  Weakly supervised text classification methods typically train a deep neural
classifier based on pseudo-labels. The quality of pseudo-labels is crucial to
final performance but they are inevitably noisy due to their heuristic nature,
so selecting the correct ones has a huge potential for performance boost. One
straightforward solution is to select samples based on the softmax probability
scores in the neural classifier corresponding to their pseudo-labels. However,
we show through our experiments that such solutions are ineffective and
unstable due to the erroneously high-confidence predictions from poorly
calibrated models. Recent studies on the memorization effects of deep neural
models suggest that these models first memorize training samples with clean
labels and then those with noisy labels. Inspired by this observation, we
propose a novel pseudo-label selection method LOPS that takes learning order of
samples into consideration. We hypothesize that the learning order reflects the
probability of wrong annotation in terms of ranking, and therefore, propose to
select the samples that are learnt earlier. LOPS can be viewed as a strong
performance-boost plug-in to most of existing weakly-supervised text
classification methods, as confirmed in extensive experiments on four
real-world datasets.


  We propose a scheme for a cavity quantum electrodynamics (QED) architecture
for a current-biased superconducting flux qubit with three Josephson junctions.
The qubit operation is performed by using a bias current coming from the
current mode of the circuit resonator. If the phase differences of junctions
are to be coupled with the bias current, the Josephson junctions should be
arranged in an asymmetric way in the qubit loop. Our QED scheme provides a
strong coupling between the flux qubit and the transmission line resonator of
the circuit.


  Customer behavioral data significantly impacts e-commerce search systems.
However, in the case of less common queries, the associated behavioral data
tends to be sparse and noisy, offering inadequate support to the search
mechanism. To address this challenge, the concept of query reformulation has
been introduced. It suggests that less common queries could utilize the
behavior patterns of their popular counterparts with similar meanings. In
Amazon product search, query reformulation has displayed its effectiveness in
improving search relevance and bolstering overall revenue. Nonetheless,
adapting this method for smaller or emerging businesses operating in regions
with lower traffic and complex multilingual settings poses the challenge in
terms of scalability and extensibility. This study focuses on overcoming this
challenge by constructing a query reformulation solution capable of functioning
effectively, even when faced with limited training data, in terms of quality
and scale, along with relatively complex linguistic characteristics. In this
paper we provide an overview of the solution implemented within Amazon product
search infrastructure, which encompasses a range of elements, including
refining the data mining process, redefining model training objectives, and
reshaping training strategies. The effectiveness of the proposed solution is
validated through online A/B testing on search ranking and Ads matching.
Notably, employing the proposed solution in search ranking resulted in 0.14%
and 0.29% increase in overall revenue in Japanese and Hindi cases,
respectively, and a 0.08\% incremental gain in the English case compared to the
legacy implementation; while in search Ads matching led to a 0.36% increase in
Ads revenue in the Japanese case.


  In this paper, for a given family of constraints and the classical Cantor
distribution we determine the constrained optimal sets of $n$-points, $n$th
constrained quantization errors for all positive integers $n$. We also
calculate the constrained quantization dimension and the constrained
quantization coefficient, and see that the constrained quantization dimension
$D(P)$ exists as a finite positive number, but the $D(P)$-dimensional
constrained quantization coefficient does not exist.


  We prove that the multiplicity of a fixed eigenvalue $\alpha$ in a random
recursive tree on $n$ vertices satisfies a central limit theorem with mean and
variance asymptotically equal to $\mu_{\alpha} n$ and $\sigma^2_{\alpha} n$
respectively. It is also shown that $\mu_{\alpha}$ and $\sigma^2_{\alpha}$ are
positive for every totally real algebraic integer. The proofs are based on a
general result on additive tree functionals due to Holmgren and Janson. In the
case of the eigenvalue $0$, the constants $\mu_0$ and $\sigma^2_0$ can be
determined explicitly by means of generating functions. Analogous results are
also obtained for Laplacian eigenvalues and binary increasing trees.


  We consider composite two-Higgs doublet models based on gauge-Yukawa theories
with strongly interacting fermions generating the top-bottom mass hierarchy.
The model features a single "universal" Higgs-Yukawa coupling, $ g $, which is
identified with the top quark $ g\equiv g_t \sim \mathcal{O}(1) $. The
top-bottom mass hierarchy arises by soft breaking of a $ \mathbb{Z}_2 $
symmetry by a condensate of strongly interacting fermions. A mass splitting
between vector-like masses of the confined techni-fermions controls this
top-bottom mass hierarchy. This mechanism can be present in a variety of models
based on vacuum misalignment. For concreteness, we demonstrate it in a
composite two-Higgs scheme.


  We give sufficient conditions for a metric space to bilipschitz embed in L_1.
In particular, if X is a length space and there is a Lipschitz map u:X--->R
such that for every interval I in R, the connected components of the inverse
image f^{-1}(I) have diameter at most a constant time the diameter of I, then X
admits a bilipschitz embedding in L_1. As a corollary, well-known examples of
Laakso bilipschitz embed in L_1, though they do not embed in any any Banach
space with the Radon-Nikodym property (e.g. the space l_1 of summable
sequences).
  The spaces appearing the statement of the bilipschitz embedding theorem have
an alternate characterization as inverse limits of systems of metric graphs
satisfying certain additional conditions. This representation, which may be of
independent interest, is the initial part of the proof of the bilipschitz
embedding theorem. The rest of the proof uses the combinatorial structure of
the inverse system of graphs and a diffusion construction, to produce the
embedding in L_1.


  The attractor mechanism for the four-dimensional ${\cal N}=2$ supergravity
black hole solution is analyzed in the case of the D0-D4 system. Our analyses
are based on newly derived exact solutions, which exhibit explicitly the
attractor mechanism for extremal non-BPS black holes. Our solutions account for
the moduli as general complex fields, while in almost all non-BPS solutions
obtained previously, the moduli fields are restricted to be purely imaginary.
It is also pointed out that our moduli solutions contain an extra parameter
that is not contained in solutions obtained by replacing the charges in the
double extremal moduli solutions by the corresponding harmonic functions.


  We propose a quantum memory protocol based on dynamically changing the
resonance frequency of an ensemble of two-level atoms. By sweeping the atomic
frequency in an adiabatic fashion, photons are reversibly transferred into
atomic coherences. We present a polaritonic description for this type of
storage, which shares some similarities with Electromagnetically Induced
Transparency (EIT) based quantum memories. On the other hand the proposed
memory is also linked to the Gradient Echo Memory (GEM) due to the effective
spatial gradient that pulses experience in the medium. We discuss a possible
implementation of the protocol in hollow-core photonic crystal fibers.


  Over the past decades, many individual nonconvex methods have been proposed
to achieve better sparse recovery performance in various scenarios. However,
how to construct a valid nonconvex regularization function remains open in
practice. In this paper, we fill in this gap by presenting a unified framework
for constructing the nonconvex regularization based on the probability density
function. Meanwhile, a new nonconvex sparse recovery method constructed via the
Weibull distribution is studied.


  Nucleus-nucleus interaction is studied in the framework of the perturbative
QCD with large number of colours and a fixed coupling constant. The pomeron
tree diagrams are summed by an effective field theory. The classical field
equations are solved by iteration procedure, which is found convergent in a
restricted domain of not too high energies and atomic numbers. The found gluon
distributions do not scale, have their maxima close to 2 GeV/c independent of
rapidity and fall towards the central rapidity region. The cross-sections
slowly grow with energy due to the contribution from peripheral collisions,
where evolution remains linear. Simple variational estimates at higher
rapidities confirm this tendency.


  We present two numerical simulations of an accretion flow from a rotating
torus onto a compact object with and without a solid surface -- representing a
neutron star and a black hole -- and investigate its influence on the process
of jet formation. We report the emergence of an additional ejection component,
launched by thermal pressure inside a boundary layer (BL) around the neutron
star and examine its structure. Finally, we suggest improvements for future
models.


  The kinematical setting of spherically symmetric quantum geometry, derived
from the full theory of loop quantum gravity, is developed. This extends
previous studies of homogeneous models to inhomogeneous ones where interesting
field theory aspects arise. A comparison between a reduced quantization and a
derivation of the model from the full theory is presented in detail, with an
emphasis on the resulting quantum representation. Similar concepts for
Einstein-Rosen waves are discussed briefly.


  A broad class of imaging modalities involve the resolution of an
inverse-scattering problem. Among them, three-dimensional optical diffraction
tomography (ODT) comes with its own challenges. These include a limited range
of views, a large size of the sample with respect to the illumination
wavelength, and optical aberrations that are inherent to the system itself. In
this work, we present an accurate and efficient implementation of the forward
model. It relies on the exact (nonlinear) Lippmann-Schwinger equation. We
address several crucial issues such as the discretization of the Green
function, the computation of the far field, and the estimation of the incident
field. We then deploy this model in a regularized variational-reconstruction
framework and show on both simulated and real data that it leads to
substantially better reconstructions than the approximate models that are
traditionally used in ODT.


  In this paper, we propose a solution that won the 10th prize in the KDD Cup
2023 Challenge Task 2 (Next Product Recommendation for Underrepresented
Languages/Locales). Our approach involves two steps: (i) Identify candidate
item sets based on co-visitation, and (ii) Re-ranking the items using LightGBM
with locale-independent features, including session-based features and product
similarity. The experiment demonstrated that the locale-independent model
performed consistently well across different test locales, and performed even
better when incorporating data from other locales into the training.


  Information theory provides powerful tools for understanding communication
systems. This analysis can be applied to intercellular signal transduction,
which is a means of chemical communication among cells and microbes. We discuss
how to apply information-theoretic analysis to ligand-receptor systems, which
form the signal carrier and receiver in intercellular signal transduction
channels. We also discuss the applications of these results to neuroscience.


  Presently available high-energy proton beams in circular accelerators carry
enough momentum to accelerate high-intensity electron and positron beams to the
TeV energy scale over several hundred meters of the plasma with a density of
about 1e15 1/cm^3. However, the plasma wavelength at this density is 100-1000
times shorter than the typical longitudinal size of the high-energy proton
beam. Therefore the self-modulation instability (SMI) of a long (~10 cm) proton
beam in the plasma should be used to create the train of micro-bunches which
would then drive the plasma wake resonantly. Changing the plasma density
profile offers a simple way to control the development of the SMI and the
acceleration of particles during this process. We present simulations of the
possible use of a plasma density gradient as a way to control the acceleration
of the electron beam during the development of the SMI of a 400 GeV proton beam
in a 10 m long plasma. This work is done in the context of the AWAKE project
--- the proof-of-principle experiment on proton driven plasma wakefield
acceleration at CERN.


  Large Language Models (LLMs) face threats from jailbreak prompts. Existing
methods for detecting jailbreak prompts are primarily online moderation APIs or
finetuned LLMs. These strategies, however, often require extensive and
resource-intensive data collection and training processes. In this study, we
propose GradSafe, which effectively detects jailbreak prompts by scrutinizing
the gradients of safety-critical parameters in LLMs. Our method is grounded in
a pivotal observation: the gradients of an LLM's loss for jailbreak prompts
paired with compliance response exhibit similar patterns on certain
safety-critical parameters. In contrast, safe prompts lead to different
gradient patterns. Building on this observation, GradSafe analyzes the
gradients from prompts (paired with compliance responses) to accurately detect
jailbreak prompts. We show that GradSafe, applied to Llama-2 without further
training, outperforms Llama Guard, despite its extensive finetuning with a
large dataset, in detecting jailbreak prompts. This superior performance is
consistent across both zero-shot and adaptation scenarios, as evidenced by our
evaluations on ToxicChat and XSTest. The source code is available at
https://github.com/xyq7/GradSafe.


  We establish a series representation of the Hill discriminant based on the
spectral parameter power series (SPPS) recently introduced by V. Kravchenko. We
also show the invariance of the Hill discriminant under a Darboux
transformation and employing the Mathieu case the feasibility of this type of
series for numerical calculations of the eigenspectrum


  We explore machine unlearning (MU) in the domain of large language models
(LLMs), referred to as LLM unlearning. This initiative aims to eliminate
undesirable data influence (e.g., sensitive or illegal information) and the
associated model capabilities, while maintaining the integrity of essential
knowledge generation and not affecting causally unrelated information. We
envision LLM unlearning becoming a pivotal element in the life-cycle management
of LLMs, potentially standing as an essential foundation for developing
generative AI that is not only safe, secure, and trustworthy, but also
resource-efficient without the need of full retraining. We navigate the
unlearning landscape in LLMs from conceptual formulation, methodologies,
metrics, and applications. In particular, we highlight the often-overlooked
aspects of existing LLM unlearning research, e.g., unlearning scope, data-model
interaction, and multifaceted efficacy assessment. We also draw connections
between LLM unlearning and related areas such as model editing, influence
functions, model explanation, adversarial training, and reinforcement learning.
Furthermore, we outline an effective assessment framework for LLM unlearning
and explore its applications in copyright and privacy safeguards and
sociotechnical harm reduction.


  Learning a smooth graph signal from partially observed data is a well-studied
task in graph-based machine learning. We consider this task from the
perspective of optimal recovery, a mathematical framework for learning a
function from observational data that adopts a worst-case perspective tied to
model assumptions on the function to be learned. Earlier work in the optimal
recovery literature has shown that minimizing a regularized objective produces
optimal solutions for a general class of problems, but did not fully identify
the regularization parameter. Our main contribution provides a way to compute
regularization parameters that are optimal or near-optimal (depending on the
setting), specifically for graph signal processing problems. Our results offer
a new interpretation for classical optimization techniques in graph-based
learning and also come with new insights for hyperparameter selection. We
illustrate the potential of our methods in numerical experiments on several
semi-synthetic graph signal processing datasets.


  The Tamari order is a central object in algebraic combinatorics and many
other areas. Defined as the transitive closure of an associativity law, the
Tamari order possesses a surprisingly rich structure: it is a
congruence-uniform lattice. We consider a larger class of posets, the
Grid-Tamari orders, which arise as an ordering on the facets of the non-kissing
complex introduced by Pylyavskyy, Petersen, and Speyer. In addition to Tamari
orders, some interesting examples of Grid-Tamari orders include the Type A
Cambrian lattices and Grassmann-Tamari orders. We prove that the Grid-Tamari
orders are congruence-uniform lattices, which resolves a conjecture of Santos,
Stump, and Welker. Towards this goal, we define a closure operator on sets of
paths in a square grid, and prove that the biclosed sets of paths, ordered by
inclusion, form a congruence-uniform lattice. We then prove that the
Grid-Tamari order is a quotient lattice of the corresponding lattice of
biclosed sets.


  Weakly supervised object localization (WSOL) focuses on localizing objects
only with the supervision of image-level classification masks. Most previous
WSOL methods follow the classification activation map (CAM) that localizes
objects based on the classification structure with the multi-instance learning
(MIL) mechanism. However, the MIL mechanism makes CAM only activate
discriminative object parts rather than the whole object, weakening its
performance for localizing objects. To avoid this problem, this work provides a
novel perspective that models WSOL as a domain adaption (DA) task, where the
score estimator trained on the source/image domain is tested on the
target/pixel domain to locate objects. Under this perspective, a DA-WSOL
pipeline is designed to better engage DA approaches into WSOL to enhance
localization performance. It utilizes a proposed target sampling strategy to
select different types of target samples. Based on these types of target
samples, domain adaption localization (DAL) loss is elaborated. It aligns the
feature distribution between the two domains by DA and makes the estimator
perceive target domain cues by Universum regularization. Experiments show that
our pipeline outperforms SOTA methods on multi benchmarks. Code are released at
\url{https://github.com/zh460045050/DA-WSOL_CVPR2022}.


  This paper can be viewed as a continuation of [KS09] that dealt with the
automorphism tower problem without Choice. Here we deal with the inequation
which connects the automorphism tower and the normalizer tower without Choice
and introduce a new proof to a theorem of Fried and Koll\'ar that any group can
be represented as an automorphism group of a field. The proof uses a simple
construction: working more in graph theory, and less in algebra.


  We outline an analytical framework for the treatment of radial Rydberg wave
packets produced by short laser pulses in the absence of external electric and
magnetic fields. Wave packets of this type are localized in the radial
coordinates and have p-state angular distributions. We argue that they can be
described by a particular analytical class of squeezed states, called radial
squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of
the corresponding hydrogenic radial squeezed states. They are found to undergo
decoherence and collapse, followed by fractional and full revivals. We also
present their uncertainty product and uncertainty ratio as functions of time.
Our results show that hydrogenic radial squeezed states provide a suitable
analytical description of hydrogenic Rydberg atoms excited by short-pulsed
laser fields.


  The current bulk materials discovery cycle has several inefficiencies from
initial computational predictions through fabrication and analyses. Materials
are generally evaluated in a singular fashion, relying largely on human-driven
compositional choices and analysis of the volumes of generated data, thus also
slowing validation of computational models. To overcome these limitations, we
developed a high-throughput rapid experimental alloy development (HT-READ)
methodology that comprises an integrated, closed-loop material screening
process inspired by broad chemical assays and modern innovations in automation.
Our method is a general framework unifying computational identification of
ideal candidate materials, fabrication of sample libraries in a configuration
amenable to multiple tests and processing routes, and analysis of the candidate
materials in a high-throughput fashion. An artificial intelligence agent is
used to find connections between compositions and material properties. New
experimental data can be leveraged in subsequent iterations or new design
objectives. The sample libraries are assigned unique identifiers and stored to
make data and samples persistent, thus preventing institutional knowledge loss.


  Unpaired image-to-image (I2I) translation often requires to maximize the
mutual information between the source and the translated images across
different domains, which is critical for the generator to keep the source
content and prevent it from unnecessary modifications. The self-supervised
contrastive learning has already been successfully applied in the I2I. By
constraining features from the same location to be closer than those from
different ones, it implicitly ensures the result to take content from the
source. However, previous work uses the features from random locations to
impose the constraint, which may not be appropriate since some locations
contain less information of source domain. Moreover, the feature itself does
not reflect the relation with others. This paper deals with these problems by
intentionally selecting significant anchor points for contrastive learning. We
design a query-selected attention (QS-Attn) module, which compares feature
distances in the source domain, giving an attention matrix with a probability
distribution in each row. Then we select queries according to their measurement
of significance, computed from the distribution. The selected ones are regarded
as anchors for contrastive loss. At the same time, the reduced attention matrix
is employed to route features in both domains, so that source relations
maintain in the synthesis. We validate our proposed method in three different
I2I datasets, showing that it increases the image quality without adding
learnable parameters.


  The prevalence of artificial intelligence (AI) has envisioned an era of
healthcare democratisation that promises every stakeholder a new and better way
of life. However, the advancement of clinical AI research is significantly
hurdled by the dearth of data democratisation in healthcare. To truly
democratise data for AI studies, challenges are two-fold: 1. the sensitive
information in clinical data should be anonymised appropriately, and 2.
AI-oriented clinical knowledge should flow freely across organisations. This
paper considers a recent deep-learning advent, dataset condensation (DC), as a
stone that kills two birds in democratising healthcare data. The condensed data
after DC, which can be viewed as statistical metadata, abstracts original
clinical records and irreversibly conceals sensitive information at individual
levels; nevertheless, it still preserves adequate knowledge for learning deep
neural networks (DNNs). More favourably, the compressed volumes and the
accelerated model learnings of condensed data portray a more efficient clinical
knowledge sharing and flowing system, as necessitated by data democratisation.
We underline DC's prospects for democratising clinical data, specifically
electrical healthcare records (EHRs), for AI research through experimental
results and analysis across three healthcare datasets of varying data types.


  The increasing need to analyse large volumes of data has led to the
development of Symbolic Data Analysis as a promising field to tackle the data
challenges of our time. New data types, such as interval-valued data, have
brought fresh theoretical and methodological problems to be solved. In this
paper, we derive explicit formulas for computing the Mallows' distance, also
known as $L_2$ Wasserstein distance, between two \textit{p}-dimensional
intervals, using information regarding the distribution of the microdata. We
establish this distance as a Mahalanobis' distance between two
2\textit{p}-dimensional vectors. Our comprehensive analysis leads to the
generalisation of the definitions of the expected value and covariance matrix
of an interval-valued random vector. These novel results bring theoretical
support and interpretability to state-of-the-art contributions. Additionally,
we discuss real examples that illustrate how we can model different levels of
available information on the microdata, leading to proper estimates of the
measures of location and association.


  For more than fifty years, scientists have been gathering evidence of the
biological impacts of weak magnetic fields. However, the lack of systematics in
experimental studies has hampered research progress on this subject. To
systematically quantify magnetic field effects in cell biology, it is crucial
to produce fields that can be automatically adjusted and that are stable
throughout an experiment's duration, usually operating inside an incubator.
Here, we report on the design of a fully automated 1D Helmholtz coil setup that
is internally water cooled, thus eliminating any confounding effects caused by
temperature fluctuations. The coils also allow cells to be exposed to magnetic
fields from multiple directions through automated controlled rotation.
Preliminary data, acquired with the coils placed inside an incubator and on a
rat vascular smooth muscle cell line, confirm previous reports that both
microtubule and actin polymerization and dynamics are altered by weak magnetic
fields.


  Recent advancements in ultra-high-resolution unpaired image-to-image
translation have aimed to mitigate the constraints imposed by limited GPU
memory through patch-wise inference. Nonetheless, existing methods often
compromise between the reduction of noticeable tiling artifacts and the
preservation of color and hue contrast, attributed to the reliance on global
image- or patch-level statistics in the instance normalization layers. In this
study, we introduce a Dense Normalization (DN) layer designed to estimate
pixel-level statistical moments. This approach effectively diminishes tiling
artifacts while concurrently preserving local color and hue contrasts. To
address the computational demands of pixel-level estimation, we further propose
an efficient interpolation algorithm. Moreover, we invent a parallelism
strategy that enables the DN layer to operate in a single pass. Through
extensive experiments, we demonstrate that our method surpasses all existing
approaches in performance. Notably, our DN layer is hyperparameter-free and can
be seamlessly integrated into most unpaired image-to-image translation
frameworks without necessitating retraining. Overall, our work paves the way
for future exploration in handling images of arbitrary resolutions within the
realm of unpaired image-to-image translation. Code is available at:
https://github.com/Kaminyou/Dense-Normalization.


  Let $P$ and $Q$ be finite point sets of the same cardinality in
$\mathbb{R}^2$, each labelled from $1$ to $n$. Two noncrossing geometric graphs
$G_P$ and $G_Q$ spanning $P$ and $Q$, respectively, are called compatible if
for every face $f$ in $G_P$, there exists a corresponding face in $G_Q$ with
the same clockwise ordering of the vertices on its boundary as in $f$. In
particular, $G_P$ and $G_Q$ must be straight-line embeddings of the same
connected $n$-vertex graph.
  Deciding whether two labelled point sets admit compatible geometric paths is
known to be NP-complete. We give polynomial-time algorithms to find compatible
paths or report that none exist in three scenarios: $O(n)$ time for points in
convex position; $O(n^2)$ time for two simple polygons, where the paths are
restricted to remain inside the closed polygons; and $O(n^2 \log n)$ time for
points in general position if the paths are restricted to be monotone.


  We present full generalisations of entropic security and entropic
indistinguishability to the quantum world where no assumption but a limit on
the knowledge of the adversary is made. This limit is quantified using the
quantum conditional min-entropy as introduced by Renato Renner. A proof of the
equivalence between the two security definitions is presented. We also provide
proofs of security for two different cyphers in this model and a proof for a
lower bound on the key length required by any such cypher. These cyphers
generalise existing schemes for approximate quantum encryption to the entropic
security model.


  We construct a (1+1)$d$ topological field theory (TFT) whose topological
defect lines (TDLs) realize the transparent Haagerup $\mathcal{H}_3$ fusion
category. This TFT has six vacua, and each of the three non-invertible simple
TDLs hosts three defect operators, giving rise to a total of 15 point-like
operators. The TFT data, including the three-point coefficients and lasso
diagrams, are determined by solving all the sphere four-point crossing
equations and torus one-point modular invariance equations. We further verify
that the Cardy states furnish a non-negative integer matrix representation
under TDL fusion. While many of the constraints we derive are not limited to
the this particular TFT with six vacua, we leave open the construction of TFTs
with two or four vacua. Finally, TFTs realizing the Haagerup $\mathcal{H}_1$
and $\mathcal{H}_2$ fusion categories can be obtained by gauging algebra
objects. This note makes a modest offering in our pursuit of exotica and the
quest for their eventual conformity.


  For a quantum system coupled to a heat bath environment the strong friction
limit is studied starting from the exact path integral formulation.
Generalizing the classical Smoluchowski limit to low temperatures a time
evolution equation for the position distribution is derived and the strong role
of quantum fluctuations in this limit is revealed.


  Scientific Machine Learning (SciML) is concerned with the development of
learned emulators of physical systems governed by partial differential
equations (PDE). In application domains such as weather forecasting, molecular
dynamics, and inverse design, ML-based surrogate models are increasingly used
to augment or replace inefficient and often non-differentiable numerical
simulation algorithms. While a number of ML-based methods for approximating the
solutions of PDEs have been proposed in recent years, they typically do not
adapt to the parameters of the PDEs, making it difficult to generalize to PDE
parameters not seen during training. We propose a Channel Attention mechanism
guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models
and a simple yet effective curriculum learning strategy. The CAPE module can be
combined with neural PDE solvers allowing them to adapt to unseen PDE
parameters. The curriculum learning strategy provides a seamless transition
between teacher-forcing and fully auto-regressive training. We compare CAPE in
conjunction with the curriculum learning strategy using a popular PDE benchmark
and obtain consistent and significant improvements over the baseline models.
The experiments also show several advantages of CAPE, such as its increased
ability to generalize to unseen PDE parameters without large increases
inference time and parameter count.


  We report deep optical integral-field spectroscopy with the MUSE of the
luminous radio-quiet QSO PG1307+085 (z=0.154) obtained during the commissioning
of the instrument. Given the high sensitivity and spatial resolution delivered
by MUSE, we are able to resolve the compact ($r_e$~1.3") elliptical host
galaxy. After careful spectroscopic deblending of the QSO and host galaxy
emission, we infer a stellar velocity dispersion of $155\pm19$km/s. This places
PG1307+085 local $M_{BH}-\sigma_*$ relation within the intrinsic scatter but
offset towards a higher black hole mass with respect to the mean relation. The
observations with MUSE also reveal a large extended ENLR around PG1307+085
reaching out to 30kpc. In addition, we detect a faint bridge of ionized gas
towards the most massive galaxy of the galaxy group being just 20" (50kpc)
away. Previous long-slit spectroscopic observations missed most of these
extended features due to a miss-aligned slit. The ionized gas kinematics does
not show any evidence for gas outflows on kpc scales despite the high QSO
luminosity of $L_\mathrm{bol}>10^{46}$ erg/s. Based on the ionized gas
distribution, kinematics and metallicity we discuss the origin of the ENLR with
respect to its group environments including minor mergers, ram-pressure
stripping or filamentary gas accretion as the most likely scenarios. We
conclude that PG1307+085 is a normal elliptical host in terms of the scaling
relations, but that the gas is most likely affected by the environment through
gravity or ambient pressure. It is possible that the ongoing interaction with
the environment, mainly seen in the ionized gas, is also be responsible for
driving sufficient gas to feed the black hole at the centre of the galaxy.


  Two mass generation mechanisms for gauge theories are studied. It is proved
that in the abelian case the topological mass generation mechanism introduced
in hep-th/9301060, hep-th/9512216 is equivalent to the mass generation
mechanism defined in hep-th/0510240, hep-th/0605050 with the help of
``localization'' of a nonlocal gauge invariant action. In the nonabelian case
the former mechanism is known to generate a unitary renormalizable quantum
field theory describing a massive vector field.


  A general theory of rigid completely integrable analytic partial differential
equations is endeavoured. The tube over the light cone in C^3 is shown to be
the unique model (up to biholomorphisms) having CR automorphism group of
maximal dimension equal to 10. Explicit formulas for the Lie prolongation of
vector fields to jets spaces are derived.


  I show that the effective action of string compactifications has a structure
that can naturally solve the supersymmetric flavour and CP problems. At leading
order in the g_s and \alpha' expansions, the hidden sector factorises. The
moduli space splits into two mirror parts that depend on Kahler and complex
structure moduli. Holomorphy implies the flavour structure of the Yukawa
couplings arises in only one part. In type IIA string theory flavour arises
through the Kahler moduli sector and in type IIB flavour arises through the
complex structure moduli sector. This factorisation gives a simple solution to
the supersymmetric flavour and CP problems: flavour physics is generated in one
sector while supersymmetry is broken in the mirror sector. This mechanism does
not require the presence of gauge, gaugino or anomaly mediation and is
explicitly realised by phenomenological models of IIB flux compactifications.


  We demonstrate the role of the mass asymmetry on the balance energy (Ebal) by
studying asymmetric reactions throughout the periodic table and over entire
colliding geometry. Our results, which are almost independent of the system
size and as well as of the colliding geometries indicate a sizeable effect of
the asymmetry of the reaction on the balance energy.


  Current threat models typically consider all possible ways an attacker can
penetrate a system and assign probabilities to each path according to some
metric (e.g. time-to-compromise). In this paper we discuss how this view
hinders the realness of both technical (e.g. attack graphs) and strategic (e.g.
game theory) approaches of current threat modeling, and propose to steer away
by looking more carefully at attack characteristics and attacker environment.
We use a toy threat model for ICS attacks to show how a realistic view of
attack instances can emerge from a simple analysis of attack phases and
attacker limitations.


  We report a tunable spin mixing conductance, up to $\pm 22\%$, in a
Y${}_{3}$Fe${}_{5}$O${}_{12}$/Platinum (YIG/Pt) bilayer.This control is
achieved by applying a gate voltage with an ionic gate technique, which
exhibits a gate-dependent ferromagnetic resonance line width. Furthermore, we
observed a gate-dependent spin pumping and spin Hall angle in the Pt layer,
which is also tunable up to $\pm$ 13.6\%. This work experimentally demonstrates
spin current control through spin pumping and a gate voltage in a YIG/Pt
bilayer, demonstrating the crucial role of the interfacial charge density for
the spin transport properties in magnetic insulator/heavy metal bilayers.


  Building on a recently introduced inverse strategy, isotropic and convex
repulsive pair potentials were designed that favor assembly of particles into
kagome and equilateral snub square lattices. The former interactions were
obtained by numerical solution of a variational problem that maximizes the
range of density for which the ground state of the potential is the kagome
lattice. Similar optimizations targeting the snub square lattice were also
carried out, employing a constraint that required a minimum chemical potential
advantage of the target over select competing structures. This constraint
helped discover isotropic interactions that meaningfully favored the snub
square lattice as the ground state structure despite the asymmetric spatial
distribution of particles in its coordination shells and the presence of
tightly competing structures. Consistent with earlier published results
[Pi\~neros et al. J. Chem. Phys. 144, 084502 (2016)], enforcement of greater
chemical potential advantages for the target lattice in the interaction
optimization led to assemblies with enhanced thermal stability.


  The synthesis of metal-organic frameworks (MOFs) in a monolithic morphology
is a promising way to achieve the transition of this class of materials from
academia to industrial applications. The sol-gel process has been widely
employed to produce MOF monoliths. It is relatively cheap and simple compared
to other techniques (e.g., mechanical densification) and moreover it allows to
produce "pure" monoliths, i.e., without the need of using binders or templates
that could affect the functional properties of the MOF. Understanding the
mechanical properties of these monoliths is crucial for their transit to
practical applications. We studied the mechanical behavior of two zeolitic
imidazolate frameworks (ZIF-8 and ZIF-71) by means of instrumented
nanoindentation and atomic force microscopy (AFM). Tip Force Microscopy (TFM),
an extension of AFM, was used to reveal the surface nanostructure of the
monoliths. We employed finite-element (FE) simulations alongside the
experiments, to establish a suitable constitutive model and determine an
improved estimate of the yield stress of ZIF monoliths. NanoFTIR was
subsequently used to pinpoint local structural alteration of the framework in
the contact area. The combination of TFM, FE simulations, and nanoFTIR enabled
us to identify the mechanical deformation mechanisms in monolithic ZIF
materials: grain boundaries sliding is dominating at low stresses, then
breakage of chemical bonds and a partial failure of the framework occurs,
eventually leading to a densification of porous framework at the contact zone.
Finally, we measured the fracture toughness using a cube corner indenter to
study the resistance of monoliths against cracking failure.


  We develop a method based on the cross-spectrum of an intensity-modulated CW
laser, which can extract a signal from an extremely noisy environment and image
objects hidden in turbid media. We theoretically analyzed our scheme and
performed the experiment by scanning the object placed in between two ground
glass diffusers. The image of the object is retrieved by collecting the
amplitudes at the modulation frequency of all the cross-spectra. Our method is
non-invasive, easy-to-implement, and can work for both static and dynamic
media.


  We present a numerical study of the random Blume-Capel model in three
dimension. The phase diagram is characterized by spin-glass/paramagnet phase
transitions both of first and second order in the thermodynamic sense.
Numerical simulations are performed using the Exchange-Monte Carlo algorithm,
providing clear evidence for inverse freezing. The main features at criticality
and in the phase coexistence region are investigated. We are not privy to other
  3D short-range systems with quenched disorder undergoing inverse freezing.


  We investigate the squeezed regions in the phase plane for non-dissipative
dynamical systems controlled by SU(1,1) Lie algebra.
  We analyze such study for the two SU(1,1) generalized coherent states,
namely, the Perelomov coherent state (PCS) and the Barut-Girardello Coherent
state (BGCS).


  This report is devoted to some C++ codes implementing the implicit LU class
algorithms for solving linear determined, and undetermined systems with $n$
variables and $m$ equations. A main program used in part of the numerical test
is given in the last section.


  We measured the decay time of the scintillation pulses produced by electron
and nuclear recoils in CaF2(Eu) by a new fitting method. In the recoil energy
region 5-30 keVee, we found differences of the decay time between electron and
nuclear recoil events. In the recoil energy region above 20 keVee, we found
that the decay time is independent of the recoil energy.


  We prove wall-crossing formulas for the motivic invariants of the moduli
spaces of framed objects in the ind-constructible abelian categories. Developed
techniques are applied in the case of the motivic Donaldson-Thomas invariants
of quivers with potentials. Another application is a new proof of the formula
for the motivic invariants of smooth models of quiver moduli spaces.


  The Singlet-Doublet model of dark matter is a minimal extension of the
Standard Model with dark matter that is a mixture of a singlet and a non-chiral
pair of electroweak doublet fermions. The stability of dark matter is ensured
by the typical parity symmetry, and, similar to a "Bino-Higgsino" system, the
extra matter content improves gauge coupling unification. We revisit the
experimental constraints on the Singlet-Doublet dark matter model, combining
the most relevant bounds from direct (spin independent and spin dependent) and
indirect searches. We show that such comprehensive analysis sets strong
constraints on a large part of the 4-dimensional parameter space, closing the
notorious "blind-spots" of spin independent direct searches. Our results
emphasise the complementarity of direct and indirect searches in probing dark
matter models in diverse mass scale regimes. We also discuss the LHC bounds on
such scenario, which play a relevant role in the low mass region of the dark
matter candidate.


  This paper considers the minimization of transmit power in Gaussian parallel
interference channels, subject to a rate constraint for each user. To derive
decentralized solutions that do not require any cooperation among the users, we
formulate this power control problem as a (generalized) Nash equilibrium game.
We obtain sufficient conditions that guarantee the existence and nonemptiness
of the solution set to our problem. Then, to compute the solutions of the game,
we propose two distributed algorithms based on the single user waterfilling
solution: The \emph{sequential} and the \emph{simultaneous} iterative
waterfilling algorithms, wherein the users update their own strategies
sequentially and simultaneously, respectively. We derive a unified set of
sufficient conditions that guarantee the uniqueness of the solution and global
convergence of both algorithms. Our results are applicable to all practical
distributed multipoint-to-multipoint interference systems, either wired or
wireless, where a quality of service in terms of information rate must be
guaranteed for each link.


  Deformable image registration (alignment) is highly sought after in numerous
clinical applications, such as computer aided diagnosis and disease progression
analysis. Deep Convolutional Neural Network (DCNN)-based image registration
methods have demonstrated advantages in terms of registration accuracy and
computational speed. However, while most methods excel at global alignment,
they often perform worse in aligning local regions. To address this challenge,
this paper proposes a mask-guided encoder-decoder DCNN-based image registration
method, named as MrRegNet. This approach employs a multi-resolution encoder for
feature extraction and subsequently estimates multi-resolution displacement
fields in the decoder to handle the substantial deformation of images.
Furthermore, segmentation masks are employed to direct the model's attention
toward aligning local regions. The results show that the proposed method
outperforms traditional methods like Demons and a well-known deep learning
method, VoxelMorph, on a public 3D brain MRI dataset (OASIS) and a local 2D
brain MRI dataset with large deformations. Importantly, the image alignment
accuracies are significantly improved at local regions guided by segmentation
masks. Github link:https://github.com/ruizhe-l/MrRegNet.


  This paper addresses motion forecasting in multi-agent environments, pivotal
for ensuring safety of autonomous vehicles. Traditional as well as recent
data-driven marginal trajectory prediction methods struggle to properly learn
non-linear agent-to-agent interactions. We present SSL-Interactions that
proposes pretext tasks to enhance interaction modeling for trajectory
prediction. We introduce four interaction-aware pretext tasks to encapsulate
various aspects of agent interactions: range gap prediction, closest distance
prediction, direction of movement prediction, and type of interaction
prediction. We further propose an approach to curate interaction-heavy
scenarios from datasets. This curated data has two advantages: it provides a
stronger learning signal to the interaction model, and facilitates generation
of pseudo-labels for interaction-centric pretext tasks. We also propose three
new metrics specifically designed to evaluate predictions in interactive
scenes. Our empirical evaluations indicate SSL-Interactions outperforms
state-of-the-art motion forecasting methods quantitatively with up to 8%
improvement, and qualitatively, for interaction-heavy scenarios.


  We show through both theoretical arguments and numerical calculations that
graphene discerns an unconventional sequence of quantized Hall conductivity,
when subject to both magnetic fields (B) and strain. The latter produces
time-reversal symmetric pseudo/axial magnetic fields (b). The single-electron
spectrum is composed of two interpenetrating sets of Landau levels (LLs),
located at $\pm \sqrt{2 n |b \pm B|}$, $n=0, 1, 2, \cdots$. For $b>B$, these
two sets of LLs have opposite \emph{chiralities}, resulting in {\em
oscillating} Hall conductivity between 0 and $\mp 2 e^2/h$ in electron and hole
doped system, respectively, as the chemical potential is tuned in the vicinity
of the neutrality point. The electron-electron interactions stabilize various
correlated ground states, e.g., spin-polarized, quantum spin-Hall insulators at
and near the neutrality point, and possibly the anomalous Hall insulating phase
at incommensurate filling $\sim B$. Such broken-symmetry ground states have
similarities as well as significant differences from their counterparts in the
absence of strain. For realistic strength of magnetic fields and interactions,
we present scaling of the interaction-induced gap for various Hall states
within the zeroth Landau level.


  A free resolution of free partially commutative monoids is constructed and
with its help the homological dimension of these monoids is calculated.


  Increased levels of tumor infiltrating lymphocytes (TILs) in cancer tissue
indicate favourable outcomes in many types of cancer. Manual quantification of
immune cells is inaccurate and time consuming for pathologists. Our aim is to
leverage a computational solution to automatically quantify TILs in whole slide
images (WSIs) of standard diagnostic haematoxylin and eosin stained sections
(H&E slides) from lung cancer patients. Our approach is to transfer an open
source machine learning method for segmentation and classification of nuclei in
H&E slides trained on public data to TIL quantification without manual labeling
of our data. Our results show that additional augmentation improves model
transferability when training on few samples/limited tissue types. Models
trained with sufficient samples/tissue types do not benefit from our additional
augmentation policy. Further, the resulting TIL quantification correlates to
patient prognosis and compares favorably to the current state-of-the-art method
for immune cell detection in non-small lung cancer (current standard CD8 cells
in DAB stained TMAs HR 0.34 95% CI 0.17-0.68 vs TILs in HE WSIs: HoVer-Net
PanNuke Aug Model HR 0.30 95% CI 0.15-0.60, HoVer-Net MoNuSAC Aug model HR 0.27
95% CI 0.14-0.53). Moreover, we implemented a cloud based system to train,
deploy and visually inspect machine learning based annotation for H&E slides.
Our pragmatic approach bridges the gap between machine learning research,
translational clinical research and clinical implementation. However,
validation in prospective studies is needed to assert that the method works in
a clinical setting.


  We make comments on Link's [{\it Phys. Rev. Lett.} 102, 131101 (2009)] paper.
It seems to us that the role of vortex core was neglected by Link during his
calculation. However, the vortex core is crucial to the interactions between
the vortex and random lattices.


  Conditional on the Lefschetz standard conjecture in degree 2, we prove that
the index of a Brauer class on a smooth projective variety divides a fixed
power of its period, uniformly in smooth families. In the other direction, we
reinterpret in more classical terms recent work of Hotchkiss which gives
Hodge-theoretic lower bounds on the index of Brauer classes. We also prove
versions of our results over arbitrary algebraically closed base fields, and as
an application construct qualitatively new counterexamples to the integral Tate
conjecture.


  This article presents a performance analysis for stochastic predictive
control (SPC) in linear systems with quadratic performance index and additive
and multiplicative uncertainties. Under a finite support assumption, the
problem can be cast as a finite-dimensional quadratic program, but the problem
becomes quickly intractable as the problem size grows exponentially in the
horizon length. SPC aims to compute approximate solutions by solving a sequence
of problems with truncated prediction horizons and committing the solution in a
receding-horizon fashion. While this approach is widely used in practice, its
performance relative to the optimal solution is not well understood. This
article reports for the first time a rigorous performance guarantee of SPC:
Under stabilizability and detectability conditions, the dynamic regret of SPC
is exponentially small in the prediction horizon length, allowing SPC to
achieve near-optimal performance at a substantially reduced computational
expense.


  The number of Connected and Autonomous Vehicles (CAVs) is increasing rapidly
in various smart transportation services and applications, considering many
benefits to society, people, and the environment. Several research surveys for
CAVs were conducted by primarily focusing on various security threats and
vulnerabilities in the domain of CAVs to classify different types of attacks,
impacts of attacks, attack features, cyber-risk, defense methodologies against
attacks, and safety standards. However, the importance of attack detection and
prevention approaches for CAVs has not been discussed extensively in the
state-of-the-art surveys, and there is a clear gap in the existing literature
on such methodologies to detect new and conventional threats and protect the
CAV systems from unexpected hazards on the road. Some surveys have a limited
discussion on Attacks Detection and Prevention Systems (ADPS), but such surveys
provide only partial coverage of different types of ADPS for CAVs. Furthermore,
there is a scope for discussing security, privacy, and efficiency challenges in
ADPS that can give an overview of important security and performance
attributes.
  This survey paper, therefore, presents the significance of CAVs in the
market, potential challenges in CAVs, key requirements of essential security
and privacy properties, various capabilities of adversaries, possible attacks
in CAVs, and performance evaluation parameters for ADPS. An extensive analysis
is discussed of different ADPS categories for CAVs and state-of-the-art
research works based on each ADPS category that gives the latest findings in
this research domain. This survey also discusses crucial and open security
research problems that are required to be focused on the secure deployment of
CAVs in the market.


  Diffractive optical neural networks have shown promising advantages over
electronic circuits for accelerating modern machine learning (ML) algorithms.
However, it is challenging to achieve fully programmable all-optical
implementation and rapid hardware deployment. Furthermore, understanding the
threat of adversarial ML in such system becomes crucial for real-world
applications, which remains unexplored. Here, we demonstrate a large-scale,
cost-effective, complex-valued, and reconfigurable diffractive all-optical
neural networks system in the visible range based on cascaded transmissive
twisted nematic liquid crystal spatial light modulators. With the assist of
categorical reparameterization, we create a physics-aware training framework
for the fast and accurate deployment of computer-trained models onto optical
hardware. Furthermore, we theoretically analyze and experimentally demonstrate
physics-aware adversarial attacks onto the system, which are generated from a
complex-valued gradient-based algorithm. The detailed adversarial robustness
comparison with conventional multiple layer perceptrons and convolutional
neural networks features a distinct statistical adversarial property in
diffractive optical neural networks. Our full stack of software and hardware
provides new opportunities of employing diffractive optics in a variety of ML
tasks and enabling the research on optical adversarial ML.


  The main purpose of the present work is an investigation of the notions
Hopfian (co-Hopfian) acts whose their surjective (injective) endomorphisms are
isomorphisms. While we investigate conditions that are relevant to these
classes of acts, their interrelationship with some other concepts for example
quasi-injective and Dedekind-finite acts is studied. Using Hopfian and
co-Hopfian concepts, several conditions are given for a quasi-injective act to
be Dedekind-finite. Moreover we bring out some properties of strongly Hopfian
and strongly co-Hopfian $S$-acts. Ultimately we introduce and study the concept
of Fitting acts and over a monoid $S$, some equivalent conditions are found to
have all its finitely generated (cyclic) acts Fitting. It is shown that an
$S$-act is Fitting if and only if it is both strongly Hopfian and strongly
co-Hopfian.


  Methanol is an important tracer to probe physical and chemical conditions in
the interstellar medium of galaxies. Methanol is also the most sensitive target
molecule for probing potential space-time variations of the proton-electron
mass ratio, mu, a dimensionless constant of nature. We present an extensive
ALMA study of the strongest submillimeter absorption lines of methanol [...] in
the z=0.89 molecular absorber toward PKS1830-211, the only high-redshift object
in which methanol has been detected. Our goals are to constrain the excitation
of the methanol lines and to investigate the cosmological invariance of mu
based on their relative kinematics. [...] We explore methanol excitation by
running the non local thermal equilibrium radiative transfer code RADEX [...]
The excitation analysis points to a cool (~10-20 K) and dense (~10^{4-5} cm-3)
methanol gas. [...] In addition, we measure an abundance ratio A/E = 1.0 +/-
0.1, an abundance ratio CH3OH/H2 ~ 2 x 10^{-8}, and a 12CH3OH/13CH3OH ratio 62
+/- 3. Our analysis shows that the bulk velocities of the different transitions
are primarily correlated with the observing epoch due to morphological changes
in the background quasar's emission. There is a weaker correlation between bulk
velocities and the lower level energies of the transitions, which could be a
signature of temperature-velocity gradients in the absorbing gas. As a result,
we do not find evidence for variations of mu, and we estimate Dmu/mu = (-1.8
+/- 1.2) x 10^{-7} at 1sigma from our multivariate linear regression. We set a
robust upper limit | \Dmu/mu | < 3.6 x 10^{-7} (3sigma) for the invariance of
mu at a look-back time of half the present age of the Universe. Our analysis
highlights that systematics need to be carefully taken into account in future
radio molecular absorption studies aimed at testing Dmu/mu below the 10^{-7}
horizon. (Abridged)


  Two legitimate parties, referred to as Alice and Bob, wish to generate secret
keys from the wireless channel in the presence of an eavesdropper, referred to
as Eve, in order to use such keys for encryption and decryption. In general,
the secret key rate highly depends on the coherence time of the channel. In
particular, a straightforward method of generating secret keys in static
environments results in ultra-low rates. In order to resolve this problem, we
introduce a low-complexity method called induced randomness. In this method,
Alice and Bob independently generate local randomness to be used together with
the uniqueness of the wireless channel coefficients in order to enable
high-rate secret key generation. In this work, two scenarios are considered:
first, when Alice and Bob share a direct communication channel, and second,
when Alice and Bob do not have a direct link and communicate through an
untrusted relay. After exchanging the induced randomness, post-processing is
done by Alice and Bob to generate highly-correlated samples that are used for
the key generation. Such samples are then converted into bits, disparities
between the sequences generated by Alice and Bob are mitigated, and the
resulting sequences are then hashed to compensate for the information leakage
to the eavesdropper and to allow consistency checking of the generated key bit
sequences. We utilize semantic security measures and information-theoretic
inequalities to upper bound the probability of successful eavesdropping attack
in terms of the mutual information measures that can be numerically computed.
Given certain reasonable system parameters this bound is numerically evaluated
to be $2^{-31}$ and $2^{-10.57}$ in the first and the second scenario,
respectively.


  In an $\mathsf{L}$-embedding of a graph, each vertex is represented by an
$\mathsf{L}$-segment, and two segments intersect each other if and only if the
corresponding vertices are adjacent in the graph. If the corner of each
$\mathsf{L}$-segment in an $\mathsf{L}$-embedding lies on a straight line, we
call it a monotone $\mathsf{L}$-embedding. In this paper we give a full
characterization of monotone $\mathsf{L}$-embeddings by introducing a new class
of graphs which we call "non-jumping" graphs. We show that a graph admits a
monotone $\mathsf{L}$-embedding if and only if the graph is a non-jumping
graph. Further, we show that outerplanar graphs, convex bipartite graphs,
interval graphs, 3-leaf power graphs, and complete graphs are subclasses of
non-jumping graphs. Finally, we show that distance-hereditary graphs and
$k$-leaf power graphs ($k\le 4$) admit $\mathsf{L}$-embeddings.


  In this paper, we study the existence of traveling waves for a fourth order
Schr\" odinger equations with mixed dispersion, that is, solutions to
$$\Delta^2 u +\beta \Delta u +i V \nabla u +\alpha u =|u|^{p-2} u,\ in\ \R^N ,\
N\geq 2.$$ We consider this equation in the Helmholtz regime, when the Fourier
symbol $P$ of our operator is strictly negative at some point. Under suitable
assumptions, we prove the existence of solution using the dual method of
Evequoz and Weth provided that $p\in (p_1 , 2N/(N-4)_+)$. The real number $p_1$
depends on the number of principal curvature of $M$ staying bounded away from
$0$, where $M$ is the hypersurface defined by the roots of $P$. We also
obtained estimates on the Green function of our operator and a $L^p - L^q$
resolvent estimate which can be of independent interest and can be applied to
other operators.


  An integer additive set-indexer is defined as an injective function
$f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $f^+:E(G)
\rightarrow 2^{\mathbb{N}_0}$ defined by $f^+ (uv) = f(u)+ f(v)$ is also
injective. A graph $G$ which admits an IASI is called an IASI graph. An
arithmetic integer additive set-indexer is an integer additive set-indexer $f$,
under which the set-labels of all elements of a given graph $G$ are arithmetic
progressions. In this paper, we discuss about admissibility of arithmetic
integer additive set-indexers by certain associated graphs of the given graph
$G$, like line graph, total graph, etc.


  We define a class of flows with exponential kinematics termed Periodic
Exponential Shear (PES) flow which involve periodic exponential stretching of
fluid elements along with their rotation. We exhibit analytical and numerical
results for PES flow by using the Oldroyd-B model for viscoelastic fluids. We
calculate the growth in the shear and the normal stresses analytically as well
as demonstrate that repeated application of the flow leads to stable
oscillatory shear and normal stresses. We define a material function applicable
to a periodic, unsteady shear flow and show numerically that this material
function exhibits deformation-rate thickening behavior for viscoelastic fluids
subject to PES flow. We demonstrate the feasibility of PES flow by presenting
preliminary experimental results from a controlled-strain rate rheometer, using
a Newtonian mineral oil.


  Many differential equations with physical backgrounds are described as
gradient systems, which are evolution equations driven by the gradient of some
functionals, and such problems have energy conservation or dissipation
properties. For numerical computation of gradient systems, numerical schemes
that inherit the energy structure of the equation play important roles, which
are called structure-preserving. The discrete gradient method is one of the
most classical framework of structure-preserving methods, which is at most
second order accurate. In this paper, we develop a higher-order
structure-preserving numerical method for gradient systems, which includes the
discrete gradient method. We reformulate the gradient system as a coupled
system and then apply the discontinuous Galerkin time-stepping method.
Numerical examples suggests that the order of accuracy of our scheme is $(k+1)$
in general and $(2k+1)$ at nodal times, where $k$ is the degree of polynomials.


  Measurements of a permanent neutron electric dipole moment (EDM) potentially
probe Beyond-the-Standard Model (BSM) sources of CP-violation. At low energy
the CP-violating BSM interactions are parametrized by flavor-conserving
CP-violating operators of dimension higher than four. QCD calculations of the
nucleon matrix elements of these operators are required to fully reconstruct
the sources and magnitudes of the different CP-violating contributions to the
nucleon EDM. Herein we study the quark-chromo electric dipole moment (qCEDM)
operator and the three-gluon Weinberg operator. The non-perturbative
determination, using lattice QCD, of the nucleon matrix elements of these
CP-violating operators is hampered by their short-distance behavior. Under
renormalization these operators mix with lower dimensional operators, which
induces power divergences in the lattice spacing, as the continuum limit is
approached. We study the short-distance behavior of the qCEDM and the Weinberg
operators using the gradient flow. We perform a short flow time expansion and
determine, in perturbation theory, the expansion coefficients of the
linearly-divergent terms stemming from the mixing with the pseudoscalar density
and the topological charge, confirming the expectations of the operator product
expansion. We introduce a new method to perform calculations at non-zero
flow-time for arbitrary values of the external momenta. This method allows us
to work in four dimensions for most of the calculations described in this
paper, avoiding the complications associated with defining $\gamma_5$ in
generic d dimensions. We show that leading contributions in the external
momenta can be reproduced by defining $\gamma_5$ using the 't
Hooft-Veltman-Breitenlohner-Maison scheme.


  Tidal disruption events (TDEs) can uncover the quiescent black holes (BHs) at
the center of galaxies and also offer a promising method to study them. In a
partial TDE (PTDE), the BH's tidal force cannot fully disrupt the star, so the
stellar core survives and only a varied portion of the stellar mass is bound to
the BH and feeds it. We calculate the event rate of PTDEs and full TDEs
(FTDEs). In general, the event rate of PTDEs is higher than that of FTDEs,
especially for the larger BHs. And the detection rate of PTDEs is about dozens
per year by Zwicky Transient Factory (ZTF). During the circularization process
of the debris stream in PTDEs, no outflow can be launched due to the efficient
radiative diffusion. The circularized debris ring then experiences viscous
evolution and forms an accretion disk. We calculate the light curves of PTDEs
contributed by these two processes, along with their radiation temperature
evolution. The light curves have double peaks and the spectra peak in UV.
Without obscuration or reprocessing of the radiation by an outflow, PTDEs
provide a clean environment to study the circularization and transient disk
formation in TDEs.


  During the years 1838-1858, the very massive star {\eta} Carinae became the
prototype supernova impostor: it released nearly as much light as a supernova
explosion and shed an impressive amount of mass, but survived as a star.1 Based
on a light-echo spectrum of that event, Rest et al.2 conclude that "a new
physical mechanism" is required to explain it, because the gas outflow appears
cooler than theoretical expectations. Here we note that (1) theory predicted a
substantially lower temperature than they quoted, and (2) their inferred
observational value is quite uncertain. Therefore, analyses so far do not
reveal any significant contradiction between the observed spectrum and most
previous discussions of the Great Eruption and its physics.


  In this paper, we present TExt Spotting TRansformers (TESTR), a generic
end-to-end text spotting framework using Transformers for text detection and
recognition in the wild. TESTR builds upon a single encoder and dual decoders
for the joint text-box control point regression and character recognition.
Other than most existing literature, our method is free from Region-of-Interest
operations and heuristics-driven post-processing procedures; TESTR is
particularly effective when dealing with curved text-boxes where special cares
are needed for the adaptation of the traditional bounding-box representations.
We show our canonical representation of control points suitable for text
instances in both Bezier curve and polygon annotations. In addition, we design
a bounding-box guided polygon detection (box-to-polygon) process. Experiments
on curved and arbitrarily shaped datasets demonstrate state-of-the-art
performances of the proposed TESTR algorithm.


  The large action space is one fundamental obstacle to deploying Reinforcement
Learning methods in the real world. The numerous redundant actions will cause
the agents to make repeated or invalid attempts, even leading to task failure.
Although current algorithms conduct some initial explorations for this issue,
they either suffer from rule-based systems or depend on expert demonstrations,
which significantly limits their applicability in many real-world settings. In
this work, we examine the theoretical analysis of what action can be eliminated
in policy optimization and propose a novel redundant action filtering
mechanism. Unlike other works, our method constructs the similarity factor by
estimating the distance between the state distributions, which requires no
prior knowledge. In addition, we combine the modified inverse model to avoid
extensive computation in high-dimensional state space. We reveal the underlying
structure of action spaces and propose a simple yet efficient redundant action
filtering mechanism named No Prior Mask (NPM) based on the above techniques. We
show the superior performance of our method by conducting extensive experiments
on high-dimensional, pixel-input, and stochastic problems with various action
redundancy. Our code is public online at https://github.com/zhongdy15/npm.


  Artificial intelligence (AI) has seen tremendous development in industry and
academia. However, striking recent advances by industry have stunned the world,
inviting a fresh perspective on the role of academic research in this field.
Here, we characterize the impact and type of AI produced by both environments
over the last 25 years and establish several patterns. We find that articles
published by teams consisting exclusively of industry researchers tend to get
greater attention, with a higher chance of being highly cited and
citation-disruptive, and several times more likely to produce state-of-the-art
models. In contrast, we find that exclusively academic teams publish the bulk
of AI research and tend to produce higher novelty work, with single papers
having several times higher likelihood of being unconventional and atypical.
The respective impact-novelty advantages of industry and academia are robust to
controls for subfield, team size, seniority, and prestige. We find that
academic-industry collaborations struggle to replicate the novelty of academic
teams and tend to look similar to industry teams. Together, our findings
identify the unique and nearly irreplaceable contributions that both academia
and industry make toward the healthy progress of AI.


  A well-preserved, ancient delta deposit, in combination with ample exposures
of Mg-carbonate rich materials, make Jezero Crater in Nili Fossae a compelling
astrobiological site and a top candidate for future landed missions to Mars. We
use CRISM observations to characterize the surface mineralogy of the crater and
surrounding watershed. We have identified a three- endmember sequence of
olivine-bearing lithologies that we hypothesize are distinguished by their Mg
content. We find that Mg-carbonates are consistently identified in association
with one of the olivine-bearing lithologies, although that lithology is not
fully carbonatized. Surprisingly, this lithology contains relatively Fe-rich
olivine. We address a range of formation scenarios, including the possibility
that these olivine and carbonate associations are indicators of
serpentinization on early Mars. These deposits provide an opportunity for
deepening our understanding of early Mars by revealing the thermal history of
the martian interior and potentially changes in its tectonic regime with time.


  After the 2016 double dissolution election, the 45th Australian Parliament
was formed. At the time of its swearing in, the Senate of the 45th Australian
Parliament consisted of nine political parties, the largest number in the
history of the Australian Parliament. Due to the breadth of the political
spectrum that the Senate represented, the situation presented an interesting
opportunity for the study of political interactions in the Australian context.
Using publicly available Senate voting data in 2016, we quantitatively analyzed
two aspects of the Senate. Firstly, we analyzed the degree to which each of the
non-government parties of the Senate are pro- or anti-government. Secondly, we
analyzed the degree to which the votes of each of the non-government Senate
parties are in concordance or discordance with one another. We utilized the
fully-visible Boltzmann machine (FVBM) model in order to conduct these
analyses. The FVBM is an artificial neural network that can be viewed as a
multivariate generalization of the Bernoulli distribution. Via a maximum
pseudolikelihood estimation approach, we conducted parameter estimation and
constructed hypotheses test that revealed the interaction structures within the
Australian Senate. The conclusions that we drew are well-supported by external
sources of information.


  The spectrum of a first-order sentence is the set of the cardinalities of its
finite models. In this paper, we consider the spectra of sentences over binary
relations that use at least three variables. We show that for every such
sentence $\Phi$, there is a sentence $\Phi'$ that uses the same number of
variables, but only one symmetric binary relation, such that its spectrum is
linearly proportional to the spectrum of $\Phi$. Moreover, the models of
$\Phi'$ are all bipartite graphs. As a corollary, we obtain that to settle
Asser's conjecture, i.e., whether the class of spectra is closed under
complement, it is sufficient to consider only sentences using only three
variables whose models are restricted to undirected bipartite graphs.


  We report the detection of eclipses in GJ 3236, a bright (I = 11.6) very low
mass binary system with an orbital period of 0.77 days. Analysis of light- and
radial velocity curves of the system yielded component masses of 0.38 +/- 0.02
and 0.28 +/- 0.02 Msol. The central values for the stellar radii are larger
than the theoretical models predict for these masses, in agreement with the
results for existing eclipsing binaries, although the present 5% observational
uncertainties limit the significance of the larger radii to approximately 1
sigma. Degeneracies in the light curve models resulting from the unknown
configuration of surface spots on the components of GJ 3236 currently dominate
the uncertainties in the radii, and could be reduced by obtaining precise,
multi-band photometry covering the full orbital period. The system appears to
be tidally synchronized and shows signs of high activity levels as expected for
such a short orbital period, evidenced by strong Halpha emission lines in the
spectra of both components. These observations probe an important region of
mass-radius parameter space around the predicted transition to fully-convective
stellar interiors, where there are a limited number of precise measurements
available in the literature.


  In [Bull. Acad. Polon. Sci. S\'{e}r. Sci. Math. 29 (1981), no.~7-8,
367--370], Philos proved the following result: Let
$f:[t_{0},\infty)_{\mathbb{R}}\to\mathbb{R}$ be an $n$-times differentiable
function such that $f^{(n)}(t)\leq0$ ($\not\equiv0$) and $f(t)>0$ for all
$t\geq{}t_{0}$. If $f$ is unbounded, then
$f(t)\geq\frac{\lambda{}t^{n-1}}{(n-1)!}f^{(n-1)}(t)$ for all sufficiently
large $t$, where $\lambda\in(0,1)_{\mathbb{R}}$. In this work, we first present
time scales unification of this result. Then, by using it, we provide
sufficient conditions for oscillation and asymptotic behaviour of solutions to
higher-order neutral dynamic equations.


  The topic is the average order $A(G)$ of a connected induced subgraph of a
graph $G$. This generalizes, to graphs in general, the average order of a
subtree of a tree. In 1984, Jamison proved that the average order, over all
trees of order $n$, is minimized by the path $P_n$, the average being
$A(P_n)=(n+2)/3$. In 2018, Kroeker, Mol, and Oellermann conjectured that $P_n$
minimizes the average order over all connected graphs $G$ - a conjecture that
was recently proved. In this short note we show that this lower bound can be
improved if the connectivity of $G$ is known. If $G$ is $k$-connected, then
\[A(G) \geq \frac{n}2 \Bigg (1- \frac{1}{2^k+1} \Bigg ).\]


  This paper studies the link between resting-state functional connectivity
(FC), measured by the correlations of the fMRI BOLD time courses, and
structural connectivity (SC), estimated through fiber tractography. Instead of
a static analysis based on the correlation between SC and the FC averaged over
the entire fMRI time series, we propose a dynamic analysis, based on the time
evolution of the correlation between SC and a suitably windowed FC. Assessing
the statistical significance of the time series against random phase
permutations, our data show a pronounced peak of significance for time window
widths around 20-30 TR (40-60 sec). Using the appropriate window width, we show
that FC patterns oscillate between phases of high modularity, primarily shaped
by anatomy, and phases of low modularity, primarily shaped by inter-network
connectivity. Building upon recent results in dynamic FC, this emphasizes the
potential role of SC as a transitory architecture between different highly
connected resting state FC patterns. Finally, we show that networks implied in
consciousness-related processes, such as the default mode network (DMN),
contribute more to these brain-level fluctuations compared to other networks,
such as the motor or somatosensory networks. This suggests that the
fluctuations between FC and SC are capturing mind-wandering effects.


  The susceptibility of nickel-based superalloys to processing-induced crack
formation during laser powder-bed additive manufacturing is studied. Twelve
different alloys -- some of existing (heritage) type but also other
newly-designed ones -- are considered. A strong inter-dependence of alloy
composition and processability is demonstrated. Stereological procedures are
developed to enable the two dominant defect types found -- solidification
cracks and solid-state ductility dip cracks -- to be distinguished and
quantified. Differential scanning calorimetry, creep stress relaxation tests at
1000$^\circ$C and measurements of tensile ductility at 800$^\circ$C are used to
interpret the effects of alloy composition. A model for solid-state cracking is
proposed, based on an incapacity to relax the thermal stress arising from
constrained differential thermal contraction; its development is supported by
experimental measurements using a constrained bar cooling test. A modified
solidification cracking criterion is proposed based upon solidification range
but including also a contribution from the stress relaxation effect. This work
provides fundamental insights into the role of composition on the additive
manufacturability of these materials.


  Estimating a distribution given access to its unnormalized density is pivotal
in Bayesian inference, where the posterior is generally known only up to an
unknown normalizing constant. Variational inference and Markov chain Monte
Carlo methods are the predominant tools for this task; however, both methods
are often challenging to apply reliably, particularly when the posterior has
complex geometry. Here, we introduce Soft Contrastive Variational Inference
(SoftCVI), which allows a family of variational objectives to be derived
through a contrastive estimation framework. These objectives have zero variance
gradient when the variational approximation is exact, without the need for
specialized gradient estimators. The approach involves parameterizing a
classifier in terms of the variational distribution, which allows the inference
task to be reframed as a contrastive estimation problem, aiming to identify a
single true posterior sample among a set of samples. Despite this framing, we
do not require positive or negative samples, but rather learn by sampling the
variational distribution and computing ground truth soft classification labels
from the unnormalized posterior itself. We empirically investigate the
performance on a variety of Bayesian inference tasks, using both using both
simple (e.g. normal) and expressive (normalizing flow) variational
distributions. We find that SoftCVI objectives often outperform other commonly
used variational objectives.


  Despite recent advances in the accuracy of brain tumor segmentation, the
results still suffer from low reliability and robustness. Uncertainty
estimation is an efficient solution to this problem, as it provides a measure
of confidence in the segmentation results. The current uncertainty estimation
methods based on quantile regression, Bayesian neural network, ensemble, and
Monte Carlo dropout are limited by their high computational cost and
inconsistency. In order to overcome these challenges, Evidential Deep Learning
(EDL) was developed in recent work but primarily for natural image
classification. In this paper, we proposed a region-based EDL segmentation
framework that can generate reliable uncertainty maps and robust segmentation
results. We used the Theory of Evidence to interpret the output of a neural
network as evidence values gathered from input features. Following Subjective
Logic, evidence was parameterized as a Dirichlet distribution, and predicted
probabilities were treated as subjective opinions. To evaluate the performance
of our model on segmentation and uncertainty estimation, we conducted
quantitative and qualitative experiments on the BraTS 2020 dataset. The results
demonstrated the top performance of the proposed method in quantifying
segmentation uncertainty and robustly segmenting tumors. Furthermore, our
proposed new framework maintained the advantages of low computational cost and
easy implementation and showed the potential for clinical application.


  Increasing reliance on Information and Communication Technology~(ICT) exposes
the power grid to cyber-attacks. In particular, Coordinated Cyber-Attacks
(CCAs) are considered highly threatening and difficult to defend against,
because they (i) possess higher disruptiveness by integrating greater resources
from multiple attack entities, and (ii) present heterogeneous traits in
cyber-space and the physical grid by hitting multiple targets to achieve the
attack goal. Thus, and as opposed to independent attacks, whose severity is
limited by the power grid's redundancy, CCAs could inflict disastrous
consequences, such as blackouts. In this paper, we propose a method to develop
Correlation Indices to defend against CCAs on static control applications.
These proposed indices relate the targets of CCAs with attack goals on the
power grid. Compared to related works, the proposed indices present the
benefits of deployment simplicity and are capable of detecting more
sophisticated attacks, such as measurement attacks. We demonstrate our method
using measurement attacks against Security Constrained Economic Dispatch.


  In ultrarelativistic nuclear collisions heavy quarks are produced out of
thermal equilibrium in the very early stage of the reaction and their
thermalization time was expected to be considerably larger than that of light
quarks. On the other hand, a strongly-interacting QGP can be envisaged in the
heavy quark sector due to the presence of heavy-light hadron-like resonances in
the QGP for temperatures up to $\sim$$2 T_{C}$. We investigate the consequences
of such states employing a relativistic Langevin simulation. Hadronization is
modeled by a coalescence-fragmentation scheme. We present the predictions for
the nuclear modification factor and elliptic flow of $D$ and $B$ mesons at LHC
energies and compare the results with the successful predictions of this model
for RHIC conditions. We find similar heavy-quark thermalization effects at LHC
and RHIC.


  We investigate the dynamics of dilatonic D-dimensional 0-branes in the
near-horizon regime. The theory is given in a twofold form: two-dimensional
dilaton gravity and nonlinear sigma model. Using asymptotic symmetries, duality
relations, and sigma model techniques we find that the theory has three
conformal points which correspond to (a) the asymptotic (Anti-de Sitter) region
of the two-dimensional spacetime, (b) the horizon of the black hole, and (c)
the infinite limit of the coupling parameter. We show that the conformal
symmetry is perturbatively preserved at one-loop, identify the corresponding
conformal field theories, and calculate the associated central charges.
Finally, we use the conformal field theories to explain the thermodynamical
properties of the two-dimensional black holes.


  We study the estimation precision attainable by entanglement-enhanced Ramsey
interferometry in the presence of spatiotemporally correlated non-classical
noise. Our analysis relies on an exact expression of the reduced density matrix
of the qubit probes under general zero-mean Gaussian stationary dephasing,
which is established through cumulant-expansion techniques and may be of
independent interest in the context of non-Markovian open dynamics. By
continuing and expanding our previous work [Beaudoin et al., Phys. Rev. A 98,
020102(R) (2018)], we analyze the effects of a non-collective coupling regime
between the qubit probes and their environment, focusing on two limiting
scenarios where the couplings may take only two or a continuum of possible
values. In the paradigmatic case of spin-boson dephasing noise from a thermal
environment, we find that it is possible to suppress, on average, the effect of
spatial correlations by randomizing the location of the probes, as long as
enough configurations are sampled where noise correlations are negative. As a
result, superclassical precision scaling is asymptotically restored for initial
entangled states, including experimentally accessible one-axis spin-squeezed
states.


  CO is the most widely used gas tracer of protoplanetary disks. Its abundance
is usually assumed to be an interstellar ratio throughout the warm molecular
layer of the disk. But recent observations of low CO gas abundance in many
protoplanetary disks challenge our understanding of physical and chemical
evolutions in disks. Here we investigate the CO abundance structures in four
well-studied disks and compare their structures with predictions of chemical
processing of CO and transport of CO ice-coated dust grains in disks. We use
spatially resolved CO isotopologue line observations and detailed
thermo-chemical models to derive CO abundance structures. We find that the CO
abundance varies with radius by an order of magnitude in these disks. We show
that although chemical processes can efficiently reduce the total column of CO
gas within 1 Myr under an ISM level of cosmic-ray ionization rate, the
depletion mostly occurs at the deep region of a disk. Without sufficient
vertical mixing, the surface layer is not depleted enough to reproduce weak CO
emissions observed. The radial profiles of CO depletion in three disks are
qualitatively consistent with predictions of pebble formation, settling, and
drifting in disks. But the dust evolution alone cannot fully explain the high
depletion observed in some disks. These results suggest that dust evolution may
play a significant role in transporting volatile materials and a coupled
chemical-dynamical study is necessary to understand what raw materials are
available for planet formation at different distances from the central star.


  Quasispecies theory predicts that there is a critical mutation probability
above which a viral population will go extinct. Above this threshold the virus
loses the ability to replicate the best adapted genotype, leading to a
population composed of low replicating mutants that is eventually doomed. We
propose a new branching model that shows that this is not necessarily so. That
is, a population composed of ever changing mutants may survive.


  We introduce the notion of a strong equivalence between graded algebras and
prove that any partially-strongly-graded algebra by a group $G$ is
strongly-graded-equivalent to the skew group algebra by a product partial
action of $G$. As to a more general idempotent graded algebra $B$, we point out
that the Cohen-Montgomery duality holds for $B$, and $B$ is graded-equivalent
to a global skew group algebra. We show that strongly-graded-equivalence
preserves strong gradings and is nicely related to Morita equivalence of
product partial actions. Furthermore, we prove that any product partial group
action $\alpha $ is globalizable up to Morita equivalence; if such a
globalization $\beta $ is minimal, then the skew group algebras by $\alpha $
and $\beta $ are graded-equivalent; moreover, $\beta $ is unique up to Morita
equivalence. Finally, we show that strongly-graded-equivalent
partially-strongly-graded algebras are stably isomorphic as graded algebras.


  A q-deformation of the ADHMN caloron construction is considered, under which
the anti-selfdual (ASD) conditions of the gauge fields are preserved. It is
shown that the q-dependent Nahm data with certain constraints are crucial to
determine the ASD gauge fields, as in the case of ordinary caloron
construction. As an application of the q-deformed ADHMN construction, we give a
q-deformed caloron of Harrington-Shepard type. Some limits of the parameters
are also considered.


  Let G = SL_2(K) with K a local function field of characteristic 2. We review
Artin-Schreier theory for the field K, and show that this leads to a
parametrization of L-packets in the smooth dual of G. We relate this to a
recent geometric conjecture. The L-packets in the principal series are
parametrized by quadratic extensions, and the supercuspidal L-packets by
biquadratic extensions. We compute the formal degrees of the elements in the
supercuspidal packets.


  The regularized signum-Gordon potential has a smooth minimum and is linear in
the modulus of the field value for higher amplitudes. The Q-ball solutions in
this model are investigated. Their existence for charges large enough is
demonstrated. In three dimensions numerical solutions are presented and the
absolute stability of large Q-balls is proved. It is also shown, that the
solutions of the regularized model approach uniformly the solution of the
unregularized signum-Gordon model. From the stability of Q-balls in the
regularized model follows the stability of the solutions in the original
theory.


  An external magnetic field, $H$, applied parallel to a quasi two-dimensional
system modifies quantitatively and qualitatively the density of states. Using a
self-consistent numerical approach, we study how this affects the entropy, $S$,
the free energy, $F$, and the magnetization, $M$, for different sheet carrier
concentrations, $N_s$. As a prototype system we employ III-V double quantum
wells. We find that although $M$ is mainly in the opposite direction of $H$,
the system is not linear. Surprisingly $\partial M / \partial H$ swings between
negative and positive values, i.e., we predict an entirely orbital diamagnetic
to paramagnetic fluctuation. This phenomenon is important compared to the ideal
de Haas-van Alphen effect i.e. the corresponding phenomenon under perpendicular
magnetic field.


  While graphene is a semi-metal, a recently synthesized hydrogenated graphene
called graphane, is an insulator. We have probed the transformation of graphene
upon hydrogenation to graphane within the framework of density functional
theory. By analyzing the electronic structure for eighteen different hydrogen
concentrations, we bring out some novel features of this transition. Our
results show that the hydrogenation favors clustered configurations leading to
the formation of compact islands. The analysis of the charge density and
electron localization function (ELF) indicates that as hydrogen coverage
increases the semi-metal turns into a metal showing a delocalized charge
density, then transforms into an insulator. The metallic phase is spatially
inhomogeneous in the sense, it contains the islands of insulating regions
formed by hydrogenated carbon atoms and the metallic channels formed by
contiguous bare carbon atoms. It turns out that it is possible to pattern the
graphene sheet to tune the electronic structure. For example removal of
hydrogen atoms along the diagonal of the unit cell yielding an armchair pattern
at the edge gives rise to a band gap of 1.4 eV. We also show that a weak
ferromagnetic state exists even for a large hydrogen coverage whenever there is
a sub-lattice imbalance in presence of odd number of hydrogen atoms.


  Advancing lithium-ion batteries (LIBs) in both design and usage is key to
promoting electrification in the coming decades to mitigate human-caused
climate change. Inadequate understanding of LIB degradation is an important
bottleneck that limits battery durability and safety. Here, we propose hybrid
physics-based and data-driven modeling for online diagnosis and prognosis of
battery degradation. Compared to existing battery modeling efforts, we aim to
build a model with physics as its backbone and statistical learning techniques
as enhancements. Such a hybrid model has better generalizability and
interpretability together with a well-calibrated uncertainty associated with
its prediction, rendering it more valuable and relevant to safety-critical
applications under realistic usage scenarios.


  We present a theory of zero-bias anomalies and dephasing rates for a
Coulomb-blockaded quantum dot, driven out of equilibrium by coupling to voltage
biased source and drain leads. We interpret our results in terms of the
statistics of voltage fluctuations in the system.


  Let $X$ be a curve of genus $g\geq 2$ over a number field $F$ of degree $d =
[F:Q]$. The conjectural existence of a uniform bound $N(g,d)$ on the number
$\#X(F)$ of $F$-rational points of $X$ is an outstanding open problem in
arithmetic geometry, known by [CHM97] to follow from the Bombieri--Lang
conjecture. A related conjecture posits the existence of a uniform bound
$N_{{\rm tors},\dagger}(g,d)$ on the number of geometric torsion points of the
Jacobian $J$ of $X$ which lie on the image of $X$ under an Abel--Jacobi map.
For fixed $X$ this quantity was conjectured to be finite by Manin--Mumford, and
was proved to be so by Raynaud [Ray83].
  We give an explicit uniform bound on $\#X(F)$ when $X$ has Mordell--Weil rank
$r\leq g-3$. This generalizes recent work of Stoll on uniform bounds on
hyperelliptic curves of small rank to arbitrary curves. Using the same
techniques, we give an explicit, unconditional uniform bound on the number of
$F$-rational torsion points of $J$ lying on the image of $X$ under an
Abel--Jacobi map. We also give an explicit uniform bound on the number of
geometric torsion points of $J$ lying on $X$ when the reduction type of $X$ is
highly degenerate.
  Our methods combine Chabauty--Coleman's $p$-adic integration, non-Archimedean
potential theory on Berkovich curves, and the theory of linear systems and
divisors on metric graphs.


  Let $X$ be a submanifold of dimension $n$ of the complex projective space
$\mathbb P^N$ ($n<N$), and let $E$ be a vector bundle of rank two on $X$ . If
$n\geq\frac{N+3}{2}\geq 4$ we prove a geometric criterion for the existence of
an extension of $E$ to a vector bundle on the first order infinitesimal
neighborhood of $X$ in $\mathbb P^N$ in terms of the splitting of the normal
bundle sequence of $Y\subset X\subset\mathbb P^N$, where $Y$ is the zero locus
of a general section of a high twist of $E$. In the last section we show that
the universal quotient vector bundle on the Grassmann variety $\mathbb G(k,m)$
of $k$-dimensional linear subspaces of $\mathbb P^m$, with $m\geq 3$ and $1\leq
k\leq m-2$ (i.e. with $\mathbb G(k,m)$ not a projective space), embedded in any
projective space $\mathbb P^N$, does not extend to the first infinitesimal
neighborhood of $\mathbb G(k,m)$ in $\mathbb P^N$ as a vector bundle.


  We discuss the notion of Jacobi forms of degree one with matrix index, we
state dimension formulas, give explicit examples, and indicate how closely
their theory is connected to the theory of invariants of Weil representations
associated to finite quadratic modules.


  The effect of proximity to a Mott insulating phase on the superflow
properties of a d-wave superconductor is studied using the slave boson-U(1)
gauge theory model. The model has two limits corresponding to superconductivity
emerging either out of a 'renormalized fermi liquid' or out of a
non-fermi-liquid regime. Three crucial physical parameters are identified: the
size of the vortex \textit{as determined from the supercurrent it induces;} the
coupling of the superflow to the quasiparticles and the 'nondissipative time
derivative' term. As the Mott phase is approached, the core size as defined
from the supercurrent diverges, the coupling between superflow and
quasiparticles vanishes, and the magnitude of the nondissipative time
derivative dramatically increases. The dissipation due to a moving vortex is
found to vary as the third power of the doping. The upper critical field and
the size of the critical regime in which paraconductivity may be observed are
estimated, and found to be controlled by the supercurrent length scale.