  Temporal abstraction in reinforcement learning is the ability of an agent to
learn and use high-level behaviors, called options. The option-critic
architecture provides a gradient-based end-to-end learning method to construct
options. We propose an attention-based extension to this framework, which
enables the agent to learn to focus different options on different aspects of
the observation space. We show that this leads to behaviorally diverse options
which are also capable of state abstraction, and prevents the degeneracy
problems of option domination and frequent option switching that occur in
option-critic, while achieving a similar sample complexity. We also demonstrate
the more efficient, interpretable, and reusable nature of the learned options
in comparison with option-critic, through different transfer learning tasks.
Experimental results in a relatively simple four-rooms environment and the more
complex ALE (Arcade Learning Environment) showcase the efficacy of our
approach.


  Marius T\u{a}rn\u{a}uceanu described the finite groups $G$ having $|G|-1$
cyclic subgroups. We describe the finite groups $G$ having $|G|-\Delta$ cyclic
subgroups for $\Delta=2, 3, 4$ and $5$.


  For a closed connected manifold N, we construct a family of functions on the
Hamiltonian group G of the cotangent bundle T^*N, and a family of functions on
the space of smooth functions with compact support on T^*N. These satisfy
properties analogous to those of partial quasi-morphisms and quasi-states of
Entov and Polterovich. The families are parametrized by the first real
cohomology of N. In the case N=T^n the family of functions on G coincides with
Viterbo's symplectic homogenization operator. These functions have applications
to the algebraic and geometric structure of G, to Aubry-Mather theory, to
restrictions on Poisson brackets, and to symplectic rigidity.


  We argue that the Penrose limit of a general string background is a
generalization of the Seiberg-Sen limit describing M(atrix) theory as the DLCQ
of M theory in flat space. The BMN theory of type IIB strings on the maximally
supersymmetric pp-wave background is understood as the exact analogue of the
BFSS M(atrix) theory, namely, a DLCQ of IIB string theory on $AdS_5 \times S^5$
in the limit of infinite longitudinal momentum. This point of view is used to
explain some features of the BMN duality.


  Beam codebooks are a recent feature to enable high dimension multiple-input
multiple-output in 5G. Codebooks comprised of customizable beamforming weights
can be used to transmit reference signals and aid the channel state information
(CSI) acquisition process. Codebooks are also used for quantizing feedback
following CSI acquisition. In this paper, we characterize the role of each
codebook used during the beam management process and design a neural network to
find codebooks that improve overall system performance. Evaluating a codebook
requires considering the system-level dependency between the codebooks,
feedback, overhead, and spectral efficiency. The proposed neural network is
built on translating codebook and feedback knowledge into a consistent
beamspace basis similar to a virtual channel model to generate initial access
codebooks. This beamspace codebook algorithm is designed to directly integrate
with current 5G beam management standards without changing the feedback format
or requiring additional side information. Our simulations show that the neural
network codebooks improve over traditional codebooks, even in dispersive
sub-6GHz environments. We further use our framework to evaluate CSI feedback
formats with regard to multi-user spectral efficiency. Our results suggest that
optimizing codebook performance can provide valuable performance improvements,
but optimizing the feedback configuration is also important in sub-6GHz bands.


  With the market competition aggravating, it becomes necessary for market
players to adopt a business model which can adopt dynamic business changes. Any
enterprise has the possibility to win in the competition only when it forms the
strategic alliance with the upstream and downstream enterprise. This paper
articulates a way of using unified modelling language (UML) to develop business
value chain activities for any enterprise to develop dynamic, adhoc and agile
business model. The results show that the UML is useful in the development of
information systems and is independent of any programming language.


  We present a model for the actin contractile ring of adherent animal cells.
The model suggests that the actin concentration within the ring and
consequently the power that the ring exerts both increase during contraction.
We demonstrate the crucial role of actin polymerization and depolymerization
throughout cytokinesis, and the dominance of viscous dissipation in the
dynamics. The physical origin of two phases in cytokinesis dynamics ("biphasic
cytokinesis") follows from a limitation on the actin density. The model is
consistent with a wide range of measurements of the midzone of dividing animal
cells.


  Process mining has gained traction over the past decade and an impressive
body of research has resulted in the introduction of a variety of process
mining approaches measuring process performance. Having this set of techniques
available, organizations might find it difficult to identify which approach is
best suited considering context, performance indicator, and data availability.
In light of this challenge, this paper aims at introducing a framework for
categorizing and selecting performance analysis approaches based on existing
research. We start from a systematic literature review for identifying the
existing works discussing how to measure process performance based on
information retrieved from event logs. Then, the proposed framework is built
starting from the information retrieved from these studies taking into
consideration different aspects of performance analysis.


  We propose KMMLU, a new Korean benchmark with 35,030 expert-level
multiple-choice questions across 45 subjects ranging from humanities to STEM.
While prior Korean benchmarks are translated from existing English benchmarks,
KMMLU is collected from original Korean exams, capturing linguistic and
cultural aspects of the Korean language. We test 27 public and proprietary LLMs
and observe the best public model to score 50.5%, leaving significant room for
improvement. This model was primarily trained for English and Chinese, not
Korean. Current LLMs tailored to Korean, such as Polyglot-Ko, perform far
worse. Surprisingly, even the most capable proprietary LLMs, e.g., GPT-4 and
HyperCLOVA X do not exceed 60%. This suggests that further work is needed to
improve LLMs for Korean, and we believe KMMLU offers the appropriate tool to
track this progress. We make our dataset publicly available on the Hugging Face
Hub and integrate the benchmark into EleutherAI's Language Model Evaluation
Harness.


  We present an analysis into the inner workings of Convolutional Neural
Networks (CNNs) for processing text. CNNs used for computer vision can be
interpreted by projecting filters into image space, but for discrete sequence
inputs CNNs remain a mystery. We aim to understand the method by which the
networks process and classify text. We examine common hypotheses to this
problem: that filters, accompanied by global max-pooling, serve as ngram
detectors. We show that filters may capture several different semantic classes
of ngrams by using different activation patterns, and that global max-pooling
induces behavior which separates important ngrams from the rest. Finally, we
show practical use cases derived from our findings in the form of model
interpretability (explaining a trained model by deriving a concrete identity
for each filter, bridging the gap between visualization tools in vision tasks
and NLP) and prediction interpretability (explaining predictions). Code
implementation is available online at
github.com/sayaendo/interpreting-cnn-for-text.


  The Delaunay filtration $\mathcal{D}_{\bullet}(X)$ of a point cloud $X\subset
\mathbb{R}^d$ is a central tool of computational topology. Its use is justified
by the topological equivalence of $\mathcal{D}_{\bullet}(X)$ and the offset
(i.e., union-of-balls) filtration of $X$. Given a function $\gamma: X \to
\mathbb{R}$, we introduce a Delaunay bifiltration
$\mathcal{DC}_{\bullet}(\gamma)$ that satisfies an analogous topological
equivalence, ensuring that $\mathcal{DC}_{\bullet}(\gamma)$ topologically
encodes the offset filtrations of all sublevel sets of $\gamma$, as well as the
topological relations between them. $\mathcal{DC}_{\bullet}(\gamma)$ is of size
$O(|X|^{\lceil\frac{d+1}{2}\rceil})$, which for $d$ odd matches the worst-case
size of $\mathcal{D}_{\bullet}(X)$. Adapting the Bowyer-Watson algorithm for
computing Delaunay triangulations, we give a simple, practical algorithm to
compute $\mathcal{DC}_{\bullet}(\gamma)$ in time $O(|X|^{\lceil
\frac{d}{2}\rceil +1})$. Our implementation, based on CGAL, computes
$\mathcal{DC}_{\bullet}(\gamma)$ with modest overhead compared to computing
$\mathcal{D}_{\bullet}(X)$, and handles tens of thousands of points in
$\mathbb{R}^3$ within seconds.


  The K0s-p invariant mass spectrum was reconstructed in several kinematic
regions with the main emphasis on the studies of the production mechanism of
the Theta+ candidate recently observed by ZEUS. The candidate Theta+ signal was
found to be produced predominantly in the forward hemisphere in the laboratory
frame. This is unlike the case for the Lambda(1520) or the Lambda(c), and
indicates that the Theta+ may have an unusual production mechanism related to
proton-remnant fragmentation. H1 does not observe a signal and sets an upper
limit at 95% C.L. which does not exclude the ZEUS observation.


  More than 30 extra-solar Jupiter-like planets have shorter periods than the
planet Mercury. It is generally accepted that they formed further out, and
migrated inwards. In order to be driven by tidal torques from the gaseous disc,
the disc exterior to the planet had to contain about a planetary mass. The fact
that the planets stopped migrating means that their outer disc was removed. We
suggest that the outer disc was accreted by the planet. In this scenario, the
endgame is a race. The planet survives if it accretes its outer disc before
being accreted by the star. The winner is determined solely by the ratio of the
mass of the outer disc to the local surface density of the disc.


  Since the invention of modern CT systems, metal artifacts have been a
persistent problem. Due to increased scattering, amplified noise, and
insufficient data collection, it is more difficult to suppress metal artifacts
in cone-beam CT, limiting its use in human- and robot-assisted spine surgeries
where metallic guidewires and screws are commonly used. In this paper, we
demonstrate that conventional image-domain segmentation-based MAR methods are
unable to eliminate metal artifacts for intraoperative CBCT images with
guidewires. To solve this problem, we present a fine-grained projection-domain
segmentation-based MAR method termed PDS-MAR, in which metal traces are
augmented and segmented in the projection domain before being inpainted using
triangular interpolation. In addition, a metal reconstruction phase is proposed
to restore metal areas in the image domain. The digital phantom study and real
CBCT data study demonstrate that the proposed algorithm achieves significantly
better artifact suppression than other comparing methods and has the potential
to advance the use of intraoperative CBCT imaging in clinical spine surgeries.


  In this paper we provide new necessary and sufficient conditions for the
existence of K\"ahler-Einstein metrics on small deformations of a Fano
K\"ahler-Einstein manifold. We also show that the Weil-Petersson metric can be
approximated by the Ricci curvatures of the canonical $L^2$ metrics on the
direct image bundles. In addition, we describe the plurisubharmonicity of the
energy functional of harmonic maps on the Kuranishi space of the deformation of
compact K\"ahler-Einstein manifolds of general type.


  In this article, the atom excitation suppression is studied in two ways. The
first way of exploring the excitation suppression is by an external DC electric
field. The second way is to study the excitation suppression caused by electric
field generated by free charges, which are created by ionizing atoms. This
suppression is called Coulomb blockade. Here the Coulomb forces are created by
ions through ionizing atoms by a UV laser. The theory shows that the
interaction, which causes the suppression, is primarily caused by charge-dipole
interactions. Here the charge is the ion, and the dipole is an atom. In this
experiment, we use $^{85}$Rb atoms. The valence electron and the ion core are
the two poles of an electric dipole. The interaction potential energy between
the ion and the atom is proportional to $\frac{1}{R^2}$, and the frequency
shift caused by this interaction is proportional to $\frac{1}{R^4}$, where $R$
is the distance between the ion and the dipole considered. This research can be
used for quantum information storage, remote control, creating hot plasmas
using cold atoms, as well as electronic devices.


  We investigate the hovering dynamics of rigid bodies with up-down asymmetry
placed in oscillating background flows. Recent experiments on inanimate
pyramid-shaped objects in oscillating flows with zero mean component
demonstrate that the resulting aerodynamic forces are sufficient to keep the
object aloft. The mechanisms responsible for this lift production are
fundamentally unsteady and depend on the shed vorticity. Here, we consider a
model system of a two-dimensional flyer and compute the unsteady, two-way
coupling between the flyer and the surrounding fluid in the context of the
vortex sheet model. We examine in detail the flow properties (frequency and
speed) required for hovering and their dependence on the flyer's
characteristics (mass and geometry). We find that the aerodynamic effort
required to hover is an intrinsic property of the flyer itself: a given flyer
requires a constant amount of effort to hover, irrespective of the frequency
and speed of the oscillating flow. This physical insight will potentially have
significant implications on the design of unmanned air vehicles as well as on
understanding active hovering of live organisms that can manipulate their
flapping motion to favor a larger oscillation amplitude or frequency.


  In this Letter we study thermoelectric effects in ultra small quantum dots.
We study the behaviour of the thermopower, Peltier coefficient and thermal
conductance both in the sequencial tunneling regime and in the regime where
Kondo correlations develope. Both cases of linear response and non-equilibrium
induced by strong temperature gradients are considered. The thermopower is a
very sensitive tool to detect Kondo correlations. It changes sign both as a
function of temperature and temperature gradient. We also discuss violations of
the Wiedemann-Franz law.


  We give a brief re-exposition of the theory due to Pauli and Sinclair of
ramification polygons of Eisenstein polynomials over p-adic fields, their
associated residual polynomials and an algorithm to produce all extensions for
a given ramification polygon. We supplement this with an algorithm to produce
all ramification polygons of a given degree, and hence we can produce all
totally ramified extensions of a given degree.


  The results of the investigation of the spectral characteristics of new
luminescent substances based on rare-earth ions Eu3 + and Tb3 + in matrices of
double molybdates are presented in the article. The luminescence and excitation
spectra are considered, the decay times of the main transitions are determined,
and the color coordinates are determined. The results show the possible
suitability of using these compounds as white phosphor phosphor components.


  A program for calculating the semi-classic transport coefficients is
described. It is based on a smoothed Fourier interpolation of the bands. From
this analytical representation we calculate the derivatives necessary for the
transport distributions. The method is compared to earlier calculations, which
in principle should be exact within Boltzmann theory, and a very convincing
agreement is found.


  Mobile robots that navigate in unknown environments need to be constantly
aware of the dynamic objects in their surroundings for mapping, localization,
and planning. It is key to reason about moving objects in the current
observation and at the same time to also update the internal model of the
static world to ensure safety. In this paper, we address the problem of jointly
estimating moving objects in the current 3D LiDAR scan and a local map of the
environment. We use sparse 4D convolutions to extract spatio-temporal features
from scan and local map and segment all 3D points into moving and non-moving
ones. Additionally, we propose to fuse these predictions in a probabilistic
representation of the dynamic environment using a Bayes filter. This volumetric
belief models, which parts of the environment can be occupied by moving
objects. Our experiments show that our approach outperforms existing moving
object segmentation baselines and even generalizes to different types of LiDAR
sensors. We demonstrate that our volumetric belief fusion can increase the
precision and recall of moving object segmentation and even retrieve previously
missed moving objects in an online mapping scenario.


  Knowledge Distillation (KD) aims at transferring knowledge from a larger
well-optimized teacher network to a smaller learnable student network.Existing
KD methods have mainly considered two types of knowledge, namely the individual
knowledge and the relational knowledge. However, these two types of knowledge
are usually modeled independently while the inherent correlations between them
are largely ignored. It is critical for sufficient student network learning to
integrate both individual knowledge and relational knowledge while reserving
their inherent correlation. In this paper, we propose to distill the novel
holistic knowledge based on an attributed graph constructed among instances.
The holistic knowledge is represented as a unified graph-based embedding by
aggregating individual knowledge from relational neighborhood samples with
graph neural networks, the student network is learned by distilling the
holistic knowledge in a contrastive manner. Extensive experiments and ablation
studies are conducted on benchmark datasets, the results demonstrate the
effectiveness of the proposed method. The code has been published in
https://github.com/wyc-ruiker/HKD


  In this paper we analyze the dilepton mass square $q^2$ dependency of single
lepton polarization asymmetries and CP violation for $\overline{B}\rightarrow
\overline{K}_0^{*}(1430) \ell^+\ell^-, \ell=\mu,\tau)$ in the 2HDM context.
Also, we study the averages of these asymmetries in the domain $4
m_{\ell}^2<q^2< (m_B-m_{{K}_0^{*}})^2$. Our study manifests that the
investigation of the above-mentioned asymmetries for $\overline{B}\rightarrow
\overline{K}_0^*(1430) \ell^+\ell^-$ processes could provide useful information
for probing new Higgs bosons in the future B-physics experiments.


  The foreground component of the X-ray Background (XRB) can be studied by
cross-correlating its intensity with galaxy catalogs. We computed the two-point
cross-correlation function $W_{xg}$ between 67 {\em Einstein} X-ray fields and
the APM galaxy catalog. We detected a signal with an amplitude of $W_{xg} = .04
\pm .01$, significant at the $3.5\sigma$ level. The reality of this signal was
tested with a series of control data sets. We discuss how this signal can be
used to constrain models of the XRB.


  We present the results of Suzaku and Chandra observations of the galaxy
cluster RXC J1053.7+5453 ($z=0.0704$), which contains a radio relic. The radio
relic is located at the distance of $\sim 540$ kpc from the X-ray peak toward
the west. We measured the temperature of this cluster for the first time. The
resultant temperature in the center is $ \sim 1.3$ keV, which is lower than the
value expected from the X-ray luminosity - temperature and the velocity
dispersion - temperature relation. Though we did not find a significant
temperature jump at the outer edge of the relic, our results suggest that the
temperature decreases outward across the relic. Assuming the existence of the
shock at the relic, its Mach number becomes $M \simeq 1.4 $. A possible spatial
variation of Mach number along the relic is suggested. Additionally, a sharp
surface brightness edge is found at the distance of $\sim 160$ kpc from the
X-ray peak toward the west in the Chandra image. We performed X-ray spectral
and surface brightness analyses around the edge with Suzaku and Chandra data,
respectively. The obtained surface brightness and temperature profiles suggest
that this edge is not a shock but likely a cold front. Alternatively, it cannot
be ruled out that thermal pressure is really discontinuous across the edge. In
this case, if the pressure across the surface brightness edge is in
equilibrium, other forms of pressure sources, such as cosmic-rays, are
necessary. We searched for the non-thermal inverse Compton component in the
relic region. Assuming the photon index $ \Gamma = 2.0$, the resultant upper
limit of the flux is $1.9 \times 10^{-14} {\rm erg \ s^{-1} \ cm^{-2}}$ for
$4.50 \times 10^{-3} {\rm \ deg^{2}}$ area in the 0.3-10 keV band, which
implies that the lower limit of magnetic field strength becomes $ 0.7 {\rm \
\mu G}$.


  We present a study of hierarchical structure in the Perseus molecular cloud,
from the scale of the entire cloud ($\gtrsim$10 pc) to smaller clumps ($\sim$1
pc), cores ($\sim$0.05-0.1 pc), envelopes ($\sim$300-3000 AU) and protostellar
objects ($\sim$15 AU). We use new observations from the Submillimeter Array
(SMA) large project "Mass Assembly of Stellar Systems and their Evolution with
the SMA (MASSES)" to probe the envelopes, and recent single-dish and
interferometric observations from the literature for the remaining scales. This
is the first study to analyze hierarchical structure over five scales in the
same cloud complex. We compare the number of fragments with the number of Jeans
masses in each scale to calculate the Jeans efficiency, or the ratio of
observed to expected number of fragments. The velocity dispersion is assumed to
arise either from purely thermal motions, or from combined thermal and
non-thermal motions inferred from observed spectral line widths. For each
scale, thermal Jeans fragmentation predicts more fragments than observed,
corresponding to inefficient thermal Jeans fragmentation. For the smallest
scale, thermal plus non-thermal Jeans fragmentation also predicts too many
protostellar objects. However at each of the larger scales thermal plus
non-thermal Jeans fragmentation predicts fewer than one fragment, corresponding
to no fragmentation into envelopes, cores, and clumps. Over all scales, the
results are inconsistent with complete Jeans fragmentation based on either
thermal or thermal plus non-thermal motions. They are more nearly consistent
with inefficient thermal Jeans fragmentation, where the thermal Jeans
efficiency increases from the largest to the smallest scale.


  Graph neural networks (GNN) have been shown to provide substantial
performance improvements for atomistic material representation and modeling
compared with descriptor-based machine learning models. While most existing GNN
models for atomistic predictions are based on atomic distance information, they
do not explicitly incorporate bond angles, which are critical for
distinguishing many atomic structures. Furthermore, many material properties
are known to be sensitive to slight changes in bond angles. We present an
Atomistic Line Graph Neural Network (ALIGNN), a GNN architecture that performs
message passing on both the interatomic bond graph and its line graph
corresponding to bond angles. We demonstrate that angle information can be
explicitly and efficiently included, leading to improved performance on
multiple atomistic prediction tasks. We ALIGNN models for predicting 52
solid-state and molecular properties available in the JARVIS-DFT, Materials
project, and QM9 databases. ALIGNN can outperform some previously reported GNN
models on atomistic prediction tasks by up to 85% in accuracy with better or
comparable model training speed.


  Although extensively investigated, the capacity of the two-hop half-duplex
(HD) relay channel is not fully understood. In particular, a capacity
expression which can be evaluated straightforwardly is not available and an
explicit coding scheme which achieves the capacity is not known either. In this
paper, we derive a new expression for the capacity of the two-hop HD relay
channel based on a simplified converse. Compared to previous results, this
capacity expression can be easily evaluated. Moreover, we propose an explicit
coding scheme which achieves the capacity. To achieve the capacity, the relay
does not only send information to the destination by transmitting
information-carrying symbols but also with the zero symbols resulting from the
relay's silence during reception. As examples, we compute the capacities of the
two-hop HD relay channel for the cases when the source-relay and
relay-destination links are both binary-symmetric channels (BSCs) and additive
white Gaussian noise (AWGN) channels, respectively, and numerically compare the
capacities with the rates achieved by conventional relaying where the relay
receives and transmits in a codeword-by-codeword fashion and switches between
reception and transmission in a strictly alternating manner. Our numerical
results show that the capacities of the two-hop HD relay channel for BSC and
AWGN links are significantly larger than the rates achieved with conventional
relaying.


  Recently, the O(alpha) and O(alpha^3 ln(alpha)) radiative corrections to the
orthopositronium lifetime have been presented in closed analytical form, in
terms of basic irrational numbers that can be evaluated numerically to
arbitrary precision [Phys. Rev. Lett. 101, 193401 (2008)]. Here, we present the
details of this calculation and reveal the nature of these new constants. We
also list explicit transformation formulas for generalized polylogarithms of
weight four, which may be useful for other applications.


  Network-valued data are encountered in a wide range of applications and pose
challenges in learning due to their complex structure and absence of vertex
correspondence. Typical examples of such problems include classification or
grouping of protein structures and social networks. Various methods, ranging
from graph kernels to graph neural networks, have been proposed that achieve
some success in graph classification problems. However, most methods have
limited theoretical justification, and their applicability beyond
classification remains unexplored. In this work, we propose methods for
clustering multiple graphs, without vertex correspondence, that are inspired by
the recent literature on estimating graphons -- symmetric functions
corresponding to infinite vertex limit of graphs. We propose a novel graph
distance based on sorting-and-smoothing graphon estimators. Using the proposed
graph distance, we present two clustering algorithms and show that they achieve
state-of-the-art results. We prove the statistical consistency of both
algorithms under Lipschitz assumptions on the graph degrees. We further study
the applicability of the proposed distance for graph two-sample testing
problems.


  Knowledge Graph (KG) alignment is to discover the mappings (i.e., equivalent
entities, relations, and others) between two KGs. The existing methods can be
divided into the embedding-based models, and the conventional reasoning and
lexical matching based systems. The former compute the similarity of entities
via their cross-KG embeddings, but they usually rely on an ideal supervised
learning setting for good performance and lack appropriate reasoning to avoid
logically wrong mappings; while the latter address the reasoning issue but are
poor at utilizing the KG graph structures and the entity contexts. In this
study, we aim at combining the above two solutions and thus propose an
iterative framework named PRASE which is based on probabilistic reasoning and
semantic embedding. It learns the KG embeddings via entity mappings from a
probabilistic reasoning system named PARIS, and feeds the resultant entity
mappings and embeddings back into PARIS for augmentation. The PRASE framework
is compatible with different embedding-based models, and our experiments on
multiple datasets have demonstrated its state-of-the-art performance.


  In this work, we study the behavior of Brazilian politicians and political
parties with the help of clustering algorithms for signed social networks. For
this purpose, we extract and analyze a collection of signed networks
representing voting sessions of the lower house of Brazilian National Congress.
We process all available voting data for the period between 2011 and 2016, by
considering voting similarities between members of the Congress to define
weighted signed links. The solutions obtained by solving Correlation Clustering
(CC) problems are the basis for investigating deputies voting networks as well
as questions about loyalty, leadership, coalitions, political crisis, and
social phenomena such as mediation and polarization.


  Fast multipole methods have O(N) complexity, are compute bound, and require
very little synchronization, which makes them a favorable algorithm on
next-generation supercomputers. Their most common application is to accelerate
N-body problems, but they can also be used to solve boundary integral
equations. When the particle distribution is irregular and the tree structure
is adaptive, load-balancing becomes a non-trivial question. A common strategy
for load-balancing FMMs is to use the work load from the previous step as
weights to statically repartition the next step. The authors discuss in the
paper another approach based on data-driven execution to efficiently tackle
this challenging load-balancing problem. The core idea consists of breaking the
most time-consuming stages of the FMMs into smaller tasks. The algorithm can
then be represented as a Directed Acyclic Graph (DAG) where nodes represent
tasks, and edges represent dependencies among them. The execution of the
algorithm is performed by asynchronously scheduling the tasks using the QUARK
runtime environment, in a way such that data dependencies are not violated for
numerical correctness purposes. This asynchronous scheduling results in an
out-of-order execution. The performance results of the data-driven FMM
execution outperform the previous strategy and show linear speedup on a
quad-socket quad-core Intel Xeon system.


  The crystal structure of MoS$_2$ with strong covalent bonds in plane and weak
Van der Waals interactions out of plane gives rise to interesting properties
for applications such as solid lubrication, optoelectronics, and catalysis,
which can be enhanced by transition-metal doping. However, the mechanisms for
improvement and even the structure of the doped material can be unclear, which
we address with theoretical calculations. Building on our previous work on
Ni-doping of the bulk 2H phase, now we compare to polytypes (1H monolayer and
3R bulk), to determine favorable sites for Ni and the doping effect on
structure, electronic properties, and the layer dissociation energy. The most
favorable intercalation/adatom sites are tetrahedral intercalation for 3R (like
2H) and Mo-atop for 1H. The relative energies indicate a possibility of phase
change from 2H to 3R with substitution of Mo or S. We find structural and
electronic properties that can be used to identify the doping sites, including
metallic behavior in Mo-substituted 3R and 2H, and in-gap states for Mo- and
S-substituted 1H, which could have interesting optoelectronic applications. We
observe a large enhancement in the interlayer interactions of Ni-doped MoS$_2$,
opposite to the effect of other transition metals. For lubrication
applications, this increased layer dissociation energy could be the mechanism
of low wear. Our systematic study shows the effect of doping concentration and
we extrapolate to the low-doping limit. This work gives insight into the
previously unclear structure of Ni-doped MoS$_2$ and how it can be detected
experimentally, the relation of energy and structures of doped monolayers and
bulk systems, the electronic properties under doping, and the effect of doping
on interlayer interactions.


  Robust position reconstruction is paramount for enabling discoveries in
astroparticle physics as backgrounds are significantly reduced by only
considering interactions within the fiducial volume. In this work, we present
for the first time a method for position reconstruction using a Bayesian
network which provides per interaction uncertainties. We demonstrate the
utility of this method with simulated data based on the XENONnT detector
design, a dual-phase xenon time-projection chamber, as a proof-of-concept. The
network structure includes variables representing the 2D position of the
interaction within the detector, the number of electrons entering the gaseous
phase, and the hits measured by each sensor in the top array of the detector.
The precision of the position reconstruction (difference between the true and
expectation value of position) is comparable to the state-of-the-art methods --
an RMS of 0.69 cm, ~0.09 of the sensor spacing, for the inner part of the
detector (<60 cm) and 0.98 cm, ~0.12 of the sensor spacing, near the wall of
the detector (>60 cm). More importantly, the uncertainty of each interaction
position was directly computed, which is not possible with other reconstruction
methods. The method found a median 3-$\sigma$ confidence region of 11 cm$^2$
for the inner part of the detector and 21 cm$^2$ near the wall of the detector.
We found the Bayesian network framework to be well suited to the problem of
position reconstruction. The performance of this proof-of-concept, even with
several simplifying assumptions, shows that this is a promising method for
providing per interaction uncertainty, which can be extended to energy
reconstruction and signal classification.


  We discuss arguments both in favor of and against dark matter. With the
repeated failure of experiment to date to detect dark matter we discuss what
could be done instead, and to this end look for clues in the data themselves.
We identify various regularities in galactic rotation curve data that correlate
the total gravitational potential with luminous matter rather than dark matter.
We identify a contribution to galactic rotation curves coming from the rest of
the visible Universe, and suggest that dark matter is just an attempt to
describe this global effect in terms of standard local Newtonian gravity within
galaxies. Thus the missing mass is not missing at all -- it has been hiding in
plain sight all along as the rest of the visible mass in the Universe.


  We study a scalar field with non-minimal kinetic coupling to itself and to
the curvature. The slow rolling conditions allowing an inflationary background
have been found. The quadratic and Higgs type potentials have been considered,
and the corresponding values for the scalar fields at the end of inflation
allows to recover the connection with particle physics.


  The performance of gradient methods has been considerably improved by the
introduction of delayed parameters. After two and a half decades, the revealing
of second-order information has recently given rise to the Cauchy-based methods
with alignment, which reduce asymptotically the search spaces in smaller and
smaller dimensions. They are generally considered as the state of the art of
gradient methods. This paper reveals the spectral properties of minimal
gradient and asymptotically optimal steps, and then suggests three fast methods
with alignment without using the Cauchy step. The convergence results are
provided, and numerical experiments show that the new methods provide
competitive and more stable alternatives to the classical Cauchy-based methods.
In particular, alignment gradient methods present advantages over the Krylov
subspace methods in some situations, which makes them attractive in practice.


  We investigate conditions in order to decide whether a given sequence of real
numbers represents expected maxima or expected ranges. The main result provides
a novel necessary and sufficient condition, relating an expected maxima
sequence to a translation of a Bernstein function through its
L\'{e}vy-Khintchine representation.
  Key words and phrases: expected maxima; expected ranges; Bernstein functions,
L\'{e}vy-Khintchine representation, order statistics.


  Let $G$ be a finite group. For all $a \in \Z$, such that $(a,|G|)=1$, the
function $\rho_a: G \to G$ sending $g$ to $g^a$ defines a permutation of the
elements of $G$. Motivated by a recent generalization of Zolotarev's proof of
classic quadratic reciprocity, due to Duke and Hopkins, we study the signature
of the permutation $\rho_a$. By introducing the group of conjugacy equivariant
maps and the symmetric difference method on groups, we exhibit an integer
$d_{G}$ such that $\text{sgn}(\rho_a)=(\frac{d_G}{a})$ for all $G$ in a large
class of groups, containing all finite nilpotent and odd order groups.


  Energy systems resilience is becoming increasingly important as the frequency
of major grid outages increases. In this work, we present a methodology to
optimize a behind-the-meter distributed energy resource system to sustain a
site's critical loads during a pre-defined utility outage period. With the
fixed system design, we then propose an outage simulation approach to estimate
the resilience potential of the DER system to sustain loads beyond the fixed
outage period - a yearlong resilience performance analysis. We apply
statistical analysis to assess the system's resilience performance over a
broader parametric problem space on an hourly, monthly, and yearly basis. We
present a case study to demonstrate the impact of the pre-defined outage period
on the resilience performance of the system. The case study shows that the
probability of surviving a random outage of a given duration changes from 20
percent to 95 percent when the outage is modeled for a weekday instead of a
weekend for the case study building.


  We consider first passage percolation on sparse random graphs with prescribed
degree distributions and general independent and identically distributed edge
weights assumed to have a density. Assuming that the degree distribution
satisfies a uniform X^2\log{X}-condition, we analyze the asymptotic
distribution for the minimal weight path between a pair of typical vertices, as
well the number of edges on this path or hopcount.
  The hopcount satisfies a central limit theorem where the norming constants
are expressible in terms of the parameters of an associated continuous-time
branching process. Centered by a multiple of \log{n}, where the constant is the
inverse of the Malthusian rate of growth of the associated branching process,
the minimal weight converges in distribution. The limiting random variable
equals the sum of the logarithms of the martingale limits of the branching
processes that measure the relative growth of neighborhoods about the two
vertices, and a Gumbel random variable, and thus shows a remarkably universal
behavior.
  The proofs rely on a refined coupling between the shortest path problems on
these graphs and continuous-time branching processes, and on a Poisson point
process limit for the potential closing edges of shortest-weight paths between
the source and destination.
  The results extend to a host of related random graph models, ranging from
random r-regular graphs, inhomogeneous random graphs and uniform random graphs
with a prescribed degree sequence.


  We review recent progress in taking the large dimension limit of Einstein's
equations. Most of our analysis is classical in nature and concerns situations
where there is a black hole horizon although we briefly discuss various
extensions that include quantum gravitational effects. The review consists of
two main parts: the first a discussion of general aspects of black holes and
effective membrane theories in this large dimension limit, and the second a
series of applications of this limit to interesting physical problems. The
first part includes a discussion of quasinormal modes which leads naturally
into a description of effective hydrodynamic-like equations that describe the
near horizon geometry. There are two main approaches to these effective
theories -- a fully covariant approach and a partially gauge-fixed one -- which
we discuss in relation to each other. In the second part we divide the
applications up into three main categories: the Gregory-Laflamme instability,
black hole collisions and mergers, and the anti-de Sitter/conformal field
theory correspondence (AdS/CFT). AdS/CFT posits an equivalence between a
gravitational theory and a strongly interacting field theory, allowing us to
extend our spectrum of applications to problems in hydrodynamics, condensed
matter physics, and nuclear physics. A final, shorter part of the review
describes further promising directions where there have been, as yet, few
published research articles.


  This paper introduces intermittent learning - the goal of which is to enable
energy harvested computing platforms capable of executing certain classes of
machine learning tasks effectively and efficiently. We identify unique
challenges to intermittent learning relating to the data and application
semantics of machine learning tasks, and to address these challenges, we devise
1) an algorithm that determines a sequence of actions to achieve the desired
learning objective under tight energy constraints, and 2) propose three
heuristics that help an intermittent learner decide whether to learn or discard
training examples at run-time which increases the energy efficiency of the
system. We implement and evaluate three intermittent learning applications that
learn the 1) air quality, 2) human presence, and 3) vibration using solar, RF,
and kinetic energy harvesters, respectively. We demonstrate that the proposed
framework improves the energy efficiency of a learner by up to 100% and cuts
down the number of learning examples by up to 50% when compared to
state-of-the-art intermittent computing systems that do not implement the
proposed intermittent learning framework.


  We propose a spin valve that is based on van der Waals antiferromagnetism and
fully electrically controlled. The device is composed of two antiferromagnetic
terminals that allow for vertical bias control and a linked central scattering
potential region. The magnetoresistance varies significantly when the bias
orientations in two terminals are switched from parallel to antiparallel
because this switch induces a mismatch of the bands for the same spin
projection in different parts of the system. It is shown from density
functional calculations that bilayer graphene encapsulated by two atomic layers
of Cr$_2$Ge$_2$Te$_6$ provides a material platform to realize the
antiferromagnetism, which is robust against the required vertical electric
fields.


  We study numerically the formation of entanglement clusters across the
many-body localization phase transition. We observe a crossover from strong
many-body entanglement in the ergodic phase to weak local correlations in the
localized phase, with contiguous clusters throughout the phase diagram.
Critical states close to the transition have a structure compatible with
fractal or multiscale-entangled states, characterized by entanglement at
multiple levels: small strongly entangled clusters are weakly entangled
together to form larger clusters. The critical point therefore features
subthermal entanglement and a power-law distributed cluster size, while the
localized phase presents an exponentially decreasing cluster distribution.
These results are consistent with some of the recently proposed
phenomenological renormalization-group schemes characterizing the many-body
localized critical point, and may serve to constrain other such schemes.


  The first aim of this article is to give information about the algebraic
properties of alternate bases $\boldsymbol{\beta}=(\beta_0,\dots,\beta_{p-1})$
determining sofic systems. We show that a necessary condition is that the
product $\delta=\prod_{i=0}^{p-1}\beta_i$ is an algebraic integer and all of
the bases $\beta_0,\ldots,\beta_{p-1}$ belong to the algebraic field ${\mathbb
Q}(\delta)$. On the other hand, we also give a sufficient condition: if
$\delta$ is a Pisot number and $\beta_0,\ldots,\beta_{p-1}\in {\mathbb
Q}(\delta)$, then the system associated with the alternate base
$\boldsymbol{\beta}=(\beta_0,\dots,\beta_{p-1})$ is sofic. The second aim of
this paper is to provide an analogy of Frougny's result concerning
normalization of real bases representations. We show that given an alternate
base $\boldsymbol{\beta}=(\beta_0,\dots,\beta_{p-1})$ such that $\delta$ is a
Pisot number and $\beta_0,\ldots,\beta_{p-1}\in {\mathbb Q}(\delta)$, the
normalization function is computable by a finite B\"uchi automaton, and
furthermore, we effectively construct such an automaton. An important tool in
our study is the spectrum of numeration systems associated with alternate
bases. The spectrum of a real number $\delta>1$ and an alphabet $A\subset
{\mathbb Z}$ was introduced by Erd\H{o}s et al. For our purposes, we use a
generalized concept with $\delta\in{\mathbb C}$ and $A\subset{\mathbb C}$ and
study its topological properties.


  We explored the effects of relative motion on the excitation of
surface-plasmon-polariton (SPP) waves guided by the planar interface of a metal
film and a dielectric slab, both materials being isotropic and homogeneous.
Electromagnetic phasors in moving and non-moving reference frames were related
directly using the corresponding Lorentz transformations. Our numerical studies
revealed that, in the case of a uniformly moving dielectric slab, the angle of
incidence for SPP-wave excitation is highly sensitive to (i) the ratio $\beta$
of the speed of motion to speed of light in free space and (ii) the direction
of motion. When the direction of motion is parallel to the plane of incidence,
the SPP wave is excited by $p$-polarized (but not $s$-polarized) incident plane
waves for low and moderate values of $\beta$, while at higher values of $\beta$
the total reflection regime breaks down. When the direction of motion is
perpendicular to the plane of incidence, the SPP wave is excited by
$p$-polarized incident plane waves for low values of $\beta$, but $s$-polarized
incident plane waves at moderate values of $\beta$, while at higher values of
$\beta$ the SPP wave is not excited. In the case of a uniformly moving metal
film, the sensitivity to $\beta$ and the direction of motion is less obvious.


  Two possible reasons for the narrow peak observation in the invariant mass
spectrum of the pK^0 close to 1.54 GeV/c^2


  Optical imaging beyond the diffraction limit was one of the primary
motivations for negative-index metamaterials, resulting in Pendry's perfect
lens and the more attainable superlens. While these approaches offer
sub-diffractional resolution, they do not provide a mechanism for magnification
of the image. Hyperbolic (or indefinite-permittivity) metamaterials have been
theoretically considered and experimentally demonstrated to provide
simultaneously subdiffractive imaging and magnification; however, they are
plagued with low efficiency and complex fabrication. In this work, we present
theoretical and experimental studies of near-field optical imaging through a
flat slab of the low-loss, natural hyperbolic material, hexagonal boron nitride
(hBN). This thin hBN layer exhibits wavelength-dependent multifunctional
operations, offering both an enhanced near-field imaging of single buried
objects with down to lambda/32 resolution (0.4 um at lambda=12.8 um), as well
as enabling an enlarged reconstruction of the geometric outline of the
investigated objects. Both the excellent resolution and the multifunctional
operation can be explained based on the volume-confined, wavelength-dependent
propagation angle of Type I hyperbolic polaritons. Our results provide both the
understanding of near-field imaging performance through this natural hyperbolic
media, as well as inspire their exciting potential for guiding and sensing of
light at an extreme sub-diffractional scale.


  We present Diffusion Model Patching (DMP), a simple method to boost the
performance of pre-trained diffusion models that have already reached
convergence, with a negligible increase in parameters. DMP inserts a small,
learnable set of prompts into the model's input space while keeping the
original model frozen. The effectiveness of DMP is not merely due to the
addition of parameters but stems from its dynamic gating mechanism, which
selects and combines a subset of learnable prompts at every step of the
generative process (e.g., reverse denoising steps). This strategy, which we
term "mixture-of-prompts", enables the model to draw on the distinct expertise
of each prompt, essentially "patching" the model's functionality at every step
with minimal yet specialized parameters. Uniquely, DMP enhances the model by
further training on the same dataset on which it was originally trained, even
in a scenario where significant improvements are typically not expected due to
model convergence. Experiments show that DMP significantly enhances the
converged FID of DiT-L/2 on FFHQ 256x256 by 10.38%, achieved with only a 1.43%
parameter increase and 50K additional training iterations.


  Let $X$ be a proper CAT(0) space and let $G$ be a cocompact group of
isometries of $X$ which acts properly discontinuously. Charney and Sultan
constructed a quasi-isometry invariant boundary for proper CAT(0) spaces which
they called the contracting boundary. The contracting boundary imitates the
Gromov boundary for $\delta$-hyperbolic spaces. We will make this comparison
more precise by establishing some well known results for the Gromov boundary in
the case of the contracting boundary. We show that the dynamics on the
contracting boundary is very similar to that of a $\delta$-hyperbolic group. In
particular the action of $G$ on $\partial_cX$ is minimal if $G$ is not
virtually cyclic. We also establish a uniform convergence result that is
similar to the $\pi$-convergence of Papasoglu and Swenson and as a consequence
we obtain a new north-south dynamics result on the contracting boundary. We
additionally investigate the topological properties of the contracting boundary
and we find necessary and sufficient conditions for $G$ to be
$\delta$-hyperbolic. We prove that if the contracting boundary is compact,
locally compact or metrizable, then $G$ is $\delta$-hyperbolic.


  The Heisenberg, interaction, and Schr\"odinger pictures of motion are
considered in Lagrangian (canonical) quantum field theory. The equations of
motion (for state vectors and field operators) are derived for arbitrary
Lagrangians which are polynomial or convergent power series in field operators
and their first derivatives. The general links between different time-dependent
pictures of motion are derived. It is pointed that all of them admit covariant
formulation, similar to the one of interaction picture. A new picture, called
the momentum picture, is proposed. It is a 4-dimensional analogue of the
Schr\"odinger picture of quantum mechanics as in it the state vectors are
spacetime-dependent, while the field operators are constant relative to the
spacetime. The equations of motion in momentum picture are derived and
partially discussed. In particular, the ones for the field operators turn to be
of algebraic type. The general idea of covariant pictures of motion is
presented. The equations of motion in these pictures are derived.


  Four different combinations of $^{96}_{44}$Ru and $^{96}_{40}$Zr nuclei, both
as projectile and target, were investigated at the same bombarding energy of
400$A$ MeV using a $4 \pi$ detector. The degree of isospin mixing between
projectile and target nucleons is mapped across a large portion of the phase
space using two different isospin-tracer observables, the number of measured
protons and the ${\rm t}/^{3}{\rm He}$ yield ratio. The experimental results
show that the global equilibrium is not reached even in the most central
collisions. Quantitative measures of stopping and mixing are extracted from the
data. They are found to exhibit a quite strong sensitivity to the in-medium
(n,n) cross section used in microscopic transport calculations.


  We present calculations of the electronic and thermal transport properties of
graphene antidot lattices with a finite length along the transport direction.
The calculations are based on a single orbital tight-binding model and the
Brenner potential. We show that both electronic and thermal transport
properties converge fast toward the bulk limit with increasing length of the
lattice: only a few repetitions (~6) of the fundamental unit cell are required
to recover the electronic band gap of the infinite lattice as a transport gap
for the finite lattice. We investigate how different antidot shapes and sizes
affect the thermoelectric properties. The resulting thermoelectric figure of
merit, ZT, can exceed 0.25, and it is highly sensitive to the atomic
arrangement of the antidot edges. Specifically, hexagonal holes with pure
zigzag edges lead to an order-of-magnitude smaller ZT as compared to pure
armchair edges. We explain this behavior as a consequence of the localization
of states, which predominantly occurs for zigzag edges, and of an increased
splitting of the electronic minibands, which reduces the power factor.


  We present the first determination of the abundance ratios of $^{13}$C
substitutions of cyanoacetylene (HC$_{3}$N),
[H$^{13}$CCCN]:[HC$^{13}$CCN]:[HCC$^{13}$CN] in Titan's atmosphere measured
using millimeter-wave spectra obtained by the Atacama Large
Millimeter-submillimeter Array. To compare the line intensities precisely,
datasets which include multiple molecular lines were extracted to suppress
effects of Titan's environmental conditions and observation settings. The
[HC$^{13}$CCN]:[HCC$^{13}$CN] and [H$^{13}$CCCN]:[HCC$^{13}$CN}] ratios were
obtained from 12 and 1 selected datasets, respectively. As a result, nearly the
uniform [H$^{13}$CCCN]:[HC$^{13}$CCN]:[HCC$^{13}$CN] abundance ratios as 1.17
($\pm$0.20) : 1.09 ($\pm$0.25) : 1 (1$\sigma$) were derived, whereas previously
reported ratios for interstellar medium (ISM) have shown large anomalies that
may be caused by $^{13}$C concentrations in precursors. The result obtained
here suggests that $^{13}$C concentration processes suggested in the ISM
studies do not work effectively on precursors of HC$_{3}$N and HC$_{3}$N itself
due to Titan's high atmospheric temperature and/or depletion of both $^{13}$C
and $^{13}$C$^+$.


  Multiparticle azimuthal correlations of prompt D$^0$ mesons are measured in
PbPb collisions at a nucleon-nucleon center-of-mass energy of
$\sqrt{s_\mathrm{NN}} =$ 5.02 TeV. For the first time, a four-particle cumulant
method is used to extract the second Fourier coefficient of the azimuthal
distribution ($v_2$) of D$^0$ mesons as a function of event centrality and the
D$^0$ transverse momentum. The ratios of the four-particle $v_2$ values to
previously measured two-particle cumulant results provide direct experimental
access to event-by-event fluctuations of charm quark azimuthal anisotropies.
These ratios are also found to be comparable to those of inclusive charged
particles in the event. However, hints of deviations are seen in the most
central and peripheral collisions. To investigate the origin of flow
fluctuations in the charm sector, these measurements are compared with models
implementing fluctuations of charm quark energy loss via collisional or
radiative processes in the quark-gluon plasma. These models cannot
quantitatively describe the data over the full transverse momentum and
centrality ranges, although the calculations with collisional energy loss
provide a better description of the data.


  Let $k \ge 2$ and $s$ be positive integers, and let $n$ be a large positive
integer subject to certain local conditions. We prove that if $s \ge k^2+k+1$
and $\theta > 31/40$, then $n$ can be expressed as a sum $p_1^k + \dots +
p_s^k$, where $p_1, \dots, p_s$ are primes with $|p_j - (n/s)^{1/k}| \le
n^{\theta/k}$. This improves on earlier work by Wei and Wooley and by Huang who
proved similar theorems when $\theta > 19/24$.


  In 1984 Rohrlich proved a modular analogue of Jensen's formula. Under certain
conditions, the Rohrlich-Jensen formula expresses an integral of the log-norm
$\log \Vert f \Vert$ of a $\text{\rm PSL}(2,\ZZ)$ modular form $f$ in terms of
the Dedekind Delta function evaluated at the divisor of $f$. Recently,
Bringmann-Kane re-interpreted the Rohrlich-Jensen formula as evaluating a
regularized inner product of $\log \Vert f \Vert$ and extended the result to
compute a regularized inner product of $\log \Vert f \Vert$ with what amounts
to powers of the Hauptmoduli of $\text{\rm PSL}(2,\ZZ)$. In the present
article, we revisit the Rohrlich-Jensen formula and prove that it can be viewed
as a regularized inner product of special values of two Poincar\'e series, one
of which is the Niebur-Poincar\'e series and the other is the resolvent kernel
of the Laplacian. The regularized inner product can be seen as a type of
Maass-Selberg relation. In this form, we develop a Rohrlich-Jensen formula
associated to any Fuchsian group $\Gamma$ of the first kind with one cusp by
employing a type of Kronecker limit formula associated to the resolvent kernel.
We present two examples of our main result: First, when $\Gamma$ is the full
modular group $\text{\rm PSL}(2,\ZZ)$, thus reproving the theorems from
\cite{BK19}; and second when $\Gamma$ is an Atkin-Lehner group
$\Gamma_{0}(N)^+$, where explicit computations are given for certain genus
zero, one and two levels.


  We obtain exact solutions of the (1+1) dimensional Klein Gordon equation with
linear vector and scalar potentials in the presence of a minimal length.
Algebraic approach to the problem has also been studied.


  The main motivation of the present work is to investigate the asymptotic
behavior as $\kappa \to 0+$ of multiradial Schramm-Loewner evolution,
SLE$_\kappa$. We show that this process with the common parameterization
satisfies a finite-time large deviation principle (LDP) in the Hausdorff metric
with non-negative rate function, the multiradial Loewner energy. We also
characterize the large-time behavior of curves with finite energy and zero
energy (whose driving functions correspond to the trigonometric Calogero-Moser
system).
  The first half of this article is of independent interest regardless of SLE
theory. It is devoted to proving a finite-time LDP for Dyson Brownian motion on
the circle for a fixed number $n$ of particles as the coupling parameter
$\beta=8/\kappa$ tends to $\infty$. To our knowledge, in the literature large
deviations of Dyson Brownian motion has only been considered for fixed $\beta$
and as $n$ tends to $\infty$. While the non-Lipschitz drift precludes the
application of the Freidlin-Wentzell theorem, we show that the rate function
has the same form as in Freidlin-Wentzell theory for diffusions with uniformly
Lipschitz drift.
  In the second half of this article, we turn to proving an LDP for multiradial
SLE$_\kappa$. Here, the main technical difficulty is that the SLE$_\kappa$
curves have a common target point, preventing the usual configurational, or
global, approach. Instead, we make careful use of the contraction principle
from the LDP for Dyson Brownian motion (proven in the first part of the
article), combined with topological results in Loewner theory: we show that
finite-energy multiradial Loewner hulls are always disjoint unions of simple
curves, except possibly at their common endpoint. A key to this is obtained
from a derivative estimate for the radial Loewner map in terms of the energy of
its driving function.


  Large model training has been using recomputation to alleviate the memory
pressure and pipelining to exploit the parallelism of data, tensor, and
devices. The existing recomputation approaches may incur up to 40% overhead
when training real-world models, e.g., the GPT model with 22B parameters. This
is because they are executed on demand in the critical training path. In this
paper, we design a new recomputation framework, Lynx, to reduce the overhead by
overlapping the recomputation with communication occurring in training
pipelines. It consists of an optimal scheduling algorithm (OPT) and a
heuristic-based scheduling algorithm (HEU). OPT achieves a global optimum but
suffers from a long search time. HEU was designed based on our observation that
there are identical structures in large DNN models so that we can apply the
same scheduling policy to all identical structures. HEU achieves a local
optimum but reduces the search time by 99% compared to OPT. Our comprehensive
evaluation using GPT models with 1.3B-20B parameters shows that both OPT and
HEU outperform the state-of-the-art recomputation approaches (e.g., Megatron-LM
and Checkmake) by 1.02-1.53x. HEU achieves a similar performance as OPT with a
search time of 0.16s on average.


  The cosmological origin of $\gamma$-ray bursts (GRBs) is now commonly
accepted and, according to several models for the central engine, GRB sources
should also emit at the same time gravitational waves bursts (GWBs). We have
performed two correlation searches between the data of the resonant
gravitational wave detector AURIGA and GRB arrival times collected in the BATSE
4B catalog. No correlation was found and an upper limit \bbox{$h_{\text{RMS}}
\leq 1.5 \times 10^{-18}$} on the averaged amplitude of gravitational waves
associated with $\gamma$-ray bursts has been set for the first time.


  We analyze how a star network topology shapes the dynamics of coupled
CO\textsubscript{2} lasers with an intracavity electro-optic modulator that
exhibit bistability. Such a network supports spreading and stationary
activation patterns. In particular, we observe an activation spreading where
the activated periphery turns on the center element, an activated center which
drifts the periphery into the active region and an activation of the whole
system from the passive into the active region. Pinned activation, namely
activation localized only in the center or the peripheral elements is also
found. Similar dynamical behavior has been observed recently in complex
networks of coupled bistable chemical reactions. The current work aims at
revealing those phenomena in laser arrays, giving emphasis on the essential
role of the coupling structure in fashioning the overall dynamics.


  A geometric graph \G is a simple graph drawn in the plane, on points in
general position, with straight-line edges. We call \G a geometric realization
of the underlying abstract graph G. A geometric homomorphism from \G to \H is a
vertex map that preserves adjacencies and crossings (but not necessarily
non-adjacencies or non-crossings). Geometric homomorphisms can be used to
define a partial order on the set of isomorphism classes of geometric
realizations of an abstract graph G. In this paper, the homomorphism poset of
K_{3,3} is determined.


  Mobile device hackers often target ambient sensing, human activity
identification, and interior floor mapping. In addition to overt signals like
microphones and cameras, covert channels like WiFi, Bluetooth, and augmented
GPS signal strengths have been employed to gather this information. Until date,
passive, receive-only satellite GPS sensing relied solely on signal strength
and location information. This paper demonstrates that semi-processed GPS data
(39 features) accessible to apps since Android 7 with precise location
permissions can be used as a highly accurate leaky channel for sensing ambient,
recognising human activity, and mapping indoor spaces (99%+ accuracy). This
report describes a longitudinal research that used semi-processed GPS readings
from mobile devices throughout a 40,000 sq. km region for a year. Data was
acquired from aeroplanes, cruise ships, and high-altitude places. To retain
crucial information, we analyse all satellite GPS signals and select the best
characteristics using cross-correlation analysis. Our work, AndroCon, combines
lin-ear discriminant analysis, unscented Kalman filtering, gradient boosting,
and random forest learning to provide an accurate ambient and human activity
sensor. At AndroCon, basic ML algorithms are used for discreet and somewhat
explainable outcomes. We can readily recognise challenging situations, such as
being in a subway, when someone is waving a hand in front of a mobile device,
in front of a stairway, or with others present (not always carrying phones).
This is the most extensive study on satellite GPS-based sensing as of yet.


  A nontrivial element in a group is a generalized torsion element if some
nonempty finite product of its conjugates is the identity. We prove that any
generalized torsion element in a free product of torsion-free groups is
conjugate to a generalized torsion element in some factor group. This implies
that the fundamental group of a compact orientable $3$-manifold $M$ has a
generalized torsion element if and only if the fundamental group of some prime
factor of $M$ has a generalized torsion element. On the other hand, we
demonstrate that there are infinitely many toroidal $3$-manifolds whose
fundamental group has a generalized torsion element, while the fundamental
group of each decomposing piece has no such elements.


  We propose a new methodology to perform mineralogic inversion from wellbore
logs based on a Bayesian linear regression model. Our method essentially relies
on three steps. The first step makes use of Approximate Bayesian Computation
(ABC) and selects from the Bayesian generator a set of candidates-volumes
corresponding closely to the wellbore data responses. The second step gathers
these candidates through a density-based clustering algorithm. A mineral
scenario is assigned to each cluster through direct mineralogical inversion,
and we provide a confidence estimate for each lithological hypothesis. The
advantage of this approach is to explore all possible mineralogy hypotheses
that match the wellbore data. This pipeline is tested on both synthetic and
real datasets.


  Being considered as a prototype for description of oceanic rogue waves (RWs),
the Peregrine breather solution of the nonlinear Schr\"odinger equation (NLS)
has been recently observed and intensely investigated experimentally in
particular within the context of water waves. Here, we report the experimental
results showing the evolution of the Peregrine solution in the presence of wind
forcing in the direction of wave propagation. The results show the persistence
of the breather evolution dynamics even in the presence of strong wind and
chaotic wave field generated by it. Furthermore, we have shown that
characteristic spectrum of the Peregrine breather persists even at the highest
values of the generated wind velocities thus making it a viable characteristic
for prediction of rogue waves.


  Colloidal self-replication represents an exciting research frontier in soft
matter physics. Currently, all reported self-replication schemes involve
coating colloidal particles with stimuli-responsive molecules to allow
switchable interactions. In this paper, we introduce a scheme using
ferromagnetic dipolar colloids and pre-programmed external magnetic fields to
create an autonomous self-replication system. Interparticle dipole-dipole
forces and periodically varying weak-strong magnetic fields cooperate to drive
colloid monomers from the solute onto templates, bind them into replicas, and
dissolve template complexes. We present three general design principles for
autonomous linear replicators, derived from a focused study of a minimalist
sphere-dimer magnetic system in which single binding sites allow formation of
dimeric templates. We show via statistical models and computer simulations that
our system exhibits nonlinear growth of templates and produces nearly
exponential growth (low error rate) upon adding an optimized competing
electrostatic potential. We devise experimental strategies for constructing the
required magnetic colloids based on documented laboratory techniques. We also
present qualitative ideas about building more complex self-replicating
structures utilizing magnetic colloids.


  We prove a local limit theorem for the Euclidian algorithms ; standard,
centred and odd, with any cost function of moderate growth.


  This article discusses the modular representation theory of finite groups of
Lie type from the viewpoint of Broue's abelian defect group conjecture.
  We discuss both the defining characteristic case, the inspiration for
Alperin's weight conjecture, and the non-defining case, the inspiration for
Broue's conjecture. The modular representation theory of general finite groups
is conjectured to behave both like that of finite groups of Lie type in
defining characteristic, and in non-defining characteristic, to a large extent.
  The expected behaviour of modular representation theory of finite groups of
Lie type in defining characteristic is particularly difficult to grasp along
the lines of Broue's conjecture and we raise a new question related to the
change of central character.
  We introduce a degeneration method in the modular representation theory of
finite groups of Lie type in non-defining characteristic. Combined with the
rigidity property of perverse equivalences, this provides a setting for two
variable decomposition matrices, for large characteristic. This should help
make progress towards finding decomposition matrices, an outstanding problem
with few general results beyond the case of general linear groups. This last
part is based on joint work with David Craven and Olivier Dudas.


  In this paper we show that in the case of noncommutative two-tori one gets in
a natural way simple structures which have analogous formal properties as Hopf
algebra structures but with a deformed multiplication on the tensor product.


  The usual, "static" version of the quantum Zeno effect consists in the
hindrance of the evolution of a quantum systems due to repeated measurements.
There is however a "dynamic" version of the same phenomenon, first discussed by
von Neumann in 1932 and subsequently explored by Aharonov and Anandan, in which
a system is forced to follow a given trajectory. A Berry phase appears if such
a trajectory is a closed loop in the projective Hilbert space. A specific
example involving neutron spin is considered and a similar situation with
photon polarization is investigated.


  The quasar 3C 454.3 is a blazar known for its rapid and violent outbursts
seen across the electromagnetic spectrum. Using gamma-ray, X-ray, multi-band
optical, and very long baseline interferometric data we investigate the nature
of two such events that occurred in 2013 and 2014 accompanied by strong
variations in optical polarization, including a 230 degree electric vector
position angle (EVPA) rotation. Our results suggest that a single disturbance
was responsible for both flaring events. We interpret the disturbance as a
shock propagating down the jet. Under this interpretation the 2013-flare
originated most likely due to changes in the viewing angle caused by perhaps a
bent or helical trajectory of the shock upstream of the radio core. The
2014-flare and optical polarization behavior are the result of the shock
exiting the 43 GHz radio core, suggesting that shock crossings are one of the
possible mechanisms for EVPA rotations.


  Consciousness is an explicit outcome of brain activity. However, the link
between consciousness and the material world remains to be explored. We applied
a new logic tool, the non-identity law, to the analysis of the visual dynamics
related to the naturalistic observation of a night-shot still life. We show
that visual awareness possesses a postponed, recurrent out-of-body projection
pathway and that the out-of-body projection is superimposed onto the original,
which is reciprocally verified by vision and touch. This suggests that the
visual system instinctually not only represents the subjective image
(brain-generated imagery) but also projects the image back onto the original or
to a specific place according to the cues of the manipulated afferent messenger
light signaling pathway. This finding provides a foundation for understanding
the subjectivity and intentionality of consciousness from the perspective of
visual awareness and the isomorphic relations between an unknowable original,
private experience, and shareable expression. The result paves the way for
scientific research on consciousness and facilitates the integration of
humanities and natural science.


  A quantitative description of the properties of hot nuclear matter will be
needed for the interpretation of the available and forthcoming astrophysical
data, providing information on the post merger phase of a neutron star
coalescence. We have employed a recently developed theoretical model, based on
a phenomenological nuclear Hamiltonian including two- and three-nucleon
potentials, to study the temperature dependence of average and single-particle
properties of nuclear matter relevant to astrophysical applications. The
possibility to represent the results of microscopic calculations using simple
and yet physically motivated parametrisations of thermal effects, suitable for
use in numerical simulations of astrophysical processes, is also discussed.


  In this Letter, we put forward a resolution to the prolonged ambiguity in
energy band gaps between theory and experiments of fabricated graphene
nanoribbons (GNRs). Band structure calculations using density functional theory
are performed on oxygen passivated GNRs supercells of customized edge
configurations without disturbing the inherent sp2 hybridization of carbon
atoms. Direct band gaps are observed for both zigzag and armchair GNRs,
consistent with the experimental reports. In addition, band gap values of GNRs
scattered about an average value curve for a given crystallographic orientation
are correlated with their width on basis of the edge configurations elucidates
the band gaps in fabricated GNRs. We conclude that edge configurations of GNRs
significantly contribute to band gap formation in addition to its width for a
given crystallographic orientation, and would play a crucial role in band gap
engineering of GNRs for future research works on fabrication of nanoelectronic
devices.


  The JVO ALMA WebQL web service - available through the JVO ALMA FITS archive
- has been upgraded to include legacy data from other telescopes, for example
Nobeyama NRO45M in Japan. The updated server software has been renamed
FITSWebQL. In addition, a standalone desktop version supporting Linux, macOS
and Windows 10 Linux Subsystem (Bash on Windows) is also available for download
from http://jvo.nao.ac.jp/~chris/ .
  The FITSWebQL server enables viewing of even 100GB-large FITS files in a web
browser running on a PC with a limited amount of RAM. Users can interactively
zoom-in to selected areas of interest with the corresponding frequency spectrum
being calculated on the server in near real-time. The client (a browser) is a
JavaScript application built on WebSockets, HTML5, WebGL and SVG.
  There are many challenges when providing a web browser-based real-time FITS
data cube preview service over high-latency low-bandwidth network connections.
The upgraded version tries to overcome the latency issue by predicting user
mouse movements with a Kalman Filter in order to speculatively deliver the
real-time spectrum data at a point where the user is likely to be looking at.
The new version also allows one to view multiple FITS files simultaneously in
an RGB composite mode (NRO45M FUGIN only), where each dataset is assigned one
RGB channel to form a colour image. Spectra from multiple FITS cubes are shown
together too.
  The paper briefly describes main features of FITSWebQL. We also touch on some
of the recent developments, such as an experimental switch from C/C++ to Rust
(see https://www.rust-lang.org/) for improved stability, better memory
management and fearless concurrency, or attempts to display FITS data cubes in
the form of interactive on-demand video streams in a web browser.


  Classification of unlabeled data is usually achieved by supervised learning
from labeled samples. Although there exist many sophisticated supervised
machine learning methods that can predict the missing labels with a high level
of accuracy, they often lack the required transparency in situations where it
is important to provide interpretable results and meaningful measures of
confidence. Body fluid classification of forensic casework data is the case in
point. We develop a new Biclustering Dirichlet Process for Class-assignment
with Random Matrices (BDP-CaRMa), with a three-level hierarchy of clustering,
and a model-based approach to classification that adapts to block structure in
the data matrix. As the class labels of some observations are missing, the
number of rows in the data matrix for each class is unknown. BDP-CaRMa handles
this and extends existing biclustering methods by simultaneously biclustering
multiple matrices each having a randomly variable number of rows. We
demonstrate our method by applying it to the motivating problem, which is the
classification of body fluids based on mRNA profiles taken from crime scenes.
The analyses of casework-like data show that our method is interpretable and
produces well-calibrated posterior probabilities. Our model can be more
generally applied to other types of data with a similar structure to the
forensic data.


  About 50% of all queries on Snapchat app are targeted at finding the right
friend to interact with. Since everyone has a unique list of friends and that
list is not very large (maximum a few thousand), it makes sense to perform this
search locally, on users' devices. In addition, the friend list is already
available for other purposes, such as showing the chat feed, and the latency
savings can be significant by avoiding a server round-trip call. Historically,
we resorted to substring matching, ranking prefix matches at the top of the
result list. Introducing the ability to perform fuzzy search on a
resource-constrained device and in the environment where typo's are prevalent
is both prudent and challenging. In this paper, we describe our efficient and
accurate two-step approach to fuzzy search, characterized by a skip-bigram
retrieval layer and a novel local Levenshtein distance computation used for
final ranking.


  The aim of the present paper is twofold. The first goal is to show that high
resolution angle-resolved photoelectron spectra from cuprates indicate the
presence of string-like excitations of the quasihole excitation in a quantum
antiferromagnet. In order to compare with the experimental intensity plots, we
calculate the spectral function of the t-J and the t-t'-t"-J models within the
self-consistent Born approximation for widely accepted values of the parameters
of these models. The main features of the high resolution photoelectron spectra
are in general agreement with the results based on the above models and can be
understood by considering not only the lowest energy quasiparticle peak but,
also, the higher energy string-like excitations of the hole. The second goal of
the present paper is to make the case that a proper analysis of both the
numerical results obtained from these models and of the experimental results,
suggests a theoretical picture for the internal structure of the
hole-quasiparticle and a string-exchange pairing mechanism due to strong
antiferromagnetic correlations among the background spins. We find that, using
a simple model in which the Hilbert space is restricted to states of only
unbroken strings attached to the holes and in which the holes are connected
with unbroken strings, we can provide a good quantitative description of the
most accurate numerical results. We find that the holes experience an effective
interaction due to a string-exchange mechanism which is characterized by a
rather large string tension and this can provide pairing energy scales much
larger that those suggested by spin-fluctuation mediated pairing models. In
addition, it is argued that such string-exchange interaction tends to bind
holes in a bound state with the $d_{x^2-y^2}$ symmetry.


  We examine the impact of different anisotropic relics on inflation, in
particular the predictions on the density perturbations. These relics can be
the source of the large scale anomalies in the cosmic microwave background.
There are two different types of background relics, one from the matter sector
and the other purely from the metric. Although the angular-dependence of the
statistical anisotropy in both cases are degenerate, the scale-dependence are
observationally distinctive. In addition, we demonstrate that non-Bunch-Davies
vacuum states can extend the statistical anisotropy to much shorter scales, and
leave a scale-dependence that is insensitive to the different backgrounds but
sensitive to the initial quantum state.


  The classical sine-Gordon model is a two-dimensional integrable field theory,
with particle like solutions the so-called solitons. Using its integrability
one can define its quantum version without the process of canonical
quantization. This bootstrap method uses the fundamental propterties of the
model and its quantum features in order to restrict the structure of the
scattering matrix as far as possible. The classical model can be extended with
integrable discontinuities, purely transmitting jump-defects. Then the quantum
version of the extended model can be determined via the bootstrap method again.
But the outcoming quantum theory contains the so-called CDD uncertainity. The
aim of this article is to carry throw the semiclassical approximation in both
the classical and the quantum side of the defect sine-Gordon theory. The CDD
ambiguity can be restricted by comparing the two results. The relation between
the classical and quantum parameters as well as the resoncances appeared in the
spectrum are other objectives.


  We present an alternate proof of the fact that given any 4-coloring of the
plane there exist two points unit distance apart which are identically colored.


  Polstar is a proposed NASA MIDEX space telescope that will provide
high-resolution, simultaneous full-Stokes spectropolarimetry in the far
ultraviolet, together with low-resolution linear polarimetry in the near
ultraviolet. In this white paper, we describe the unprecedented capabilities
this observatory would offer in order to obtain unique information on the
magnetic and plasma properties of the magnetospheres of hot stars. This would
enable a test of the fundamental hypothesis that magnetospheres should act to
rapidly drain angular momentum, thereby spinning the star down, whilst
simultaneously reducing the net mass-loss rate. Both effects are expected to
lead to dramatic differences in the evolution of magnetic vs. non-magnetic
stars.


  Spinal cord injury (SCI) is a devastating incidence leading to permanent
paralysis and loss of sensory-motor functions potentially resulting in the
formation of lesions within the spinal cord. Imaging biomarkers obtained from
magnetic resonance imaging (MRI) scans can predict the functional recovery of
individuals with SCI and help choose the optimal treatment strategy. Currently,
most studies employ manual quantification of these MRI-derived biomarkers,
which is a subjective and tedious task. In this work, we propose (i) a
universal tool for the automatic segmentation of intramedullary SCI lesions,
dubbed \texttt{SCIsegV2}, and (ii) a method to automatically compute the width
of the tissue bridges from the segmented lesion. Tissue bridges represent the
spared spinal tissue adjacent to the lesion, which is associated with
functional recovery in SCI patients. The tool was trained and validated on a
heterogeneous dataset from 7 sites comprising patients from different SCI
phases (acute, sub-acute, and chronic) and etiologies (traumatic SCI, ischemic
SCI, and degenerative cervical myelopathy). Tissue bridges quantified
automatically did not significantly differ from those computed manually,
suggesting that the proposed automatic tool can be used to derive relevant MRI
biomarkers. \texttt{SCIsegV2} and the automatic tissue bridges computation are
open-source and available in Spinal Cord Toolbox (v6.4 and above) via the
\texttt{sct\_deepseg -task seg\_sc\_lesion\_t2w\_sci} and
\texttt{sct\_analyze\_lesion} functions, respectively.


  We consider the problem of learning implicit neural representations (INRs)
for signals on non-Euclidean domains. In the Euclidean case, INRs are trained
on a discrete sampling of a signal over a regular lattice. Here, we assume that
the continuous signal exists on some unknown topological space from which we
sample a discrete graph. In the absence of a coordinate system to identify the
sampled nodes, we propose approximating their location with a spectral
embedding of the graph. This allows us to train INRs without knowing the
underlying continuous domain, which is the case for most graph signals in
nature, while also making the INRs independent of any choice of coordinate
system. We show experiments with our method on various real-world signals on
non-Euclidean domains.


  We present confusion-limited SCUBA-2 450-$\mu$m observations in the
COSMOS-CANDELS region as part of the JCMT Large Program, SCUBA-2 Ultra Deep
Imaging EAO Survey (STUDIES). Our maps at 450 and 850 $\mu$m cover an area of
450 arcmin$^2$. We achieved instrumental noise levels of
$\sigma_{\mathrm{450}}=$ 0.59 mJy beam$^{-1}$ and $\sigma_{\mathrm{850}}=$ 0.09
mJy beam$^{-1}$ in the deepest area of each map. The corresponding confusion
noise levels are estimated to be 0.65 and 0.36 mJy beam$^{-1}$. Above the 4
(3.5) $\sigma$ threshold, we detected 360 (479) sources at 450 $\mu$m and 237
(314) sources at 850 $\mu$m. We derive the deepest blank-field number counts at
450 $\mu$m, covering the flux-density range of 2 to 43 mJy. These are in
agreement with other SCUBA-2 blank-field and lensing-cluster observations, but
are lower than various model counts. We compare the counts with those in other
fields and find that the field-to-field variance observed at 450 $\mu$m at the
$R=6^\prime$ scale is consistent with Poisson noise, so there is no evidence of
strong 2-D clustering at this scale. Additionally, we derive the integrated
surface brightness at 450 $\mu$m down to 2.1 mJy to be $57.3^{+1.0}_{-6.2}$~Jy
deg$^{-2}$, contributing to (41$\pm$4)\% of the 450-$\mu$m extragalactic
background light (EBL) measured by COBE and Planck. Our results suggest that
the 450-$\mu$m EBL may be fully resolved at $0.08^{+0.09}_{-0.08}$~mJy, which
extremely deep lensing-cluster observations and next-generation submillimeter
instruments with large aperture sizes may be able to achieve.


  We propose a manifold matching approach to generative models which includes a
distribution generator (or data generator) and a metric generator. In our
framework, we view the real data set as some manifold embedded in a
high-dimensional Euclidean space. The distribution generator aims at generating
samples that follow some distribution condensed around the real data manifold.
It is achieved by matching two sets of points using their geometric shape
descriptors, such as centroid and $p$-diameter, with learned distance metric;
the metric generator utilizes both real data and generated samples to learn a
distance metric which is close to some intrinsic geodesic distance on the real
data manifold. The produced distance metric is further used for manifold
matching. The two networks are learned simultaneously during the training
process. We apply the approach on both unsupervised and supervised learning
tasks: in unconditional image generation task, the proposed method obtains
competitive results compared with existing generative models; in
super-resolution task, we incorporate the framework in perception-based models
and improve visual qualities by producing samples with more natural textures.
Experiments and analysis demonstrate the feasibility and effectiveness of the
proposed framework.


  We show that warped throats of the Klebanov-Strassler kind, regarded as 5d
flux compactifications on K\"ahler-Einstein manifolds $\bf{X}_5$ describe fully
backreacted solutions of transplanckian axion monodromy. We show that the
asymptotic Klebanov-Tseytlin solution features a 5d axion physically rolling
through its dependence on an spatial coordinate, and traversing arbitrarily
large geodesic distances in field space. The solution includes the backreaction
on the breathing mode of the compactification space and on the vacuum energy,
which yields a novel form of flattening. We establish the description of the
system in terms of an effective 5d theory for the axion, and verify its
validity in transplanckian regimes. In this context, rolling axion monodromy
configurations with limited field space range would correspond, in the
holographic dual field theory, to duality walls, which admit no embedding in
string theory so far. We present an identical realization of transplanckian
axion monodromy in 4d in fluxed version of AdS$_4\times \bf{X}_7$. We speculate
that similar models in which the axion rolls in the time direction naturally
correspond to embedding of the same mechanism in de Sitter vacua, thus
providing a natural arena for large field inflation, and potentially linking
the swampland de Sitter and distance conjectures.


  In order to study the quantum geometry of random surfaces in Liouville
gravity, we propose a definition of geodesic distance associated to a Gaussian
free field on a regular lattice. This geodesic distance is used to numerically
determine the Hausdorff dimension associated to shortest cycles of 2d quantum
gravity on the torus coupled to conformal matter fields, showing agreement with
a conjectured formula by Y. Watabiki. Finally, the numerical tools are put to
test by quantitatively comparing the distribution of lengths of shortest cycles
to the corresponding distribution in large random triangulations.


  New results from the 2010 RHIC low energy program show a substantial
suppression of neutral pions in central Au+Au collisions at both sqrt{s_NN}=39
and 62.4 GeV c.m.s. energies. At high pT the 62.4 GeV and 200 GeV data follow
the same suppression pattern. On the other hand, otherwise successful pQCD
predictions do not describe the 39 GeV data. These observations indicate that
initial state effects may play a dominant role at smaller c.m.s. energies and
at lower pT . The azimuthal dependence of the nuclear modification factor R_AA
is strongly correlated with the (approximately elliptical) geometry of the
overlap region. The dependence of R_AA on the reaction plane, determined up to
pT=20 GeV/c from 2007 high-luminosity sqrt{s_NN}=200 GeV Au+Au data provides
great selectivity among theories, and favours the ASW scenario with AdS/CFT
correspondence over the pQCD-based models.


  Suppose a customer is faced with a sequence of fluctuating prices, such as
for airfare or a product sold by a large online retailer. Given distributional
information about what price they might face each day, how should they choose
when to purchase in order to maximize the likelihood of getting the best price
in retrospect? This is related to the classical secretary problem, but with
values drawn from known distributions. In their pioneering work, Gilbert and
Mosteller [\textit{J. Amer. Statist. Assoc. 1966}] showed that when the values
are drawn i.i.d., there is a thresholding algorithm that selects the best value
with probability approximately $0.5801$. However, the more general problem with
non-identical distributions has remained unsolved.
  In this paper we provide an algorithm for the case of non-identical
distributions that selects the maximum element with probability $1/e$, and we
show that this is tight. We further show that if the observations arrive in a
random order, this barrier of $1/e$ can be broken using a static threshold
algorithm, and we show that our success probability is the best possible for
any single-threshold algorithm under random observation order. Moreover, we
prove that one can achieve a strictly better success probability using more
general multi-threshold algorithms, unlike the non-random-order case. Along the
way, we show that the best achievable success probability for the random-order
case matches that of the i.i.d.\ case, which is approximately $0.5801$, under a
"no-superstars" condition that no single distribution is very likely ex ante to
generate the maximum value. We also extend our results to the problem of
selecting one of the $k$ best values.


  The density matrix renormalization group method is applied to obtain the
ground state phase diagram of the single impurity Anderson model on the
honeycomb lattice at half filling. The calculation of local static quantities
shows that the phase diagram contains two distinct phases, the local moment
(LM) phase and the asymmetric strong coupling (ASC) phase. These results are
supported by the local spin and charge excitation spectra, which exhibit
qualitatively different behavior in these two phases and also reveal the
existence of the valence fluctuating point at the phase boundary. For
comparison, we also study the low-energy effective pseudogap Anderson model.
Although the high-energy excitations are obviously different, we find that the
ground state phase diagram and the asymptotically low-energy excitations are in
good quantitative agreement with those for the single impurity Anderson model
on the honeycomb lattice, thus providing the first quantitative justification
for the previous studies based on low-energy approximate approaches.
Furthermore, we find that the lowest entanglement level is doubly degenerate
for the LM phase, whereas it is singlet for the ASC phase and is accidentally
three fold degenerate at the valence fluctuating point. Our results therefore
clearly demonstrate that the low-lying entanglement spectrum can be used to
determine with high accuracy the phase boundary of the impurity quantum phase
transition.


  Canonical expressions are representative of implicative propositions upto
renaming of variables. In this paper we explore, using a Monte-Carlo approach,
the model of canonical expressions in order to confirm the paradox that says
that asymptotically almost all classical theorems are intuitionistic.


  Semantic segmentation methods can not directly identify abnormal objects in
images. Anomaly Segmentation algorithm from this realistic setting can
distinguish between in-distribution objects and Out-Of-Distribution (OOD)
objects and output the anomaly probability for pixels. In this paper, a
Prototype Guided Anomaly segmentation Network (PGAN) is proposed to extract
semantic prototypes for in-distribution training data from limited annotated
images. In the model, prototypes are used to model the hierarchical category
semantic information and distinguish OOD pixels. The proposed PGAN model
includes a semantic segmentation network and a prototype extraction network.
Similarity measures are adopted to optimize the prototypes. The learned
semantic prototypes are used as category semantics to compare the similarity
with features extracted from test images and then to generate semantic
segmentation prediction. The proposed prototype extraction network can also be
integrated into most semantic segmentation networks and recognize OOD pixels.
On the StreetHazards dataset, the proposed PGAN model produced mIoU of 53.4%
for anomaly segmentation. The experimental results demonstrate PGAN may achieve
the SOTA performance in the anomaly segmentation tasks.


  We carefully compute the gluon propagator in the background of a non--Abelian
Weizs\"{a}cker--Williams field. This background field is generated by the
valence quarks in very large nuclei. We find contact terms in the small
fluctuation equations of motion which induce corrections to a previously
incorrect result for the gluon propagator in such a background field. The well
known problem of the Hermiticity of certain operators in Light Cone gauge is
resolved for the Weizs\"{a}cker--Williams background field. This is achieved by
working in a gauge where singular terms in the equations of motion are absent
and then gauge transforming the small fluctuation fields to Light Cone gauge.


  We study the large-$N$ limit of superconformal index for two strongly
interacting Chern-Simons theories in three dimensions with $\mathcal{N}=2$
supersymmetry, and compare the result against the AdS/CFT dual, namely the data
of full Kaluza-Klein reduction spectra obtained using the exceptional field
theory technique. The two theories of interest are mABJM and GJV theories,
which are obtained as IR fixed point of RG whose UV description is ABJM and
maximally supersymmetric Yang-Mills theory respectively. We confirm agreement
and the duality persists. For the case of mABJM it turns out that we need a
refinement of the gravity index which reflects the fact that the UV description
on the field theory side has enhanced global symmetry.


  We used the mark weighted correlation functions (MCFs), $W(s)$, to study the
large scale structure of the Universe. We studied five types of MCFs with the
weighting scheme $\rho^\alpha$, where $\rho$ is the local density, and $\alpha$
is taken as $-1,\ -0.5,\ 0,\ 0.5$, and 1. We found that different MCFs have
very different amplitudes and scale-dependence. Some of the MCFs exhibit
distinctive peaks and valleys that do not exist in the standard correlation
functions. Their locations are robust against the redshifts and the background
geometry, however it is unlikely that they can be used as ``standard rulers''
to probe the cosmic expansion history. Nonetheless we find that these features
may be used to probe parameters related with the structure formation history,
such as the values of $\sigma_8$ and the galaxy bias. Finally, after conducting
a comprehensive analysis using the full shapes of the $W(s)$s and $W_{\Delta
s}(\mu)$s, we found that, combining different types of MCFs can significantly
improve the cosmological parameter constraints. Compared with using only the
standard correlation function, the combinations of MCFs with $\alpha=0,\ 0.5,\
1$ and $\alpha=0,\ -1,\ -0.5,\ 0.5,\ 1$ can improve the constraints on
$\Omega_m$ and $w$ by $\approx30\%$ and $50\%$, respectively. We find highly
significant evidence that MCFs can improve cosmological parameter constraints.