  We study the magnetic relaxation of a system of localized spins interacting
through weak dipole interactions, at a temperature large with respect to the
ordering temperature but low with respect to the crystal field level splitting.
The relaxation results from quantum spin tunneling but is only allowed on sites
where the dipole field is very small. At low times, the magnetization decrease
is proportional to $\sqrt{t}$ as predicted by Prokofiev and Stamp, and at long
times the relaxation can be described as an extension of a relaxed zone. The
results can be directly compared with very recent experimental data on Fe_8
molecular clusters.


  A recent line of work has shown the unconditional advantage of constant-depth
quantum computation, or $\mathsf{QNC^0}$, over $\mathsf{NC^0}$,
$\mathsf{AC^0}$, and related models of classical computation. Problems
exhibiting this advantage include search and sampling tasks related to the
parity function, and it is natural to ask whether $\mathsf{QNC^0}$ can be used
to help compute parity itself. We study $\mathsf{AC^0\circ QNC^0}$ -- a hybrid
circuit model where $\mathsf{AC^0}$ operates on measurement outcomes of a
$\mathsf{QNC^0}$ circuit, and conjecture $\mathsf{AC^0\circ QNC^0}$ cannot
achieve $\Omega(1)$ correlation with parity. As evidence for this conjecture,
we prove:
  $\bullet$ When the $\mathsf{QNC^0}$ circuit is ancilla-free, this model
achieves only negligible correlation with parity.
  $\bullet$ For the general (non-ancilla-free) case, we show via a connection
to nonlocal games that the conjecture holds for any class of postprocessing
functions that has approximate degree $o(n)$ and is closed under restrictions,
even when the $\mathsf{QNC^0}$ circuit is given arbitrary quantum advice. By
known results this confirms the conjecture for linear-size $\mathsf{AC^0}$
circuits.
  $\bullet$ Towards a switching lemma for $\mathsf{AC^0\circ QNC^0}$, we study
the effect of quantum preprocessing on the decision tree complexity of Boolean
functions. We find that from this perspective, nonlocal channels are no better
than randomness: a Boolean function $f$ precomposed with an $n$-party nonlocal
channel is together equal to a randomized decision tree with worst-case depth
at most $\mathrm{DT}_\mathrm{depth}[f]$.
  Our results suggest that while $\mathsf{QNC^0}$ is surprisingly powerful for
search and sampling tasks, that power is "locked away" in the global
correlations of its output, inaccessible to simple classical computation for
solving decision problems.


  The spectral statistics of a Cayley-tree is numerically studied. The
statistics are non-universal due to the high ratio of boundary sites. Once the
boundary sites are connected to each other in a way that preserves the local
structure of the tree the universal statistics of the spectra is recovered. A
clear localization transition is observed as function of on-site disorder
strength, with a critical disorder $W_c=11.44^{+0.08}_{-0.04}$ and critical
index $\nu=0.51^{+0.05}_{-0.04}$. The value of $\nu$ fits nicely to its mean
field value, while the value of $W_c$ is puzzling.


  Understanding the spatial distribution of animals, during all their life
phases, as well as how the distributions are influenced by environmental
covariates, is a fundamental requirement for the effective management of animal
populations. Several geostatistical models have been proposed in the
literature, however often the data structure presents an excess of zeros and
extreme values, which can lead to unreliable estimates when these are ignored
in the modelling process. To deal with these issues, we propose a
point-referenced zero-inflated model to model the probability of presence
together with the positive observations and a point-referenced generalised
Pareto model for the extremes. Finally, we combine the results of these two
models to get the spatial predictions of the variable of interest. We follow a
Bayesian approach and the inference is made using the package R-INLA in the
software R. Our proposed methodology was illustrated through the analysis of
the spatial distribution of sardine eggs density (eggs/$m^3$). The results
showed that the combined model for zero-inflated and extreme values improved
the spatial prediction accuracy. Accordingly, our conclusion is that it is
relevant to consider the data structure in the modelling process. Also, the
hierarchical model considered can be widely applicable in many ecological
problems and even in other contexts.


  We consider the non-stationary stochastic lot sizing problem with backorder
costs and make a cost comparison among different lot-sizing strategies. We
initially provide an overview of the strategies and some corresponding solution
approaches in the literature. We then compare the cost performances of the
lot-sizing strategies on a common test bed while taking into account the added
value of realized demand information. The results of this numerical experience
enable us to derive novel insights about the cost performance of different
stochastic lot-sizing strategies under re-planning with respect to demand
realization.


  We study the evolution, rotation, and surface abundances of O-type dwarfs in
the Small Magellanic Cloud. We analyzed the UV and optical spectra of
twenty-three objects and derived photospheric and wind properties. The observed
binary fraction of the sample is ~ 26%, which is compatible with more
systematic studies, if one considers that the actual binary fraction is
potentially larger owing to low-luminosity companions and that the sample
excluded obvious spectroscopic binaries. The location of the fastest rotators
in the H-R diagram indicates that these could be several Myr old. The offset in
the position of these fast rotators compared with the other stars confirms the
predictions of evolutionary models that fast-rotating stars tend to evolve more
vertically in the H-R diagram. Only one star of luminosity-class Vz, expected
to best characterize extreme youth, is located on the ZAMS, the other two stars
are more evolved. The distribution of nitrogen abundance of O and B stars
suggests that the mechanisms responsible for the chemical enrichment of slowly
rotating massive stars depends only weakly on the star's mass. We confirm that
the group of slowly rotating N-rich stars is not reproduced by the evolutionary
tracks. Our results call for stronger mixing in the models to explain the range
of observed N abundances. All stars have an N/C ratio as a function of stellar
luminosity that matches the predictions of the stellar evolution models well.
More massive stars have a higher N/C ratio than the less massive stars. Faster
rotators show on average a higher N/C ratio than slower rotators. The N/O
versus N/C ratios agree qualitatively well with those of stellar evolution
models. The only discrepant behavior is observed for the youngest two stars of
the sample, which both show very strong signs of mixing, which is unexpected
for their evolutionary status.


  The Dirac cone underlies many unique electronic properties of graphene and
topological insulators, and its band structure--two conical bands touching at a
single point--has also been realized for photons in waveguide arrays, atoms in
optical lattices, and through accidental degeneracy. Deformations of the Dirac
cone often reveal intriguing properties; an example is the quantum Hall effect,
where a constant magnetic field breaks the Dirac cone into isolated Landau
levels. A seemingly unrelated phenomenon is the exceptional point, also known
as the parity-time symmetry breaking point, where two resonances coincide in
both their positions and widths. Exceptional points lead to counter-intuitive
phenomena such as loss-induced transparency, unidirectional transmission or
reflection, and lasers with reversed pump dependence or single-mode operation.
These two fields of research are in fact connected: here we discover the
ability of a Dirac cone to evolve into a ring of exceptional points, which we
call an "exceptional ring." We experimentally demonstrate this concept in a
photonic crystal slab. Angle-resolved reflection measurements of the photonic
crystal slab reveal that the peaks of reflectivity follow the conical band
structure of a Dirac cone from accidental degeneracy, whereas the complex
eigenvalues of the system are deformed into a two-dimensional flat band
enclosed by an exceptional ring. This deformation arises from the dissimilar
radiation rates of dipole and quadrupole resonances, which play a role
analogous to the loss and gain in parity-time symmetric systems. Our results
indicate that the radiation that exists in any open system can fundamentally
alter its physical properties in ways previously expected only in the presence
of material loss and gain.


  This work proposes a framework that incorporates trust in an ad hoc teamwork
scenario with human-agent teams, where an agent must collaborate with a human
to perform a task. During the task, the agent must infer, through interactions
and observations, how much the human trusts it and adapt its behaviour to
maximize the team's performance. To achieve this, we propose collecting data
from human participants in experiments to define different settings (based on
trust levels) and learning optimal policies for each of them. Then, we create a
module to infer the current setting (depending on the amount of trust).
Finally, we validate this framework in a real-world scenario and analyse how
this adaptable behaviour affects trust.


  Let $Q$ be the doubled of a quiver. According to Efimov, Kontsevich and
Soibelman, the cohomological Hall algebra (CoHA) associated to $Q$ is a free
super-commutative algebra. In this short note, we confirm a conjecture of
Hausel which gives a geometric realisation of the generators of the CoHA.


  We consider a class of misspecified dynamical models where the governing term
is only approximately known. Under the assumption that observations of the
system's evolution are accessible for various initial conditions, our goal is
to infer a non-parametric correction to the misspecified driving term such as
to faithfully represent the system dynamics and devise system evolution
predictions for unobserved initial conditions.
  We model the unknown correction term as a Gaussian Process and analyze the
problem of efficient experimental design to find an optimal correction term
under constraints such as a limited experimental budget. We suggest a novel
formulation for experimental design for this Gaussian Process and show that
approximately optimal (up to a constant factor) designs may be efficiently
derived by utilizing results from the literature on submodular optimization.
Our numerical experiments exemplify the effectiveness of these techniques.


  We are concerned with the inverse boundary problem of determining anomalies
associated with a semilinear elliptic equation of the form $-\Delta u+a(\mathbf
x, u)=0$, where $a(\mathbf x, u)$ is a general nonlinear term that belongs to a
H\"older class. It is assumed that the inhomogeneity of $f(\mathbf x, u)$ is
contained in a bounded domain $D$ in the sense that outside $D$, $a(\mathbf x,
u)=\lambda u$ with $\lambda\in\mathbb{C}$. We establish novel unique
identifiability results in several general scenarios of practical interest.
These include determining the support of the inclusion (i.e. $D$) independent
of its content (i.e. $a(\mathbf{x}, u)$ in $D$) by a single boundary
measurement; and determining both $D$ and $a(\mathbf{x}, u)|_D$ by $M$ boundary
measurements, where $M\in\mathbb{N}$ signifies the number of unknown
coefficients in $a(\mathbf x, u)$. The mathematical argument is based on
microlocally characterising the singularities in the solution $u$ induced by
the geometric singularities of $D$, and does not rely on any linearisation
technique.


  This paper presents a safety-critical approach to the coordinated control of
cooperative robots locomoting in the presence of fixed (holonomic) constraints.
To this end, we leverage control barrier functions (CBFs) to ensure the safe
cooperation of the robots while maintaining a desired formation and avoiding
obstacles. The top-level planner generates a set of feasible trajectories,
accounting for both kinematic constraints between the robots and physical
constraints of the environment. This planner leverages CBFs to ensure
safety-critical coordination control, i.e., guarantee safety of the
collaborative robots during locomotion. The middle-level trajectory planner
incorporates interconnected single rigid body (SRB) dynamics to generate
optimal ground reaction forces (GRFs) to track the safety-ensured trajectories
from the top-level planner while addressing the interconnection dynamics
between agents. Distributed low-level controllers generate whole-body motion to
follow the prescribed optimal GRFs while ensuring the friction cone condition
at each end of the stance legs. The effectiveness of the approach is
demonstrated through numerical simulations and experimentally on a pair of
quadrupedal robots.


  We experimentally probe the vicinity of the jamming point J, located at a
density $\phi$ corresponding to random close packing ($\phi_{rcp} = 0.842$), in
two dimensional, bidisperse packings of foam bubbles. We vary the density of
the foam layer and extract geometrical measures by image analysis. We confirm
the predicted scaling of the average contact number Z with $\phi$ and compare
the distribution of local contact numbers to a simple model. We further
establish that the distribution of areas $p(A)$ strongly depends on $\phi$.
Finally, we find that the distribution of contact forces $p(f)$ systematically
varies with density.


  An asymptotic technique is developed to find the
Signal-to-Interference-plus-Noise-Ratio (SINR) and spectral efficiency of a
link with N receiver antennas in wireless networks with non-homogeneous
distributions of nodes. It is found that with appropriate normalization, the
SINR and spectral efficiency converge with probability 1 to asymptotic limits
as N increases. This technique is applied to networks with power-law node
intensities, which includes homogeneous networks as a special case, to find a
simple approximation for the spectral efficiency. It is found that for
receivers in dense clusters, the SINR grows with N at rates higher than that of
homogeneous networks and that constant spectral efficiencies can be maintained
if the ratio of N to node density is constant. This result also enables the
analysis of a new scaling regime where the distribution of nodes in the network
flattens rather than increases uniformly. It is found that in many cases in
this regime, N needs to grow approximately exponentially to maintain a constant
spectral efficiency. In addition to strengthening previously known results for
homogeneous networks, these results provide insight into the benefit of using
antenna arrays in non-homogeneous wireless networks, for which few results are
available in the literature.


  Based on large-scale pre-trained multilingual representations, recent
cross-lingual transfer methods have achieved impressive transfer performances.
However, the performance of target languages still lags far behind the source
language. In this paper, our analyses indicate such a performance gap is
strongly associated with the cross-lingual representation discrepancy. To
achieve better cross-lingual transfer performance, we propose the cross-lingual
manifold mixup (X-Mixup) method, which adaptively calibrates the representation
discrepancy and gives a compromised representation for target languages.
Experiments on the XTREME benchmark show X-Mixup achieves 1.8% performance
gains on multiple text understanding tasks, compared with strong baselines, and
significantly reduces the cross-lingual representation discrepancy.


  The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most
popular risk measures in banking and insurance regulation. To bridge between
the two regulatory risk measures, the Probability Equivalent Level of VaR-ES
(PELVE) was recently proposed to convert a level of VaR to that of ES. It is
straightforward to compute the value of PELVE for a given distribution model.
In this paper, we study the converse problem of PELVE calibration, that is, to
find a distribution model that yields a given PELVE, which may either be
obtained from data or from expert opinion. We discuss separately the cases when
one-point, two-point, n-point and curve constraints are given. In the most
complicated case of a curve constraint, we convert the calibration problem to
that of an advanced differential equation. We apply the model calibration
techniques to estimation and simulation for datasets used in insurance. We
further study some technical properties of PELVE by offering a few new results
on monotonicity and convergence.


  The initial energy transfer in photosynthesis occurs between the
light-harvesting pigments and on ultrafast timescales. We analyze the
carotenoid to bacteriochlorophyll energy transfer in LH2 Marichromatium
purpuratum as well as in an artificial light-harvesting dyad system by using
transient grating and two-dimensional electronic spectroscopy with 10 fs time
resolution. We find that F\"orster-type models reproduce the experimentally
observed 60 fs transfer times, but overestimate coupling constants, which leads
to a disagreement with both linear absorption and electronic 2D-spectra. We
show that a vibronic model, which treats carotenoid vibrations on both
electronic ground and excited state as part of the system's Hamiltonian,
reproduces all measured quantities. Importantly, the vibronic model presented
here can explain the fast energy transfer rates with only moderate coupling
constants, which are in agreement with structure based calculations.
Counterintuitively, the vibrational levels on the carotenoid electronic ground
state play a central role in the excited state population transfer to
bacteriochlorophyll as the resonance between the donor-acceptor energy gap and
vibrational ground state energies is the physical basis of the ultrafast energy
transfer rates in these systems.


  LiDAR sensors have been widely used in many autonomous vehicle modalities,
such as perception, mapping, and localization. This paper presents an
FPGA-based deep learning platform for real-time point cloud processing targeted
on autonomous vehicles. The software driver for the Velodyne LiDAR sensor is
modified and moved into the on-chip processor system, while the programmable
logic is designed as a customized hardware accelerator. As the state-of-art
deep learning algorithm for point cloud processing, PointNet is successfully
implemented on the proposed FPGA platform. Targeted on a Xilinx Zynq
UltraScale+ MPSoC ZCU104 development board, the FPGA implementations of
PointNet achieve the computing performance of 182.1 GOPS and 280.0 GOPS for
classification and segmentation respectively. The proposed design can support
an input up to 4096 points per frame. The processing time is 19.8 ms for
classification and 34.6 ms for segmentation, which meets the real-time
requirement for most of the existing LiDAR sensors.


  Rare event sampling algorithms are essential for understanding processes that
occur infrequently on the molecular scale, yet they are important for the
long-time dynamics of complex molecular systems. One of these algorithms,
transition path sampling, has become a standard technique to study such rare
processes since no prior knowledge on the transition region is required. Most
TPS methods generate new trajectories from old trajectories by selecting a
point along the old trajectory, modifying its momentum in some way, and then
``shooting'' a new trajectory by integrating forward and backward in time. In
some procedures, the shooting point is selected independently for each trial
move, but in others, the shooting point evolves from one path to the next so
that successive shooting points are related to each other. We provide an
extended detailed balance criterion for shooting methods. We affirm detailed
balance for most TPS methods, but the new criteria reveals the need for amended
acceptance criteria in the flexible length aimless shooting and spring shooting
methods.


  Parabolic integro-differential Kolmogorov equations with different
space-dependent operators are considered in H\"{o}lder-type spaces defined by a
scalable L\'{e}vy measure. Probabilistic representations are used to prove
continuity of the operator. Existence and uniqueness of the solution are
established and some regularity estimates are obtained.


  We are entering the era of high-precision and high-resolution spectroscopy of
exoplanets. Such observations herald the need for robust self-consistent
spectral models of exoplanetary atmospheres to investigate intricate
atmospheric processes and to make observable predictions. Spectral models of
plane-parallel exoplanetary atmospheres exist, mostly adapted from other
astrophysical applications, with different levels of sophistication and
accuracy. There is a growing need for a new generation of models custom-built
for exoplanets and incorporating state-of-the-art numerical methods and
opacities. The present work is a step in this direction. Here we introduce
GENESIS, a plane-parallel, self-consistent, line-by-line exoplanetary
atmospheric modelling code which includes (a) formal solution of radiative
transfer using the Feautrier method, (b) radiative-convective equilibrium with
temperature correction based on the Rybicki linearisation scheme, (c) latest
absorption cross sections, and (d) internal flux and external irradiation,
under the assumptions of hydrostatic equilibrium, local thermodynamic
equilibrium and thermochemical equilibrium. We demonstrate the code here with
cloud-free models of giant exoplanetary atmospheres over a range of equilibrium
temperatures, metallicities, C/O ratios and spanning non-irradiated and
irradiated planets, with and without thermal inversions. We provide the
community with theoretical emergent spectra and pressure-temperature profiles
over this range, along with those for several known hot Jupiters. The code can
generate self-consistent spectra at high resolution and has the potential to be
integrated into general circulation and non-equilibrium chemistry models as it
is optimised for efficiency and convergence. GENESIS paves the way for
high-fidelity remote sensing of exoplanetary atmospheres at high resolution
with current and upcoming observations.


  Recently, the growth of deep learning has produced a large number of deep
neural networks. How to describe these networks unifiedly is becoming an
important issue. We first formalize neural networks in a mathematical
definition, give their directed graph representations, and prove a generation
theorem about the induced networks of connected directed acyclic graphs. Then,
using the concept of capsule to extend neural networks, we set up a
capsule-unified framework for deep learning, including a mathematical
definition of capsules, an induced model for capsule networks and a universal
backpropagation algorithm for training them. Finally, we discuss potential
applications of the framework to graphical programming with standard graphical
symbols of capsules, neurons, and connections.


  We systematically derive a length scale characterizing the size of a
low-lying, beta stable nucleus from empirical data for the diffraction peak
angle in the proton inelastic differential cross section of incident energy of
\sim 1 GeV. In doing so, we assume that the target nucleus in the ground state
is a completely absorptive "black" sphere of radius a. The cross section \pi
a^2, where a is determined in such a way as to reproduce the empirical proton
diffraction peak angle in the elastic channel, is known to agree with empirical
total reaction cross sections for incident protons to within error bars. By
comparing the inelastic diffraction patterns obtained in the Fraunhofer
approximation with the experimental ones, one can likewise derive the black
sphere radius a_l for the excited state with spin l. We find that for ^{12}C,
^{58,60,62,64}Ni, and ^{208}Pb, the value of a_l obtained from the inelastic
channel is generally larger than the value of a from the elastic channel and
tends to increase with the excitation energy. This increase is remarkable for
the Hoyle state. Finally, we discuss the relation between a_l and the size of
excited nuclei.


  More than 23 million people are suffered by Heart failure worldwide. Despite
the modern transplant operation is well established, the lack of heart
donations becomes a big restriction on transplantation frequency. With respect
to this matter, ventricular assist devices (VADs) can play an important role in
supporting patients during waiting period and after the surgery. Moreover, it
has been shown that VADs by means of blood pump have advantages for working
under different conditions. While a lot of work has been done on modeling the
functionality of the blood pump, but quantifying uncertainties in a numerical
model is a challenging task. We consider the Polynomial Chaos (PC) method,
which is introduced by Wiener for modeling stochastic process with Gaussian
distribution. The Galerkin projection, the intrusive version of the generalized
Polynomial Chaos (gPC), has been densely studied and applied for various
problems. The intrusive Galerkin approach could represent stochastic process
directly at once with Polynomial Chaos series expansions, it would therefore
optimize the total computing effort comparing with classical non-intrusive
methods. We compared different preconditioning techniques for a steady state
simulation of a blood pump configuration in our previous work, the comparison
shows that an inexact multilevel preconditioner has a promising performance. In
this work, we show an instationary blood flow through a FDA blood pump
configuration with Galerkin Projection method, which is implemented in our open
source Finite Element library Hiflow3. Three uncertainty sources are
considered: inflow boundary condition, rotor angular speed and dynamic
viscosity, the numerical results are demonstrated with more than 30 Million
degrees of freedom by using supercomputer.


  We investigate the behavior of liquidity providers (LPs) by modeling a
decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with
heterogeneous characteristics choose optimal liquidity positions subject to
uncertainty regarding the size of exogenous incoming transactions and the
prices of assets in the wider market. They engage in a game among themselves,
and the resulting liquidity distribution determines the exchange rate dynamics
and potential arbitrage opportunities of the pool. We calibrate the
distribution of LP characteristics based on Uniswap data and the equilibrium
strategy resulting from this mean-field game produces pool exchange rate
dynamics and liquidity evolution consistent with observed pool behavior. We
subsequently introduce Maximal Extractable Value (MEV) bots who perform
Just-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between
LPs and bots. This addition results in more accurate simulated pool exchange
rate dynamics and stronger predictive power regarding the evolution of the pool
liquidity distribution.


  This work proves that semantic segmentation on minimally invasive surgical
instruments can be improved by using training data that has been augmented
through domain adaptation. The benefit of this method is twofold. Firstly, it
suppresses the need of manually labeling thousands of images by transforming
synthetic data into realistic-looking data. To achieve this, a CycleGAN model
is used, which transforms a source dataset to approximate the domain
distribution of a target dataset. Secondly, this newly generated data with
perfect labels is utilized to train a semantic segmentation neural network,
U-Net. This method shows generalization capabilities on data with variability
regarding its rotation- position- and lighting conditions. Nevertheless, one of
the caveats of this approach is that the model is unable to generalize well to
other surgical instruments with a different shape from the one used for
training. This is driven by the lack of a high variance in the geometric
distribution of the training data. Future work will focus on making the model
more scale-invariant and able to adapt to other types of surgical instruments
previously unseen by the training.


  We apply the bosonization technique to derive the phase diagram of a balanced
unit density two-component dipolar Fermi gas in a one dimensional lattice
geometry. The considered interaction processes are of the usual contact and
dipolar long-range density-density type together with peculiar correlated
hopping terms which can be generated dynamically. Rigorous bounds for the
transition lines are obtained in the weak coupling regime. In addition to the
standard bosonization description, we derive the low energy phase diagram
taking place when part of the interaction is embodied non-perturbatively in the
single component Hamiltonians. In this case the Luttinger liquid regime is
shown to become unstable with respect to the opening of further gapped phases,
among which insulating bond ordered wave and Haldane phases, the latter with
degenerate edge modes.


  In this paper, we propose a regularized Newton method for computing ground
states of Bose-Einstein condensates (BECs), which can be formulated as an
energy minimization problem with a spherical constraint. The energy functional
and constraint are discretized by either the finite difference, or sine or
Fourier pseudospectral discretization schemes and thus the original infinite
dimensional nonconvex minimization problem is approximated by a finite
dimensional constrained nonconvex minimization problem. Then an initial
solution is first constructed by using a feasible gradient type method, which
is an explicit scheme and maintains the spherical constraint automatically. To
accelerate the convergence of the gradient type method, we approximate the
energy functional by its second-order Taylor expansion with a regularized term
at each Newton iteration and adopt a cascadic multigrid technique for selecting
initial data. It leads to a standard trust-region subproblem and we solve it
again by the feasible gradient type method. The convergence of the regularized
Newton method is established by adjusting the regularization parameter as the
standard trust-region strategy. Extensive numerical experiments on challenging
examples, including a BEC in three dimensions with an optical lattice potential
and rotating BECs in two dimensions with rapid rotation and strongly repulsive
interaction, show that our method is efficient, accurate and robust.


  Using a one-loop renormalization group improvement for the effective
potential in the Higgs model of electrodynamics with electrically and
magnetically charged scalar fields, we argue for the existence of a triple
(critical) point in the phase diagram ($\lambda_{run}, g_{run}^4$), where
$\lambda_{run}$ is the renormalised running selfinteraction constant of the
Higgs scalar monopoles and $g_{run}$ is their running magnetic charge. This
triple point is a boundary point of three first-order phase transitions in the
dual sector of the Higgs scalar electrodynamics: The "Coulomb" and two
confinement phases meet together at this critical point. Considering the
arguments for the one-loop approximation validity in the region of parameters
around the triple point A we have obtained the following triple point values of
the running couplings: $(\lambda_{(A)}, g^2_{(A)})\approx(-13.4; 18.6)$, which
are independent of the electric charge influence and two--loop corrections to
$g^2_{run}$ with high accuracy of deviations. At the triple point the mass of
monopoles is equal to zero. The corresponding critical value of the electric
fine structure constant turns out to be $\alpha_{crit} =
\pi/g^2_{(A)}\approx{0.17}$ by the Dirac relation. This value is close to the
$\alpha_{crit}^{lat}\approx{0.20\pm 0.015}$, which in a U(1) lattice gauge
theory corresponds to the phase transition between the "Coulomb" and
confinement phases. In our theory for $\alpha \ge \alpha_{crit}$ there are two
phases for the confinement of the electrically charged particles. The results
of the present paper are very encouraging for the Anti--grand unification
theory which was developed previously as a realistic alternative to SUSY GUTs.
The paper is also devoted to the discussion of this problem.


  In this article, I put forward the idea that the neoplastic process (NP) has
deep evolutionary roots and make specific predictions about the connection
between cancer and the formation of the first embryo, which allowed for the
evolutionary radiation of metazoans. My main hypothesis is that the NP is at
the heart of cellular mechanisms responsible for animal morphogenesis and,
given its embryological basis, also at the center of animal evolution. It is
thus understood that NP-associated mechanisms are deeply rooted in evolutionary
history and tied to the formation of the first animal embryo. In my
consideration of these arguments, I expound on how cancer biology is perfectly
intertwined with evolutionary biology. I describe essential cellular components
of unicellular holozoans that served as a basis for the formation of the
neoplastic functional module (NFM) and its subsequent exaptation, which brought
forth two great biophysical revolutions within the first embryo. Finally, I
examine the role of Physics in the modeling of the NFM and its contribution to
morphogenesis to reveal the totipotency of the zygote.


  We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum many-body interacting systems. We discuss, in
general terms, both quasiparticle excitations and quasiparticle-density-wave
excitations (collective modes). In application to quantum antiferromagnets, we
reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of
spin $\pm 1$. In addition, we obtain new, spin-zero magnon-density-wave
excitations which has been missing in Anserson's spin-wave theory. Implications
of these new collective modes are discussed.


  Let R be a commutative ring with identity. We investigate some ring-theoretic
properties of weakly Laskerian R-modules. Our results indicate that weakly
Laskerian rings behave as Noetherian ones in many respects. However, we provide
some examples to illustrate the strange behavior of these rings in some other
respects.


  There has been growing observational evidence for the presence of condensates
in the atmospheres and/or comet-like tails of extrasolar planets. As a result,
systematic and homogeneous tables of dust properties are useful in order to
facilitate further observational and theoretical studies. In this paper we
present calculations and analysis of non-isotropic phase functions, asymmetry
parameter (mean cosine of the scattering angle), absorption and scattering
opacities, single scattering albedos, equilibrium temperatures, and radiative
accelerations of dust grains relevant for extrasolar planets. Our assumptions
include spherical grain shape, Deirmendjian particle size distribution, and Mie
theory. We consider several species: corundum/alumina, perovskite, olivines
with 0\% and 50\% iron content, pyroxenes with 0\%, 20\% and 60\% iron content,
pure iron, carbon at two different temperatures, water ice, liquid water, and
ammonia. The presented tables cover the wavelength range of 0.2 to 500 micron
and modal particle radii from 0.01 micron to 100 micron. Equilibrium
temperatures and radiative accelerations assume irradiation by a non-black-body
source of light with temperatures from 7000K to 700K seen at solid angles from
2$\pi$ to $10^{-6}$ sr. The tables are provided to the community together with
a simple code which allows for an optional, finite, angular dimension of the
source of light (star) in the phase function.


  Social network sites allow users to publicly tag people in their posts. These
tagged posts allow users to share to both the general public and a targeted
audience, dynamically assembled via notifications that alert the people
mentioned. We investigate people's perceptions of this mixed sharing mode
through a qualitative study with 120 participants. We found that individuals
like this sharing modality as they believe it strengthens their relationships.
Individuals also report using tags to have more control of Facebook's ranking
algorithm, and to expose one another to novel information and people. This work
helps us understand people's complex relationships with the algorithms that
mediate their interactions with each another. We conclude by discussing the
design implications of these findings.


  Understanding realistic complex systems requires confronting significant
conceptual, theoretical and experimental limitations rooted in the persistence
of views that originated in the mechanics of simple moving bodies. We define
the category of complex multiscale stochastic systems as a useful device for
capturing the minimally required complexity of many types of phenomena. In
doing so, we provide evidence indicating that determinism, continuity and
reversibility can lead to theoretical inadequacies that manifest as
intractability, inaccuracies or non-representativeness when applied to complex
systems. We take the view that interactions are fundamental and summarize their
portrayal across many disciplines. Despite their centrality, interactions
remain largely neglected as subjects of research interest of their own. We
hypothesize that a generalized theory of interactions may help organize
evidence from multiple scientific domains towards a more unified realistic view
of systems.


  Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001)
have analyzed the statistics of local deformation in a granular solid
undergoing plastic deformation. Experiments report strongly anisotropic
correlation between events, with a characteristic angle that was interpreted
using elasticity theory and the concept of Eshelby transformations with
dilation; interestingly, the shear bands that characterize macroscopic failure
occur at an angle that is different from the one observed in microscopic
correlations. Here, we interpret this behavior using a mesoscale elastoplastic
model of solid flow that incorporates a local Mohr-Coulomb failure criterion.
We show that the angle observed in the microscopic correlations can be
understood by combining the elastic interactions associated with Eshelby
transformation with the local failure criterion. At large strains, we also
induce permanent shear bands at an angle that is different from the one
observed in the correlation pattern. We interpret this angle as the one that
leads to the maximal instability of slip lines.


  Using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched
level, we study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is
another chiral order parameter. For each current quark mass of m_q=21, 36, 52
MeV, we generate 100 gauge configurations in the 16^4 lattice with \beta = 6.0,
and perform the measurement of the mixed condensate at 16 points in each gauge
configuration. Using the 1600 data for each m_q, we find the ratio between the
mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q>/
<\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale in the chiral limit. The large
value of the mixed condensate suggests its importance in the operator product
expansion in QCD.


  Despite several decades of development, microfluidics lacks a sealing
material that can be readily fabricated, leak-tight under high liquid water
pressure, stable over a long time, and vacuum compatible. In this paper, we
report the performances of a micro-scale processable sealing material for
nanofluidic/microfluidics chip fabrication, which enables us to achieve all
these requirements. We observed that micrometric walls made of SU-8
photoresist, whose thickness can be as low as 35 $\mu$m, exhibit water pressure
leak-tightness from 1.5 bar up to 5.5 bar, no water porosity even after 2
months of aging, and are able to sustain under $10^{-5}$ mbar vacuum. This
sealing material is therefore reliable and versatile for building microchips,
part of which must be isolated from liquid water under pressure or vacuum.
Moreover, the fabrication process we propose does not require the use of
aggressive chemicals or high-temperature or high-energy plasma treatment. It
thus opens a new perspective to seal microchips where delicate surfaces such as
nanomaterials are present.


  The nonlinear interaction of a time-harmonic acoustic wave with an
anisotropic particle gives rise to the radiation force and torque effects.
These phenomena are at the heart of the acoustofluidics technology, where
microparticles such as cells and microorganisms are acoustically manipulated.
We present a theoretical model considering a generic acoustic beam interacting
with a subwavelength spheroidal particle in a nonviscous fluid. Concise
analytical expressions of the radiation force and torque are obtained in the
scattering dipole approximation. The radiation force is given in terms of a
gradient and scattering force; while the radiation torque has two fundamental
contributions, namely, the momentum arm and acoustic spin (spin-torque effect).
As a practical example, we use the theory to describe the interaction of two
crossed plane waves and a prolate spheroidal particle. The results reveal the
particle is transversely trapped in a pressure node and is axially pushed by
the radiation force. Also, the momentum arm aligns the particle in the axial
direction. At certain specific positions, only the spin-torque occurs. Our
findings are remarkably consistent with finite-element simulations. The success
of our model enables its use as an investigation tool for the manipulation of
anisotropic microparticles in acoustofluidics.


  This article is to understand the critical values of $L$-functions
$L(s,\Pi\otimes \chi)$ and to establish the relation of the relevant global
periods at the critical places. Here $\Pi$ is an irreducible regular algebraic
cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb A)$ of
symplectic type and $\chi$ is a finite order automorphic character of
$\mathrm{GL}_1(\mathbb A)$, with $\mathbb A$ is the ring of adeles of a number
field $\mathrm k$.


  A long-standing challenge in Reinforcement Learning is enabling agents to
learn a model of their environment which can be transferred to solve other
problems in a world with the same underlying rules. One reason this is
difficult is the challenge of learning accurate models of an environment. If
such a model is inaccurate, the agent's plans and actions will likely be
sub-optimal, and likely lead to the wrong outcomes. Recent progress in
model-based reinforcement learning has improved the ability for agents to learn
and use predictive models. In this paper, we extend a recent deep learning
architecture which learns a predictive model of the environment that aims to
predict only the value of a few key measurements, which are be indicative of an
agent's performance. Predicting only a few measurements rather than the entire
future state of an environment makes it more feasible to learn a valuable
predictive model. We extend this predictive model with a small, evolving neural
network that suggests the best goals to pursue in the current state. We
demonstrate that this allows the predictive model to transfer to new scenarios
where goals are different, and that the adaptive goals can even adjust agent
behavior on-line, changing its strategy to fit the current context.


  We present first-principles calculations of the linear and nonlinear
susceptibilities of N$_2$, O$_2$, and air in the mid-infrared wavelength
regime, from $1-4$ $\mu$m. We extract the frequency-dependent susceptibilities
from the full time-dependent dipole moment that is calculated using
time-dependent density functional theory. We find good agreement with curves
derived from experimental results for the linear susceptibility, and with
measurements for the nonlinear susceptibility up to 2.4 $\mu$m. We also find
that the susceptibilities are insensitive to the laser intensity even in the
strong field regime up to $5\times 10^{13}$ W/cm$^2$. Our results will allow
accurate calculations of the long-distance propagation of intense MIR laser
pulses in air.


  In this paper, we study the properties of the critical points of
Yang-Mills-Higgs functional, which are called Yang-Mills-Higgs pairs. We first
consider the properties of weakly stable Yang-Mills-Higgs pairs on a vector
bundle over S^n (n > 3). When n > 3, we prove that the norm of its Higgs field
is 1 and the connection is actually Yang-Mills. More precisely, its curvature
vanishes when n > 4. We also use the bubble-neck decomposition to prove the
energy identity of a sequence of Yang-Mills-Higgs pairs over a 4-dimensional
compact manifold with uniformly bounded energy. We show there is a subsequence
converges smoothly to a Yang-Mills-Higgs pair up to gauge modulo finitely many
4-dimensional spheres with Yang-Mills connections.


  Consider a singular curve $\Gamma$ contained in a smooth 3-fold $X$. Assuming
the general elephant conjecture, the general hypersurface section
$\Gamma\subset S\subset X$ is Du Val. Under that assumption, this paper
describes the construction of a divisorial extraction from $\Gamma$ by
Kustin--Miller unprojection. Terminal extractions from $\Gamma\subset X$ are
proved not to exist if $S$ is of type $D_{2k}, E_7$ or $E_8$ and are classified
if $S$ is of type $A_1,A_2$ or $E_6$. The $A_n$ and $D_{2k+1}$ cases shall be
considered in a further paper.


  When most patients visit physicians in a clinic or a hospital, they are asked
about their medical history and related medical tests' results which might not
exist or might simply have been lost over time. In emergency situations, many
patients suffer or sadly die because of lack of pertinent medical information.
Patient's Health information (PHI) saved by Electronic Medical Record (EMR)
could be accessible only by a hospital using their EMR system. Furthermore,
Personal Health Record (PHR) information cannot be solely relied on since it is
controlled solely by patients. This paper introduces a novel framework for
accessing, sharing, and controlling the medical records for patients and their
physicians globally, while patients' PHI are securely stored and their privacy
is taken into consideration. Based on the framework, a proof of concept
prototype is implemented. Preliminary performance evaluation results indicate
the validity and viability of the proposed framework.


  In this work we construct and analyze exact solutions describing Ricci flows
and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It
is outlined a new geometric techniques of constructing Ricci flow solutions.
Some conceptual issues on spacetimes provided with generic off-diagonal metrics
and associated nonlinear connection structures are analyzed. The limit from
gravity/Ricci flow models with nontrivial torsion to configurations with the
Levi-Civita connection is allowed in some specific physical circumstances by
constraining the class of integral varieties for the Einstein and Ricci flow
equations.


  We consider the dynamics of cargo driven by a collection of interacting
molecular motors in the context of an asymmetric simple exclusion processes
(ASEP). The model is formulated to account for i) excluded volume interactions,
ii) the observed asymmetry of the stochastic movement of individual motors and
iii) interactions between motors and cargo. Items (i) and (ii) form the basis
of ASEP models and have already been considered in the literature to study the
behavior of motor density profile [Parmeggiani 03]. Item (iii) is new. It is
introduced here as an attempt to describe explicitly the dependence of cargo
movement on the dynamics of motors. The steady-state solutions of the model
indicate that the system undergoes a phase transition of condensation type as
the motor density varies. We study the consequences of this transition to the
properties of cargo velocity.


  Herbig Ae/Be objects are pre-main sequence stars surrounded by gas- and
dust-rich circumstellar discs. These objects are in the throes of star and
planet formation, and their characterisation informs us of the processes and
outcomes of planet formation processes around intermediate mass stars. Here we
analyse the spectral energy distributions of disc host stars observed by the
Herschel Open Time Key Programme `Gas in Protoplanetary Systems'. We present
Herschel/PACS far-infrared imaging observations of 22 Herbig Ae/Bes and 5
debris discs, combined with ancillary photometry spanning ultraviolet to
sub-millimetre wavelengths. From these measurements we determine the
diagnostics of disc evolution, along with the total excess, in three regimes
spanning near-, mid-, and far-infrared wavelengths. Using appropriate
statistical tests, these diagnostics are examined for correlations. We find
that the far-infrared flux, where the disc becomes optically thin, is
correlated with the millimetre flux, which provides a measure of the total dust
mass. The ratio of far-infrared to sub-millimetre flux is found to be greater
for targets with discs that are brighter at millimetre wavelengths and that
have steeper sub-millimetre slopes. Furthermore, discs with flared geometry
have, on average, larger excesses than flat geometry discs. Finally, we
estimate the extents of these discs (or provide upper limits) from the
observations.


  Neural networks have been shown to be vulnerable against minor adversarial
perturbations of their inputs, especially for high dimensional data under
$\ell_\infty$ attacks. To combat this problem, techniques like adversarial
training have been employed to obtain models which are robust on the training
set. However, the robustness of such models against adversarial perturbations
may not generalize to unseen data. To study how robustness generalizes, recent
works assume that the inputs have bounded $\ell_2$-norm in order to bound the
adversarial risk for $\ell_\infty$ attacks with no explicit dimension
dependence. In this work we focus on $\ell_\infty$ attacks on $\ell_\infty$
bounded inputs and prove margin-based bounds. Specifically, we use a
compression based approach that relies on efficiently compressing the set of
tunable parameters without distorting the adversarial risk. To achieve this, we
apply the concept of effective sparsity and effective joint sparsity on the
weight matrices of neural networks. This leads to bounds with no explicit
dependence on the input dimension, neither on the number of classes. Our
results show that neural networks with approximately sparse weight matrices not
only enjoy enhanced robustness, but also better generalization.


  We study the family of closed Riemannian n-manifolds with holonomy group
isomorphic to $Z_2^{n-1}$, which we call generalized Hantzsche-Wendt manifolds.
We prove results on their structures, compute some invariants, and find
relations between them, illustrated in graph connecting the family.


  The excitable behaviour is considered as motion of a particle in a potential
field in the presence of dissipation. The dynamics of the oscillator proposed
in the present paper corresponds to the excitable behaviour in a potential well
under condition of positive dissipation. Type-II excitability of the offered
system results from intrinsic peculiarities of the potential well, whose shape
depends on a system state. Concept of an excitable potential well is
introduced. The effect of coherence resonance and self-oscillation excitation
in a state-dependent potential well under condition of positive dissipation are
explored in numerical experiments.


  Very recently, the experimental demonstration of Quantum Secure Direct
Communication (QSDC) with state-of-the-art atomic quantum memory has been
reported (Phys. Rev. Lett., 2017). Quantum Dialogue (QD) falls under QSDC where
the secrete messages are communicated simultaneously between two legitimate
parties. The successful experimental demonstration of QSDC opens up the
possibilities for practical implementation of QD protocols. Thus, it is
necessary to analyze the practical security issues of QD protocols for future
implementation. Since the very first proposal for QD by Nguyen (Phys. Lett. A,
2004) a large number of variants and extensions have been presented till date.
However, all of those leak half of the secret bits to the adversary through
classical communications of the measurement results. In this direction,
motivated by the idea of Lo et al. (Phys. Rev. Lett., 2012), we propose a
Measurement Device Independent Quantum Dialogue (MDI-QD) scheme which is
resistant to such information leakage as well as side channel attacks. In the
proposed protocol, Alice and Bob, two legitimate parties, are allowed to
prepare the states only. The states are measured by an untrusted third party
(UTP) who may himself behave as an adversary. We show that our protocol is
secure under this adversarial model. The current protocol does not require any
quantum memory and thus it is inherently robust against memory attacks. Such
robustness might not be guaranteed in the QSDC protocol with quantum memory
(Phys. Rev. Lett., 2017).


  We study finitely generated groups whose word problems are accepted by
counter automata. We show that a group has word problem accepted by a blind
n-counter automaton in the sense of Greibach if and only if it is virtually
free abelian of rank n; this result, which answers a question of Gilman, is in
a very precise sense an abelian analogue of the Muller-Schupp theorem. More
generally, if G is a virtually abelian group then every group with word problem
recognised by a G-automaton is virtually abelian with growth class bounded
above by the growth class of G. We consider also other types of counter
automata.


  Despite significant progress over the past few years, ambiguity is still a
key challenge in Facial Expression Recognition (FER). It can lead to noisy and
inconsistent annotation, which hinders the performance of deep learning models
in real-world scenarios. In this paper, we propose a new uncertainty-aware
label distribution learning method to improve the robustness of deep models
against uncertainty and ambiguity. We leverage neighborhood information in the
valence-arousal space to adaptively construct emotion distributions for
training samples. We also consider the uncertainty of provided labels when
incorporating them into the label distributions. Our method can be easily
integrated into a deep network to obtain more training supervision and improve
recognition accuracy. Intensive experiments on several datasets under various
noisy and ambiguous settings show that our method achieves competitive results
and outperforms recent state-of-the-art approaches. Our code and models are
available at https://github.com/minhnhatvt/label-distribution-learning-fer-tf.


  For a positive integer $k$, the $k$-recolouring graph of a graph $G$ has as
vertex set all proper $k$-colourings of $G$ with two $k$-colourings being
adjacent if they differ by the colour of exactly one vertex. A result of Dyer
et al. regarding graphs of bounded degeneracy implies that the $7$-recolouring
graphs of planar graphs, the $5$-recolouring graphs of triangle-free planar
graphs and the $4$-recolouring graphs planar graphs of girth at least six are
connected. On the other hand, there are planar graphs whose $6$-recolouring
graph is disconnected, triangle-free planar graphs whose $4$-recolouring graph
is disconnected and planar graphs of any given girth whose $3$-recolouring
graph is disconnected.
  The main result of this paper consists in showing, via a novel application of
the discharging method, that the $4$-recolouring graph of every planar graph of
girth five is connected. This completes the classification of the connectedness
of the recolouring graph for planar graphs of given girth. We also prove some
theorems regarding the diameter of the recolouring graph of planar graphs.


  Ortholog detection (OD) is a critical step for comparative genomic analysis
of protein-coding sequences. In this paper, we begin with a comprehensive
comparison of four popular, methodologically diverse OD methods: MultiParanoid,
Blat, Multiz, and OMA. In head-to-head comparisons, these methods are shown to
significantly outperform one another 12-30% of the time. This high
complementarity motivates the presentation of the first tool for integrating
methodologically diverse OD methods. We term this program MOSAIC, or Multiple
Orthologous Sequence Analysis and Integration by Cluster optimization. Relative
to component and competing methods, we demonstrate that MOSAIC more than
quintuples the number of alignments for which all species are present, while
simultaneously maintaining or improving functional-, phylogenetic-, and
sequence identity-based measures of ortholog quality. Further, we demonstrate
that this improvement in alignment quality yields 40-280% more confidently
aligned sites. Combined, these factors translate to higher estimated levels of
overall conservation, while at the same time allowing for the detection of up
to 180% more positively selected sites. MOSAIC is available as python package.
MOSAIC alignments, source code, and full documentation are available at
http://pythonhosted.org/bio-MOSAIC.


  $CMO$ functions are completely multiplicative functions $f$ for which
$\sum_{n=1}^\infty f(n)$ $=0$. These functions were first introduced and
studied by Kahane and Sa\"{i}as [5]. The main purpose of this paper is to
generalise such functions to multiplicative functions and we shall call them
$MO$ functions. More precisely, we define $MO$ functions to be multiplicative
functions for which $\sum_{n=1}^\infty f(n) = 0$ and $\sum_{k=0}^\infty f(p^k)$
$\ne 0$ for all $p \in \mathbb{P}$. We give some properties and find examples
of $MO$ functions, as well as pointing out the connection between these
functions and the Riemann hypothesis at the end of the paper.


  A strictly linear evolution of the scale factor is a characteristic feature
in several classes of alternative gravity theories. In this article we
investigate the overall viability of an open linear coasting cosmological
model. We report that this model is consistent with gravitational lensing
statistics (within $1\sigma$) and accomodates old high-redshift galaxies. We
finally conclude that such a linear coasting, $\a(t) = t$, is not ruled out on
basis of these observational tests.


  Many results in stochastic analysis and mathematical finance involve local
martingales. However, specific examples of strict local martingales are rare
and analytically often rather unhandy. We study local martingales that follow a
given deterministic function up to a random time $\gamma$ at which they jump
and stay constant afterwards. The (local) martingale properties of these single
jump local martingales are characterised in terms of conditions on the input
parameters. This classification allows an easy construction of strict local
martingales, uniformly integrable martingales that are not in $H^1$, etc. As an
application, we provide a construction of a (uniformly integrable) martingale
$M$ and a bounded (deterministic) integrand $H$ such that the stochastic
integral $H\bullet M$ is a strict local martingale.


  A recommendation system assists users in finding items that are relevant to
them. Existing recommendation models are primarily based on predicting
relationships between users and items and use complex matching models or
incorporate extensive external information to capture association patterns in
data. However, recommendation is not only a problem of inductive statistics
using data; it is also a cognitive task of reasoning decisions based on
knowledge extracted from information. Hence, a logic system could naturally be
incorporated for the reasoning in a recommendation task. However, although
hard-rule approaches based on logic systems can provide powerful reasoning
ability, they struggle to cope with inconsistent and incomplete knowledge in
real-world tasks, especially for complex tasks such as recommendation.
Therefore, in this paper, we propose a neuro-symbolic recommendation model,
which transforms the user history interactions into a logic expression and then
transforms the recommendation prediction into a query task based on this logic
expression. The logic expressions are then computed based on the modular logic
operations of the neural network. We also construct an implicit logic encoder
to reasonably reduce the complexity of the logic computation. Finally, a user's
interest items can be queried in the vector space based on the computation
results. Experiments on three well-known datasets verified that our method
performs better compared to state of the art shallow, deep, session, and
reasoning models.


  In this paper, the author establishes the boundedness of parametric
Littlewood-Paley operators from Musielak-Orlicz Hardy space to Musielak-Orlicz
space, or to weak Musielak-Orlicz space at the critical index. Part of these
results are new even for classical Hardy space of Fefferman and Stein.


  We study the anomalous Hall conductivity in spin-polarized, asymmetrically
confined two-dimensional electron and hole systems, focusing on skew-scattering
contributions to the transport. We find that the skew scattering, principally
responsible for the extrinsic contribution to the anomalous Hall effect,
vanishes for the two-dimensional electron system if both chiral Rashba subbands
are partially occupied, and vanishes always for the two-dimensional hole gas
studied here, regardless of the band filling. Our prediction can be tested with
the proposed coplanar two-dimensional electron/hole gas device and can be used
as a benchmark to understand the crossover from the intrisic to the extrinsic
anomalous Hall effect.


  Bayesian cross-validation (CV) is a popular method for predictive model
assessment that is simple to implement and broadly applicable. A wide range of
CV schemes is available for time series applications, including generic
leave-one-out (LOO) and K-fold methods, as well as specialized approaches
intended to deal with serial dependence such as leave-future-out (LFO),
h-block, and hv-block.
  Existing large-sample results show that both specialized and generic methods
are applicable to models of serially-dependent data. However, large sample
consistency results overlook the impact of sampling variability on accuracy in
finite samples. Moreover, the accuracy of a CV scheme depends on many aspects
of the procedure. We show that poor design choices can lead to elevated rates
of adverse selection.
  In this paper, we consider the problem of identifying the regression
component of an important class of models of data with serial dependence,
autoregressions of order p with q exogenous regressors (ARX(p,q)), under the
logarithmic scoring rule. We show that when serial dependence is present,
scores computed using the joint (multivariate) density have lower variance and
better model selection accuracy than the popular pointwise estimator. In
addition, we present a detailed case study of the special case of ARX models
with fixed autoregressive structure and variance. For this class, we derive the
finite-sample distribution of the CV estimators and the model selection
statistic. We conclude with recommendations for practitioners.


  A Magnetic field Aided Inertial Navigation System (MAINS) for indoor
navigation is proposed in this paper. MAINS leverages an array of magnetometers
to measure spatial variations in the magnetic field, which are then used to
estimate the displacement and orientation changes of the system, thereby aiding
the inertial navigation system (INS). Experiments show that MAINS significantly
outperforms the stand-alone INS, demonstrating a remarkable two orders of
magnitude reduction in position error. Furthermore, when compared to the
state-of-the-art magnetic-field-aided navigation approach, the proposed method
exhibits slightly improved horizontal position accuracy. On the other hand, it
has noticeably larger vertical error on datasets with large magnetic field
variations. However, one of the main advantages of MAINS compared to the
state-of-the-art is that it enables flexible sensor configurations. The
experimental results show that the position error after 2 minutes of navigation
in most cases is less than 3 meters when using an array of 30 magnetometers.
Thus, the proposed navigation solution has the potential to solve one of the
key challenges faced with current magnetic-field simultaneous localization and
mapping (SLAM) solutions: the very limited allowable length of the exploration
phase during which unvisited areas are mapped.


  We present the very long baseline interferometry H2O maser monitoring
observations of the red supergiant, PZ Cas, at 12 epochs from 2006 April to
2008 May. We fitted maser motions to a simple model composed of a common annual
parallax and linear motions of the individual masers. The maser motions with
the parallax subtracted were well modeled by a combination of a common stellar
proper motion and a radial expansion motion of the circumstellar envelope. We
obtained an annual parallax of 0.356+/-0.026 mas and a stellar proper motion of
{\mu}*{\alpha}cos{\delta}=-3.7+/-0.2 and {\mu}*{\delta}=-2.0+/-0.3 mas/yr
eastward and northward, respectively. The annual parallax corresponds to a
trigonometric parallax of 2.81+0.22-0.19 kpc. By rescaling the luminosity of PZ
Cas in any previous studies using our trigonometric parallax, we estimated the
location of PZ Cas on a Hertzsprung-Russell diagram and found that it
approaches a theoretically evolutionary track around an initial mass of
~25M(sun). The sky position and the distance to PZ Cas are consistent with the
OB association, Cas OB5, which is located in a molecular gas super shell. The
proper motion of PZ Cas is close to that of the OB stars and other red
supergiants in Cas OB5 measured by the Hipparcos satellite. We derived the
peculiar motion of PZ Cas of Us = 22.8+/-1.5, Vs = 7.1+/-4.4, and Ws =
-5.7+/-4.4 km/s. This peculiar motion has rather a large Us component, unlike
those of near high-mass star-forming regions with negatively large Vs motions.
The uniform proper motions of the Cas OB5 member stars suggest random motions
of giant molecular clouds moving into local potential minima in a
time-dependent spiral arm, rather than a velocity field caused by the spiral
arm density wave.


  The aghq package for implementing approximate Bayesian inference using
adaptive quadrature is introduced. The method and software are described, and
use of the package in making approximate Bayesian inferences in several
challenging low- and high-dimensional models is illustrated. Examples include
an infectious disease model; an astrostatistical model for estimating the mass
of the Milky Way; two examples in non-Gaussian model-based geostatistics
including one incorporating zero-inflation which is not easily fit using other
methods; and a model for zero-inflated, overdispersed count data. The aghq
package is especially compatible with the popular TMB interface for automatic
differentiation and Laplace approximation, and existing users of that software
can make approximate Bayesian inferences with aghq using very little additional
code. The aghq package is available from CRAN and complete code for all
examples in this paper can be found at
https://github.com/awstringer1/aghq-software-paper-code.


  First-principles molecular dynamics simulations having a duration of 8 ps
have been used to study the static, dynamic and electronic properties of l-Ga
at the temperatures 702 K and 982 K. The simulations use the density-functional
pseudopotential method and the system is maintained on the Born-Oppenheimer
surface by conjugate gradients relaxation. The static structure factor and
radial distribution function of the simulated system agree very closely with
experimental data, but the diffusion coefficient is noticeably lower than
measured values. The long simulations allow us to calculate the dynamical
structure factor $S(q,\omega)$. A sound-wave peak is clearly visible in
$S(q,\omega)$ at small wavevectors, and we present results for the dispersion
curve and hence the sound velocity, which is close to the experimental value.
The electronic density of states is very close to the free-electron form.
Values of the electrical conductivity calculated from Kubo-Greenwood formula
are in satisfactory accord with measured data.


  We construct the duality groups for N=2 Supersymmetric QCD with gauge group
SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The
groups are generated by two elements $S$ and $T$ that satisfy a relation
$(STS^{-1}T)^{2n+1}=1$. Thus, the groups are not subgroups of $SL(2,Z)$. We
also construct automorphic functions that map the fundamental region of the
group generated by $T$ and $STS$ to the Riemann sphere. These automorphic
functions faithfully represent the duality symmetry in the Seiberg-Witten
curve.


  Exploration algorithms for explicit-state transition systems are a core
back-end technology in program verification. They can be applied to programs by
generating the transition system on the fly, avoiding an expensive up-front
translation. An on-the-fly strategy requires significant modifications to the
implementation, into a form that stores states directly as valuations of
program variables. Performed manually on a per-algorithm basis, such
modifications are laborious and error-prone.
  In this paper we present the IJIT Application Programming Interface (API),
which allows users to automatically transform a given transition system
exploration algorithm to one that operates on Boolean programs. The API
converts system states temporarily to program states just in time for expansion
via image computations, forward or backward. Using our API, we have
effortlessly extended various non-trivial (e.g. infinite-state) model checking
algorithms to operate on multi-threaded Boolean programs. We demonstrate the
ease of use of the API, and present a case study on the impact of the
just-in-time translation on these algorithms.


  This paper outlines the results from experiments performed to gain further
information about the structure and properties of cleaved silicon surfaces,
using vacuum cleavage luminescence detection methods. The experiments involved
detecting the luminescence produced by cleaving thin silicon plates within a
high vacuum, by a process of converting the luminescence to an amplified
electrical signal.


  Our recent studies of axial-symmetry breaking in the nearby ($d <3 \,{\rm
kpc}$) star counts are sensitive to the distortions of stellar orbits
perpendicular and parallel to the orientation of the bar just within and beyond
the outer Lindblad resonance (OLR) radius. Using the location of the sign flip
in the left-right asymmetry in stars counts about the anticenter line to
determine the OLR radius $R_{\rm OLR}$, and treating the bar as if it were a
weakly non-axisymmetric effect, we use $R_{\rm OLR}$ and recent measurements of
the Galactic rotation curve and the Sun-Galactic-center distance $R_{0}$ to
determine the pattern speed $\Omega_{\rm p}$ of the Galactic bar, as well as
the Galactic corotation radius $R_{\rm CR}$. After removing the effect of the
Large and Small Magellanic clouds from our asymmetry measurement, we find that
$R_{\rm OLR}=(0.96 \pm 0.03)R_0 = 7.85 \pm 0.25 \ \rm kpc$, $\Omega_{\rm p} =
49.3 \pm 2.2 \ \rm km \ s^{-1} \ kpc^{-1}$, $R_{\rm CR}=(0.58 \pm 0.04)R_0 =
4.76 \pm 0.27 \ \rm kpc$, revealing, as we shall show, that the Milky Way's bar
is likely both weak and fast, though we also note possible evidence for
non-steady-state effects in the bar region.


  We present electron and phonon spectral functions calculated from determinant
quantum Monte Carlo simulations of the half-filled two-dimensional
Hubbard-Holstein model on a square lattice. By tuning the relative
electron-electron ($e$-$e$) and electron-phonon ($e$-$ph$) interaction
strengths, we show the electron spectral function evolving between
antiferromagnetic insulating, metallic, and charge density wave insulating
phases. The phonon spectra concurrently gain a strong momentum dependence and
soften in energy upon approaching the charge density wave phase. In particular,
we study how the $e$-$e$ and $e$-$ph$ interactions renormalize the spectra, and
analyze how the interplay of these interactions influence the spectral
renormalizations. We find that the presence of both interactions suppresses the
amount of renormalization at low energy, thus allowing the emergence of a
metallic phase. These findings demonstrate the importance of considering the
influence of multiple interactions in spectroscopically determining any one
interaction strength in strongly correlated materials.


  We examine the minimization of information entropy for measures on the phase
space of bounded domains, subject to constraints that are averages of grand
canonical distributions. We describe the set of all such constraints and show
that it equals the set of averages of all probability measures absolutely
continuous with respect to the standard measure on the phase space (with the
exception of the measure concentrated on the empty configuration). We also
investigate how the set of constrains relates to the domain of the
microcanonical thermodynamic limit entropy. We then show that, for fixed
constraints, the parameters of the corresponding grand canonical distribution
converge, as volume increases, to the corresponding parameters (derivatives,
when they exist) of the thermodynamic limit entropy. The results hold when the
energy is the sum of any stable, tempered interaction potential that satisfies
the Gibbs variational principle (e.g.~Lennard-Jones) and the kinetic energy.
The same tools and the strict convexity of the thermodynamic limit pressure for
continuous systems (valid whenever the Gibbs variational principle holds) give
solid foundation to the folklore local homeomorphism between thermodynamic and
macroscopic quantities.


  The slope of the best fit line from minimizing the sum of both the squared
vertical errors and the squared horizontal errors is shown to be the root of a
fourth degree polynomial.


  The resilience to averaging over an initial energy distribution of
reducibility and thermal scaling observed in nuclear multifragmentation is
studied. Poissonian reducibility and the associated thermal scaling of the mean
are shown to be robust. Binomial reducibility and thermal scaling of the
elementary probability are robust under a broad range of conditions. The
experimental data do not show any indication of deviation due to averaging.


  We study the motion of an undamped single-ion harmonic oscillator, resonantly
driven with a pulsed radiation pressure force. We demonstrate that a barium
ion, initially cooled to the Doppler limit, quickly phase locks to the drive
and builds up coherent oscillations above the thermal distribution after
scattering of order one hundred photons. In our experiment, this seeded motion
is subsequently amplified and then analyzed by Doppler velocimetry. Since the
coherent oscillation is conditional upon the internal quantum state of the ion,
this motional excitation technique could be useful in atomic or molecular
single-ion spectroscopy experiments, providing a simple protocol for state
readout of non-fluorescing ions with partially closed-cycle transitions.


  We construct an ensemble of second--quantized Hamiltonians with two bosonic
degrees of freedom, whose members display with probability one GOE or GUE
statistics. Nevertheless, these Hamiltonians have a second integral of motion,
namely the boson number, and thus are integrable. To construct this ensemble we
use some ``reverse engineering'' starting from the fact that $n$--bosons in a
two--level system with random interactions have an integrable classical limit
by the old Heisenberg association of boson operators to actions and angles. By
choosing an $n$--body random interaction and degenerate levels we end up with
GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.


  We study ${\cal N}=2$ compactifications of heterotic string theory on the CHL
orbifold $(K3\times T^2)/\mathbb{Z}_N$ with $N= 2, 3, 5, 7$. $\mathbb{Z}_N$
acts as an involution on $K3$ together with a shift of $1/N$ along one of the
circles of $T^2$. These compactifications generalize the example of the
heterotic string on $K3\times T^2$ studied in the context of dualities in
${\cal N}=2$ string theories. We evaluate the new supersymmetric index for
these theories and show that their expansion can written in terms of the
McKay-Thompson series associated with the $\mathbb{Z}_N$ involution embedded in
the Mathieu group $M_{24}$. We then evaluate the difference in one-loop
threshold corrections to the non-Abelian gauge couplings with Wilson lines and
show that their moduli dependence is captured by Siegel modular forms related
to dyon partition functions of ${\cal N}=4$ string theories.


  Lemmatization holds significance in both natural language processing (NLP)
and linguistics, as it effectively decreases data density and aids in
comprehending contextual meaning. However, due to the highly inflected nature
and morphological richness, lemmatization in Bangla text poses a complex
challenge. In this study, we propose linguistic rules for lemmatization and
utilize a dictionary along with the rules to design a lemmatizer specifically
for Bangla. Our system aims to lemmatize words based on their parts of speech
class within a given sentence. Unlike previous rule-based approaches, we
analyzed the suffix marker occurrence according to the morpho-syntactic values
and then utilized sequences of suffix markers instead of entire suffixes. To
develop our rules, we analyze a large corpus of Bangla text from various
domains, sources, and time periods to observe the word formation of inflected
words. The lemmatizer achieves an accuracy of 96.36% when tested against a
manually annotated test dataset by trained linguists and demonstrates
competitive performance on three previously published Bangla lemmatization
datasets. We are making the code and datasets publicly available at
https://github.com/eblict-gigatech/BanLemma in order to contribute to the
further advancement of Bangla NLP.


  Using an analytical model for the Cosmic Microwave Background anisotropies
produced by textures, we compute the resulting collapsed three--point
correlation function and the {\it rms} expected value due to the cosmic
variance. We apply our calculations to the {\sl COBE}--DMR experiment and test
the consistency of the model with the observational results. We also show that
an experiment with smaller angular resolution can put bounds to the model
parameters.


  We present numerical investigations into the formation of massive stars from
centrally condensed turbulent cores. The results of five hydrodynamical
simulations are described, following the collapse of the core, fragmentation
and the formation of small clusters of protostars. We generate two different
initial turbulent velocity fields corresponding to power-law spectra with power
varying as k^{-4} and k^{-3.5}, and apply two different initial core radii.
Calculations are included for both completely isothermal collapse, and a
non-isothermal equation of state above a critical density 10^{-14}gcm^{-3}. Our
calculations reveal the preference of fragmentation over monolithic star
formation in turbulent cores. Fragmentation was prevalent in all the isothermal
cases. Although disc fragmentation was largely suppressed in the non-isothermal
runs due to the small dynamic range between the initial density and the
critical density, our results show that some fragmentation still persisted.
This is inconsistent with previous suggestions that turbulent cores result in
the formation of a single massive star. We conclude that turbulence cannot be
measured as an isotropic pressure term.


  This paper investigates the existence and stability of Einstein universe in
the context of $f(R,T,Q)$ gravity, where $Q=R_{\mu\nu}T^{\mu\nu}$. Considering
linear homogeneous perturbations around scale factor and energy density, we
formulate static as well as perturbed field equations. We parameterize the
stability regions corresponding to conserved as well as non-conserved
energy-momentum tensor using linear equation of state parameter for particular
models of this gravity. The graphical analysis concludes that for a suitable
choice of parameters, the stable regions of the Einstein universe are obtained.


  In the spirit of the paper "Large conformal metrics of prescribed Gauss
curvature on surfaces of higher genus" by Borer-Galimberti-Struwe, where we
dealt with the case of a closed Riemann surface $(M,g_0)$ of genus greater than
one, here we study the behaviour of the conformal metrics $g_\lambda$ of
prescribed Gauss curvature $K_{g_\lambda} = f_0 + \lambda$ on the torus, when
the parameter $\lambda$ tends to one of the boundary points of the interval of
existence of $g_\lambda$, and we characterize their "bubbling behaviour".


  The surface structure of Few-Layer Graphene (FLG) epitaxially grown on the
C-face of SiC has been investigated by TM-AFM in ambient air and upon
interaction with diluted aqueous solutions of bio-organic molecules (dimethyl
sulfoxide, DMSO, and L-Methionine). On pristine FLG we observe nicely ordered,
three-fold oriented rippled domains, with a 4.7+/-0.2 nm periodicity (small
periodicity, SP) and a peak-to-valley distance in the range 0.1-0.2 nm. Upon
mild interaction of the FLG surface with the molecular solution, the ripple
periodicity relaxes to 6.2+/-0.2 nm (large periodicity, LP), while the
peak-to-valley height increases to 0.2-0.3 nm. When additional energy is
transferred to the system through sonication in solution, graphene planes are
peeled off from FLG, as shown by quantitative analysis of XPS and Raman
spectroscopy data which indicate a neat reduction of thickness. Upon sonication
rippled domains are no longer observed. Regarding HOPG, we could not observe
ripples on cleaved samples in ambient air, while LP ripples develop upon
interaction with the molecular solutions. Recent literature on similar systems
is not univocal regarding the interpretation of rippling. The complex of our
comparative observations on FLG and HOPG can be hardly rationalized solely on
the base of surface assembly of molecules, either organic molecules coming from
the solution or adventitious species. We propose to consider the ripples as the
manifestation of the free-energy minimization of quasi-2D layers, eventually
affected by factors such as the interplane stacking, the interaction with
molecules and/or with the AFM tip.


  Recent theoretical predictions of "unprecedented proximity" of the electronic
ground state of iridium fluorides to the SU(2) symmetric $j_{\mathrm{eff}}=1/2$
limit, relevant for superconductivity in iridates, motivated us to investigate
their crystal and electronic structure. To this aim, we performed
high-resolution x-ray powder diffraction, Ir L$_3$-edge resonant inelastic
x-ray scattering, and quantum chemical calculations on Rb$_2$[IrF$_6$] and
other iridium fluorides. Our results are consistent with the Mott insulating
scenario predicted by Birol and Haule [Phys. Rev. Lett. 114, 096403 (2015)],
but we observe a sizable deviation of the $j_{\mathrm{eff}}=1/2$ state from the
SU(2) symmetric limit. Interactions beyond the first coordination shell of
iridium are negligible, hence the iridium fluorides do not show any magnetic
ordering down to at least 20 K. A larger spin-orbit coupling in iridium
fluorides compared to oxides is ascribed to a reduction of the degree of
covalency, with consequences on the possibility to realize spin-orbit-induced
strongly correlated physics in iridium fluorides.


  We present a method for the determination of [alpha/Fe] ratios from
low-resolution (R = 2000) SDSS/SEGUE stellar spectra. By means of a
star-by-star comparison with degraded spectra from the ELODIE spectral library
and with a set of moderately high-resolution (R = 15,000) and medium-resolution
(R = 6000) spectra of SDSS/SEGUE stars, we demonstrate that we are able to
measure [alpha/Fe] from SDSS/SEGUE spectra (with S/N > 20/1) to a precision of
better than 0.1 dex, for stars with atmospheric parameters in the range Teff =
[4500, 7000] K, log g = [1.5, 5.0], and [Fe/H] = [-1.4, +0.3], over the range
[alpha/Fe] = [-0.1, +0.6]. For stars with [Fe/H] < -1.4, our method requires
spectra with slightly higher signal-to-noise to achieve this precision (S/N >
25/1). Over the full temperature range considered, the lowest metallicity star
for which a confident estimate of [alpha/Fe] can be obtained from our approach
is [Fe/H] ~ -2.5; preliminary tests indicate that a metallicity limit as low as
[Fe/H] ~ -3.0 may apply to cooler stars. As a further validation of this
approach, weighted averages of [alpha/Fe] obtained for SEGUE spectra of likely
member stars of Galactic globular clusters (M15, M13, and M71) and open
clusters (NGC 2420, M67, and NGC 6791) exhibit good agreement with the values
of [alpha/Fe] from previous studies. The results of the comparison with NGC
6791 imply that the metallicity range for the method may extend to ~ +0.5.


  We study lattice points in d-dimensional spheres, and count their number in
thin spherical segments. We found an upper bound depending only on the radius
of the sphere and opening angle of the segment. To obtain this bound we slice
the segment by hyperplanes of rational direction, and then cover an arbitrary
segment with one having rational direction. Diophantine approximation can be
used to obtain the best rational direction possible.


  The combination of deep neural nets and theory-driven models, which we call
deep grey-box modeling, can be inherently interpretable to some extent thanks
to the theory backbone. Deep grey-box models are usually learned with a
regularized risk minimization to prevent a theory-driven part from being
overwritten and ignored by a deep neural net. However, an estimation of the
theory-driven part obtained by uncritically optimizing a regularizer can hardly
be trustworthy when we are not sure what regularizer is suitable for the given
data, which may harm the interpretability. Toward a trustworthy estimation of
the theory-driven part, we should analyze regularizers' behavior to compare
different candidates and to justify a specific choice. In this paper, we
present a framework that enables us to analyze a regularizer's behavior
empirically with a slight change in the neural net's architecture and the
training objective.


  The twist construction is a geometric model of T-duality that includes
constructions of nilmanifolds from tori. This paper shows how one-dimensional
foliations on manifolds may be used in a shear construction, which in algebraic
form builds certain solvable Lie groups from Abelian ones. We discuss other
examples of geometric structures that may be obtained from the shear
construction.


  We investigated compact stars consisting of cold quark matter and fermionic
dark matter treated as two admixed fluids. We computed the stellar structures
and fundamental radial oscillation frequencies for different masses of the dark
fermion in the cases of weak and strong self-interacting dark matter. We found
that the fundamental frequency can be dramatically modified and, in some cases,
stable dark strange planets and dark strangelets with very low masses and radii
can be formed.


  With increasing complexity of Automated Driving Systems (ADS), ensuring their
safety and reliability has become a critical challenge. The Verification and
Validation (V&V) of these systems are particularly demanding when AI components
are employed to implement perception and/or control functions. In ESA-funded
project VIVAS, we developed a generic framework for system-level
simulation-based V&V of autonomous systems. The approach is based on a
simulation model of the system, an abstract model that describes symbolically
the system behavior, and formal methods to generate scenarios and verify the
simulation executions. Various coverage criteria can be defined to guide the
automated generation of the scenarios.
  In this paper, we describe the instantiation of the VIVAS framework for an
ADS case study. This is based on the integration of CARLA, a widely-used
driving simulator, and its ScenarioRunner tool, which enables the creation of
diverse and complex driving scenarios. This is also used in the CARLA
Autonomous Driving Challenge to validate different ADS agents for perception
and control based on AI, shared by the CARLA community. We describe the
development of an abstract ADS model and the formulation of a coverage
criterion that focuses on the behaviors of vehicles relative to the vehicle
with ADS under verification. Leveraging the VIVAS framework, we generate and
execute various driving scenarios, thus testing the capabilities of the AI
components. The results show the effectiveness of VIVAS in automatically
generating scenarios for system-level simulation-based V&V of an automated
driving system using CARLA and ScenarioRunner. Therefore, they highlight the
potential of the approach as a powerful tool in the future of ADS V&V
methodologies.


  In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model
solitons to generic scalar-field solitons for an infinitely stiff potential.
The static k-lump moduli space C^k/S_k features a natural K"ahler metric
induced from an embedding Grassmannian. The moduli-space dynamics is blind
against adding a WZW-like term to the sigma-model action and thus also applies
to the integrable U(1) Ward model. For the latter's two-soliton motion we
compare the exact field configurations with their supposed moduli-space
approximations. Surprisingly, the two do not match, which questions the
adiabatic method for noncommutative solitons.


  A Homomorphic Secret Sharing (HSS) scheme is a secret-sharing scheme that
shares a secret $x$ among $s$ servers, and additionally allows an output client
to reconstruct some function $f(x)$ using information that can be locally
computed by each server. A key parameter in HSS schemes is download rate, which
quantifies how much information the output client needs to download from the
servers. Often, download rate is improved by amortizing over $\ell$ instances
of the problem, making $\ell$ also a key parameter of interest.
  Recent work (Fosli, Ishai, Kolobov, and Wootters 2022) established a limit on
the download rate of linear HSS schemes for computing low-degree polynomials
and constructed schemes that achieve this optimal download rate; their schemes
required amortization over $\ell = \Omega(s \log(s))$ instances of the problem.
Subsequent work (Blackwell and Wootters, 2023) completely characterized linear
HSS schemes that achieve optimal download rate in terms of a coding-theoretic
notion termed optimal labelweight codes. A consequence of this characterization
was that $\ell = \Omega(s \log(s))$ is in fact necessary to achieve optimal
download rate.
  In this paper, we characterize all linear HSS schemes, showing that schemes
of any download rate are equivalent to a generalization of optimal labelweight
codes. This equivalence is constructive and provides a way to obtain an
explicit linear HSS scheme from any linear code. Using this characterization,
we present explicit linear HSS schemes with slightly sub-optimal rate but with
much improved amortization $\ell = O(s)$. Our constructions are based on
algebraic geometry codes (specifically Hermitian codes and Goppa codes).


  We used multi-component profiles to model H$\beta$ and [O III]$\lambda
\lambda $4959,5007 lines for SDSS J143030.22-001115.1, a narrow-line Seyfert 1
galaxy (NLS1) in a sample of 150 NLS1s candidates selected from the Sloan
Digital Sky Survey (SDSS) Early Data Release (EDR). After subtracting the
H$\beta$ contribution from narrow line regions (NLRs), we found that its full
width half maximum (FWHM) of broad H$\beta$ line is nearly 2900 \kms,
significantly larger than the customarily adopted criterion of 2000 \kms. With
its weak Fe II multiples, we think that SDSS J143030.22-001115.1 can't be
classified as a genuine NLS1. When we calculate the virial black hole masses of
NLS1s, we should use the H$\beta$ linewidth after subtracting the H$\beta$
contribution from NLRs.


  In this paper, we consider the isoperimetric problem in the space
$\mathbb{R}^N$ with density. Our result states that, if the density f is l.s.c.
and converges to a positive limit at infinity, being smaller than this limit
far from the origin, then isoperimetric sets exist for all volumes. Several
known results or counterexamples show that the present result is essentially
sharp. The special case of our result for radial and increasing densities
positively answers a conjecture made in [10].


  This paper proposes a category-level 6D object pose and shape estimation
approach iCaps, which allows tracking 6D poses of unseen objects in a category
and estimating their 3D shapes. We develop a category-level auto-encoder
network using depth images as input, where feature embeddings from the
auto-encoder encode poses of objects in a category. The auto-encoder can be
used in a particle filter framework to estimate and track 6D poses of objects
in a category. By exploiting an implicit shape representation based on signed
distance functions, we build a LatentNet to estimate a latent representation of
the 3D shape given the estimated pose of an object. Then the estimated pose and
shape can be used to update each other in an iterative way. Our category-level
6D object pose and shape estimation pipeline only requires 2D detection and
segmentation for initialization. We evaluate our approach on a publicly
available dataset and demonstrate its effectiveness. In particular, our method
achieves comparably high accuracy on shape estimation.


  We investigate the uplink throughput achievable by a multiple-user (MU)
massive multiple-input multiple-output (MIMO) system in which the base station
is equipped with a large number of low-resolution analog-to-digital converters
(ADCs). Our focus is on the case where neither the transmitter nor the receiver
have any a priori channel state information. This implies that the fading
realizations have to be learned through pilot transmission followed by channel
estimation at the receiver, based on coarsely quantized observations. We
propose a novel channel estimator, based on Bussgang's decomposition, and a
novel approximation to the rate achievable with finite-resolution ADCs, both
for the case of finite-cardinality constellations and of Gaussian inputs, that
is accurate for a broad range of system parameters. Through numerical results,
we illustrate that, for the 1-bit quantized case, pilot-based channel
estimation together with maximal-ratio combing or zero-forcing detection
enables reliable multi-user communication with high-order constellations in
spite of the severe nonlinearity introduced by the ADCs. Furthermore, we show
that the rate achievable in the infinite-resolution (no quantization) case can
be approached using ADCs with only a few bits of resolution. We finally
investigate the robustness of low-ADC-resolution MU-MIMO uplink against receive
power imbalances between the different users, caused for example by imperfect
power control.


  It is clarified how cohomologies and Gerstenhaber algebras can be associated
with linear pre-operads (comp algebras). Their relation to mechanics and
operadic physics is concisely discussed.


  The maximum independent set problem is a classical NP-hard problem in
theoretical computer science. In this work, we study a special case where the
family of graphs considered is restricted to intersection graphs of sets of
axis-aligned hyperrectangles and the input is provided in an online fashion. We
prove bounds on the competitive ratio of an optimal online algorithm under the
adaptive offline, adaptive online, and oblivious adversary models, for several
classes of hyperrectangles and restrictions on the order of the input.
  We are the first to present results on this problem under the oblivious
adversary model. We prove bounds on the competitive ratio for unit hypercubes,
$\sigma$-bounded hypercubes, unit-volume hypercubes, arbitrary hypercubes, and
arbitrary hyperrectangles, in both arbitrary and non-dominated order. We are
also the first to present results under the adaptive offline and adaptive
online adversary models with input in non-dominated order, proving bounds on
the competitive ratio for the same classes of hyperrectangles; for input in
arbitrary order, we present the first results on $\sigma$-bounded hypercubes,
unit-volume hyperrectangles, arbitrary hypercubes, and arbitrary
hyperrectangles. For input in dominating order, we show that the performance of
the naive greedy algorithm matches the performance of an optimal offline
algorithm in all cases. We also give lower bounds on the competitive ratio of a
probabilistic greedy algorithm under the oblivious adversary model. We conclude
by discussing several promising directions for future work.


  The study of how science is discussed and how scholarly actors interact on
social media has increasingly become popular in the field of scientometrics in
recent years. While most prior studies focused on research outputs discussed on
global platforms, such as Twitter or Facebook, the presence of scholarly
journals on local platforms was seldom studied, especially in the Chinese
social media context. To fill this gap, this study investigates the uptake of
WeChat (a Chinese social network app) by the Chinese scholarly journals indexed
by the Chinese Social Sciences Citation Index (CSSCI). The results show that
65.3% of CSSCI-indexed journals have created WeChat public accounts and posted
over 193 thousand WeChat posts in total. At the journal level, bibliometric
indicators (e.g., citations, downloads, and journal impact factors) and WeChat
indicators (e.g., clicks, likes, replies, and recommendations) are weakly
correlated with each other, reinforcing the idea of fundamentally
differentiated dimensions of indicators between bibliometrics and social media
metrics. Results also show that journals with WeChat public accounts slightly
outperform those without WeChat public accounts in terms of citation impact,
suggesting that the WeChat presence of scientific journals is mostly positively
associated with their citation impact.