  The decrease rate of dust mass due to strong shock waves ($v_s\geq 150$ km
s$^{-1}$) from supernovae (SNe) estimated for the Milky Way interstellar medium
significantly exceeds the overall production rate by both asymptotic giant
branch stars and core collapse SNe. The interplay between the production and
destruction rates is critically important for evaluation of the net dust
outcome from SNe at different conditions. In light of this, we study the
dynamics of initially polydisperse dust grains pre-existed in an ambient medium
swept up the SN shock front depending on magnitude of inhomogeneity
(clumpiness) in {the} medium. We find that dust destruction inside the bubble
is inhibited in more inhomogeneous medium: the larger amount of dust survives
for the higher dispersion of density. This trend is set by the interrelation
between radiative gas cooling and dust sputtering in different environment.
After several radiative times the mass fraction of the survived dust saturates
at the level almost independent on the gas mean density. We note that for more
clumpy medium the distributions of dust over thermal phases of a gas inside the
bubble and over sizes are smoother and flatter in comparison with those in a
nearly homogeneous medium.


  The He-shell flash convection in AGB stars is the site for the
high-temperature component of the s-process in low- and intermediate mass
giants, driven by the Ne22 neutron source. [...] The upper convection boundary
plays a critical role during the H-ingestion episode that may lead to
neutron-bursts in the most metal-poor AGB stars. We address these problems
through global 3-dimensional hydrodynamic simulations including the entire
spherical He-shell flash convection zone (as oposed to the 3D box-in-a-star
simulations). An important aspect of our current effort is to establish the
feasibility of our appoach. We explain why we favour the explicit treatment
over the anelastic approximation for this problem. The simulations presented in
this paper use a Cartesian grid of 512^3 cells and have been run on four 8-core
workstations for four days to simulate ~5000s, which corresponds to almost ten
convective turn-over times. The convection layer extends radially at the
simulated point in the flash evolution over 7 H_p pressure scale-heights and
exceeds the size of the underlying core. Convection is dominated by large
convective cells that fill more than an entire octant. [...]


  This correspondence paper studies a network integrated sensing and
communication (ISAC) system that unifies the interference channel for
communication and distributed radar sensing. In this system, a set of
distributed ISAC transmitters send individual messages to their respective
communication users (CUs), and at the same time cooperate with multiple sensing
receivers to estimate the location of one target. We exploit the coordinated
power control among ISAC transmitters to minimize their total transmit power
while ensuring the minimum signal-to-interference-plus-noise ratio (SINR)
constraints at individual CUs and the maximum Cram\'{e}r-Rao lower bound (CRLB)
requirement for target location estimation. Although the formulated coordinated
power control problem is non-convex and difficult to solve in general, we
propose two efficient algorithms to obtain high-quality solutions based on the
semi-definite relaxation (SDR) and CRLB approximation, respectively. Numerical
results show that the proposed designs achieve substantial performance gains in
terms of power reduction, as compared to the benchmark with a heuristic
separate communication-sensing design.


  Mutation analysis measures test suite adequacy, the degree to which a test
suite detects seeded faults: one test suite is better than another if it
detects more mutants. Mutation analysis effectiveness rests on the assumption
that mutants are coupled with real faults i.e. mutant detection is strongly
correlated with real fault detection. The work that validated this also showed
that a large portion of defects remain out of reach.
  We introduce tailored mutation operators to reach and capture these defects.
Tailored mutation operators are built from and apply to an existing codebase
and its history. They can, for instance, identify and replay errors specific to
the project for which they are tailored. As our point of departure, we define
tailored mutation operators for identifiers, which mutation analysis has
largely ignored, because there are too many ways to mutate them. Evaluated on
the Defects4J dataset, our new mutation operators creates mutants coupled to
14% more faults, compared to traditional mutation operators.
  These new mutation operators, however, quadruple the number of mutants. To
combat this problem, we propose a new approach to mutant selection focusing on
the location at which to apply mutation operators and the unnaturalness of the
mutated code. The results demonstrate that the location selection heuristics
produce mutants more closely coupled to real faults for a given budget of
mutation operator applications.
  In summary, this paper defines and explores tailored mutation operators,
advancing the state of the art in mutation testing in two ways: 1) it suggests
mutation operators that mutate identifiers and literals, extending mutation
analysis to a new class of faults and 2) it demonstrates that selecting the
location where a mutation operator is applied decreases the number of generated
mutants without affecting the coupling of mutants and real faults.


  The quantum-mechanical description of the world, including human observers,
makes substantial use of entanglement. In order to understand this, we need to
adopt concepts of truth, probability and time which are unfamiliar in modern
scientific thought. There are two kinds of statements about the world: those
made from inside the world, and those from outside. The conflict between
contradictory statements which both appear to be true can be resolved by
recognising that they are made in different perspectives. Probability, in an
objective sense, belongs in the internal perspective, and to statements in the
future tense. Such statements obey a many-valued logic, in which the truth
values are identified as probabilities.


  For a finite group $G$ and a positive integer $n$, let $G(n)$ be the set of
all elements in $G$ such that $x^{n}=1$. The groups $G$ and $H$ are said to be
of the same (order) type if $G(n)=H(n)$, for all $n$. The main aim of this
paper is to show that if $G$ is a finite group of the same type as Suzuki
groups $Sz(q)$, where $q=2^{2m+1}\geq 8$, then $G$ is isomorphic to $Sz(q)$.
This addresses the well-known J. G. Thompson's problem (1987) for simple
groups.


  For a positive integer $k$, we say that an association scheme $(\Omega,S)$ is
$k$-equivalenced if each non-diagonal element of $S$ has valency $k$.
$k$-equivalenced is weaker than pseudocyclic. It is known that every
$k$-equivalenced association scheme is Frobenius when $k=2,3$ and every
$4$-equivalenced association scheme is pseudocyclic. In this paper, we will
show that every $4$-equivalenced association scheme is Frobenius.


  Starting from a general material system of $N$ particles coupled to a cavity,
we use a coherent-state path integral formulation to produce a non-perturbative
effective theory for the material degrees of freedom. We tackle the effects of
image charges, the $A^2$ term and a multimode arbitrary-geometry cavity. The
resulting (non-local) action has the photonic degrees of freedom replaced by an
effective position-dependent interaction between the particles. In the
large-$N$ limit, we discuss how the theory can be cast into an effective
Hamiltonian where the cavity induced interactions are made explicit. The theory
is applicable, beyond cavity QED, to any system where bulk material is linearly
coupled to a diagonalizable bosonic bath. We highlight the differences of the
theory with other well-known methods and numerically study its finite-size
scaling on the Dicke model. Finally, we showcase its descriptive power with
three examples: photon condensation, the 2D free electron gas in a cavity and
the modification of magnetic interactions between molecular spins; recovering,
condensing and extending some recent results in the literature.


  We address low-density two-dimensional circular quantum dots with
spin-restricted Kohn-Sham density functional theory. By using an
exchange-correlation functional that encodes the effects of the
strongly-correlated regime (and that becomes exact in the limit of infinite
correlation), we are able to reproduce characteristic phenomena such as the
formation of ring structures in the electronic total density, preserving the
fundamental circular symmetry of the system. The observation of this and other
well-known effects in Wigner-localized quantum dots such as the flattening of
the addition energy spectra, has until now only been within the scope of other,
numerically more demanding theoretical approaches


  Stress or strain analysis for each atom around structural defects in a
crystal is difficult. We propose a new analytical approach based on the eminent
Embedding Atom Method(EAM) potential. We observe that the ratio $R$ between the
repulsive and binding terms of the EAM is a definite measure for calculating
the strain field of a single atom subject to an irregular coordination number.
The determination of adequate potential parameters and their application to the
calculation of the properties of surface, vacancy, and boundary of pure Al are
shown.


  The chiral spin textures of a two-dimensional (2D) triangular system, where
both antiferromagnetic (AF) Heisenberg exchange and chiral Dzyaloshinsky-Moriya
interactions co-exist, are investigated numerically with an optimized quantum
Monte Carlo method based on mean-field theory. We find that: helical,
skyrmionic and vortical AF crystals can be formed when an external magnetic
field is applied perpendicular to the 2D monolayer; the sizes of these
skyrmions and vortices change abruptly at several critical points of the
external magnetic field; each of these AF crystals can be decomposed into three
periodical ferromagnetic (FM) sublattices. The quantum ingredient implemented
into the theoeretical framework helps to track the existence of AF skyrmion
lattices down to low temperatures.


  We propose a dual-path self-attention recurrent neural network (DP-SARNN) for
time-domain speech enhancement. We improve dual-path RNN (DP-RNN) by augmenting
inter-chunk and intra-chunk RNN with a recently proposed efficient attention
mechanism. The combination of inter-chunk and intra-chunk attention improves
the attention mechanism for long sequences of speech frames. DP-SARNN
outperforms a baseline DP-RNN by using a frame shift four times larger than in
DP-RNN, which leads to a substantially reduced computation time per utterance.
As a result, we develop a real-time DP-SARNN by using long short-term memory
(LSTM) RNN and causal attention in inter-chunk SARNN. DP-SARNN significantly
outperforms existing approaches to speech enhancement, and on average takes 7.9
ms CPU time to process a signal chunk of 32 ms.


  We discuss full-sky convolution of the instrumental beam with the CMB sky
signal in CMB single-dish and interferometry experiments, using the method
(Challinor et al. 2000) that the measured temperature and polarization
anisotropies are defined globally on the group manifold of the
three-dimensional rotation by means of Wigner D-functions. We re-derive the
anisotropy and polarization correlation functions incorporated with asymmetric
window functions, which are then explicitly calculated for a single-dish
elliptical Gaussian beam and an interferometric Gaussian beam.


  The dynamics of soft colloids in solutions is characterized by internal
collective motion as well as center-of-mass diffusion. Using neutron scattering
we demonstrate that the competition between the relaxation processes associated
with these two degrees of freedom results in strong dependence of dynamics and
structure on colloid concentration, c, even well below the overlap
concentration c*. We show that concurrent with increasing inter-particle
collisions, substantial structural dehydration and slowing-down of internal
dynamics occur before geometrically defined colloidal overlap develops. While
previous experiments have shown that the average size of soft colloids changes
very little below c*, we find a marked change in both the internal structure
and internal dynamics with concentration. The competition between these two
relaxation processes gives rise to a new dynamically-defined dilute threshold
concentration well below c*.


  This paper is focused on the double-grid integration with
interpolation-projection (DoGIP), which is a novel matrix-free discretisation
method of variational formulations introduced for Fourier--Galerkin
approximation. Here, it is described as a more general approach with an
application to the finite element method (FEM) on simplexes. The approach is
based on treating the trial and a test function in variational formulation
together, which leads to the decomposition of a linear system into
interpolation and (block) diagonal matrices. It usually leads to reduced memory
demands, especially for higher-order basis functions, but with higher
computational requirements. The numerical examples are studied here for two
variational formulations: weighted projection and scalar elliptic problem
modelling, e.g. diffusion or stationary heat transfer. This paper also opens a
room for further investigation, which is discussed in the conclusion.


  Eight percent of global carbon dioxide emissions can be attributed to the
production of cement, the main component of concrete, which is also the
dominant source of CO2 emissions in the construction of data centers. The
discovery of lower-carbon concrete formulae is therefore of high significance
for sustainability. However, experimenting with new concrete formulae is time
consuming and labor intensive, as one usually has to wait to record the
concrete's 28-day compressive strength, a quantity whose measurement can by its
definition not be accelerated. This provides an opportunity for experimental
design methodology like Bayesian Optimization (BO) to accelerate the search for
strong and sustainable concrete formulae. Herein, we 1) propose modeling steps
that make concrete strength amenable to be predicted accurately by a Gaussian
process model with relatively few measurements, 2) formulate the search for
sustainable concrete as a multi-objective optimization problem, and 3) leverage
the proposed model to carry out multi-objective BO with real-world strength
measurements of the algorithmically proposed mixes. Our experimental results
show improved trade-offs between the mixtures' global warming potential (GWP)
and their associated compressive strengths, compared to mixes based on current
industry practices. Our methods are open-sourced at
github.com/facebookresearch/SustainableConcrete.


  The formation of a planar hydraulic jump has been analysed in the framework
of a full depth-averaged thin film model (DAM) with surface tension effects
included. We have demonstrated regular weak solutions of the full DAM and
analysed surface tension effects. It has been shown that surface tension
effects within the parameter range relevant to the recent experiments are
expected to be very weak and practically negligible. The developed methodology
can be used in the analysis of laminar flow regimes and as a benchmark in
developing full scale hydrodynamic models.


  We address the problem of designing micro-fluidic chips for sample
preparation, which is a crucial step in many experimental processes in chemical
and biological sciences. One of the objectives of sample preparation is to
dilute the sample fluid, called reactant, using another fluid called buffer, to
produce desired volumes of fluid with prespecified reactant concentrations. In
the model we adopt, these fluids are manipulated in discrete volumes called
droplets. The dilution process is represented by a mixing graph whose nodes
represent 1-1 micro-mixers and edges represent channels for transporting
fluids. In this work we focus on designing such mixing graphs when the given
sample (also referred to as the target) consists of a single-droplet, and the
objective is to minimize total fluid waste. Our main contribution is an
efficient algorithm called RPRIS that guarantees a better provable worst-case
bound on waste and significantly outperforms state-of-the-art algorithms in
experimental comparison.


  We present a simultaneous Chandra and XMM-Newton observation of the Castor
sextett, focusing on Castor A and Castor B, two spectroscopic binaries with
early-type primaries. Of the present day X-ray instruments only Chandra can
isolate the X-ray lightcurves and spectra of A and B. We compare the Chandra
observation with XMM-Newton data obtained simultaneously. Albeit not able to
resolve Castor A and Castor B from each other, the higher sensitivity of
XMM-Newton allows for a quantitative analysis of their combined high-resolution
spectrum. He-like line triplets are used to examine the temperature and the
density in the corona of Castor AB. The temporal variability of Castor AB is
studied using data collected with the European Photon Imaging Camera onboard
XMM-Newton. Strong flare activity is observed, and combining the data acquired
simultaneously with Chandra and XMM-Newton each flare can be assigned to its
host. Our comparison with the conditions of the coronal plasma of other stars
shows that Castor AB behave like typical late-type coronal X-ray emitters
supporting the common notion that the late-type secondaries within each
spectroscopic binary are the sites of the X-ray production.


  Within the Euclidean effective action approach we propose criteria for the
ground state of QCD. Despite a nonvanishing field strength the ground state
should be invariant with respect to modified Poincar\'e transformations
consisting of a combination of translations and rotations with suitable gauge
transformations. We have found candidate states for QCD with four or more
colours. The formation of gluon condensates shows similarities with the Higgs
phenomenon.


  The combination of the many-body Green's function $GW$ approximation and the
Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative
to time-dependent density-functional theory (TD-DFT) for computing vertical
transition energies and oscillator strengths in molecular systems. The BSE
formalism can also be employed to compute ground-state correlation energies
thanks to the adiabatic-connection fluctuation-dissipation theorem (ACFDT).
Here, we study the topology of the ground-state potential energy surfaces (PES)
of several diatomic molecules near their equilibrium bond length. Thanks to
comparisons with state-of-art computational approaches (CC3), we show that
ACFDT@BSE is surprisingly accurate, and can even compete with lower-order
coupled cluster methods (CC2 and CCSD) in terms of total energies and
equilibrium bond distances for the considered systems. However, we sometimes
observe unphysical irregularities on the ground-state PES in relation with
difficulties in the identification of a few $GW$ quasiparticle energies.


  Graphene is a 2-dimensional material with high carrier mobility and thermal
conductivity, suitable for high-speed electronics. Conduction and valence bands
touch at the Dirac point. The absorptivity of single-layer graphene is 2.3%,
nearly independent of wavelength. Here we investigate the thermal radiation
from biased graphene transistors. We find that the emission spectrum of
single-layer graphene follows that of a grey body with constant emissivity (1.6
\pm 0.8)%. Most importantly, we can extract the temperature distribution in the
ambipolar graphene channel, as confirmed by Stokes/anti-Stokes measurements.
The biased graphene exhibits a temperature maximum whose location can be
controlled by the gate voltage. We show that this peak in temperature reveals
the spatial location of the minimum in carrier density, i.e. the Dirac point.


  The class of Sturm-Liouville operators on the space of square integrable
functions on a finite interval is considered. According to the Riesz-spectral
property, the self-adjointness and the positivity of such unbounded linear
operators on that space, a class of Hilbert spaces constructed as the domains
of the positive (in particular, fractional) powers of any Sturm-Liouville
operator is considered. On these spaces, it is shown that any Sturm-Liouville
operator is a Riesz-spectral operator that possesses the same eigenvalues as
the original ones, associated to rescaled eigenfunctions. This constitutes the
first central result of this paper. Properties related to the C_0-semigroup
generated by the opposite of such Riesz-spectral operator are also highlighted.
In addition as second central result, a characterization of approximate
observability by means of point measurement operators is established for such
systems. The main results are applied on a diffusion-convection-reaction system
in order notably to show that the dynamics operator is the infinitesimal
generator of a compact C_0-semigroup on some Sobolev space of integer order,
and to establish its observability.


  The mechanical unfolding of a simple RNA hairpin and of a 236--bases portion
of the Tetrahymena thermophila ribozyme is studied by means of an Ising--like
model. Phase diagrams and free energy landscapes are computed exactly and
suggest a simple two--state behaviour for the hairpin and the presence of
intermediate states for the ribozyme. Nonequilibrium simulations give the
possible unfolding pathways for the ribozyme, and the dominant pathway
corresponds to the experimentally observed one.


  Manipulating valley-dependent Berry phase effects provides remarkable
opportunities for both fundamental research and practical applications. Here,
by referring to effective model analysis, we propose a general scheme for
realizing topological magneto-valley phase transitions. More importantly, by
using valley-half-semiconducting VSi2N4 as an outstanding example, we
investigate sign change of valley-dependent Berry phase effects which drive the
change-in-sign valley anomalous transport characteristics via external means
such as biaxial strain, electric field, and correlation effects. As a result,
this gives rise to quantized versions of valley anomalous transport phenomena.
Our findings not only uncover a general framework to control valley degree of
freedom, but also motivate further research in the direction of multifunctional
quantum devices in valleytronics and spintronics.


  Rich information on the prebiotic evolution is still stored in contemporary
genomic data. The statistical mechanism at the sequence level may play a
significant role in the prebiotic evolution. Based on statistical analysis of
genome sequences, it has been observed that there is a close relationship
between the evolution of the genetic code and the organisation of genomes. A
biodiversity space for species is constructed based on comparing the
distributions of codons in genomes for different species according to
recruitment order of codons in the prebiotic evolution, by which a closely
relationship between the evolution of the genetic code and the tree of life has
been confirmed. On one hand, the three domain tree of life can be reconstructed
according to the distance matrix of species in this biodiversity space, which
supports the three-domain tree rather than the eocyte tree. On the other hand,
an evolutionary tree of codons can be obtained by comparing the distributions
of the 64 codons in genomes, which agrees with the recruitment order of codons
on the roadmap. This is a simple phylogenomic method to study the origins of
metazoan, the evolution of primates, etc. This study should be regarded as an
exploratory attempt to explain the diversification of the three domains of life
by statistical mechanism in prebiotic sequence evolution. It is indicated that
the number of bases in the triplet codons might be explained statistically by
the number of strands in the triplex DNAs. The adaptation of life to the
changing environment might be due to assembly of redundant genomes at the
sequence level.


  Time crystals are an eagerly sought phase of matter with broken
time-translation symmetry. Quantum time crystals with discretely broken
time-translation symmetry have been demonstrated in trapped ions, atoms and
spins while continuously broken time-translation symmetry has been observed in
an atomic condensate inside an optical cavity. Here we report that a classical
metamaterial nanostructure, a two-dimensional array of plasmonic metamolecules
supported on flexible nanowires, can be driven to a state possessing all of the
key features of a continuous time crystal: continuous coherent illumination by
light resonant with the metamolecules' plasmonic mode triggers a spontaneous
phase transition to a superradiant-like state of transmissivity oscillations,
resulting from many-body interactions among the metamolecules, characterized by
long-range order in space and time. The phenomenon is of interest to the study
of dynamic classical many-body states in the strongly correlated regime and
applications in all-optical modulation, frequency conversion and timing.


  We present minimum chi-squared fits of power law and Hernquist density
profiles to F-turnoff stars in eight 2.5 deg wide stripes of SDSS data: five in
the North Galactic Cap and three in the South Galactic cap. Portions of the
stellar Galactic halo that are known to contain large streams of tidal debris
or other lumpy structure, or that may include significant contamination from
the thick disk, are avoided. The data strongly favor a model that is not
symmetric about the Galaxy's axis of rotation. If included as a free parameter,
the best fit to the center of the spheroid is surprisingly approx 3 kpc from
the Galactic center in the direction of the Sun's motion. The model fits favor
a low value of the density of halo stars at the solar position. The alternative
to a non-axisymmetric stellar distribution is that our fits are contaminated by
previously unidentified lumpy substructure.


  In this paper, spindle starshaped sets are introduced and investigated, which
apart from normalization form an everywhere dense subfamily within the family
of starshaped sets. We focus on proving spindle starshaped analogues of recent
theorems of Bobylev, Breen, Toranzos, and Zamfirescu on starshaped sets.
Finally, we consider the problem of guarding treasures in an art gallery (in
the traditional linear way as well as via spindles).


  I. Introduction (Preface, Basic properties of semiconductor nanostructures).
  II. Theory of Coulomb-blockade oscillations (Periodicity of the oscillations,
Amplitude and lineshape).
  III. Experiments on Coulomb-blockade oscillations (Quantum dots, Disordered
quantum wires, Relation to earlier work on disordered quantum wires).
  IV. Quantum Hall effect regime (The Aharonov-Bohm effect in a quantum dot,
Coulomb blockade of the Aharonov-Bohm effect, Experiments on quantum dots,
Experiments on disordered quantum wires).


  Let $G$ be a definable group in a $p$-adically closed field $M$. We show that
$G$ has finitely satisfiable generics (fsg) if and only if $G$ is definably
compact. The case $M = \mathbb{Q}_p$ was previously proved by Onshuus and
Pillay.


  This paper descibes a new method for deriving incidence rates of a chronic
disease from prevalence data. It is based on a new ordinary differential
equation, which relates the change in the age-specific prevalence to the
agespecific incidence and mortality rates. The method allows the extraction of
longtudinal information from cross-sectional studies. Applicability of the
method is tested in the prevalence of dementia in Germany. The derived
age-specific incidence is in good agreement with published values.


  We present recent advances in theoretical studies of the formation and
evolution of dust in primordial supernovae (SNe) that are considered to be the
main sources of dust in the early universe. Being combined with the results of
calculations of dust formation in the ejecta of Population III SNe, the
investigations of the evolution of newly formed dust within supernova remnants
(SNRs) show that smaller grains are predominantly destroyed by sputtering in
the shocked gas, while larger grains are injected into the ambient medium. The
mass of dust grains surviving the destruction in SNRs reaches up to 0.1--15
$M_\odot$, which is high enough to account for the content of dust observed for
the host galaxies of quasars at $z > 5$. In addition, the transport of dust
formed in the ejecta causes the formation of low-mass stars in the dense shell
of primordial SNRs and affects the elemental composition of those stars. We
also show that the flat extinction curve is expected in the high-redshift
universe where SNe are the possible sources of dust.


  Learning on Graphs has attracted immense attention due to its wide real-world
applications. The most popular pipeline for learning on graphs with textual
node attributes primarily relies on Graph Neural Networks (GNNs), and utilizes
shallow text embedding as initial node representations, which has limitations
in general knowledge and profound semantic understanding. In recent years,
Large Language Models (LLMs) have been proven to possess extensive common
knowledge and powerful semantic comprehension abilities that have
revolutionized existing workflows to handle text data. In this paper, we aim to
explore the potential of LLMs in graph machine learning, especially the node
classification task, and investigate two possible pipelines: LLMs-as-Enhancers
and LLMs-as-Predictors. The former leverages LLMs to enhance nodes' text
attributes with their massive knowledge and then generate predictions through
GNNs. The latter attempts to directly employ LLMs as standalone predictors. We
conduct comprehensive and systematical studies on these two pipelines under
various settings. From comprehensive empirical results, we make original
observations and find new insights that open new possibilities and suggest
promising directions to leverage LLMs for learning on graphs. Our codes and
datasets are available at https://github.com/CurryTang/Graph-LLM.


  We present an algorithm for constructing an optimal slate of sponsored search
advertisements which respects the ordering that is the outcome of a generalized
second price auction, but which must also accommodate complicating factors such
as overall budget constraints. The algorithm is easily fast enough to use on
the fly for typical problem sizes, or as a subroutine in an overall
optimization.


  This is a note for the conference proceedings Topological and Geometrical
Problems related to Quantum Field Theory. We summarize our joint work with Dai
about eta invariants on manifolds with boundary. Then we apply these results to
prove the curvature and holonomy formulas for the natural connection on the
determinant line bundle of a family of Dirac operators. These were originally
proved by Bismut and the author--the proofs here are much simpler.


  We prove that, for every compact Kaehler manifold, the period map of its
Kuranishi family is induced by a natural L-infinity morphism. This implies, by
standard facts about L-infinity algebras, that the period map is a "morphism of
deformation theories" and then commutes with all deformation theoretic
constructions (e.g. obstructions).


  The spatial search problem aims to find a marked vertex of a finite graph
using a dynamic with two constraints: (1) The walker has no compass and (2) the
walker can check whether a vertex is marked only after reaching it. This
problem is a generalization of unsorted database search and has many
applications to algorithms. Classical algorithms that solve the spatial search
problem are based on random walks and the computational complexity is
determined by the hitting time. On the other hand, quantum algorithms are based
on quantum walks and the computational complexity is determined not only by the
number of steps to reach a marked vertex, but also by the success probability,
since we need to perform a measurement at the end of the algorithm to determine
the walker's position. In this work, we address the spatial search problem on
Johnson graphs using the coined quantum walk model. Since Johnson graphs are
vertex- and distance-transitive, we have found an invariant subspace of the
Hilbert space, which aids in the calculation of the computational complexity.
We have shown that, for every fixed diameter, the asymptotic success
probability is $1/2$ after taking $\pi\sqrt N/(2\sqrt 2)$ steps, where $N$ is
the number of vertices of the Johnson graph.


  We prove that the number gamma(N) of the zeros of a two-parameter simple
random walk in its first N-by-N time steps is almost surely equal to N to the
power 1+o(1) as N goes to infinity. This is in contrast with our earlier joint
effort with Z. Shi [4]; that work shows that the number of zero crossings in
the first N-by-N time steps is N to the power (3/2)+o(1) as N goes to infinity.
We prove also that the number of zeros on the diagonal in the first N time
steps is (c+o(1)) log N as N goes to infinity, where c is 2\pi.


  Motivated by the recent development of fast and ultra-sensitive thermometry
in nanoscale systems, we investigate quantum calorimetric detection of
individual heat pulses in the sub-meV energy range. We propose a hybrid
superconducting injector-calorimeter set-up, with the energy of injected pulses
carried by tunneling electrons. Treating all heat transfer events
microscopically, we analyse the statistics of the calorimeter temperature
fluctuations and derive conditions for an accurate measurement of the heat
pulse energies. Our results pave the way for novel, fundamental quantum
thermodynamics experiments, including calorimetric detection of single
microwave photons.


  Accurate and reliable estimation of generator's dynamic state vectors in real
time are critical to the monitoring and control of power systems. A robust
Cubature Kalman Filter (RCKF) based approach is proposed for dynamic state
estimation (DSE) of generators under cyber attacks in this paper. First, two
types of cyber attacks, namely false data injection and denial of service
attacks, are modelled and thereby introduced into DSE of a generator by mixing
the attack vectors with the measurement data; Second, under cyber attacks with
different degrees of sophistication, the RCKF algorithm and the Cubature Kalman
Filter (CKF) algorithm are adopted to the DSE, and then the two algorithms are
compared and discussed. The novelty of this study lies primarily in our attempt
to introduce cyber attacks into DSE of generators. The simulation results on
the IEEE 9-bus system and the New England 16-machine 68-bus system verify the
effectiveness and superiority of the RCKF.


  We study a model of vector dark matter with the complex scalar Higgs portal.
Renormalisation group equations at the 2-loop level are used to analyse
perturbativity and stability of the vacuum. We impose experimental and
theoretical constraints on the model and find regions in the parameter space
consistent with the dark matter relic abundance inferred from the Planck data
and bounds on DM-nucleon scattering cross-section from XENON and LUX
experiments.


  We have used the Scheutjens-Fleer self-consistent field (SF-SCF) method to
predict the self-assembly of triblock copolymers with a solvophilic middle
block and sufficiently long solvophobic outer blocks. We model copolymers
consisting of polyethylene oxide (PEO) as solvophilic block and
poly(lactic-co-glycolic) acid (PLGA) or poly({\ko}-caprolactone) (PCL) as
solvophobic block. These copolymers form structurally quenched spherical
micelles provided the solvophilic block is long enough. Predictions are
calibrated on experimental data for micelles composed of PCL-PEO-PCL and
PLGA-PEO-PLGA triblock copolymers prepared via the nanoprecipitation method. We
establish effective interaction parameters that enable us to predict various
micelle properties such as the hydrodynamic size, the aggregation number and
the loading capacity of the micelles for hydrophobic species that are
consistent with experimental finding.


  The classical-dS scenario in the type II string theories proposes to search
for dS vacua of orientifold flux compactifications in a regime where string
corrections to the compactified effective field theory are negligible. We study
a minimal extension of this scenario in which the leading string corrections to
the O-plane/D-brane actions at the 4-derivative order are included but higher
orders as well as string corrections in the bulk are self-consistently
neglected. Our proposal is motivated by a recent debate about dS solutions with
O8-planes which circumvent a classical no-go theorem due to unusual sources
leading to so-called permissive boundary conditions for the 10D supergravity
fields. We argue that such sources do not arise in classical supergravity but
ask whether including the 4-derivative corrections leads to sources that have a
similar effect. However, we find that the 4-derivative corrections do not allow
meta-stable dS in a class of models with O8-planes and/or D8-branes we
consider. We also study related models which in addition contain
O6-planes/D6-branes and find that again no meta-stable dS is allowed, both
classically and including the 4-derivative corrections. While some of the
arguments in this work require the backreaction of the O-plane/D-brane sources
to be small, others are valid including the full backreaction.


  Multiclass logistic regression is a fundamental task in machine learning with
applications in classification and boosting. Previous work (Foster et al.,
2018) has highlighted the importance of improper predictors for achieving "fast
rates" in the online multiclass logistic regression problem without suffering
exponentially from secondary problem parameters, such as the norm of the
predictors in the comparison class. While Foster et al. (2018) introduced a
statistically optimal algorithm, it is in practice computationally intractable
due to its run-time complexity being a large polynomial in the time horizon and
dimension of input feature vectors. In this paper, we develop a new algorithm,
FOLKLORE, for the problem which runs significantly faster than the algorithm of
Foster et al.(2018) -- the running time per iteration scales quadratically in
the dimension -- at the cost of a linear dependence on the norm of the
predictors in the regret bound. This yields the first practical algorithm for
online multiclass logistic regression, resolving an open problem of Foster et
al.(2018). Furthermore, we show that our algorithm can be applied to online
bandit multiclass prediction and online multiclass boosting, yielding more
practical algorithms for both problems compared to the ones in Foster et
al.(2018) with similar performance guarantees. Finally, we also provide an
online-to-batch conversion result for our algorithm.


  In Cardaliaguet-Ley (2006) we have defined a viscosity solution for the
gradient flow of the exterior Bernoulli free boundary problem. We prove here
that the associated energy is non decreasing along the flow. This justifies the
"gradient flow" approach for such kind of problem. The proof relies on the
construction of a discrete gradient flow in the flavour of Almgren-Taylor-Wang
(1993) and on proving it converges to the viscosity solution.


  In our previous work, we have defined a nonlinear connection of Finsler
manifold which preserves the Finsler metric $L=L(x,dx)$. To make the method
easier and more useful in applications, moving frame (vielbein)
$\theta^a={e^a}_\mu dx^\mu$ formalism for the nonlinear connection is newly
considered. We derive formulae to calculate the Finsler connection in the
specific case that the Finsler metric depends not on coordinates $x^\mu$, but
only on moving frame $\theta^a$: $L=L(\theta)$.


  A $2$-semiarc is a pointset ${\mathcal S}_k$ with the property that the
number of tangent lines to ${\mathcal S}_k$ at each of its points is two. Using
some theoretical results and computer aided search, the complete classification
of $2$-semiarcs in PG$(2,q)$ is given for $q\leq 7,$ the spectrum of their
sizes is determined for $q\leq 9$, and some results about the existence are
proven for $q=11$ and $q=13.$ For several sizes of $2$-semiarcs in
$\mathrm{PG}(2,q)$, $q\leq 7$, classification results have been obtained by
theoretical proofs.


  Deep learning-based fault diagnosis (FD) approaches require a large amount of
training data, which are difficult to obtain since they are located across
different entities. Federated learning (FL) enables multiple clients to
collaboratively train a shared model with data privacy guaranteed. However, the
domain discrepancy and data scarcity problems among clients deteriorate the
performance of the global FL model. To tackle these issues, we propose a novel
framework called representation encoding-based federated meta-learning (REFML)
for few-shot FD. First, a novel training strategy based on representation
encoding and meta-learning is developed. It harnesses the inherent
heterogeneity among training clients, effectively transforming it into an
advantage for out-of-distribution generalization on unseen working conditions
or equipment types. Additionally, an adaptive interpolation method that
calculates the optimal combination of local and global models as the
initialization of local training is proposed. This helps to further utilize
local information to mitigate the negative effects of domain discrepancy. As a
result, high diagnostic accuracy can be achieved on unseen working conditions
or equipment types with limited training data. Compared with the
state-of-the-art methods, such as FedProx, the proposed REFML framework
achieves an increase in accuracy by 2.17%-6.50% when tested on unseen working
conditions of the same equipment type and 13.44%-18.33% when tested on totally
unseen equipment types, respectively.


  Tunka-Rex is a $3\,$km$^2$ large antenna array for cosmic-ray air showers at
the TAIGA observatory in Siberia close to Lake Baikal. In autumn 2016 Tunka-Rex
has been extended to a total of 63 stations, each equipped with SALLA antennas
for two polarization directions operating in the band of $30-80\,$MHz. All
antenna stations are triggered by the other cosmic-ray detectors at the site,
i.e., Tunka-Rex runs in coincidence with the Tunka-Grande array of
scintillation detectors and during clear nights additionally in coincidence
with the Tunka-133 non-imaging air-Cherenkov array. Compared to previous
measurements, the day-time and bad-weather trigger increases the annual
exposure by an order of magnitude, and the higher density of antennas is
expected to increase the accuracy - in particular for the cosmic-ray mass
composition. In addition to the status and potential of Tunka-Rex an overview
of recently published results will be presented: by comparing the radio and the
air-Cherenkov signals of the same air showers, the Tunka-Rex precision for the
most important shower parameters has been determined. The direction precision
is about $1^\circ$, the precision for the depth of the shower maximum,
$X_\mathrm{max}$, is better than $40\,$g/cm$^2$ for high-quality events, and
the energy precision is better than $15\,\%$. A rough estimation of the shower
energy and of $X_\mathrm{max}$ is even possible with only a single antenna
station when using the shower geometry measured by Tunka-133. Moreover, by
using exactly the same external calibration source for the antennas as at the
LOPES experiment we have shown that the absolute energy scale of different
air-shower arrays can be compared with each other at $10\,\%$ precision. Thus,
Tunka-Rex will improve the total accuracy of TAIGA for the energy as well as
for the mass composition of cosmic rays of energy above $0.1\,$EeV.


  The smart kinetic self-avoiding walk (SKSAW) is a random walk which never
intersects itself and grows forever when run in the full-plane. At each time
step the walk chooses the next step uniformly from among the allowable nearest
neighbors of the current endpoint of the walk. In the full-plane a nearest
neighbor is allowable if it has not been visited before and there is a path
from the nearest neighbor to infinity through sites that have not been visited
before. It is well known that on the hexagonal lattice the SKSAW in a bounded
domain between two boundary points is equivalent to an interface in critical
percolation, and hence its scaling limit is the chordal Schramm-Loewner
evolution with kappa=6 (SLE_6). Like SLE there are variants of the SKSAW
depending on the domain and the initial and terminal points. On the hexagonal
lattice these variants have been shown to converge to the corresponding version
of SLE_6. We conjecture that the scaling limit of all these variants on any
regular lattice is the corresponding version of SLE_6. We test this conjecture
for the square lattice by simulating the SKSAW in the full-plane and find
excellent agreement with the predictions of full-plane SLE_6.


  Inspired by the classical theory of modules over a monoid, we give a first
account of the natural notion of module over a monad. The associated notion of
morphism of left modules ("Linear" natural transformations) captures an
important property of compatibility with substitution, in the heterogeneous
case where "terms" and variables therein could be of different types as well as
in the homogeneous case. In this paper, we present basic constructions of
modules and we show examples concerning in particular abstract syntax and
lambda-calculus.


  Following previous works about integro-differential equations of parabolic
type modelling the Darwinian evolution of a population, we study a
two-population system in the cooperative case. First, we provide a theoretical
study of the limit of rare mutations and we prove that the limit is described
by a constrained Hamilton-Jacobi equation. This equation is given by an
eigenvalue of a matrix which accounts for the diffusion parameters and the
coefficients of the system. Then, we focus on a particular application: the
understanding of a phenomenon called Adaptation to DNA damage. In this
framework, we provide several numerical simulations to illustrate our
theoretical results and investigate mathematical and biological questions.


  We investigate the effects of nonlinear couplings and external magnetic field
on the thermal entanglement in a two-spin-qutrit system by applying the concept
of negativity. It is found that the nonlinear couplings favor the thermal
entanglement creating. Only when the nonlinear couplings $|K|$ are larger than
a certain critical value does the entanglement exist. The dependence of the
thermal entanglement in this system on the magnetic field and temperature is
also presented. The critical magnetic field increases with the increasing
nonlinear couplings constant $|K|$. And for a fixed nonlinear couplings
constant, the critical temperature is independent of the magnetic field $B$.


  We consider a nanoelectromechanical system composed of a carbon nanotube
suspended between two normal leads and coupled to a superconducting scanning
tunneling microscope (STM) tip via vacuum tunnel barrier. Treating the nanotube
as a single-level quantum dot, it is shown that an applied voltage between the
superconducting STM tip and normal leads gives rise to a pumping or a cooling
of the mechanical subsystem depending on the direction of the electronic flow.
It is also demonstrated that the transition between these two regimes is
controlled by the strength of the tunnel coupling between the nanotube and
superconducting STM tip and the relative position of the electronic level. Such
phenomena are realized due to a specific electromechanical coupling that is
fully governed by the quantum dynamics of the Cooper pairs. The amplitude of
the self-sustained oscillations in the pumping regime is analyzed numerically,
and the effective temperature of the mechanical subsystem in the cooling regime
is obtained.


  The formation of brown dwarfs (BDs) poses a key challenge to star formation
theory. The observed dearth of nearby ($\leq 5$ AU) brown dwarf companions to
solar-mass stars, known as the brown dwarf desert, as well as the tendency for
low-mass binary systems to be more tightly-bound than stellar binaries, have
been cited as evidence for distinct formation mechanisms for brown dwarfs and
stars. In this paper, we explore the implications of the minimal hypothesis
that brown dwarfs in binary systems originate via the same fundamental
fragmentation mechanism as stars, within isolated, turbulent giant molecular
cloud cores. We demonstrate analytically that the scaling of specific angular
momentum with turbulent core mass naturally gives rise to the brown dwarf
desert, as well as wide brown-dwarf binary systems. Further, we show that the
turbulent core fragmentation model also naturally predicts that very low-mass
(VLM) binary and BD/BD systems are more tightly-bound than stellar systems. In
addition, in order to capture the stochastic variation intrinsic to turbulence,
we generate $10^4$ model turbulent cores with synthetic turbulent velocity
fields to show that the turbulent fragmentation model accommodates a small
fraction of binary brown dwarfs with wide separations, similar to observations.
Indeed, the picture which emerges from the turbulent fragmentation model is
that a single fragmentation mechanism may largely shape both stellar and brown
dwarf binary distributions during formation.


  The problem of the phase transition of a Z(3) spin system is a complex issue.
A numerical simulation in the framework of the mean field theory using the
Metropolis algorithm reveals: (a) the existence of second order phase
transition with a degenerated critical point which could be considered as a
state of resonance (b) hysteresis phenomena which are accompanied with
tricritical crossover around the end point of first order transition. Based on
these results we propose a scenario about confinement-deconfinement phase
transition in SU(3) symmetry of color QCD which, as it is known, has the same
center with Z(3) spin system symmetry.


  We prove that each complete flat cone metric on a surface, perhaps with
boundary and punctures, can be triangulated with finitely many types of
triangles. We derive Gauss-Bonnet formula for this kind of cone metrics. In
addition, we prove that each free homotopy class of paths has a geodesic
representative.


  We consider skew ruled surfaces in the three-dimensional Euclidean space and
some geometrically distinguished families of curves on them whose normal
curvature has a concrete form. The aim of this paper is to find and classify
all ruled surfaces with the mentioned property.


  Purpose: We propose and evaluate a new structured low-rank method for EPI
ghost correction called Robust Autocalibrated LORAKS (RAC-LORAKS). The method
can be used to suppress EPI ghosts arising from the differences between
different readout gradient polarities and/or the differences between different
shots. It does not require conventional EPI navigator signals, and is robust to
imperfect autocalibration data.
  Methods: Autocalibrated LORAKS is a previous structured low-rank method for
EPI ghost correction that uses GRAPPA-type autocalibration data to enable
high-quality ghost correction. This method works well when the autocalibration
data is pristine, but performance degrades substantially when the
autocalibration information is imperfect. RAC-LORAKS generalizes Autocalibrated
LORAKS in two ways. First, it does not completely trust the information from
autocalibration data, and instead considers the autocalibration and EPI data
simultaneously when estimating low-rank matrix structure. And second, it uses
complementary information from the autocalibration data to improve EPI
reconstruction in a multi-contrast joint reconstruction framework. RAC-LORAKS
is evaluated using simulations and in vivo data, including comparisons to
state-of-the-art methods.
  Results: RAC-LORAKS is demonstrated to have good ghost elimination
performance compared to state-of-the-art methods in several complicated EPI
acquisition scenarios (including gradient-echo brain imaging, diffusion-encoded
brain imaging, and cardiac imaging).
  Conclusion: RAC-LORAKS provides effective suppression of EPI ghosts and is
robust to imperfect autocalibration data.


  Anomaly-based intrusion detection (AID) techniques are useful for detecting
novel intrusions into computing resources. One of the most successful AID
detectors proposed to date is stide, which is based on analysis of system call
sequences. In this paper, we present a detailed formal framework to analyze,
understand and improve the performance of stide and similar AID techniques.
Several important properties of stide-like detectors are established through
formal proofs, and validated by carefully conducted experiments using test
datasets. Finally, the framework is utilized to design two applications to
improve the cost and performance of stide-like detectors which are based on
sequence analysis. The first application reduces the cost of developing AID
detectors by identifying the critical sections in the training dataset, and the
second application identifies the intrusion context in the intrusive dataset,
that helps to fine-tune the detectors. Such fine-tuning in turn helps to
improve detection rate and reduce false alarm rate, thereby increasing the
effectiveness and efficiency of the intrusion detectors.


  For a given polygonal region $P$, the Lawn Mowing Problem (LMP) asks for a
shortest tour $T$ that gets within Euclidean distance 1/2 of every point in
$P$; this is equivalent to computing a shortest tour for a unit-diameter cutter
$C$ that covers all of $P$. As a generalization of the Traveling Salesman
Problem, the LMP is NP-hard; unlike the discrete TSP, however, the LMP has
defied efforts to achieve exact solutions, due to its combination of
combinatorial complexity with continuous geometry.
  We provide a number of new contributions that provide insights into the
involved difficulties, as well as positive results that enable both theoretical
and practical progress. (1) We show that the LMP is algebraically hard: it is
not solvable by radicals over the field of rationals, even for the simple case
in which $P$ is a $2\times 2$ square. This implies that it is impossible to
compute exact optimal solutions under models of computation that rely on
elementary arithmetic operations and the extraction of $k$th roots, and
explains the perceived practical difficulty. (2) We exploit this algebraic
analysis for the natural class of polygons with axis-parallel edges and integer
vertices (i.e., polyominoes), highlighting the relevance of turn-cost
minimization for Lawn Mowing tours, and leading to a general construction
method for feasible tours. (3) We show that this construction method achieves
theoretical worst-case guarantees that improve previous approximation factors
for polyominoes. (4) We demonstrate the practical usefulness \emph{beyond
polyominoes} by performing an extensive practical study on a spectrum of more
general benchmark polygons: We obtain solutions that are better than the
previous best values by Fekete et al., for instance sizes up to $20$ times
larger.


  We have demonstrated, both theoretically and experimentally, that it is
possible to control (i.e., to enhance or cancel) the contrast of the
interference pattern appearing in the intensity images obtained with a laser
optical feedback imaging (LOFI) setup using a bimode laser. The laser is
composed of two coupled orthogonally polarized states that interact (i.e.,
interfere) through the cross saturation laser dynamics. We created the contrast
control by choosing the frequency shift (i.e., the beating frequency) between
the feedback electric fields and the intracavity electric fields. We have shown
that the interference contrast of the output power modulation of the laser
total intensity is independent from the frequency shift and is always maximal.
On the other hand, the interference contrast of each polarization state is
frequency dependent. We obtained the maximal contrast when the frequency shift
was equal to one of the resonance frequencies of the bimode dynamics, and was
very low (and almost cancels) for an intermediate frequency located at the
intersection of the two resonance curves.


  Influenced by ChatGPT, artificial intelligence (AI) large models have
witnessed a global upsurge in large model research and development. As people
enjoy the convenience by this AI large model, more and more large models in
subdivided fields are gradually being proposed, especially large models in
radiology imaging field. This article first introduces the development history
of large models, technical details, workflow, working principles of multimodal
large models and working principles of video generation large models. Secondly,
we summarize the latest research progress of AI large models in radiology
education, radiology report generation, applications of unimodal and multimodal
radiology. Finally, this paper also summarizes some of the challenges of large
AI models in radiology, with the aim of better promoting the rapid revolution
in the field of radiography.


  We introduce a new concept of interval rearrangement ensembles (IRE), which
is a generalization of interval exchange transformations (IET). This
construction expands the space of IETs in accordance with the natural duality
that we pinpoint. Induction of Rauzy\,--\,Veech kind is applicable to IREs. It
is conjugate to the reverse operation by the duality mentioned above. A natural
extension of an IRE is associated with two transversal flows on a flat
translation surface with branching points.


  In this communication, we describe some interrelations between generalized
$q$-entropies and a generalized version of Fisher information. In information
theory, the de Bruijn identity links the Fisher information and the derivative
of the entropy. We show that this identity can be extended to generalized
versions of entropy and Fisher information. More precisely, a generalized
Fisher information naturally pops up in the expression of the derivative of the
Tsallis entropy. This generalized Fisher information also appears as a special
case of a generalized Fisher information for estimation problems. Indeed, we
derive here a new Cram\'er-Rao inequality for the estimation of a parameter,
which involves a generalized form of Fisher information. This generalized
Fisher information reduces to the standard Fisher information as a particular
case. In the case of a translation parameter, the general Cram\'er-Rao
inequality leads to an inequality for distributions which is saturated by
generalized $q$-Gaussian distributions. These generalized $q$-Gaussians are
important in several areas of physics and mathematics. They are known to
maximize the $q$-entropies subject to a moment constraint. The Cram\'er-Rao
inequality shows that the generalized $q$-Gaussians also minimize the
generalized Fisher information among distributions with a fixed moment.
Similarly, the generalized $q$-Gaussians also minimize the generalized Fisher
information among distributions with a given $q$-entropy.


  In this paper, we contribute operator-splitting methods improved by the
Zassenhaus product for the numerical solution of linear partial differential
equations. We address iterative splitting methods, that can be improved by
means of the Zassenhaus product formula, which is a sequnential splitting
scheme. The coupling of iterative and sequential splitting techniques are
discussed and can be combined with respect to their compuational time. While
the iterative splitting schemes are cheap to compute, the Zassenhaus product
formula is more expensive, based on the commutators but achieves higher order
accuracy. Iterative splitting schemes and also Zassenhaus products are applied
in physics and physical chemistry are important and are predestinated to their
combinations of each benefits. Here we consider phase models in CFD
(computational fluid dynamics). We present an underlying analysis for obtaining
higher order operator-splitting methods based on the Zassenhaus product.
  Computational benefits are given with sparse matrices, which arose of spatial
discretization of the underlying partial differential equations. While
Zassenhaus formula allows higher accuracy, due to the fact that we obtain
higher order commutators, we combine such an improved initialization process to
cheap computable to linear convergent iterative splitting schemes.
  Theoretical discussion about convergence and application examples are
discussed with CFD problems.


  The outer crust of a cold nonaccreting neutron star has been generally
assumed to be stratified into different layers, each of which consists of a
pure body-centered cubic ionic crystal in a charge compensating background of
highly degenerate electrons. The validity of this assumption is examined by
analyzing the stability of multinary ionic compounds in dense stellar matter.
It is thus shown that their stability against phase separation is uniquely
determined by their structure and their composition irrespective of the stellar
conditions. However, equilibrium with respect to weak and strong nuclear
processes imposes very stringent constraints on the composition of multinary
compounds, and thereby on their formation. By examining different cubic and
noncubic lattices, it is found that substitutional compounds having the same
structure as cesium chloride are the most likely to exist in the outer crust of
a nonaccreting neutron star. The presence of ternary compounds is also
investigated. Very accurate analytical expressions are obtained for the
threshold pressure, as well as for the densities of the different phases
irrespective of the degree of relativity of the electron gas. Finally,
numerical calculations of the ground-state structure and of the equation of
state of the outer crust of a cold nonaccreting neutron star are carried out
using recent experimental and microscopic nuclear mass tables.


  Investigating the extinction properties in dense molecular clouds is of
significant importance for understanding the behavior of interstellar dust and
its impact on observations. In this study, we comprehensively examined the
extinction law in the Ophiuchus cloud across a wavelength range from
0.8$\,\mu\rm m$ to 8$\,\mu\rm m$. To achieve this, we analyzed NIR and MIR data
obtained from the UKIDSS GCS and the Spitzer c2d survey, respectively. By
fitting a series of color-color diagrams, we determined color-excess ratios
$E_{J-\lambda}/E_{J-K}$ for seven passbands. These ratios were then directly
converted to derive the relative extinction law $A_\lambda/A_K$. Our findings
demonstrate that the Ophiuchus cloud exhibits a characteristic of flat MIR
extinction, consistent with previous studies. Additionally, our results reveal
variations in the extinction law with extinction depth, indicating a flatter
trend from the NIR to MIR bands as extinction increases. Notably, our analysis
reveals no significant difference in the MIR extinction law among the four dark
clouds: L1712, L1689, L1709, and L1688. However, distinct variations were
observed in the extinction law for regions outside the dark clouds,
specifically L1688N and L1688W. These regions displayed lower color-excess
ratios $E_{J-\lambda}/E_{J-K}$ in the Spitzer/IRAC bands. This observation
lends support to the dust growth occurring in the dense regions of the
Ophiuchus cloud.


  The orbital angular momentum (OAM) spatial degree of freedom of light has
been widely explored in many applications, including telecommunications,
quantum information and light-based micro-manipulation. The ability to separate
and distinguish between the different transverse spatial modes is called mode
sorting or mode demultiplexing, and it is essential to recover the encoded
information in such applications. An ideal $d$ mode sorter should be able to
faithfully distinguish between the different $d$ spatial modes, with minimal
losses, have $d$ outputs, and have fast response times. All previous mode
sorters rely on bulk optical elements such as spatial light modulators, which
cannot be quickly tuned and have additional losses if they are to be integrated
with optical fiber systems. Here we propose and experimentally demonstrate, to
the best of our knowledge, the first all-in-fiber method for OAM mode sorting
with ultra-fast dynamic reconfigurability. Our scheme first decomposes the OAM
mode in fiber-optical linearly polarized (LP) modes, and then
interferometrically recombines them to determine the topological charge, thus
correctly sorting the OAM mode. In addition, our setup can also be used to
perform ultra-fast routing of the OAM modes. These results show a novel and
fiber integrated form of optical spatial mode sorting that can be readily used
for many new applications in classical and quantum information processing.


  The problem of a relativistic bound-state system consisting of two scalar
bosons interacting through the exchange of another scalar boson, in 2+1
space-time dimensions, has been studied. The Bethe-Salpeter equation (BSE) was
solved by adopting the Nakanishi integral representation (NIR) and the
Light-Front projection. The NIR allows us to solve the BSE in Minkowski space,
which is a big and important challenge, since most of non-perturbative
calculations are done in Euclidean space, e.g. Lattice and Schwinger-Dyson
calculations. We have in this work adopted an interaction kernel containing the
ladder and cross-ladder exchanges. In order to check that the NIR is also a
good representation in 2+1, the coupling constants and Wick-rotated amplitudes
have been computed and compared with calculations performed in Euclidean space.
Very good agreement between the calculations performed in the Minkowski and
Euclidean spaces has been found. This is an important consistence test that
allows Minkowski calculations with the Nakanishi representation in 2+1
dimensions. This relativistic approach will allow us to perform applications in
condensed matter problems in a near future.


  In this paper, we are concerned with the global Cauchy problem for the
semilinear generalized Tricomi equation $\partial_t^2 u-t^m \Delta u=|u|^p$
with initial data $(u(0,\cdot), \partial_t u(0,\cdot))= (u_0, u_1)$, where
$t\geq 0$, $x\in{\mathbb R}^n$ ($n\ge 3$), $m\in\mathbb N$, $p>1$, and $u_i\in
C_0^{\infty}({\mathbb R}^n)$ ($i=0,1$). We show that there exists a critical
exponent $p_{\text{crit}}(m,n)>1$ such that the solution $u$, in general, blows
up in finite time when $1<p<p_{\text{crit}}(m,n)$. We further show that there
exists a conformal exponent $p_{\text{conf}}(m,n)> p_{\text{crit}}(m,n)$ such
that the solution $u$ exists globally when $p>p_{\text{conf}}(m,n)$ provided
that the initial data is small enough. In case $p_{\text{crit}}(m,n)<p\leq
p_{\text{conf}}(m,n)$, we will establish global existence of small data
solutions $u$ in a subsequent paper.


  We propose a deep learning method for single image super-resolution (SR). Our
method directly learns an end-to-end mapping between the low/high-resolution
images. The mapping is represented as a deep convolutional neural network (CNN)
that takes the low-resolution image as the input and outputs the
high-resolution one. We further show that traditional sparse-coding-based SR
methods can also be viewed as a deep convolutional network. But unlike
traditional methods that handle each component separately, our method jointly
optimizes all layers. Our deep CNN has a lightweight structure, yet
demonstrates state-of-the-art restoration quality, and achieves fast speed for
practical on-line usage. We explore different network structures and parameter
settings to achieve trade-offs between performance and speed. Moreover, we
extend our network to cope with three color channels simultaneously, and show
better overall reconstruction quality.


  We present a dimensionally split method for computing solutions to the
compressible Navier-Stokes equations on Cartesian cut cell meshes. The method
is globally second order accurate in the L1 norm, fully conservative, and
allows the use of time steps determined by the regular grid spacing. We provide
a description of the three-dimensional implementation of the method and
evaluate its numerical performance by computing solutions to a number of test
problems ranging from the nearly incompressible to the highly compressible flow
regimes. All the computed results show good agreement with reference results
from theory, experiment and previous numerical studies. To the best of our
knowledge, this is the first presentation of a dimensionally split cut cell
method for the compressible Navier-Stokes equations in the literature.


  Fluid antennas (FAs) and movable antennas (MAs) have emerged as promising
technologies in wireless communications, which offer the flexibility to improve
channel conditions by adjusting transmit/receive antenna positions within a
spatial region. In this letter, we focus on an MA-enhanced multiple-input
single-output (MISO) communication system, aiming to optimize the positions of
multiple transmit MAs to maximize the received signal power. Unlike the prior
works on continuously searching for the optimal MA positions, we propose to
sample the transmit region into discrete points, such that the continuous
antenna position optimization problem is transformed to a discrete sampling
point selection problem based on the point-wise channel information. However,
such a point selection problem is combinatory and challenging to be optimally
solved. To tackle this challenge, we ingeniously recast it as an equivalent
fixed-hop shortest path problem in graph theory and propose a customized
algorithm to solve it optimally in polynomial time. To further reduce the
complexity, a linear-time sequential update algorithm is also proposed to
obtain a high-quality suboptimal solution. Numerical results demonstrate that
the proposed algorithms can yield considerable performance gains over the
conventional fixed-position antennas with/without antenna selection.


  We present the calculations of steady, spherical gas outflows from galaxies
in an effort to understand the effects of the galaxy mass on the flow
properties such as the size of the outflow regions, the efficiency of radiative
cooling, and the fate of the cooled gas. We show that there exist no transonic
flows but either subsonic or supersonic flows are obtainable, in an analogy
with the stellar wind or accretion problems. Solutions of the supersonic
outflows are studied in detail as they are most likely to carry gas to large
distances away from galaxies. In case the gas does cool radiatively, the cooled
gas is most likely to form clouds via various instabilities. The clouds coast
farther away from the galaxy because of the finite kinetic energy they inherit.
Depending on the initial energies, the clouds can either leave the galaxy or
fall back ballistically. Applications of the calculations to dwarf and normal
galaxies are made, and we argue that normal galaxies like our own should have
relatively small gaseous halos formed through this mechanism. We discuss the
implications of cold clouds from dwarf galaxies on recent observations of the
QSO absorption line systems. For massive galaxies, satellites provide
alternative ways to form large gaseous halos. We show how dynamical friction
can increase tidal stripping of the gas as the satellite spirals in toward the
primary, and that the gas ejected from satellites may account for the QSO heavy
element absorption lines.


  We construct five-dimensional non-Lorentzian Lagrangian gauge field theories
with an SU(1,3) conformal symmetry and 12 (conformal) supersymmetries. Such
theories are interesting in their own right but can arise from six-dimensional
(1,0) superconformal field theories on a conformally compactified Minkowski
spacetime. In the limit that the conformal compactification is removed the
Lagrangians we find give field theory formulations of DLCQ constructions of
six-dimensional (1,0) conformal field theories.


  Turbulent flows laden with inertial particles present multiple open questions
and are a subject of great interest in current research. Due to their higher
density compared to the carrier fluid, inertial particles tend to form high
concentration regions, i.e. clusters, and low concentration regions, i.e.
voids, due to the interaction with the turbulence. In this work, we present an
experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov
particles in homogeneous isotropic turbulent flows. Three control parameters
have been varied over significant ranges: $Re_{\lambda} \in [170 - 450]$,
$St\in [0.1 - 5]$ and volume fraction $\phi_v\in [2\times 10^{-6} - 2\times
10^{-5}]$. The scaling of clustering characteristics, such as the distribution
of Vorono\"i areas and the dimensions of cluster and void regions, with the
three parameters are discussed. In particular, for the polydispersed size
distributions considered here, clustering is found to be enhanced strongly
(quasi-linearly) by $Re_{\lambda}$ and noticeably (with a square-root
dependency) with $\phi_v$, while the cluster and void sizes, scaled with the
Kolmogorov lengthscale $\eta$, are driven primarily by $Re_{\lambda}$. Cluster
length $\sqrt{\langle A_c \rangle}$ scales up to $\approx 100 {\eta}$, measured
at the highest $Re_{\lambda}$, while void length $\sqrt{\langle A_v \rangle}$
scaled also with $\eta$ is typically two times larger ($\approx 200 {\eta}$).
The lack of sensitivity of the above characteristics to the Stokes number lends
support to the "sweep-stick" particle accumulation scenario. The non-negligible
influence of the volume fraction, however, is not considered by that model and
can be connected with collective effects.


  This survey on crystallographic groups, geometric structures on Lie groups
and associated algebraic structures is based on a lecture given in the Ostrava
research seminar in $2017$.


  This study presents a comprehensive spatial eigenanalysis of fully-discrete
discontinuous spectral element methods, now generalizing previous spatial
eigenanalysis that did not include time integration errors. The influence of
discrete time integration is discussed in detail for different explicit
Runge-Kutta (1st to 4th order accurate) schemes combined with either
Discontinuous Galerkin (DG) or Spectral Difference (SD) methods, both here
recovered from the Flux Reconstruction (FR) scheme. Selected numerical
experiments using the improved SD method by Liang and Jameson [1] are performed
to quantify the influence of time integration errors on actual simulations.
These involve test cases of varied complexity, from one-dimensional linear
advection equation studies to well-resolved and under-resolved inviscid
vortical flows. It is shown that, while both well-resolved and under-resolved
simulations of linear problems correlate well with the eigenanalysis prediction
of time integration errors, the correlation can be much worse for
under-resolved nonlinear problems. The effect of mesh regularity is also
considered, where time integration errors are found to be, in the case of
irregular grids, less pronounced than those of the spatial discretisation. In
fact, for the under-resolved vortical flows considered, the predominance of
spatial errors made it practically impossible for time integration errors to be
distinctly identified. Nevertheless, for well-resolved nonlinear simulations,
the effect of time integration errors could still be recognized. This
highlights that the interaction between space and time discretisation errors is
more complex than otherwise anticipated, contributing to the current
understanding about when eigenanalysis can effectively predict the behaviour of
numerical errors in practical under-resolved nonlinear problems, including
under-resolved turbulence computations.


  Cross-group externalities and network effects in two-sided platform markets
shape market structure and competition policy, and are the subject of extensive
study. Less understood are the within-group externalities that arise when the
platform designs many-to-many matchings: the value to agent $i$ of matching
with agent $j$ may depend on the set of agents with which $j$ is matched. These
effects are present in a wide range of settings in which firms compete for
individuals' custom or attention. I characterize platform-optimal matchings in
a general model of many-to-many matching with within-group externalities. I
prove a set of comparative statics results for optimal matchings, and show how
these can be used to analyze the welfare effects various changes, including
vertical integration by the platform, horizontal mergers between firms on one
side of the market, and changes in the platform's information structure. I then
explore market structure and regulation in two in-depth applications. The first
is monopolistic competition between firms on a retail platform such as Amazon.
The second is a multi-channel video program distributor (MVPD) negotiating
transfer fees with television channels and bundling these to sell to
individuals.


  The goal of this research was to develop and examine the performance of a
geostatistical coregionalization modeling approach for combining field
inventory measurements, strip samples of airborne lidar and Landsat-based
remote sensing data products to predict aboveground biomass (AGB) in interior
Alaska's Tanana Valley. The proposed modeling strategy facilitates pixel-level
mapping of AGB density predictions across the entire spatial domain.
Additionally, the coregionalization framework allows for statistically sound
estimation of total AGB for arbitrary areal units within the study area---a key
advance to support diverse management objectives in interior Alaska. This
research focuses on appropriate characterization of prediction uncertainty in
the form of posterior predictive coverage intervals and standard deviations.
Using the framework detailed here, it is possible to quantify estimation
uncertainty for any spatial extent, ranging from pixel-level predictions of AGB
density to estimates of AGB stocks for the full domain. The lidar-informed
coregionalization models consistently outperformed their counterpart lidar-free
models in terms of point-level predictive performance and total AGB precision.
Additionally, the inclusion of Landsat-derived forest cover as a covariate
further improved estimation precision in regions with lower lidar sampling
intensity. Our findings also demonstrate that model-based approaches that do
not explicitly account for residual spatial dependence can grossly
underestimate uncertainty, resulting in falsely precise estimates of AGB. On
the other hand, in a geostatistical setting, residual spatial structure can be
modeled within a Bayesian hierarchical framework to obtain statistically
defensible assessments of uncertainty for AGB estimates.


  We consider a matching market where buyers and sellers arrive according to
independent Poisson processes at the same rate and independently abandon the
market if not matched after an exponential amount of time with the same mean.
In this centralized market, the utility for the system manager from matching
any buyer and any seller is a general random variable. We consider a sequence
of systems indexed by $n$ where the arrivals in the $n^{\mathrm{th}}$ system
are sped up by a factor of $n$. We analyze two families of one-parameter
policies: the population threshold policy immediately matches an arriving agent
to its best available mate only if the number of mates in the system is above a
threshold, and the utility threshold policy matches an arriving agent to its
best available mate only if the corresponding utility is above a threshold.
Using a fluid analysis of the two-dimensional Markov process of buyers and
sellers, we show that when the matching utility distribution is light-tailed,
the population threshold policy with threshold $\frac{n}{\ln n}$ is
asymptotically optimal among all policies that make matches only at agent
arrival epochs. In the heavy-tailed case, we characterize the optimal threshold
level for both policies. We also study the utility threshold policy in an
unbalanced matching market with heavy-tailed matching utilities and find that
the buyers and sellers have the same asymptotically optimal utility threshold.
We derive optimal thresholds when the matching utility distribution is
exponential, uniform, Pareto, and correlated Pareto. We find that as the right
tail of the matching utility distribution gets heavier, the threshold level of
each policy (and hence market thickness) increases, as does the magnitude by
which the utility threshold policy outperforms the population threshold policy.


  We study the transients of matrices in max-plus algebra. Our approach is
based on the weak CSR expansion. Using this expansion, the transient can be
expressed by $\max\{T_1,T_2\}$, where $T_1$ is the weak CSR threshold and $T_2$
is the time after which the purely pseudoperiodic CSR terms start to dominate
in the expansion. Various bounds have been derived for $T_1$ and $T_2$,
naturally leading to the question which matrices, if any, attain these bounds.
  In the present paper we characterize the matrices attaining two particular
bounds on $T_1$, which are generalizations of the bounds of Wielandt and
Dulmage-Mendelsohn on the indices of non-weighted digraphs. This also leads to
a characterization of tightness for the same bounds on the transients of
critical rows and columns. The characterizations themselves are generalizations
of those for the non-weighted case.


  Many barred galaxies, possibly including the Milky Way, have cusps in the
centres. There is a widespread belief, however, that usual bar instability
taking place in bulgeless galaxy models is impossible for the cuspy models,
because of the presence of the inner Lindblad resonance for any pattern speed.
At the same time there are numerical evidences that the bar instability can
form a bar. We analyse this discrepancy, by accurate and diverse N-body
simulations and using the calculation of normal modes. We show that bar
formation in cuspy galaxies can be explained by taking into account the disc
thickness. The exponential growth time is moderate for typical current disc
masses (about 250 Myr), but considerably increases (factor 2 or more) upon
substitution of the live halo and bulge with a rigid halo/bulge potential;
meanwhile pattern speeds remain almost the same. Normal mode analysis with
different disc mass favours a young bar hypothesis, according to which the bar
instability saturated only recently.


  We initiate the analysis of the Kaluza--Klein mass spectrum of massive IIA
supergravity on the warped AdS$_6 \times_w S^4$ background, by deriving the
linearised equations of motion of bosonic and fermionic fluctuations, and
determining the mass spectrum of those of spin-2. The spin-2 modes are given in
terms of hypergeometric functions and a careful analysis of their boundary
conditions uncovers the existence of two branches of mass spectra, bounded from
below. The modes that saturate the bounds belong to short multiplets which we
identify in the representation theory of the $\mathfrak{f}(4)$ symmetry
superalgebra of the AdS$_6 \times_w S^4$ solution.


  Program repair is an important but difficult software engineering problem.
One way to achieve acceptable performance is to focus on classes of simple
bugs, such as bugs with single statement fixes, or that match a small set of
bug templates. However, it is very difficult to estimate the recall of repair
techniques for simple bugs, as there are no datasets about how often the
associated bugs occur in code. To fill this gap, we provide a dataset of
153,652 single statement bug-fix changes mined from 1,000 popular open-source
Java projects, annotated by whether they match any of a set of 16 bug
templates, inspired by state-of-the-art program repair techniques. In an
initial analysis, we find that about 33% of the simple bug fixes match the
templates, indicating that a remarkable number of single-statement bugs can be
repaired with a relatively small set of templates. Further, we find that
template fitting bugs appear with a frequency of about one bug per 1,600-2,500
lines of code (as measured by the size of the project's latest version). We
hope that the dataset will prove a resource for both future work in program
repair and studies in empirical software engineering.


  We focus on classical and quantum list decoding. The capacity of list
decoding was obtained by Nishimura in the case when the number of list does not
increase exponentially. However, the capacity of the exponential-list case is
open even in the classical case while its converse part was obtained by
Nishimura. We derive the channel capacities in the classical and quantum case
with an exponentially increasing list. The converse part of the quantum case is
obtained by modifying Nagaoka's simple proof for strong converse theorem for
channel capacity. The direct part is derived by a quite simple argument.


  In this paper, we analyze an eigenvalue problem for nonlinear elliptic
operators involving homogeneous Dirichlet boundary conditions in a open smooth
bounded domain. We prove bifurcation results from trivial solutions and from
infinity for the considered nonlinear eigenvalue problem. We also show the
existence of multiple solutions of the nonlinear problem using variational
methods.


  Categorization is necessary for many decision making tasks. However, the
categorization process may interfere the decision making result and the law of
total probability can be violated in some situations. To predict the
interference effect of categorization, some model based on quantum probability
has been proposed. In this paper, a new quantum dynamic belief (QDB) model is
proposed. Considering the precise decision may not be made during the process,
the concept of uncertainty is introduced in our model to simulate real human
thinking process. Then the interference effect categorization can be predicted
by handling the uncertain information. The proposed model is applied to a
categorization decision-making experiment to explain the interference effect of
categorization. Compared with other models, our model is relatively more
succinct and the result shows the correctness and effectiveness of our model.


  The year 2020 has seen the COVID-19 virus lead to one of the worst global
pandemics in history. As a result, governments around the world are faced with
the challenge of protecting public health, while keeping the economy running to
the greatest extent possible. Epidemiological models provide insight into the
spread of these types of diseases and predict the effects of possible
intervention policies. However, to date,the even the most data-driven
intervention policies rely on heuristics. In this paper, we study how
reinforcement learning (RL) can be used to optimize mitigation policies that
minimize the economic impact without overwhelming the hospital capacity. Our
main contributions are (1) a novel agent-based pandemic simulator which, unlike
traditional models, is able to model fine-grained interactions among people at
specific locations in a community; and (2) an RL-based methodology for
optimizing fine-grained mitigation policies within this simulator. Our results
validate both the overall simulator behavior and the learned policies under
realistic conditions.


  The Horton-Strahler number, also called the register function, is a
combinatorial tool that quantifies the branching complexity of a rooted tree.
We study the law of the Horton-Strahler number of stable Galton-Watson trees
conditioned to have size $n$, including the Catalan trees. While these random
variables are known to grow as a multiple of $\ln n$ in probability, their
fluctuations are not well understood because they are coupled with
deterministic oscillations. To rule out the latter, we introduce a real-valued
variant of the Horton-Strahler number. We show that a rescaled exponential of
this quantity jointly converges in distribution to a measurable function of the
scaling limit of the trees, i.e. the stable L\'evy tree. We call this limit the
Strahler dilation and we discuss its similarities with the Horton-Strahler
number.


  Little is known about the role of network rigidity in light-induced
structural rearrangements in network glasses due to a lack of supporting
experiments and theories. In this report, we demonstrate for the first time the
ultrafast structural rearrangements manifested as induced absorption (IA) over
a broad spectral range in a-GexAs35-xSe65 thin films above the mean-field
rigidity percolation transition, quantified by the mean coordination number <r>
= 2.40. The IA spectrum arising from self-trapped excitons, induced structural
rearrangements by softening the glass network that strikingly reveal two
relaxation mechanisms which differ by one order of magnitude. The fast kinetics
of electron-lattice interaction occurs within 1 ps, exhibits a weak dependence
on rigidity and dominates in the sub-bandgap region. In a stark contrast, the
slow kinetics are associated with the structural changes in the bandgap region
and depends strongly on network rigidity. Our results further demonstrate that
amplitude of IA scales a linear relationship with excitation fluence which
provides a unique way to induce structural rearrangements in over-coordinated
network to exploit it for practical purposes. Our results modify the
conventional concept of rigidity dependence of light-induced effects in network
glasses, when excited with an ultrafast laser.


  Paper is published in J. Phys. A: Math. Theor. 43 (2010) 225001,
doi:10.1088/1751-8113/43/22/225001. Exact analytical solution for the universal
probability distribution of the order parameter fluctuations as well as for the
universal statistical and thermodynamic functions of an ideal gas in the whole
critical region of Bose-Einstein condensation is obtained. A universal
constraint nonlinearity is found that is responsible for all nontrivial
critical phenomena of the BEC phase transition. Simple analytical
approximations, which describe the universal structure of the critical region
in terms of confluent hypergeometric or parabolic cylinder functions, as well
as asymptotics of the exact solution are derived. The results for the order
parameter, all higher-order moments of BEC fluctuations, and thermodynamic
quantities, including specific heat, perfectly match the known asymptotics
outside critical region as well as the phenomenological renormalization-group
ansatz with known critical exponents in the close vicinity of the critical
point. Thus, a full analytical solution to a long-standing problem of finding a
universal structure of the lambda-point for BEC in an ideal gas is found.


  Clinicians require substantial training and experience to become comfortable
with steering Intracardiac echocardiography (ICE) catheter to localize and
measure the area of treatment to watch for complications while device catheters
are deployed in another access. Thus, it is reasonable that a robotic-assist
system to hold and actively manipulate the ICE catheter could ease the workload
of the physician. Existing commercially-available robotic systems and research
prototypes all use existing commercially available ICE catheters based on
multiple tendon-sheath mechanism (TSM). To motorize the existing TSM-based ICE
catheter, the actuators interface with the outer handle knobs to manipulate
four internal tendons. However, in practice, the actuators are located at a
sterile, safe place far away from the ICE handle. Thus, to interface with
knobs, there exist multiple coupled gear structures between two, leading to a
highly nonlinear behavior (e.g. various slack, elasticity) alongside hysteresis
phenomena in TSM.
  Since ICE catheters are designed for single use, the expensive actuators need
to be located in a safe place so as to be reusable. Moreover, these actuators
should interface as directly as possible with the tendons for accurate tip
controls. In this paper, we introduce a separable ICE catheter robot with four
tendon actuation: one part reusable and another disposable. Moreover, we
propose a practical model and calibration method for our proposed mechanism so
that four tendons are actuated simultaneously allowing for precise tip control
and mitigating issues with conventional devices such as dead-zone and
hysteresis with simple linear compensation. We consider an open-loop controller
since many available ICE catheters are used without position-tracking sensors
at the tip due to costs and single use


  We present a number of examples and counterexamples to illustrate the results
on cost-efficiency in an incomplete market obtained in [BS24]. These examples
and counterexamples do not only illustrate the results obtained in [BS24], but
show the limitations of the results and the sharpness of the key assumptions.
In particular, we make use of a simple 3-state model in which we are able to
recover and illustrate all key results of the paper. This example also shows
how our characterization of perfectly cost-efficient claims allows to solve an
expected utility maximization problem in a simple incomplete market (trinomial
model) and recover results from [DS06, Chapter 3], there obtained using
duality.


  Solving partial differential equations (PDEs) is a central task in scientific
computing. Recently, neural network approximation of PDEs has received
increasing attention due to its flexible meshless discretization and its
potential for high-dimensional problems. One fundamental numerical difficulty
is that random samples in the training set introduce statistical errors into
the discretization of loss functional which may become the dominant error in
the final approximation, and therefore overshadow the modeling capability of
the neural network. In this work, we propose a new minmax formulation to
optimize simultaneously the approximate solution, given by a neural network
model, and the random samples in the training set, provided by a deep
generative model. The key idea is to use a deep generative model to adjust
random samples in the training set such that the residual induced by the
approximate PDE solution can maintain a smooth profile when it is being
minimized. Such an idea is achieved by implicitly embedding the Wasserstein
distance between the residual-induced distribution and the uniform distribution
into the loss, which is then minimized together with the residual. A nearly
uniform residual profile means that its variance is small for any normalized
weight function such that the Monte Carlo approximation error of the loss
functional is reduced significantly for a certain sample size. The adversarial
adaptive sampling (AAS) approach proposed in this work is the first attempt to
formulate two essential components, minimizing the residual and seeking the
optimal training set, into one minmax objective functional for the neural
network approximation of PDEs.


  Bayesian computational algorithms tend to scale poorly as data size
increases. This has motivated divide-and-conquer-based approaches for scalable
inference. These divide the data into subsets, perform inference for each
subset in parallel, and then combine these inferences. While appealing
theoretical properties and practical performance have been demonstrated for
independent observations, scalable inference for dependent data remains
challenging. In this work, we study the problem of Bayesian inference from very
long time series. The literature in this area focuses mainly on approximate
approaches that usually lack rigorous theoretical guarantees and may provide
arbitrarily poor accuracy in practice. We propose a simple and scalable
divide-and-conquer method, and provide accuracy guarantees. Numerical
simulations and real data applications demonstrate the effectiveness of our
approach.


  The small change in the spectral slope of the overall intensity of cosmic
rays near 1 PeV may be associated with the endpoint energy of supernova shock
acceleration. A crucial test of this connection and other ideas of the origin
of the spectral `knee' is the reliable determination of the variation of
elemental composition in this region. Recent measurements at the DICE/CASA/MIA
air shower installation in Dugway, Utah, USA have provided several independent
air shower parameters for each event. The derivation of elemental composition
from a combination of Cherenkov size, depth of shower maximum in the
atmosphere, muon size and electron size at ground level and the reliability of
these results are discussed. There is no evidence from these data for a large
change in the mean mass of cosmic rays across the `knee'. These measurements
show the cosmic rays are composed of ~ 70% protons and alpha-particles near
total energies of 10PeV.


  Visual question answering (VQA) demands simultaneous comprehension of both
the image visual content and natural language questions. In some cases, the
reasoning needs the help of common sense or general knowledge which usually
appear in the form of text. Current methods jointly embed both the visual
information and the textual feature into the same space. However, how to model
the complex interactions between the two different modalities is not an easy
task. In contrast to struggling on multimodal feature fusion, in this paper, we
propose to unify all the input information by natural language so as to convert
VQA into a machine reading comprehension problem. With this transformation, our
method not only can tackle VQA datasets that focus on observation based
questions, but can also be naturally extended to handle knowledge-based VQA
which requires to explore large-scale external knowledge base. It is a step
towards being able to exploit large volumes of text and natural language
processing techniques to address VQA problem. Two types of models are proposed
to deal with open-ended VQA and multiple-choice VQA respectively. We evaluate
our models on three VQA benchmarks. The comparable performance with the
state-of-the-art demonstrates the effectiveness of the proposed method.