession dominated with periods
of 40 kyr and 102 kyr for precession and obliquity if the rotation period is 3
d. A rotation period of about 1.5 d could cause extreme obliquity variations
because of capture in a Cassini state. For faster rotation rates the periods
converge to 10 kyr and 20 kyr. The large uncertainty in the precession period
does not change the overall outcome.


  Gamma-ray bursts (GRBs) are luminous enough to be detectable up to redshift
$z\sim 10$. They are often proposed as complementary tools to type-Ia
supernovae (SNe Ia) in tracing the Hubble diagram of the Universe. The distance
calibrations of GRBs usually make use one or some of the empirical luminosity
correlations, such as $\tau_{\rm lag}-L$, $V-L$, $E_p-L$, $E_p-E_{\gamma}$,
$\tau_{\rm RT}-L$ and $E_p-E_{\rm iso}$ relations. These calibrating methods
are based on the underling assumption that the empirical luminosity
correlations are universal over all redshift range. In this paper, we test the
possible redshift dependence of six luminosity correlations by dividing GRBs
into low-$z$ and high-$z$ classes according to their redshift smaller or larger
than 1.4. It is shown that the $E_p-E_{\gamma}$ relation for low-$z$ GRBs is
consistent with that for high-$z$ GRBs within $1\sigma$ uncertainty. The
intrinsic scatter of $V-L$ relation is too larger to make a convincing
conclusion. For the rest four correlations, however, low-$z$ GRBs differ from
high-$z$ GRBs at more than $3\sigma$ confidence level. As such, we calibrate
GRBs using the $E_p-E_{\gamma}$ relation in a model-independent way. The
constraint of high-$z$ GRBs on the $\Lambda$CDM model gives $\Omega_M=0.302\pm
0.142(1\sigma)$, well consistent with the Planck 2015 results.


  In this note we define geometric classical r-matrices and quantum R-matrices,
and show how any geometric classical r-matrix can be quantized to a geometric
quantum R-matrix. This is one of the simplest nontrivial examples of
quantization of solutions of the classical Yang-Baxter equation, which can be
explicitly computed.


  We compare different modes of pseudo almost automorphy and variants for
stochastic processes: in probability, in quadratic mean, or in distribution in
various senses. We show by a counterexample that square-mean (pseudo) almost
automorphy is a property which is too strong for stochastic differential
equations (SDEs). Finally, we consider two semilinear SDEs, one with almost
automorphic coefficients and the second one with pseudo almost automorphic
coefficients, and we prove the existence and uniqueness of a mild solution
which is almost automorphic in distribution in the first case, and pseudo
almost automorphic in distribution in the second case.


  Using the notion of a root datum of a reductive group $G$ we propose a
tropical analogue of a principal $G$-bundle on a metric graph. We focus on the
case $G=\mathrm{GL}_n$, i.e. the case of vector bundles. Here we give a
characterization of vector bundles in terms of multidivisors and use this
description to prove analogues of the Weil--Riemann--Roch theorem and the
Narasimhan--Seshadri correspondence. We proceed by studying the process of
tropicalization. In particular, we show that the non-Archimedean skeleton of
the moduli space of semistable vector bundles on a Tate curve is isomorphic to
a certain component of the moduli space of semistable tropical vector bundles
on its dual metric graph.


  Conversational recommendation systems (CRS) could acquire dynamic user
preferences towards desired items through multi-round interactive dialogue.
Previous CRS mainly focuses on the single conversation (subsession) that user
quits after a successful recommendation, neglecting the common scenario where
user has multiple conversations (multi-subsession) over a short period.
Therefore, we propose a novel conversational recommendation scenario named
Multi-Subsession Multi-round Conversational Recommendation (MSMCR), where user
would still resort to CRS after several subsessions and might preserve vague
interests, and system would proactively ask attributes to activate user
interests in the current subsession. To fill the gap in this new CRS scenario,
we devise a novel framework called Multi-Subsession Conversational Recommender
with Activation Attributes (MSCAA). Specifically, we first develop a
context-aware recommendation module, comprehensively modeling user interests
from historical interactions, previous subsessions, and feedback in the current
subsession. Furthermore, an attribute selection policy module is proposed to
learn a flexible strategy for asking appropriate attributes to elicit user
interests. Finally, we design a conversation policy module to manage the above
two modules to decide actions between asking and recommending. Extensive
experiments on four datasets verify the effectiveness of our MSCAA framework
for the MSMCR setting.


  We investigate theoretically momentum-resolved radio-frequency (rf)
spectroscopy of a noninteracting atomic Fermi gas in a spin-orbit coupled
lattice. This lattice configuration has been recently created at MIT [Cheuk et
al., arXiv:1205.3483] for 6Li atoms, by coupling the two hyperfine spin-states
with a pair of Raman laser beams and additional rf coupling. Here, we show that
momentum-resolved rf spectroscopy can measure single-particle energies and
eigenstates and therefore resolve the band structure of the spin-orbit coupled
lattice. In our calculations, we take into account the effects of temperatures
and harmonic traps. Our predictions are to be confronted with future
experiments on spin-orbit coupled Fermi gases of 40K atoms in a lattice
potential.


  Using the methods developed for the proof that the 2-universality criterion
is unique, we partially characterize criteria for the n-universality of
positive-definite integer-matrix quadratic forms. We then obtain the uniqueness
of Oh's 8-universality criterion as an application of our characterization
results.


  Statistical models of 3D human shape and pose learned from scan databases
have developed into valuable tools to solve a variety of vision and graphics
problems. Unfortunately, most publicly available models are of limited
expressiveness as they were learned on very small databases that hardly reflect
the true variety in human body shapes. In this paper, we contribute by
rebuilding a widely used statistical body representation from the largest
commercially available scan database, and making the resulting model available
to the community (visit http://humanshape.mpi-inf.mpg.de). As preprocessing
several thousand scans for learning the model is a challenge in itself, we
contribute by developing robust best practice solutions for scan alignment that
quantitatively lead to the best learned models. We make implementations of
these preprocessing steps also publicly available. We extensively evaluate the
improved accuracy and generality of our new model, and show its improved
performance for human body reconstruction from sparse input data.