  We study a 4-orbital tight-binding (TB) model for ZrSiS from the square
sublattice generated by the Si atoms. After studying three other alternatives,
we endow such model with a new effective spin-orbit coupling (SOC) consistent
with {\em ab initio} dispersions around the Fermi energy ($E_F$) in four
systematic steps: (1) We calculate the electronic dispersion of bulk ZrSiS
using an implementation of density-functional theory (DFT) based on numeric
atomic orbitals [{\em J. Phys.: Condens. Matter} {\bf 14}, 2745 (2002)] in
which on-site and off-site SOC can be told apart. As a result, we determine
that local SOC-induced band gaps around $E_F$ are predominantly created by the
on-site contribution. (2) Gradually reducing the atomic basis set size, we then
create an electronic band structure with 16 orbitals per unit cell (u.c.) which
retains the qualitative features of the dispersion around $E_F$, including
SOC-induced band gaps. (3) Zr is the heaviest element on this compound and it
has a non-negligible contribution to the electronic dispersion around $E_F$; we
show that it provides the strongest contribution to the SOC-induced band gap.
(4) Using L\"{o}wdin partitioning approach, we project the effect of SOC onto
the 4-orbital Hamiltonian. This way, we facilitate an effective SOC interaction
that was explicitly informed by {\em ab initio} input.


  We study the weight and length of the minimum mean-weight cycle in the
stochastic mean-field distance model, i.e., in the complete graph on $n$
vertices with edges weighted by independent exponential random variables.
Mathieu and Wilson showed that the minimum mean-weight cycle exhibits one of
two distinct behaviors, according to whether its mean weight is smaller or
larger than $1/(ne)$; and that both scenarios occur with positive probability
in the limit $n\to\infty$. If the mean weight is $< 1/(ne)$, the length is of
constant order. If the mean weight is $> 1/(ne)$, it is concentrated just above
$1/(n e)$, and the length diverges with $n$. The analysis of Mathieu--Wilson
gives a detailed characterization of the subcritical regime, including the
(non-degenerate) limiting distributions of the weight and length, but leaves
open the supercritical behavior. We determine the asymptotics for the
supercritical regime, showing that with high probability, the minimum mean
weight is $(n e)^{-1}[1 + \pi^2/(2 \log^2 n) + O((\log n)^{-3})]$, and the
cycle achieving this minimum has length on the order of $(\log n)^3$.


  Medical image translation (e.g. CT to MR) is a challenging task as it
requires I) faithful translation of domain-invariant features (e.g. shape
information of anatomical structures) and II) realistic synthesis of
target-domain features (e.g. tissue appearance in MR). In this work, we propose
Manifold Disentanglement Generative Adversarial Network (MDGAN), a novel image
translation framework that explicitly models these two types of features. It
employs a fully convolutional generator to model domain-invariant features, and
it uses style codes to separately model target-domain features as a manifold.
This design aims to explicitly disentangle domain-invariant features and
domain-specific features while gaining individual control of both. The image
translation process is formulated as a stylisation task, where the input is
"stylised" (translated) into diverse target-domain images based on style codes
sampled from the learnt manifold. We test MDGAN for multi-modal medical image
translation, where we create two domain-specific manifold clusters on the
manifold to translate segmentation maps into pseudo-CT and pseudo-MR images,
respectively. We show that by traversing a path across the MR manifold cluster,
the target output can be manipulated while still retaining the shape
information from the input.


  Evolutionary dynamics on graphs can lead to many interesting and
counterintuitive findings. We study the Moran process, a discrete time
birth-death process, that describes the invasion of a mutant type into a
population of wild-type individuals. Remarkably, the fixation probability of a
single mutant is the same on all regular networks. But non-regular networks can
increase or decrease the fixation probability. While the time until fixation
formally depends on the same transition probabilities as the fixation
probabilities, there is no obvious relation between them. For example, an
amplifier of selection, which increases the fixation probability and thus
decreases the number of mutations needed until one of them is successful, can
at the same time slow down the process of fixation. Based on small networks, we
show analytically that (i) the time to fixation can decrease when links are
removed from the network and (ii) the node providing the best starting
conditions in terms of the shortest fixation time depends on the fitness of the
mutant. Our results are obtained analytically on small networks, but numerical
simulations show that they are qualitatively valid even in much larger
populations.


  The wave operators $W_\pm(H_1,H_0)$ of two selfadjoint operators $H_0$ and
$H_1$ are analyzed at asymptotic spectral values. Sufficient conditions for
$\|(W_\pm(H_1,H_0)-P_{1}^\mathrm{ac}P_{0}^\mathrm{ac})f(H_0)\| <\infty$ are
given, where $P_{j}^\mathrm{ac}$ projects onto the subspace of absolutely
continuous spectrum of $H_j$ and $f$ is an unbounded function
($f$-boundedness), both in the case of trace-class perturbations and in terms
of the high-energy behaviour of the boundary values of the resolvent of $H_0$
(smooth method). Examples include $f$-boundedness for the perturbed
polyharmonic operator and for Schr\"odinger operators with matrix-valued
potentials. We discuss an application to the problem of quantum backflow.


  Clustering partitions a dataset such that observations placed together in a
group are similar but different from those in other groups. Hierarchical and
$K$-means clustering are two approaches but have different strengths and
weaknesses. For instance, hierarchical clustering identifies groups in a
tree-like structure but suffers from computational complexity in large datasets
while $K$-means clustering is efficient but designed to identify homogeneous
spherically-shaped clusters. We present a hybrid non-parametric clustering
approach that amalgamates the two methods to identify general-shaped clusters
and that can be applied to larger datasets. Specifically, we first partition
the dataset into spherical groups using $K$-means. We next merge these groups
using hierarchical methods with a data-driven distance measure as a stopping
criterion. Our proposal has the potential to reveal groups with general shapes
and structure in a dataset. We demonstrate good performance on several
simulated and real datasets.


  We consider supergravity in five-dimensional Anti-De Sitter space $AdS_{5}$
with minimal supersymmetry, encoded by a Sasaki-Einstein metric on a
five-dimensional compact manifold $M$. Our main result reveals how the
Sasaki-Einstein metric emerges from a canonical state in the dual CFT, defined
by a superconformal gauge theory in four dimensional Minkowski space
$\mathbb{R}^{3,1}$in the t'Hooft limit where the rank $N$ tends to infinity. We
obtain explicit finite $N-$approximations to the Sasaki-Einstein metric,
expressed in terms of a canonical (i.e. background free) BPS-state on the gauge
theory side. We also provide a string theory interpretation of the BPS-state in
question, which sheds new light on the previously noted intriguing duality of
giant gravitons.


  We study some measures which are related to the notion of the
$\e$-complexity. We prove that measure of $\e$-complexity defined on the base
of the notion of $\e$-separability is equivalent to the dual measure that is
defined through $\e$-nets.
  Keywords: Complexity, Separability, Bernoulli measure


  A linearly coupled chain of spin-polarized quantum dots is investigated under
the condition that the number of electrons is equal to or less than the number
of the dots. The chemical potential of the system, $\mu_{N}=E(N)-E(N-1)$,
satisfies, $(\mu_{N}+\mu_{N_{\ell}+2-N)}/2 \approx V+2t (N, N_{\ell}, V, E(N)$
and $t$ are the number of electrons, the number of dots, and the strength of
nearest neighbor electron-electron interactions, the total groundstate energy
and the hopping integral between two adjacent dots). This property will be
reflected in the spacing between the conductance peaks. The electron density
structures are determined using a quantum Monte Carlo method. As the number of
electrons is varied several correlated structures are found that are
commensurate/incommensurate with the periodic dot system. Hartree-Fock theory
fails to predict the correct electronic structures of this system because
several nearly degenerate solutions exist.


  In this article we present a detailed description of an electron in a uniform
magnetic field evolving under the Schr\"odinger equation using ladder
operators. Based on this analysis, we describe the same physical system using
the Dirac equation, known from relativistic quantum mechanics. The main
differences between these two quantum mechanical approaches are discussed and
we observe specifically how the relativistic phenomena modify the description
of this particular quantum system.


  The calculation of the transfer matrix for a large non-periodic multilayered
system may become unstable in the presence of absorption. We discuss the origin
of this instability and we explore two methods to overcome it: the use of a
total matrix to solve for all the fields at all the interfaces simultaneously
and an expansion in the Bloch-like modes of a periodic artificially repeated
system. We apply both methods to obtain the reflectance spectra of multilayered
chirped structures composed of nanostructured porous silicon (PS). Both methods
yield reliable and numerically stable results. The former allows an analysis of
the field within all layers while the latter is much more efficient
computationally, allowing the design of novel structures and the optimization
of their parameters. We compare numerical and experimental results across a
wide spectral range from the infrared to the ultraviolet.


  Given a polytope $\sigma\subset \mathbb{R}^m$, its characteristic
distribution $\delta_\sigma$ generates a $D$-module which we call the
characteristic $D$-module of $\sigma$ and denote by $M_\sigma$. More generally,
the characteristic distributions of a cell complex $K$ with polyhedral cells
generate a $D$-module $M_K$, which we call the characteristic $D$-module of the
cell complex. We prove various basic properties of $M_K$, and show that under
certain mild topological conditions on $K$, the $D$-module theoretic direct
image of $M_K$ coincides with the module generated by the $B$-splines
associated to the cells of $K$ (considered as distributions). We also give
techniques for computing $D$-annihilator ideals of polytopes.


  In the realm of fashion object detection and segmentation for online shopping
images, existing state-of-the-art fashion parsing models encounter limitations,
particularly when exposed to non-model-worn apparel and close-up shots. To
address these failures, we introduce FashionFail; a new fashion dataset with
e-commerce images for object detection and segmentation. The dataset is
efficiently curated using our novel annotation tool that leverages recent
foundation models. The primary objective of FashionFail is to serve as a test
bed for evaluating the robustness of models. Our analysis reveals the
shortcomings of leading models, such as Attribute-Mask R-CNN and Fashionformer.
Additionally, we propose a baseline approach using naive data augmentation to
mitigate common failure cases and improve model robustness. Through this work,
we aim to inspire and support further research in fashion item detection and
segmentation for industrial applications. The dataset, annotation tool, code,
and models are available at \url{https://rizavelioglu.github.io/fashionfail/}.


  A short biographical note on the life and works of K. Ramachandra, one of the
leading mathematicians in the field of analytic number theory in the second
half of the twentieth century.


  In this paper, we introduce and study five families of Lie groups in
degenerate Clifford geometric algebras. These Lie groups preserve the even and
odd subspaces and some other subspaces under the adjoint representation and the
twisted adjoint representation. The considered Lie groups contain degenerate
spin groups, Lipschitz groups, and Clifford groups as subgroups in the case of
arbitrary dimension and signature. The considered Lie groups can be of interest
for various applications in physics, engineering, and computer science.


  We introduce a class of labeled graphs (with legs) which contains two classes
of GKM graphs of $4n$-dimensional manifolds with $T^{n}\times S^{1}$-actions,
i.e., GKM graphs of the toric hyperK${\rm\ddot{a}}$hler manifolds and of the
cotangent bundles of toric manifolds. Under some conditions, the graph
equivariant cohomology ring of such a labeled graph is computed. We also give a
module basis of the graph equivariant cohomology by using a shelling structure
of such a labeled graph and study their multiplicative structure.


  Classifying isomorphism classes of group gradings on algebras presents a
compelling challenge, particularly within the realms of non-simple and
infinite-dimensional algebras, which have been relatively unexplored. This
study focuses on a kind of algebra that is neither simple nor
finite-dimensional, aiming to classify the group gradings on triangularizable
algebras as defined by Mesyan in 2019. The topology of infinite-dimensional
algebras, along with the role of idempotent elements, plays a crucial role in
our findings, leading to new insights and a deeper understanding of their
structure.


  Two counterexamples, addressing questions raised in \cite{AD} and \cite{PZ},
are provided. Both counterexamples are related to chaoses. Let $F_n=Y_n+Z_n$.
It may be that $F_n\overset{a.s.}\longrightarrow 0$,
$F_n\overset{L_{2+\delta}}\longrightarrow 0$ and
$E\bigl\{\sup_n\,\abs{F_n}^\delta\bigr\}<\infty$, where $\delta>0$ and $Y_n$
and $Z_n$ belong to chaoses of uniformly bounded degree, and yet $Y_n$ fails to
converge to 0 a.s.


  Physics-based simulation has been actively employed in generating offline
visual effects in the film and animation industry. However, the computations
required for high-quality scenarios are generally immense, deterring its
adoption in real-time applications, e.g., virtual production, avatar
live-streaming, and cloud gaming. We summarize the principles that can
accelerate the computation pipeline on single-GPU and multi-GPU platforms
through extensive investigation and comprehension of modern GPU architecture.
We further demonstrate the effectiveness of these principles by applying them
to the material point method to build up our framework, which achieves
$1.7\times$--$8.6\times$ speedup on a single GPU and $2.5\times$--$14.8\times$
on four GPUs compared to the state-of-the-art. Our pipeline is specifically
designed for real-time applications (i.e., scenarios with small to medium
particles) and achieves significant multi-GPU efficiency. We demonstrate our
pipeline by simulating a snow scenario with 1.33M particles and a fountain
scenario with 143K particles in real-time (on average, 68.5 and 55.9
frame-per-second, respectively) on four NVIDIA Tesla V100 GPUs interconnected
with NVLinks.


  Large-scale pre-training models have promoted the development of
histopathology image analysis. However, existing self-supervised methods for
histopathology images focus on learning patch features, while there is still a
lack of available pre-training models for WSI-level feature learning. In this
paper, we propose a novel self-supervised learning framework for pan-cancer
WSI-level representation pre-training with the designed position-aware masked
autoencoder (PAMA). Meanwhile, we propose the position-aware cross-attention
(PACA) module with a kernel reorientation (KRO) strategy and an anchor dropout
(AD) mechanism. The KRO strategy can capture the complete semantic structure
and eliminate ambiguity in WSIs, and the AD contributes to enhancing the
robustness and generalization of the model. We evaluated our method on 6
large-scale datasets from multiple organs for pan-cancer classification tasks.
The results have demonstrated the effectiveness of PAMA in generalized and
discriminative WSI representation learning and pan-cancer WSI pre-training. The
proposed method was also compared with 7 WSI analysis methods. The experimental
results have indicated that our proposed PAMA is superior to the
state-of-the-art methods.The code and checkpoints are available at
https://github.com/WkEEn/PAMA.


  In this paper, we derive entropy functions whose local equilibria are
suitable to recover the Euler-like equations in the framework of the Lattice
Boltzmann method. Numerical examples are also given, which are consistent with
the above theoretical arguments.


  The paper deals with variational approaches to the segmentation of time
series into smooth pieces, but allowing for sharp breaks. In discrete time, the
corresponding functionals are of Blake-Zisserman type. Their natural
counterpart in continuous time are the Mumford-Shah functionals. Time series
which minimise these functionals are proper estimates or representations of the
signals behind recorded data. We focus on consistent behaviour of the
functionals and the estimates, as parameters vary or as the sampling rate
increases. For each time continuous time series $f\in L^2 (\lbrack 0,1\rbrack)$
we take conditional expectations w.r.t. to $\sigma$-algebras generated by finer
and finer partitions of the time domain into intervals, and thereby construct a
sequence $(f_n)_{n\in\N}$ of discrete time series. As $n$ increases this
amounts to sampling the continuous time series with more and more accuracy. Our
main result is consistent behaviour of segmentations w.r.t. to variation of
parameters and increasing sampling rate.


  Bayesian optimization (BO) is a popular black-box function optimization
method, which makes sequential decisions based on a Bayesian model, typically a
Gaussian process (GP), of the function. To ensure the quality of the model,
transfer learning approaches have been developed to automatically design GP
priors by learning from observations on "training" functions. These training
functions are typically required to have the same domain as the "test" function
(black-box function to be optimized). In this paper, we introduce MPHD, a model
pre-training method on heterogeneous domains, which uses a neural net mapping
from domain-specific contexts to specifications of hierarchical GPs. MPHD can
be seamlessly integrated with BO to transfer knowledge across heterogeneous
search spaces. Our theoretical and empirical results demonstrate the validity
of MPHD and its superior performance on challenging black-box function
optimization tasks.


  We propose that general D-dimensional quantum field theories are dual to
(D+1)-dimensional local quantum theories which in general include objects with
spin two or higher. Using a general prescription, we construct a
(D+1)-dimensional theory which is holographically dual to the D-dimensional
O(N) vector model. From the holographic theory, the phase transition and
critical properties of the model in dimensions D>2 are described.


  Determining the position and orientation of a calibrated camera from a single
image with respect to a 3D model is an essential task for many applications.
When 2D-3D correspondences can be obtained reliably, perspective-n-point
solvers can be used to recover the camera pose. However, without the pose it is
non-trivial to find cross-modality correspondences between 2D images and 3D
models, particularly when the latter only contains geometric information.
Consequently, the problem becomes one of estimating pose and correspondences
jointly. Since outliers and local optima are so prevalent, robust objective
functions and global search strategies are desirable. Hence, we cast the
problem as a 2D-3D mixture model alignment task and propose the first
globally-optimal solution to this formulation under the robust $L_2$ distance
between mixture distributions. We search the 6D camera pose space using
branch-and-bound, which requires novel bounds, to obviate the need for a pose
estimate and guarantee global optimality. To accelerate convergence, we
integrate local optimization, implement GPU bound computations, and provide an
intuitive way to incorporate side information such as semantic labels. The
algorithm is evaluated on challenging synthetic and real datasets,
outperforming existing approaches and reliably converging to the global
optimum.


  Here we report the first angle-resolved photoemission measurement on nearly
optimally-doped multi-layer Tl-based superconducting cuprates (Tl-2212 and
Tl-1223) and a comparison study to single layer (Tl-2201) compound. A "kink" in
the band dispersion is found in all three compounds but exhibits different
momentum dependence for the single layer and multi-layer compounds, reminiscent
to that of Bi-based cuprates. This layer number dependent renormalization
effect strongly implies that the spin resonance mode is unlikely responsible
for the dramatic renormalization effect near the antinodal region.


  We present Gran Telescopio CANARIAS CanariCam 8.7$\mu$m imaging and
7.5-13$\mu$m spectroscopy of six local systems known to host an active galactic
nucleus (AGN) and have nuclear star formation. Our main goal is to investigate
whether the molecules responsible for the 11.3$\mu$m polyclyclic aromatic
hydrocarbon (PAH) feature are destroyed in the close vicinity of an AGN. We
detect 11.3$\mu$m PAH feature emission in the nuclear regions of the galaxies
as well as extended PAH emission over a few hundred parsecs. The equivalent
width (EW) of the feature shows a minimum at the nucleus but increases with
increasing radial distances, reaching typical star-forming values a few hundred
parsecs away from the nucleus. The reduced nuclear EW are interpreted as due to
increased dilution from the AGN continuum rather than destruction of the PAH
molecules. We conclude that at least those molecules responsible for the
11.3$\mu$m PAH feature survive in the nuclear environments as close as 10pc
from the AGN and for Seyfert-like AGN luminosities. We propose that material in
the dusty tori, nuclear gas disks, and/or host galaxies of AGN is likely to
provide the column densities necessary to protect the PAH molecules from the
AGN radiation field.


  Increased deployment of residential smart meters has made it possible to
record energy consumption data on short intervals. These data, if used
efficiently, carry valuable information for managing power demand and
increasing energy consumption efficiency. However, analyzing smart meter data
of millions of customers in a timely manner is quite challenging. An efficient
way to analyze these data is to first identify clusters of customers, and then
focus on analyzing these clusters. Deciding on the optimal number of clusters
is a challenging task. In this manuscript, we propose a metric to efficiently
find the optimal number of clusters. A genetic algorithm based feature
selection is used to reduce the number of features, which are then fed into
self-organizing maps for clustering. We apply the proposed clustering technique
on two electricity consumption datasets from Victoria, Australia and Ireland.
The numerical simulations reveal effectiveness of the proposed method in
finding the optimal clusters.


  In this note, a general approach to the study of non-stationary Markov chains
with catastrophes and the corresponding queuing models is considered, as well
as to obtain estimates of the limiting regime itself. As an illustration, an
example of a queuing model is studied.


  Users of social platforms often perceive these sites as supportive spaces to
post about their mental health issues. Those conversations contain important
traces about individuals' health risks. Recently, researchers have exploited
this online information to construct mental health detection models, which aim
to identify users at risk on platforms like Twitter, Reddit or Facebook. Most
of these models are centred on achieving good classification results, ignoring
the explainability and interpretability of the decisions. Recent research has
pointed out the importance of using clinical markers, such as the use of
symptoms, to improve trust in the computational models by health professionals.
In this paper, we propose using transformer-based architectures to detect and
explain the appearance of depressive symptom markers in the users' writings. We
present two approaches: i) train a model to classify, and another one to
explain the classifier's decision separately and ii) unify the two tasks
simultaneously using a single model. Additionally, for this latter manner, we
also investigated the performance of recent conversational LLMs when using
in-context learning. Our natural language explanations enable clinicians to
interpret the models' decisions based on validated symptoms, enhancing trust in
the automated process. We evaluate our approach using recent symptom-based
datasets, employing both offline and expert-in-the-loop metrics to assess the
quality of the explanations generated by our models. The experimental results
show that it is possible to achieve good classification results while
generating interpretable symptom-based explanations.


  In this paper, we consider a non-convex problem which is the sum of
$\ell_0$-norm and a convex smooth function under box constraint. We propose one
proximal iterative hard thresholding type method with extrapolation step used
for acceleration and establish its global convergence results. In detail, the
sequence generated by the proposed method globally converges to a local
minimizer of the objective function. Finally, we conduct numerical experiments
to show the proposed method's effectiveness on comparison with some other
efficient methods.


  In bacterial populations, cells are able to cooperate in order to yield
complex collective functionalities. Interest in population-level cellular
behaviour is increasing, due to both our expanding knowledge of the underlying
biological principles, and the growing range of possible applications for
engineered microbial consortia. Researchers in the field of synthetic biology -
the application of engineering principles to living systems - have, for
example, recently shown how useful decision-making circuits may be distributed
across a bacterial population. The ability of cells to interact through small
signalling molecules (a mechanism known as it quorum sensing) is the basis for
the majority of existing engineered systems. However, horizontal gene transfer
(or conjugation) offers the possibility of cells exchanging messages (using
DNA) that are much more information-rich. The potential of engineering this
conjugation mechanism to suit specific goals will guide future developments in
this area. Motivated by a lack of computational models for examining the
specific dynamics of conjugation, we present a simulation framework for its
further study. We present an agent-based model for conjugation dynamics, with
realistic handling of physical forces. Our framework combines the management of
intercellular interactions together with simulation of intracellular genetic
networks, to provide a general-purpose platform. We validate our simulations
against existing experimental data, and then demonstrate how the emergent
mixing patterns of multi-strain populations can affect conjugation dynamics.
Our model of conjugation, based on a probability distribution, may be easily
tuned to correspond to the behaviour of different cell types. Simulation code
and movies are available at http://code.google.com/p/discus/.


  Using a multiplicative reparametrization, I show that a subclass of $L_q$
penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It
follows that the lasso and other norm-penalized regression estimates may be
obtained using a very simple and intuitive alternating ridge regression
algorithm. As compared to a similarly intuitive EM algorithm for $L_q$
optimization, the proposed algorithm avoids some numerical instability issues
and is also competitive in terms of speed. Furthermore, the proposed algorithm
can be extended to accommodate sparse high-dimensional scenarios, generalized
linear models, and can be used to create structured sparsity via penalties
derived from covariance models for the parameters. Such model-based penalties
may be useful for sparse estimation of spatially or temporally structured
parameters.


  This paper proposes a method for the deployment of a multi-agent system of
unmanned aerial vehicles (UAVs) as a shield with potential applications in the
protection of infrastructures. The shield shape is modeled as a quadric surface
in the 3D space. To design the desired formation (target distances between
agents and interconnections), an algorithm is proposed where the input
parameters are just the parametrization of the quadric and the number of agents
of the system. This algorithm guarantees that the agents are almost uniformly
distributed over the virtual surface and that the topology is a Delaunay
triangulation. Moreover, a new method is proposed to check if the resulting
triangulation meets that condition and is executed locally. Because this
topology ensures that the formation is rigid, a distributed control law based
on the gradient of a potential function is proposed to acquire the desired
shield shape and proofs of stability are provided. Finally, simulation and
experimental results illustrate the effectiveness of the proposed approach.


  F-theory models are constructed where the 7-brane has a non-trivial
fundamental group. The base manifolds used are a toric Fano variety and a
smooth toric threefold coming from a reflexive polyhedron. The discriminant
locus of the elliptically fibered Calabi-Yau fourfold can be chosen such that
one irreducible component it is not simply connected (namely, an Enriques
surface) and supports a non-Abelian gauge theory.


  We study a one-dimensional Josephson junction chain embedded in a magnetic
field. We show that when the magnetic flux per elementary loop equals half the
superconducting flux quantum $\phi_0=h/2e$, a local $\nbZ_2$ symmetry arises.
This symmetry is responsible for a nematic Luttinger liquid state associated to
bound states of Cooper pairs. We analyze the phase diagram and we discuss some
experimental possibilities to observe this exotic phase.


  The electromagnetic transitions between ($J^{P}={3/2}^{+}$) and
($J^{P}={1/2}^{+}$) baryons are important decay modes to observe new hadronic
states experimentally. For the estimation of these transitions widths, we
employ a non-relativistic quark potential model description with color coulomb
plus linear confinement potential. Such a description has been employed to
compute the ground state masses and magnetic moments of the single heavy flavor
baryons. The magnetic moments of the baryons are obtained using the spin-flavor
structure of the constituting quark composition of the baryon. Here, we also
define an effective constituent mass of the quarks (ecqm) by taking into
account the binding effects of the quarks within the baryon. The radiative
transition widths are computed in terms of the magnetic moments of the baryon
and the photon energy. Our results are compared with other theoretical models.


  We study families of $K3$ surfaces obtained by double covering of the
projective plane branching along curves of $(2,3)$-torus type. In the first
part, we study the Picard lattices of the families, and a lattice duality of
them. In the second part, we describe a deformation of singularities of
Gorenstein $K3$ surfaces in these families.


  We demonstrate that the magnetic nanoskyrmion lattice on the Fe monolayer on
Ir(111) and the positions of the Fe atoms can be resolved simultaneously using
magnetic exchange force microscopy. Thus, the relation between magnetic and
atomic structure can be determined straightforwardly by evaluating the Fourier
transformation of the real space image data. We further show that the magnetic
contrast can be mapped on a Heisenberg-like magnetic interaction between tip
and sample spins. Since our imaging technique is based on measuring forces, our
observation paves the way to study skyrmions or other complex spin textures on
insulating sample systems with atomic resolution.


  I investigate the effects of the gluon self-energy in the color-flavor-locked
phase of color superconductivity on the value of the gap. The light plasmon
modes, which appear for energies smaller than twice the gap energy, provide the
largest contribution. They modify the subsubleading term in the solution of the
gap equation.


  We study special regularity and decay properties of solutions to the IVP
associated to the $k$-generalized KdV equations. In particular, for datum
$u_0\in H^{3/4^+}(\mathbb R)$ whose restriction belongs to $H^l((b,\infty))$
for some $l\in\mathbb Z^+$ and $b\in \mathbb R$ we prove that the restriction
of the corresponding solution $u(\cdot,t)$ belongs to $H^l((\beta,\infty))$ for
any $\beta \in \mathbb R$ and any $t\in (0,T)$. Thus, this type of regularity
propagates with infinite speed to its left as time evolves.


  Fermi arc surface states are the hallmark of Weyl semimetals, whose
identification is usually challenged by their coexistence with gapless bulk
states. Surface transport measurements by fabricating setups on the sample
boundary provide a natural solution to this problem. Here, we study the Andreev
reflection (AR) in a planar normal metal-superconductor junction on the Weyl
semimetal surface with a pair of Fermi arcs. For a conserved transverse
momentum, the occurrence of normal reflection depends on the relative
orientation between the Fermi arcs and the normal of the junction, which is a
direct result of the disconnected Fermi arcs. Consequently, a crossover from
the suppressed to perfect AR occurs with varying the orientation of the planar
junction, giving rise to a change from double-peak to plateau structure in
conductance spectra. Moreover, such a crossover can be facilitated by imposing
a magnetic field, making electrons slide along the Fermi arcs so as to switch
between two regimes of the AR. Our results provide a decisive signature for the
detection of Fermi arcs and open the possibilities of exploring novel
phenomenology through their interplay with superconductivity.


  The probabilistic study of effective interface models has been quite active
in recent years, with a particular emphasis on the effect of various external
potentials (wall, pinning potential, ...) leading to
localization/delocalization transitions. I review some of the results that have
been obtained. In particular, I discuss pinning by a local potential, entropic
repulsion and the (pre)wetting transition, both for models with continuous and
discrete heights.


  In the current work, we report the investigation of RbLn$_2$Fe$_4$As$_4$O$_2$
(Ln = Tb, Dy and Ho) and RbFe$_2$As$_2$ by $^{57}$Fe M\"ossbauer spectroscopy.
Singlet pattern has been observed for all the samples indicating the absence of
static magnetic ordering down to 5.9\,K on the Fe sublattice. The observed
intermediate value of the isomer shift confirms the effective self charge
transfer effect for the studied superconductors. Debye temperatures of these
samples have been determined by the temperature dependence of the isomer shift.
Most importantly, we observe different spectral line width broadening behaviors
for samples with different rare earth elements, and no line width broadenings
for samples Ln=Tb and Ho. These results suggest that the observed magnetic
fluctuations at the Fe site might be sensitive to the magnetic behaviors of the
rare earth magnetic moments.


  A tetrahedral complex all of whose tetrahedra meet at a common vertex is
called a \textit{vertex star}. Vertex stars are a natural generalization of
planar triangulations, and understanding splines on vertex stars is a crucial
step to analyzing trivariate splines. It is particularly difficult to compute
the dimension of splines on vertex stars in which the vertex is completely
surrounded by tetrahedra -- we call these \textit{closed} vertex stars. A
formula due to Alfeld, Neamtu, and Schumaker gives the dimension of $C^r$
splines on closed vertex stars of degree at least $3r+2$. We show that this
formula is a lower bound on the dimension of $C^r$ splines of degree at least
$(3r+2)/2$. Our proof uses apolarity and the so-called \textit{Waldschmidt
constant} of the set of points dual to the interior faces of the vertex star.
We also use an argument of Whiteley to show that the only splines of degree at
most $(3r+1)/2$ on a generic closed vertex star are global polynomials.


  We show how a minimal (littlest) seesaw model involving two right-handed
neutrinos and a very constrained Dirac mass matrix, with one texture zero and
two independent Dirac masses, may arise from $S_4\times U(1)$ symmetry in a
semi-direct supersymmetric model. The resulting CSD3 form of neutrino mass
matrix only depends on two real mass parameters plus one undetermined phase. We
show how the phase may be fixed to be one of the cube roots of unity by
extending the $S_4\times U(1)$ symmetry to include a product of $Z_3$ factors
together with a CP symmetry, which is spontaneously broken leaving a single
residual $Z_3$ in the charged lepton sector and a residual $Z_2$ in the
neutrino sector, with suppressed higher order corrections. With the phase
chosen from the cube roots of unity to be $-2\pi/3$, the model predicts a
normal neutrino mass hierarchy with $m_1=0$, reactor angle
$\theta_{13}=8.7^\circ$, solar angle $\theta_{12}=34^\circ$, atmospheric angle
$\theta_{23}=44^\circ$, and CP violating oscillation phase $\delta_{\rm
CP}=-93^\circ$, depending on the fit of the model to the neutrino masses.


  We propose a method to infer semantic segmentation maps from images captured
under adverse weather conditions. We begin by examining existing models on
images degraded by weather conditions such as rain, fog, or snow, and found
that they exhibit a large performance drop as compared to those captured under
clear weather. To control for changes in scene structures, we propose
WeatherProof, the first semantic segmentation dataset with accurate clear and
adverse weather image pairs that share an underlying scene. Through this
dataset, we analyze the error modes in existing models and found that they were
sensitive to the highly complex combination of different weather effects
induced on the image during capture. To improve robustness, we propose a way to
use language as guidance by identifying contributions of adverse weather
conditions and injecting that as "side information". Models trained using our
language guidance exhibit performance gains by up to 10.2% in mIoU on
WeatherProof, up to 8.44% in mIoU on the widely used ACDC dataset compared to
standard training techniques, and up to 6.21% in mIoU on the ACDC dataset as
compared to previous SOTA methods.


  I use Unified Spinor Fields (USF), to discuss the creation of magnetic
monopoles during preinflation, as excitations of the quantum vacuum coming from
a condensate of massive charged vector bosons. For a primordial universe with
total energy $M_p$, and for magnetic monopoles created with a total Planck
magnetic charge $q_M=q_P=\pm e/\sqrt{\alpha}$ and a total mass $m_M$, it is
obtained after quantisation of the action that the fine-structure constant is
given by: $\alpha= \frac{5}{6} \left(1- \frac{16 \,m_M}{5 \,M_p}\right)
\,\left(\frac{e}{q_M}\right)^2$. If these magnetic monopoles were with total
magnetic charge $q_M=\pm e$ and a small mass $m=m_M/n$, there would be a large
number of small quantum magnetic monopoles which could be candidates to explain
the presence of dark matter with a $30.97\,\%$ of the energy in the primordial
universe at the Planck era. The case of milli-magnetically charged particles is
also analysed. We demonstrate that magnetic monopoles (MM) with masses less
than $3.6\times 10^3$ GeV, can exist with a very small charges of up to
$10^{-14}\,e$, which are quantities of interest for searches to be performed in
the ATLAS and MoEDAL experiments.


  This study presents a theoretical model for a self-replicating mechanical
system inspired by biological processes within living cells and supported by
computer simulations. The model decomposes self-replication into core
components, each of which is executed by a single machine constructed from a
set of basic block types. Key functionalities such as sorting, copying, and
building, are demonstrated. The model provides valuable insights into the
constraints of self-replicating systems. The discussion also addresses the
spatial and timing behavior of the system, as well as its efficiency and
complexity. This work provides a foundational framework for future studies on
self-replicating mechanisms and their information-processing applications.


  A favorable population schedule for the entire potential human family is
sought, under the overlapping generations framework, by treating population (or
fertility) as a planning variable in a dynamical social welfare maximization
context. The utilitarian and maximin social welfare functions are examined,
with zero future discounting, while infinity in the maximand is circumvented by
introducing the depletion of energy resources and its postponement through
technological innovations. The model is formulated as a free-horizon dynamical
planning problem, solved via a non-linear optimizer. Under exploratory
scenarios, we visualize the potential trade-offs between the two welfare
criteria.


  In this article, we define an independence system for a classical knot
diagram and prove that the independence system is a knot invariant for
alternating knots. We also discuss the exchange property for minimal unknotting
sets. Finally, we show that there are knot diagrams where the independence
system is a matroid and there are knot diagrams where it is not.


  We give a $(2 + \epsilon)$-approximation algorithm for minimizing total
weighted completion time on a single machine under release time and precedence
constraints. This settles a recent conjecture made in [18]


  The order of the chiral phase transition of lattice QCD with unimproved
staggered fermions is known to depend on the number of quark flavours, their
masses and the lattice spacing. Previous studies in the literature for $N_f \in
\{ 3,4 \}$ show first-order transitions, which weaken with decreasing lattice
spacing. Here we investigate what happens when lattices are made coarser to
establish contact to the strong coupling region. For $N_f \in \{4,8 \}$ we find
a drastic weakening of the transition when going from $N_{\tau}=4$ to
$N_{\tau}=2$, which is consistent with a second-order chiral transition
reported in the literature for $N_f=4$ in the strong coupling limit. This
implies a non-monotonic behaviour of the critical quark or pseudo-scalar meson
mass, which separates first-order transitions from crossover behaviour, as a
function of lattice spacing.


  We provide a permutation-invariant version of the Koml\'os' theorem for
non-negative random variables. The proof is quite elementary in the sense that
it did not use the Axiom of Choice, and was based on a recent result in [3].


  Coupled multi-component $\mathbb{C}P^N$ models with V-shaped potentials are
analyzed. It is shown that the model has solutions being combinations of
compact Q-balls and Q-shells. The compact nature of solutions permits the
existence of novel harbor-type solutions having the form of Q-balls sheltered
by Q-shells. The relation between the energy $E$ and Noether charge $Q$ is
discussed both analytically and numerically. The energy of the solutions
behaves as $E\sim |Q|^\alpha,~\alpha<1$, i.e., as for the standard Q-ball.
Furthermore, the ratio $E/Q$ for various configurations in the multi-component
model suggests that the solutions are at least classically stable.


  We prove a semi-Riemannian version of the celebrated Morse Index Theorem for
geodesics in semi-Riemannian manifolds; we consider the general case of both
endpoints variable on two submanifolds. The key role of the theory is played by
the notion of the {\em Maslov index} of a semi-Riemannian geodesic, which is a
homological invariant and it substitutes the notion of geometric index in
Riemannian geometry. Under generic circumstances, the Maslov index of a
geodesic is computed as a sort of {\em algebraic count} of the conjugate points
along the geodesic. For non positive definite metrics the index of the index
form is always infinite; in this paper we prove that the space of all
variations of a given geodesic has a {\em natural} splitting into two infinite
dimensional subspaces, and the Maslov index is given by the difference of the
index and the coindex of the restriction of the index form to these subspaces.
In the case of variable endpoints, two suitable correction terms, defined in
terms of the endmanifolds, are added to the equality. Using appropriate change
of variables, the theory is entirely extended to the more general case of {\em
symplectic differential systems}, that can be obtained as linearizations of the
Hamilton equations.


  Text-driven motion generation has achieved substantial progress with the
emergence of diffusion models. However, existing methods still struggle to
generate complex motion sequences that correspond to fine-grained descriptions,
depicting detailed and accurate spatio-temporal actions. This lack of fine
controllability limits the usage of motion generation to a larger audience. To
tackle these challenges, we present FineMoGen, a diffusion-based motion
generation and editing framework that can synthesize fine-grained motions, with
spatial-temporal composition to the user instructions. Specifically, FineMoGen
builds upon diffusion model with a novel transformer architecture dubbed
Spatio-Temporal Mixture Attention (SAMI). SAMI optimizes the generation of the
global attention template from two perspectives: 1) explicitly modeling the
constraints of spatio-temporal composition; and 2) utilizing sparsely-activated
mixture-of-experts to adaptively extract fine-grained features. To facilitate a
large-scale study on this new fine-grained motion generation task, we
contribute the HuMMan-MoGen dataset, which consists of 2,968 videos and 102,336
fine-grained spatio-temporal descriptions. Extensive experiments validate that
FineMoGen exhibits superior motion generation quality over state-of-the-art
methods. Notably, FineMoGen further enables zero-shot motion editing
capabilities with the aid of modern large language models (LLM), which
faithfully manipulates motion sequences with fine-grained instructions. Project
Page: https://mingyuan-zhang.github.io/projects/FineMoGen.html


  We present a simulation probing the formation of water in the remnant of
low-mass Population III supernovae in a cosmological minihalo, and provide a
tentative lower mass limit on host minihaloes that can recollapse on a short
enough timescale and efficiently mix metals at high densities. We start from
cosmological initial conditions and end the simulation when the central density
undergoes catastrophic recollapse, whereby the water abundance is reported.
During the Population III stars lifetime, the minihalo (M$ = 5 \times 10^5$
M$_{\odot}$) becomes blown out, and consequently the faint supernova explosion
(E$_{\mathrm{SN}} = 5\times 10^{50}$ ergs) is completely unconfined to the
virial radius of the minihalo. At the end of the simulation there is no
significant water formation anywhere throughout the remnant, and the central
recollapsing region is inefficient at incorporating the first metals into
itself, remaining at low metallicity. The majority of metals are ejected from
the core via bipolar outflow into the void and reach a peak metallicity of
$\mathrm{Z} \sim 10^{-6}\ \mathrm{Z}_{\odot}$ at very low densities. The mass
of the minihalo is low enough such that the recollapse timescale is
unreasonable for this configuration to be the primary avenue of water formation
in the early universe. We also provide a comparison with a regular CCSN
(E$_{\mathrm{SN}} = 10^{51}$ ergs) and find the same effect, but amplified. As
such, we can suggest that the minimum minihalo mass required for a confined
explosion, and therefore the possibility of water formation is at least
$10^{6}$ M$_{\odot}$ and the chemo-thermal evolution of a supernova remnant is
more sensitive to the mass of the host minihalo than the mass of the Population
III star residing within it.


  This essay looks at decision-making with interval-valued probability
measures. Existing decision methods have either supplemented expected utility
methods with additional criteria of optimality, or have attempted to supplement
the interval-valued measures. We advocate a new approach, which makes the
following questions moot: 1. which additional criteria to use, and 2. how wide
intervals should be. In order to implement the approach, we need more
epistemological information. Such information can be generated by a rule of
acceptance with a parameter that allows various attitudes toward error, or can
simply be declared. In sketch, the argument is: 1. probability intervals are
useful and natural in All. systems; 2. wide intervals avoid error, but are
useless in some risk sensitive decision-making; 3. one may obtain narrower
intervals if one is less cautious; 4. if bodies of knowledge can be ordered by
their caution, one should perform the decision analysis with the acceptable
body of knowledge that is the most cautious, of those that are useful. The
resulting behavior differs from that of a behavioral probabilist (a Bayesian)
because in the proposal, 5. intervals based on successive bodies of knowledge
are not always nested; 6. if the agent uses a probability for a particular
decision, she need not commit to that probability for credence or future
decision; and 7. there may be no acceptable body of knowledge that is useful;
hence, sometimes no decision is mandated.


  We develop a Bayesian hierarchical model to identify communities in networks
for which we do not observe the edges directly, but instead observe a series of
interdependent signals for each of the nodes. Fitting the model provides an
end-to-end community detection algorithm that does not extract information as a
sequence of point estimates but propagates uncertainties from the raw data to
the community labels. Our approach naturally supports multiscale community
detection as well as the selection of an optimal scale using model comparison.
We study the properties of the algorithm using synthetic data and apply it to
daily returns of constituents of the S&P100 index as well as climate data from
US cities.


  Hydrogen can be produced from water, using electricity. The hydrogen can
subsequently be kept in inventory in large quantities, unlike the electricity
itself. This enables solar and wind energy generation to occur asynchronously
from its usage. For this reason, hydrogen is expected to be a key ingredient
for reaching a climate-neutral economy. However, the logistics for hydrogen are
complex. Inventory policies must be determined for multiple locations in the
network, and transportation of hydrogen from the production location to
customers must be scheduled. At the same time, production patterns of hydrogen
are intermittent, which affects the possibilities to realize the planned
transportation and inventory levels. To provide policies for efficient
transportation and storage of hydrogen, this paper proposes a parameterized
cost function approximation approach to the stochastic cyclic inventory routing
problem. Firstly, our approach includes a parameterized mixed integer
programming (MIP) model which yields fixed and repetitive schedules for vehicle
transportation of hydrogen. Secondly, buying and selling decisions in case of
underproduction or overproduction are optimized further via a Markov decision
process (MDP) model, taking into account the uncertainties in production and
demand quantities. To jointly optimize the parameterized MIP and the MDP model,
our approach includes an algorithm that searches the parameter space by
iteratively solving the MIP and MDP models. We conduct computational
experiments to validate our model in various problem settings and show that it
provides near-optimal solutions. Moreover, we test our approach on an
expert-reviewed case study at two hydrogen production locations in the
Netherlands. We offer insights for the stakeholders in the region and analyze
the impact of various problem elements in these case studies.


  In this review we discuss and extend the study of the inclusive production of
vector quarkonia, $J/\psi$ and $\Upsilon$, emitted with large transverse
momenta and rapidities at the LHC. We adopt the novel ZCW19$^+$ determination
to depict the quarkonium production mechanism at the next-to-leading level of
perturbative QCD. This approach is based on the nonrelativistic QCD formalism
well adapted to describe the production of a quarkonium state from the
collinear fragmentation of a gluon or a constituent heavy quark at the lowest
energy scale. We rely upon the NLL/NLO$^+$ hybrid high-energy and collinear
factorization for differential cross sections, where the standard collinear
formalism is enhanced by the BFKL resummation of next-to-leading energy
logarithms arising in the $t$-channel. We employ the JETHAD method to analyze
the behavior of rapidity distributions for double inclusive vector-quarkonium
and inclusive vector-quarkonium plus jet emissions. We discovered that the
natural stability of the high-energy series, previously observed in observables
sensitive to the emission of hadrons with heavy flavor detected in the rapidity
acceptance of LHC barrel calorimeters, becomes even more manifest when these
particles are tagged in forward regions covered by endcaps. Our findings brace
the important message that vector quarkonia at the LHC via the hybrid
factorization offer a unique chance to perform precision studies of high-energy
QCD, as well as an intriguing opportunity to shed light on the quarkonium
production puzzle.


  Currently the most precise LHC measurements of the top quark mass are
determinations of the top quark mass parameter of Monte-Carlo (MC) event
generators reaching uncertainties of well below $1$ GeV. However, there is an
additional theoretical problem when using the MC top mass $m_t^{\rm MC}$ as an
input for theoretical predictions, because a rigorous relation of $m_t^{\rm
MC}$ to a renormalized field theory mass is, at the very strict level, absent.
In this talk I show how - nevertheless - some concrete statements on $m_t^{\rm
MC}$ can be deduced assuming that the MC generator behaves like a rigorous
first principles QCD calculator for the observables that are used for the
analyses. I give simple conceptual arguments showing that in this context
$m_t^{\rm MC}$ can be interpreted like the mass of a heavy-light top meson, and
that there is a conversion relation to field theory top quark masses that
requires a non-perturbative input. The situation is in analogy to B physics
where a similar relation exists between experimental B meson masses and field
theory bottom masses. The relation gives a prescription how to use $m_t^{\rm
MC}$ as an input for theoretical predictions in perturbative QCD. The outcome
is that at this time an additional uncertainty of about $1$ GeV has to be
accounted for. I discuss limitations of the arguments I give and possible ways
to test them, or even to improve the current situation.


  We formulate a set of mass relations for the baryon octet and decuplet with
positive and negative parity in terms of the order parameter of QCD chiral
symmetry. The Gell-Mann--Okubo mass formula and Gell-Mann's equal spacing rule
hold manifestly in this approach. Thermal masses of the baryons are calculated
in the mean field approximation for various pion masses, and the results are
compared with the recent lattice studies. A general trend of the nucleon,
$\Delta$ and $\Omega$ parity-doublers seen in the available lattice data can be
understood qualitatively. Expected mass modifications of other strange baryons
are also given with the physical and heavier pion masses.


  Domain experts often rely on most recent knowledge for apprehending and
disseminating specific biological processes that help them design strategies
for developing prevention and therapeutic decision-making in various disease
scenarios. A challenging scenarios for artificial intelligence (AI) is using
biomedical data (e.g., texts, imaging, omics, and clinical) to provide
diagnosis and treatment recommendations for cancerous conditions.~Data and
knowledge about biomedical entities like cancer, drugs, genes, proteins, and
their mechanism is spread across structured (knowledge bases (KBs)) and
unstructured (e.g., scientific articles) sources. A large-scale knowledge graph
(KG) can be constructed by integrating and extracting facts about semantically
interrelated entities and relations. Such a KG not only allows exploration and
question answering (QA) but also enables domain experts to deduce new
knowledge. However, exploring and querying large-scale KGs is tedious for
non-domain users due to their lack of understanding of the data assets and
semantic technologies. In this paper, we develop a domain KG to leverage
cancer-specific biomarker discovery and interactive QA. For this, we
constructed a domain ontology called OncoNet Ontology (ONO), which enables
semantic reasoning for validating gene-disease (different types of cancer)
relations. The KG is further enriched by harmonizing the ONO, metadata,
controlled vocabularies, and biomedical concepts from scientific articles by
employing BioBERT- and SciBERT-based information extractors. Further, since the
biomedical domain is evolving, where new findings often replace old ones,
without having access to up-to-date scientific findings, there is a high chance
an AI system exhibits concept drift while providing diagnosis and treatment.
Therefore, we fine-tune the KG using large language models (LLMs) based on more
recent articles and KBs.


  We experimentally demonstrate intensity amplification of repetitive
picosecond optical pulses with an input-to-output gain up to 5.5 dB using a
passive Talbot amplifier. Through the dispersion-induced temporal Talbot
effect, the amplifier uses electro-optic phase modulation and a low-loss
dispersive medium to exploit and coherently redistribute the energy of the
original pulse train into fewer, replica, amplified pulses. In addition, we
show how our passive amplifier mitigates the pulse train timing-jitter and
pulse-to-pulse intensity fluctuations above a specific cutoff frequency.


  Let G be a connected linear semisimple Lie group with Lie algebra g and
maximal compact subgroup K. Let K_C -> Aut(p_C) be the complexified isotropy
representation at the identity coset of the corresponding symmetric space.
Suppose that O is a nilpotent K_C-orbit in p_C, and bar(O} is its Zariski
closure in p_C. We study the K-type decomposition of the ring of regular
functions on bar(O} when O is spherical and ``small''. We also show that this
decomposition gives the asymptotic directions of K-types in any irreducible
(g_C, K)-module whose associated variety is bar(O).


  Once integrated into clinical care, patient risk stratification models may
perform worse compared to their retrospective performance. To date, it is
widely accepted that performance will degrade over time due to changes in care
processes and patient populations. However, the extent to which this occurs is
poorly understood, in part because few researchers report prospective
validation performance. In this study, we compare the 2020-2021 ('20-'21)
prospective performance of a patient risk stratification model for predicting
healthcare-associated infections to a 2019-2020 ('19-'20) retrospective
validation of the same model. We define the difference in retrospective and
prospective performance as the performance gap. We estimate how i) "temporal
shift", i.e., changes in clinical workflows and patient populations, and ii)
"infrastructure shift", i.e., changes in access, extraction and transformation
of data, both contribute to the performance gap. Applied prospectively to
26,864 hospital encounters during a twelve-month period from July 2020 to June
2021, the model achieved an area under the receiver operating characteristic
curve (AUROC) of 0.767 (95% confidence interval (CI): 0.737, 0.801) and a Brier
score of 0.189 (95% CI: 0.186, 0.191). Prospective performance decreased
slightly compared to '19-'20 retrospective performance, in which the model
achieved an AUROC of 0.778 (95% CI: 0.744, 0.815) and a Brier score of 0.163
(95% CI: 0.161, 0.165). The resulting performance gap was primarily due to
infrastructure shift and not temporal shift. So long as we continue to develop
and validate models using data stored in large research data warehouses, we
must consider differences in how and when data are accessed, measure how these
differences may affect prospective performance, and work to mitigate those
differences.


  We define a weighted multiplicity function for closed geodesics of given
length on a finite area Riemann surface. These weighted multiplicities appear
naturally in the Selberg trace formula, and in particular their mean square
plays an important role in the study of statistics of the eigenvalues of the
Laplacian on the surface.
  In the case of the modular domain, E. Bogomolny, F. Leyvraz and C. Schmit
gave a formula for the mean square, which was rigorously proved by M. Peter. In
this paper we calculate the mean square of weighted multiplicities for some
surfaces associated to congruence subgroups of the unit group of a rational
quaternion algebra, in particular for congruence subgroups of the modular
group. Remarkably, the result turns out to be a rational multiple of the mean
square for the modular domain.


  Single-photon devices at microwave frequencies are important for applications
in quantum information processing and communication in the microwave regime. In
this work, we describe a proposal of a multi-output single-photon device. We
consider two superconducting resonators coupled to a gap-tunable qubit via both
its longitudinal and transverse degrees of freedom. Thus, this qubit-resonator
coupling differs from the coupling in standard circuit quantum-electrodynamic
systems described by the Jaynes-Cummings model. We demonstrate that an
effective quadratic coupling between one of the normal modes and the qubit can
be induced, and this induced second-order nonlinearity is much larger than that
for conventional Kerr-type systems exhibiting photon blockade. Assuming that a
coupled normal mode is resonantly driven, we observe that the output fields
from the resonators exhibit strong sub-Poissonian photon-number statistics and
photon antibunching. Contrary to previous studies on resonant photon blockade,
the first-excited state of our device is a pure single-photon Fock state rather
than a polariton state, i.e., a highly hybridized qubit-photon state. In
addition, it is found that the optical state truncation caused by the strong
qubit-induced nonlinearity can lead to an entanglement between the two
resonators, even in their steady state under the Markov approximation.


  Active galactic nuclei (AGNs) exhibit variability across the entire
electromagnetic spectrum with distinct flaring episodes at different
frequencies. The high sensitivity and nearly uniform sky coverage of the Large
Area Telescope on board the Fermi satellite make it a powerful tool for
monitoring a large number of AGNs over long timescales. This allowed us to
detect several flaring AGNs in gamma rays, triggering dedicated multifrequency
campaigns on these sources from radio to TeV energies. We discuss the results
for two different types of flaring AGN: the flat spectrum radio quasar 3C 279,
in particular the coincidence of a gamma-ray flare from this source with the
drastic change of the optical polarization angle, and the first gamma-ray flare
from a radio-loud narrow-line Seyfert 1, PMN J0948+0022.


  We present an attempt to measure the large angular scale fluctuations in the
X-Ray Background (XRB) from the HEAO1-A2 data, expressed in terms of spherical
harmonics. We model the harmonic coefficients assuming a power spectrum and an
epoch-dependent bias parameter, and using a phenomenological scenario
describing the evolution of the X-ray sources. From the few low-order
multipoles detected above shot noise, we estimate the power-spectrum
normalization on scales intermediate between those explored by local galaxy
redshift surveys (~ 100 Mpc) and by the COBE Microwave Background measurements
(~ 1000 Mpc). We find that the HEAO1 harmonics are consistent with present
epoch rms fluctuations of the X-ray sources bx(0)sigma8 ~ 1-2 in 8 Mpc spheres.
Therefore the observed fluctuations in the XRB are roughly as expected from
interpolating between the local galaxy surveys and the COBE CMB experiment. We
predict that an X-ray all-sky surface brightness survey resolving sources a
factor of 10 fainter than HEAO1, may reveal fluctuations to significantly
larger angular scales and therefore more strongly constrain the large scale
structure of the Universe on scales of hundreds of Mpcs.


  We first consider the sequential detection of transient signals by
generalizing the moving average chart to exponential family and study the false
detection probability (FDP) and power of detection (POD) in the steady state.
Then windowed adjusted signed (or modified directed) likelihood ratio chart is
studied by treating it as normal random variable. In the multi-parameter
exponential family, the detection of the transient change of one of the
canonical parameters or a function of canonical parameters is considered by
using the generalized adjusted signed likelihood ratio chart. Comparisons with
window restricted CUSUM and Shiryayev-Roberts (S-R) procedures show that the
generalized signed likelihood ratio chart performs quite well. Several
important examples including the mean or variance change under normal model and
a real example are used for illustration.


  In a recent paper on SU(16) grand unification, because of the presence of
intermediate-energy gauge groups containing products of U(1) factors which are
not orthogonal among themselves, the renormalization-group treatment has a few
small errors. I correct it. I emphasize that one should not switch gauge
couplings at the various thresholds. It is easier, and it avoids errors, to use
throughout the gauge couplings of the standard model, and compute at each
threshold, in the usual way, the extra contributions to the beta functions from
the extra non-decoupled fields. I also point out that the SU(16) grand
unification theory, due to the large number of scalars present in it, is not
asymptotically free. It becomes a strong-coupling theory at energies only
slightly larger than the unification scale.


  We consider negotiation settings in which two agents use natural language to
bargain on goods. Agents need to decide on both high-level strategy (e.g.,
proposing \$50) and the execution of that strategy (e.g., generating "The bike
is brand new. Selling for just \$50."). Recent work on negotiation trains
neural models, but their end-to-end nature makes it hard to control their
strategy, and reinforcement learning tends to lead to degenerate solutions. In
this paper, we propose a modular approach based on coarse di- alogue acts
(e.g., propose(price=50)) that decouples strategy and generation. We show that
we can flexibly set the strategy using supervised learning, reinforcement
learning, or domain-specific knowledge without degeneracy, while our
retrieval-based generation can maintain context-awareness and produce diverse
utterances. We test our approach on the recently proposed DEALORNODEAL game,
and we also collect a richer dataset based on real items on Craigslist. Human
evaluation shows that our systems achieve higher task success rate and more
human-like negotiation behavior than previous approaches.


  In this paper we show how to relate European call and put options on multiple
assets to certain convex bodies called lift zonoids. Based on this, geometric
properties can be translated into economic statements and vice versa. For
instance, the European call-put parity corresponds to the central symmetry
property, while the concept of dual markets can be explained by reflection with
respect to a plane. It is known that the classical univariate log-normal model
belongs to a large class of distributions with an extra property, analytically
known as put-call symmetry. The geometric interpretation of this symmetry
property motivates a natural multivariate extension. The financial meaning of
this extension is explained, the asset price distributions that have this
property are characterised and their further properties explored. It is also
shown how to relate some multivariate asymmetric distributions to symmetric
ones by a power transformation that is useful to adjust for carrying costs. A
particular attention is devoted to the case of asset prices driven by L\'evy
processes. Based on this, semi-static hedging techniques for multiasset barrier
options are suggested.


  Two-dimensional (2D) hexagonal boron nitride (hBN) is a wide-bandgap van der
Waals crystal with a unique combination of properties, including exceptional
strength, large oxidation resistance at high temperatures and optical
functionalities. Furthermore, in recent years hBN crystals have become the
material of choice for encapsulating other 2D crystals in a variety of
technological applications, from optoelectronic and tunnelling devices to
composites. Monolayer hBN, which has no center of symmetry, has been predicted
to exhibit piezoelectric properties, yet experimental evidence is lacking.
Here, by using electrostatic force microscopy, we observed this effect as a
strain-induced change in the local electric field around bubbles and creases,
in agreement with theoretical calculations. No piezoelectricity was found in
bilayer and bulk hBN, where the centre of symmetry is restored. These results
add piezoelectricity to the known properties of monolayer hBN, which makes it a
desirable candidate for novel electromechanical and stretchable optoelectronic
devices, and pave a way to control the local electric field and carrier
concentration in van der Waals heterostructures via strain. The experimental
approach used here also shows a way to investigate the piezoelectric properties
of other materials on the nanoscale by using electrostatic scanning probe
techniques.


  Quantum systems whose classical counterparts are chaotic typically have
highly correlated eigenvalues and level statistics that coincide with those
from ensembles of full random matrices. A dynamical manifestation of these
correlations comes in the form of the so-called correlation hole, which is a
dip below the saturation point of the survival probability's time evolution. In
this work, we study the correlation hole in the spin-boson (Dicke) model, which
presents a chaotic regime and can be realized in experiments with ultracold
atoms and ion traps. We derive an analytical expression that describes the
entire evolution of the survival probability and allows us to determine the
timescales of its relaxation to equilibrium. This expression shows remarkable
agreement with our numerical results. While the initial decay and the time to
reach the minimum of the correlation hole depend on the initial state, the
dynamics beyond the hole up to equilibration is universal. We find that the
relaxation time of the survival probability for the Dicke model increases
linearly with system size.


  We give a full classification of continuous flexible discrete axial
cone-nets, which are called axial C-hedra. The obtained result can also be used
to construct their semi-discrete analogs. Moreover, we identify a novel
subclass within the determined class of (semi-)discrete axial cone-nets, whose
members are named axial P-nets as they fulfill the proportion (P) of the
intercept theorem. Known special cases of these axial P-nets are the smooth and
discrete conic crease patterns with reflecting rule lines. By using a
parallelism operation one can even generalize axial P-nets. The resulting
general P-nets constitute a rich novel class of continuous flexible
(semi-)discrete surfaces, which allow direct access to their spatial shapes by
three control polylines. This intuitive method makes them suitable for
transformable design tasks using interactive tools.


  We study the voter model and related random-copying processes on arbitrarily
complex network structures. Through a representation of the dynamics as a
particle reaction process, we show that a quantity measuring the degree of
order in a finite system is, under certain conditions, exactly governed by a
universal diffusion equation. Whenever this reduction occurs, the details of
the network structure and random-copying process affect only a single parameter
in the diffusion equation. The validity of the reduction can be established
with considerably less information than one might expect: it suffices to know
just two characteristic timescales within the dynamics of a single pair of
reacting particles. We develop methods to identify these timescales, and apply
them to deterministic and random network structures. We focus in particular on
how the ordering time is affected by degree correlations, since such effects
are hard to access by existing theoretical approaches.


  We construct the open string boundary states corresponding to various
time-dependent deformations of the D-brane and explore several ways in which
they may be used to study stringy soliton collective coordinate quantum
dynamics. Among other things, we find that D-strings have exact moduli
corresponding to arbitrary chiral excitations of the basic soliton. These are
presumably the duals of the BPS-saturated excitations of the fundamental Type
IIB string. These first steps in a systematic study of the dynamics and
interactions of Dirichlet-brane solitons give further evidence of the
consistency of Polchinski's new approach to string soliton physics.


  The acquisition and evaluation of pavement surface data play an essential
role in pavement condition evaluation. In this paper, an efficient and
effective end-to-end network for automatic pavement crack segmentation, called
RHA-Net, is proposed to improve the pavement crack segmentation accuracy. The
RHA-Net is built by integrating residual blocks (ResBlocks) and hybrid
attention blocks into the encoder-decoder architecture. The ResBlocks are used
to improve the ability of RHA-Net to extract high-level abstract features. The
hybrid attention blocks are designed to fuse both low-level features and
high-level features to help the model focus on correct channels and areas of
cracks, thereby improving the feature presentation ability of RHA-Net. An image
data set containing 789 pavement crack images collected by a self-designed
mobile robot is constructed and used for training and evaluating the proposed
model. Compared with other state-of-the-art networks, the proposed model
achieves better performance and the functionalities of adding residual blocks
and hybrid attention mechanisms are validated in a comprehensive ablation
study. Additionally, a light-weighted version of the model generated by
introducing depthwise separable convolution achieves better a performance and a
much faster processing speed with 1/30 of the number of U-Net parameters. The
developed system can segment pavement crack in real-time on an embedded device
Jetson TX2 (25 FPS). The video taken in real-time experiments is released at
https://youtu.be/3XIogk0fiG4.


  We prove that every trajectory of a polynomial vector field on the complex
projective plane accumulates to the singular locus of the vector field. This
statement represents a holomorphic version of the Poincare-Bendixson theorem
and solves the complex analytic counterpart of Hilbert's 16th problem. The main
result can be also reformulated as the nonexistence of "exceptional minimals"
of holomorphic foliations on $\pp^2$ and, in particular, implies the
nonexistence of real analytic Levi flat hypersurfaces in the complex projective
plane. Finally, we describe (in the first approximation) the way a minimal
complex trajectory approaches the singular locus of the vector field.


  The consumption of online videos on the Internet grows every year, making it
a market that increasingly generates a greater volume of income. This paper
deals with a problem of great interest in this context: the allocation of the
generated revenues in a video website between the website and the video
creators. For this, we consider a dynamic model of the revenues generation. We
will consider that revenue can come from two sources: through the pay-per-view
system and through the insertion of advertisements in the videos. Then to study
how to divide the revenues in a reasonable and fair way between the two
parties, we consider a dynamic cooperative game that reflects the importance of
each part in generating revenue. From this game, we determine how its Shapley
value is and introduce other allocation rules derived from it. We provide a
structure of algorithm to calculate the Shapley value and its derived rules. We
show that the computational complexity of the algorithms is polynomial.
Finally, we provide some illustrative examples and simulations to illustrate
how the proposed allocation rules perform.


  We use a Z_2-orbifold of the vertex operator algebra associated to the
Niemeier lattice with root lattice A_3^8 and the no-ghost theorem of string
theory to construct a generalized Kac-Moody algebra. Borcherds' theory of
automorphic products allows us to determine the simple roots and identify the
algebra with the fake baby monster Lie algebra.


  Computational simulations have the potential to assist in liver resection
surgeries by facilitating surgical planning, optimizing resection strategies,
and predicting postoperative outcomes. The modeling of liver tissue across
multiple length scales constitutes a significant challenge, primarily due to
the multiphysics coupling of mechanical response and perfusion within the
complex multiscale vascularization of the organ. In this paper, we present a
modeling framework that connects continuum poroelasticity and discrete vascular
tree structures to model liver tissue across disparate levels of the perfusion
hierarchy. The connection is achieved through a series of modeling decisions,
which include source terms in the pressure equation to model inflow from the
supplying tree, pressure boundary conditions to model outflow into the draining
tree, and contact conditions to model surrounding tissue. We investigate the
numerical behaviour of our framework and apply it to a patient-specific
full-scale liver problem that demonstrates its potential to help assess
surgical liver resection procedures


  Few-shot learning has recently attracted significant interest in drug
discovery, with a recent, fast-growing literature mostly involving convoluted
meta-learning strategies. We revisit the more straightforward fine-tuning
approach for molecular data, and propose a regularized quadratic-probe loss
based on the the Mahalanobis distance. We design a dedicated block-coordinate
descent optimizer, which avoid the degenerate solutions of our loss.
Interestingly, our simple fine-tuning approach achieves highly competitive
performances in comparison to state-of-the-art methods, while being applicable
to black-box settings and removing the need for specific episodic pre-training
strategies. Furthermore, we introduce a new benchmark to assess the robustness
of the competing methods to domain shifts. In this setting, our fine-tuning
baseline obtains consistently better results than meta-learning methods.


  Given a p-order A over a universe of strings (i.e., a transitive, reflexive,
antisymmetric relation such that if (x, y) is an element of A then |x| is
polynomially bounded by |y|), an interval size function of A returns, for each
string x in the universe, the number of strings in the interval between strings
b(x) and t(x) (with respect to A), where b(x) and t(x) are functions that are
polynomial-time computable in the length of x.
  By choosing sets of interval size functions based on feasibility requirements
for their underlying p-orders, we obtain new characterizations of complexity
classes. We prove that the set of all interval size functions whose underlying
p-orders are polynomial-time decidable is exactly #P. We show that the interval
size functions for orders with polynomial-time adjacency checks are closely
related to the class FPSPACE(poly). Indeed, FPSPACE(poly) is exactly the class
of all nonnegative functions that are an interval size function minus a
polynomial-time computable function.
  We study two important functions in relation to interval size functions. The
function #DIV maps each natural number n to the number of nontrivial divisors
of n. We show that #DIV is an interval size function of a polynomial-time
decidable partial p-order with polynomial-time adjacency checks. The function
#MONSAT maps each monotone boolean formula F to the number of satisfying
assignments of F. We show that #MONSAT is an interval size function of a
polynomial-time decidable total p-order with polynomial-time adjacency checks.
  Finally, we explore the related notion of cluster computation.


  Simulations of quantum systems in finite volume have proven to be a useful
tool for calculating physical observables. Such studies to date have focused
primarily on understanding the volume dependence of binding energies, from
which it is possible to extract asymptotic properties of the corresponding
bound state, as well as on extracting scattering information. For bound states,
all properties depend on the size of the finite volume, and for precision
studies it is important to understand such effects. In this work, we therefore
derive the volume dependence of the mean squared radius of a two-body bound
state, using a technique that can be generalized to other static properties in
the future. We test our results with explicit numerical examples and
demonstrate that we can robustly extract infinite-volume radii from
finite-volume simulations in cubic boxes with periodic boundary conditions.


  The AMIGA project (Analysis of the interstellar Medium of Isolated GAlaxies)
is an international collaboration led from the Instituto de Astrof\'isica de
Andaluc\'ia (CSIC). The group's experience in radio astronomy databases turned,
as a natural evolution, into an active participation in the development of data
archives and radio astronomy software. The contributions of the group to the VO
have been mostly oriented towards the deployment of large VO compliant
databases and the development of access interfaces (IRAM 30m Pico Veleta,
DSS-63 70m in Robledo de Chavela). We also have been working in the development
of an API for VO tools that will ease access to VO registries and communication
between different VO software. A collaboration with the Kapteyn Astronomical
Institute has started recently in order to perform a complete renovation of the
only existing high-level software (GIPSY) for the analysis of datacubes,
allowing its fully integration in the VO.


  The quasar HE 0047-1756, at z=1.67, is found to be split into two images
1.44" apart by an intervening galaxy acting as a gravitational lens. The flux
ratio for the two components is roughly 3.5:1, depending slightly upon
wavelength. The lensing galaxy is seen on images obtained at 800 nm and 2.1
\mu; there is also a nearby faint object which may be responsible for some
shear. The spectra of the two quasar images are nearly identical, but the
emission line ratio between the two components scale differently from the
continuum. Moreover, the fainter component has a bluer continuum slope than the
brighter one. We argue that these small differences are probably due to
microlensing. There are hints of an Einstein ring emanating from the brighter
image toward the fainter one.


  This paper has two aims. The first is to give a description of irreducible
tempered representations of classical p-adic groups which follows naturally the
classification of irreducible square integrable representations modulo cuspidal
data obtained by C. Moeglin and the author. The second aim of the paper is to
give description of an invariant (partially defined function) of irreducible
square integrable representation of a classical p-adic group (defined by C.
Moeglin using embeddings) in terms of subquotients of Jacquet modules. As an
application, we describe behavior of partially defined function in one
construction of square integrable representations of a bigger group from such
representations of a smaller group (which is related to deformation of Jordan
blocks of representations).


  Achieving control over chemical reaction's rate and stereoselectivity
realizes one of the Holy Grails in chemistry that can revolutionize chemical
and pharmaceutical industries. Strong light-matter interaction in optical or
nanoplasmonic cavities might provide the knob to reach such control. In this
work, we demonstrate the catalytic and selectivity control of an optical cavity
for two selected Diels-Alder cycloaddition reactions using the quantum
electrodynamics coupled cluster (QED-CC) method. Herein, we find that by
changing the molecular orientation with respect to the polarization of the
cavity mode the reactions can be significantly inhibited or selectively
enhanced to produce major endo or exo products on demand. This work highlights
the potential of utilizing quantum vacuum fluctuations of an optical cavity to
modulate the rate of Diels-Alder cycloaddition reactions and to achieve
stereoselectivity in a practical and non-intrusive way. We expect that the
present findings will be applicable to a larger set of relevant click chemical
reactions under strong light-matter coupling conditions.


  We consider dynamo action driven by three-dimensional rotating anelastic
convection in a spherical shell. Motivated by the behaviour of the solar
dynamo, we examine the interaction of hydromagnetic modes with different
symmetries and demonstrate how complicated interactions between convection,
differential rotation and magnetic fields may lead to modulation of the basic
cycle. For some parameters, Type 1 modulation occurs by the transfer of energy
between modes of different symmetries with little change in the overall
amplitude, for other parameters, the modulation is of Type 2, where the
amplitude is significantly affected (leading to grand minima in activity)
without significant changes in symmetry. Most importantly, we identify the
presence of "supermodulation" in the solutions, where the activity switches
chaotically between Type 1 and Type 2 modulation, this is believed to be an
important process in solar activity.


  We study large-scale kinematic dynamo action of steady mirror-antisymmetric
flows of incompressible fluid, that involve small spatial scales only, by
asymptotic methods of the multiscale stability theory. It turns out that, due
to the magnetic $\alpha$-effect in such flows, the large-scale mean field
experiences harmonic oscillations in time on the scale O($\varepsilon t$)
without growth or decay. Here $\varepsilon$ is the spatial scale ratio and $t$
is the fast time of the order of the flow turnover time. The interaction of the
accompanying fluctuating magnetic field with the flow gives rise to an
anisotropic magnetic eddy diffusivity, whose dependence on the direction of the
large-scale wave vector generically exhibits a singular behaviour, and thus to
negative eddy diffusivity for whichever molecular magnetic diffusivity.
Consequently, such flows always act as kinematic dynamos on the time scale
O($\varepsilon^2t$); for the directions at which eddy diffusivity is infinite,
the large-scale mean-field growth rate is finite on the scale
O($\varepsilon^{3/2}t$). We investigate numerically this dynamo mechanism for
two sample flows.


  Fast radio bursts (FRBs) are bright, millisecond-duration radio bursts of
cosmic origin. There have been several dozen FRBs found to repeat. Among them,
those precisely localized provide the best opportunity to probe their
multi-wavelength counterparts, local environment, and host galaxy that would
reveal their origins. Here we report our X-ray, ultraviolet (UV) and optical
observations with the $Swift$ satellite that were performed simultaneously in
the radio band with the Five-hundred-meter Aperture Spherical radio Telescope
(FAST) observations of the repeating FRB 20190520B, aiming at detection of
possible multi-wavelength bursts in association with radio bursts and
multi-wavelength counterpart of the persistent radio source (PRS). While a
total of 10 radio bursts were detected by FAST at the same time of $Swift$
observations, we detected neither X-ray, UV or optical bursts in accompany of
the radio bursts, nor persistent multi-wavelength counterpart of the PRS. We
obtained the energy upper limits ($3\sigma$) on any multi-wavelength bursts as
$5.03 \times 10^{47}$ erg in the hard X-ray band (15-150 keV), $7.98 \times
10^{45}$ erg in the soft X-ray band (0.3-10 keV), and $4.51 \times 10^{44}$ erg
in the U band, respectively. The energy ratio between soft X-ray (0.3-10 keV)
and radio emission of the bursts is constrained as $<6\times10^{7}$, and the
ratio between optical (U band) and radio as $<1.19\times10^{6}$. The 3$\sigma$
luminosity upper limits at the position of PRS are 1.04$\times10^{47}$ (15-150
keV), 8.81$\times10^{42}$ (0.3-10 keV), 9.26$\times10^{42}$ (UVW1), and
2.54$\times10^{42}$ erg s$^{-1}$ (U), respectively. We show that the PRS is
much more radio loud than representative pulsar wind nebulae, supernova
remnants, extended jet of Galactic X-ray binaries and ultraluminous X-ray
sources, suggestive of boosted radio emission of the PRS.


  In [L-L-Y1, III: Sec. 5.4] on mirror principle, a method was developed to
compute the integral $\int_{X}\tau^{\ast}e^{H\cdot t}\cap {\mathbf 1}_d$ for a
flag manifold $X=\Fl_{r_1, ..., r_I}({\Bbb C}^n)$ via an extended mirror
principle diagram. This method turns the required localization computation on
the augmented moduli stack $\bar{\cal M}_{0,0}(\CP^1\times X)$ of stable maps
to a localization computation on a hyper-Quot-scheme $\HQuot({\cal E}^n)$. In
this article, the detail of this localization computation on $\HQuot({\cal
E}^n)$ is carried out. The necessary ingredients in the computation, notably,
the $S^1$-fixed-point components and the distinguished ones $E_{(A;0)}$ in
$\HQuot({\cal E}^n)$, the $S^1$-equivariant Euler class of $E_{(A;0)}$ in
$\HQuot({\cal E}^n)$, and a push-forward formula of cohomology classes involved
in the problem from the total space of a restrictive flag manifold bundle to
its base manifold are given. With these, an exact expression of
$\int_{X}\tau^{\ast}e^{H\cdot t}\cap {\mathbf 1}_d$ is obtained. Comments on
the Hori-Vafa conjecture are given in the end.


  Recently we proposed a family of magic state distillation protocols that
obtains asymptotic performance that is conjectured to be optimal. This family
depends upon several codes, called "inner codes" and "outer codes." We
presented some small examples of these codes as well as an analysis of codes in
the asymptotic limit. Here, we analyze such protocols in an intermediate size
regime, using hundreds to thousands of qubits. We use BCH inner codes, combined
with various outer codes. We extend our protocols by adding error correction in
some cases. We present a variety of protocols in various input error regimes;
in many cases these protocols require significantly fewer input magic states to
obtain a given output error than previous protocols.


  In this article we consider linear codes coming from skew-symmetric
determinantal varieties, which are defined by the vanishing of minors of a
certain fixed size in the space of skew-symmetric matrices. In odd
characteristic, the minimum distances of these codes are determined and a
recursive formula for the weight of a general codeword in these codes is given.


We prove that a homogeneous bounded domain admits a Berezin quantization.


  To ensure proper functioning of a Wireless Sensor Network (WSN), it is
crucial that the network is able to detect anomalies in communication quality
(e.g., RSSI), which may cause performance degradation, so that the network can
react accordingly. In this paper, we introduce RADIUS, a lightweight system for
the purpose. The design of RADIUS is aimed at minimizing the detection error
(caused by normal randomness of RSSI) in discriminating good links from weak
links and at reaching high detection accuracy under diverse link conditions and
dynamic environment changes. Central to the design is a threshold-based
decision approach that has its foundation on the Bayes decision theory. In
RADIUS, various techniques are developed to address challenges inherent in
applying this approach. In addition, through extensive experiments, proper
configuration of the parameters involved in these techniques is identified for
an indoor environment. In a prototype implementation of the RADIUS system
deployed in an indoor testbed, the results show that RADIUS is accurate in
detecting anomalous link quality degradation for all links across the network,
maintaining a stable error rate of 6.13% on average.


  We present the results of targeted searches for gravitational-wave transients
associated with gamma-ray bursts during the second observing run of Advanced
LIGO and Advanced Virgo, which took place from 2016 November to 2017 August. We
have analyzed 98 gamma-ray bursts using an unmodeled search method that
searches for generic transient gravitational waves and 42 with a modeled search
method that targets compact-binary mergers as progenitors of short gamma-ray
bursts. Both methods clearly detect the previously reported binary merger
signal GW170817, with p-values of $<9.38 \times 10^{-6}$ (modeled) and $3.1
\times 10^{-4}$ (unmodeled). We do not find any significant evidence for
gravitational-wave signals associated with the other gamma-ray bursts analyzed,
and therefore we report lower bounds on the distance to each of these, assuming
various source types and signal morphologies. Using our final modeled search
results, short gamma-ray burst observations, and assuming binary neutron star
progenitors, we place bounds on the rate of short gamma-ray bursts as a
function of redshift for $z \leq 1$. We estimate 0.07-1.80 joint detections
with Fermi-GBM per year for the 2019-20 LIGO-Virgo observing run and 0.15-3.90
per year when current gravitational-wave detectors are operating at their
design sensitivities.


  Electroencephalogram (EEG) is a common base signal used to monitor brain
activity and diagnose sleep disorders. Manual sleep stage scoring is a
time-consuming task for sleep experts and is limited by inter-rater
reliability. In this paper, we propose an automatic sleep stage annotation
method called SleepEEGNet using a single-channel EEG signal. The SleepEEGNet is
composed of deep convolutional neural networks (CNNs) to extract time-invariant
features, frequency information, and a sequence to sequence model to capture
the complex and long short-term context dependencies between sleep epochs and
scores. In addition, to reduce the effect of the class imbalance problem
presented in the available sleep datasets, we applied novel loss functions to
have an equal misclassified error for each sleep stage while training the
network. We evaluated the proposed method on different single-EEG channels
(i.e., Fpz-Cz and Pz-Oz EEG channels) from the Physionet Sleep-EDF datasets
published in 2013 and 2018. The evaluation results demonstrate that the
proposed method achieved the best annotation performance compared to current
literature, with an overall accuracy of 84.26%, a macro F1-score of 79.66% and
Cohen's Kappa coefficient = 0.79. Our developed model is ready to test with
more sleep EEG signals and aid the sleep specialists to arrive at an accurate
diagnosis. The source code is available at
https://github.com/SajadMo/SleepEEGNet.


  We present a method for controlling a simulated humanoid to grasp an object
and move it to follow an object trajectory. Due to the challenges in
controlling a humanoid with dexterous hands, prior methods often use a
disembodied hand and only consider vertical lifts or short trajectories. This
limited scope hampers their applicability for object manipulation required for
animation and simulation. To close this gap, we learn a controller that can
pick up a large number (>1200) of objects and carry them to follow randomly
generated trajectories. Our key insight is to leverage a humanoid motion
representation that provides human-like motor skills and significantly speeds
up training. Using only simplistic reward, state, and object representations,
our method shows favorable scalability on diverse object and trajectories. For
training, we do not need dataset of paired full-body motion and object
trajectories. At test time, we only require the object mesh and desired
trajectories for grasping and transporting. To demonstrate the capabilities of
our method, we show state-of-the-art success rates in following object
trajectories and generalizing to unseen objects. Code and models will be
released.


  Convolutional Neural Networks (CNNs) are propelling advances in a range of
different computer vision tasks such as object detection and object
segmentation. Their success has motivated research in applications of such
models for medical image analysis. If CNN-based models are to be helpful in a
medical context, they need to be precise, interpretable, and uncertainty in
predictions must be well understood. In this paper, we develop and evaluate
recent advances in uncertainty estimation and model interpretability in the
context of semantic segmentation of polyps from colonoscopy images. We evaluate
and enhance several architectures of Fully Convolutional Networks (FCNs) for
semantic segmentation of colorectal polyps and provide a comparison between
these models. Our highest performing model achieves a 76.06\% mean IOU accuracy
on the EndoScene dataset, a considerable improvement over the previous
state-of-the-art.