  In this report we address the question whether aging in the non equilibrium
glassy state is controlled by the equilibrium alpha-relaxation process which
occur at temperatures above Tg. Recently Lunkenheimer et. al. [Phys. Rev. Lett.
95, 055702 (2005)] proposed a model for the glassy aging data of dielectric
relaxation using a modified Kohlrausch-Williams-Watts (KWW) form. The aging
time dependence of the relaxation time is defined by these authors through a
functional relation involving the corresponding frequency but the stretching
exponent is same as the alpha-relaxation stretching exponent. We present here
an alternative functional form directly involving the relaxation time itself.
The proposed model fits the data of Lunkenheimer et. al. perfectly with a
stretching exponent different from the alpha-relaxation stretching exponent.


  We apply the results established in arXiv:2109.15263 to prove some new
fractional Leibniz rules involving $BV^{\alpha,p}$ and $S^{\alpha,p}$
functions, following the distributional approach adopted in the previous works
arXiv:1809.08575, arXiv:1910.13419, arXiv:2011.03928. In order to achieve our
main results, we revise the elementary properties of the fractional operators
involved in the framework of Besov spaces and we rephraze the Kenig-Ponce-Vega
Leibniz-type rule in our fractional context. We apply our results to prove the
well-posedness of the boundary-value problem for a general $2\alpha$-order
fractional elliptic operator in divergence form.


  This paper shows that calculating $k$-CLIQUE on $n$ vertex graphs, requires
the AND of at least $2^{n/4k}$ monotone, constant-depth, and polynomial-sized
circuits, for sufficiently large values of $k$. The proof relies on a new,
monotone, one-sided switching lemma, designed for cliques.


  This is a mostly expository note concerning the following question: How fast
can we compute the value of an L-function at the center of the critical strip?
It is the writeup of my talk at the Matrix Ensembles and L-Functions workshop
at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK on
July 2005.


  We study the effect of external forcing on the saddle-node bifurcation
pattern of interval maps. By replacing fixed points of unperturbed maps by
invariant graphs, we obtain direct analogues to the classical result both for
random forcing by measure-preserving dynamical systems and for deterministic
forcing by homeomorphisms of compact metric spaces. Additional assumptions like
ergodicity or minimality of the forcing process then yield further information
about the dynamics. The main difference to the unforced situation is that at
the critical bifurcation parameter, two alternatives exist. In addition to the
possibility of a unique neutral invariant graph, corresponding to a neutral
fixed point, a pair of so-called pinched invariant graphs may occur. In
quasiperiodically forced systems, these are often referred to as 'strange
non-chaotic attractors'. The results on deterministic forcing can be considered
as an extension of the work of Novo, Nunez, Obaya and Sanz on nonautonomous
convex scalar differential equations. As a by-product, we also give a
generalisation of a result by Sturman and Stark on the structure of minimal
sets in forced systems.


  Statistical problems often involve linear equality and inequality constraints
on model parameters. Direct estimation of parameters restricted to general
polyhedral cones, particularly when one is interested in estimating low
dimensional features, may be challenging. We use a dual form parameterization
to characterize parameter vectors restricted to lower dimensional faces of
polyhedral cones and use the characterization to define a notion of 'sparsity'
on such cones. We show that the proposed notion agrees with the usual notion of
sparsity in the unrestricted case and prove the validity of the proposed
definition as a measure of sparsity. The identifiable parameterization of the
lower dimensional faces allows a generalization of popular spike-and-slab
priors to a closed convex polyhedral cone. The prior measure utilizes the
geometry of the cone by defining a Markov random field over the adjacency graph
of the extreme rays of the cone. We describe an efficient way of computing the
posterior of the parameters in the restricted case. We illustrate the
usefulness of the proposed methodology for imposing linear equality and
inequality constraints by using wearables data from the National Health and
Nutrition Examination Survey (NHANES) actigraph study where the daily average
activity profiles of participants exhibit patterns that seem to obey such
constraints.


  Generating combined visual and auditory sensory experiences is critical for
the consumption of immersive content. Recent advances in neural generative
models have enabled the creation of high-resolution content across multiple
modalities such as images, text, speech, and videos. Despite these successes,
there remains a significant gap in the generation of high-quality spatial audio
that complements generated visual content. Furthermore, current audio
generation models excel in either generating natural audio or speech or music
but fall short in integrating spatial audio cues necessary for immersive
experiences. In this work, we introduce SEE-2-SOUND, a zero-shot approach that
decomposes the task into (1) identifying visual regions of interest; (2)
locating these elements in 3D space; (3) generating mono-audio for each; and
(4) integrating them into spatial audio. Using our framework, we demonstrate
compelling results for generating spatial audio for high-quality videos,
images, and dynamic images from the internet, as well as media generated by
learned approaches.


  We present a probabilistic graphical model formulation for the graph
clustering problem. This enables to locally represent uncertainty of image
partitions by approximate marginal distributions in a mathematically
substantiated way, and to rectify local data term cues so as to close contours
and to obtain valid partitions.
  We exploit recent progress on globally optimal MAP inference by integer
programming and on perturbation-based approximations of the log-partition
function, in order to sample clusterings and to estimate marginal distributions
of node-pairs both more accurately and more efficiently than state-of-the-art
methods. Our approach works for any graphically represented problem instance.
This is demonstrated for image segmentation and social network cluster
analysis. Our mathematical ansatz should be relevant also for other
combinatorial problems.


  We introduce a general-purpose framework for interconnecting scientific
simulation programs using a homogeneous, unified interface. Our framework is
intrinsically parallel, and conveniently separates all component numerical
modules in memory. This strict separation allows automatic unit conversion,
distributed execution of modules on different cores within a cluster or grid,
and orderly recovery from errors. The framework can be efficiently implemented
and incurs an acceptable overhead. In practice, we measure the time spent in
the framework to be less than 1% of the wall-clock time. Due to the unified
structure of the interface, incorporating multiple modules addressing the same
physics in different ways is relatively straightforward. Different modules may
be advanced serially or in parallel. Despite initial concerns, we have
encountered relatively few problems with this strict separation between
modules, and the results of our simulations are consistent with earlier results
using more traditional monolithic approaches. This framework provides a
platform to combine existing simulation codes or develop new physical solver
codes within a rich "ecosystem" of interchangeable modules.


  A Brody curve, a.k.a. normal curve, is a holomorphic map from the complex
line to the complex projective space of dimension n, such that the family of
its translations is normal. We prove that Brody curves omitting n hyperplanes
in general position have growth order at most one, normal type. This
generalizes a result of Clunie and Hayman who proved it for n=1.


  This paper considers three different partition relations from partition
calculus, two of which are pair relations and one of which is a triple
relation. An examination of the first partition relation and the ramification
argument used to prove it will motivate questions regarding how to strengthen
it. These questions will lead to an examination of the second partition
relation and its submodel argument where the answers to those questions will
motivate further questions. The final partition relation will then be compared
to the prior two and an analysis of its strength will motivate final questions
that will guide future mathematicians who wish to prove claims about positive
or negative triple partition relations.


  I review some aspects of supersymmetric grand unification and emphasize a
recent development in the area of gauge coupling unification.


  In the application of data clustering to human-centric decision-making
systems, such as loan applications and advertisement recommendations, the
clustering outcome might discriminate against people across different
demographic groups, leading to unfairness. A natural conflict occurs between
the cost of clustering (in terms of distance to cluster centers) and the
balance representation of all demographic groups across the clusters, leading
to a bi-objective optimization problem that is nonconvex and nonsmooth. To
determine the complete trade-off between these two competing goals, we design a
novel stochastic alternating balance fair $k$-means (SAfairKM) algorithm, which
consists of alternating classical mini-batch $k$-means updates and group swap
updates. The number of $k$-means updates and the number of swap updates
essentially parameterize the weight put on optimizing each objective function.
Our numerical experiments show that the proposed SAfairKM algorithm is robust
and computationally efficient in constructing well-spread and high-quality
Pareto fronts both on synthetic and real datasets.


  In this paper, we consider the parabolic frequency for positive solutions of
two nonlinear parabolic equations under the Ricci flow on closed manifolds. We
obtain the monotonicity of parabolic frequency for the solution of two
nonlinear parabolic equations with bounded Ricci curvature, then we apply the
parabolic frequency monotonicity to get some integral type Harnack inequalities
and we use -K1 instead of the lower bound 0 of Ricci curvature from Theorem 4.3
in 16, where K1 is any positive constant.


  Bound states in the continuum (BSCs) were reported in a linear vibronic
coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev.
Lett. 90, 013001 (2003)]. It was also found that these states are destroyed
within the Born-Oppenheimer approximation (BOA). We investigate whether a
nontrivial topological or geometric phase (GP) associated with the CI is
responsible for BSCs. To address this question we explore modifications of the
original two-dimensional two-state linear vibronic coupling model supporting
BSCs. These modifications either add GP effects after the BOA or remove the GP
within a two-state problem. Using the stabilization graph technique we shown
that the GP is crucial for emergence of BSCs.


  We present the discovery of peculiar extended X-ray emission around
1E1740.7-2942, a black hole candidate that is known to produce prominent,
persistent radio jets. The data was obtained with the High-Energy Transmission
Grating Spectrometer (HETGS) aboard the Chandra X-ray Observatory. The
zeroth-order image reveals an elongated feature about 3" in length that is
roughly perpendicular to the radio lobes (or jets). The feature is roughly
symmetric about the point source. It is spatially resolved in the long
direction but not in the short direction.
  The position of 1E1740.7-2942 was determined with a statistical accuracy of
\~0.06" in the right ascension and ~0.04" in the declination, thanks to
Chandra's unprecedented spatial resolution. It is about 0.6" from the radio
position but the difference is well within the uncertainty in the absolute
aspect solutions of the observation. The dispersed HETGS spectra of
1E1740.7-2942 show evidence for the presence of weak, narrow emission lines,
although the statistics are quite limited. We discuss possible origins of the
extended emission and the implications of the emission lines.


  Mapping road networks is currently both expensive and labor-intensive.
High-resolution aerial imagery provides a promising avenue to automatically
infer a road network. Prior work uses convolutional neural networks (CNNs) to
detect which pixels belong to a road (segmentation), and then uses complex
post-processing heuristics to infer graph connectivity. We show that these
segmentation methods have high error rates because noisy CNN outputs are
difficult to correct. We propose RoadTracer, a new method to automatically
construct accurate road network maps from aerial images. RoadTracer uses an
iterative search process guided by a CNN-based decision function to derive the
road network graph directly from the output of the CNN. We compare our approach
with a segmentation method on fifteen cities, and find that at a 5% error rate,
RoadTracer correctly captures 45% more junctions across these cities.


  Lineage tracing, the determination and mapping of progeny arising from single
cells, is an important approach enabling the elucidation of mechanisms
underlying diverse biological processes ranging from development to disease. We
developed a dynamic sequence-based barcode for lineage tracing and have
demonstrated its performance in C. elegans, a model organism whose lineage tree
is well established. The strategy we use creates lineage trees based upon the
introduction of specific mutations into cells and the propagation of these
mutations to daughter cells at each cell division. We present an experimental
proof of concept along with a corresponding simulation and analytical model for
deeper understanding of the coding capacity of the system. By introducing
mutations in a predictable manner using CRISPR/Cas9, our technology will enable
more complete investigations of cellular processes.


  We report the detection of optical and X-ray variability in the least
luminous known Seyfert galaxy, NGC4395. The featureless continuum changed by a
factor of 2 in 6 months, which is typical of more luminous AGN. The largest
variation was seen at shorter wavelengths, so that the spectrum becomes
`harder' during higher activity states. In a one week optical broad band
monitoring program, a 20% change was seen between successive nights. In a 1
month period the spectral shape changed from a power law with spectral index
alpha ~0 (characteristic of quasars) to a spectral index alpha ~2 (as observed
in other dwarf AGN). ROSAT HRI and PSPC archive data show a variable X-ray
source coincident with the galactic nucleus. A change in X-ray flux by a factor
\~2 in 15 days has been observed. When compared with more luminous AGN, NGC4395
appears to be very X-ray quiet. The hardness ratio obtained from the PSPC data
suggests that the spectrum could be absorbed. We also report the discovery of
weak CaIIK absorption, suggesting the presence of a young stellar cluster
providing of the order of 10% of the blue light. Using HST UV archive data,
together with the optical and X-ray observations, we examine the spectral
energy distribution for NGC4395 and discuss the physical conditions implied by
the nuclear activity under the standard AGN model. The observations can be
explained by either an accreting massive black hole emitting at about 10^(-3)
L_(Edd) or by a single old compact SNR with an age of 50 to 500 yr generated by
a small nuclear starburst.


  Let $E$ be an elliptic curve defined over a number field $k$ and $\ell$ a
prime integer. When $E$ has at least one $k$-rational point of exact order
$\ell$, we derive a uniform upper bound $\exp(C \log B / \log \log B)$ for the
number of points of $E(k)$ of (exponential) height at most $B$. Here the
constant $C = C(k)$ depends on the number field $k$ and is effective. For $\ell
= 2$ this generalizes a result of Naccarato which applies for $k=\mathbb{Q}$.
We follow methods previously developed by Bombieri and Zannier and further by
Naccarato, with the main novelty being the application of Rosen's result on
bounding $\ell$-ranks of class groups in certain extensions, which is derived
using relative genus theory.


  Extreme value theory is part and parcel of any study of order statistics in
one dimension. Our aim here is to consider such large sample theory for the
maximum distance to the origin, and the related maximum "interpoint distance,"
in multidimensions. We show that for a family of spherically symmetric
distributions, these statistics have a Gumbel-type limit, generalizing several
existing results. We also discuss the other two types of limit laws and suggest
some open problems. This work complements our earlier study on the minimum
interpoint distance.


  This paper presents a pilot study that explores the application of active
learning, traditionally studied in the context of discriminative models, to
generative models. We specifically focus on image synthesis personalization
tasks. The primary challenge in conducting active learning on generative models
lies in the open-ended nature of querying, which differs from the closed form
of querying in discriminative models that typically target a single concept. We
introduce the concept of anchor directions to transform the querying process
into a semi-open problem. We propose a direction-based uncertainty sampling
strategy to enable generative active learning and tackle the
exploitation-exploration dilemma. Extensive experiments are conducted to
validate the effectiveness of our approach, demonstrating that an open-source
model can achieve superior performance compared to closed-source models
developed by large companies, such as Google's StyleDrop. The source code is
available at https://github.com/zhangxulu1996/GAL4Personalization.


  We study a hierarchical disordered pinning model with site disorder for
which, like in the bond disordered case [6, 9], there exists a value of a
parameter b (enters in the definition of the hierarchical lattice) that
separates an irrelevant disorder regime and a relevant disorder regime. We show
that for such a value of b the critical point of the disordered system is
different from the critical point of the annealed version of the model. The
proof goes beyond the technique used in [9] and it takes explicitly advantage
of the inhomogeneous character of the Green function of the model.


  The paper describes the usage of intelligent approaches for field development
tasks that may assist a decision-making process. We focused on the problem of
wells location optimization and two tasks within it: improving the quality of
oil production estimation and estimation of reservoir characteristics for
appropriate wells allocation and parametrization, using machine learning
methods. For oil production estimation, we implemented and investigated the
quality of forecasting models: physics-based, pure data-driven, and hybrid one.
The CRMIP model was chosen as a physics-based approach. We compare it with the
machine learning and hybrid methods in a frame of oil production forecasting
task. In the investigation of reservoir characteristics for wells location
choice, we automated the seismic analysis using evolutionary identification of
convolutional neural network for the reservoir detection. The Volve oil field
dataset was used as a case study to conduct the experiments. The implemented
approaches can be used to analyze different oil fields or adapted to similar
physics-related problems.


  We consider models of supersymmetry which can incorporate sizeable mixing
between different generations of sfermions. While the mixing is constrained by
the non-observation of various flavour changing neutral current (FCNC)
processes, there exist regions of SUSY parameter space where the effects of
such mixing can be probed at colliders. In this work, we explore this
possibility by focussing on the slepton sector. The sleptons are produced
through cascade decays in direct neutralino-chargino ($\chi_2^0\chi_1^\pm$)
pair production at the LHC. The final state is characterized by 3 leptons and
missing energy. We probe the lepton flavour violating (LFV) vertex originating
from $\chi_2^0$ decay and identify a distinct and unambiguous combination of
the tri-lepton final state which include a lepton pair with same flavour and
same sign (SFSS) in addition to a pair with opposite flavour and opposite sign
(OFOS). This combination of tri-lepton final state containing both OFOS and
SFSS pairs, can not only suppress the SM background but can also differentiate
the flavour violating decays of $\chi_2^0$ from its corresponding flavour
conserving decays. We present results for various signal benchmark points
taking into account background contributions assuming two luminosity options
(100 fb$^{-1}$ and 1000 fb$^{-1}$) for LHC Run 2 experiment.


  In this paper we study various convolution-type algebras associated with a
locally compact quantum group from cohomological and geometrical points of
view. The quantum group duality endows the space of trace class operators over
a locally compact quantum group with two products which are operator versions
of convolution and pointwise multiplication, respectively; we investigate the
relation between these two products, and derive a formula linking them.
Furthermore, we define some canonical module structures on these convolution
algebras, and prove that certain topological properties of a quantum group, can
be completely characterized in terms of cohomological properties of these
modules. We also prove a quantum group version of a theorem of Hulanicki
characterizing group amenability. Finally, we study the Radon--Nikodym property
of the $L^1$-algebra of locally compact quantum groups. In particular, we
obtain a criterion that distinguishes discreteness from the Radon--Nikodym
property in this setting.


  Results obtained by the H1 and ZEUS Collaborations on jet production in
photoproduction and deep-inelastic scattering are presented and compared to NLO
QCD models.


  In optical fiber communication, system identification (SI) for the nonlinear
Schr\"odinger equation (NLSE) has long been studied mainly for fiber
nonlinearity compensation (NLC). One recent line of inquiry to combine a
behavioral-model approach like digital backpropagation (DBP) and a data-driven
approach like neural network (NN). These works are aimed for more NLC gain;
however, by directing our attention to the learned parameters in such a SI
process, system status information, i.e., optical fiber parameters, will
possibly be extracted. Here, we show that the model-based optimization and
interpretable nature of the learned parameters in NN-based DBP enable
transmission line monitoring, fully extracting the actual in-line NLSE
parameter distributions. Specifically, we demonstrate that longitudinal loss
and dispersion profiles along a multi-span link can be obtained at once,
directly from data-carrying signals without any dedicated analog devices such
as optical time-domain reflectometry. We apply the method to a long-haul
(~2,080 km) link and various link conditions are tested, including excess loss
inserted, different fiber input power, and non-uniform level diagram. The
measurement performance is also investigated in terms of measurement range,
accuracy, and fiber launch power. These results provide a path toward
simplified and automated network management as another application of DBP.


  We study the stellar halo color properties of six nearby massive highly
inclined disk galaxies using Hubble Space Telescope Advanced Camera for Surveys
and Wide Field Camera 3 observations in both F606W and F814W filters from the
GHOSTS survey. The observed fields, placed both along the minor and major axis
of each galaxy, probe the stellar outskirts out to projected distances of ~
50-70 kpc from their galactic centre along the minor axis. The 50% completeness
levels of the color magnitude diagrams are typically at two mag below the tip
of the red giant branch. We find that all galaxies have extended stellar halos
out to ~ 50 kpc and two out to ~ 70 kpc. We determined the halo color
distribution and color profile for each galaxy using the median colors of stars
in the RGB. Within each galaxy we find variations in the median colors as a
function of radius which likely indicates population variations, reflecting
that their outskirts were built from several small accreted objects. We find
that half of the galaxies (NGC 0891, NGC 4565, and NGC 7814) present a clear
negative color gradient, reflecting a declining metallicity in their halos; the
other have no significant color or population gradient. In addition,
notwithstanding the modest sample size of galaxies, there is no strong
correlation between their halo color/metallicity or gradient with galaxy's
properties such as rotational velocity or stellar mass. The diversity in halo
color profiles observed in the GHOSTS galaxies qualitatively supports the
predicted galaxy-to-galaxy scatter in halo stellar properties; a consequence of
the stochasticity inherent in the assembling history of galaxies.


  We introduce a linear algebraic object called a bidiagonal pair. Roughly
speaking, a bidiagonal pair is a pair of diagonalizable linear transformations
on a finite-dimensional vector space, each of which acts in a bidiagonal
fashion on the eigenspaces of the other. We associate to each bidiagonal pair a
sequence of scalars called a parameter array. Using this concept of a parameter
array we present a classification of bidiagonal pairs up to isomorphism. The
statement of this classification does not explicitly mention the Lie algebra
$\SL$ or the quantum group $\uq$. However, its proof makes use of the
finite-dimensional representation theory of $\SL$ and $\uq$. In addition to the
classification we make explicit the relationship between bidiagonal pairs and
modules for $\SL$ and $\uq$.


  Willmore surfaces are the extremals of the Willmore functional (possibly
under a constraint on the conformal structure). With the characterization of
Willmore surfaces by the (possibly perturbed) harmonicity of the mean curvature
sphere congruence [Blaschke, Ejiri, Rigoli, Burstall-Calderbank], a
zero-curvature formulation follows [Burstall-Calderbank]. Deformations on the
level of harmonic maps prove to give rise to deformations on the level of
surfaces, with the definition of a spectral deformation
[Burstall-Pedit-Pinkall, Burstall-Calderbank] and of a Baecklund transformation
[Burstall-Quintino] of Willmore surfaces into new ones, with a Bianchi
permutability between the two [Burstall-Quintino]. This text is dedicated to a
self-contained account of the topic, from a conformally-invariant viewpoint, in
Darboux's light-cone model of the conformal $n$-sphere.


  We construct a categorification of parabolic Verma modules for symmetrizable
Kac-Moody algebras using KLR-like diagrammatic algebras. We show that our
construction arises naturally from a dg-enhancement of the cyclotomic quotients
of the KLR-algebras. As a consequence, we are able to recover the usual
categorification of integrable modules. We also introduce a notion of
dg-2-representation for quantum Kac--Moody algebras, and in particular of
parabolic 2-Verma module.


  We propose a novel performance metric for articulated robots with distributed
directional sensors called the sensor observability analysis (SOA). These
robot-mounted distributed directional sensors (e.g., joint torque sensors)
change their individual sensing directions as the joints move. SOA transforms
individual sensors axes in joint space to provide the cumulative sensing
quality of these sensors to observe each task-space axis, akin to forward
kinematics for sensors. For example, certain joint configurations may align
joint torque sensors in such a way that they are unable to observe interaction
forces in one or more task-space axes. The resultant sensor observability
performance metrics can then be used in optimization and in null-space control
to avoid sensor observability singular configurations or to maximize sensor
observability in particular directions. We use the specific case of force
sensing in serial robot manipulators to showcase the analysis. Parallels are
drawn between sensor observability and the traditional kinematic
manipulability; SOA is shown to be more generalizable in terms of analysing
non-joint-mounted sensors and can potentially be applied to sensor types other
than for force sensing. Simulations and experiments using a custom 3-DOF robot
and the Baxter robot demonstrate the utility and importance of sensor
observability in physical interactions.


  The text is a synthetic presentation of the state of the knowledge about the
capitulation for the class-groups of numbers fields, shortly before the
demonstration by Suzuki of the main conjecture on this question.


  A lattice polytope is "free" (or "empty") if its vertices are the only
lattice points it contains. In the context of valuation theory, Klain (1999)
proposed to study the functions $\alpha_i(P;n)$ that count the number of free
polytopes in $nP$ with $i$ vertices. For $i=1$, this is the famous Ehrhart
polynomial. For $i > 3$, the computation is likely impossible and for $i=2,3$
computationally challenging.
  In this paper, we develop a theory of coprime Ehrhart functions, that count
lattice points with relatively prime coordinates, and use it to compute
$\alpha_2(P;n)$ for unimodular simplices. We show that the coprime Ehrhart
function can be explicitly determined from the Ehrhart polynomial and we give
some applications to combinatorial counting.


  We consider the collapse behavior of cavitation bubbles near walls under high
ambient pressure conditions. Generic configurations with different stand-off
distances are investigated by numerical simulation using a fully compressible
two-phase flow solver including phase change. The results show that the
stand-off distance has significant effects on collapse dynamics, micro-jet
formation, rebound, and maximum wall pressure. A relation between cavitation
induced material damage and corresponding collapse mechanisms is obtained from
pressure-impact data at the wall. We analyze the resolution dependence of
collapse and rebound and the observed maximum pressure distributions. The
comparison of the results on six different grid resolutions shows that main
collapse features are already captured on the coarsest resolution, while the
peak pressures are strongly resolution dependent.


  The landscape of causal relations that can hold among a set of systems in
quantum theory is richer than in classical physics. In particular, a pair of
time-ordered systems can be related as cause and effect or as the effects of a
common cause, and each of these causal mechanisms can be coherent or not.
Furthermore, one can combine these mechanisms in different ways: by
probabilistically realizing either one or the other or by having both act
simultaneously (termed a physical mixture). In the latter case, it is possible
for the two mechanisms to be combined quantum-coherently. Previous work has
shown how to experimentally realize one example of each class of possible
causal relations. Here, we make a theoretical and experimental study of the
transitions between these classes. In particular, for each of the two distinct
types of coherence that can exist in mixtures of common-cause and cause-effect
relations--coherence in the individual causal pathways and coherence in the way
the causal relations are combined--we determine how it degrades under noise and
we confirm these expectations in a quantum-optical experiment.


  Sentiment analysis is attracting more and more attentions and has become a
very hot research topic due to its potential applications in personalized
recommendation, opinion mining, etc. Most of the existing methods are based on
either textual or visual data and can not achieve satisfactory results, as it
is very hard to extract sufficient information from only one single modality
data. Inspired by the observation that there exists strong semantic correlation
between visual and textual data in social medias, we propose an end-to-end deep
fusion convolutional neural network to jointly learn textual and visual
sentiment representations from training examples. The two modality information
are fused together in a pooling layer and fed into fully-connected layers to
predict the sentiment polarity. We evaluate the proposed approach on two widely
used data sets. Results show that our method achieves promising result compared
with the state-of-the-art methods which clearly demonstrate its competency.


  We present results obtained by a consideration of the non-classical energy
momentum tensor associated with Euclidean Instantons outside the event horizon
of black holes. We demonstrate here how this allows an analytic estimate to be
made of the effect of discrete quantum hair on the temperature of the black
hole, in which the role of violations of the weak energy condition associated
with instantons is made explicit, and in which the previous results of Coleman,
Preskill, and Wilczek are extended. Last, we demonstrate how the existence of a
non-classical electric field outside the event horizon of black holes,
uncovered by these authors, can be identified with a well-known effect in the
Abelian-Higgs model in two dimensions. In this case, there is a one-to-one
connection between the discrete charge of a black hole and a topological phase
in two dimensions.


  We present a neural network for predicting purchasing intent in an Ecommerce
setting. Our main contribution is to address the significant investment in
feature engineering that is usually associated with state-of-the-art methods
such as Gradient Boosted Machines. We use trainable vector spaces to model
varied, semi-structured input data comprising categoricals, quantities and
unique instances. Multi-layer recurrent neural networks capture both
session-local and dataset-global event dependencies and relationships for user
sessions of any length. An exploration of model design decisions including
parameter sharing and skip connections further increase model accuracy. Results
on benchmark datasets deliver classification accuracy within 98% of
state-of-the-art on one and exceed state-of-the-art on the second without the
need for any domain / dataset-specific feature engineering on both short and
long event sequences.


  The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng
provides a hybrid approach to the t-product based third-order tensor singular
value decomposition with the transform matrix being a factor matrix of the
higher order singular value decomposition. Continuing along this vein, this
paper explores realizing the O-SVD more efficiently by the tensor-train rank-1
decomposition and gives a truncated O-SVD. Motivated by the success of
probabilistic algorithms, we develop a randomized version of the O-SVD and
present its detailed error analysis. The new algorithm has advantages in
efficiency while keeping good accuracy compared with the current tensor
decompositions. Our claims are supported by numerical experiments on several
oriented tensors from real applications.


  We consider the problem of the limit of bio-inspired spatially extended
neuronal networks including an infinite number of neuronal types (space
locations), with space-dependent propagation delays modeling neural fields. The
propagation of chaos property is proved in this setting under mild assumptions
on the neuronal dynamics, valid for most models used in neuroscience, in a
mesoscopic limit, the neural-field limit, in which we can resolve the quite
fine structure of the neuron's activity in space and where averaging effects
occur. The mean-field equations obtained are of a new type: they take the form
of well-posed infinite-dimensional delayed integro-differential equations with
a nonlocal mean-field term and a singular spatio-temporal Brownian motion. We
also show how these intricate equations can be used in practice to uncover
mathematically the precise mesoscopic dynamics of the neural field in a
particular model where the mean-field equations exactly reduce to deterministic
nonlinear delayed integro-differential equations. These results have several
theoretical implications in neuroscience we review in the discussion.


  We present spectral energy distribution modelling of 6875 stars in omega
Centauri, obtaining stellar luminosities and temperatures by fitting literature
photometry to state-of-the-art MARCS stellar models. By comparison to four
different sets of isochrones, we provide a new distance estimate to the cluster
of 4850 +/- 200 (random) +/- 120 (systematic error) pc, a reddening of E(B-V) =
0.08 +/- 0.02 +/- 0.02 mag and a differential reddening of Delta[E(B-V)] < 0.02
mag for an age of 12 Gyr. Several new post-early-AGB candidates are also found.
Infra-red excesses of stars were used to measure total mass-loss rates for
individual stars down to ~7 x 10^-8 Msun/yr. We find a total dust mass-loss
rate from the cluster of 1.3 (+0.8/-0.5) x 10^-9 Msun/yr, with the total gas
mass-loss rate being > 1.2 (+0.6/-0.5) x 10^-6 Msun/yr. Half of the cluster's
dust production and 30% of its gas production comes from the two most extreme
stars - V6 and V42 - for which we present new Gemini/T-ReCS mid-infrared
spectroscopy, possibly showing that V42 has carbon-rich dust. The cluster's
dust temperatures are found to be typically >~550 K. Mass loss apparently does
not vary significantly with metallicity within the cluster, but shows some
correlation with barium enhancement, which appears to occur in cooler stars,
and especially on the anomalous RGB. Limits to outflow velocities, dust-to-gas
ratios for the dusty objects and the possibility of short-timescale mass-loss
variability are also discussed in the context of mass loss from low-metallicity
stars. The ubiquity of dust around stars near the RGB-tip suggests significant
dusty mass loss on the RGB; we estimate that typically 0.20--0.25 Msun of mass
loss occurs on the RGB. From observational limits on intra-cluster material, we
suggest the dust is being cleared on a timescale of <~10^5 years.


  Markov processes are omnipresent in any dimension, especially in statistical
mechanics; however their algebraic description is complete only in dimension 1
(which is often interpreted as "time"), for which linear algebra provides many
tools complementary to the probabilistic approach: in particular invariant
measures are eigenvectors. In larger dimension, such algebraic tools are
absent, in particular because boundaries are more involved. We introduce new
operadic tools to describe Markov processes in any dimension on the square
lattice. The main consequence is a natural description of probabilistic
boundary weights in terms of matrix product representations, for which we
generalize the eigenvector property of 1D invariant measures. This new approach
leads to new very interesting algebraic objects, with a local-to-global
perspective. Moreover, finite size Markov processes on the square lattice can
also be seen as a toy case of statistical Euclidean field theory: our algebraic
tools are related to other categorical approaches to field theory, with the
advantage of providing concrete computational tools.


  We study analytically and numerically the noise-induced transition between an
absorbing and an oscillatory state in a Duffing oscillator subject to
multiplicative, Gaussian white noise. We show in a non-perturbative manner that
a stochastic bifurcation occurs when the Lyapunov exponent of the linearised
system becomes positive. We deduce from a simple formula for the Lyapunov
exponent the phase diagram of the stochastic Duffing oscillator. The behaviour
of physical observables, such as the oscillator's mean energy, is studied both
close to and far from the bifurcation.


  Understanding the latent causal factors of a dynamical system from visual
observations is considered a crucial step towards agents reasoning in complex
environments. In this paper, we propose CITRIS, a variational autoencoder
framework that learns causal representations from temporal sequences of images
in which underlying causal factors have possibly been intervened upon. In
contrast to the recent literature, CITRIS exploits temporality and observing
intervention targets to identify scalar and multidimensional causal factors,
such as 3D rotation angles. Furthermore, by introducing a normalizing flow,
CITRIS can be easily extended to leverage and disentangle representations
obtained by already pretrained autoencoders. Extending previous results on
scalar causal factors, we prove identifiability in a more general setting, in
which only some components of a causal factor are affected by interventions. In
experiments on 3D rendered image sequences, CITRIS outperforms previous methods
on recovering the underlying causal variables. Moreover, using pretrained
autoencoders, CITRIS can even generalize to unseen instantiations of causal
factors, opening future research areas in sim-to-real generalization for causal
representation learning.


  We explore some properties of Lyapunov exponents of measures preserved by
smooth maps of the interval, and study the behaviour of the Lyapunov exponents
under topological conjugacy.


  We give examples of finite quantum permutation groups which arise from the
twisting construction or as bicrossed products associated to exact
factorizations in finite groups. We also give examples of finite quantum groups
which are not quantum permutation groups: one such example occurs as a split
abelian extension associated to the exact factorization $\mathbb S_4 = \mathbb
Z_4 \mathbb S_3$ and has dimension 24. We show that, in fact, this is the
smallest possible dimension that a non quantum permutation group can have.


  In this paper, we present some new inequalities for the gamma function. The
main tools are the multiple-correction method developed in our previous works,
and a generalized Mortici's lemma.


  In this note, we establish a Poincar\'e-type inequality on the hyperbolic
space $\mathbb H^n$, namely \[ \|u\|_{p} \leqslant C(n,m,p) \|\nabla^m_g
u\|_{p} \] for any $u \in W^{m,p}(\mathbb H^n)$. We prove that the sharp
constant $C(n,m,p)$ for the above inequality is \[ C(n,m,p) = \begin{cases}
\left( p p'/(n-1)^2 \right)^{m/2}&\mbox{if $m$ is even},\\ (p/(n-1))\left( p
p'/(n-1)^2\right)^{(m-1)/2} &\mbox{if $m$ is odd}, \end{cases} \] with $p' =
p/(p-1)$ and this sharp constant is never achieved in $W^{m,p}(\mathbb H^n)$.
Our proofs rely on the symmetrization method extended to hyperbolic spaces.


  The incredible generative ability of large-scale text-to-image (T2I) models
has demonstrated strong power of learning complex structures and meaningful
semantics. However, relying solely on text prompts cannot fully take advantage
of the knowledge learned by the model, especially when flexible and accurate
controlling (e.g., color and structure) is needed. In this paper, we aim to
``dig out" the capabilities that T2I models have implicitly learned, and then
explicitly use them to control the generation more granularly. Specifically, we
propose to learn simple and lightweight T2I-Adapters to align internal
knowledge in T2I models with external control signals, while freezing the
original large T2I models. In this way, we can train various adapters according
to different conditions, achieving rich control and editing effects in the
color and structure of the generation results. Further, the proposed
T2I-Adapters have attractive properties of practical value, such as
composability and generalization ability. Extensive experiments demonstrate
that our T2I-Adapter has promising generation quality and a wide range of
applications.


  Non-Hermitian Hamiltonians, which effectively describe dissipative systems,
and analogue gravity models, which simulate properties of gravitational
objects, comprise seemingly different areas of current research. Here, we
investigate the interplay between the two by relating parity-time-symmetric
dissipative Weyl-type Hamiltonians to analogue Schwarzschild black holes
emitting Hawking radiation. We show that the exceptional points of these
Hamiltonians form tilted cones mimicking the behavior of the light cone of a
radially infalling observer approaching a black hole horizon. We further
investigate the presence of tunneling processes, reminiscent of those happening
in black holes, in a concrete example model. We interpret the non-trivial
result as the purely thermal contribution to analogue Hawking radiation in a
Schwarzschild black hole. Assuming that our particular Hamiltonian models a
photonic crystal, we discuss the concrete nature of the analogue Hawking
radiation in this particular setup.


  Reflectionless potentials (RPs) represent a class of potentials that offer
total transmission in the context of one dimensional scattering. Optical
realization of RPs in stratified medium can exhibit broadband omnidirectional
antireflection property. In addition to the antireflection property, RPs are
also expected to demonstrate negative delay. We designed refractive index
profiles conforming to RPs and realize them in stratified media consisting of
Al2O3 and TiO2 heterolayers. In these structures we observed < 1% reflection
over the broad wavelength range of 350 nm to 2500 nm for angles of incidence 0
- 50 degrees. The observed reflection and transmission response of RPs are
polarization independent. A negative delay of about 31 fsec with discernible
pulse narrowing was observed in passage through two RPs. These RPs can be
interesting for optical instrumentation as broadband, omni-directional
antireflection coatings as well as in pulse control and transmission
applications like delay lines.


  Orbital variation in reflected starlight from exoplanets could eventually be
used to detect surface oceans. Exoplanets with rough surfaces, or dominated by
atmospheric Rayleigh scattering, should reach peak brightness in full phase,
orbital longitude = 180 deg, whereas ocean planets with transparent atmospheres
should reach peak brightness in crescent phase near OL = 30 deg. Application of
Fresnel theory to a planet with no atmosphere covered by a calm ocean predicts
a peak polarization fraction of 1 at OL = 74 deg; however, our model shows that
clouds, wind-driven waves, aerosols, absorption, and Rayleigh scattering in the
atmosphere and within the water column, dilute the polarization fraction and
shift the peak to other OLs. Observing at longer wavelengths reduces the
obfuscation of the water polarization signature by Rayleigh scattering but does
not mitigate the other effects. Planets with thick Rayleigh scattering
atmospheres reach peak polarization near OL = 90 deg, but clouds and Lambertian
surface scattering dilute and shift this peak to smaller OL. A shifted Rayleigh
peak might be mistaken for a water signature unless data from multiple
wavelength bands are available. Our calculations suggest that polarization
alone may not positively identify the presence of an ocean under an Earth-like
atmosphere; however polarization adds another dimension which can be used, in
combination with unpolarized orbital light curves and contrast ratios, to
detect extrasolar oceans, atmospheric water aerosols, and water clouds.
Additionally, the presence and direction of the polarization vector could be
used to determine planet association with the star, and constrain orbit
inclination.


  We study the optimization of the expected long-term reward in finite
partially observable Markov decision processes over the set of stationary
stochastic policies. In the case of deterministic observations, also known as
state aggregation, the problem is equivalent to optimizing a linear objective
subject to quadratic constraints. We characterize the feasible set of this
problem as the intersection of a product of affine varieties of rank one
matrices and a polytope. Based on this description, we obtain bounds on the
number of critical points of the optimization problem. Finally, we conduct
experiments in which we solve the KKT equations or the Lagrange equations over
different boundary components of the feasible set, and compare the result to
the theoretical bounds and to other constrained optimization methods.


  From astrophysics there are indications that the finestructure constant
$\alpha $ has changed during the past 10 billion years. Within grand
unification one can deduce that also the QCD scale has changed. Tests for a
time variation of this scale are described. The result of the new experiment in
Munich is discussed.


  Reinforcement learning (RL) has been widely applied to game-playing and
surpassed the best human-level performance in many domains, yet there are few
use-cases in industrial or commercial settings. We introduce OR-Gym, an
open-source library for developing reinforcement learning algorithms to address
operations research problems. In this paper, we apply reinforcement learning to
the knapsack, multi-dimensional bin packing, multi-echelon supply chain, and
multi-period asset allocation model problems, as well as benchmark the RL
solutions against MILP and heuristic models. These problems are used in
logistics, finance, engineering, and are common in many business operation
settings. We develop environments based on prototypical models in the
literature and implement various optimization and heuristic models in order to
benchmark the RL results. By re-framing a series of classic optimization
problems as RL tasks, we seek to provide a new tool for the operations research
community, while also opening those in the RL community to many of the problems
and challenges in the OR field.


  The transport of fermions through nanocircuits plays a major role in
mesoscopic physics. Exploring the analogy with classical wave scattering, basic
notions of nanoscale transport can be explained in a simple way, even at the
level of undergraduate Solid State Physics courses, and more so if these
explanations are supported by numerical simulations of these nanocircuits. This
paper presents a simple tight-binding method for the study of the conductance
of quantum nanorings connected to one-dimensional leads. We show how to address
the effects of applied magnetic and electric fields and illustrate concepts
such as Aharonov-Bohm conductance oscillations, resonant tunneling and
destructive interference.


  We introduce a neural network-based approach for modeling wave functions that
satisfy Bose-Einstein statistics. Applying this model to small $^4He_N$
clusters (with N ranging from 2 to 14 atoms), we accurately predict ground
state energies, pair density functions, and two-body contact parameters
$C^{(N)}_2$ related to weak unitarity. The results obtained via the variational
Monte Carlo method exhibit remarkable agreement with previous studies using the
diffusion Monte Carlo method, which is considered exact within its statistical
uncertainties. This indicates the effectiveness of our neural network approach
for investigating many-body systems governed by Bose-Einstein statistics.


  Accessible categories admit a purely category-theoretic replacement for
cardinality: the internal size. Generalizing results and methods from
arXiv:1708.06782, we examine set-theoretic problems related to internal sizes
and prove several L\"owenheim-Skolem theorems for accessible categories. For
example, assuming the singular cardinal hypothesis, we show that a large
accessible category has an object in all internal sizes of high-enough
cofinality. We also prove that accessible categories with directed colimits
have filtrations: any object of sufficiently high internal size is (the retract
of) a colimit of a chain of strictly smaller objects.


  Let $A$ be a commutative arithmetical ring. The ring $A$ has Krull dimension
if and only if every factor ring of $A$ is finite-dimensional and does not have
idempotent proper essential ideals. The study is supported by Russian Science
Foundation (project no. 16-11-10013).


  The generalized liquid drop model (GLDM) is firstly extended to study the
two-proton ($2p$) radioactivity half-lives of the ground-state of nuclei.
According to the comparison between the calculated half-lives and the
experimental data, it is shown that the GLDM describes the $2p$ radioactivity
half-lives well. In addition, by comparing its accuracy with other models, it
is found that the GLDM has a comparable accuracy with them. Finally, the $2p$
radioactivity half-lives of some most probable candidates are predicted with
the GLDM by inputting the \textit{Q}$_{2p}$ values (the released energy of the
$2p$ radioactivity) from the updated AME 2016 Mass Table, which may be useful
for future experiments.


  Recent experiment [Sigrist et al., Phys. Rev. Lett. {\bf 98}, 036805 (2007)]
reported switches between 0 and $\pi$ in the phase of Aharonov-Bohm
oscillations of the two-terminal differential conductance through a two-dot
ring with increasing voltage bias. Using a simple model, where one of the dots
contains multiple interacting levels, these findings are explained as a result
of transport through the interferometer being dominated at different biases by
quantum dot levels of different "parity" (i.e. the sign of the overlap integral
between the dot state and the states in the leads). The redistribution of
electron population between different levels with bias leads to the fact that
the number of switching events is not necessarily equal to the number of dot
levels, in agreement with experiment. For the same reason switching does not
always imply that the parity of levels is strictly alternating. Lastly, it is
demonstrated that the correlation between the first switching of the phase and
the onset of the inelastic cotunneling, as well as the sharp (rather than
gradual) change of phase when switching occurs, give reason to think that the
present interpretation of the experiment is preferable to the one based on
electrostatic AB effect.


  We give two double copy prescriptions which construct asymptotically flat
solutions in gravity from asymptotically flat gauge fields. The first
prescription applies to radiative fields, which are non-linear vacuum solutions
determined by characteristic data at null infinity. For any two such radiative
gauge fields (linear or non-linear), the characteristic data of a radiative
metric, dilaton and axion is constructed by a simple `squaring' procedure,
giving a classical double copy at the level of radiation fields. We demonstrate
the procedure with several examples where the characteristic data can be
explicitly integrated; for linear fields this also sheds light on the
twistorial description of Weyl double copy. Our second prescription applies to
all asymptotically flat fields at the level of their asymptotic equations of
motion: we give a map between any solution of the asymptotic Maxwell equations
and any solution of the asymptotic Einstein equations at null infinity. This
also extends to the asymptotic charges and their duals, preserves the soft and
hard sectors between gauge theory and gravity, and is related to the usual
notion of double copy in scattering amplitudes.


  QCTL extends the temporal logic CTL with quantifications over atomic
propositions. This extension is known to be very expressive: QCTL allows us to
express complex properties over Kripke structures (it is as expressive as MSO).
Several semantics exist for the quantifications: here, we work with the
structure semantics, where the extra propositions label the Kripke structure
(and not its execution tree), and the model-checking problem is known to be
PSPACE-complete in this framework. We propose a model-checking algorithm for
QCTL based on a reduction to QBF. We consider several reduction strategies, and
we compare them with a prototype (based on the SMT-solver Z3) on several
examples.


  One of the major challenges in coreference resolution is how to make use of
entity-level features defined over clusters of mentions rather than mention
pairs. However, coreferent mentions usually spread far apart in an entire text,
which makes it extremely difficult to incorporate entity-level features. We
propose a graph neural network-based coreference resolution method that can
capture the entity-centric information by encouraging the sharing of features
across all mentions that probably refer to the same real-world entity. Mentions
are linked to each other via the edges modeling how likely two linked mentions
point to the same entity. Modeling by such graphs, the features between
mentions can be shared by message passing operations in an entity-centric
manner. A global inference algorithm up to second-order features is also
presented to optimally cluster mentions into consistent groups. Experimental
results show our graph neural network-based method combing with the
second-order decoding algorithm (named GNNCR) achieved close to
state-of-the-art performance on the English CoNLL-2012 Shared Task dataset.


  We study the maximum flow problem in directed H-minor-free graphs where H can
be drawn in the plane with one crossing. If a structural decomposition of the
graph as a clique-sum of planar graphs and graphs of constant complexity is
given, we show that a maximum flow can be computed in O(n log n) time. In
particular, maximum flows in directed K_{3,3}-minor-free graphs and directed
K_5-minor-free graphs can be computed in O(n log n) time without additional
assumptions.


  Blockchain or Distributed Ledger Technology is a disruptive technology that
provides the infrastructure for developing decentralized applications enabling
the implementation of novel business models even in traditionally centralized
domains. In the last years it has drawn high interest from the academic
community, technology developers and startups thus lots of solutions have been
developed to address blockchain technology limitations and the requirements of
applications software engineering. In this paper, we provide a comprehensive
overview of DLT solutions analyzing the addressed challenges, provided
solutions and their usage for developing decentralized applications. Our study
reviews over 100 blockchain papers and startup initiatives from which we
construct a 3-tier based architecture for decentralized applications and we use
it to systematically classify the technology solutions. Protocol and Network
Tier solutions address the digital assets registration, transactions, data
structure, and privacy and business rules implementation and the creation of
peer-to-peer networks, ledger replication, and consensus-based state
validation. Scaling Tier solutions address the scalability problems in terms of
storage size, transaction throughput, and computational capability. Finally,
Federated Tier aggregates integrative solutions across multiple blockchain
applications deployments. The paper closes with a discussion on challenges and
opportunities for developing decentralized applications by providing a
multi-step guideline for decentralizing the design of traditional systems and
implementing decentralized applications.


  Seven years of pulse time-of-arrival measurements have been collected from
observations of the young pulsar PSR B2334+61 using the Nanshan radio telescope
of Urumqi Observatory. A phase-connected solution has been obtained over the
whole data span, 2002 August to 2009 August. This includes a very large glitch
that occurred between 2005 August 26 and September 8 (MJDs 53608 and 53621).
The relative increase in rotational frequency for this glitch,
$\Delta\nu_{g}/\nu~\sim~20.5\times10^{-6}$, is the largest ever seen. Although
accounting for less than 1\% of the glitch, there were two well-defined
exponential decay terms with time constants of 21 and 147 days respectively.
There was also a large long-term increase in the spindown rate with
$\Delta\dot\nu_p/\dot\nu \sim 0.011$ at the time of the glitch. A highly
significant oscillation with a period of close to one year is seen in the
post-glitch residuals. It is very unlikely that this can be accounted for by a
pulsar position error or proper motion -- it appears to result from effects
interior to the neutron star. Implications of these results for pulsar glitch
models are discussed.


  We prove that in most cases relevant to cryptography, the Frobenius
endomorphism on the Jacobian of a genus two curve is represented by a diagonal
matrix with respect to an appropriate basis of the subgroup of l-torsion
points. From this fact we get an explicit description of the Weil-pairing on
the subgroup of l-torsion points. Finally, the explicit description of the
Weil-pairing provides us with an efficient, probabilistic algorithm to find
generators of the subgroup of l-torsion points on the Jacobian of a genus two
curve.


  We present CD2Alloy, a novel, powerful translation of UML class diagrams
(CDs) to Alloy. Unlike existing translations, which are based on a shallow
embedding strategy, and are thus limited to checking consistency and generating
conforming object models of a single CD, and support a limited set of CD
language features, CD2Alloy uses a deeper embedding strategy. Rather than
mapping each CD construct to a semantically equivalent Alloy construct,
CD2Alloy defines (some) CD constructs as new concepts within Alloy. This
enables solving several analysis problems that involve more than one CD and
could not be solved by earlier works, and supporting an extended list of CD
language features. The ideas are implemented in a prototype Eclipse plug-in.
The work advances the state-of-the-art in CD analysis, and can also be viewed
as an interesting case study for the different possible translations of one
modeling language to another, their strengths and weaknesses.


  Recently, Coffman, Kundu, and Wootters introduced the residual entanglement
for three qubits to quantify the three-qubit entanglement in Phys. Rev. A 61,
052306 (2000). In Phys. Rev. A 65, 032304 (2007), we defined the residual
entanglement for $n$ qubits, whose values are between 0 and 1. In this paper,
we want to show that the residual entanglement for $n$ qubits is a natural
measure of entanglement by demonstrating the following properties. (1). It is
SL-invariant, especially LU-invariant. (2). It is an entanglement monotone.
(3). It is invariant under permutations of the qubits. (4). It vanishes or is
multiplicative for product states.


  Podolsky's electromagnetism which explains some of unresolved problems of
usual QED has been investigated in the framework of finite field dependent
(FFBRST) BRST transformation. In this generalized QED (GQED), BRST invariant
effective theories are written using generalized Lorenz gauge, $(1+\frac{\Box
}{m_p^2})\partial^\mu A_\mu=0$ and no mixing gauge condition $(1+\frac{\Box
}{m_p^2})^\frac{1}{2} \ \partial^\mu A_\mu=0$, it contains higher order
derivative terms. No Mixing gauge is free from UV divergences in the radiative
correction and easier to handle. We construct appropriate FFBRST transformation
to obtain generating functional in no mixing gauge from that of in Lorenz
gauge. We show that all these BRST invariant effective theories in GQED are
basically same and are inter-connected with appropriately constructed FFBRST
transformations.


  In the burgeoning realm of cryptocurrency, social media platforms like
Twitter have become pivotal in influencing market trends and investor
sentiments. In our study, we leverage GPT-4 and a fine-tuned transformer-based
BERT model for a multimodal sentiment analysis, focusing on the impact of emoji
sentiment on cryptocurrency markets. By translating emojis into quantifiable
sentiment data, we correlate these insights with key market indicators like BTC
Price and the VCRIX index. Our architecture's analysis of emoji sentiment
demonstrated a distinct advantage over FinBERT's pure text sentiment analysis
in such predicting power. This approach may be fed into the development of
trading strategies aimed at utilizing social media elements to identify and
forecast market trends. Crucially, our findings suggest that strategies based
on emoji sentiment can facilitate the avoidance of significant market downturns
and contribute to the stabilization of returns. This research underscores the
practical benefits of integrating advanced AI-driven analyses into financial
strategies, offering a nuanced perspective on the interplay between digital
communication and market dynamics in an academic context.


  The recent availability of data describing social networks is changing our
understanding of the "microscopic structure" of a social tie. A social tie
indeed is an aggregated outcome of many social interactions such as
face-to-face conversations or phone-calls. Analysis of data on face-to-face
interactions shows that such events, as many other human activities, are
bursty, with very heterogeneous durations. In this paper we present a model for
social interactions at short time scales, aimed at describing contexts such as
conference venues in which individuals interact in small groups. We present a
detailed anayltical and numerical study of the model's dynamical properties,
and show that it reproduces important features of empirical data. The model
allows for many generalizations toward an increasingly realistic description of
social interactions. In particular in this paper we investigate the case where
the agents have intrinsic heterogeneities in their social behavior, or where
dynamic variations of the local number of individuals are included. Finally we
propose this model as a very flexible framework to investigate how dynamical
processes unfold in social networks.


  We consider a routing game among non-atomic agents where link latency
functions are conditional on an uncertain state of the network. The agents have
the same prior belief about the state, but only a fixed fraction receive
private route recommendations or a common message, which are generated by a
known randomization, referred to as private or public signaling policy
respectively. The remaining agents choose route according to Bayes Nash flow
with respect to the prior. We develop a computational approach to solve the
optimal information design problem, i.e., to minimize expected social latency
over all public or obedient private signaling policies. For a fixed flow
induced by non-participating agents, design of an optimal private signaling
policy is shown to be a generalized problem of moments for polynomial link
latency functions, and to admit an atomic solution with a provable upper bound
on the number of atoms. This implies that, for polynomial link latency
functions, information design can be equivalently cast as a polynomial
optimization problem. This in turn can be arbitrarily lower bounded by a known
hierarchy of semidefinite relaxations. The first level of this hierarchy is
shown to be exact for the basic two link case with affine latency functions. We
also identify a class of private signaling policies over which the optimal
social cost is non-increasing with increasing fraction of participating agents
for parallel networks. This is in contrast to existing results where the cost
of participating agents under a fixed signaling policy may increase with their
increasing fraction.


  It is known that D$_p$-brane effective action at the leading order of
$\alpha'$ in flat space-time which is given by DBI action, transforms to
D$_{p-1}$-brane effective action under standard T-duality transformations of
the open string gauge bosons and transverse scalar fields. Extending this
duality to order $\alpha'$, one may find corrections to the DBI action which
include the second fundamental form $\Omega$ and the covariant derivative of
gauge field strength $DF$, as well as the corrections to the T-duality
transformations. Using this idea, up to two parameters, we have found all 81
covariant couplings of $D FD F$ and $\Omega\Omega$ with zero, two, four and six
$F$'s. The four gauge field couplings that the T-duality constraint fixes are
consistent with the known couplings in the literature.


  F-theory is perhaps the most general currently available approach to study
non-perturbative string compactifications in their geometric, large radius
regime. It opens up a wide and ever-growing range of applications and
connections to string model building, quantum gravity, (non-perturbative)
quantum field theories in various dimensions and mathematics. Its computational
power derives from the geometrisation of physical reasoning, establishing a
deep correspondence between fundamental concepts in gauge theory and beautiful
structures of elliptic fibrations. These lecture notes, which are an extended
version of my lectures given at TASI 2017, introduce some of the main concepts
underlying the recent technical advances in F-theory compactifications and
their various applications. The main focus is put on explaining the F-theory
dictionary between the local and global data of an elliptic fibration and the
physics of 7-branes in Type IIB compactifications to various dimensions via
duality with M-theory. The geometric concepts underlying this dictionary
include the behaviour of elliptic fibrations in codimension one, two, three and
four, the Mordell-Weil group of rational sections, and the Deligne cohomology
group specifying gauge backgrounds.


  We discuss the conditions under which 4D gravity is localized on domain walls
in 5D anti-de Sitter spaces. Our approach is based on considering the limits in
which the localized gravity decouples. We find that gravity is localized if the
wall is located a finite distance from the boundary of the anti-de Sitter space
and has a finite tension. In addition, it has to be a $\delta$-function source
of gravity.


  Large liquid xenon detectors aiming for dark matter direct detection will
soon become viable tools also for investigating neutrino physics. Information
on the effects of nuclear structure in neutrino-nucleus scattering can be
important in distinguishing neutrino backgrounds in such detectors. We perform
calculations for differential and total cross sections of neutral-current
neutrino scattering off the most abundant xenon isotopes. The nuclear structure
calculations are made in the nuclear shell model for elastic scattering, and
also in the quasiparticle random-phase approximation (QRPA) and microscopic
quasiparticle phonon model (MQPM) for both elastic and inelastic scattering.
Using suitable neutrino energy distributions, we compute estimates of total
averaged cross sections for 8B solar neutrinos and supernova neutrinos.


  The theory of classical types of curves in normed planes is not strongly
developed. In particular, the knowledge on existing concepts of curvatures of
planar curves is widespread and not systematized in the literature. Giving a
comprehensive overview on geometric properties of and relations between all
introduced curvature concepts, we try to fill this gap. Certainly, this yields
a basis for further research and also for possible extensions of the whole
existing framework. In addition, we derive various new results referring in
full broadness to the variety of known curvature types in normed planes. These
new results involve characterizations of curves of constant curvature, new
characterizations of Radon planes and the Euclidean subcase, and analogues to
classical statements like the four vertex theorem and the fundamental theorem
on planar curves. We also introduce a new curvature type, for which we verify
corresponding properties. As applications of the little theory developed in our
expository paper, we study the curvature behaviour of curves of constant width
and obtain also new results on notions like evolutes, involutes, and parallel
curves.


  The classical model of an isolated selfrgavitating gaseous star is given by
the Euler-Poisson system with a polytropic pressure law $P(\rho)=\rho^\gamma$,
$\gamma>1$. For any $1<\gamma<\frac43$, we construct an infinite-dimensional
family of collapsing solutions to the Euler-Poisson system whose density is in
general space inhomogeneous and undergoes gravitational blowup along a
prescribed space-time surface, with continuous mass absorption at the origin.
The leading order singular behavior is described by an explicit collapsing
solution of the pressureless Euler-Poisson system.


  This talk describes a proposal, due to Hull, for a conformally invariant
limit of superstring theory in six dimensions.


  The vacuum of quantum fields contains correlated fluctuations. When
restricted to one side of a surface these have a huge entropy of entanglement
that scales with the surface area. If UV physics renders this entropy finite,
then a thermodynamic argument implies the existence of gravity. That is, the
causal structure of spacetime must be dynamical and governed by the Einstein
equation with Newton's constant inversely proportional to the entropy density.
Conversely, the existence of gravity makes the entanglement entropy finite.
This thermodynamic reasoning is powerful despite the lack of a detailed
description of the dynamics at the cutoff scale, but it has its limitations. In
particular, we should not expect to understand corrections to Einstein gravity
in this way.


  We study the breaking of an Abelian symmetry close to the horizon of an
uncharged rotating Anti-de Sitter black string in 3+1 dimensions. The boundary
theory living on R^2 x S^1 has no rotation, but a magnetic field that is
aligned with the axis of the black string. This boundary theory decribes
non-rotating (2+1)-dimensional holographic superfluids with non-vanishing
superfluid velocity. We study these superfluids in the grand canonical ensemble
and show that for sufficiently small angular momentum of the dual black string
and sufficiently small superfluid velocity the phase transition is 2nd order,
while it becomes 1st order for larger superfluid velocity. Moreover, we observe
that the phase transition is always 1st order above a critical value of the
angular momentum independent of the choice of the superfluid velocity.


  We calculated the mass and width of the $d'$ resonance inside nuclei within a
nucleon-$\Delta$ model by including the self-energy of the $\Delta$ in the
$N\Delta$ propagator. We found that in the nuclear medium the width of the $d'$
is increased by one order of magnitude while its mass changes only by a few
MeV. This broadening of the width of the $d'$ resonance embedded in nuclei is
consistent with the experimental observations so that the $d'$ can be
understood as a $N\Delta$ resonance. Thus, given the freedom between either
isospin 0 or isospin 2 for the $d'$, our results give weigth to the isospin-2
assignment.


  Purpose: To separate the effects of magnetic susceptibility and chemical
shift/exchange in a phantom with isotropic magnetic susceptibility. To generate
a chemical shift/exchange-corrected quantitative susceptibility mapping (QSM)
result.
  Theory and Methods: Magnetic susceptibility and chemical shift/exchange are
the properties of a material. Both are known to induce the resonance frequency
shift in MRI. In current QSM, the susceptibility is reconstructed from the
frequency shift, ignoring the contribution of the chemical shift/exchange. In
this work, a simple geometric approach, which averages the frequency shift maps
from three orthogonal B0 directions to generate a chemical shift/exchange map,
is developed using the fact that the average nullifies the (isotropic)
susceptibility effects. The resulting chemical shift/exchange map is subtracted
from the total frequency shift, producing a frequency shift map solely from
susceptibility. Finally, this frequency shift map is reconstructed to a
susceptibility map using a QSM algorithm. The proposed method is validated in
numerical simulations and applied to phantom experiments with olive oil, bovine
serum albumin, ferritin, and iron oxide solutions.
  Results: Both simulations and experiments confirm that the method
successfully separates the contributions of the susceptibility and chemical
shift/exchange, reporting the susceptibility and chemical shift/exchange of
olive oil (susceptibility: 0.62 ppm, chemical shift: -3.60 ppm), bovine serum
albumin (susceptibility: -0.059 ppm, chemical shift: 0.008 ppm), ferritin
(susceptibility: 0.125 ppm, chemical shift: -0.005 ppm), and iron oxide
(susceptibility: 0.30 ppm, chemical shift: -0.039 ppm) solutions.
  Conclusion: The proposed method successfully separates the susceptibility and
chemical shift/exchange in phantoms with isotropic magnetic susceptibility.


  In a dynamic retrieval system, documents must be ingested as they arrive, and
be immediately findable by queries. Our purpose in this paper is to describe an
index structure and processing regime that accommodates that requirement for
immediate access, seeking to make the ingestion process as streamlined as
possible, while at the same time seeking to make the growing index as small as
possible, and seeking to make term-based querying via the index as efficient as
possible. We describe a new compression operation and a novel approach to
extensible lists which together facilitate that triple goal. In particular, the
structure we describe provides incremental document-level indexing using as
little as two bytes per posting and only a small amount more for word-level
indexing; provides fast document insertion; supports immediate and continuous
queryability; provides support for fast conjunctive queries and similarity
score-based ranked queries; and facilitates fast conversion of the dynamic
index to a "normal" static compressed inverted index structure. Measurement of
our new mechanism confirms that in-memory dynamic document-level indexes for
collections into the gigabyte range can be constructed at a rate of two
gigabytes/minute using a typical server architecture, that multi-term
conjunctive Boolean queries can be resolved in just a few milliseconds each on
average even while new documents are being concurrently ingested, and that the
net memory space required for all of the required data structures amounts to an
average of as little as two bytes per stored posting, less than half the space
required by the best previous mechanism.


  In this paper, we give some existence and nonexistence results for nonradial
entire large solutions of the Hessian equation $S_k\left(D^2 u\right)=b(x)
u^\gamma$ in the sublinear case $0<\gamma<k$. The exact asymptotic behavior of
large solutions at infinity is also studied when $b(x)$ is the oscillation of a
radial function $|x|^{-l}$ at infinity for $l\leq k-1$.


  We initiate the study of representations of elementary abelian $p$-groups via
restrictions to truncated polynomial subalgebras of the group algebra generated
by $r$ nilpotent elements, $k[t_1,..., t_r]/(t^p_1,..., t_r^p)$. We introduce
new geometric invariants based on the behavior of modules upon restrictions to
such subalgebras. We also introduce modules of constant radical and socle type
generalizing modules of constant Jordan type and provide several general
constructions of modules with these properties. We show that modules of
constant radical and socle type lead to families of algebraic vector bundles on
Grassmannians and illustrate our theory with numerous examples.


  The quantum wave-function of a massive particle with small initial
uncertainties (consistent with the uncertainty relation) is believed to spread
very slowly, so that the dynamics is deterministic. This assumes that the
classical motions for given initial data are unique. In fluid turbulence
non-uniqueness due to "roughness" of the advecting velocity field is known to
lead to stochastic motion of classical particles. Vanishingly small random
perturbations are magnified by Richardson diffusion in a "nearly rough"
velocity field so that motion remains stochastic as the noise disappears, or
classical spontaneous stochasticity, . Analogies between stochastic particle
motion in turbulence and quantum evolution suggest that there should be quantum
spontaneous stochasticity (QSS). We show this for 1D models of a particle in a
repulsive potential that is "nearly rough" with $V(x) \sim C|x|^{1+\alpha}$ at
distances $|x|\gg \ell$ , for some UV cut-off $\ell$, and for initial Gaussian
wave-packet centered at 0. We consider the WKB limit with $\hbar/m \to 0$, then
position-spread $\sigma\to 0$. The limit of the position density is
non-deterministic, with equal probabilities of the particle following either of
two, non-unique classical solutions and with "Richardson-like" spreading of the
wave-packet. The splitting of the wave-packet occurs in a very short time
$t\sim(\ell^{1+\alpha}/C)^{1/2}$ for small $\ell$. QSS also occurs in the
scattering of a wave-packet off the rough potential, for careful fine-tuning.
We also consider other semi-classical limits by a numerical solution of the
Schr\"odinger equation, observing QSS both in position- and momentum-space.
Although the wave-function remains split into two widely separated branches in
the classical limit, rapid phase oscillations within each branch prevent any
coherent superposition. These effects should be observable in laboratory
experiments.


  Tree-structured recursive neural networks (TreeRNNs) for sentence meaning
have been successful for many applications, but it remains an open question
whether the fixed-length representations that they learn can support tasks as
demanding as logical deduction. We pursue this question by evaluating whether
two such models---plain TreeRNNs and tree-structured neural tensor networks
(TreeRNTNs)---can correctly learn to identify logical relationships such as
entailment and contradiction using these representations. In our first set of
experiments, we generate artificial data from a logical grammar and use it to
evaluate the models' ability to learn to handle basic relational reasoning,
recursive structures, and quantification. We then evaluate the models on the
more natural SICK challenge data. Both models perform competitively on the SICK
data and generalize well in all three experiments on simulated data, suggesting
that they can learn suitable representations for logical inference in natural
language.


  Two variable $\Lambda$ models, viz. $\Lambda \sim (\dot a/a)^2$ and $\Lambda
\sim \rho$ have been studied under the assumption that the equation of state
parameter $\omega$ is a function of time. The selected $\Lambda$ models are
found to be equivalent both in four and five dimensions. The possibility of
signature flip of the deceleration parameter is also shown.


  We present a study of the mid-infrared properties and dust content of a
sample of 27 HII ``blobs'', a rare class of compact HII regions in the
Magellanic Clouds. A unique feature of this sample is that even though these
HII regions are of high and low excitation they have nearly the same physical
sizes ~1.5-3 pc. We base our analysis on archival 3-8 microns infrared imagery
obtained with the Infrared Array Camera (IRAC) on board the Spitzer Space
Telescope. We find that despite their youth, sub-solar metallicity and varied
degrees of excitation, the mid-infrared colors of these regions are similar to
those of typical HII regions. Higher excitation ``blobs'' (HEBs) display
stronger 8 micron emission and redder colors than their low-excitation
counterparts (LEBs).


  A new type of curved subwavelength light beam, a photonic hook (PH), emerged
from the diffraction of a light wave at a mesoscale dielectric object with
broken internal symmetry (Janus particle) was recently reported. For efficient
and technically simpler generation of PHs, we propose a new type of asymmetric
Janus microparticles, the orthogonal microbars, composed from materials with
different refractive indices. Based on the numerical simulations by means of
the Finite Elements Method, we investigate the physical mechanism of PH
formation by analyzing the field intensity distribution and the energy fluxes
near such particles. The influence of dielectric substrate is also studied for
the first time. We show that by changing the refractive index contrast between
two parts of Janus bar the shape and curvature of the PHs can be efficiently
controlled. The criteria of PH quality for complex characterizing the photonic
hook curvature is introduced and discussed as well.


  Chernozhukov et al. (2018) proposed the sorted effect method for nonlinear
regression models. This method consists of reporting percentiles of the partial
effects in addition to the average commonly used to summarize the heterogeneity
in the partial effects. They also proposed to use the sorted effects to carry
out classification analysis where the observational units are classified as
most and least affected if their causal effects are above or below some tail
sorted effects. The R package SortedEffects implements the estimation and
inference methods therein and provides tools to visualize the results. This
vignette serves as an introduction to the package and displays basic
functionality of the functions within.


  We consider a heat conduction problem $S$ with mixed boundary conditions in a
n-dimensional domain $\Omega$ with regular boundary $\Gamma$ and a family of
problems $S_{\alpha}$, where the parameter $\alpha>0$ is the heat transfer
coefficient on the portion of the boundary $\Gamma_{1}$. In relation to these
state systems, we formulate simultaneous \emph{distributed-boundary} optimal
control problems on the internal energy $g$ and the heat flux $q$ on the
complementary portion of the boundary $\Gamma_{2}$. We obtain existence and
uniqueness of the optimal controls, the first order optimality conditions in
terms of the adjoint state and the convergence of the optimal controls, the
system and the adjoint states when the heat transfer coefficient $\alpha$ goes
to infinity. Finally, we prove estimations between the simultaneous
distributed-boundary optimal control and the distributed optimal control
problem studied in a previous paper of the first author.


  There are now 10 firm time delay measurements in gravitational lenses. The
physics of time delays is well understood, and the only important variable for
interpreting the time delays to determine H_0 is the mean surface mass density
<k> (in units of the critical density for gravitational lensing) of the lens
galaxy at the radius of the lensed images. More centrally concentrated mass
distributions with lower <k> predict higher Hubble constants, with H_0~1-<k> to
lowest order. While we cannot determine <k> directly given the available data
on the current time delay lenses, we find H_0=48+/-3 km/s/Mpc for the
isothermal (flat rotation curve) models, which are our best present estimate
for the mass distributions of the lens galaxies. Only if we eliminate the dark
matter halo of the lenses and use a constant mass-to-light ratio (M/L) model to
find H_0=71+/-3 km/s/Mpc is the result consistent with local estimates.
Measurements of time delays in better-constrained systems or observations to
obtain new constraints on the current systems provide a clear path to
eliminating the <k> degeneracy and making estimates of H_0 with smaller
uncertainties than are possible locally. Independent of the value of H_0, the
time delay lenses provide a new and unique probe of the dark matter
distributions of galaxies and clusters because they measure the total (light +
dark) matter surface density.


  Gaussian processes (GPs) stand as crucial tools in machine learning and
signal processing, with their effectiveness hinging on kernel design and
hyper-parameter optimization. This paper presents a novel GP linear multiple
kernel (LMK) and a generic sparsity-aware distributed learning framework to
optimize the hyper-parameters. The newly proposed grid spectral mixture (GSM)
kernel is tailored for multi-dimensional data, effectively reducing the number
of hyper-parameters while maintaining good approximation capabilities. We
further demonstrate that the associated hyper-parameter optimization of this
kernel yields sparse solutions. To exploit the inherent sparsity property of
the solutions, we introduce the Sparse LInear Multiple Kernel Learning
(SLIM-KL) framework. The framework incorporates a quantized alternating
direction method of multipliers (ADMM) scheme for collaborative learning among
multiple agents, where the local optimization problem is solved using a
distributed successive convex approximation (DSCA) algorithm. SLIM-KL
effectively manages large-scale hyper-parameter optimization for the proposed
kernel, simultaneously ensuring data privacy and minimizing communication
costs. Theoretical analysis establishes convergence guarantees for the learning
framework, while experiments on diverse datasets demonstrate the superior
prediction performance and efficiency of our proposed methods.


  The object of this article is to construct certain classes of arithmetically
significant, holomorphic Siegel cusp forms F of genus 2, which are neither of
Saito-Kurokawa type, in which case the degree 4 spinor L-function L(s, F) is
divisible by an abelian L-function, nor of Yoshida type, in which case L(s,F)
is a product of L-series of a pair of elliptic cusp forms. Two key examples are
the forms F defined by the symmetric cube of a non-CM elliptic curve E over the
rationals, and those defined by anticyclotomic twists (of even non-zero weight)
of the base change of such an E to an imaginary quadratic field K. One of the
main ingredients is the transfer, albeit indirect, of cusp forms \pi on GL(4)
to GSp(4) with many of the expected properties, and this might be of
independent interest. The transfer information is shown to be complete when \pi
is regular and associated to an \ell-adic Galois representation. We also appeal
to the (independent) results of Laumon and Weissauer on the zeta functions of
Siegel modular threefolds.


  We construct the foliation of aspace associated to correlation functions of
vertex operator algebras on considered on Riemann surfaces. We prove that the
computation of general genus $g$ correlation functions determines a foliation
on the space associated to these correlation functions a sewn Riemann surface.
Certain further applications of the definition are proposed.


  Once mixed in the ambient galactic plane stellar population, young stars are
virtually indiscernible because neither their global photometric properties nor
the presence of nearby gas can help to disentangle them from older ones.
Nevertheless, the study of the RasTyc sample revealed 4 lithium-rich field
stars displaying the same space motion, which are located within a few degrees
from each other on the celestial sphere near the Cepheus-Cassiopeia complex and
at a similar distance from the Sun. Both physical and kinematical indicators
show that all these stars are young, with ages in the range 10-30 Myr. Using
multivariate analysis methods, we selected optical counterparts of ROSAT
All-Sky Survey / XMM-Newton X-ray sources cross-identified with late-type stars
around these 4 young stars. Recent spectroscopic observations of this sample
allowed us to discover additional lithium-rich sources. Our preliminary results
showed that some of them share the same space motion as the 4 young comoving
stars. They have properties rather similar to the members of the TW Hydrae
association, although they seem to be slightly older and are located in the
northern hemisphere. Nearby young stars in the field are of great importance to
understand the recent local history of star formation, as well as to give new
insight into the process of star formation outside standard star-forming
regions and to study the evolution of circumstellar discs.


  Topological insulators (TIs) having intrinsic or proximity-coupled s-wave
superconductivity host Majorana zero modes (MZMs) at the ends of vortex lines.
The MZMs survive up to a critical doping of the TI at which there is a vortex
phase transition that eliminates the MZMs. In this work, we show that the
phenomenology in higher-order topological insulators (HOTIs) can be
qualitatively distinct. In particular, we find two distinct features. (i) We
find that vortices placed on the gapped (side) surfaces of the HOTI, exhibit a
pair of phase transitions as a function of doping. The first transition is a
surface phase transition after which MZMs appear. The second transition is the
well-known vortex phase transition. We find that the surface transition appears
because of the competition between the superconducting gap and the local
$\mathcal{T}$-breaking gap on the surface. (ii) We present numerical evidence
that shows strong variation of the critical doping for the vortex phase
transition as the center of the vortex is moved toward or away from the hinges
of the sample. We believe our work provides new phenomenology that can help
identify HOTIs, as well as illustrating a promising platform for the
realization of MZMs.


  We explore in detail the possibility that gravitational wave signals from
binary inspirals are affected by a new force that couples only to dark matter
particles. We discuss the impact of both the new force acting between the
binary partners as well as radiation of the force carrier. We identify numerous
constraints on any such scenario, ultimately concluding that observable effects
on the dynamics of binary inspirals due to such a force are not possible if the
dark matter is accrued during ordinary stellar evolution. Constraints arise
from the requirement that the astronomical body be able to collect and bind at
small enough radius an adequate number of dark matter particles, from the
requirement that the particles thus collected remain bound to neutron stars in
the presence of another neutron star, and from the requirement that the theory
allows old neutron stars to exist and retain their charge. Thus, we show that
any deviation from the predictions of general relativity observed in binary
inspirals must be due either to the material properties of the inspiraling
objects themselves, such as a tidal deformability, to a true fifth force
coupled to baryons, or to a non-standard production mechanism for the dark
matter cores of neutron stars. Viable scenarios of the latter type include
production of dark matter in exotic neutron decays, or the formation of compact
dark matter objects in the early Universe that later seed star formation or are
captured by stars.


  For two given nonnegative integers $h$ and $k$, an $L(h,k)$-edge labeling of
a graph $G$ is the assignment of labels $\{0,1, \cdots, n\}$ to the edges so
that two edges having a common vertex are labeled with difference at least $h$
and two edges not having any common vertex but having a common edge connecting
them are labeled with difference at least $k$. The span $\lambda'_{h,k}{(G)}$
is the minimum $n$ such that $G$ admits an $L(h,k)$-edge labeling. Here our
main focus is on finding $\lambda'_{1,2}{(G)}$ for $L(1,2)$-edge labeling of
infinite regular hexagonal ($T_3$), square ($T_4$), triangular ($T_6$) and
octagonal ($T_8$) grids. It was known that $7 \leq \lambda'_{1,2}{(T_3)} \leq
8$, $10 \leq \lambda'_{1,2}{(T_4)} \leq 11$, $16 \leq \lambda'_{1,2}{(T_6)}
\leq 20$ and $25 \leq \lambda'_{1,2}{(T_8)} \leq 28$. Here we settle two long
standing open questions i.e. $\lambda'_{1,2}{(T_3)}$ and
$\lambda'_{1,2}{(T_4)}$. We show $\lambda'_{1,2}{(T_3)} =7$,
$\lambda'_{1,2}{(T_4)}= 11$. We also improve the bound for $T_6$ and $T_8$ and
prove $\lambda'_{1,2}{(T_6)} \geq 18$, $ \lambda'_{1,2}{(T_8)} \geq 26$.


  The defect-rich morphology of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO) thin
films leads to a glass-like arrangement of Abrikosov vortices which causes the
resistance to disappear in vanishing current densities. This vortex glass
consists of entangled vortex lines and is identified by a characteristic
scaling of the voltage-current isotherms. Randomly distributed columnar defects
stratify the vortex lines and lead to a Bose glass. Here, we report on the
observation of an ordered Bose glass in a YBCO thin film with a hexagonal array
of columnar defects with 30 nm spacings. The periodic pinning landscape was
engineered by a focused beam of 30 keV He$^+$ ions in a helium-ion microscope.


  Exploring and understanding language data is a fundamental stage in all areas
dealing with human language. It allows NLP practitioners to uncover quality
concerns and harmful biases in data before training, and helps linguists and
social scientists to gain insight into language use and human behavior. Yet,
there is currently a lack of a unified, customizable tool to seamlessly inspect
and visualize language variation and bias across multiple variables, language
units, and diverse metrics that go beyond descriptive statistics. In this
paper, we introduce Variationist, a highly-modular, extensible, and
task-agnostic tool that fills this gap. Variationist handles at once a
potentially unlimited combination of variable types and semantics across
diversity and association metrics with regards to the language unit of choice,
and orchestrates the creation of up to five-dimensional interactive charts for
over 30 variable type-semantics combinations. Through our case studies on
computational dialectology, human label variation, and text generation, we show
how Variationist enables researchers from different disciplines to effortlessly
answer specific research questions or unveil undesired associations in language
data. A Python library, code, documentation, and tutorials are made publicly
available to the research community.


  We define pseudo-Riemannian spectral triples, an analytic context broad
enough to encompass a spectral description of a wide class of pseudo-Riemannian
manifolds, as well as their noncommutative generalisations. Our main theorem
shows that to each pseudo-Riemannian spectral triple we can associate a genuine
spectral triple, and so a K-homology class. With some additional assumptions we
can then apply the local index theorem. We give a range of examples and some
applications. The example of the harmonic oscillator in particular shows that
our main theorem applies to much more than just classical pseudo-Riemannian
manifolds.