  Identifying predictive biomarkers, which forecast individual treatment
effectiveness, is crucial for personalized medicine and informs decision-making
across diverse disciplines. These biomarkers are extracted from pre-treatment
data, often within randomized controlled trials, and have to be distinguished
from prognostic biomarkers, which are independent of treatment assignment. Our
study focuses on the discovery of predictive imaging biomarkers, aiming to
leverage pre-treatment images to unveil new causal relationships. Previous
approaches relied on labor-intensive handcrafted or manually derived features,
which may introduce biases. In response, we present a new task of discovering
predictive imaging biomarkers directly from the pre-treatment images to learn
relevant image features. We propose an evaluation protocol for this task to
assess a model's ability to identify predictive imaging biomarkers and
differentiate them from prognostic ones. It employs statistical testing and a
comprehensive analysis of image feature attribution. We explore the suitability
of deep learning models originally designed for estimating the conditional
average treatment effect (CATE) for this task, which previously have been
primarily assessed for the precision of CATE estimation, overlooking the
evaluation of imaging biomarker discovery. Our proof-of-concept analysis
demonstrates promising results in discovering and validating predictive imaging
biomarkers from synthetic outcomes and real-world image datasets.


  In this paper, we show that the B\"acklund transformations of Painlev\'e
equations come from birational maps of rational surfaces constructed by Okamoto
as the spaces of initial conditions.
  The simultaneous resolutions of rational double points of the families of
rational surfaces give rise to flops which are origins of symmetry groups of
Painlev\'e equation. Moreover we point out that Kodaira--Spencer theory of
deformations of rational surfaces explains a geomrtric meaning of Painlev\'e
equations.


  We consider Artinian algebras $A$ over a field $\mathsf{k}$, both graded and
local algebras. The Lefschetz properties of graded Artinian algebras have been
long studied, but more recently the Jordan type invariant of a pair $(\ell,A)$
where $\ell$ is an element of the maximal ideal of $A$, has been introduced.
The Jordan type gives the sizes of the Jordan blocks for multiplication by
$\ell$ on $A$, and it is a finer invariant than the pair $(\ell,A)$ being
strong or weak Lefschetz. The Jordan degree type for a graded Artinian algebra
adds to the Jordan type the initial degree of ``strings'' in the decomposition
of $A$ as a $\mathsf{k}[\ell]$ module. We here give a brief survey of Jordan
type for Artinian algebras, Jordan degree type for graded Artinian algebras,
and related invariants for local Artinian algebras, with a focus on recent work
and open problems.


  The singular value decomposition is widely used to approximate data matrices
with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654]
developed tests on dimensionality of the mean structure of a data matrix based
on the singular value decomposition. However, the first singular values and
vectors can be driven by a small number of outlying measurements. In this
paper, we consider a robust alternative that moderates the effect of outliers
in low-rank approximations. Under the assumption of random row effects, we
provide the asymptotic representations of the robust low-rank approximation.
These representations may be used in testing the adequacy of a low-rank
approximation. We use oligonucleotide gene microarray data to demonstrate how
robust singular value decomposition compares with the its traditional
counterparts. Examples show that the robust methods often lead to a more
meaningful assessment of the dimensionality of gene intensity data matrices.


  We study the sensitivity of atmospheric neutrino experiments to the neutrino
non-standard interactions (NSI) which is motivated by the tension between the
two mass squared differences extracted from the KamLAND and solar neutrino
experiments. In this study the sensitivity of the future Hyper-Kamiokande
experiments for 4438 days to NSI is shown. Assuming that the mass hierarchy is
known, we find that the best-fit value from the solar neutrino and KamLAND data
can be tested at more than 8 $\sigma$, while the one from the global analysis
can be examined at 5.0 $\sigma$ (1.4 $\sigma$) for the normal (inverted) mass
hierarchy.


  When the action of a reductive group on a projective variety has a suitable
linearisation, Mumford's geometric invariant theory (GIT) can be used to
construct and study an associated quotient variety. In this article we describe
how Mumford's GIT can be extended effectively to suitable actions of linear
algebraic groups which are not necessarily reductive, with the extra data of a
graded linearisation for the action. Any linearisation in the traditional sense
for a reductive group action induces a graded linearisation in a natural way.
The classical examples of moduli spaces which can be constructed using
Mumford's GIT are moduli spaces of stable curves and of (semi)stable bundles
over a fixed nonsingular curve. This more general construction can be used to
construct moduli spaces of unstable objects, such as unstable curves or
unstable bundles (with suitable fixed discrete invariants in each case, related
to their singularities or Harder--Narasimhan type).


  We give a one-dimensional quantum cellular automaton (QCA) capable of
simulating all others. By this we mean that the initial configuration and the
local transition rule of any one-dimensional QCA can be encoded within the
initial configuration of the universal QCA. Several steps of the universal QCA
will then correspond to one step of the simulated QCA. The simulation preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. The encoding is linear and hence
does not carry any of the cost of the computation. We do this in two flavours:
a weak one which requires an infinite but periodic initial configuration and a
strong one which needs only a finite initial configuration. KEYWORDS: Quantum
cellular automata, Intrinsic universality, Quantum computation.


  In this article, we propose the fractional weak adversarial networks (f-WANs)
for the stationary fractional advection dispersion equations (FADE) based on
their weak formulas. This enables us to handle less regular solutions for the
fractional equations. To handle the non-local property of the fractional
derivatives, convolutional layers and special loss functions are introduced in
this neural network. Numerical experiments for both smooth and less regular
solutions show the validity of f-WANs.


  In this paper, we report the performance benchmarking results of deep
learning models on MLCommons' Science cloud-masking benchmark using a
high-performance computing cluster at New York University (NYU): NYU Greene.
MLCommons is a consortium that develops and maintains several scientific
benchmarks that can benefit from developments in AI. We provide a description
of the cloud-masking benchmark task, updated code, and the best model for this
benchmark when using our selected hyperparameter settings. Our benchmarking
results include the highest accuracy achieved on the NYU system as well as the
average time taken for both training and inference on the benchmark across
several runs/seeds. Our code can be found on GitHub. MLCommons team has been
kept informed about our progress and may use the developed code for their
future work.


  The paper is devoted to projective Clifford groups of quantum $N$-dimensional
systems. Clearly, Clifford gates allow only the simplest quantum computations
which can be simulated on a classical computer (Gottesmann-Knill theorem).
However, it may serve as a cornerstone of full quantum computation. As to its
group structure it is well-known that -- in $N$-dimensional quantum mechanics
-- the Clifford group is a natural semidirect product provided the dimension
$N$ is an odd number. For even $N$ special results on the Clifford groups are
scattered in the mathematical literature, but they don't concern the semidirect
structure. Using appropriate group presentation of $SL(2,Z_N)$ it is proved
that for even $N$ projective Clifford groups are not natural semidirect
products if and only if $N$ is divisible by four.


  Experimental energy spectrum and B(E2) values in 68Ni and 90Zr indicate a
double-magic character in these neutron-rich nuclei with N or Z=40. The data
nevertheless do not show any pronounced irregularity in two-nucleon separation
energy. To understand the underlying physics, we carry out both shell-model and
mean-field calculations. The shell-model calculation can well reproduce all the
observations. It is understood from the mean-field results for 68Ni that the
shell gap at N=40 disappears due to dynamical correlations of the isovector J=0
pairing interaction. In 90Zr, however, such a dynamic process with the J=0
pairing appears not important because of the strong contribution of the J>0
interaction. We study also level schemes in the Ni isotopes and N=50 isotones.
We predict a new band built on the $0_{2}^{+}$ state in both 68Ni and 90Zr. The
states of this band are dominated by two-particle-two-hole excitations from the
fp-shell to the intruder g_{9/2} orbit.


  In this paper, we prove some BMO end-point estimates for some vector-valued
multilinear operators related to certain singular integral operators.


  The design of products and services such as a Smart doorbell, demonstrating
video analytics software/algorithm functionality, is expected to address a new
kind of requirements such as designing a scalable solution while considering
the trade-off between cost and accuracy; a flexible architecture to deploy new
AI-based models or update existing models, as user requirements evolve; as well
as seamlessly integrating different kinds of user interfaces and devices. To
address these challenges, we propose a smart doorbell that orchestrates video
analytics across Edge and Cloud resources. The proposal uses AWS as a base
platform for implementation and leverages Commercially Available
Off-The-Shelf(COTS) affordable devices such as Raspberry Pi in the form of an
Edge device.


  We make a phenomenological model of optical two-beam interaction in a model
planar liquid crystal cell. The liquid crystal is subject to homeotropic
anchoring at the cell walls, is surrounded by thin photosensitive layers, and
is subject to a variable potential across the cell. These systems are often
known as liquid crystal photorefractive systems. The interference between the
two obliquely incident beams causes a time-independent periodic modulation in
electric field intensity in the direction transverse to the cell normal. Our
model includes this field phenomenologically by affecting the potential at the
walls of the cell. The transverse periodic surface potential causes spatially
periodic departures from a pure homeotropic texture. The texture modulation
acts as a grating for the incident light. The incident light is both directly
transmitted and also subject to diffraction. The first diffracted beams result
in energy exchange between the beams. We find that the degree of energy
exchange can be strongly sensitive to the mean angle of incidence, the angle
between the beams, and the imposed potential across the cell. We use the model
to speculate about what factors optimize non-linear optical interaction in
liquid crystalline photorefractive systems.


  We report the successful growth and the impurity scattering effect of single
crystals of Na(Fe$_{0.97-x}$Co$_{0.03}$T$_x$)As (T=Cu, Mn). The temperature
dependence of DC magnetization at high magnetic fields is measured for
different concentrations of Cu and Mn. Detailed analysis based on the
Curie-Weiss law indicates that the Cu doping weakens the average magnetic
moments, while doping Mn enhances the local magnetic moments greatly,
suggesting that the former may be non- or very weak magnetic impurities, and
the latter give rise to magnetic impurities. However, it is found that both
doping Cu and Mn will enhance the residual resistivity and suppress the
superconductivity at the same rate in the low doping region, being consistent
with the prediction of the S$^{\pm}$ model. For the Cu-doped system, the
superconductivity is suppressed completely at a residual resistivity $\rho_0$ =
0.87 m$\Omega$ cm at which a strong localization effect is observed. However,
in the case of Mn doping, the behavior of suppression to \emph{T}$_{c}$ changes
from a fast speed to a slow one and keeps superconductive even up to a residual
resistivity of 2.86 m$\Omega$ cm. Clearly the magnetic Mn impurities are even
not as detrimental as the non- or very weak magnetic Cu impurities to
superconductivity in the high doping regime.


  We consider the effect of a local interatomic repulsion on synthetic
heterostructures where a discrete synthetic dimension is created by Raman
processes on top of $SU(N)$-symmetric two-dimensional lattice systems. At a
filling of one fermion per site, increasing the interaction strength, the
system is driven towards a Mott state which is adiabatically connected to a
band insulator. The chiral currents associated with the synthetic magnetic
field increase all the way to the Mott transition, where they reach the maximum
value, and they remain finite in the whole insulating state. The transition
towards the Mott-band insulator is associated with the opening of a gap within
the low-energy quasiparticle peak, while a mean-field picture is recovered deep
in the insulating state.


  The Advanced Photon Source (APS) primary and backup injectors consist of two
thermionic-cathode rf guns. These guns are being upgraded to provide improved
performance, to improve ease of maintenance, and to reduce downtime required
for repair or replacement of a failed injector. As part of the process, an
injector test stand is being prepared. This stand is effectively independent of
the APS linac and will allow for complete characterization and validation of an
injector prior to its installation into the APS linac.
  A modular control system for the test stand has been developed using standard
APS control solutions with EPICS to deliver a flexible and comprehensive
control system. The modularity of the system will allow both future expansion
of test stand functionality and evaluation of new control techniques and
solutions.


  We propose to model hadronization of parton showers in QCD jets through a
hybrid approach involving quark recombination and string fragmentation. This is
achieved by allowing gluons at the end of the perturbative shower evolution to
undergo a non-perturbative splitting into quark and antiquark pairs, then
applying a Monte-Carlo version of instantaneous quark recombination, and
finally subjecting remnant quarks (those which have not found a recombination
partner) to Lund string fragmentation. When applied to parton showers from the
PYTHIA Monte Carlo event generator, the final hadron spectra from our
calculation compare quite well to PYTHIA jets that have been hadronized with
the default Lund string fragmentation. Our new approach opens up the
possibility to generalize hadronization to jets embedded in a quark gluon
plasma.


  We present the results of a survey of nearby, young M stars for wide low-mass
companions with IRAC on the Spitzer Space Telescope. We observed 40 young M
dwarfs within 20 pc of the Sun, selected through X-ray emission criteria. A
total of 10 candidate companions were found with IRAC colors consistent with T
dwarfs. Extensive ground-based NIR follow-up observations rejected all these
candidates. Two additional candidates were discovered via common proper motion
measurements, one of which was rejected as a background object and the other is
a bona fide companion to GJ 2060, a member of the AB Doradus moving group.


  In a recent Letter, Alberg and Miller presented a calculation of the pion
contributions to the self-energy of the nucleon computed from a pseudoscalar
(PS) pion-nucleon interaction, with the claim that the result would be
equivalent to that with the pseudovector (PV) form. We demonstrate that the PV
and PS pion-nucleon couplings do in fact lead to different results for the
self-energy. In particular, for the model-independent, leading nonanalytic
behavior of the self-energy, the PV theory yields the well-known m_\pi^3
dependence in the chiral limit, while the PS interaction involves an
additional, lower-order term ~ m_\pi^2 log(m_\pi^2).


  We establish the Brownian bridge asymptotics for a scaled self-avoiding walk
conditioned on arriving to a far away point
  $n \vec{a}$ for $\vec{a}$ in $Z^d$, as $n$ increases to infinity.


  We classify the simply-connected supersymmetric parallelisable backgrounds of
heterotic supergravity. They are all given by parallelised Lie groups admitting
a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14
and 16 of the 16 supersymmetries.


  We study spectral and steady-state properties of generic Markovian
dissipative systems described by quadratic fermionic Liouvillian operators of
the Lindblad form. The Hamiltonian dynamics is modeled by a generic random
quadratic operator, i.e., as a featureless superconductor of class D, whereas
the Markovian dissipation is described by $M$ random linear jump operators. By
varying the dissipation strength and the ratio of dissipative channels per
fermion, $m=M/(2N_F)$, we find two distinct phases where the support of the
single-particle spectrum has one or two connected components. In the strongly
dissipative regime, this transition occurs for $m=1/2$ and is concomitant with
a qualitative change in both the steady-state and the spectral gap that rules
the large-time dynamics. Above this threshold, the spectral gap and the
steady-state purity qualitatively agree with the fully generic (i.e.,
non-quadratic) case studied recently. Below $m=1/2$, the spectral gap closes in
the thermodynamic limit and the steady-state decouples into an ergodic and a
nonergodic sector yielding a non-monotonic steady-state purity as a function of
the dissipation strength. Our results show that some of the universal features
previously observed for fully random Liouvillians are generic for a
sufficiently large number of jump operators. On the other hand, if the number
of dissipation channels is decreased the system can exhibit nonergodic
features, rendering it possible to suppress dissipation in protected subspaces
even in the presence of strong system-environment coupling.


  In contrast to the cuprates, where the proximity of antiferromagnetism (AFM)
and superconductivity is well established, first indications for AFM
interactions in superconducting infinite-layer nickelates were only recently
obtained. Here, we explore, based on first-principles simulations, the nature
of the magnetic coupling in NdNiO2 as a function of the on-site Coulomb and
exchange interaction, varying the explicit hole doping and the treatment of the
Nd $4f$ electrons. The $U$-$J$ phase diagrams for undoped nickelates and
cuprates indicate $G$-type ordering, yet show different $U$ dependency. By
either Sr hole doping or explicit treatment of the Nd $4f$ electrons, we find a
transition to a Ni $C$-type AFM ground state. We trace the effect of Sr doping
back to a distinct accommodation of the holes by the Ni versus Cu $e_g$
orbitals. The interaction between Nd $4f$ and Ni $3d$ states stabilizes
$C$-type AFM order on both sublattices. Though spin-orbit interactions induce a
band splitting near the Fermi energy, the bad-metal state is retained even
under epitaxial strain. These results establish the distinct role of the
magnetic interactions in the nickelates versus the cuprates and suggest the
former as a unique platform to investigate the relation to unconventional
superconductivity.


  Let $T : \Omega \rightarrow \bbC^{n \times n}$ be a matrix-valued function
that is analytic on some simply-connected domain $\Omega \subset \bbC$. A point
$\lambda \in \Omega$ is an eigenvalue if the matrix $T(\lambda)$ is singular.
In this paper, we describe new localization results for nonlinear eigenvalue
problems that generalize Gershgorin's theorem, pseudospectral inclusion
theorems, and the Bauer-Fike theorem. We use our results to analyze three
nonlinear eigenvalue problems: an example from delay differential equations, a
problem due to Hadeler, and a quantum resonance computation.


  ``The Strength of Weak Ties" argument (Granovetter 1973) says that the most
valuable information is best collected through bridging ties with other social
circles than one's own, and that those ties tend to be weak. Aral and Van
Alstyne (2011) added that to access complex information, actors need strong
ties (``high bandwidth") instead. These insights I integrate and generalize by
pointing at actors' benefits and costs. Weak ties are well-suited for
relatively simple information at low costs, whereas for complex information,
the best outcomes are expected for those actors who vary their bandwidths along
with the value of information accessed. To support my claim I use all patents
in the USA (two million) over the period 1975---1999.


  We study a nonlinear elliptic equation driven by the degenerate fractional
p-Laplacian, with Dirichlet type condition and a jumping reaction, i.e.,
(p-1)-linear both at infinity and at zero but with different slopes crossing
the principal eigenvalue. Under two different sets of hypotheses, entailing
different types of asymmetry, we prove the existence of at least two nontrivial
solutions. Our method is based on degree theory for monotone operators and
nonlinear fractional spectral theory.


  Novel microstamping tool for microarray printing is proposed. The tool is
capable to spot up to 127 droplets of different solutions in single touch. It
is easily compatible with commercially available microarray spotters. The tool
is based on multichannel funnel with polypropylene capillaries inserted into
its channels. Superior flexibility is achieved by ability to replace any
printing capillary of the tool. As a practical implementation, hydrogel-based
microarrays were stamped and successfully applied to identify the Mycobacterium
tuberculosis drug resistance.


  Usability is a crucial factor but one of the most neglected concerns in open
source software (OSS). While far from an ideal approach, a common practice that
OSS communities adopt to collaboratively address usability is through
discussions on issue tracking systems (ITSs). However, there is little
knowledge about the extent to which OSS community members engage in usability
issue discussions, the aspects of usability they frequently target, and the
characteristics of their collaboration around usability issue discussions. This
knowledge is important for providing practical recommendations and research
directions to better support OSS communities in addressing this important topic
and improve OSS usability in general. To help achieve this goal, we performed
an extensive empirical study on issues discussed in five popular OSS
applications: three data science notebook projects (Jupyter Lab, Google Colab,
and CoCalc) and two code editor projects (VSCode and Atom). Our results
indicated that while usability issues are extensively discussed in the OSS
projects, their scope tended to be limited to efficiency and aesthetics.
Additionally, these issues are more frequently posted by experienced community
members and display distinguishable characteristics, such as involving more
visual communication and more participants. Our results provide important
implications that can inform the OSS practitioners to better engage the
community in usability issue discussion and shed light on future research
efforts toward collaboration techniques and tools for discussing niche topics
in diverse communities, such as the usability issues in the OSS context.


  This article documents the muon reconstruction and identification efficiency
obtained by the ATLAS experiment for 139 fb$^{-1}$ of $pp$ collision data at
$\sqrt{s}=13$ TeV collected between 2015 and 2018 during Run 2 of the LHC. The
increased instantaneous luminosity delivered by the LHC over this period
required a reoptimisation of the criteria for the identification of prompt
muons. Improved and newly developed algorithms were deployed to preserve high
muon identification efficiency with a low misidentification rate and good
momentum resolution. The availability of large samples of $Z\to\mu\mu$ and
$J/\psi\to\mu\mu$ decays, and the minimisation of systematic uncertainties,
allows the efficiencies of criteria for muon identification, primary vertex
association, and isolation to be measured with an accuracy at the per-mille
level in the bulk of the phase space, and up to the percent level in complex
kinematic configurations. Excellent performance is achieved over a range of
transverse momenta from 3 GeV to several hundred GeV, and across the full muon
detector acceptance of $|\eta|<2.7$.


  To harness the ever growing capacity and decreasing cost of storage,
providing an abstraction of dependable storage in the presence of crash-stop
and Byzantine failures is compulsory. We propose a decentralized Reed Solomon
coding mechanism with minimum communication overhead. Using a progressive data
retrieval scheme, a data collector contacts only the necessary number of
storage nodes needed to guarantee data integrity. The scheme gracefully adapts
the cost of successful data retrieval to the number of storage node failures.
Moreover, by leveraging the Welch-Berlekamp algorithm, it avoids unnecessary
computations. Compared to the state-of-the-art decoding scheme, the
implementation and evaluation results show that our progressive data retrieval
scheme has up to 35 times better computation performance for low Byzantine node
rates. Additionally, the communication cost in data retrieval is derived
analytically and corroborated by Monte-Carlo simulation results. Our
implementation is flexible in that the level of redundancy it provides is
independent of the number of data generating nodes, a requirement for
distributed storage systems


  Recent work has attempted to directly approximate the `function-space' or
predictive posterior distribution of Bayesian models, without approximating the
posterior distribution over the parameters. This is appealing in e.g. Bayesian
neural networks, where we only need the former, and the latter is hard to
represent. In this work, we highlight some advantages and limitations of
employing the Kullback-Leibler divergence in this setting. For example, we show
that minimizing the KL divergence between a wide class of parametric
distributions and the posterior induced by a (non-degenerate) Gaussian process
prior leads to an ill-defined objective function. Then, we propose (featurized)
Bayesian linear regression as a benchmark for `function-space' inference
methods that directly measures approximation quality. We apply this methodology
to assess aspects of the objective function and inference scheme considered in
Sun, Zhang, Shi, and Grosse (2018), emphasizing the quality of approximation to
Bayesian inference as opposed to predictive performance.


  The large survey programs being performed nowadays, being the SDSS their
flagship, provide us with morphological parameters which allow for extraction
of large galaxy samples. We will analyze the methodology for obtaining an
AMIGA-like catalogue of isolated galaxies from the SDSS DR5 photometric
catalogue of galaxy objects, together with the roadblocks found in the process,
and suggested workarounds.


  A review of the present experimental status of the rates and the Dalitz-plot
slope parameters in CP conserving K->2\pi and K->3\pi decays is given. The
corresponding isospin amplitudes have been determined by a common fit to the
recent experimental data and have been used as an input to a consequent fit
based on the constraints from O(p^4) chiral lagrangian. It has been found that
the constraints of the chiral fit are well satisfied by the experimental data,
allowing to estimate the weak coupling constants and to predict the quadratic
amplitudes in K->3\pi decays and the one-loop strong rescattering phases. The
consistency of the obtained weak coupling constants with weak resonance models
has been also considered.


  For a class of stochastic differential equations with reflection for which a
certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown
that any weak solution that is a strong Markov process can be decomposed into
the sum of a local martingale and a continuous, adapted process of zero
$p$-variation. When $p=2$, this implies that the reflected diffusion is a
Dirichlet process. Two examples are provided to motivate such a
characterization. The first example is a class of multidimensional reflected
diffusions in polyhedral conical domains that arise as approximations of
certain stochastic networks, and the second example is a family of
two-dimensional reflected diffusions in curved domains. In both cases, the
reflected diffusions are shown to be Dirichlet processes, but not
semimartingales.


  We provide a counterexample to the Sarason Conjecture for the Bergman space
and present a characterisation of bounded Toeplitz products on the Bergman
space in terms of test functions by means of a dyadic model approach. We also
present some results about two-weighted estimates for the Bergman projection.
Finally, we introduce the class $B_{\infty}$ and give sharp estimates for the
one-weighted Bergman projection.


  A powerful and flexible approach to structured prediction consists in
embedding the structured objects to be predicted into a feature space of
possibly infinite dimension by means of output kernels, and then, solving a
regression problem in this output space. A prediction in the original space is
computed by solving a pre-image problem. In such an approach, the embedding,
linked to the target loss, is defined prior to the learning phase. In this
work, we propose to jointly learn a finite approximation of the output
embedding and the regression function into the new feature space. For that
purpose, we leverage a priori information on the outputs and also unexploited
unsupervised output data, which are both often available in structured
prediction problems. We prove that the resulting structured predictor is a
consistent estimator, and derive an excess risk bound. Moreover, the novel
structured prediction tool enjoys a significantly smaller computational
complexity than former output kernel methods. The approach empirically tested
on various structured prediction problems reveals to be versatile and able to
handle large datasets.


  We investigate generic heat engines and refrigerators operating between two
heat reservoirs, for the condition when their efficiencies are equal to each
other. It is shown that the corresponding value of efficiency is given as the
inverse of the generalized golden mean, $\phi_p$, where the parameter $p$
depends on the degree of irreversibility of both engine and refrigerator. The
reversible case ($p=1$) yields the efficiency in terms of the standard golden
mean. We also extend the analysis to a three-heat-resrervoir setup.


  Molecular Dynamics method is based on solution of Newtonian differential
equations of motion. A new very accurate and efficient time-reversible explicit
integrator was derived on the basis of second order Tailor expansion of force.
There is good reason to think the new method will be easy-to-use for MD and,
possibly, celestial mechanics applications.


  The pseudomoments of the Riemann zeta function, denoted $\mathcal{M}_k(N)$,
are defined as the $2k$th integral moments of the $N$th partial sum of
$\zeta(s)$ on the critical line. We improve the upper and lower bounds for the
constants in the estimate $\mathcal{M}_k(N) \asymp_k (\log{N})^{k^2}$ as
$N\to\infty$ for fixed $k\geq1$, thereby determining the two first terms of the
asymptotic expansion. We also investigate uniform ranges of $k$ where this
improved estimate holds and when $\mathcal{M}_k(N)$ may be lower bounded by the
$2k$th power of the $L^\infty$ norm of the $N$th partial sum of $\zeta(s)$ on
the critical line.


  Coalition negotiations are a cornerstone of parliamentary democracies,
characterised by complex interactions and strategic communications among
political parties. Despite its significance, the modelling of these
negotiations has remained unexplored with the domain of Natural Language
Processing (NLP), mostly due to lack of proper data. In this paper, we
introduce coalition negotiations as a novel NLP task, and model it as a
negotiation between large language model-based agents. We introduce a
multilingual dataset, POLCA, comprising manifestos of European political
parties and coalition agreements over a number of elections in these countries.
This dataset addresses the challenge of the current scope limitations in
political negotiation modelling by providing a diverse, real-world basis for
simulation. Additionally, we propose a hierarchical Markov decision process
designed to simulate the process of coalition negotiation between political
parties and predict the outcomes. We evaluate the performance of
state-of-the-art large language models (LLMs) as agents in handling coalition
negotiations, offering insights into their capabilities and paving the way for
future advancements in political modelling.


  A new model, which uses the frequency of individuals' annual home run totals,
is employed to predict future home run totals and records in Major League
Baseball. Complete home run frequency data from 1903--2005 is analyzed,
resulting in annual exponential distributions whose changes can be a used as a
measure of progression in the sport and serve as a basis against which
record-setting performances can be compared. We show that there is an 80%
chance that Barry Bonds' current 73 home run record will be broken in the next
10 years, despite the longevity of previous records held by baseball legends
Babe Ruth and Roger Marris.


  If $M$ is an atomic monoid and $x$ is a nonzero non-unit element of $M$, then
the set of lengths $\mathsf{L}(x)$ of $x$ is the set of all possible lengths of
factorizations of $x$, where the length of a factorization is the number of
irreducible factors (counting repetitions). In a recent paper, F. Gotti and C.
O'Neil studied the sets of elasticities $\mathcal{R}(P) := \{\sup
\mathsf{L}(x)/\inf \mathsf{L}(x) : x \in P\}$ of Puiseux monoids $P$. Here we
take this study a step forward and explore the local $k$-elasticities of the
same class of monoids. We find conditions under which Puiseux monoids have all
their local elasticities finite as well as conditions under which they have
infinite local $k$-elasticities for sufficiently large $k$. Finally, we focus
our study of the $k$-elasticities on the class of primary Puiseux monoids,
proving that they have finite local $k$-elasticities if either they are
boundedly generated and do not have any stable atoms or if they do not contain
$0$ as a limit point.


  Given graphs $X$ and $Y$, we define two conic feasibility programs which we
show have a solution over the completely positive cone if and only if there
exists a homomorphism from $X$ to $Y$. By varying the cone, we obtain similar
characterizations of quantum/entanglement-assisted homomorphisms and three
previously studied relaxations of these relations. Motivated by this, we
investigate the properties of these "conic homomorphisms" for general
(suitable) cones. We also consider two generalized versions of the Lov\'asz
theta function, and how they interact with these conic homomorphisms. We prove
analogs of several results on classical graph homomorphisms as well as some
monotonicity theorems. We also show that one of the generalized theta functions
is multiplicative on lexicographic and disjunctive graph products.


  Measurements of the UV-continuum slopes provide valuable information on the
physical properties of galaxies forming in the early universe, probing the dust
reddening, age, metal content, and even the escape fraction. While constraints
on these slopes generally become more challenging at higher redshifts as the UV
continuum shifts out of the Hubble Space Telescope bands (particularly at z>7),
such a characterisation actually becomes abruptly easier for galaxies in the
redshift window z=9.5-10.5 due to the Spitzer/IRAC 3.6um-band probing the
rest-UV continuum and the long wavelength baseline between this Spitzer band
and the Hubble H-band. Higher S/N constraints on the UV slope are possible at
z~10 than at z=8. Here we take advantage of this opportunity and five recently
discovered bright z=9.5-10.5 galaxies to present the first measurements of the
mean slope for a multi-object sample of galaxy candidates at z~10. We find the
measured observed slopes of these candidates are $-2.1\pm0.3\pm0.2$ (random and
systematic), only slightly bluer than the measured slopes at 3.5<z<7.5 for
galaxies of similar luminosities. Small increases in the stellar ages,
metallicities, and dust content of the galaxy population from z~10 to z~7 could
easily explain the apparent evolution in slopes.


  The worldsheet S matrix of strings on the $AdS_3\times S^3\times T^4$
background is almost entirely fixed by symmetries, up to five functions -- the
dressing factors. These must satisfy several consistency conditions, in
particular a set of crossing equations. We find that the existing proposal for
the dressing factors, while crossing invariant, violates some of these
consistency conditions. We put forward a new set of dressing factors and
discuss in detail their analytic properties in the string and mirror region, as
well as under bound-state fusion.


  Over the last few years, the concept of Artificial Intelligence has become
central in different tasks concerning both our daily life and several working
scenarios. Among these tasks automated planning has always been central in the
AI research community. In particular, this manuscript is focused on a
specialized kind of planning known as Multi-agent Epistemic Planning (MEP).
Epistemic Planning (EP) refers to an automated planning setting where the agent
reasons in the space of knowledge/beliefs states and tries to find a plan to
reach a desirable state from a starting one. Its general form, the MEP problem,
involves multiple agents who need to reason about both the state of the world
and the information flows between agents. To tackle the MEP problem several
tools have been developed and, while the diversity of approaches has led to a
deeper understanding of the problem space, each proposed tool lacks some
abilities and does not allow for a comprehensive investigation of the
information flows. That is why, the objective of our work is to formalize an
environment where a complete characterization of the agents' knowledge/beliefs
interaction and update is possible. In particular, we aim to achieve such goal
by defining a new action-based language for multi-agent epistemic planning and
to implement an epistemic planner based on it. This solver should provide a
tool flexible enough to reason on different domains, e.g., economy, security,
justice and politics, where considering others' knowledge/beliefs could lead to
winning strategies.


  We continue with the ideas of Bonatti-Langevin-Jeandenans towards a
constructive and algorithmic classification of pseudo-Anosov homeomorphisms
(possibly with spines), up to topological conjugacy. We begin by indicating how
to assign to every pseudo-Anosov homeomorphism an abstract geometric type
through a Markov partition whose rectangles have been endowed with a vertical
direction; these are known as geometric Markov partitions. Such assignment is
not unique, as it depends on the specific geometric Markov partition, and not
every abstract geometric type is realized by a pseudo-Anosov homeomorphism.
This poses interesting problems related to the algorithmic computability of the
classification. The article contains three main results: $i)$ the geometric
type is a total invariant of conjugacy, $(ii)$ a pictorial and combinatorial
criterion for determining when a given geometric type is realizable by a
pseudo-Anosov homeomorphism is provided, and $(iii)$ we describe an algorithmic
procedure for determining when two geometric types correspond to topologically
conjugate pseudo-Anosov homeomorphisms.


  Transition-metal honeycomb compounds are capturing scientific attention due
to their distinctive electronic configurations, underscored by the
triangular-lattice spin-orbit coupling and competition between multiple
interactions, paving the way for potential manifestations of phenomena such as
Dirac semimetal, superconductivity, and quantum spin liquid states. These
compounds can undergo discernible pressure-induced alterations in their
crystallographic and electronic paradigms, as exemplified by our high-pressure
(HP) synthesis and exploration of the honeycomb polymorph of ReO3 (P6322). This
HP-P6322 polymorph bears a phase transition from P6322 to P63/mmc upon cooling
around Tp = 250 K, as evidenced by the evolution of temperature-dependent
magnetization (M-T curves), cell dimension, and conductivity initiated by an
inherent bifurcation of the oxygen position in the ab plane. Insightful
analysis of its band structure positions suggests this HP-P6322 polymorph being
a plausible candidate for Dirac semimetal properties. This phase transition
evokes anomalies in the temperature-dependent variation of paramagnetism
(non-linearity) and a crossover from semiconductor to temperature-independent
metal, showing a temperature independent conductivity behavior below ~200 K.
Under increasing external pressure, both the Tp and resistance of this
HP-polymorph is slightly magnetic-field dependent and undergo a "V"-style
evolution (decreasing and then increasing) before becoming pressure independent
up to 20.2 GPa. Theoretical calculations pinpoint this anionic disorder as a
probable catalyst for the decrement in the conductive efficiency and muted
temperature-dependent conductivity response.


  Emergent phases often appear when the electronic kinetic energy is comparable
to the Coulomb interactions. One approach to seek material systems as hosts of
such emergent phases is to realize localization of electronic wavefunctions due
to the geometric frustration inherent in the crystal structure, resulting in
flat electronic bands. Recently, such efforts have found a wide range of exotic
phases in the two-dimensional kagome lattice, including magnetic order,
time-reversal symmetry breaking charge order, nematicity, and
superconductivity. However, the interlayer coupling of the kagome layers
disrupts the destructive interference needed to completely quench the kinetic
energy. Here we demonstrate that an interwoven kagome network-a pyrochlore
lattice-can host a three dimensional (3D) localization of electron
wavefunctions. Meanwhile, the nonsymmorphic symmetry of the pyrochlore lattice
guarantees all band crossings at the Brillouin zone X point to be 3D gapless
Dirac points, which was predicted theoretically but never yet observed
experimentally. Through a combination of angle-resolved photoemission
spectroscopy, fundamental lattice model and density functional theory
calculations, we investigate the novel electronic structure of a Laves phase
superconductor with a pyrochlore sublattice, CeRu$_2$. We observe flat bands
originating from both the Ce 4$f$ orbitals as well as from the 3D destructive
interference of the Ru 4$d$ orbitals. We further observe the nonsymmorphic
symmetry-protected 3D gapless Dirac cones at the X point. Our work establishes
the pyrochlore structure as a promising lattice platform to realize and tune
novel emergent phases intertwining topology and many-body interactions.


  Multi-level preconditioners for Discontinuous Galerkin (DG) discretizations
are widely used to solve elliptic equations, and a main ingredient of such
solvers is the interpolation operator to transfer information from the coarse
to the fine grid. Classical interpolation operators give continuous
interpolated values, but since DG solutions are naturally discontinuous, one
might wonder if one should not use discontinuous interpolation operators for DG
discretizations. We consider a discontinuous interpolation operator with a
parameter that controls the discontinuity, and determine the optimal choice for
the discontinuity, leading to the fastest solver for a specific 1D symmetric
interior penalty DG discretization model problem. We show in addition that our
optimization delivers a perfectly clustered spectrum with a high geometric
multiplicity, which is very advantageous for a Krylov solver using the method
as its preconditioner. Finally, we show the applicability of the optimal choice
to higher dimensions.


  We propose a framework of Lagrangian Coherent Structures (LCS) to elucidate
the shear layers and coherent structures to understand the mechanism of
generation of tonal sound during thermoacoustic instability. Experiments were
performed on a bluff-body stabilized turbulent combustor in the state of
thermoacoustic instability. We use dynamic mode decomposition (DMD) on the
flow-field to identify dynamical regions where the acoustic frequency is
dominant. We find that the separating shear layer from the backward-facing step
of the combustor envelops a cylindrical vortex in the outer recirculation zone
(ORZ), eventually impinging on the top wall of the combustor during
thermoacoustic instability. The production of tonal sound is due to the
synchronous motion of this shear layer with the shear layer emerging from the
leading edge of the bluff-body causing the fluid to squeeze and expand between
them periodically. To de-synchronize the oscillations in an optimal manner, we
track the Lagrangian saddle points in the shear layer emerging from the
backward facing step over several acoustic cycles. A passive control strategy
is then developed by injecting a steady stream of secondary air targeting the
optimal locations thus identified. After implementing the control action, the
flow-field is also analysed using LCS to understand the key differences in flow
dynamics. We find that the shear layer emerging from the dump plane are
deflected in a direction almost parallel to the axis of the combustor after the
control action. This deflection in turn prevents the shear layer from
enveloping the vortex and impinging on the combustor walls, resulting in a
drastic reduction of the amplitude of the acoustic field.


  We show a spectral sequence for the rational Khovanov homology of an oriented
link in terms of the rational Khovanov complexes and homologies of the link
surgeries along an admissible cut. As a non trivial corollary, we give an
explicit splitting formula for the Jones polynomial.


  Some quantum-gravity theories suggest that the absorbing horizon of a
classical black hole should be replaced by a reflective surface which is
located a microscopic distance above the would-be classical horizon. Instead of
an absorbing black hole, the resulting horizonless spacetime describes a
reflective exotic compact object. Motivated by this intriguing prediction, in
the present paper we explore the physical properties of exotic compact objects
which are linearly coupled to stationary bound-state massive scalar field
configurations. In particular, solving the Klein-Gordon wave equation for a
stationary scalar field of proper mass $\mu$ and spheroidal harmonic indices
$(l,m)$ in the background of a rapidly-rotating exotic compact object of mass
$M$ and angular momentum $J=Ma$, we derive a compact analytical formula for the
{\it discrete} radii $\{r_{\text{c}}(\mu,l,m,M,a;n)\}$ of the exotic compact
objects which can support the stationary bound-state massive scalar field
configurations. We confirm our analytical results by direct numerical
computations.


  This paper describes an agent based simulation used to model human actions in
belief space, a high-dimensional subset of information space associated with
opinions. Using insights from animal collective behavior, we are able to
simulate and identify behavior patterns that are similar to nomadic, flocking
and stampeding patterns of animal groups. These behaviors have analogous
manifestations in human interaction, emerging as solitary explorers, the
fashion-conscious, and members of polarized echo chambers. We demonstrate that
a small portion of nomadic agents that widely traverse belief space can disrupt
a larger population of stampeding agents. Extending the model, we introduce the
concept of Adversarial Herding, where bad actors can exploit properties of
technologically mediated communication to artificially create self sustaining
runaway polarization. We call this condition the Pishkin Effect as it recalls
the large scale buffalo stampedes that could be created by native Americans
hunters. We then discuss opportunities for system design that could leverage
the ability to recognize these negative patterns, and discuss affordances that
may disrupt the formation of natural and deliberate echo chambers.


  Colloidal cuboids have the potential to self-assemble into biaxial liquid
crystal phases, which exhibit two independent optical axes. Over the last few
decades, several theoretical works predicted the existence of a wide region of
the phase diagram where the biaxial nematic phase would be stable, but imposed
rather strong constraints on the particle rotational degrees of freedom. In
this work, we employ molecular simulation to investigate the impact of size
dispersity on the phase behaviour of freely-rotating hard cuboids, here
modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in
between oblate and prolate geometry, has been proposed as the most appropriate
to promote phase biaxiality. We observe that size dispersity radically changes
the phase behaviour of monodisperse systems and leads to the formation of the
elusive biaxial nematic phase, being found in an large region of the packing
fraction vs polydispersity phase diagram. Although our results confirm the
tendencies reported in past experimental observations on colloidal dispersions
of slightly prolate goethite particles, they cannot reproduce the direct
isotropic-to-biaxial nematic phase transition observed in these experiments.


  We present constraints on the number of relativistic species from a joint
analysis of cosmic microwave background (CMB) fluctuations and light element
abundances (helium and deuterium) compared to big bang nucleosynthesis (BBN)
predictions. Our BBN calculations include updates of nuclear rates in light of
recent experimental and theoretical information, with the most significant
change occuring for the d(p,gamma)^3He cross section. We calculate a likelihood
function for BBN theory and observations that accounts for both observational
errors and nuclear rate uncertainties and can be easily embedded in
cosmological parameter fitting. We then demonstrate that CMB and BBN are in
good agreement, suggesting that the number of relativistic species did not
change between the time of BBN and the time of recombination. The level of
agreement between BBN and CMB, as well as the agreement with the standard model
of particle physics, depends somewhat on systematic differences among
determinations of the primordial helium abundance. We demonstrate that
interesting constraints can be derived combining only CMB and D/H observations
with BBN theory, suggesting that an improved D/H constraint would be an
extremely valuable probe of cosmology.


  We consider two-dimensional Brans-Dicke theory to study the initial
singularity problem. It turns out that the initial curvature singularity can be
finite for a certain Brans-Dicke constant $\omega$ by considering the quantum
back reaction of the geometry. For $\omega=1$, the universe starts with the
finite curvature scalar and evolves into the flat spacetime. Furthermore the
divergent gravitational coupling at the initial time can be finite effectively
with the help of quantum correction. The other type of universe is studied for
the case of $0<\omega<1$.


  We study the problem of computing maximin share guarantees, a recently
introduced fairness notion. Given a set of $n$ agents and a set of goods, the
maximin share of a single agent is the best that she can guarantee to herself,
if she would be allowed to partition the goods in any way she prefers, into $n$
bundles, and then receive her least desirable bundle. The objective then in our
problem is to find a partition, so that each agent is guaranteed her maximin
share. In settings with indivisible goods, such allocations are not guaranteed
to exist, so we resort to approximation algorithms. Our main result is a
$2/3$-approximation, that runs in polynomial time for any number of agents.
This improves upon the algorithm of Procaccia and Wang, which also produces a
$2/3$-approximation but runs in polynomial time only for a constant number of
agents. To achieve this, we redesign certain parts of their algorithm.
Furthermore, motivated by the apparent difficulty, both theoretically and
experimentally, in finding lower bounds on the existence of approximate
solutions, we undertake a probabilistic analysis. We prove that in randomly
generated instances, with high probability there exists a maximin share
allocation. This can be seen as a justification of the experimental evidence
reported in relevant works. Finally, we provide further positive results for
two special cases that arise from previous works. The first one is the
intriguing case of $3$ agents, for which it is already known that exact maximin
share allocations do not always exist (contrary to the case of $2$ agents). We
provide a $7/8$-approximation algorithm, improving the previously known result
of $3/4$. The second case is when all item values belong to $\{0, 1, 2\}$,
extending the $\{0, 1\}$ setting studied in Bouveret and Lema\^itre. We obtain
an exact algorithm for any number of agents in this case.


  We give a formula for the v-number of a graded ideal that can be used to
compute this number. Then we show that for the edge ideal $I(G)$ of a graph $G$
the induced matching number of $G$ is an upper bound for the v-number of $I(G)$
when $G$ is very well-covered, or $G$ has a simplicial partition, or $G$ is
well-covered connected and contain neither $4$- nor $5$-cycles. In all these
cases the v-number of $I(G)$ is a lower bound for the regularity of the edge
ring of $G$. We classify when the upper bound holds when $G$ is a cycle, and
classify when all vertices of a graph are shedding vertices to gain insight on
$W_2$-graphs.


  Networks are a fundamental model of complex systems throughout the sciences,
and network datasets are typically analyzed through lower-order connectivity
patterns described at the level of individual nodes and edges. However,
higher-order connectivity patterns captured by small subgraphs, also called
network motifs, describe the fundamental structures that control and mediate
the behavior of many complex systems. We develop three tools for network
analysis that use higher-order connectivity patterns to gain new insights into
network datasets: (1) a framework to cluster nodes into modules based on joint
participation in network motifs; (2) a generalization of the clustering
coefficient measurement to investigate higher-order closure patterns; and (3) a
definition of network motifs for temporal networks and fast algorithms for
counting them. Using these tools, we analyze data from biology, ecology,
economics, neuroscience, online social networks, scientific collaborations,
telecommunications, transportation, and the World Wide Web.


  This thesis deals with new backgrounds and concepts in Double Field Theory
(DFT), a T-Duality invariant reformulation of supergravity (SUGRA). We begin by
reviewing the basic concepts and notions of DFT. Afterwards, we turn to Double
Field Theory on group manifolds (DFT$_{\mathrm{WZW}}$). In order to obtain its
action and gauge transformations, Closed String Field Theory (CSFT)
computations are performed on a worldsheet, governed by a Wess-Zumino-Witten
model on a group manifold. We consider generalized diffeomorphisms and their
gauge algebra, which closes under a modified strong constraint. To explore the
connection between this theory and DFT, we recast it in terms of doubled
generalized objects and extrapolate it to all orders in fields. This yields a
generalized metric formulation and a flux formulation. We study the underlying
symmetries and field equations for both formulations. A novel feature in
DFT$_{\mathrm{WZW}}$ is an additional $2D$-diffeomorphism invariance. An
additional extended strong constraint which breaks the $2D$-diffeomorphism
invariance can be imposed to reduce DFT$_{\mathrm{WZW}}$ to DFT. Furthermore,
we perform a generalized Scherk-Schwarz compactification to recover the bosonic
subsector of half-maximal, electrically gauged supergravities. In this context,
we show how to construct twists for each embedding tensor solution explicitly
by using Maurer-Cartan forms. Finally, we generalize the ideas and notions from
DFT$_\mathrm{WZW}$ to geometric Exceptional Field Theory (gEFT). This allows us
to present a systematic construction for generalized parallelizable spaces in
dim M = 4 SL(5) Exceptional Field Theory (EFT). These spaces permit a unified
treatment of consistent maximally supersymmetric truncations of ten- and
eleven-dimensional supergravity in Generalized Geometry (GG) and their
systematic construction has always been an open question.


  A reduced-bias nonparametric estimator of the cumulative distribution
function (CDF) and the survival function is proposed using infinite-order
kernels. Fourier transform theory on generalized functions is utilized to
obtain the improved bias estimates. The new estimators are analyzed in terms of
their relative deficiency to the empirical distribution function and
Kaplan-Meier estimator, and even improvements in terms of asymptotic relative
efficiency (ARE) are present under specified assumptions on the data. The
deficiency analysis introduces a deficiency rate which provides a continuum
between the classical deficiency analysis and an efficiency analysis.
Additionally, an automatic bandwidth selection algorithm, specially tailored to
the infinite-order kernels, is incorporated into the estimators. In small
sample sizes these estimators can significantly improve the estimation of the
CDF and survival function as is illustrated through the deficiency analysis and
computer simulations.


  Single nucleotide polymorphisms (SNPs) represent an important type of dynamic
sites within the human genome. These common variants often locally correlate
into more complex multi-SNP haploblocks that are maintained throughout
generations in a stable population. The information encoded in the structure of
common SNPs and SNP haploblock variation can be characterized through a
normalized information content (NIC) metric. Such an intrinsic measure allows
disparate regions of individual genomes and the genomes of various populations
to be quantitatively compared in a meaningful way.
  Using our defined measures of genomic information, the interplay of
maintained statistical variations due to the environmental baths within which
stable populations exist can be interrogated. We develop the analogous
"thermodynamics" characterizing the state variables for genomic populations
that are stable under stochastic environmental stresses. Since living systems
have not been found to develop in the absence of environmental influences, we
focus on describing the analogous genomic free energy measures in this
development.
  The intensive parameter describing how an environment drives genomic
diversity is found to depend inversely upon the NIC of the genome of a stable
population within that environment. Once this environmental potential has been
determined from the whole genome of a population, additive state variables can
be directly related to the probabilities of the occurrence of given viable SNP
based units (alleles) within that genome. This formulation allows the
determination of both population averaged state variables as well as the
genomic energies of individual alleles and their combinations. The
determination of individual allelic potentials then should allow the
parameterization of specific environmental influences upon shared alleles
across populations in varying environments.


  We give a pedagogical review of how concepts from quantum information theory
build up the gravitational side of the AdS/CFT correspondence. The review is
self-contained in that it only presupposes knowledge of quantum mechanics and
general relativity; other tools--including holographic duality itself--are
introduced in the text. We have aimed to give researchers interested in
entering this field a working knowledge sufficient for initiating original
projects.
  The review begins with the laws of black hole thermodynamics, which form the
basis of this subject, then introduces the Ryu-Takayanagi proposal, the JLMS
relation, and subregion duality. We discuss tensor networks as a visualization
tool and analyze various network architectures in detail. Next, several modern
concepts and techniques are discussed: Renyi entropies and the replica trick,
differential entropy and kinematic space, modular Berry phases, modular minimal
entropy, entanglement wedge cross sections, bit threads, and others. We discuss
the extent to which bulk geometries are fixed by boundary entanglement
entropies, and analyze the relations such as the monogamy of mutual
information, which boundary entanglement entropies must obey if a state has a
semiclassical bulk dual. We close with a discussion of black holes, including
holographic complexity, firewalls and the black hole information paradox,
islands, and replica wormholes.


  We study the nonlinear effects of the clustering and smooth quintessence. We
present numerical and also approximate semi-analytical expressions of nonlinear
power spectrum both for clustering and smooth dark energy models beyond the
Baryon Acoustic Oscillations (BAO) scale. This approximation is motivated by
the extension of the resummation method of Anselmi $\&$ Pietroni (J Cosmol
Astro-Part Phys 12:13, 2012. \url{arXiv:1205.2235}) for the dark energy models
with evolving equation of state. The results of this scheme allow us for the
prediction of the nonlinear power spectrum in the mildly nonlinear regime up to
few percentage accuracies compared to the other available tools to compute the
nonlinear power spectrum for the evolving dark energy models.


  The Quintuplet star cluster is one of only three known young ($<10$ Myr)
massive (M $>10^4$ M$_\odot$) clusters within $\sim100$ pc of the Galactic
Center. In order to explore star cluster formation and evolution in this
extreme environment, we analyze the Quintuplet's dynamical structure. Using the
HST WFC3-IR instrument, we take astrometric and photometric observations of the
Quintuplet covering a $120''\times120''$ field-of-view, which is $19$ times
larger than those of previous proper motion studies of the Quintuplet. We
generate a catalog of the Quintuplet region with multi-band, near-infrared
photometry, proper motions, and cluster membership probabilities for $10,543$
stars. We present the radial density profile of $715$ candidate Quintuplet
cluster members with $M\gtrsim4.7$ M$_\odot$ out to $3.2$ pc from the cluster
center. A $3\sigma$ lower limit of $3$ pc is placed on the tidal radius,
indicating the lack of a tidal truncation within this radius range. Only weak
evidence for mass segregation is found, in contrast to the strong mass
segregation found in the Arches cluster, a second and slightly younger massive
cluster near the Galactic Center. It is possible that tidal stripping hampers a
mass segregation signature, though we find no evidence of spatial asymmetry.
Assuming that the Arches and Quintuplet formed with comparable extent, our
measurement of the Quintuplet's comparatively large core radius of
$0.62^{+0.10}_{-0.10}$ pc provides strong empirical evidence that young massive
clusters in the Galactic Center dissolve on a several Myr timescale.


  Renewable and sustainable energy is one of the most important challenges
currently facing mankind. Wind has made an increasing contribution to the
world's energy supply mix, but still remains a long way from reaching its full
potential. In this paper, we investigate the use of artificial evolution to
design vertical-axis wind turbine prototypes that are physically instantiated
and evaluated under approximated wind tunnel conditions. An artificial neural
network is used as a surrogate model to assist learning and found to reduce the
number of fabrications required to reach a higher aerodynamic efficiency,
resulting in an important cost reduction. Unlike in other approaches, such as
computational fluid dynamics simulations, no mathematical formulations are used
and no model assumptions are made.


  We present a detailed study of mechanically compliant, photonic-crystal-based
microcavities featuring a quasi-bound state in the continuum. Such systems have
recently been predicted to reduce the optical loss in Fabry-Perot-type
optomechanical cavities. However, they require two identical photonic-crystal
slabs facing each other, which poses a considerable challenge for experimental
implementation. We investigate how such an ideal system can be simplified and
still exhibit a quasi-bound state in the continuum. We find that a suspended
photonic-crystal slab facing a distributed Bragg reflector realizes an
optomechanical system with a quasi-bound state in the continuum. In this
system, the radiative cavity loss can be eliminated to the extent that the
cavity loss is dominated by dissipative loss originating from material
absorption only. These proposed optomechanical cavity designs are predicted to
feature optical quality factors in excess of 10^5.


  ChatGPT is currently the most popular large language model (LLM), with over
100 million users, making a significant impact on people's lives. However, due
to the presence of jailbreak vulnerabilities, ChatGPT might have negative
effects on people's lives, potentially even facilitating criminal activities.
Testing whether ChatGPT can cause jailbreak is crucial because it can enhance
ChatGPT's security, reliability, and social responsibility. Inspired by
previous research revealing the varied performance of LLMs in different
language translations, we suspected that wrapping prompts in multiple languages
might lead to ChatGPT jailbreak. To investigate this, we designed a study with
a fuzzing testing approach to analyzing ChatGPT's cross-linguistic proficiency.
Our study includes three strategies by automatically posing different formats
of malicious questions to ChatGPT: (1) each malicious question involving only
one language, (2) multilingual malicious questions, (3) specifying that ChatGPT
responds in a language different from the prompts. In addition, we also combine
our strategies by utilizing prompt injection templates to wrap the three
aforementioned types of questions. We examined a total of 7,892 Q&A data
points, discovering that multilingual wrapping can indeed lead to ChatGPT's
jailbreak, with different wrapping methods having varying effects on jailbreak
probability. Prompt injection can amplify the probability of jailbreak caused
by multilingual wrapping. This work provides insights for OpenAI developers to
enhance ChatGPT's support for language diversity and inclusion.


  The spin transfer effect in ferromagnet-quantum dot (insulator)-ferromagnet
Aharonov-Bohm (AB) ring system with Rashba spin-orbit (SO) interactions is
investigated by means of Keldysh nonequilibrium Green function method. It is
found that both the magnitude and direction of the spin transfer torque (STT)
acting on the right ferromagnet electrode can be effectively controlled by
changing the magnetic flux threading the AB ring or the gate voltage on the
quantum dot. The STT can be greatly augmented by matching a proper magnetic
flux and an SO interaction at a cost of low electrical current. The STT,
electrical current, and spin current are uncovered to oscillate with the
magnetic flux. The present results are expected to be useful for information
storage in nanospintronics.


  Binary hypothesis testing under the Neyman-Pearson formalism is a statistical
inference framework for distinguishing data generated by two different source
distributions. Privacy restrictions may require the curator of the data or the
data respondents themselves to share data with the test only after applying a
randomizing privacy mechanism. Using mutual information as the privacy metric
and the relative entropy between the two distributions of the output
(postrandomization) source classes as the utility metric (motivated by the
Chernoff-Stein Lemma), this work focuses on finding an optimal mechanism that
maximizes the chosen utility function while ensuring that the mutual
information based leakage for both source distributions is bounded. Focusing on
the high privacy regime, an Euclidean information-theoretic (E-IT)
approximation to the tradeoff problem is presented. It is shown that the
solution to the E-IT approximation is independent of the alphabet size and
clarifies that a mutual information based privacy metric preserves the privacy
of the source symbols in inverse proportion to their likelihood.


  Artificial ecosystems provide an additional experimental tool to support
laboratory work, field work, and theoretical development in competitive
exclusion research. A novel application of a spatiotemporal agent based model
is presented which simulates two foraging species of different intrinsic growth
rates competing for the same replenishing resource in stable and seasonal
environments. This experimental approach provides precise control over the
parameters for the environment, the species, and individual movements. Detailed
trajectories of these non-equilibrium populations and their characteristics are
produced. Narrow zones of potential coexistence are identified within the
environmental and intrinsic growth parameter spaces. An example of commensalism
driven by the local spatial dynamics is identified. Results of these
experiments are discussed in context of modern coexistence theory and research
in movement-mediated community assembly. Constraints on possible origination
scenarios are identified.


  Visual Question Answering (VQA) models have achieved significant success in
recent times. Despite the success of VQA models, they are mostly black-box
models providing no reasoning about the predicted answer, thus raising
questions for their applicability in safety-critical such as autonomous systems
and cyber-security. Current state of the art fail to better complex questions
and thus are unable to exploit compositionality. To minimize the black-box
effect of these models and also to make them better exploit compositionality,
we propose a Dynamic Neural Network (DMN), which can understand a particular
question and then dynamically assemble various relatively shallow deep learning
modules from a pool of modules to form a network. We incorporate compositional
temporal attention to these deep learning based modules to increase
compositionality exploitation. This results in achieving better understanding
of complex questions and also provides reasoning as to why the module predicts
a particular answer. Experimental analysis on the two benchmark datasets,
VQA2.0 and CLEVR, depicts that our model outperforms the previous approaches
for Visual Question Answering task as well as provides better reasoning, thus
making it reliable for mission critical applications like safety and security.


  Current motion planning approaches for autonomous mobile robots often assume
that the low level controller of the system is able to track the planned motion
with very high accuracy. In practice, however, tracking error can be affected
by many factors, and could lead to potential collisions when the robot must
traverse a cluttered environment. To address this problem, this paper proposes
a novel receding-horizon motion planning approach based on Model Predictive
Path Integral (MPPI) control theory -- a flexible sampling-based control
technique that requires minimal assumptions on vehicle dynamics and cost
functions. This flexibility is leveraged to propose a motion planning framework
that also considers a data-informed risk function. Using the MPPI algorithm as
a motion planner also reduces the number of samples required by the algorithm,
relaxing the hardware requirements for implementation. The proposed approach is
validated through trajectory generation for a quadrotor unmanned aerial vehicle
(UAV), where fast motion increases trajectory tracking error and can lead to
collisions with nearby obstacles. Simulations and hardware experiments
demonstrate that the MPPI motion planner proactively adapts to the obstacles
that the UAV must negotiate, slowing down when near obstacles and moving
quickly when away from obstacles, resulting in a complete reduction of
collisions while still producing lively motion.


  In random expected utility (Gul and Pesendorfer, 2006), the distribution of
preferences is uniquely recoverable from random choice. This paper shows
through two examples that such uniqueness fails in general if risk preferences
are random but do not conform to expected utility theory. In the first,
non-uniqueness obtains even if all preferences are confined to the betweenness
class (Dekel, 1986) and are suitably monotone. The second example illustrates
random choice behavior consistent with random expected utility that is also
consistent with random non-expected utility. On the other hand, we find that if
risk preferences conform to weighted utility theory (Chew, 1983) and are
monotone in first-order stochastic dominance, random choice again uniquely
identifies the distribution of preferences. Finally, we argue that, depending
on the domain of risk preferences, uniqueness may be restored if joint
distributions of choice across a limited number of feasible sets are available.


  Despite remarkable successes, deep reinforcement learning algorithms remain
sample inefficient: they require an enormous amount of trial and error to find
good policies. Model-based algorithms promise sample efficiency by building an
environment model that can be used for planning. Posterior Sampling for
Reinforcement Learning is such a model-based algorithm that has attracted
significant interest due to its performance in the tabular setting. This paper
introduces Posterior Sampling for Deep Reinforcement Learning (PSDRL), the
first truly scalable approximation of Posterior Sampling for Reinforcement
Learning that retains its model-based essence. PSDRL combines efficient
uncertainty quantification over latent state space models with a specially
tailored continual planning algorithm based on value-function approximation.
Extensive experiments on the Atari benchmark show that PSDRL significantly
outperforms previous state-of-the-art attempts at scaling up posterior sampling
while being competitive with a state-of-the-art (model-based) reinforcement
learning method, both in sample efficiency and computational efficiency.


  With their expansion, national power grid have had to work with huge sets of
data received from a vast number of substations and power plants. Given their
large volume and variety, these data can be classified as big data. Managing
this massive amount of data is certainly challenging. Depending on the
application, parts of these data are more important for real-time network
operation. Computing a network's observability score without assigning weights
to different signals may not provide a complete picture of the received data's
validity and thus lead to incorrect assessments of the network status.
Consequently, signals critical to the network operation and functions of an
energy management system (EMS) should be assigned higher weights in
observability calculations. The weighted observability alongside the classic
non-weighted observability can serve as an indicator of each area's condition
in comparison to that of other areas and so greatly facilitate the monitoring
and verification of transmitted data. For calculating a weighted observability,
the current paper presents a method based on the Analytic Hierarchy Process
(AHP), in which higher weights are assigned to data that are more valuable for
and widely used by operators. The national electricity network of Iran was
chosen for the evaluation of the proposed method's effect on data quality and
operational risk. The results indicated that the introduced method positively
affects the quality of received data and also corrects erroneous data in the
network.


  We consider graph modeling for a knowledge graph for vehicle development,
with a focus on crash safety. An organized schema that incorporates information
from various structured and unstructured data sources is provided, which
includes relevant concepts within the domain. In particular, we propose
semantics for crash computer aided engineering (CAE) data, which enables
searchability, filtering, recommendation, and prediction for crash CAE data
during the development process. This graph modeling considers the CAE data in
the context of the R\&D development process and vehicle safety. Consequently,
we connect CAE data to the protocols that are used to assess vehicle safety
performances. The R\&D process includes CAD engineering and safety attributes,
with a focus on multidisciplinary problem-solving. We describe previous efforts
in graph modeling in comparison to our proposal, discuss its strengths and
limitations, and identify areas for future work.


  Test-time training provides a new approach solving the problem of domain
shift. In its framework, a test-time training phase is inserted between
training phase and test phase. During test-time training phase, usually parts
of the model are updated with test sample(s). Then the updated model will be
used in the test phase. However, utilizing test samples for test-time training
has some limitations. Firstly, it will lead to overfitting to the test-time
procedure thus hurt the performance on the main task. Besides, updating part of
the model without changing other parts will induce a mismatch problem. Thus it
is hard to perform better on the main task. To relieve above problems, we
propose to use mixup in test-time training (MixTTT) which controls the change
of model's parameters as well as completing the test-time procedure. We
theoretically show its contribution in alleviating the mismatch problem of
updated part and static part for the main task as a specific regularization
effect for test-time training. MixTTT can be used as an add-on module in
general test-time training based methods to further improve their performance.
Experimental results show the effectiveness of our method.


  Using $1310.6\times10^6$ $J/\psi$ and $447.9\times10^6$ $\psi(3686)$ events
collected with the BESIII detector at the BEPCII $e^{+}e^{-}$ collider, the
branching fractions and the angular distributions of $J/\psi$ and $\psi(3686)$
decays to $\Lambda\bar{\Lambda}$ and $\Sigma^0\bar{\Sigma}^0$ final states are
measured. The branching fractions are in agreement with, and much more precise
than, the averages of previously published results. The polar angular
distributions of $\psi(3686)$ decays are measured for the first time, while
those of $J/\psi$ decays are measured with much improved precision. In
addition, the ratios of branching fractions
$\frac{\mathcal{B}(\psi(3686)\to\Lambda\bar{\Lambda})}{\mathcal{B}(J/\psi\to\Lambda\bar{\Lambda})}$
and
$\frac{\mathcal{B}(\psi(3686)\to\Sigma^0\bar{\Sigma}^0)}{\mathcal{B}(J/\psi\to\Sigma^0\bar{\Sigma}^0)}$
are determined to test the "12\% rule".


  We designed a completely automated Maple ($\geqslant 15$) worksheet for
deriving Edgeworth and Cornish-Fisher expansions as well as the acceleration
constant of the bootstrap bias-corrected and accelerated technique. It is valid
for non-parametric or parametric bootstrap, of any (studentized) statistics
that is -a regular enough- function of the mean of an iid sample of an
absolutely continuous distribution.
  This worksheet allowed us to point out one error in the second-order
Cornish-Fisher expansion of the studentized mean stated in Theorem 13.5 by Das
Gupta in [8, p. 194] as well as lay the stress on the influence of the slight
change of the normalizing constant when computing the second-order Edgeworth
and Cornish-Fisher expansions of the t-distribution as stated in Theorem 11.4.2
by Lehman and Romano in [14, p. 460].
  In addition, we successfully applied the worksheet to a complex maximum
likelihood estimator as a first step to derive more accurate confidence
intervals in order to enhance quality controls. The worksheet also features
export of Maple results into R code. In addition, we provide R code to plot
these expansions as well as their increasing rearrangements. All these
supplemental materials are available upon request.


  We theoretically show that the topology of a non-simply-connected annular
atomic Bose-Einstein condensate enforces the inner surface waves to be always
excited with outer surface excitations and that the inner surface modes are
associated with induced vortex dipoles unlike the surface waves of a
simply-connected one with vortex monopoles. Consequently, under stirring to
drive an inner surface wave, a peculiar population oscillation between the
inner and outer surface is generated regardless of annulus thickness. Moreover,
a new vortex nucleation process by stirring is observed that can merge the
inner vortex dipoles and outer vortex into a single vortex inside the annulus.
The energy spectrum for a rotating annular condensate with a vortex at the
center also reveals the distinct connection of the Tkachenko modes of a vortex
lattice to its inner surface excitations.


  Battery degradation, which is the reduction of performance over time, is one
of the main roadblocks to the wide deployment of lithium-ion batteries.
Physics-based models, such as those based on the Doyle-Fuller-Newman model, are
invaluable tools to understand and predict such phenomena. However, these
models are often too complex for practical applications, so reduced models are
needed. In this article we introduce the Single Particle Model with electrolyte
and Side Reactions, a reduced model with electrochemical degradation which has
been formally derived from the Doyle-Fuller-Newman model with Side Reactions
using asymptotic methods. The reduced model has been validated against the full
model for three scenarios (solid-electrolyte interphase growth, lithium
plating, and both effects combined) showing similar accuracy at a much lower
computational cost. The implications of the results are twofold: the reduced
model is simple and accurate enough to be used in most real practical
applications, and the reduction framework used is robust so it can be extended
to account for further degradation effects.


  Many methods for modelling spatial processes assume global smoothness
properties; such assumptions are often violated in practice. We introduce a
method for modelling spatial processes that display heterogeneity or contain
discontinuities. The problem of non-stationarity is dealt with by using a
combination of Voronoi tessellation to partition the input space, and a
separate Gaussian process to model the data on each region of the partitioned
space. Our method is highly flexible because we allow the Voronoi cells to form
relationships with each other, which can enable non-convex and disconnected
regions to be considered. In such problems, identifying the borders between
regions is often of great importance and we propose an adaptive sampling method
to gain extra information along such borders. The method is illustrated with
simulation studies and application to real data.


  Online adaptive radiation therapy (ART) promises the ability to deliver an
optimal treatment in response to daily patient anatomic variation. A major
technical barrier for the clinical implementation of online ART is the
requirement of rapid image segmentation. Deformable image registration (DIR)
has been used as an automated segmentation method to transfer tumor/organ
contours from the planning image to daily images. However, the current
computational time of DIR is insufficient for online ART. In this work, this
issue is addressed by using computer graphics processing units (GPUs). A
grey-scale based DIR algorithm called demons and five of its variants were
implemented on GPUs using the Compute Unified Device Architecture (CUDA)
programming environment. The spatial accuracy of these algorithms was evaluated
over five sets of pulmonary 4DCT images with an average size of 256x256x100 and
more than 1,100 expert-determined landmark point pairs each. For all the
testing scenarios presented in this paper, the GPU-based DIR computation
required around 7 to 11 seconds to yield an average 3D error ranging from 1.5
to 1.8 mm. It is interesting to find out that the original passive force demons
algorithms outperform subsequently proposed variants based on the combination
of accuracy, efficiency, and ease of implementation.


  Whether the spiral structure of galaxies is trailing or leading has been a
subject of debate. We present a new spin parity catalog of 146 spiral galaxies
that lists the following three pieces of information: whether the spiral
structure observed on the sky is S-wise or Z-wise; which side of the minor axis
of the galaxy is darker and redder, based on examination of Pan-STARRS and/or
ESO/DSS2 red image archives, and which side of the major axis of the galaxy is
approaching to us based on the published literature. This paper confirms that
all of the spiral galaxies in the catalog show a consistent relationship among
these three parameters, without any confirmed counterexamples, that supports
the generally accepted interpretation that all the spiral galaxies are trailing
and that the darker/redder side of the galactic disk is closer to us. Although
the results of this paper may not be surprising, they provide a rationale for
analyzing the S/Z winding distribution of spiral galaxies, using the large and
uniform image data bases available now and in the near future, to study the
spin vorticity distribution of galaxies in order to constrain the formation
scenarios of galaxies and the large-scale structure of the Universe.


  This paper addresses the problem of multitarget tracking using a network of
sensing agents with unknown positions. Agents have to both localize themselves
in the sensor network and, at the same time, perform multitarget tracking in
the presence of clutter and miss detection. These two problems are jointly
resolved using a holistic and centralized approach where graph theory is used
to describe the statistical relationships among agent states, target states,
and observations. A scalable message passing scheme, based on the sum-product
algorithm, enables to efficiently approximate the marginal posterior
distributions of both agent and target states. The proposed method is general
enough to accommodate a full multistatic network configuration, with multiple
transmitters and receivers. Numerical simulations show superior performance of
the proposed joint approach with respect to the case in which cooperative
self-localization and multitarget tracking are performed separately, as the
former manages to extract valuable information from targets. Lastly, data
acquired in 2018 by the NATO Science and Technology Organization (STO) Centre
for Maritime Research and Experimentation (CMRE) through a network of
autonomous underwater vehicles demonstrates the effectiveness of the approach
in a practical application.


  It is not difficult to think of applications that can be modelled as graph
problems in which placing some facility or commodity at a vertex has some
positive or negative effect on the values of all the vertices out to some
distance, and we want to be able to calculate quickly the cumulative effect on
any vertex's value at any time or the list of the most beneficial or most
detrimential effects on a vertex. In this paper we show how, given an
edge-weighted graph with constant-size separators, we can support the following
operations on it in time polylogarithmic in the number of vertices and the
number of facilities placed on the vertices, where distances between vertices
are measured with respect to the edge weights:
  Add (v, f, w, d) places a facility of weight w and with effect radius d onto
vertex v.
  Remove (v, f) removes a facility f previously placed on v using Add from v.
  Sum (v) or Sum (v, d) returns the total weight of all facilities affecting v
or, with a distance parameter d, the total weight of all facilities whose
effect region intersects the ``circle'' with radius d around v.
  Top (v, k) or Top (v, k, d) returns the k facilities of greatest weight that
affect v or, with a distance parameter d, whose effect region intersects the
``circle'' with radius d around v.
  The weights of the facilities and the operation that Sum uses to ``sum'' them
must form a semigroup. For Top queries, the weights must be drawn from a total
order.


  We construct a full, strongly exceptional collection of line bundles on the
variety X that is the blow up of the projectivization of the vector bundle
O_{P^{n-1}}\oplus O_{P^{n-1}}(b) along a linear space of dimension n-2, where b
is a non-negative integer.


  Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is a modern imaging
technique used in material research to study nanoscale materials.
Reconstruction of the parameters of an imaged object imposes an ill-posed
inverse problem that is further complicated when only an in-plane GISAXS signal
is available. Traditionally used inference algorithms such as Approximate
Bayesian Computation (ABC) rely on computationally expensive scattering
simulation software, rendering analysis highly time-consuming. We propose a
simulation-based framework that combines variational auto-encoders and
normalizing flows to estimate the posterior distribution of object parameters
given its GISAXS data. We apply the inference pipeline to experimental data and
demonstrate that our method reduces the inference cost by orders of magnitude
while producing consistent results with ABC.


  We present the first implementation of the Cho--Faddeev--Niemi ecomposition
of the SU(2) Yang-Mills field on a lattice. Our construction retains the color
symmetry (global SU(2) gauge invariance) even after a new type of Maximally
Abelian gauge, as explicitly demonstrated by numerical simulations.


  In this contribution, we extend the hybridization framework for the Hodge
Laplacian [Awanou et al., Hybridization and postprocessing in finite element
exterior calculus, 2023 ] to port-Hamiltonian systems describing linear wave
propagation phenomena. To this aim, a dual field mixed Galerkin discretization
is introduced, in which one variable is approximated via conforming finite
element spaces, whereas the second is completely local. This scheme is
equivalent to the second order mixed Galerkin formulation and retains a
discrete power balance and discrete conservation laws. The mixed formulation is
also equivalent to the hybrid formulation. The hybrid system can be efficiently
solved using a static condensation procedure in discrete time. The size
reduction achieved thanks to the hybridization is greater than the one obtained
for the Hodge Laplacian as one field is completely discarded. Numerical
experiments on the 3D wave and Maxwell equations show the convergence of the
method and the size reduction achieved by the hybridization.


  We study $g$-vector cones in a cluster algebra defined from a weighted
orbifold of rank $n$ introduced by Felikson, Shapiro and Tumarkin. We determine
the closure of the union of the $g$-vector cones. It is equal to $\mathbb{R}^n$
except for a weighted orbifold with empty boundary and exactly one puncture, in
which case it is equal to the half space of a certain explicit hyperplane in
$\mathbb{R}^n$.


  In product search, users tend to browse results on multiple search result
pages (SERPs) (e.g., for queries on clothing and shoes) before deciding which
item to purchase. Users' clicks can be considered as implicit feedback which
indicates their preferences and used to re-rank subsequent SERPs. Relevance
feedback (RF) techniques are usually involved to deal with such scenarios.
However, these methods are designed for document retrieval, where relevance is
the most important criterion. In contrast, product search engines need to
retrieve items that are not only relevant but also satisfactory in terms of
customers' preferences. Personalization based on users' purchase history has
been shown to be effective in product search. However, this method captures
users' long-term interest, which does not always align with their short-term
interest, and does not benefit customers with little or no purchase history. In
this paper, we study RF techniques based on both long-term and short-term
context dependencies in multi-page product search. We also propose an
end-to-end context-aware embedding model which can capture both types of
context. Our experimental results show that short-term context leads to much
better performance compared with long-term and no context. Moreover, our
proposed model is more effective than state-of-art word-based RF models.


  This paper is concerned with forecast error, particularly in relation to loss
reserving. This is generally regarded as consisting of three components, namely
parameter, process and model errors. The first two of these components, and
their estimation, are well understood, but less so model error. Model error
itself is considered in two parts: one part that is capable of estimation from
past data (internal model error), and another part that is not (external model
error). Attention is focused here on internal model error. Estimation of this
error component is approached by means of Bayesian model averaging, using the
Bayesian interpretation of the LASSO. This is used to generate a set of
admissible models, each with its prior probability and the likelihood of
observed data. A posterior on the model set, conditional on the data, results,
and an estimate of model error (contained in a loss reserve) is obtained as the
variance of the loss reserve according to this posterior. The population of
models entering materially into the support of the posterior may turn out to be
thinner than desired, and bootstrapping of the LASSO is used to gain bulk. This
provides the bonus of an estimate of parameter error also. It turns out that
the estimates of parameter and model errors are entangled, and dissociation of
them is at least difficult, and possibly not even meaningful. These matters are
discussed. The majority of the discussion applies to forecasting generally, but
numerical illustration of the concepts is given in relation to insurance data
and the problem of insurance loss reserving.


  Deep learning using multi-layer neural networks (NNs) architecture manifests
superb power in modern machine learning systems. The trained Deep Neural
Networks (DNNs) are typically large. The question we would like to address is
whether it is possible to simplify the NN during training process to achieve a
reasonable performance within an acceptable computational time. We presented a
novel approach of optimising a deep neural network through regularisation of
net- work architecture. We proposed regularisers which support a simple
mechanism of dropping neurons during a network training process. The method
supports the construction of a simpler deep neural networks with compatible
performance with its simplified version. As a proof of concept, we evaluate the
proposed method with examples including sparse linear regression, deep
autoencoder and convolutional neural network. The valuations demonstrate
excellent performance.
  The code for this work can be found in
http://www.github.com/panweihit/DropNeuron


  The instability in the selection of models is a major concern with data sets
containing a large number of covariates. We focus on stability selection which
is used as a technique to improve variable selection performance for a range of
selection methods, based on aggregating the results of applying a selection
procedure to sub-samples of the data where the observations are subject to
right censoring. The accelerated failure time (AFT) models have proved useful
in many contexts including the heavy censoring (as for example in cancer
survival) and the high dimensionality (as for example in micro-array data). We
implement the stability selection approach using three variable selection
techniques--Lasso, ridge regression, and elastic net applied to censored data
using AFT models. We compare the performances of these regularized techniques
with and without stability selection approaches with simulation studies and a
breast cancer data analysis. The results suggest that stability selection gives
always stable scenario about the selection of variables and that as the
dimension of data increases the performance of methods with stability selection
also improves compared to methods without stability selection irrespective of
the collinearity between the covariates.