  In 2007, G.E. Andrews introduced the $(n+1)$-variable combinatorial
generating function $R_n(x_1,x_2,\cdots,x_n;q)$ for ranks of $n$-marked Durfee
symbols, an $(n+1)$-dimensional multisum, as a vast generalization to the
ordinary two-variable partition rank generating function. Since then, it has
been a problem of interest to understand the automorphic properties of this
function; in special cases and under suitable specializations of parameters,
$R_n$ has been shown to possess modular, quasimodular, and mock modular
properties when viewed as a function on the upper half complex plane $\mathbb
H$, in work of Bringmann, Folsom, Garvan, Kimport, Mahlburg, and Ono. Quantum
modular forms, defined by Zagier in 2010, are similar to modular or mock
modular forms but are defined on the rationals $\mathbb Q$ as opposed to
$\mathbb H$, and exhibit modular transformations there up to suitably analytic
error functions in $\mathbb R$; in general, they have been related to diverse
areas including number theory, topology, and representation theory. Here, we
establish quantum modular properties of $R_n$.


  We present ALMA $^{12}$CO (J=1-0, 3-2 and 6-5), $^{13}$CO (J=1-0) and
C$^{18}$O (J=1-0) observations of the local Ultra Luminous Infrared Galaxy,
IRAS 13120-5453 (dubbed "The Yo-yo"). The morphologies of the three isotopic
species differ, where $^{13}$CO shows a hole in emission towards the center. We
measure integrated brightness temperature line ratios of $^{12}$CO/$^{13}$CO
$\geq$ 60 (exceeding 200) and $^{13}$CO/C$^{18}$O $\leq$ 1 in the central
region. Assuming optical thin emission, C$^{18}$O is more abundant than
$^{13}$CO in several regions. The abundances within the central 500 pc are
consistent with enrichment of the ISM via a young starburst ($<$7Myr), a
top-heavy initial mass function or a combination of both.


  Recent results of Grepstad and Lev are used to show that weighted
cut-and-project sets with one-dimensional physical space and one-dimensional
internal space are bounded distance equivalent to some lattice if the weight
function $h$ is continuous on the internal space, and if $h$ is either
piecewise linear, or twice differentiable with bounded curvature.


  Document Question Answering (QA) presents a challenge in understanding
visually-rich documents (VRD), particularly those dominated by lengthy textual
content like research journal articles. Existing studies primarily focus on
real-world documents with sparse text, while challenges persist in
comprehending the hierarchical semantic relations among multiple pages to
locate multimodal components. To address this gap, we propose PDF-MVQA, which
is tailored for research journal articles, encompassing multiple pages and
multimodal information retrieval. Unlike traditional machine reading
comprehension (MRC) tasks, our approach aims to retrieve entire paragraphs
containing answers or visually rich document entities like tables and figures.
Our contributions include the introduction of a comprehensive PDF Document VQA
dataset, allowing the examination of semantically hierarchical layout
structures in text-dominant documents. We also present new VRD-QA frameworks
designed to grasp textual contents and relations among document layouts
simultaneously, extending page-level understanding to the entire multi-page
document. Through this work, we aim to enhance the capabilities of existing
vision-and-language models in handling challenges posed by text-dominant
documents in VRD-QA.


  Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and
Meulenberg. In this paper, we introduce the notion of $q$-analogs of divisible
design graphs and show that all $q$-analogs of divisible design graphs come
from spreads, and are actually $q$-analogs of strongly regular graphs. Deza
graphs were introduced by Erickson, Fernando, Haemers and Hardy in 1999. In
this paper, we introduce $q$-analogs of Deza graphs. Further, we determine
possible parameters, give examples of $q$-analogs of Deza graphs and
characterize all non-strongly regular $q$-analogs of Deza graphs with the
smallest parameters.


  We study the Yamabe flow on compact Riemannian manifolds of dimensions
greater than two with minimal boundary. Convergence to a metric with constant
scalar curvature and minimal boundary is established in dimensions up to seven,
and in any dimensions if the manifold is spin.


  The reconstruction of non pointing photons is a key feature for studying
gauge mediated supersymmetry breaking (GMSB) models at the LHC. In this article
the angular resolution of the ATLAS electromagnetic calorimeter is
characterized from a detailed simulation of the detector. Resulting
performances are used to reconstruct GMSB events with a fast simulation
program, taking into account reconstruction effects. Finally, the sensitivity
to extract the sparticles masses and the lightest neutralino lifetime is
estimated.


  Let $G$ be a finite abelian abelian group of exponent $m\ge 2$. For subsets
$A,S\subset G$, denote by $\partial_S(A)$ the number of edges from $A$ to its
complement $G\setminus A$ in the directed Cayley graph, induced by $S$ on $G$.
We show that if $S$ generates $G$, and $A$ is non-empty, then
  $$ \partial_S(A) \ge \frac{e}m\,|A|\ln\frac{|G|}{|A|}. $$
  Here the coefficient $e=2.718...$ is best possible and cannot be replaced
with a number larger than $e$.
  For homocyclic groups $G$ of exponent $m$, we find an explicit closed-form
expression for $\partial_S(A)$ in the case where $S$ is a "standard" generating
subset of $G$, and $A$ is an initial segment of $G$ with respect to the
lexicographic order, induced by $S$ on $G$. Namely, we show that in this
situation
  $$ \partial_S(A) = |G|\,\omega_m(|A|/|G|), $$ where $\omega_2$ is the Takagi
function, and $\omega_m$ for $m\ge 3$ is an appropriate generalization thereof.
This particular case is of special interest, since for $m\in\{2,3,4\}$ it is
known to yield the smallest possible value of $\partial_S(A)$, over all sets
$A\subset G$ of given size. We give this classical result a new proof, somewhat
different from the standard one.
  We also give a new, short proof of the Boros-Pales inequality
$$\omega_2(\frac{x+y}2) \le \frac{\omega_2(x) + \omega_2(y)}2 + \frac12\,|y-x|,
$$ establish an extremal characterization of the Takagi function as the
(pointwise) maximal function, satisfying this inequality and the boundary
condition $\max\{\omega_2(0),\omega_2(1)\}\le 0$, and obtain similar results
for the 3-adic analog $\omega_3$ of the Takagi function.


  Dynamical systems can autonomously adapt their organization so that the
required target dynamics is reproduced. In the previous Rapid Communication
[Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be
designed using delayed feedbacks. Here, the proposed method is further analyzed
and improved. Its extension to adaptable systems, where delays are absent and
inertial feedbacks are instead employed, is suggested. Numerical tests for
three different models, including networks of phase and amplitude oscillators,
are performed.


  Nucleon selfenergies and spectral functions are calculated at the saturation
density of symmetric nuclear matter at finite temperatures. In particular, the
behaviour of these quantities at temperatures above and close to the critical
temperature for the superfluid phase transition in nuclear matter is discussed.
It is shown how the singularity in the thermodynamic T-matrix at the critical
temperature for superfluidity (Thouless criterion) reflects in the selfenergy
and correspondingly in the spectral function. The real part of the on-shell
selfenergy (optical potential) shows an anomalous behaviour for momenta near
the Fermi momentum and temperatures close to the critical temperature related
to the pairing singularity in the imaginary part. For comparison the selfenergy
derived from the K-matrix of Brueckner theory is also calculated. It is found,
that there is no pairing singularity in the imaginary part of the selfenergy in
this case, which is due to the neglect of hole-hole scattering in the K-matrix.
From the selfenergy the spectral function and the occupation numbers for finite
temperatures are calculated.


  Tilted and warped discs inside tilted dark matter haloes are predicted from
numerical and semi-analytical studies. In this paper, we use deep imaging to
demonstrate the likely existence of tilted outer structures in real galaxies.
We consider two SB0 edge-on galaxies, NGC4469 and NGC4452, which exhibit
apparent tilted outer discs with respect to the inner structure. In NGC4469,
this structure has a boxy shape, inclined by $\Delta$PA$\approx$3$^{\circ}$
with respect to the inner disc, whereas NGC4452 harbours a discy outer
structure with $\Delta$PA$\approx$6$^{\circ}$. In spite of the different
shapes, both structures have surface brightness profiles close to exponential
and make a large contribution ($\sim30$%) to the total galaxy luminosity. In
the case of NGC4452, we propose that its tilted disc likely originates from a
former fast tidal encounter (probably with IC3381). For NGC4469, a plausible
explanation may also be galaxy harassment, which resulted in a tilted or even a
tumbling dark matter halo. A less likely possibility is accretion of gas-rich
satellites several Gyr ago. New deep observations may potentially reveal more
such galaxies with tilted outer structures, especially in clusters. We also
consider galaxies, mentioned in the literature, where a central component (a
bar or a bulge) is tilted with respect to the stellar disc. According to our
numerical simulations, one of the plausible explanations of such observed
"tilts" of the bulge/bar is a projection effect due to a not exactly edge-on
orientation of the galaxy coupled with a skew angle of the triaxial bulge/bar.


  Motivated by CO2 capture and sequestration (CCS) design considerations, we
consider the coupled effects of permeability heterogeneity and background flow
on the dissolution of a supercritical CO2 lens into an underlying deep,
confined aquifer. We present the results of a large-scale Monte Carlo
simulation study examining the interaction of background flow rate and three
parameters describing multi-Gaussian log-permeability fields: mean, variance,
and correlation length. Hundreds of high-resolution simulations were performed
using the PFLOTRAN finite volume software to model CO2 dissolution in a
kilometer-scale aquifer over 1000 y. Predictive dimensionless scaling
relationships relating CO2 dissolution rate to heterogeneity statistics,
Rayleigh (Ra) and Peclet (Pe) numbers were developed for both gravitationally
dominated free convection to background flow-dominated forced convection
regimes. An empirical criterion, $\rm Pe\ = Ra^{3/4}$, was discovered for
regime transition. All simulations converged quickly to a quasi-steady,
approximately linear dissolution rate. However, this rate displayed profound
variability between permeability field realizations sharing the same
heterogeneity statistics, even under mild permeability heterogeneity. In
general, increased heterogeneity was associated with a lower mean and higher
variance of dissolution rate, undesirable from a CCS design perspective. The
relationship between dissolution rate and background flow was found to be
complex and nonlinear. Dimensionless scaling relationships were uncovered for a
number of special cases. Results call into question the validity of the
Boussinesq approximation in the context of modest-to-high background flow rates
and the general applicability of numerical simulations without background flow.


  Nowadays, data-centers are largely under-utilized because resource allocation
is based on reservation mechanisms which ignore actual resource utilization.
Indeed, it is common to reserve resources for peak demand, which may occur only
for a small portion of the application life time. As a consequence, cluster
resources often go under-utilized.
  In this work, we propose a mechanism that improves cluster utilization, thus
decreasing the average turnaround time, while preventing application failures
due to contention in accessing finite resources such as RAM. Our approach
monitors resource utilization and employs a data-driven approach to resource
demand forecasting, featuring quantification of uncertainty in the predictions.
Using demand forecast and its confidence, our mechanism modulates cluster
resources assigned to running applications, and reduces the turnaround time by
more than one order of magnitude while keeping application failures under
control. Thus, tenants enjoy a responsive system and providers benefit from an
efficient cluster utilization.


  We propose a new stabilised finite element method for the classical
Kolmogorov equation. The latter serves as a basic model problem for large
classes of kinetic-type equations and, crucially, is characterised by
degenerate diffusion. The stabilisation is constructed so that the resulting
method admits a \emph{numerical hypocoercivity} property, analogous to the
corresponding property of the PDE problem. More specifically, the stabilisation
is constructed so that spectral gap is possible in the resulting
``stronger-than-energy'' stabilisation norm, despite the degenerate nature of
the diffusion in Kolmogorov, thereby the method has a provably robust behaviour
as the ``time'' variable goes to infinity. We consider both a spatially
discrete version of the stabilised finite element method and a fully discrete
version, with the time discretisation realised by discontinuous Galerkin
timestepping. Both stability and a priori error bounds are proven in all cases.
Numerical experiments verify the theoretical findings.


  Visualization and assessment of copula structures are crucial for accurately
understanding and modeling the dependencies in multivariate data analysis. In
this paper, we introduce an innovative method that employs functional boxplots
and rank-based testing procedures to evaluate copula symmetry. This approach is
specifically designed to assess key characteristics such as reflection
symmetry, radial symmetry, and joint symmetry. We first construct test
functions for each specific property and then investigate the asymptotic
properties of their empirical estimators. We demonstrate that the functional
boxplot of these sample test functions serves as an informative visualization
tool of a given copula structure, effectively measuring the departure from zero
of the test function. Furthermore, we introduce a nonparametric testing
procedure to assess the significance of deviations from symmetry, ensuring the
accuracy and reliability of our visualization method. Through extensive
simulation studies involving various copula models, we demonstrate the
effectiveness of our testing approach. Finally, we apply our visualization and
testing techniques to two real-world datasets: a nutritional habits survey with
five variables and wind speed data from three locations in Saudi Arabia.


  Previously, it has been established that axion dark matter (DM) is clustered
to form clumps (axion miniclusters) with masses $M\sim10^{-12}M_\odot$. The
passages of such clumps through the Earth are very rare events occurring once
in $10^5$ years. It has also been shown that the Earth's passage through DM
streams, which are the remnants of clumps destroyed by tidal gravitational
forces from Galactic stars, is a much more probable event occurring once in
several years. In this paper we have performed details calculations of the
destruction of miniclusters by taking into account their distribution in orbits
in the Galactic halo. We have investigated two DM halo models, the
Navarro-Frenk-White and isothermal density profiles. Apart from the Galactic
disk stars, we have also taken into account the halo and bulge stars. We show
that about 2-5% of the axion miniclusters are destroyed when passing near stars
and transform into axion streams, while the clump destruction efficiency
depends on the DM halo model. The expected detection rate of streams with an
overdensity exceeding an order of magnitude is 1-2 in 20 years. The possibility
of detecting streams by their tidal gravitational effect on gravitational-wave
interferometers is also considered.


  We summarize recent developments in the Standard-Model evaluation of the
anomalous magnetic moment of the muon $a_\mu$, both in the
hadronic-light-by-light and hadronic-vacuum-polarization contributions. The
current situation for the latter is puzzling as we are confronted with multiple
discrepancies that are not yet understood. We present updated fits of a
dispersive representation of the pion vector form factor to the new CMD-3 data
set and quantify the tensions with the other high-statistics
$e^+e^-\to\pi^+\pi^-$ experiments in the contribution to $a_\mu$ in the energy
range up to 1 GeV, as well as in the corresponding contribution to the
intermediate Euclidean window.


  We hypothesize that existing sentence-level machine translation (MT) metrics
become less effective when the human reference contains ambiguities. To verify
this hypothesis, we present a very simple method for extending pretrained
metrics to incorporate context at the document level. We apply our method to
three popular metrics, BERTScore, Prism, and COMET, and to the reference free
metric COMET-QE. We evaluate the extended metrics on the WMT 2021 metrics
shared task using the provided MQM annotations. Our results show that the
extended metrics outperform their sentence-level counterparts in about 85% of
the tested conditions, when excluding results on low-quality human references.
Additionally, we show that our document-level extension of COMET-QE
dramatically improves its accuracy on discourse phenomena tasks, outperforming
a dedicated baseline by up to 6.1%. Our experimental results support our
initial hypothesis and show that a simple extension of the metrics permits them
to take advantage of context to resolve ambiguities in the reference.


  Most debuggers are notoriously machine-dependent, but some recent research
prototypes achieve varying degrees of machine-independence with novel designs.
Cdb, a simple source-level debugger for C, is completely independent of its
target architecture. This independence is achieved by embedding symbol tables
and debugging code in the target program, which costs both time and space. This
paper describes a revised design and implementation of cdb that reduces the
space cost by nearly one-half and the time cost by 13% by storing symbol tables
in external files. A symbol table is defined by a 31-line grammar in the
Abstract Syntax Description Language (ASDL). ASDL is a domain-specific language
for specifying tree data structures. The ASDL tools accept an ASDL grammar and
generate code to construct, read, and write these data structures. Using ASDL
automates implementing parts of the debugger, and the grammar documents the
symbol table concisely. Using ASDL also suggested simplifications to the
interface between the debugger and the target program. Perhaps most important,
ASDL emphasizes that symbol tables are data structures, not file formats. Many
of the pitfalls of working with low-level file formats can be avoided by
focusing instead on high-level data structures and automating the
implementation details.


  We introduce the wrapped Donaldson-Fukaya category of a (generalized)
semi-toric SYZ fibration with Lagrangian section satisfying a tameness
condition at infinity. Examples include the Gross fibration on the complement
of an anti-canonical divisor in a toric Calabi-Yau 3-fold. We compute the
wrapped Floer cohomology of a Lagrangian section and find that it is the
algebra of functions on the Hori-Vafa mirror. The latter result is the key step
in proving homological mirror symmetry for this case. The techniques developed
here allow the construction in general of the wrapped Fukaya category on an
open Calabi-Yau manifold carrying an SYZ fibration with nice behavior at
infinity. We discuss the relation of this to the algebraic vs analytic aspects
of mirror symmetry.


  This paper is concerned with learning to solve tasks that require a chain of
interdependent steps of relational inference, like answering complex questions
about the relationships between objects, or solving puzzles where the smaller
elements of a solution mutually constrain each other. We introduce the
recurrent relational network, a general purpose module that operates on a graph
representation of objects. As a generalization of Santoro et al. [2017]'s
relational network, it can augment any neural network model with the capacity
to do many-step relational reasoning. We achieve state of the art results on
the bAbI textual question-answering dataset with the recurrent relational
network, consistently solving 20/20 tasks. As bAbI is not particularly
challenging from a relational reasoning point of view, we introduce
Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the
Pretty-CLEVR set-up, we can vary the question to control for the number of
relational reasoning steps that are required to obtain the answer. Using
Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational
and recurrent relational networks. Finally, we show how recurrent relational
networks can learn to solve Sudoku puzzles from supervised training data, a
challenging task requiring upwards of 64 steps of relational reasoning. We
achieve state-of-the-art results amongst comparable methods by solving 96.6% of
the hardest Sudoku puzzles.


  On the basis of a previous theoretical approach to the plastic flow of highly
refined materials, a physical explanation for diffusion bonding is essayed,
which yields closed--form equations relating the bonding progress with time,
temperature, applied pressure and the constants characterizing the material.
Excellent agreement with experiment is attained, with no adjustable parameter.
In the novel scheme, diffusion bonding is caused by the interpenetration of the
two sufaces at the grain level. The process is driven by the strong tensile
stress field induced in the plane of the interface by the plastic deformation
in the normal direction. The grain boundaries of each joining surface yield to
host grains of the other surface, releasing this way the internally generated
tensile stresses. Voids gradually close with the increment of the
interpenetrated areas. In this scheme bonding is not a matter of contacting and
atomic interdiffusion, but of grain exchange.


  We consider anomalous non-Markovian transport of Brownian particles in
viscoelastic fluid-like media with very large but finite macroscopic viscosity
under the influence of a constant force field F. The viscoelastic properties of
the medium are characterized by a power-law viscoelastic memory kernel which
ultra slow decays in time on the time scale \tau of strong viscoelastic
correlations. The subdiffusive transport regime emerges transiently for t<\tau.
However, the transport becomes asymptotically normal for t>>\tau. It is shown
that even though transiently the mean displacement and the variance both scale
sublinearly, i.e. anomalously slow, in time, <\delta x(t)> ~ F t^\alpha,
<\delta x^2(t)> ~ t^\alpha, 0<\alpha<1, the mean displacement at each instant
of time is nevertheless always larger than one obtained for normal transport in
a purely viscous medium with the same macroscopic viscosity obtained in the
Markovian approximation. This can have profound implications for the
subdiffusive transport in biological cells as the notion of "ultra-slowness"
can be misleading in the context of anomalous diffusion-limited transport and
reaction processes occurring on nano- and mesoscales.


  We investigate filtered clover fermions, built from fat gauge links, both in
one-loop perturbation theory and in numerical simulations. We use a variety of
filtering recipes (APE, HYP, EXP, HEX), some of which are suitable for a HMC
with dynamical fermions. A generic filtering together with a (fat-link) clover
term yields fermions with much reduced chiral symmetry breaking.


  Strategic Environmental Assessment is a procedure aimed at introducing
systematic assessment of the environmental effects of plans and programs. This
procedure is based on the so-called coaxial matrices that define dependencies
between plan activities (infrastructures, plants, resource extractions,
buildings, etc.) and positive and negative environmental impacts, and
dependencies between these impacts and environmental receptors. Up to now, this
procedure is manually implemented by environmental experts for checking the
environmental effects of a given plan or program, but it is never applied
during the plan/program construction. A decision support system, based on a
clear logic semantics, would be an invaluable tool not only in assessing a
single, already defined plan, but also during the planning process in order to
produce an optimized, environmentally assessed plan and to study possible
alternative scenarios. We propose two logic-based approaches to the problem,
one based on Constraint Logic Programming and one on Probabilistic Logic
Programming that could be, in the future, conveniently merged to exploit the
advantages of both. We test the proposed approaches on a real energy plan and
we discuss their limitations and advantages.


  Social dilemmas are an integral part of social interactions. Cooperative
actions, ranging from secreting extra-cellular products in microbial
populations to donating blood in humans, are costly to the actor and hence
create an incentive to shirk and avoid the costs. Nevertheless, cooperation is
ubiquitous in nature. Both costs and benefits often depend non-linearly on the
number and types of individuals involved -- as captured by idioms such as `too
many cooks spoil the broth' where additional contributions are discounted, or
`two heads are better than one' where cooperators synergistically enhance the
group benefit. Interaction group sizes may depend on the size of the population
and hence on ecological processes. This results in feedback mechanisms between
ecological and evolutionary processes, which jointly affect and determine the
evolutionary trajectory. Only recently combined eco-evolutionary processes
became experimentally tractable in microbial social dilemmas. Here we analyse
the evolutionary dynamics of non-linear social dilemmas in settings where the
population fluctuates in size and the environment changes over time. In
particular, cooperation is often supported and maintained at high densities
through ecological fluctuations. Moreover, we find that the combination of the
two processes routinely reveals highly complex dynamics, which suggests common
occurrence in nature.


  Heavy neutrinos were sought in pion decays $\pi^+ \rightarrow \mu^+ \nu$ by
examining the observed muon energy spectrum for extra peaks in addition to the
expected peak for a massless neutrino. No evidence for heavy neutrinos was
observed. Upper limits were set on the neutrino mixing matrix $|U_{\mu i}|^2$
in the neutrino mass region of 15.7--33.8 MeV/c$^2$, improving on previous
results by an order of magnitude.


  Data science and informatics tools have been proliferating recently within
the computational materials science and catalysis fields. This proliferation
has spurned the creation of various frameworks for automated materials
screening, discovery, and design. Underpinning these frameworks are surrogate
models with uncertainty estimates on their predictions. These uncertainty
estimates are instrumental for determining which materials to screen next, but
the computational catalysis field does not yet have a standard procedure for
judging the quality of such uncertainty estimates. Here we present a suite of
figures and performance metrics derived from the machine learning community
that can be used to judge the quality of such uncertainty estimates. This suite
probes the accuracy, calibration, and sharpness of a model quantitatively. We
then show a case study where we judge various methods for predicting
density-functional-theory-calculated adsorption energies. Of the methods
studied here, we find that the best performer is a model where a convolutional
neural network is used to supply features to a Gaussian process regressor,
which then makes predictions of adsorption energies along with corresponding
uncertainty estimates.


  Systems which incrementally create 3D semantic maps from image sequences must
store and update representations of both geometry and semantic entities.
However, while there has been much work on the correct formulation for
geometrical estimation, state-of-the-art systems usually rely on simple
semantic representations which store and update independent label estimates for
each surface element (depth pixels, surfels, or voxels). Spatial correlation is
discarded, and fused label maps are incoherent and noisy.
  We introduce a new compact and optimisable semantic representation by
training a variational auto-encoder that is conditioned on a colour image.
Using this learned latent space, we can tackle semantic label fusion by jointly
optimising the low-dimenional codes associated with each of a set of
overlapping images, producing consistent fused label maps which preserve
spatial correlation. We also show how this approach can be used within a
monocular keyframe based semantic mapping system where a similar code approach
is used for geometry. The probabilistic formulation allows a flexible
formulation where we can jointly estimate motion, geometry and semantics in a
unified optimisation.


  This study tackles the challenges associated with interpreting Application
Programming Interface (API) documentation, an integral aspect of software
development. Official API documentation, while essential, can be lengthy and
challenging to navigate, prompting developers to seek unofficial sources such
as Stack Overflow. Leveraging the vast user-generated content on Stack
Overflow, including code snippets and discussions, we employ BERTopic and
extractive summarization to automatically generate concise and informative API
summaries. These summaries encompass key insights like general usage, common
developer issues, and potential solutions, sourced from the wealth of knowledge
on Stack Overflow. Software developers evaluate these summaries for
performance, coherence, and interoperability, providing valuable feedback on
the practicality of our approach.


  This paper has been withdrawn by the authors, the main result being known
since Lam and Leung, J. Algebra 2000.


  We consider multidimensional gravity with a Lagrangian containing the Ricci
tensor squared and the Kretschmann invariant. In a Kaluza-Klein approach with a
single compact extra space of arbitrary dimension, with the aid of a
slow-change approximation (as compared with the Planck scale), we build a class
of spatially flat cosmological models in which both the observed scale factor
$a(\tau)$ and the extra-dimensional one, $b(\tau)$, grow exponentially at large
times, but $b(\tau)$ grows slowly enough to admit variations of the effective
gravitational constant $G$ within observational limits. Such models predict a
drastic change in the physical laws of our Universe in the remote future due to
further growth of the extra dimensions.


  Contrastive divergence (CD) is a promising method of inference in high
dimensional distributions with intractable normalizing constants, however, the
theoretical foundations justifying its use are somewhat shaky. This document
proposes a framework for understanding CD inference, how/when it works, and
provides multiple justifications for the CD moment conditions, including
framing them as a variational approximation. Algorithms for performing
inference are discussed and are applied to social network data using an
exponential-family random graph models (ERGM). The framework also provides
guidance about how to construct MCMC kernels providing good CD inference, which
turn out to be quite different from those used typically to provide fast global
mixing.


  Various concepts of mean shape previously unrelated in the literature are
brought into relation. In particular for non-manifolds such as Kendall's 3D
shape space, this paper answers the question, for which means one may apply a
two-sample test. The answer is positive if intrinsic or Ziezold means are used.
The underlying general result of manifold stability of a mean on a shape space,
the quotient due to an isometric action of a compact Lie group on a Riemannian
manifold, blends the Slice Theorem from differential geometry with the
statistics of shape. For 3D Procrustes means, however, a counterexample is
given. To further elucidate on subtleties of means, for spheres and Kendall's
shape spaces, a first order relationship between intrinsic,
residual/Procrustean and extrinsic/Ziezold means is derived stating that for
high concentration the latter approximately divides the (generalized) geodesic
segment between the former two by the ratio $1:3$. This fact, consequences of
coordinate choices for the power of tests and other details, e.g. that
extrinsic Schoenberg means may increase dimension are discussed and illustrated
by simulations and exemplary datasets.


  Recent technical advancements allow cardiac MRI (CMR) examinations in the
presence of so-called MRI conditional active cardiac implants at 3.0T. However,
the artifact burden caused by susceptibility effects remain an obstacle. All
measurements were obtained at a clinical 3.0T scanner using an in-house
designed cubic phantom and optimized sequences for artifact evaluation (3D
gradient echo sequence, multi-slice 2D turbo spin echo sequence), as well as
reference sequences according to the ASTM were applied. Four representative
active cardiac devices and a generic setup were analysed regarding volume and
shape of the signal void. For analysis, a threshold operation applied to the
grey value profle of each data data set was used. The presented approach allows
the evaluation of signal void and shape even for larger implants such as ICDs.
The void shape is influenced by the orientation of the B0-field and the chosen
sequence type, as well as the distribution of magnetic material within the
implants. The void volume depends both on the device itself, and the sequence
type. Disturbances in the B0 and B1 fields exceed the visual signal void. This
work presents a reproducible and highly defined approach towards characterising
both signal void artifacts at 3.0T and their influencing factors.


  The integral monodromy on the Milnor lattice of an isolated quasihomogeneous
singularity is subject of an almost untouched conjecture of Orlik from 1972. We
prove this conjecture for all iterated Thom-Sebastiani sums of chain type
singularities and cycle type singularities. The main part of the paper is
purely algebraic. It provides tools for dealing with sums and tensor products
of ${\mathbb Z}$-lattices with automorphisms of finite order and with cyclic
generators. The calculations are involved. They use fine properties of unit
roots, cyclotomic polynomials, their resultants and discriminants.


  This note focuses on the optimization of neural architectures for stock index
movement forecasting following a major market disruption or crisis. Given that
such crises may introduce a shift in market dynamics, this study aims to
investigate whether the training data from market dynamics prior to the crisis
are compatible with the data during the crisis period. To this end, two
distinct learning environments are designed to evaluate and reconcile the
effects of possibly different market dynamics. These environments differ
principally based on the role assigned to the pre-crisis data. In both
environments, a set of non-dominated architectures are identified to satisfy
the multi-criteria co-evolution problem, which simultaneously addresses the
selection issues related to features and hidden layer topology. To test the
hypothesis of pre-crisis data incompatibility, the day-ahead movement
prediction of the NASDAQ index is considered during two recent and major market
disruptions; the 2008 financial crisis and the COVID-19 pandemic. The results
of a detailed comparative evaluation convincingly support the incompatibility
hypothesis and highlight the need to select re-training windows carefully.


  In general relativity, greybody factor is a quantity related to the quantum
nature of a black hole. A high value of greybody factor indicates a high
probability that Hawking radiation can reach infinity. Although general
relativity is correct and has been successful in describing many phenomena,
there are some questions that general relativity cannot answer. Therefore,
general relativity is often modified to attain answers. One of the
modifications is the `massive gravity'. The viable model of the massive gravity
theory belongs to de Rham, Gabadadze and Tolley (dRGT). In this paper, we
calculate the gravitational potential for the de Sitter black hole and for the
dRGT black hole. We also derive the rigorous bound on the greybody factor for
the de Sitter black hole and the dRGT black hole. It is found that the
structure of potentials determines how much the rigorous bound on the greybody
factor should be. That is, the higher the potential, the lesser the bound on
the greybody factor will be. Moreover, we compare the greybody factor derived
from the rigorous bound with the greybody factor derived from the matching
technique. The result shows that the rigorous bound is a true lower bound
because it is less than the greybody factor obtained from the matching
technique.


  We discuss an effect of the intergalactic absorption of the TeV gamma-rays in
time-averaged spectrum of Mkn 501 measured by the HEGRA Collaboration. Analysis
of the spectral behavior, variability time scale and relevant calculations of
TeV gamma-ray emission allow to conclude the presence of a noticeable
absorption of the TeV gamma-rays in the Mkn 501 energy spectrum.


  The generalized Oberwolfach problem asks for a factorization of the complete
graph $K_v$ into prescribed $2$-factors and at most a $1$-factor. When all
$2$-factors are pairwise isomorphic and $v$ is odd, we have the classic
Oberwolfach problem, which was originally stated as a seating problem: given
$v$ attendees at a conference with $t$ circular tables such that the $i$th
table seats $a_i$ people and ${\sum_{i=1}^t a_i = v}$, find a seating
arrangement over the $\frac{v-1}{2}$ days of the conference, so that every
person sits next to each other person exactly once.
  In this paper we introduce the related {\em minisymposium problem}, which
requires a solution to the generalized Oberwolfach problem on $v$ vertices that
contains a subsystem on $m$ vertices. That is, the decomposition restricted to
the required $m$ vertices is a solution to the generalized Oberwolfach problem
on $m$ vertices. In the seating context above, the larger conference contains a
minisymposium of $m$ participants, and we also require that pairs of these $m$
participants be seated next to each other for
$\left\lfloor\frac{m-1}{2}\right\rfloor$ of the days.
  When the cycles are as long as possible, i.e.\ $v$, $m$ and $v-m$, a flexible
method of Hilton and Johnson provides a solution. We use this result to provide
further solutions when $v \equiv m \equiv 2 \pmod 4$ and all cycle lengths are
even. In addition, we provide extensive results in the case where all cycle
lengths are equal to $k$, solving all cases when $m\mid v$, except possibly
when $k$ is odd and $v$ is even.


  We study the effect of electric charge in compact stars assuming that the
charge distribution is proportional to the mass density. The pressure and the
density of the matter inside the stars are large, and the gravitational field
is intense. This indicates that electric charge and a strong electric field can
also be present. The relativistic hydrostatic equilibrium equation, i.e., the
Tolman-Oppenheimer-Volkoff equation, is modified in order to include electric
charge. We perform a detailed numerical study of the effect of electric charge
using a polytropic equation of state. We conclude that in order to see any
appreciable effect on the phenomenology of the compact stars, the electric
fields have to be huge (~ 10^{21} V/m), which implies that the total charge is
Q ~ 10^{20} Coulomb. From the local effect of the forces experienced on a
single charged particle, it is expected that each individual charged particle
is quickly ejected from the star. This in turn produces a huge force imbalance,
and the gravitational force overwhelms the repulsive Coulomb and fluid pressure
forces. The star can then collapse to form a charged black hole before all the
charge leaves the system.


  We propose that Bayesian variable selection for linear parametrisations with
Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised
parameter space. Our r-prior results in closed forms for the evidence for four
examples, including the hyper-g prior and the Zellner-Siow prior, which are
shown to be special cases. Scenarios of a single variable dispersion parameter
and of fixed dispersion are studied, and asymptotic forms comparable to the
traditional information criteria are derived. A simulation exercise shows that
model comparison based on our r-prior gives good results comparable to or
better than current model comparison schemes.


  We present LiRank, a large-scale ranking framework at LinkedIn that brings to
production state-of-the-art modeling architectures and optimization methods. We
unveil several modeling improvements, including Residual DCN, which adds
attention and residual connections to the famous DCNv2 architecture. We share
insights into combining and tuning SOTA architectures to create a unified
model, including Dense Gating, Transformers and Residual DCN. We also propose
novel techniques for calibration and describe how we productionalized deep
learning based explore/exploit methods. To enable effective, production-grade
serving of large ranking models, we detail how to train and compress models
using quantization and vocabulary compression. We provide details about the
deployment setup for large-scale use cases of Feed ranking, Jobs
Recommendations, and Ads click-through rate (CTR) prediction. We summarize our
learnings from various A/B tests by elucidating the most effective technical
approaches. These ideas have contributed to relative metrics improvements
across the board at LinkedIn: +0.5% member sessions in the Feed, +1.76%
qualified job applications for Jobs search and recommendations, and +4.3% for
Ads CTR. We hope this work can provide practical insights and solutions for
practitioners interested in leveraging large-scale deep ranking systems.


  The field of the globular cluster M22 (NGC 6656) was monitored between 2000
and 2008 in a search for variable stars. $BV$ light curves were obtained for
359 periodic, likely periodic, and long-term variables, 238 of which are new
detections. Thirty nine newly detected variables, and 63 previously known ones
are members or likely members of the cluster, including 20 SX Phe, 10 RRab and
16 RRc-type pulsators, one BL Her-type pulsator, 21 contact binaries, and 9
detached or semi-detached eclipsing binaries. The most interesting among the
identified objects are V112 - a bright multimode SX Phe pulsator, V125 - a
$\beta$ Lyr-type binary on the blue horizontal branch, V129 - a blue/yellow
straggler with a W UMa-like light curve, located halfway between the extreme
horizontal branch and red giant branch, and V134 - an extreme horizontal branch
object with $P=2.33$ d and a nearly sinusoidal light curve; all four of them
are proper motion (PM) members of the cluster. Among nonmembers, a $P=2.83$ d
detached eclipsing binary hosting a $\delta$ Sct-type pulsator was found, and a
peculiar $P=0.93$ d binary with ellipsoidal modulation and narrow minimum in
the middle of one of the descending shoulders of the sinusoid. We also
collected substantial new data for previously known variables; in particular we
revise the statistics of the occurrence of the Blazhko effect in RR Lyr-type
variables of M22.


  We study the interaction between the microstructures of Hayward-AdS black
hole using Ruppeiner geometry. Our investigation shows that the dominant
interaction between the black hole molecules is attractive in most part of the
parametric space of temperature and volume, as in van der Waals system.
However, in contrast to the van der Waals fluid, there exists a weak dominant
repulsive interaction for small black hole phase in some parameter range. This
result clearly distinguishes the interactions in a magnetically charged black
hole from that of van der Waals fluid. However, these sort of interactions are
characteristic for charged black holes since they do not dependent on magnetic
charge or temperature.


  Given a parity-check matrix $H_m$ of a $q$-ary Hamming code, we consider a
partition of the columns into two subsets. Then, we consider the two codes that
have these submatrices as parity-check matrices. We say that anyone of these
two codes is the supplementary code of the other one.
  We obtain that if one of these codes is a Hamming code, then the
supplementary code is completely regular and completely transitive. If one of
the codes is completely regular with covering radius $2$, then the
supplementary code is also completely regular with covering radius at most $2$.
Moreover, in this case, either both codes are completely transitive, or both
are not.
  With this technique, we obtain infinite families of completely regular and
completely transitive codes which are quasi-perfect uniformly packed.


  In this paper we target the problem of transferring policies across multiple
environments with different dynamics parameters and motor noise variations, by
introducing a framework that decouples the processes of policy learning and
system identification. Efficiently transferring learned policies to an unknown
environment with changes in dynamics configurations in the presence of motor
noise is very important for operating robots in the real world, and our work is
a novel attempt in that direction. We introduce MANGA: Method Agnostic
Neural-policy Generalization and Adaptation, that trains dynamics conditioned
policies and efficiently learns to estimate the dynamics parameters of the
environment given off-policy state-transition rollouts in the environment. Our
scheme is agnostic to the type of training method used - both reinforcement
learning (RL) and imitation learning (IL) strategies can be used. We
demonstrate the effectiveness of our approach by experimenting with four
different MuJoCo agents and comparing against previously proposed transfer
baselines.


  Capacitance-Voltage (CV) measurements along with the Mott-Schottky (MS)
analysis are widely used for characterization of material and device
parameters. Using a simple analytical model, supported by detailed numerical
simulations, here we predict that the capacitance of thin film devices scale as
V^-2 (V is the applied potential), instead of the often used V^-0.5 dependence
of MS analysis- with significant implications towards extraction of parameters
like doping density, built-in voltage, etc. Surprisingly, we find that the
predicted trends are already hidden in multiple instances of existing
literature. As such, our results constitute a fundamental contribution to
semiconductor device physics and are directly applicable and immediately
relevant to a broad range of optoelectronic devices like organic solar cells,
perovskite-based solar cells, and LEDs, thin film a-Si devices, etc.


  Critically sized defects are currently treated via autologous or allograft
bone grafting, distraction osteogenesis, and membrane induction. However, these
methods have major weaknesses which encourage the development of synthetic bone
graft substitutes. A bioresorbable and physiologically load sustaining graft
substitute was fabricated from polylactic acid using 3D printing, a versatile
method which enables parameters to be customizable in a patient-specific
manner. The internal architecture consists of vertical and horizontal conduits
that are organized to achieve gradients in porosity and pore size in the radial
direction to emulate cortical bone encapsulating cancellous bone. A diameter of
30mm and height of 10mm was designed to target the repair of critically sized
long bone defects. The compressive properties of these graft substitutes were
determined to be comparable to adult human femurs. Furthermore, dynamic fatigue
testing at twice the human torso weight (800N) indicated that the bone graft
substitute achieved stability as quickly as 200,000 cycles, suggesting its
ability to support weight bearing loads while it gradually degrades as bone
cells proliferate and mineralize. Additionally, the graft substitutes were
seeded with human fetal osteoblasts to validate homogenous cellular attachment
and cytocompatibility. Graft substitutes were also dynamically cultured for 28
days under various loading regimens using human mesenchymal stem cell
differentiated osteoblasts, and these resulting tissue constructs were
subjected to fatigue testing. The frequency of loading during dynamic culturing
had a profound effect on the rate of mineralization which was particularly high
at 2Hz, confirmed by Alizarin Red staining of the calcium deposits. Taken
together, these bone graft substitutes have potential for use as orthopaedic
implants to facilitate the repair of critically sized bone defects.


  This paper studies identifiability and convergence behaviors for parameters
of multiple types in finite mixtures, and the effects of model fitting with
extra mixing components. First, we present a general theory for strong
identifiability, which extends from the previous work of Nguyen [2013] and Chen
[1995] to address a broad range of mixture models and to handle matrix-variate
parameters. These models are shown to share the same Wasserstein distance based
optimal rates of convergence for the space of mixing distributions ---
$n^{-1/2}$ under $W_1$ for the exact-fitted and $n^{-1/4}$ under $W_2$ for the
over-fitted setting, where $n$ is the sample size. This theory, however, is not
applicable to several important model classes, including location-scale
multivariate Gaussian mixtures, shape-scale Gamma mixtures and
location-scale-shape skew-normal mixtures. The second part of this work is
devoted to demonstrating that for these "weakly identifiable" classes,
algebraic structures of the density family play a fundamental role in
determining convergence rates of the model parameters, which display a very
rich spectrum of behaviors. For instance, the optimal rate of parameter
estimation in an over-fitted location-covariance Gaussian mixture is precisely
determined by the order of a solvable system of polynomial equations --- these
rates deteriorate rapidly as more extra components are added to the model. The
established rates for a variety of settings are illustrated by a simulation
study.


  The convex hull on three points in two dimensional euclidean space of three
flat edges (trihedron) was studied. The Bohr-Sommerfeld quantization of the
area of space is performed. It is shown that it reproduces exactly the
equidistant spacing spectrum found elsewhere.


  Using a novel electrochemical phase-field model, we question the common
belief that LixFePO4 nanoparticles separate into Li-rich and Li-poor phases
during battery discharge. For small currents, spinodal decomposition or
nucleation leads to moving phase boundaries. Above a critical current density
(in the Tafel regime), the spinodal disappears, and particles fill
homogeneously, which may explain the superior rate capability and long cycle
life of nano-LiFePO4 cathodes.


  We test the claim by Yu et al. -- presented in Science 322, 104 (2008) --
that the degree distribution of the yeast (Saccharomyces cerevisiae)
protein-interaction network is best approximated by a power law. Yu et al.
consider three versions of this network. In all three cases, however, we find
the most likely power-law model of the data is distinct from and incompatible
with the one given by Yu et al. Only one network admits good statistical
support for any power law, and in that case, the power law explains only the
distribution of the upper 10% of node degrees. These results imply that there
is considerably more structure present in the yeast interactome than suggested
by Yu et al., and that these networks should probably not be called "scale
free."


  Generalization error bounds are critical to understanding the performance of
machine learning models. In this work, we propose a new information-theoretic
based generalization error upper bound applicable to supervised learning
scenarios. We show that our general bound can specialize in various previous
bounds. We also show that our general bound can be specialized under some
conditions to a new bound involving the Jensen-Shannon information between a
random variable modelling the set of training samples and another random
variable modelling the hypothesis. We also prove that our bound can be tighter
than mutual information-based bounds under some conditions.


  When producing a model to object detection in a specific context, the first
obstacle is to have a dataset labeling the desired classes. In RoboCup, some
leagues already have more than one dataset to train and evaluate a model.
However, in the Small Size League (SSL), there is not such dataset available
yet. This paper presents an open-source dataset to be used as a benchmark for
real-time object detection in SSL. This work also presented a pipeline to
train, deploy, and evaluate Convolutional Neural Networks (CNNs) models in a
low-power embedded system. This pipeline was used to evaluate the proposed
dataset with state-of-art optimized models. In this dataset, the MobileNet SSD
v1 achieves 44.88% AP (68.81% AP50) at 94 Frames Per Second (FPS) while running
on an SSL robot.


  Unifying acoustic and linguistic representation learning has become
increasingly crucial to transfer the knowledge learned on the abundance of
high-resource language data for low-resource speech recognition. Existing
approaches simply cascade pre-trained acoustic and language models to learn the
transfer from speech to text. However, how to solve the representation
discrepancy of speech and text is unexplored, which hinders the utilization of
acoustic and linguistic information. Moreover, previous works simply replace
the embedding layer of the pre-trained language model with the acoustic
features, which may cause the catastrophic forgetting problem. In this work, we
introduce Wav-BERT, a cooperative acoustic and linguistic representation
learning method to fuse and utilize the contextual information of speech and
text. Specifically, we unify a pre-trained acoustic model (wav2vec 2.0) and a
language model (BERT) into an end-to-end trainable framework. A Representation
Aggregation Module is designed to aggregate acoustic and linguistic
representation, and an Embedding Attention Module is introduced to incorporate
acoustic information into BERT, which can effectively facilitate the
cooperation of two pre-trained models and thus boost the representation
learning. Extensive experiments show that our Wav-BERT significantly
outperforms the existing approaches and achieves state-of-the-art performance
on low-resource speech recognition.


  Syntactic parsing is an important step in the automated text analysis which
aims at information extraction. Quality of the syntactic parsing determines to
a large extent the recall and precision of the text mining results. In this
paper we evaluate the performance of several popular syntactic parsers in
application to the biomedical text mining.


  To cope with the increasing variability and sophistication of modern attacks,
machine learning has been widely adopted as a statistically-sound tool for
malware detection. However, its security against well-crafted attacks has not
only been recently questioned, but it has been shown that machine learning
exhibits inherent vulnerabilities that can be exploited to evade detection at
test time. In other words, machine learning itself can be the weakest link in a
security system. In this paper, we rely upon a previously-proposed attack
framework to categorize potential attack scenarios against learning-based
malware detection tools, by modeling attackers with different skills and
capabilities. We then define and implement a set of corresponding evasion
attacks to thoroughly assess the security of Drebin, an Android malware
detector. The main contribution of this work is the proposal of a simple and
scalable secure-learning paradigm that mitigates the impact of evasion attacks,
while only slightly worsening the detection rate in the absence of attack. We
finally argue that our secure-learning approach can also be readily applied to
other malware detection tasks.


  A geometrical interpretation of Schr\"odinger's kinetic and potential energy
operators is proposed, allowing for a covariant momentum space formulation of
the dynamics that is relevant for the theories with the deformation of the
momentum space structure. Some specific examples are discussed in the context
of flat space deformations and the Euclidean Snyder (spherical momentum space)
model. In this formulation the dynamics for the deformations of the flat
momentum space becomes trivial, while different versions of the Snyder model
turn out to be dynamically equivalent.


  Supersymmetry and Lorentz invariance are closely related as both are
spacetime symmetries. Terms can be added to Lagrangians that explicitly break
either supersymmetry or Lorentz invariance. It is possible to include terms
which violate Lorentz invariance but maintain invariance under supersymmetric
transformations. I illustrate this with some simple extensions of the original
Wess-Zumino model.


  We define a collection of topological Ramsey spaces consisting of equivalence
relations on $\omega$ with the property that the minimal representatives of the
equivalence classes alternate according to a fixed partition of $\omega$. To
prove the associated pigeonhole principles, we make use of the left-variable
Hales-Jewett theorem and its extension to an infinite alphabet. We also show
how to transfer the corresponding infinite-dimensional Ramsey results to
equivalence relations on countable limit ordinals (up to a necessary
restriction on the set of minimal representatives of the equivalence classes)
in order to obtain a dual Ramsey theorem for such ordinals.


  Transformer has shown great successes in natural language processing,
computer vision, and audio processing. As one of its core components, the
softmax attention helps to capture long-range dependencies yet prohibits its
scale-up due to the quadratic space and time complexity to the sequence length.
Kernel methods are often adopted to reduce the complexity by approximating the
softmax operator. Nevertheless, due to the approximation errors, their
performances vary in different tasks/corpus and suffer crucial performance
drops when compared with the vanilla softmax attention. In this paper, we
propose a linear transformer called cosFormer that can achieve comparable or
better accuracy to the vanilla transformer in both casual and cross attentions.
cosFormer is based on two key properties of softmax attention: i).
non-negativeness of the attention matrix; ii). a non-linear re-weighting scheme
that can concentrate the distribution of the attention matrix. As its linear
substitute, cosFormer fulfills these properties with a linear operator and a
cosine-based distance re-weighting mechanism. Extensive experiments on language
modeling and text understanding tasks demonstrate the effectiveness of our
method. We further examine our method on long sequences and achieve
state-of-the-art performance on the Long-Range Arena benchmark. The source code
is available at https://github.com/OpenNLPLab/cosFormer.


  We study the behavior of a Time-Aware Long Short-Term Memory Autoencoder, a
state-of-the-art method, in the context of learning latent representations from
irregularly sampled patient data. We identify a key issue in the way such
recurrent neural network models are being currently used and show that the
solution of the issue leads to significant improvements in the learnt
representations on both synthetic and real datasets. A detailed analysis of the
improved methodology for representing patients suffering from Chronic Kidney
Disease (CKD) using clinical data is provided. Experimental results show that
the proposed T-LSTM model is able to capture the long-term trends in the data,
while effectively handling the noise in the signal. Finally, we show that by
using the latent representations of the CKD patients obtained from the T-LSTM
autoencoder, one can identify unusual patient profiles from the target
population.


  In the Bayesian community, an ongoing imperative is to develop efficient
algorithms. An appealing approach is to form a hybrid algorithm by combining
ideas from competing existing techniques. This paper addresses issues in
designing hybrid methods by considering selected case studies: the delayed
rejection algorithm, the pinball sampler, the Metropolis adjusted Langevin
algorithm, and the population Monte Carlo algorithm. We observe that even if
each component of a hybrid algorithm has individual strengths, they may not
contribute equally or even positively when they are combined. Moreover, even if
the statistical efficiency is improved, from a practical perspective there are
technical issues to be considered such as applicability and computational
workload. In order to optimize performance of the algorithm in real time, these
issues should be taken into account.


  In recent years, the near diagonal asymptotics of the equivariant components
of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic
manifold have been studied extensively by many authors. As a natural
generalization of this theme, here we consider the local scaling asymptotics of
the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically
how they concentrate on the graph of the underlying classical map.


  We study $\mathcal{N}=4$ supersymmetric QED in three dimensions, on a
three-sphere, with 2N massive hypermultiplets and a Fayet-Iliopoulos parameter.
We identify the exact partition function of the theory with a conical (Mehler)
function. This implies a number of analytical formulas, including a recurrence
relation and a second-order differential equation, associated with an
integrable system. In the large N limit, the theory undergoes a second-order
phase transition on a critical line in the parameter space. We discuss the
critical behavior and compute the two-point correlation function of a gauge
invariant mass operator, which is shown to diverge as one approaches
criticality from the subcritical phase. Finally, we comment on the asymptotic
1/N expansion and on mirror symmetry.


  We analyze {\it Spitzer} and Magellan observations of a star forming core
near IRS-2 in the young cluster NGC 2264. The submillimeter source IRAS 12 S1,
previously believed to be an intermediate mass Class 0 object is shown to be a
dense collection of embedded, low mass stars. We argue that this group of stars
represents the fragmenting collapse of a dense, turbulent core, based on a
number of indicators of extreme youth. With reasonable estimates for the
velocity dispersion in the group, we estimate a dynamical lifetime of only a
few x 10$^{4}$ years. Spectral energy distributions of stars in the core are
consistent with Class I or Class 0 assignments. We present observations of an
extensive system of molecular hydrogen emission knots. The luminosity of the
objects in the core region are consistent with roughly solar mass protostars.


  We introduce a functional of the local spectral electron density which can be
used to to compute the total energy and the local spectral function of
strongly-correlated materials. We illustrate the applicability of the method by
using as an example the long-standing problem of the electronic structure of
metallic plutonium.


  We present a novel methodology to compute relaxed dislocations core
configurations, and their energies in crystalline metallic materials using
large-scale \emph{ab-intio} simulations. The approach is based on MacroDFT, a
coarse-grained density functional theory method that accurately computes the
electronic structure but with sub-linear scaling resulting in a tremendous
reduction in cost. Due to its implementation in \emph{real-space}, MacroDFT has
the ability to harness petascale resources to study materials and alloys
through accurate \emph{ab-initio} calculations. Thus, the proposed methodology
can be used to investigate dislocation cores and other defects where long range
elastic defects play an important role, such as in dislocation cores, grain
boundaries and near precipitates in crystalline materials. We demonstrate the
method by computing the relaxed dislocation cores in prismatic dislocation
loops and dislocation segments in magnesium (Mg). We also study the interaction
energy with a line of Aluminum (Al) solutes. Our simulations elucidate the
essential coupling between the quantum mechanical aspects of the dislocation
core and the long range elastic fields that they generate. In particular, our
quantum mechanical simulations are able to describe the logarithmic divergence
of the energy in the far field as is known from classical elastic theory. In
order to reach such scaling, the number of atoms in the simulation cell has to
be exceedingly large, and cannot be achieved with the state-of-the-art density
functional theory implementations.


  Convolutional neural networks have demonstrated high accuracy on various
tasks in recent years. However, they are extremely vulnerable to adversarial
examples. For example, imperceptible perturbations added to clean images can
cause convolutional neural networks to fail. In this paper, we propose to
utilize randomization at inference time to mitigate adversarial effects.
Specifically, we use two randomization operations: random resizing, which
resizes the input images to a random size, and random padding, which pads zeros
around the input images in a random manner. Extensive experiments demonstrate
that the proposed randomization method is very effective at defending against
both single-step and iterative attacks. Our method provides the following
advantages: 1) no additional training or fine-tuning, 2) very few additional
computations, 3) compatible with other adversarial defense methods. By
combining the proposed randomization method with an adversarially trained
model, it achieves a normalized score of 0.924 (ranked No.2 among 107 defense
teams) in the NIPS 2017 adversarial examples defense challenge, which is far
better than using adversarial training alone with a normalized score of 0.773
(ranked No.56). The code is public available at
https://github.com/cihangxie/NIPS2017_adv_challenge_defense.


  Two unavoidable processes punctuate our century: The unprecedented
urbanisation of our planet (United Nations, 2014) and the spread of ubiquitous
computing (Weiser, 1991) and urban data streams. This process of urbanisation
corresponds with the process of digitalisation of urban life: while
urbanisation acts on a physical infrastructural level, the digital develops as
a kind of metastructure above the infrastructure. This metastructural level
offers a flexible framework through which information is continuously and
operatively being symbolized. Today, Information technology and the
availability of abundant urban data streams could be considered as forerunners
of our time, having unprecedented impacts comparable to the ones brought by the
steam engine at the dawn of industrialisation and the electrification of
cities. It is therefore no longer conceivable to think of the physical
structure of the city without including its digital counterpart. Against this
background, we will explore the role of computational power and information
technologies as dominant factors in the formation of computational urban models
and normative city theories. We will show how these models and theories,
emerging mainly during the 19th and 20th centuries, present leaping
correspondences with more ancient conceptions of the city, when observed from a
meta-level or episteme (Foucault, 2002) approach. First, and for the sake of
clarity, we will deal with some methodological elucidations around the concepts
of theory, model and episteme, and how we will refer conceptually to these
terms throughout this paper. Secondly, we will review these evolving
technological and computational levels of abstraction and their influence on
the different conceptions of the city. Thirdly, we will develop the hypothesis
of a conceptual gap, between our current technological capacity -- grounded on
the abundance and availability of urban data streams -- and the state of the
art in urban modelling and city theory. Lastly, building upon Foucault's
concept of episteme (Foucault, 1970) and genealogy (Foucault, 1977b), we will
explore this gap by speculating around the possibility of an inversion in
computational urban modelling and city theory. And above all, we will question
the terms in which we can think of the city, in an age where the world can be
virtually conceived as fully urban, and the continuity and abundance of urban
data streams giving account of it can be taken for granted. How are we
articulating the phenomena we call city on top of this generic common ground?


  We study the application of the classical equations of motion (EOM) within
the framework of an effective low-energy Lagrangian treated at the loop level.
Gauge-fixing and ghost terms, which enter naturally in the EOM, are found to
lead to no physical effects --- neither through operator mixing nor in matrix
elements. Beyond first order in the effective interactions, contact terms have
to be included when reducing the effective Lagrangian and we present an
explicit procedure to construct them. Applied to (hadronic) rare B-decays, the
EOM drastically simplify the effective Lagrangian and its matching to the
underlying theory, and certain cancellations of large (logarithmic)
contributions become more transparent. Finally, we discuss details of the
`matching' of the effective Lagrangian, which may be helpful in incorporating
short distance QCD corrections in further phenomenological studies.


  We present numerical simulations of circumbinary accretion onto eccentric and
circular binaries using the moving-mesh code AREPO. This is the first set of
simulations to tackle the problem of binary accretion using a finite-volume
scheme on a freely moving mesh, which allows for accurate measurements of
accretion onto individual stars for arbitrary binary eccentricity. While
accretion onto a circular binary shows bursts with period of ~5 times the
binary period P_b,accretion onto an eccentric binary is predominantly modulated
at the period ~1P_b. For an equal-mass circular binary, the accretion rates
onto individual stars are quite similar to each other, following the same
variable pattern in time. By contrast, for eccentric binaries, one of the stars
can accrete at a rate 10-20 times larger than its companion. This "symmetry
breaking" between the stars, however, alternates over timescales of order 200
P_b, and can be attributed to a slowly precessing, eccentric circumbinary disk.
Over longer timescales, the net accretion rates onto individual stars are the
same, reaching a quasi-steady state with the circumbinary disk. These results
have important implications for the accretion behavior of binary T-Tauri stars
and supermassive binary black holes.


  Recently H. Georgi suggested that a scale invariant unparticle
${\mathcal{U}}$ sector with an infrared fixed point at high energy can couple
with the SM matter via a higher-dimensional operator suppressed by a high
cut-off scale. Intense phenomenological search of this unparticle sector in the
collider and flavour physics context has already been made. Here we explore
it's impact in cosmology, particularly it's possible role in the supernovae
cooling. We found that the energy-loss rate (and thus the cooling) is strongly
dependent on the effective scale \LdaU and the anomalous dimension \dU of this
unparticle theory.


  Combination of neutron scattering and thermal expansion measurements under
pressure shows that the so-called hidden order phase of URu2Si2 reenters in
magnetic field when antiferromagnetism (AF) collapses at H_AF (T). Macroscopic
pressure studies of the HO-AF boundaries were realized at different pressures
via thermal expansion measurements under magnetic field using a strain gauge.
Microscopic proof at a given pressure is the reappearance of the resonance at
Q_0=(1,0,0) under field which is correlated with the collapse of the AF Bragg
reflections at Q_0.


  A rapidly growing number of voices argue that AI research, and computer
vision in particular, is powering mass surveillance. Yet the direct path from
computer vision research to surveillance has remained obscured and difficult to
assess. Here, we reveal the Surveillance AI pipeline by analyzing three decades
of computer vision research papers and downstream patents, more than 40,000
documents. We find the large majority of annotated computer vision papers and
patents self-report their technology enables extracting data about humans.
Moreover, the majority of these technologies specifically enable extracting
data about human bodies and body parts. We present both quantitative and rich
qualitative analysis illuminating these practices of human data extraction.
Studying the roots of this pipeline, we find that institutions that
prolifically produce computer vision research, namely elite universities and
"big tech" corporations, are subsequently cited in thousands of surveillance
patents. Further, we find consistent evidence against the narrative that only
these few rogue entities are contributing to surveillance. Rather, we expose
the fieldwide norm that when an institution, nation, or subfield authors
computer vision papers with downstream patents, the majority of these papers
are used in surveillance patents. In total, we find the number of papers with
downstream surveillance patents increased more than five-fold between the 1990s
and the 2010s, with computer vision research now having been used in more than
11,000 surveillance patents. Finally, in addition to the high levels of
surveillance we find documented in computer vision papers and patents, we
unearth pervasive patterns of documents using language that obfuscates the
extent of surveillance. Our analysis reveals the pipeline by which computer
vision research has powered the ongoing expansion of surveillance.


  We present an example of quantum process tomography performed on a single
solid state qubit. The qubit used is two energy levels of the triplet state in
the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied
to a qubit which has been allowed to decohere for three different time periods.
In each case the process is found in terms of the $\chi$ matrix representation
and the affine map representation. The discrepancy between experimentally
estimated process and the closest physically valid process is noted.


  We investigate the joint asymptotic behavior of so-called blocks estimator of
the extremal index, that determines the mean length of clusters of extremes,
based on the exceedances over different thresholds. Due to the large bias of
these estimators, the resulting estimates are usually very sensitive to the
choice of the threshold and thus difficult to interpret. We propose and examine
a bias correction that asymptotically removes the leading bias term while the
rate of convergence of the random error is preserved.


  For the traditional denial-of-service attack detection methods have complex
algorithms and high computational overhead, which are difficult to meet the
demand of online detection; and the experimental environment is mostly a
simulation platform, which is difficult to deploy in real network environment,
we propose a real network environment-oriented LDoS attack detection method
based on the time-frequency characteristics of traffic data. All the traffic
data flowing through the Web server is obtained through the acquisition storage
system, and the detection data set is constructed using pre-processing; the
simple features of the flow fragments are used as input, and the deep neural
network is used to learn the time-frequency domain features of normal traffic
features and generate reconstructed sequences, and the LDoS attack is
discriminated based on the differences between the reconstructed sequences and
the input data in the time-frequency domain. The experimental results show that
the proposed method can accurately detect the attack features in the flow
fragments in a very short time and achieve high detection accuracy for complex
and diverse LDoS attacks; since only the statistical features of the packets
are used, there is no need to parse the packet data, which can be adapted to
different network environments.


  This paper explores using generative AI and aesthetics to promote cultural
creativity in rural China amidst COVID-19's impact. Through literature reviews,
case studies, surveys, and text analysis, it examines art and technology
applications in rural contexts and identifies key challenges. The study finds
artworks often fail to resonate locally, while reliance on external artists
limits sustainability. Hence, nurturing grassroots "artist villagers" through
AI is proposed. Our approach involves training machine learning on subjective
aesthetics to generate culturally relevant content. Interactive AI media can
also boost tourism while preserving heritage. This pioneering research puts
forth original perspectives on the intersection of AI and aesthetics to
invigorate rural culture. It advocates holistic integration of technology and
emphasizes AI's potential as a creative enabler versus replacement. Ultimately,
it lays the groundwork for further exploration of leveraging AI innovations to
empower rural communities. This timely study contributes to growing interest in
emerging technologies to address critical issues facing rural China.


  Deep neural network models trained on large labeled datasets are the
state-of-the-art in a large variety of computer vision tasks. In many
applications, however, labeled data is expensive to obtain or requires a time
consuming manual annotation process. In contrast, unlabeled data is often
abundant and available in large quantities. We present a principled framework
to capitalize on unlabeled data by training deep generative models on both
labeled and unlabeled data. We show that such a combination is beneficial
because the unlabeled data acts as a data-driven form of regularization,
allowing generative models trained on few labeled samples to reach the
performance of fully-supervised generative models trained on much larger
datasets. We call our method Hybrid VAE (H-VAE) as it contains both the
generative and the discriminative parts. We validate H-VAE on three large-scale
datasets of different modalities: two face datasets: (MultiPIE, CelebA) and a
hand pose dataset (NYU Hand Pose). Our qualitative visualizations further
support improvements achieved by using partial observations.


  In this paper we are consider radiating solitary wave solutions of coupled
regularised Boussinesq equations. This type of solution consists of a leading
solitary wave with a small-amplitude co-propagating oscillatory tail, and
emerges from a pure solitary wave solution of a symmetric reduction of the full
system. We construct an asymptotic solution, where the leading order
approximation in both components is obtained as a particular solution of the
regularised Boussinesq equations in the symmetric case. At the next order, the
system uncouples into two linear non-homogeneous ordinary differential
equations with variable coefficients, one correcting the localised part of the
solution, which we find analytically, and the other describing the
co-propagating oscillatory tail. This latter equation is a fourth-order
ordinary differential equation and is solved approximately by two different
methods, each exploiting the assumption that the leading solitary wave has a
small amplitude, and thus enabling an explicit estimate for the amplitude of
the oscillating tail. These estimates are compared with corresponding numerical
simulations.


  Although the conventional mask-based minimum variance distortionless response
(MVDR) could reduce the non-linear distortion, the residual noise level of the
MVDR separated speech is still high. In this paper, we propose a
spatio-temporal recurrent neural network based beamformer (RNN-BF) for target
speech separation. This new beamforming framework directly learns the
beamforming weights from the estimated speech and noise spatial covariance
matrices. Leveraging on the temporal modeling capability of RNNs, the RNN-BF
could automatically accumulate the statistics of the speech and noise
covariance matrices to learn the frame-level beamforming weights in a recursive
way. An RNN-based generalized eigenvalue (RNN-GEV) beamformer and a more
generalized RNN beamformer (GRNN-BF) are proposed. We further improve the
RNN-GEV and the GRNN-BF by using layer normalization to replace the commonly
used mask normalization on the covariance matrices. The proposed GRNN-BF
obtains better performance against prior arts in terms of speech quality
(PESQ), speech-to-noise ratio (SNR) and word error rate (WER).


  A hallmark of modern large language models (LLMs) is their impressive general
zero-shot and few-shot abilities, often elicited through in-context learning
(ICL) via prompting. However, while highly coveted and being the most general,
zero-shot performances in LLMs are still typically weaker due to the lack of
guidance and the difficulty of applying existing automatic prompt design
methods in general tasks when ground-truth labels are unavailable. In this
study, we address this by presenting Universal Self-Adaptive Prompting (USP),
an automatic prompt design approach specifically tailored for zero-shot
learning (while compatible with few-shot). Requiring only a small amount of
unlabeled data and an inference-only LLM, USP is highly versatile: to achieve
universal prompting, USP categorizes a possible NLP task into one of the three
possible task types and then uses a corresponding selector to select the most
suitable queries and zero-shot model-generated responses as
pseudo-demonstrations, thereby generalizing ICL to the zero-shot setup in a
fully automated way. We evaluate USP with PaLM and PaLM 2 models and
demonstrate performances that are considerably stronger than standard zero-shot
baselines and often comparable to or even superior to few-shot baselines across
more than 40 natural language understanding, natural language generation, and
reasoning tasks.


  In this work, we investigate the equilibrium figures of a dumb-bell-shaped
sequence with which we are still not well acquainted. Studies have shown that
these elongated and nonconvex figures may realistically replace the classic
"Roche binary approximation" for modeling putative peanut-shaped or contact
binary asteroids. The best-fit dumb-bell shapes, combined with the known
rotational period of the objects, provide estimates of the bulk density of
these objects. This new class of mathematical figures has been successfully
tested on the observed light curves of three noteworthy small bodies: main-belt
asteroid 216 Kleopatra, Trojan asteroid 624 Hektor and Edgeworth-Kuiper-belt
object 2001 QG298. Using the direct observations of Kleopatra and Hektor
obtained with high spatial resolution techniques and fitting the size of the
dumb-bell-shaped solutions, we derived new physical characteristics in terms of
equivalent radius and bulk density. In particular, the growing inadequacy of
the radar shape model for interpreting any type of observations of Kleopatra
(light curves, AO images, stellar occultations) in a satisfactory manner
suggests that Kleopatra is more likely to be a dumb-bell-shaped object than a
"dog-bone".


  A novel mechanism of baryogenesis is proposed on the basis of the phase
transition from the conformal invariant space-time to the Einstein space-time
in quantum gravity. Strong-coupling gravitational excitations with dynamical
mass about 10^17 GeV are generated at the transition. They eventually decay
into ordinary matters. As a realization of unparticle physics we show that the
low energy effective interactions between the gravitational potential
describing the excitation and the non-conserving matter currents by the axial
anomalies can explain matter asymmetry out of thermal equilibrium.


  We discuss non-ideal torque control in wind turbine systems (WTS). Most
high-level controllers generate a reference torque which is then send to the
underlying electrical drive system (generator+inverter) of the WTS to steer the
turbine/generator to its optimal operation point (depending on the wind speed).
The energy production heavily depends on the mechanical power (i.e. the product
of rotational speed and generator torque). However, since torque sensors in the
MW range are not available or extremely expensive, the torque controllers are
implemented as feedforward controllers and, therefore, are inherently sensitive
to parameter variations/uncertainties. Based on real wind data and a dynamical
WTS model, we discuss causes and impacts of non-ideal (feedforward) torque
control on the energy production and the gross earnings.


  Using a modified spin-wave theory which artificially restores zero sublattice
magnetization on finite lattices, we investigate the entanglement properties of
the N\'eel ordered $J_1 - J_2$ Heisenberg antiferromagnet on the square
lattice. Different kinds of subsystem geometries are studied, either
corner-free (line, strip) or with sharp corners (square). Contributions from
the $n_G=2$ Nambu-Goldstone modes give additive logarithmic corrections with a
prefactor ${n_G}/{2}$ independent of the R\'enyi index. On the other hand,
corners lead to additional (negative) logarithmic corrections with a prefactor
$l^{c}_q$ which does depend on both $n_G$ and the R\'enyi index $q$, in good
agreement with scalar field theory predictions. By varying the second neighbor
coupling $J_2$ we also explore universality across the N\'eel ordered side of
the phase diagram of the $J_1 - J_2$ antiferromagnet, from the frustrated side
$0<J_2/J_1<1/2$ where the area law term is maximal, to the strongly
ferromagnetic regime $-J_2/J_1\gg1$ with a purely logarithmic growth
$S_q=\frac{n_G}{2}\ln N$, thus recovering the mean-field limit for a subsystem
of $N$ sites. Finally, a universal subleading constant term $\gamma_q^{\rm
ord}$ is extracted in the case of strip subsystems, and a direct relation is
found (in the large-S limit) with the same constant extracted from free lattice
systems. The singular limit of vanishing aspect ratios is also explored, where
we identify for $\gamma_q^\text{ord}$ a regular part and a singular component,
explaining the discrepancy of the linear scaling term for fixed width {\it{vs}}
fixed aspect ratio subsystems.


  While Physics-Based Simulation (PBS) can accurately drape a 3D garment on a
3D body, it remains too costly for real-time applications, such as virtual
try-on. By contrast, inference in a deep network, requiring a single forward
pass, is much faster. Taking advantage of this, we propose a novel architecture
to fit a 3D garment template to a 3D body. Specifically, we build upon the
recent progress in 3D point cloud processing with deep networks to extract
garment features at varying levels of detail, including point-wise, patch-wise
and global features. We fuse these features with those extracted in parallel
from the 3D body, so as to model the cloth-body interactions. The resulting
two-stream architecture, which we call as GarNet, is trained using a loss
function inspired by physics-based modeling, and delivers visually plausible
garment shapes whose 3D points are, on average, less than 1 cm away from those
of a PBS method, while running 100 times faster. Moreover, the proposed method
can model various garment types with different cutting patterns when parameters
of those patterns are given as input to the network.


  Little Higgs models provide a natural explanation of the little hierarchy
between the electroweak scale and a few TeV scale, where new physics is
expected. Under the same inspiring naturalness arguments, this work completes a
previous study on lepton flavor-changing processes in the Littlest Higgs model
with T-parity exploring the channel that will eventually turn out to be the
most sensitive, \mu-e conversion in nuclei. All one-loop contributions are
carefully taken into account, results for the most relevant nuclei are provided
and a discussion of the influence of the quark mixing is included. The results
for the Ti nucleus are in good agreement with earlier work by Blanke et al.,
where a degenerate mirror quark sector was assumed. The conclusion is that,
although this particular model reduces the tension with electroweak precision
tests, if the restrictions on the parameter space derived from lepton flavor
violation are taken seriously, the degree of fine tuning necessary to meet
these constraints also disfavors this model.


  We investigate fluid transport in random velocity fields with unsteady drift.
First, we propose to quantify fluid transport between flow regimes of different
characteristic motion, by escape probability and mean residence time. We then
develop numerical algorithms to solve for escape probability and mean residence
time, which are described by backward Fokker-Planck type partial differential
equations. A few computational issues are also discussed. Finally, we apply
these ideas and numerical algorithms to a tidal flow model.


  Texture models based on Generative Adversarial Networks (GANs) use
zero-padding to implicitly encode positional information of the image features.
However, when extending the spatial input to generate images at large sizes,
zero-padding can often lead to degradation of quality due to the incorrect
positional information at the center of the image and limit the diversity
within the generated images. In this paper, we propose a novel approach for
generating stochastic texture images at large arbitrary sizes using GANs model
that is based on patch-by-patch generation. Instead of zero-padding, the model
uses \textit{local padding} in the generator that shares border features
between the generated patches; providing positional context and ensuring
consistency at the boundaries. The proposed models are trainable on a single
texture image and have a constant GPU scalability with respect to the output
image size, and hence can generate images of infinite sizes. We show in the
experiments that our method has a significant advancement beyond existing
texture models in terms of the quality and diversity of the generated textures.
Furthermore, the implementation of local padding in the state-of-the-art
super-resolution models effectively eliminates tiling artifacts enabling
large-scale super-resolution. Our code is available at
\url{https://github.com/ai4netzero/Infinite_Texture_GANs


  A two-fluid model is proposed to describe the transport properties of
granular superconductors. Using the resistively shunted junction model and some
aspects of the two-level system theory, a statistical model is developed which
takes into account the ratio between the number of normal and superconducting
electrons carrying the applied current. The theoretical model reveals excellent
agreement when compared to transport properties of four high-Tc
superconductors. The results suggest that the two-fluid model is independent of
the sample composition, critical temperature and whether the superconducting
compound is electron or hole-doped.


  One of the major goals of future cosmic microwave background (CMB) $B$-mode
polarization experiments is the detection of primordial gravitational waves
through an unbiased measurement of the tensor-to-scalar ratio $r$. Robust
detection of this signal will require mitigating all possible contamination to
the $B$-mode polarization from astrophysical origins. One such extragalactic
contamination arises from the patchiness in the electron density during the
reionization epoch. Along with the signature on CMB polarization, the patchy
reionization can source secondary anisotropies on the CMB temperature through
the kinetic Sunyaev-Zeldovich (kSZ) effect. In order to study the impact of
this foreground for the upcoming CMB missions, we present a self-consistent
framework to compute the CMB anisotropies based on a physically motivated model
of reionization. We show that the value of $r$ can bias towards a higher value
if the secondary contribution from reionization is neglected. However,
combining small-scale kSZ signal, large-scale $E$-mode polarization, and
$B$-mode polarization measurements, we can put constraints on the patchiness in
electron density during reionization and can mitigate its impact on the value
of $r$. CMB missions such as CMB-S4 and PICO may experience a bias of
$>0.17\sigma$ which can go as high as $\sim 0.73\sigma$ for extreme
reionization models allowed by the Planck and SPT CMB measurements. As future
experiments target to measure $r$ at $5\sigma$, this is likely to affect the
measurement significance and hence possibly affect the claim of detection of
$r$, if not mitigated properly by using joint estimations of different
reionization observables.


  Approximate Bayesian computation (ABC) and other likelihood-free inference
methods have gained popularity in the last decade, as they allow rigorous
statistical inference for complex models without analytically tractable
likelihood functions. A key component for accurate inference with ABC is the
choice of summary statistics, which summarize the information in the data, but
at the same time should be low-dimensional for efficiency. Several dimension
reduction techniques have been introduced to automatically construct
informative and low-dimensional summaries from a possibly large pool of
candidate summaries. Projection-based methods, which are based on learning
simple functional relationships from the summaries to parameters, are widely
used and usually perform well, but might fail when the assumptions behind the
transformation are not satisfied. We introduce a localization strategy for any
projection-based dimension reduction method, in which the transformation is
estimated in the neighborhood of the observed data instead of the whole space.
Localization strategies have been suggested before, but the performance of the
transformed summaries outside the local neighborhood has not been guaranteed.
In our localization approach the transformation is validated and optimized over
validation datasets, ensuring reliable performance. We demonstrate the
improvement in the estimation accuracy for localized versions of linear
regression and partial least squares, for three different models of varying
complexity.


  We establish a min-max estimate on the volume width of a closed Riemannian
manifold with nonnegative Ricci curvature. More precisely, we show that every
closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse
function whose level set volume is bounded in terms of the volume of the
manifold. As a consequence of this sweep-out estimate, there exists an
embedded, closed (possibly singular) minimal hypersurface whose volume is
bounded in terms of the volume of the manifold.


  Recently, a method to image molecular electronic wave functions using high
harmonic generation (HHG) was introduced by Itatani \textit{et al.\} [Nature
{\textbf{432}}, 876 (2004)]. We show that, while the tomographic reconstruction
of general orbitals with arbitrary symmetry cannot be performed with long laser
pulses, this becomes possible when extremely short pulses are used. An
alternative reconstruction equation based on momentum matrix elements, rather
than on dipole matrix elements, is proposed. We present simulations of the
procedure for 2D model systems based on numerical solutions of the
time-dependent Schr\"{o}dinger equation, and present results from further
post-processing of the reconstructed orbitals.


  In this report we give a detailed account on Hanbury Brown/Twiss (HBT)
particle interferometric methods for relativistic heavy-ion collisions. These
exploit identical two-particle correlations to gain access to the space-time
geometry and dynamics of the final freeze-out stage. The connection between the
measured correlations in momentum space and the phase-space structure of the
particle emitter is established, both with and without final state
interactions. Suitable Gaussian parametrizations for the two-particle
correlation function are derived and the physical interpretation of their
parameters is explained. After reviewing various model studies, we show how a
combined analysis of single- and two-particle spectra allows to reconstruct the
final state of relativistic heavy-ion collisions.


  In this paper, we will first summarize known results concerning continued
fractions. Then we will limit our consideration to continued fractions of
quadratic numbers. The second author described periods and sometimes precise
form of continued fractions of $\sqrt{N}$, where $N$ is a natural number. In
cases where we were able to find such results in literature, we recall the
original authors, however many results seem to be new.


  Boyer, Gordon, and Watson have conjectured that an irreducible rational
homology 3-sphere is an L-space if and only if its fundamental group is not
left-orderable. Since Dehn surgeries on knots in $S^3$ can produce large
families of L-spaces, it is natural to examine the conjecture on these
3-manifolds. Greene, Lewallen, and Vafaee have proved that all 1-bridge braids
are L-space knots. In this paper, we consider three families of 1-bridge
braids. First we calculate the knot groups and peripheral subgroups. We then
verify the conjecture on the three cases by applying the criterion developed by
Christianson, Goluboff, Hamann, and Varadaraj, when they verified the same
conjecture for certain twisted torus knots and generalized the criteria of Clay
and Watson and of Ichihara and Temma.


  We formulate language modeling as a matrix factorization problem, and show
that the expressiveness of Softmax-based models (including the majority of
neural language models) is limited by a Softmax bottleneck. Given that natural
language is highly context-dependent, this further implies that in practice
Softmax with distributed word embeddings does not have enough capacity to model
natural language. We propose a simple and effective method to address this
issue, and improve the state-of-the-art perplexities on Penn Treebank and
WikiText-2 to 47.69 and 40.68 respectively. The proposed method also excels on
the large-scale 1B Word dataset, outperforming the baseline by over 5.6 points
in perplexity.