  Many researchers implicitly assume that neural networks learn relations and
generalise them to new unseen data. It has been shown recently, however, that
the generalisation of feed-forward networks fails for identity relations.The
proposed solution for this problem is to create an inductive bias with
Differential Rectifier (DR) units. In this work we explore various factors in
the neural network architecture and learning process whether they make a
difference to the generalisation on equality detection of Neural Networks
without and and with DR units in early and mid fusion architectures.
  We find in experiments with synthetic data effects of the number of hidden
layers, the activation function and the data representation. The training set
size in relation to the total possible set of vectors also makes a difference.
However, the accuracy never exceeds 61% without DR units at 50% chance level.
DR units improve generalisation in all tasks and lead to almost perfect test
accuracy in the Mid Fusion setting. Thus, DR units seem to be a promising
approach for creating generalisation abilities that standard networks lack.


  We perform a series of controlled N-body simulations to study realizations of
the recently discovered Antlia 2 galaxy in cold dark matter (CDM) and
self-interacting dark matter (SIDM) scenarios. Our simulations contain six
benchmark models, where we vary the initial halo concentration and the
self-scattering cross section. We adopt well-motivated initial stellar and halo
masses, and our fiducial orbit has a small pericenter. After evolving in the
Milky Way's tidal field, the simulated galaxies experience significant mass
loss and their stellar distributions expand accordingly. These tidal effects
are more prominent if the initial halo concentration is lower and if the
self-scattering cross section is larger. Our results show that Antlia 2-like
galaxies could be realized in CDM if the halo concentration is low and the
stellar distribution is diffuse at the infall time, while these conditions
could be relaxed in SIDM. We also find all the simulated galaxies predict
approximately the same stellar velocity dispersion after imposing selection
criteria for stellar particles. This has important implications for testing
dark matter models using tidally disturbed systems.


  A non-fungible token (NFT) is a data unit stored on the blockchain. Nowadays,
more and more investors and collectors (NFT traders), who participate in
transactions of NFTs, have an urgent need to assess the performance of NFTs.
However, there are two challenges for NFT traders when analyzing the
performance of NFT. First, the current rarity models have flaws and are
sometimes not convincing. In addition, NFT performance is dependent on multiple
factors, such as images (high-dimensional data), history transactions
(network), and market evolution (time series). It is difficult to take
comprehensive consideration and analyze NFT performance efficiently. To address
these challenges, we propose NFTVis, a visual analysis system that facilitates
assessing individual NFT performance. A new NFT rarity model is proposed to
quantify NFTs with images. Four well-coordinated views are designed to
represent the various factors affecting the performance of the NFT. Finally, we
evaluate the usefulness and effectiveness of our system using two case studies
and user studies.


  The large volume of publications in any research area can make it difficult
for researchers to track their research areas' trends, challenges, and
characteristics. Bibliometrics solves this problem by bringing statistical
tools to help the analysis of selected publications from an online database.
Although there are different works in security, our study aims to fill the
bibliometric gap in the authentication and threat model area. As a result, a
description of the dataset obtained, an overview of some selected variables,
and an analysis of the ten most cited articles in this selected dataset is
presented, which brings together publications from the last 28 years in these
areas combined.


  We investigate pseudo-polynomial time algorithms for Subset Sum. Given a
multi-set $X$ of $n$ positive integers and a target $t$, Subset Sum asks
whether some subset of $X$ sums to $t$. Bringmann proposes an $\tilde{O}(n +
t)$-time algorithm [Bringmann SODA'17], and an open question has naturally
arisen: can Subset Sum be solved in $O(n + w)$ time? Here $w$ is the maximum
integer in $X$. We make a progress towards resolving the open question by
proposing an $\tilde{O}(n + \sqrt{wt})$-time algorithm.


  We prove a reverse Lieb--Thirring inequality with a sharp constant for the
matrix Schr\"odinger equation on the half-line.


  The cone-beam computed tomography (CBCT) provides 3D volumetric imaging of a
target with low radiation dose and cost compared with conventional computed
tomography, and it is widely used in the detection of paranasal sinus disease.
However, it lacks the sensitivity to detect soft tissue lesions owing to
reconstruction constraints. Consequently, only physicians with expertise in
CBCT reading can distinguish between inherent artifacts or noise and diseases,
restricting the use of this imaging modality. The development of artificial
intelligence (AI)-based computer-aided diagnosis methods for CBCT to overcome
the shortage of experienced physicians has attracted substantial attention.
However, advanced AI-based diagnosis addressing intrinsic noise in CBCT has not
been devised, discouraging the practical use of AI solutions for CBCT. To
address this issue, we propose an AI-based computer-aided diagnosis method
using CBCT with a denoising module. This module is implemented before diagnosis
to reconstruct the internal ground-truth full-dose scan corresponding to an
input CBCT image and thereby improve the diagnostic performance. The external
validation results for the unified diagnosis of sinus fungal ball, chronic
rhinosinusitis, and normal cases show that the proposed method improves the
micro-, macro-average AUC, and accuracy by 7.4, 5.6, and 9.6% (from 86.2, 87.0,
and 73.4 to 93.6, 92.6, and 83.0%), respectively, compared with a baseline
while improving human diagnosis accuracy by 11% (from 71.7 to 83.0%),
demonstrating technical differentiation and clinical effectiveness. This
pioneering study on AI-based diagnosis using CBCT indicates denoising can
improve diagnostic performance and reader interpretability in images from the
sinonasal area, thereby providing a new approach and direction to radiographic
image reconstruction regarding the development of AI-based diagnostic
solutions.


  The DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN)
is intended as a platform both for large scale experiments related to geo- and
astrophysics as well as for experiments related to thermohydraulic and safety
aspects of liquid metal batteries and liquid metal fast reactors. The most
ambitious projects in the framework of DRESDYN are a homogeneous hydromagnetic
dynamo driven solely by precession and a large Taylor-Couette type experiment
for the combined investigation of the magnetorotational instability and the
Tayler instability. In this paper we give a short summary about the ongoing
preparations and delineate the next steps for the realization of DRESDYN.


  A string theory in $3$ euclidean spacetime dimensions is found to describe
the semiclassical behavior of a certain exact physical state of quantum general
relativity in $4$ dimensions. Both the worldsheet and the three dimensional
metric emerge as collective coordinates that describe a sector of the solution
space of quantum general relativity. Additional collective coordinates exist
which are interpreted as worldsheet degrees of freedom. The construction may be
extended to the case in which the Kalb-Ramond field is included in the
non-perturbative dynamics. It is possible that this mechanism is the inverse of
the strong coupling limit by which some $D$ dimensional string theories are
conjectured to give rise to $D+1$ dimensional field theories.


  Maths-type q-deformed coherent states with $q > 1$ allow a resolution of
unity in the form of an ordinary integral. They are sub-Poissonian and
squeezed. They may be associated with a harmonic oscillator with minimal
uncertainties in both position and momentum and are intelligent coherent states
for the corresponding deformed Heisenberg algebra.


  We report the observation of an unexpected, long-range field-effect in
WTe$_2$ devices, leading to large gate-induced changes of the transport
properties of crystals much thicker than the electrostatic screening length.
The phenomenon --which manifests itself very differently from the conventional
field-effect-- originates from the non-local nature of transport in the devices
that are thinner than the carrier mean free path, because of the dominant role
of surface scattering. We reproduce theoretically the gate dependence of the
measured classical and quantum magneto-transport in all detail, and show that
the phenomenon is caused by the gate-tuning of the bulk carrier mobility by
changing the scattering at the surface. Our results demonstrate the possibility
to gate tune the electronic properties deep in the interior of conducting
materials, avoiding limitations imposed by electrostatic screening.


  In this work we propose a new orbital architecture for the two proposed
circumbinary planets around the polar eclipsing binary HU Aquarii. We base the
new two-planet, light-travel time model on the result of a Monte Carlo
simulation driving a least-squares Levenberg-Marquardt minimisation algorithm
on the observed eclipse egress times. Our best-fitting model with
$\chi_{r}^2=1.43$ resulted in high final eccentricities for the two companions
leading to an unstable orbital configuration. From a large ensemble of initial
guesses we examined the distribution of final eccentricities and semi-major
axes for different $\chi_{r}^2$ parameter intervals and encountered
qualitatively a second population of best-fitting parameters. The main
characteristic of this population is described by low-eccentric orbits
favouring long-term orbital stability of the system. We present our
best-fitting model candidate for the proposed two-planet system and demonstrate
orbital stability over one million years using numerical integrations.


  The dispersion relations of magnons in ferromagnetic pyrochlores with
Dzyaloshinskii-Moriya interaction is shown to possess Weyl points, i.\,e.,
pairs of topological nontrivial crossings of two magnon branches with opposite
topological charge. As a consequence of their topological nature, their
projections onto a surface are connected by magnon arcs, thereby resembling
closely Fermi arcs of electronic Weyl semimetals. On top of this, the positions
of the Weyl points in reciprocal space can be tuned widely by an external
magnetic field: rotated within the surface plane, the Weyl points and magnon
arcs are rotated as well; tilting the magnetic field out-of-plane shifts the
Weyl points toward the center $\bar{\Gamma}$ of the surface Brillouin zone. The
theory is valid for the class of ferromagnetic pyrochlores, i.\,e.,
three-dimensional extensions of topological magnon insulators on kagome
lattices. In this Letter, we focus on the $(111)$ surface, identify candidates
of established ferromagnetic pyrochlores which apply to the considered spin
model, and suggest experiments for the detection of the topological features.


  In this paper machine learning networks are explored for their use in
restoring degraded and compressed speech audio. The project intent is to build
a new trained model from voice data to learn features of compression
artifacting distortion introduced by data loss from lossy compression and
resolution loss with an existing algorithm presented in SEGAN: Speech
Enhancement Generative Adversarial Network. The resulting generator from the
model was then to be used to restore degraded speech audio. This paper details
an examination of the subsequent compatibility and operational issues presented
by working with deprecated code, which obstructed the trained model from
successfully being developed. This paper further serves as an examination of
the challenges, limitations, and compatibility in the current state of machine
learning.


  In the spirit of the Schur-Weyl duality, we study the connections between the
Racah algebra and the centralizers of tensor products of three (possibly
different) irreducible representations of su(2). As a first step we show that
the Racah algebra always surjects onto the centralizer. We then offer a
conjecture regarding the description of the kernel of the map, which depends on
the irreducible representations. If true, this conjecture would provide a
presentation of the centralizer as a quotient of the Racah algebra. We prove
this conjecture in several cases. In particular, while doing so, we explicitly
obtain the Temperley-Lieb algebra, the Brauer algebra and the one-boundary
Temperley-Lieb algebra as quotients of the Racah algebra.


  The homotopy fiber of the inclusion from the long embedding space to the long
immersion space is known to be an iterated based loop space (if the codimension
is greater than two). In this paper we deloop the homotopy fiber to obtain the
topological Stiefel manifold, combining results of Lashof and of Lees. We also
give a delooping of the long embedding space, which can be regarded as a
version of Morlet-Burghelea-Lashof's delooping of the diffeomorphism group of
the disk relative to the boundary. As a corollary, we show that the homotopy
fiber is weakly equivalent to a space on which the framed little disks operad
acts possibly nontrivially, and hence its rational homology is a (higher)
BV-algebra in a stable range of dimensions.


  The purpose of class distribution estimation (also known as quantification)
is to determine the values of the prior class probabilities in a test dataset
without class label observations. A variety of methods to achieve this have
been proposed in the literature, most of them based on the assumption that the
distributions of the training and test data are related through prior
probability shift (also known as label shift). Among these methods, Friedman's
method has recently been found to perform relatively well both for binary and
multi-class quantification. We discuss the properties of Friedman's method and
another approach mentioned by Friedman (called DeBias method in the literature)
in the context of a general framework for designing linear equation systems for
class distribution estimation.


  Electrocatalytic hydrogenation of nitrobenzene (Ph-NO2) reaction (EHNR) has
been considered as a potential alternative to the traditional thermocatalytic
process in the production of high-value aniline (Ph-NH2). However, due to the
absence of robust catalyst and low surface H* coverage, the EHNR faces the
challenges of undesired performance and indetermined mechanism. Herein, we
construct a type of noble-metal free topological FeSi (M-FeSi) materials
through a solvent-free microwave strategy for efficient EHNR in neutral medium.
Impressively, benefiting from abundant active H* intermediates on the surface
of M-FeSi catalyst, the topological M-FeSi catalyst exhibits 99.7% conversion
of Ph-NO2 and 93.8% yield of Ph-NH2 after 200 C in neutral medium, which are
superior to previous candidates and FeSi catalyst synthesized via the
traditional arc-melting method under same conditions. Besides, theoretical
calculations validate that high surface H* coverage over M-FeSi catalyst is
conducive to switching the rate-determining step from Ph-NO2* Ph-NO* to Ph-NO*
Ph-NHOH*, and thus decreasing the total energy barrier of electrocatalytic
Ph-NH2 production.


  Policy networks are a central feature of deep reinforcement learning (RL)
algorithms for continuous control, enabling the estimation and sampling of
high-value actions. From the variational inference perspective on RL, policy
networks, when used with entropy or KL regularization, are a form of
\textit{amortized optimization}, optimizing network parameters rather than the
policy distributions directly. However, \textit{direct} amortized mappings can
yield suboptimal policy estimates and restricted distributions, limiting
performance and exploration. Given this perspective, we consider the more
flexible class of \textit{iterative} amortized optimizers. We demonstrate that
the resulting technique, iterative amortized policy optimization, yields
performance improvements over direct amortization on benchmark continuous
control tasks.


  Traditional machine learning is generally treated as a black-box optimization
problem and does not typically produce interpretable functions that connect
inputs and outputs. However, the ability to discover such interpretable
functions is desirable. In this work, we propose GINN-LP, an interpretable
neural network to discover the form and coefficients of the underlying equation
of a dataset, when the equation is assumed to take the form of a multivariate
Laurent Polynomial. This is facilitated by a new type of interpretable neural
network block, named the "power-term approximator block", consisting of
logarithmic and exponential activation functions. GINN-LP is end-to-end
differentiable, making it possible to use backpropagation for training. We
propose a neural network growth strategy that will enable finding the suitable
number of terms in the Laurent polynomial that represents the data, along with
sparsity regularization to promote the discovery of concise equations. To the
best of our knowledge, this is the first model that can discover arbitrary
multivariate Laurent polynomial terms without any prior information on the
order. Our approach is first evaluated on a subset of data used in SRBench, a
benchmark for symbolic regression. We first show that GINN-LP outperforms the
state-of-the-art symbolic regression methods on datasets generated using 48
real-world equations in the form of multivariate Laurent polynomials. Next, we
propose an ensemble method that combines our method with a high-performing
symbolic regression method, enabling us to discover non-Laurent polynomial
equations. We achieve state-of-the-art results in equation discovery, showing
an absolute improvement of 7.1% over the best contender, by applying this
ensemble method to 113 datasets within SRBench with known ground-truth
equations.


  Transformer based code models have impressive performance in many software
engineering tasks. However, their effectiveness degrades when symbols are
missing or not informative. The reason is that the model may not learn to pay
attention to the right correlations/contexts without the help of symbols. We
propose a new method to pre-train general code models when symbols are lacking.
We observe that in such cases, programs degenerate to something written in a
very primitive language. We hence propose to use program analysis to extract
contexts a priori (instead of relying on symbols and masked language modeling
as in vanilla models). We then leverage a novel attention masking method to
only allow the model attending to these contexts, e.g., bi-directional program
dependence transitive closures and token co-occurrences. In the meantime, the
inherent self-attention mechanism is utilized to learn which of the allowed
attentions are more important compared to others. To realize the idea, we
enhance the vanilla tokenization and model architecture of a BERT model,
construct and utilize attention masks, and introduce a new pre-training
algorithm. We pre-train this BERT-like model from scratch, using a dataset of
26 million stripped binary functions with explicit program dependence
information extracted by our tool. We apply the model in three downstream
tasks: binary similarity, type inference, and malware family classification.
Our pre-trained model can improve the SOTAs in these tasks from 53% to 64%, 49%
to 60%, and 74% to 94%, respectively. It also substantially outperforms other
general pre-training techniques of code understanding models.


  This note revisits the SWIFT method based on Shannon wavelets to price
European options under models with a known characteristic function in 2023. In
particular, it discusses some possible improvements and exposes some concrete
drawbacks of the method.


  The Bohr-Sommerfeld quantization rule is useful to study the area spectrum of
black holes by employing adiabatic invariants. This method is extended to
charged dilaton black holes in 2+1 dimensions. We put the background space-time
into the Kruskal-like coordinate to find the period with respect to Euclidian
time. Also assuming that the adiabatic invariant obeys Bohr-Sommerfeld
quantization rule, detailed study of area and entropy spectrum has been done.
It is dependent on the charge and is equally spaced as well.
  We also investigate the thermodynamics of the charged dilaton black hole.


  This paper presents the winning system for the propaganda Technique
Classification (TC) task and the second-placed system for the propaganda Span
Identification (SI) task. The purpose of TC task was to identify an applied
propaganda technique given propaganda text fragment. The goal of SI task was to
find specific text fragments which contain at least one propaganda technique.
Both of the developed solutions used semi-supervised learning technique of
self-training. Interestingly, although CRF is barely used with
transformer-based language models, the SI task was approached with RoBERTa-CRF
architecture. An ensemble of RoBERTa-based models was proposed for the TC task,
with one of them making use of Span CLS layers we introduce in the present
paper. In addition to describing the submitted systems, an impact of
architectural decisions and training schemes is investigated along with remarks
regarding training models of the same or better quality with lower
computational budget. Finally, the results of error analysis are presented.


  This paper proposes a new multi-Bernoulli filter called the Adaptive Labeled
Multi-Bernoulli filter. It combines the relative strengths of the known
Delta-Generalized Labeled Multi-Bernoulli and the Labeled Multi-Bernoulli
filter. The proposed filter provides a more precise target tracking in critical
situations, where the Labeled Multi-Bernoulli filter looses information through
the approximation error in the update step. In noncritical situations it
inherits the advantage of the Labeled Multi-Bernoulli filter to reduce the
computational complexity by using the LMB approximation.


  It is suggested that an AI inference system should reflect an inference
policy that is tailored to the domain of problems to which it is applied -- and
furthermore that an inference policy need not conform to any general theory of
rational inference or induction. We note, for instance, that Bayesian reasoning
about the probabilistic characteristics of an inference domain may result in
the specification of an nonBayesian procedure for reasoning within the
inference domain. In this paper, the idea of an inference policy is explored in
some detail. To support this exploration, the characteristics of some standard
and nonstandard inference policies are examined.


  Grim-trigger strategies are a fundamental mechanism for sustaining equilibria
in iterated games: the players cooperate along an agreed path, and as soon as
one player deviates, the others form a coalition to play him down to his minmax
level. A precondition to triggering such a strategy is that the identity of the
deviating player becomes common knowledge among the other players. This can be
difficult or impossible to attain in games where the information structure
allows only imperfect monitoring of the played actions or of the global state.
  We study the problem of synthesising finite-state strategies for detecting
the deviator from an agreed strategy profile in games played on finite graphs
with different information structures. We show that the problem is undecidable
in the general case where the global state cannot be monitored. On the other
hand, we prove that under perfect monitoring of the global state and imperfect
monitoring of actions, the problem becomes decidable, and we present an
effective synthesis procedure that covers infinitely repeated games with
private monitoring.


  We propose a method for estimating the bone mineral density (BMD) from a
plain x-ray image. Dual-energy X-ray absorptiometry (DXA) and quantitative
computed tomography (QCT) provide high accuracy in diagnosing osteoporosis;
however, these modalities require special equipment and scan protocols.
Measuring BMD from an x-ray image provides an opportunistic screening, which is
potentially useful for early diagnosis. The previous methods that directly
learn the relationship between x-ray images and BMD require a large training
dataset to achieve high accuracy because of large intensity variations in the
x-ray images. Therefore, we propose an approach using the QCT for training a
generative adversarial network (GAN) and decomposing an x-ray image into a
projection of bone-segmented QCT. The proposed hierarchical learning improved
the robustness and accuracy of quantitatively decomposing a small-area target.
The evaluation of 200 patients with osteoarthritis using the proposed method,
which we named BMD-GAN, demonstrated a Pearson correlation coefficient of 0.888
between the predicted and ground truth DXA-measured BMD. Besides not requiring
a large-scale training database, another advantage of our method is its
extensibility to other anatomical areas, such as the vertebrae and rib bones.


  We investigate the ground and low excited states of a rotating, weakly
interacting Bose-Einstein condensed gas in a harmonic trap for a given angular
momentum. Analytical results in various limits, as well as numerical results
are presented, and these are compared with those of previous studies. Within
the mean-field approximation and for repulsive interaction between the atoms,
we find that for very low values of the total angular momentum per particle,
$L/N \to 0$, where $L \hbar$ is the angular momentum and $N$ is the total
number of particles, the angular momentum is carried by quadrupolar ($|m| = 2$)
surface modes. For $L/N =1$ a vortex-like state is formed and all the atoms
occupy the $m=1$ state. For small negative values of $L/N-1$ the states with
$m=0$ and $m=2$ become populated, and for small positive values of $L/N-1$
atoms in the states with $m=5$ and $m=6$ carry the additional angular momentum.
In the whole region $0 \le L/N \le 1$ we have strong analytic and numerical
evidence that the interaction energy drops linearly as a function of $L/N$. We
have also found that an array of singly quantized vortices is formed as $L/N$
increases. Finally we have gone beyond the mean-field approximation and have
calculated the energy of the lowest state up to order $N$ for small negative
values of $L/N-1$, as well as the energy of the low-lying excited states.


  We demonstrate locally coherent heteroepitaxial growth of silicon carbide
(SiC) on diamond, a result contrary to current understanding of heterojunctions
as the lattice mismatch exceeds $20\%$. High-resolution transmission electron
microscopy (HRTEM) confirms the quality and atomic structure near the
interface. Guided by molecular dynamics simulations, a theoretical model is
proposed for the interface wherein the large lattice strain is alleviated via
point dislocations in a two-dimensional plane without forming extended defects
in three dimensions. The possibility of realising heterojunctions of
technologically important materials such as SiC with diamond offers promising
pathways for thermal management of high power electronics. At a fundamental
level, the study redefines our understanding of heterostructure formation with
large lattice mismatch.


  Medical diagnosis is the process of making a prediction of the disease a
patient is likely to have, given a set of symptoms and observations. This
requires extensive expert knowledge, in particular when covering a large
variety of diseases. Such knowledge can be coded in a knowledge graph --
encompassing diseases, symptoms, and diagnosis paths. Since both the knowledge
itself and its encoding can be incomplete, refining the knowledge graph with
additional information helps physicians making better predictions. At the same
time, for deployment in a hospital, the diagnosis must be explainable and
transparent. In this paper, we present an approach using diagnosis paths in a
medical knowledge graph. We show that those graphs can be refined using latent
representations with RDF2vec, while the final diagnosis is still made in an
explainable way. Using both an intrinsic as well as an expert-based evaluation,
we show that the embedding-based prediction approach is beneficial for refining
the graph with additional valid conditions.


  In VLSI physical design, many algorithms require the solution of difficult
combinatorial optimization problems such as max/min-cut, max-flow problems etc.
Due to the vast number of elements typically found in this problem domain,
these problems are computationally intractable leading to the use of
approximate solutions. In this work, we explore the Ising spin glass model as a
solution methodology for hard combinatorial optimization problems using the
general purpose GPU (GPGPU). The Ising model is a mathematical model of
ferromagnetism in statistical mechanics. Ising computing finds a minimum energy
state for the Ising model which essentially corresponds to the expected optimal
solution of the original problem. Many combinatorial optimization problems can
be mapped into the Ising model. In our work, we focus on the max-cut problem as
it is relevant to many VLSI physical design problems. Our method is inspired by
the observation that Ising annealing process is very amenable to fine-grain
massive parallel GPU computing. We will illustrate how the natural randomness
of GPU thread scheduling can be exploited during the annealing process to
create random update patterns and allow better GPU resource utilization.
Furthermore, the proposed GPU-based Ising computing can handle any general
Ising graph with arbitrary connections, which was shown to be difficult for
existing FPGA and other hardware based implementation methods. Numerical
results show that the proposed GPU Ising max-cut solver can deliver more than
2000X speedup over the CPU version of the algorithm on some large examples,
which shows huge performance improvement for addressing many hard optimization
algorithms for practical VLSI physical design.


  This paper studies the optimal extraction and taxation of nonrenewable
natural resources. It is well known that the market values of the main
strategic resources such as oil, natural gas, uranium, copper,..., etc,
fluctuate randomly following global and seasonal macroeconomic parameters,
these values are modeled using Markov switching L\'evy processes. We formulate
this problem as a differential game. The two players of this differential game
are the mining company whose aim is to maximize the revenues generated from its
extracting activities and the government agency in charge of regulating and
taxing natural resources. We prove the existence of a Nash equilibrium. The
corresponding Hamilton Jacobi Isaacs equations are completely solved and the
value functions as well as the optimal extraction and taxation rates are
derived in closed-form. A Numerical example is presented to illustrate our
findings.


  This paper studies the asymptotic behavior of several continuous-time
dynamical systems which are analogs of ant colony optimization algorithms that
solve shortest path problems. Local asymptotic stability of the equilibrium
corresponding to the shortest path is shown under mild assumptions. A complete
study is given for a recently proposed model called EigenAnt: global asymptotic
stability is shown, and the speed of convergence is calculated explicitly and
shown to be proportional to the difference between the reciprocals of the
second shortest and the shortest paths.


  Recently discovered (CaFe$_{1-x}$Pt$_x$As)$_{10}$Pt$_3$As$_8$ and
(CaFeAs)$_{10}$Pt$_{4-y}$As$_8$ superconductors are very similar materials
having the same elemental composition and structurally similar superconducting
FeAs slabs. Yet the maximal critical temperature achieved by changing Pt
concentration is approximately twice higher in the latter. Using angle-resolved
photoemission spectroscopy(ARPES) we compare the electronic structure of their
optimally doped compounds and find drastic differences. Our results highlight
the sensitivity of critical temperature to the details of fermiology and point
to the decisive role of band-edge singularities in the mechanism of high-$T_c$
superconductivity.


  In this article, we continue the study of monadic distributive lattices (or
m-lattices) which are a natural generalization of monadic Heyting algebras,
introduced by Monteiro and Varsavsky and developed exhaustively by
Bezhanishvili. First, we extended the duality obtained by Cignoli for
Q-distributive lattices to m-lattices. This new duality allows us to describe
in a simple way the subdirectly irreducible algebras in this variety and in
particular, to characterize the finite ones. Next, we introduce the category
mKF whose objects are monadic augmented Kripke frames and whose morphisms are
increasing continuous functions verifying certain additional conditions and we
prove that it is equivalent to the one obtained above. Finally, we show that
the category of perfect augmented Kripke frames given by Bezhanishvili for
monadic Heyting algebras is a proper subcategory of mKF.


  Compact radio cores associated with relativistic jets are often observed in
both active galactic nuclei and X-ray binaries. Their radiative properties
follow some general scaling laws which primarily depend on their masses and
accretion rates. However, it has been suggested that the black hole spin can
also strongly influence the power and radio flux of these. Here, we attempt to
estimate the dependency of the radio luminosity of steady jets launched by
accretion disks on black hole mass, accretion rate and spin using numerical
simulations. We make use of 3D GRMHD simulations of accretion disks around
low-luminosity black holes in which the jet radio emission is produced by the
jet sheath. We find that the radio flux increases roughly by a factor of 6 as
the back hole spin increases from a~0 to a=0.98. This is comparable to the
increase in accretion power with spin, meaning that the ratio between radio jet
and accretion power is hardly changing. Although our jet spine power scales as
expected for the Blandford-Znajek process, the dependency of jet radio
luminosity on the black hole spin is somewhat weaker. Also weakly rotating
black holes can produce visible radio jets. The overall scaling of the radio
emission with black hole mass and accretion rate is consistent with the
scale-invariant analytical models used to explain the fundamental plane of
black hole activity. Spin does not introduce a significant scatter in this
model. The jet-sheath model can describe well resolved accreting systems, such
as SgrA* and M87, as well as the general scaling behavior of low-luminosity
black holes. Hence the model should be applicable to a wide range of radio jets
in sub-Eddington black holes. The black hole spin has an effect on the
production of visible radio jet, but it may not be the main driver to produce
visible radio jets. An extension of our findings to powerful quasars remains
speculative.


  State estimation of dynamical systems is crucial for providing new
decision-making and system automation information in different applications.
However, the assumptions on the standard computational models for sensor
measurements can be violated in practice due to different types of data
abnormalities such as outliers and biases. In this work, we focus on the
occurrence of measurement biases and propose a robust filter for their
detection and mitigation during state estimation of nonlinear dynamical
systems. We model the presence of bias in each dimension within the generative
structure of the state-space models. Subsequently, employing the theory of
Variational Bayes and general Gaussian filtering, we devise a recursive filter
which we call the Bias Detecting and Mitigating (BDM) filter. As the error
detection mechanism is embedded within the filter structure its dependence on
any external detector is obviated. Simulations verify the performance gains of
the proposed BDM filter compared to similar Kalman filtering-based approaches
in terms of robustness to temporary and persistent bias presence.


  We present a method for quantum entanglement distribution over a so-called
code-division-multiple-access network, in which two pairs of users share the
same quantum channel to transmit information. The main idea of this method is
to use different broad-band chaotic phase shifts, generated by electro-optic
modulators (EOMs) and chaotic Colpitts circuits, to encode the
information-bearing quantum signals coming from different users, and then
recover the masked quantum signals at the receiver side by imposing opposite
chaotic phase shifts. The chaotic phase shifts given to different pairs of
users are almost uncorrelated due to the randomness of chaos and thus the
quantum signals from different pair of users can be distinguished even when
they are sent via the same quantum channel. It is shown that two
maximally-entangled states can be generated between two pairs of users by our
method mediated by bright coherent lights, which can be more easily implemented
in experiments compared with single-photon lights. Our method is robust under
the channel noises if only the decay rates of the information-bearing fields
induced by the channel noises are not quite high. Our study opens up new
perspectives for addressing and transmitting quantum information in future
quantum networks.


  Supervised learning models have been used in various domains such as lending,
college admission, face recognition, natural language processing, etc. However,
they may inherit pre-existing biases from training data and exhibit
discrimination against protected social groups. Various fairness notions have
been proposed to address unfairness issues. In this work, we focus on Equalized
Loss (EL), a fairness notion that requires the expected loss to be
(approximately) equalized across different groups. Imposing EL on the learning
process leads to a non-convex optimization problem even if the loss function is
convex, and the existing fair learning algorithms cannot properly be adopted to
find the fair predictor under the EL constraint. This paper introduces an
algorithm that can leverage off-the-shelf convex programming tools (e.g.,
CVXPY) to efficiently find the global optimum of this non-convex optimization.
In particular, we propose the ELminimizer algorithm, which finds the optimal
fair predictor under EL by reducing the non-convex optimization to a sequence
of convex optimization problems. We theoretically prove that our algorithm
finds the global optimal solution under certain conditions. Then, we support
our theoretical results through several empirical studies.


  Solving optimization problems leads to elegant and practical solutions in a
wide variety of real-world applications. In many of those real-world
applications, some of the information required to specify the relevant
optimization problem is noisy, uncertain, and expensive to obtain. In this
work, we study how much of that information needs to be queried in order to
obtain an approximately optimal solution to the relevant problem. In
particular, we focus on the shortest path problem in graphs with dynamic edge
costs. We adopt the $\textit{first passage percolation}$ model from probability
theory wherein a graph $G'$ is derived from a weighted base graph $G$ by
multiplying each edge weight by an independently chosen random number in $[1,
\rho]$. Mathematicians have studied this model extensively when $G$ is a
$d$-dimensional grid graph, but the behavior of shortest paths in this model is
still poorly understood in general graphs. We make progress in this direction
for a class of graphs that resemble real-world road networks. Specifically, we
prove that if $G$ has a constant continuous doubling dimension, then for a
given $s-t$ pair, we only need to probe the weights on $((\rho \log n )/
\epsilon)^{O(1)}$ edges in $G'$ in order to obtain a $(1 +
\epsilon)$-approximation to the $s-t$ distance in $G'$. We also generalize the
result to a correlated setting and demonstrate experimentally that probing
improves accuracy in estimating $s-t$ distances.


  Despite the remarkable success of deep neural networks in a myriad of
settings, several works have demonstrated their overwhelming sensitivity to
near-imperceptible perturbations, known as adversarial attacks. On the other
hand, prior works have also observed that deep networks can be under-sensitive,
wherein large-magnitude perturbations in input space do not induce appreciable
changes to network activations. In this work, we study in detail the phenomenon
of under-sensitivity in vision models such as CNNs and Transformers, and
present techniques to study the geometry and extent of "equi-confidence" level
sets of such networks. We propose a Level Set Traversal algorithm that
iteratively explores regions of high confidence with respect to the input space
using orthogonal components of the local gradients. Given a source image, we
use this algorithm to identify inputs that lie in the same equi-confidence
level set as the source image despite being perceptually similar to arbitrary
images from other classes. We further observe that the source image is linearly
connected by a high-confidence path to these inputs, uncovering a star-like
structure for level sets of deep networks. Furthermore, we attempt to identify
and estimate the extent of these connected higher-dimensional regions over
which the model maintains a high degree of confidence. The code for this
project is publicly available at
https://github.com/SriramB-98/blindspots-neurips-sub


  This review examined the current advancements in data-driven methods for
analyzing flow and transport in porous media, which has various applications in
energy, chemical engineering, environmental science, and beyond. Although there
has been progress in recent years, the challenges of current experimental and
high-fidelity numerical simulations, such as high computational costs and
difficulties in accurately representing complex, heterogeneous structures, can
still potentially be addressed by state-of-the-art data-driven methods. We
analyzed the synergistic potential of these methods, addressed their
limitations, and suggested how they can be effectively integrated to improve
both the fidelity and efficiency of current research. A discussion on future
research directions in this field was conducted, emphasizing the need for
collaborative efforts that combine domain expertise in physics and advanced
computationald and data-driven methodologies.


  We consider the behavior of the quantity $p(\beta)$; the free energy of
directed polymers in random environment in $1+2$ dimension, where $\beta$ is
inverse temperature. We know that the free energy is strictly negative when
$\beta$ is not zero. In this paper, we will prove that $p(\beta)$ is bounded
from above by $-\exp\left( -\frac{c_\varepsilon}{\beta^{2+\varepsilon}}
\right)$ for small $\beta$, where $c_\varepsilon>0$ is a constant depending on
$\varepsilon>0$. Also, we will suggest a strategy to get a sharper asymptotics.


  An interrelationship is found between the accumulation points of zeros of
non-trivial solutions of $f"+Af=0$ and the boundary behavior of the analytic
coefficient $A$ in the unit disc $\mathbb{D}$ of the complex plane
$\mathbb{C}$.
  It is also shown that the geometric distribution of zeros of any non-trivial
solution of $f"+Af=0$ is severely restricted if $$\label{eq:cs_a}\tag{$\star$}
|A(z)| (1-|z|^2)^2 \leq 1 + C (1-|z|), \quad z\in\mathbb{D}, $$ for any
constant $0<C<\infty$. These considerations are related to the open problem
whether \eqref{eq:cs_a} implies finite oscillation for all non-trivial
solutions.


  Recommendation systems often face exploration-exploitation tradeoffs: the
system can only learn about the desirability of new options by recommending
them to some user. Such systems can thus be modeled as multi-armed bandit
settings; however, users are self-interested and cannot be made to follow
recommendations. We ask whether exploration can nevertheless be performed in a
way that scrupulously respects agents' interests---i.e., by a system that acts
as a fiduciary. More formally, we introduce a model in which a recommendation
system faces an exploration-exploitation tradeoff under the constraint that it
can never recommend any action that it knows yields lower reward in expectation
than an agent would achieve if it acted alone. Our main contribution is a
positive result: an asymptotically optimal, incentive compatible, and ex-ante
individually rational recommendation algorithm.


  Initial-boundary value problems on a half-strip with different types of
boundary conditions for the generalized Kawahara-Zakharov-Kuznetsov equation
with nonlinearity of higher order are considered. In particular, nonlinearity
can be quadratic and cubic. Results on global existence and uniqueness in
classes of weak and strong solutions and large-time decay of small solutions
are established. The solutions are considered in weighted at infinity Sobolev
spaces. The use of weighted spaces is crucial for the study. To this end new
interpolating inequalities in weighted anisotropic Sobolev spaces are
established. Both exponential and power weights are admissible.


  The optic nerve head represents the intraocular section of the optic nerve
(ONH), which is prone to damage by intraocular pressure. The advent of optical
coherence tomography (OCT) has enabled the evaluation of novel optic nerve head
parameters, namely the depth and curvature of the lamina cribrosa (LC).
Together with the Bruch's membrane opening minimum-rim-width, these seem to be
promising optic nerve head parameters for diagnosis and monitoring of retinal
diseases such as glaucoma. Nonetheless, these optical coherence tomography
derived biomarkers are mostly extracted through manual segmentation, which is
time-consuming and prone to bias, thus limiting their usability in clinical
practice. The automatic segmentation of optic nerve head in OCT scans could
further improve the current clinical management of glaucoma and other diseases.
  This review summarizes the current state-of-the-art in automatic segmentation
of the ONH in OCT. PubMed and Scopus were used to perform a systematic review.
Additional works from other databases (IEEE, Google Scholar and ARVO IOVS) were
also included, resulting in a total of 27 reviewed studies.
  For each algorithm, the methods, the size and type of dataset used for
validation, and the respective results were carefully analyzed. The results
show that deep learning-based algorithms provide the highest accuracy,
sensitivity and specificity for segmenting the different structures of the ONH
including the LC. However, a lack of consensus regarding the definition of
segmented regions, extracted parameters and validation approaches has been
observed, highlighting the importance and need of standardized methodologies
for ONH segmentation.


  Analytical expressions for spectrum, eigenfunctions and dipole matrix
elements of a square double quantum well (DQW) are presented for a general case
when the potential in different regions of the DQW has different heights and
effective masses are different. This was achieved by Gr\"obner basis algorithm
which allows to disentangle the resulting coupled polynomials without
explicitly solving the transcendental eigenvalue equation.


  The goal of this paper is to discuss the possibility of finding an algorithm
that can give all distinct knots up to a desired complexity. Two such
algorithms are presented, one based on projections on a plane, the other on
closed self-avoiding walks.


  We present an elementary proof of the prime number theorem. The relative
error follows a golden ratio scaling law and respects the bound obtained from
the Riemann's hypothesis. The proof is derived in the framework of a scale free
nonarchimedean extension of the real number system exploiting the concept of
relative infinitesimals introduced recently in connection with ultrametric
models of Cantor sets. The extended real number system is realized as a
completion of the field of rational numbers $Q$ under a {\em new}
nonarchimedean absolute value, which treats arbitrarily small and large numbers
separately from a finite real number.


  Soft Gamma Repeaters (SGRs) undergo changes in their pulse properties and
persistent emission during episodes of intense burst activity. SGR 1900+14 has
undergone large flux increases following recent burst activity. Both SGR
1900+14 and SGR 1806-20 have shown significant changes in their pulse profile
and spin-down rates during the last several years. The pulse profile changes
are linked with the burst activity whereas the torque variations are not
directly correlated with the bursts. Here, we review the observed dynamics of
the pulsed and persistent emission of SGR 1900+14 and SGR 1806-20 during burst
active episodes and discuss what implications these results have for the burst
emission mechanism, the magnetic field dynamics of magnetars, the nature of the
torque variability, and SGRs in general.


  We investigate the squeezed back-to-back correlations (BBC) of $K^+$$K^-$,
caused by the mass modification of the particle in the dense medium formed in
d+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Au+Au collisions at
$\sqrt{s_{NN}}=62.4$ GeV. Considering some kaons may be not affected by the
medium, we further study the BBC functions of $K^+$$K^-$ when parts of all
kaons have a mass-shift. Our results indicate that the BBC functions of
$K^+$$K^-$ can be observed when only about 10$\%$ of all kaons have a
mass-shift in d+Au collisions at $\sqrt{s_{NN}}=200$ GeV and the peripheral
collisions of Au+Au at $\sqrt{s_{NN}}=62.4$ GeV. Since the BBC function is
caused by the mass-shift due to the interaction between the particle and the
medium, the successful detection of the BBC function indirectly marks that the
dense medium has formed in these collision systems. We suggest to measure the
BBC function of $K^+$$K^-$ experimentally in d+Au collisions at
$\sqrt{s_{NN}}=200$ GeV and peripheral collisions of Au+Au at
$\sqrt{s_{NN}}=62.4$ GeV.


  We re-investigated the `spectro-temporal' behaviour of the source XTE
J1859+226 in X-rays during its outburst phase in 1999, by analysing the RXTE
PCA/HEXTE data in 2 - 150 keV spectral band. Detailed analysis shows that
although the evolution pattern of the outburst followed the typical q-shaped
profile, an absence of `canonical' soft state and a weak presence of
`secondary' emission are observed. The broad-band spectra, modeled with high
energy cutoff, shows that the fold-energy increases monotonically in the hard
and hard-intermediate states followed by a random variation in the
soft-intermediate state. We attempted to estimate the mass of the source based
on the evolution of Quasi-Periodic Oscillation (QPO) frequencies during rising
phase modeled with the propagating oscillatory shock solution, and from the
correlation of photon index and QPO frequency. It is also observed that during
multiple ejections (observed as radio flares) the QPO frequencies are not
present in the power spectra which is followed by softening of the spectra
(disk flux increases or high energy flux decreases). These results are the
`possible' indication that the Comptonized corona, which could be responsible
for the generation of QPO and for the non-thermal Comptonized component of the
spectrum, is disrupted and the matter gets evacuated in the form of jet. We
attempted to explain the complex behaviour of the source during the entire
outburst and the nature of the disk-jet connection in the context of two
different types of accreting flow material, in presence of magnetic field.


  The objective of this paper is to study the tidally locked 3:2 spin-orbit
resonance of Mercury around the Sun. In order to achieve this goal, the
effective potential energy that determines the spinning motion of an
ellipsoidal planet around its axis is considered. By studying the rotational
potential energy of an ellipsoidal planet orbiting a spherical star on an
elliptic orbit with fixed eccentricity and semi-major axis, it is shown that
the system presents an infinite number of metastable equilibrium
configurations. These states correspond to local minima of the rotational
potential energy averaged over an orbit, where the ratio between the rotational
period of the planet around its axis and the revolution period around the star
is fixed. The configurations in which this ratio is an integer or an half
integer are of particular interest. Among these configurations, the deepest
minimum in the average potential energy corresponds to a situation where the
rotational and orbital motion of the planet are synchronous, and the system is
tidally locked. The next-to-the deepest minimum corresponds to the case in
which the planet rotates three times around its axis in the time that it needs
to complete two orbits around the Sun. The latter is indeed the case that
describes Mercury's motion. The method discussed in this work allows one to
identify the integer and half-integer ratios that correspond to spin-orbit
resonances and to describe the motion of the planet in the resonant orbit.


  We explore the relative importance of the stellar mass density as compared to
the inner dark halo, for the observed gas kinematics thoughout the disks of
spiral galaxies. We perform hydrodynamical simulations of the gas flow in a
sequence of potentials with varying the stellar contribution to the total
potential. The stellar portion of the potential was derived empirically from
K-band photometry. The output of the simulations - namely the gas density and
the gas velocity field - are then compared to the observed spiral arm
morphology and the H-alpha gas kinematics. We solve for the best matching
spiral pattern speed and draw conclusions on how massive the stellar disk can
be at most. For the case of the galaxy NGC 4254 (Messier 99) we demonstrate
that the prominent spiral arms of the stellar component would overpredict the
non-circular gas motions unless an axisymmetric dark halo component adds
significantly in the radial range R_exp < R < 3*R_exp.


  We report a new STAR measurement of the longitudinal double-spin asymmetry
A_LL for inclusive jet production at mid-rapidity in polarized p+p collisions
at a center-of-mass energy of sqrt(s) = 200 GeV. The data, which cover jet
transverse momenta 5 < p_T < 30 GeV/c, are substantially more precise than
previous measurements. They provide significant new constraints on the gluon
spin contribution to the nucleon spin through the comparison to predictions
derived from one global fit of polarized deep-inelastic scattering
measurements.


  Data protection and privacy is becoming increasingly crucial in the digital
era. Numerous companies depend on third-party vendors and service providers to
carry out critical functions within their operations, encompassing tasks such
as data handling and storage. However, this reliance introduces potential
vulnerabilities, as these vendors' security measures and practices may not
always align with the standards expected by regulatory bodies. Businesses are
required, often under the penalty of law, to ensure compliance with the
evolving regulatory rules. Interpreting and implementing these regulations pose
challenges due to their complexity. Regulatory documents are extensive,
demanding significant effort for interpretation, while vendor-drafted privacy
policies often lack the detail required for full legal compliance, leading to
ambiguity. To ensure a concise interpretation of the regulatory requirements
and compliance of organizational privacy policy with said regulations, we
propose a Large Language Model (LLM) and Semantic Web based approach for
privacy compliance. In this paper, we develop the novel Privacy Policy
Compliance Verification Knowledge Graph, PrivComp-KG. It is designed to
efficiently store and retrieve comprehensive information concerning privacy
policies, regulatory frameworks, and domain-specific knowledge pertaining to
the legal landscape of privacy. Using Retrieval Augmented Generation, we
identify the relevant sections in a privacy policy with corresponding
regulatory rules. This information about individual privacy policies is
populated into the PrivComp-KG. Combining this with the domain context and
rules, the PrivComp-KG can be queried to check for compliance with privacy
policies by each vendor against relevant policy regulations. We demonstrate the
relevance of the PrivComp-KG, by verifying compliance of privacy policy
documents for various organizations.


  We present an efficient method for producing $N$ particle entangled states
using Rydberg blockade interactions. Optical excitation of Rydberg states that
interact weakly, yet have a strong coupling to a second control state is used
to achieve state dependent qubit rotations in small ensembles. On the basis of
quantitative calculations we predict that an N=8 Schr\"odinger cat state can be
produced with a fidelity of 84% in cold Rb atoms.


  An assessment is made of the J-integral test procedure for initial crack
growth in an open-cell aluminium alloy foam by combining finite element (FE)
simulations with experiment. It is found experimentally that a zone of randomly
failed struts develops ahead of the primary crack tip, and is comparable in
size to that of the plastic zone. Hence, a crack tip J-field is absent at the
initiation of crack growth from the primary crack tip. This implies that the
measured J_IC value and the J versus crack extension Da curve cannot be treated
as material properties despite the fact that the specimen size meets the usual
criteria for J validity. The toughness tests were performed on a single-edge
notched bend specimen, and crack extension was measured by the direct current
potential drop method, by digital image correlation and by X-ray computed
tomography. The crack growth resistance of the foam is associated with two
distinct zones of plastic dissipation: (i) a bulk plastic zone emanating from
the crack tip (containing a cluster of randomly failed struts), and (ii) a
crack bridging zone behind the advancing crack tip. The applicability of a
cohesive zone model to predict the fracture response is explored for the
observed case of large scale bridging. To do so, FE simulations are performed
by replacing the discrete lattice of the open-cell metallic foam by a
compressible, elastic-plastic hardening solid while the fracture process zone
in the foam is represented by a cohesive zone, as characterised by a tensile
traction versus separation law. A detailed comparison of the cohesive zone
model with experimental observations reveals that it is possible to capture the
load versus displacement response but not the details of the fracture process
zone using a single set of process zone parameters.


  We introduce an equilibrium asset pricing model, which we build on the
relationship between a novel risk measure, the Expected Downside Risk (EDR) and
the expected return. On the one hand, our proposed risk measure uses a
nonparametric approach that allows us to get rid of any assumption on the
distribution of returns. On the other hand, our asset pricing model is based on
loss-averse investors of Prospect Theory, through which we implement the
risk-seeking behaviour of investors in a dynamic setting. By including EDR in
our proposed model unrealistic assumptions of commonly used equilibrium models
- such as the exclusion of risk-seeking or price-maker investors and the
assumption of unlimited leverage opportunity for a unique interest rate - can
be omitted. Therefore, we argue that based on more realistic assumptions our
model is able to describe equilibrium expected returns with higher accuracy,
which we support by empirical evidence as well.


  An electromagnetic truncated Gaussian pulse propagates through a waveguide
with piecewise different dielectric constants. The waveguide contains a
barrier, namely a region of a lower dielectric constant compared to the
neighboring regions. This set-up yields a purely imaginary wave vector in the
region of the barrier ('electromagnetic tunneling'). We exactly calculate the
time-dependent Green's function for a slightly simplified dispersion relation.
In order to observe the plain tunneling effect we neglect the distortions
caused by the wave guide in obtaining the transmitted pulse. The wave front of
the pulse travels with the vacuum speed of light. Nevertheless, behind the
barrier, the maximum of the transmitted pulse turns up at an earlier time than
in the case without an barrier. This effect will be explained in terms of the
energy flow across the barrier. The solutions obtained reproduce the shape of
the pulses measured in the tunneling experiments of Enders and Nimtz [J. Phys.
(France) I2, 1693 (1992); Phys. Rev. E48, 632 (1993); Phys. Rev. B47, 9605
(1993); J. Phys. (France) I3, 1089 (1993); 4, 565 (1994)].


  Motivated by recent observational studies of the environment of z~6 QSOs, we
have used the Millennium Run (MR) simulations to construct a very large (~20
deg^2) mock redshift survey of star-forming galaxies at z~6. We use this
simulated survey to study the relation between density enhancements in the
distribution of i-dropouts and Lya-emitters, and their relation to the most
massive halos and protocluster regions at z~6. Our simulation predicts
significant variations in surface density across the sky with some voids and
filaments extending over scales of 1 degree, much larger than probed by current
surveys. Approximately one third of all z~6 halos hosting i-dropouts brighter
than z=26.5 mag (~M* at z=6) become part of z=0 galaxy clusters. i-dropouts
associated with protocluster regions are found in regions where the surface
density is enhanced on scales ranging from a few to several tens of arcminutes
on the sky. We analyze two structures of i-dropouts and Lya-emitters observed
with the Subaru Telescope and show that these structures must be the seeds of
massive clusters-in-formation. In striking contrast, six z~6 QSO fields
observed with HST show no significant enhancements in their i-dropout number
counts. With the present data, we cannot rule out the QSOs being hosted by the
most massive halos. However, neither can we confirm this widely used
assumption. We conclude by giving detailed recommendations for the
interpretation and planning of observations by current and future ground- and
space based instruments that will shed new light on questions related to the
large-scale structure at z~6.


  We develop two mathematical lumped parameter models for blood pressure
distribution in the Fontan blood flow circulation: an ODE based spatially
homogeneous model and a PDE based spatially inhomogeneous model. We present
numerical simulations of the cardiac pressure-volume cycle and study the effect
of pulmonary resistance on cardiac output. We analyze solutions of two
initial-boundary value problems for a non-linear parabolic partial differential
equation (PDE models) with switching in the time dynamic boundary conditions
which model blood pressure distribution in the cardiovascular system with and
without Fontan surgery. We also obtain necessary conditions for parameter
values of the PDE models for existence and uniqueness of non-negative bounded
periodic solutions.


  We present results of a survey of CCS, HC$_{3}$N, and HC$_{5}$N toward 40
dark cloud cores to search for "Carbon-Chain--Producing Regions(CCPRs)", where
carbon-chain molecules are extremely abundant relative to NH$_{3}$, as in
L1495B, L1521B, L1521E, and the cyanopolyyne peak of TMC-1. We have mainly
observed toward cores where the NH$_{3}$ lines are weak, not detected, or not
observed in previous surveys, and the CCS, HC$_{3}$N, and HC$_{5}$N lines have
been detected toward 17, 17, and 5 sources, respectively. Among them, we have
found a CCPR, L492, and its possible candidates, L1517D, L530D, L1147, and
L1172B. They all show low abundance ratios of [NH$_{3}$]/[CCS] (hereafter
called the NH$_{3}$/CCS ratio) indicating the chemical youth. Combining our
results with those of previous surveys, we have found a significant variation
of the NH$_{3}$/CCS ratio among dark cloud cores and among molecular cloud
complexes. Such a variation is also suggested by the detection rates of
carbon-chain molecules. For instance, the NH$_{3}$/CCS ratios are higher and
the detection rates of carbon-chain molecules are lower in the Ophiuchus cores
than in the Taurus cores. An origin of these systematic abundance variation is
discussed in terms of the difference in the evolutionary stage or the
contraction timescale. We have also identified a carbon-chain-rich star-forming
core, L483, where intense HC$_{3}$N and HC$_{5}$N lines are detected. This is a
possible candidate for a core with "Warm Carbon-Chain Chemistry".


  Tsetlin Machines (TMs) provide a fundamental shift from arithmetic-based to
logic-based machine learning. Supporting convolution, they deal successfully
with image classification datasets like MNIST, Fashion-MNIST, and CIFAR-2.
However, the TM struggles with getting state-of-the-art performance on CIFAR-10
and CIFAR-100, representing more complex tasks. This paper introduces
plug-and-play collaboration between specialized TMs, referred to as TM
Composites. The collaboration relies on a TM's ability to specialize during
learning and to assess its competence during inference. When teaming up, the
most confident TMs make the decisions, relieving the uncertain ones. In this
manner, a TM Composite becomes more competent than its members, benefiting from
their specializations. The collaboration is plug-and-play in that members can
be combined in any way, at any time, without fine-tuning. We implement three TM
specializations in our empirical evaluation: Histogram of Gradients, Adaptive
Gaussian Thresholding, and Color Thermometers. The resulting TM Composite
increases accuracy on Fashion-MNIST by two percentage points, CIFAR-10 by
twelve points, and CIFAR-100 by nine points, yielding new state-of-the-art
results for TMs. Overall, we envision that TM Composites will enable an
ultra-low energy and transparent alternative to state-of-the-art deep learning
on more tasks and datasets.


  We study the geometry of spaces of planes on smooth complete intersections of
three quadrics, with a view toward rationality questions.


  We investigate approval-based committee voting with incomplete information
about the approval preferences of voters. We consider several models of
incompleteness where each voter partitions the set of candidates into approved,
disapproved, and unknown candidates, possibly with ordinal preference
constraints among candidates in the latter category. This captures scenarios
where voters have not evaluated all candidates and/or it is unknown where
voters draw the threshold between approved and disapproved candidates. We study
the complexity of some fundamental computational problems for a number of
classic approval-based committee voting rules including Proportional Approval
Voting and Chamberlin--Courant. These problems include that of determining
whether a given set of candidates is a possible or necessary winning committee
and whether it forms a committee that possibly or necessarily satisfies
representation axioms. We also consider the problem whether a given candidate
is possibly or necessarily a member of the winning committee.


  In this work, we study the following basic question: "How much parallelism
does a distributed task permit?" Our definition of parallelism (or symmetry)
here is not in terms of speed, but in terms of identical roles that processes
have at the same time in the execution. We initiate this study in population
protocols, a very simple model that not only allows for a straightforward
definition of what a role is, but also encloses the challenge of isolating the
properties that are due to the protocol from those that are due to the
adversary scheduler, who controls the interactions between the processes. We
(i) give a partial characterization of the set of predicates on input
assignments that can be stably computed with maximum symmetry, i.e.,
$\Theta(N_{min})$, where $N_{min}$ is the minimum multiplicity of a state in
the initial configuration, and (ii) we turn our attention to the remaining
predicates and prove a strong impossibility result for the parity predicate:
the inherent symmetry of any protocol that stably computes it is upper bounded
by a constant that depends on the size of the protocol.


  We consider the Sudakov form factor in N=4 SYM in the off-shell kinematical
regime, which can be achieved by considering the theory on its Coulomb branch.
We demonstrate that up two three loops both the infrared-divergent as well as
the finite terms do exponentiate, with the coefficient accompanying
$\log^2(m^2)$ determined by the octagon anomalous dimension $\Gamma_{oct}$.
This behaviour is in strike contrast to previous conjectural accounts in the
literature. Together with the finite terms we observe that up to three loops
the logarithm of the Sudakov form factor is identical to twice the logarithm of
the null octagon $\mathbb{O}_0$, which was recently introduced within the
context of integrability-based approaches to four point correlation functions
with infinitely-large R-charges. The null octagon $\mathbb{O}_0$ is known in a
closed form for all values of the 't Hooft coupling constant and kinematical
parameters. We conjecture that the relation between $\mathbb{O}_0$ and the
off-shell Sudakov form factor will hold to all loop orders.


  In natural and artificial light-harvesting complexes (LHC) the resonant
energy transfer (RET) between chromophores enables an efficient and directional
transport of solar energy between collection and reaction centers. The detailed
mechanisms involved in this energy funneling are intensely debated, essentially
because they rely on a succession of individual RET steps that can hardly be
addressed separately. Here, we developed a scanning tunnelling
microscopy-induced luminescence (STML) approach allowing visualizing,
addressing and manipulating energy funneling within multi-chromophoric
structures with sub-molecular precision. We first rationalize the efficiency of
the RET process at the level of chromophore dimers. We then use highly resolved
fluorescence microscopy (HRFM) maps to follow energy transfer paths along an
artificial trimer of descending excitonic energies which reveals a cascaded RET
from high- to low-energy gap molecules. Mimicking strategies developed by
photosynthetic systems, this experiment demonstrates that intermediate gap
molecules can be used as efficient ancillary units to convey energy between
distant donor and acceptor chromophores. Eventually, we demonstrate that the
RET between donors and acceptors is enhanced by the insertion of passive
molecules acting as non-covalent RET bridges. This mechanism, that occurs in
experiments performed in inhomogeneous media and which plays a decisive role in
fastening RET in photosynthetic systems, is reported at the level of individual
chromophores with atomic-scale resolution. As it relies on organic chromophores
as elementary components, our approach constitutes a powerful model to address
fundamental physical processes at play in natural LHC.


  Program correctness is one of the most difficult challenges in parallel
programming. Message Passing Interface MPI is widely used in writing parallel
applications. Since MPI is not a compiled language, the programmer will be
enfaced with several programming bugs.This paper presents the most common
programming bugs arise in MPI programs to help the programmer to compromise
between the advantage of parallelism and the extra effort needed to detect and
fix such bugs. An algebraic specification of an MPI-like programming language,
called Simple MPI (SMPI), to be used in writing MPI programs specification has
also been proposed. In addition, both nondeterminacy and deadlocks arise in
SMPI programs have been verified using Maud system.


  Flagella and cilia are examples of actively oscillating, whiplike biological
filaments that are crucial to processes as diverse as locomotion, mucus
clearance, embryogenesis and cell motility. Elastic driven rod-like filaments
subjected to compressive follower forces provide a way to mimic oscillatory
beating in synthetic settings. In the continuum limit, this spatiotemporal
response is an emergent phenomenon resulting from the interplay between the
structural elastic instability of the slender rods subjected to the
non-conservative follower forces, geometric constraints that control the onset
of this instability, and viscous dissipation due to fluid drag by ambient
media. In this paper, we use an elastic rod model to characterize beating
frequencies, the critical follower forces and the non-linear rod shapes, for
prestressed, clamped rods subject to two types of fluid drag forces, namely,
linear Stokes drag and non-linear Morrison drag. We find that the critical
follower force depends strongly on the initial slack and weakly on the nature
of the drag force. The emergent frequencies however, depend strongly on both
the extent of pre-stress as well as the nature of the fluid drag.


  We generalise the concept of radially self-accelerating beams, to the domain
of optical pulses. In particular, we show, how radially self-accelerating
optical pulses (RSAPs) can be constructed by suitable superpositions of
X-waves, which are a natural extension of Bessel beams in the pulsed domain.
Moreover, we show, that while field rotating RSAPs preserve their
self-acceleration character, intensity rotating RSAPs only possess pseudo
self-acceleration, as their transverse intensity distribution is deformed
during propagation, due to their propagation-dependent angular velocity.


  We compute the rates of capture of stars by supermassive black holes, using
time-dependent Fokker--Planck equation with initial conditions that have a
deficit of stars on low-angular-momentum orbits. One class of initial
conditions has a gap in phase space created by a binary black hole, and the
other has a globally tangentially-anisotropic velocity distribution. We find
that for galactic nuclei that are younger than ~0.1 relaxation times, the flux
of stars into the black hole is suppressed with respect to the steady-state
value. This effect may substantially reduce the number of observable tidal
disruption flares in galaxies with black hole masses M>10^7 Msun.


  We derive self-reciprocity properties for a number of polyomino generating
functions, including several families of column-convex polygons, three-choice
polygons and staircase polygons with a staircase hole. In so doing, we
establish a connection between the reciprocity results known to
combinatorialists and the inversion relations used by physicists to solve
models in statistical mechanics. For several classes of convex polygons, the
inversion (reciprocity) relation, augmented by certain symmetry and analyticity
properties, completely determines the anisotropic perimeter generating
function.


  We determined the effects of the first nonlinear corrections to the gluon
distribution using the solution of the QCD nonlinear
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation at
small x. By using a Laplace-transform technique, the behavior of the gluon
distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu
(GLR-MQ) evolution equation with the nonlinear shadowing term incorporated. We
show that the strong rise that is corresponding to the linear QCD evolution
equations at small x can be tamed by screening effects. Consequently, the
nonlinear effects for the gluon distributions are calculated and compared with
the results for the integrated gluon density from the Balitsky-Kovchegov (BK)
equation. The resulting analytic expression allows us to predict the shadowing
correction to the logarithmic derivative $F_{2}(x,Q^{2})$ with respect to $ln
Q^{2}$ and to compare the results with H1 data and a QCD analysis fit.


  Depth completion is the task of recovering dense depth maps from sparse ones,
usually with the help of color images. Existing image-guided methods perform
well on daytime depth perception self-driving benchmarks, but struggle in
nighttime scenarios with poor visibility and complex illumination. To address
these challenges, we propose a simple yet effective framework called LDCNet.
Our key idea is to use Recurrent Inter-Convolution Differencing (RICD) and
Illumination-Affinitive Intra-Convolution Differencing (IAICD) to enhance the
nighttime color images and reduce the negative effects of the varying
illumination, respectively. RICD explicitly estimates global illumination by
differencing two convolutions with different kernels, treating the
small-kernel-convolution feature as the center of the large-kernel-convolution
feature in a new perspective. IAICD softly alleviates local relative light
intensity by differencing a single convolution, where the center is dynamically
aggregated based on neighboring pixels and the estimated illumination map in
RICD. On both nighttime depth completion and depth estimation tasks, extensive
experiments demonstrate the effectiveness of our LDCNet, reaching the state of
the art.


  We discuss a novel approach to estimate the partition function in effective
model frameworks when the effective potentials have multiple extrema, so that
ascertaining a mean field becomes difficult. Using this approach we present a
consistent model to study the thermodynamic properties of gluon quasi-particles
as a function of temperature, both in the color confined and the color
deconfined phases.


  Policy-based reinforcement learning algorithms are widely used in various
fields. Among them, mainstream policy optimization algorithms such as TRPO and
PPO introduce importance sampling into policy iteration, which allows the reuse
of historical data. However, this can also lead to a high variance of the
surrogate objective and indirectly affects the stability and convergence of the
algorithm. In this paper, we first derived an upper bound of the surrogate
objective variance, which can grow quadratically with the increase of the
surrogate objective. Next, we proposed the dropout technique to avoid the
excessive increase of the surrogate objective variance caused by importance
sampling. Then, we introduced a general reinforcement learning framework
applicable to mainstream policy optimization methods, and applied the dropout
technique to the PPO algorithm to obtain the D-PPO variant. Finally, we conduct
comparative experiments between D-PPO and PPO algorithms in the Atari 2600
environment, and the results show that D-PPO achieved significant performance
improvements compared to PPO, and effectively limited the excessive increase of
the surrogate objective variance during training.


  Using world line fermions $\Upsilon_{\pm}^{m}=\Upsilon_{\pm}^{m}(\tau) $
valued in vector representation of $SO(d,4-d) $ with $d=2,3,4,$ we develop a
pure fermionic analog of Penrose twistor construction. First, we show that
Fermi antisymmetry requiring $(\Upsilon_{\pm}^{m}) ^{2}=0$ can be solved by
using twistor like variables. Then we study the corresponding dual twistor like
field action and show that quantum spectrum exhibits naturally 4D
$\mathcal{N}=1$ target space supersymmetry. Higher spin world line field
solutions of the constraint $(\Pi_{s}^{m}) ^{2}=0$, $s\in \mathbb{Z}$ are also
discussed.


  A survey of goodness-of-fit and symmetry tests based on the characterization
properties of distributions is presented. This approach became popular in
recent years. In most cases the test statistics are functionals of
$U$-empirical processes. The limiting distributions and large deviations of new
statistics under the null hypothesis are described. Their local Bahadur
efficiency for various parametric alternatives is calculated and compared with
each other as well as with diverse previously known tests. We also describe new
directions of possible research in this domain.


  Nanomaterials with core-shell architectures are prominent examples of
strain-engineered materials, where material properties can be designed by
fine-tuning the misfit strain at the interface. Here, we elucidate the full 3D
atomic structure of Pd@Pt core-shell nanoparticles at the single-atom level via
atomic electron tomography. Full 3D displacement fields and strain profiles of
core-shell nanoparticles were obtained, which revealed a direct correlation
between the surface and interface strain. It also showed clear Poisson effects
at the scale of the full nanoparticle as well as the local atomic bonds. The
strain distributions show a strong shape-dependent anisotropy, whose nature was
further corroborated by molecular statics simulations. From the observed
surface strains, the surface oxygen reduction reaction activities were
predicted. These findings give a deep understanding of structure-property
relationships in strain-engineerable core-shell systems, which could pave a new
way toward direct control over the resulting catalytic properties.


  The properties of discrete two-dimensional spin glasses depend strongly on
the way the zero-temperature limit is taken. We discuss this phenomenon in the
context of the Migdal-Kadanoff renormalization group. We see, in particular,
how these properties are connected with the presence of a cascade of fixed
points in the renormalization group flow. Of particular interest are two
unstable fixed points that correspond to two different spin-glass phases at
zero temperature. We discuss how these phenomena are related with the presence
of entropy fluctuations and temperature chaos, and universality in this model.


  The transition mechanism of metal-insulator in metal oxides is discussed in
detail, which is a part of the mechanism of superconductivity. Through the
study of magic angle twisted bilayer graphene superconductor and other new
findings on superconductivity, we further demonstrate that the physical
mechanism of superconductivity proposed in Part I is the only correct way to
handle the properties of superconductivity in various materials. We propose
that superfluid helium consists of normal liquid helium mixed with high-energy
helium atoms. Based on this new model, all peculiar features discovered in
superfluid helium can be truly understood, such as the climb of superfluid
helium on the container's wall, the fountain effect, the discontinuity of
specific heat capacity at phase transition point, and the maintaining mass
current in a ring-shaped container. We demonstrate that the high-energy
particles play a driving force role in both superconductors and superfluid
helium, and therefore dominate their properties.


  We bound the higher-order Dehn functions and other filling invariants of
certain Carnot groups using approximation techniques. These groups include the
higher-dimensional Heisenberg groups, jet groups, and central products of
two-step nilpotent groups. Some consequences of this work are a construction of
groups with arbitrarily large nilpotency class that have euclidean
n-dimensional filling volume functions, and a proof of part of a conjecture of
Gromov on the higher-order filling functions of the higher-dimensional
Heisenberg groups.


  The Atacama Cosmology Telescope is a 6-meter telescope designed to map the
Cosmic Microwave Background simultaneously at 145 GHz, 215 GHz, and 280 GHz
with arcminute resolution. Each frequency will have a 32 by 32 element focal
plane array of TES bolometers. This paper describes the design of the telescope
and the cold reimaging optics, which is optimized for millimeter-wave
observations with these sensitive detectors.


  The pyrite compound CoS2 has been intensively studied in the past due to its
itinerant ferromagnetism and potential for half-metallicity, which make it a
promising material for spintronic applications. However, its electronic
structure remains only poorly understood. Here we use complementary bulk- and
surface-sensitive angle-resolved photoelectron spectroscopy and ab-initio
calculations to provide a complete picture of its band structure. We discover
Weyl-cones at the Fermi-level, which presents CoS2 in a new light as a rare
member of the recently discovered class of magnetic topological metals. We
directly observe the topological Fermi-arc surface states that link the
Weyl-nodes, which will influence the performance of CoS2 as a spin-injector by
modifying its spin-polarization at interfaces. Additionally, we are for the
first time able to directly observe a minority-spin bulk electron pocket in the
corner of the Brillouin zone, which proves that CoS2 cannot be a true
half-metal. Beyond settling the longstanding debate about half-metallicity in
CoS2, our results provide a prime example of how the topology of magnetic
materials can affect their use in spintronic applications.


  We use hydrodynamic simulations to provide quantitative estimates of the
effects of the impact of the accretion stream on disks in interacting binaries.
For low accretion rates, efficient radiative cooling of the hotspot region can
occur, and the primary consequence of the stream impact is stream overflow
toward smaller disk radii. The stream is well described by a ballistic
trajectory, but larger masses of gas are swept up and overflow at smaller, but
still highly supersonic, velocities. If cooling is inefficient, overflow still
occurs, but there is no coherent stream inward of the disk rim. Qualitatively,
the resulting structure appears as a bulge extending downstream along the disk
rim. We calculate the mass fraction and velocity of the overflowing component
as a function of the important system parameters, and discuss the implications
of the results for X-ray observations and doppler tomography of cataclysmic
variables, low-mass X-ray binaries and supersoft X-ray sources.


  In this paper we introduce a simple discrete stochastic model of eternal
inflation that shares many of the most important features of the continuum
theory as it is now understood. The model allows us to construct a multiverse
and rigorously analyze its properties. Although simple and easy to solve, it
has a rich mathematical structure underlying it. Despite the discreteness of
the space-time the theory exhibits an unexpected non-perturbative analog of
conformal symmetry that acts on the boundary of the geometry. The symmetry is
rooted in the mathematical properties of trees, p-adic numbers, and ultrametric
spaces; and in the physical property of detailed balance. We provide
self-contained elementary explanations of the unfamiliar mathematical concepts,
which have have also appeared in the study of the p-adic string.
  The symmetry acts on a huge collection of very low dimensional "multiverse
fields" that are not associated with the usual perturbative degrees of freedom.
They are connected with the late-time statistical distribution of
bubble-universes in the multiverse.
  The conformal symmetry which acts on the multiverse fields is broken by the
existence of terminal decays - to hats or crunches - but in a particularly
simple way. We interpret this symmetry breaking as giving rise to an arrow of
time.
  The model is used to calculate statistical correlations at late time and to
discuss the measure problem. We show that the natural cutoff in the model is
the analog of the so-called light-cone-time cutoff. Applying the model to the
problem of the cosmological constant, we find agreement with earlier work.


  We consider finite-dimensional nonlinear systems with linear part described
by a parity-time (PT-) symmetric operator. We investigate bifurcations of
stationary nonlinear modes from the eigenstates of the linear operator and
consider a class of PT-symmetric nonlinearities allowing for existence of the
families of nonlinear modes. We pay particular attention to the situations when
the underlying linear PT-symmetric operator is characterized by the presence of
degenerate eigenvalues or exceptional-point singularity. In each of the cases
we construct formal expansions for small-amplitude nonlinear modes. We also
report a class of nonlinearities allowing for the system to admit one or
several integrals of motion, which turn out to be determined by the
pseudo-Hermiticity of the nonlinear operator.


  An initial-boundary value problem for a model of stimulated Raman scattering
was considered in [Moskovchenko E.A., Kotlyarov V.P., J. Phys. A: Math. Theor.
43 (2010), 055205, 31 pages]. The authors showed that in the long-time range
$t\to+\infty$ the $x>0$, $t>0$ quarter plane is divided into 3 regions with
qualitatively different asymptotic behavior of the solution: a region of a
finite amplitude plane wave, a modulated elliptic wave region and a vanishing
dispersive wave region. The asymptotics in the modulated elliptic region was
studied under an implicit assumption of the solvability of the corresponding
Whitham type equations. Here we establish the existence of these parameters,
and thus justify the results by Moskovchenko and Kotlyarov.


  Bipartite entanglement entropies are calculated for the ground state of the
two-excitation subspace in a two-site coupled cavity model. Each region in the
phase diagram (atomic insulator, polaritonic insulator, photonic superfluid,
and polaritonic superfluid) is found to be characterized by unique entanglement
properties. In particular, the polaritonic superfluid region exhibits
multipartite entanglement among the two atoms and two cavity fields. This
system provides a toy model in which a number of intriguing aspects of
entanglement can be studied, such as the relationship of entanglement to phase
transitions, entanglement of particles with different dimensionality, and the
connection between experimentally accessible local observables and entanglement
entropies.


  Fusing data from cameras and LiDAR sensors is an essential technique to
achieve robust 3D object detection. One key challenge in camera-LiDAR fusion
involves mitigating the large domain gap between the two sensors in terms of
coordinates and data distribution when fusing their features. In this paper, we
propose a novel camera-LiDAR fusion architecture called, 3D Dual-Fusion, which
is designed to mitigate the gap between the feature representations of camera
and LiDAR data. The proposed method fuses the features of the camera-view and
3D voxel-view domain and models their interactions through deformable
attention. We redesign the transformer fusion encoder to aggregate the
information from the two domains. Two major changes include 1) dual query-based
deformable attention to fuse the dual-domain features interactively and 2) 3D
local self-attention to encode the voxel-domain queries prior to dual-query
decoding. The results of an experimental evaluation show that the proposed
camera-LiDAR fusion architecture achieved competitive performance on the KITTI
and nuScenes datasets, with state-of-the-art performances in some 3D object
detection benchmarks categories.


  A concise, somewhat personal, review of the problem of superfluidity and
quantum criticality in regular and disordered interacting Bose systems is
given, concentrating on general features and important symmetries that are
exhibited in different parts of the phase diagram, and that govern the
different possible types of critical behavior. A number of exact results for
various insulating phase boundaries, which may be used to constrain the results
of numerical simulations, can be derived using large rare region type
arguments. The nature of the insulator-superfluid transition is explored
through general scaling arguments, exact model calculations in one dimension,
numerical results in two dimensions, and approximate renormalization group
results in higher dimensions. Experiments on He-4 adsorbed in porous Vycor
glass, on thin film superconductors, and magnetically trapped atomic vapors in
a periodic optical potential, are used to illustrate many of the concepts.


  We explore the thermodynamics of stochastic heat engines in presence of
stochastic resetting. The set-up comprises an engine whose working substance is
a Brownian particle undergoing overdamped Langevin dynamics in a harmonic
potential with a time-dependent stiffness, with the dynamics interrupted at
random times with a resetting to a fixed location. The effect of resetting to
the potential minimum is shown to enhance the efficiency of the engine, while
the output work is shown to have a non-monotonic dependence on the rate of
resetting. The resetting events are found to drive the system out of linear
response regime even for small differences in the bath temperatures. Shifting
the reset point from the potential minimum is observed to reduce the engine
efficiency. The experimental set-up for the realization of such an engine is
briefly discussed.


  Recent years have seen dramatic progress in the development of techniques for
measuring the activity and connectivity of large populations of neurons in the
brain. However, as these techniques grow ever more powerful---allowing us to
even contemplate measuring every neuron in entire brain---a new problem arises:
how do we make sense of the mountains of data that these techniques produce?
Here, we argue that the time is ripe for building an intermediate or
"mesoscale" computational theory that can bridge between single-cell
(microscale) accounts of neural function and behavioral (macroscale) accounts
of animal cognition and environmental complexity. Just as digital accounts of
computation in conventional computers abstract away the non-essential dynamics
of the analog circuits that implementing gates and registers, so too a
computational account of animal cognition can afford to abstract from the
non-essential dynamics of neurons. We argue that the geometry of neural
circuits is essential in explaining the computational limitations and
technological innovations inherent in biological information processing. We
propose a blueprint for how to employ tools from modern machine learning to
automatically infer a satisfying mesoscale account of neural computation that
combines functional and structural data, with an emphasis on learning and
exploiting regularity and repeating motifs in neuronal circuits. Rather than
suggest a specific theory, we present a new class of scientific instruments
that can enable neuroscientists to design, propose, implement and test
mesoscale theories of neural computation.


  We prove a representability theorem for moduli functors of framed
torsion-free sheaves on nonsingular complex projective surfaces, using formal
geometry along a curve in the surface. This has as a consequence that a certain
restriction morphism for moduli stacks of sheaves has fibers that are schemes.


  Small area estimation has received enormous attention in recent years due to
its wide range of application, particularly in policy making decisions. The
variance based on direct sample size of small area estimator is unduly large
and there is a need of constructing model based estimator with low mean squared
prediction error (MSPE). Estimation of MSPE and in particular the bias
correction of MSPE plays the central piece of small area estimation research.
In this article, a new technique of bias correction for the estimated MSPE is
proposed. It is shown that that the new MSPE estimator attains the same level
of bias correction as the existing estimators based on straight Taylor
expansion and jackknife methods. However, unlike the existing methods, the
proposed estimate of MSPE is always nonnegative. Furthermore, the proposed
method can be used for general two-level small area models where the variables
at each level can be discrete or continuous and, in particular, be nonnormal.


  Self-supervised monocular depth estimation has garnered considerable
attention for its applications in autonomous driving and robotics. While recent
methods have made strides in leveraging techniques like the Self Query Layer
(SQL) to infer depth from motion, they often overlook the potential of
strengthening pose information. In this paper, we introduce SPIdepth, a novel
approach that prioritizes enhancing the pose network for improved depth
estimation. Building upon the foundation laid by SQL, SPIdepth emphasizes the
importance of pose information in capturing fine-grained scene structures. By
enhancing the pose network's capabilities, SPIdepth achieves remarkable
advancements in scene understanding and depth estimation. Experimental results
on benchmark datasets such as KITTI, Cityscapes, and Make3D showcase SPIdepth's
state-of-the-art performance, surpassing previous methods by significant
margins. Specifically, SPIdepth tops the self-supervised KITTI benchmark.
Additionally, SPIdepth achieves the lowest AbsRel (0.029), SqRel (0.069), and
RMSE (1.394) on KITTI, establishing new state-of-the-art results. On
Cityscapes, SPIdepth shows improvements over SQLdepth of 21.7% in AbsRel, 36.8%
in SqRel, and 16.5% in RMSE, even without using motion masks. On Make3D,
SPIdepth in zero-shot outperforms all other models. Remarkably, SPIdepth
achieves these results using only a single image for inference, surpassing even
methods that utilize video sequences for inference, thus demonstrating its
efficacy and efficiency in real-world applications. Our approach represents a
significant leap forward in self-supervised monocular depth estimation,
underscoring the importance of strengthening pose information for advancing
scene understanding in real-world applications.


  $P$-values have been the focus of considerable criticism based on various
considerations. Still, the $P$-value represents one of the most commonly used
statistical tools. When assessing the suitability of a single hypothesized
distribution, it is not clear that there is a better choice for a measure of
surprise. This paper is concerned with the definition of appropriate
model-based $P$-values for model checking.