  Improved bounds on the blocklength required to communicate over binary-input
channels using polar codes, below some given error probability, are derived.
For that purpose, an improved bound on the number of non-polarizing channels is
obtained. The main result is that the blocklength required to communicate
reliably scales at most as $O((I(W)-R)^{-5.77})$ where $R$ is the code rate and
$I(W)$ the symmetric capacity of the channel, $W$. The results are then
extended to polar lossy source coding at rate $R$ of a source with symmetric
distortion-rate function $D(\cdot)$. The blocklength required scales at most as
$O((D_N-D(R))^{-5.77})$ where $D_N$ is the actual distortion.


  For each complex semisimple group $G_{\mathbb{C}}$, Moore and Tachikawa
conjectured the existence of a certain two-dimensional topological quantum
field theory $\eta_{G_{\mathbb{C}}} : \mathrm{Cob}_2 \to \mathrm{MT}$ whose
target category has complex Lie groups as objects and holomorphic symplectic
varieties with Hamiltonian actions of the groups as morphisms. The conjecture
is motivated by string theory, where $\eta_{G_{\mathbb{C}}}$ is obtained by
taking the Higgs branch of some supersymmetric quantum field theories (called
theories of class $S$) depending on $G_{\mathbb{C}}$ and a Riemann surface. The
goal of this paper is to define a real analogue $\mathrm{MT}_{\mathbb{R}}$ of
the target category $\mathrm{MT}$ and to rigorously prove that it is a
category.


  Under the key assumption of finite {\rho}-variation, {\rho}\in[1,2), of the
covariance of the underlying Gaussian process, sharp a.s. convergence rates for
approximations of Gaussian rough paths are established. When applied to
Brownian resp. fractional Brownian motion (fBM), {\rho}=1 resp. {\rho}=1/(2H),
we recover and extend the respective results of [Hu--Nualart; Rough path
analysis via fractional calculus; TAMS 361 (2009) 2689-2718] and
[Deya--Neuenkirch--Tindel; A Milstein-type scheme without L\'evy area terms for
SDEs driven by fractional Brownian motion; AIHP (2011)]. In particular, we
establish an a.s. rate k^{-(1/{\rho}-1/2-{\epsilon})}, any {\epsilon}>0, for
Wong-Zakai and Milstein-type approximations with mesh-size 1/k. When applied to
fBM this answers a conjecture in the afore-mentioned references.


  3D scene representations have gained immense popularity in recent years.
Methods that use Neural Radiance fields are versatile for traditional tasks
such as novel view synthesis. In recent times, some work has emerged that aims
to extend the functionality of NeRF beyond view synthesis, for semantically
aware tasks such as editing and segmentation using 3D feature field
distillation from 2D foundation models. However, these methods have two major
limitations: (a) they are limited by the rendering speed of NeRF pipelines, and
(b) implicitly represented feature fields suffer from continuity artifacts
reducing feature quality. Recently, 3D Gaussian Splatting has shown
state-of-the-art performance on real-time radiance field rendering. In this
work, we go one step further: in addition to radiance field rendering, we
enable 3D Gaussian splatting on arbitrary-dimension semantic features via 2D
foundation model distillation. This translation is not straightforward: naively
incorporating feature fields in the 3DGS framework encounters significant
challenges, notably the disparities in spatial resolution and channel
consistency between RGB images and feature maps. We propose architectural and
training changes to efficiently avert this problem. Our proposed method is
general, and our experiments showcase novel view semantic segmentation,
language-guided editing and segment anything through learning feature fields
from state-of-the-art 2D foundation models such as SAM and CLIP-LSeg. Across
experiments, our distillation method is able to provide comparable or better
results, while being significantly faster to both train and render.
Additionally, to the best of our knowledge, we are the first method to enable
point and bounding-box prompting for radiance field manipulation, by leveraging
the SAM model. Project website at: https://feature-3dgs.github.io/


  This work is based upon a coupled, lattice-based continuum formulation that
was previously applied to problems involving strong coupling between mechanics
and mass transport; e.g. diffusional creep and electromigration. Here we
discuss an enhancement of this formulation to account for migrating grain
boundaries. The level set method is used to model grain-boundary migration in
an Eulerian framework where a grain boundary is represented as the zero level
set of an evolving higher-dimensional function. This approach can easily be
generalized to model other problems involving migrating interfaces; e.g. void
evolution and free-surface morphology evolution. The level-set equation is
recast in a remarkably simple form which obviates the need for spatial
stabilization techniques. This simplified level-set formulation makes use of
velocity extension and field re-initialization techniques. In addition, a
least-squares smoothing technique is used to compute the local curvature of a
grain boundary directly from the level-set field without resorting to
higher-order interpolation. A notable feature is that the coupling between mass
transport, mechanics and grain-boundary migration is fully accounted for. The
complexities associated with this coupling are highlighted and the
operator-split algorithm used to solve the coupled equations is described.


  A new integral with respect to an integer-valued random measure is
introduced. In contrast to the finite variation integral ubiquitous in
semimartingale theory (Jacod and Shiryaev, 2003, II.1.5), the new integral is
closed under stochastic integration, composition, and smooth transformations.
The new integral gives rise to a previously unstudied class of pure-jump
processes: the sigma-locally finite variation pure-jump processes. As an
application, it is shown that every semimartingale $X$ has a unique
decomposition $$X = X_0 + X^{\mathrm{qc}}+X^{\mathrm{dp}},$$ where
$X^{\mathrm{qc}}$ is quasi-left-continuous and $X^{\mathrm{dp}}$ is a
sigma-locally finite variation pure-jump process that jumps only at predictable
times, both starting at zero. The decomposition mirrors the classical result
for local martingales (Yoeurp, 1976, Theoreme~1.4) and gives a rigorous meaning
to the notions of continuous-time and discrete-time components of a
semimartingale. Against this backdrop, the paper investigates a wider class of
processes that are equal to the sum of their jumps in the semimartingale
topology and constructs a taxonomic hierarchy of pure-jump semimartingales.


  This paper is devoted to the lifespan estimates of small classical solutions
of the initial value problems for one dimensional wave equations with
semilinear terms of the spatial derivative of the unknown function. It is
natural that the result is same as the one for semilinear terms of the
time-derivative. But there are so many differences among their proofs.
Moreover, it is meaningful to study this problem in the sense that it may help
us to investigate its blow-up boundary in the near future.


  A proof of a formula, discovered by V.Fateev, on some Gamma products
connected with root systems is given.


  Many features of a molecule which are of physical interest (e.g. molecular
conformations, reaction rates) are described in terms of its dynamics in
configuration space. This article deals with the projection of molecular
dynamics in phase space onto configuration space. Specifically, we study the
situation that the phase space dynamics is governed by a stochastic Langevin
equation and study its relation with the configurational Smoluchowski equation
in the three different scaling regimes: Firstly, the Smoluchowski equations in
non-Cartesian geometries are derived from the overdamped limit of the Langevin
equation. Secondly, transfer operator methods are used to describe the
metastable behaviour of the system at hand, and an explicit small-time
asymptotics is derived on which the Smoluchowski equation turns out to govern
the dynamics of the position coordinate (without any assumptions on the
damping). By using an adequate reduction technique, these considerations are
then extended to one-dimensional reaction coordinates. Thirdly, we sketch three
different approaches to approximate the metastable dynamics based on time-local
information only.


  We study $T$ violation in the three-body charmless baryonic decay of $\bar
B^0 \ra \Lambda \bar p \pi^+$ through the $T$-odd triple product correlation in
the standard model. We find that the $T$ violating asymmetry is 10%, which is
accessible to the current B factories at KEK and SLAC, while the CP violating
one 1.1%. We emphasize that this triple product correlation would be the first
measurable direct $T$ violating effect predicted in the standard model.


  In this paper we present new estimates of the coalescence rate of neutron
star binaries in the local universe and we discuss its consequences for the
first generations of ground based interferometers. Our approach based on both
evolutionary and statistical methods gives a galactic merging rate of 1.7
10$^{-5}$ yr$^{-1}$, in the range of previous estimates 10$^{-6}$ - 10$^{-4}$
yr$^{-1}$. The local rate which includes the contribution of elliptical
galaxies is two times higher, in the order of 3.4 10$^{-5}$ yr$^{-1}$. We
predict one detection every 148 and 125 years with initial VIRGO and LIGO, and
up to 6 events per year with their advanced configuration. Our recent detection
rate estimates from investigations on VIRGO future improvements are quoted.


  Our aim is to give a version of the Moser-Trudinger inequality in the setting
of complex geometry. As a very particular case, our result already gives a new
Moser-Trudinger inequality for functions in the Sobolev space $W^{1,2}$ of a
domain in $R^2$. We also deduce a new necessary condition for the complex
Monge-Ampere equation for a given measure on a compact Kahler manifold to admit
a Holder continuous solution.


  Mixing of axion fields is widely used to generate EFTs with
phenomenologically advantageous features, such as hierarchies between axion
couplings to different gauge fields and/or large effective field ranges. While
these features are strongly constrained by periodicity for models with only a
single axion, mixing has been used in the literature (sometimes incorrectly) to
try to evade some of these constraints. In this paper, we ask whether it is
possible to use axion mixing to generate an EFT of axions that evades these
constraints by flowing to a theory of a non-compact scalar in the IR. We
conclude that as long as the light axion is exactly massless, it will inherit
the periodicity and associated constraints of the UV theory. However, by giving
the light axion a mass, we can relax these constraints with effects
proportional to the axion mass squared, including non-quantized couplings and
the realignment of monodromy to a light axion with a larger field range. To
show this, we consider various examples of axions mixing with other axions or
with non-compact scalar fields, and work in a basis where coupling quantization
is manifest. This basis makes it clear that in the case where an axion is eaten
through the Higgs or Stuckelberg mechanism, the light axion does not have a
large effective field range, in contrast to some recent claims in the
literature. Additionally, we relate our results about axion EFTs to a
well-known fact about gauge theory: that QFTs with compact gauge groups in the
UV flow to QFTs with compact gauge groups in the IR, and make this
correspondence precise in the 2+1 dimensional case.


  Statements analogous to the Hard Lefschetz Theorem (HLT) and the
Hodge-Riemann bilinear relations (HRR) hold in a variety of contexts: they
impose restrictions on the cohomology algebra of a smooth compact K\"ahler
manifold or on the intersection cohomology of a projective toric variety; they
restrict the local monodromy of a polarized variation of Hodge structure; they
impose conditions on the possible $f$-vectors of convex polytopes. While the
statements of these theorems depend on the choice of a K\"ahler class, or its
analog, there is usually a cone of possible K\"ahler classes. It is then
natural to ask whether the HLT and HRR remain true in a mixed context. In this
note we present a unified approach to proving the mixed HLT and HRR,
generalizing the previously known results, and proving it in new cases such as
the intersection cohomology of non-rational polytopes.


  We investigate phase transitions of the quasi-one-dimensional XXZ model in a
magnetic field, using the bosonization combined with the mean field treatment
of the inter-chain interaction. We then find that the field induced
incommensurate order is certainly realized in the low field region, while the
transverse staggered order appears in the high field region. On the basis of
the result, we discuss the field-induced phase transition recently observed for
BaCo2V2O8.


  We consider an approximating sequence of interacting population models with
branching, mutation and competition. Each individual is characterized by its
trait and the traits of its ancestors. Birth- and death-events happen at
exponential times. Traits are hereditarily transmitted unless mutation occurs.
The present model is an extension of the model used in [M\'el\'eard and Tran,
EJP, 2012], where for large populations with small individual biomasses and
under additional assumptions, the diffusive limit is shown to converge to a
nonlinear historical superprocess. The main goal of the present article is to
verify a compact containment condition in the more general setup of Polish
trait-spaces and general mutation kernels that allow for a dependence on the
parent's trait. As a by-product, a result on the paths of individuals is
obtained. An application to evolving genealogies on marked metric measure
spaces is mentioned where genealogical distance, counted in terms of the number
of births without mutation, can be regarded as a trait. Because of the use of
exponential times in the modeling of birth- and death-events the analysis of
the modulus of continuity of the trait-history of a particle plays a major role
in obtaining appropriate bounds.


  In this paper, we investigate the Seiberg-Witten gauge theory for Seifert
fibered spaces. The monopoles over these three-manifolds, for a particular
choice of metric and perturbation, are completely described. Gradient flow
lines between monopoles are identified with holomorphic data on an associated
ruled surface, and a dimension formula for such flows is calculated.


  A diversity of decision-making systems has been observed in animal
collectives. In some species, choices depend on the differences of the numbers
of animals that have chosen each of the available options, while in other
species on the relative differences (a behavior known as Weber's law) or follow
more complex rules. We here show that this diversity of decision systems
corresponds to a single rule of decision-making in collectives. We first
obtained a decision rule based on Bayesian estimation that uses the information
provided by the behaviors of the other individuals to improve the estimation of
the structure of the world. We then tested this rule in decision experiments
using zebrafish (Danio rerio), and in existing rich datasets of argentine ants
(Linepithema humile) and sticklebacks (Gasterosteus aculeatus), showing that a
unified model across species can quantitatively explain the diversity of
decision systems. Further, these results show that the different counting
systems used by animals, including humans, can emerge from the common principle
of using social information to make good decisions.


  Over the past decade, studies of dust in the Andromeda galaxy (M31) have
shown radial variations in the dust emissivity index ($\beta$). Understanding
the astrophysical reasons behind these radial variations may give clues about
the chemical composition of dust grains, their physical structure, and the
evolution of dust. We use $^{12}$CO(J=1-0) observations taken by the Combined
Array for Research in Millimeter Astronomy (CARMA) and dust maps derived from
\textit{Herschel} images, both with an angular resolution of 8" and spatial
resolution of 30 pc, to study variations in $\beta$ across an area of $\approx$
18.6 kpc$^2$ in M31. We extract sources, which we identify as molecular clouds,
by applying the astrodendro algorithm to the $^{12}$CO and dust maps, which as
a byproduct allows us to compare continuum emission from dust and CO emission
as alternative ways of finding molecular clouds. We then use these catalogues
to investigate whether there is evidence that $\beta$ is different inside and
outside molecular clouds. Our results confirm the radial variations of $\beta$
seen in previous studies. However, we find little difference between the
average $\beta$ inside molecular clouds compared to outside molecular clouds,
in disagreement with models which predict an increase of $\beta$ in dense
environments. Finally, we find some clouds traced by dust with very little CO
which may be either clouds dominated by atomic gas or clouds of molecular gas
that contain little CO.


  In this paper, we investigate joint optimal relay selection and resource
allocation under bandwidth exchange (BE) enabled incentivized cooperative
forwarding in wireless networks. We consider an autonomous network where N
nodes transmit data in the uplink to an access point (AP) / base station (BS).
We consider the scenario where each node gets an initial amount (equal, optimal
based on direct path or arbitrary) of bandwidth, and uses this bandwidth as a
flexible incentive for two hop relaying. We focus on alpha-fair network utility
maximization (NUM) and outage reduction in this environment. Our contribution
is two-fold. First, we propose an incentivized forwarding based resource
allocation algorithm which maximizes the global utility while preserving the
initial utility of each cooperative node. Second, defining the link weight of
each relay pair as the utility gain due to cooperation (over noncooperation),
we show that the optimal relay selection in alpha-fair NUM reduces to the
maximum weighted matching (MWM) problem in a non-bipartite graph. Numerical
results show that the proposed algorithms provide 20- 25% gain in spectral
efficiency and 90-98% reduction in outage probability.


  Witten suggested that fixed-point theorems can be derived by the
supersymmetric sigma model on a Riemann manifold M with potential term induced
from Killing vector on M. One of the well-known fixed-point theorem is the Bott
residue formula which represents intersection number of Chern classes of
holomorphic vector bundles on a Kahler manifold M as sum of contributions from
fixed point sets of a holomorphic vector field K on M. In this paper, we derive
the Bott residue formula by using topological sigma model (A-model) that
describes dynamics of maps from CP^{1} to M, with potential term induced from
the vector field $K$. Our strategy is to restrict phase space of path integral
to maps homotopic to constant maps. As an effect of adding a potential term to
topological sigma model, we are forced to modify BRST symmetry of the original
topological sigma model. Our potential term and BRST symmetry are closely
related to the idea used in the paper by Beasley and Witten where potential
terms induced from holomorphic section of a holomorphic vector bundle and
corresponding supersymmetry are considered.


  Recommender algorithms performance is often associated with the availability
of sufficient historical rating data. Unfortunately, when it comes to children,
this data is seldom available. In this paper, we report on an initial analysis
conducted to examine the degree to which data about traditional users, i.e.,
adults, can be leveraged to enhance the recommendation process for children.


  The central issue in direct-sequence code-division multiple-access (DS-CDMA)
ad hoc networks is the prevention of a near-far problem. This paper considers
two types of guard zones that may be used to control the near-far problem: a
fundamental exclusion zone and an additional CSMA guard zone that may be
established by the carrier-sense multiple-access (CSMA) protocol. In the
exclusion zone, no mobiles are physically present, modeling the minimum
physical separation among mobiles that is always present in actual networks.
Potentially interfering mobiles beyond a transmitting mobile's exclusion zone,
but within its CSMA guard zone, are deactivated by the protocol. This paper
provides an analysis of DS-CSMA networks with either or both types of guard
zones. A network of finite extent with a finite number of mobiles and uniform
clustering as the spatial distribution is modeled. The analysis applies a
closed-form expression for the outage probability in the presence of Nakagami
fading, conditioned on the network geometry. The tradeoffs between exclusion
zones and CSMA guard zones are explored for DS-CDMA and unspread networks. The
spreading factor and the guard-zone radius provide design flexibility in
achieving specified levels of average outage probability and transmission
capacity. The advantage of an exclusion zone over a CSMA guard zone is that
since the network is not thinned, the number of active mobiles remains
constant, and higher transmission capacities can be achieved.


  In this paper, the problem of semantic-based efficient image transmission is
studied over the Internet of Vehicles (IoV). In the considered model, a vehicle
shares massive amount of visual data perceived by its visual sensors to assist
other vehicles in making driving decisions. However, it is hard to maintain a
high reliable visual data transmission due to the limited spectrum resources.
To tackle this problem, a semantic communication approach is introduced to
reduce the transmission data amount while ensuring the semantic-level accuracy.
Particularly, an image segmentation semantic communication (ISSC) system is
proposed, which can extract the semantic features from the perceived images and
transmit the features to the receiving vehicle that reconstructs the image
segmentations. The ISSC system consists of an encoder and a decoder at the
transmitter and the receiver, respectively. To accurately extract the image
semantic features, the ISSC system encoder employs a Swin Transformer based
multi-scale semantic feature extractor. Then, to resist the wireless noise and
reconstruct the image segmentation, a semantic feature decoder and a
reconstructor are designed at the receiver. Simulation results show that the
proposed ISSC system can reconstruct the image segmentation accurately with a
high compression ratio, and can achieve robust transmission performance against
channel noise, especially at the low signal-to-noise ratio (SNR). In terms of
mean Intersection over Union (mIoU), the ISSC system can achieve an increase by
75%, compared to the baselines using traditional coding method


  This work proposes a system for retrieving clothing and fashion products from
video content. Although films and television are the perfect showcase for
fashion brands to promote their products, spectators are not always aware of
where to buy the latest trends they see on screen. Here, a framework for
breaking the gap between fashion products shown on videos and users is
presented. By relating clothing items and video frames in an indexed database
and performing frame retrieval with temporal aggregation and fast indexing
techniques, we can find fashion products from videos in a simple and
non-intrusive way. Experiments in a large-scale dataset conducted here show
that, by using the proposed framework, memory requirements can be reduced by
42.5X with respect to linear search, whereas accuracy is maintained at around
90%.


  Procedural computer languages have long been used in many aspects of
mathematics pedagogy. In this work, we examine the use of Prolog, a declarative
language for the same purpose. We find the facts+rules aspect of Prolog to be a
novel platform for developing coding lessons to supplement the learning of
mathematics. Specific examples are presented.


  We report on the first observation of white-eye pattern in an air dielectric
barrier discharge. The patterned discharges undergo a development as following:
random spots - quasihexagonal pattern - hexagonal pattern (type I) - hexagonal
pattern (type II) - white-eye pattern - chaos as the voltage is increased. The
spatiotemporal characteristics of patterned discharges are investigated by
using an optical method. Results show that the two discharge modes, uniform
mode and filamentary mode, are actually two different spatial presentations of
the same origin: the microdischarge. From the viewpoint of pattern dynamics,
the white-eye pattern results from a 3-wave resonance interaction.


  Several recent works have directly extended the image masked autoencoder
(MAE) with random masking into video domain, achieving promising results.
However, unlike images, both spatial and temporal information are important for
video understanding. This suggests that the random masking strategy that is
inherited from the image MAE is less effective for video MAE. This motivates
the design of a novel masking algorithm that can more efficiently make use of
video saliency. Specifically, we propose a motion-guided masking algorithm
(MGM) which leverages motion vectors to guide the position of each mask over
time. Crucially, these motion-based correspondences can be directly obtained
from information stored in the compressed format of the video, which makes our
method efficient and scalable. On two challenging large-scale video benchmarks
(Kinetics-400 and Something-Something V2), we equip video MAE with our MGM and
achieve up to +$1.3\%$ improvement compared to previous state-of-the-art
methods. Additionally, our MGM achieves equivalent performance to previous
video MAE using up to $66\%$ fewer training epochs. Lastly, we show that MGM
generalizes better to downstream transfer learning and domain adaptation tasks
on the UCF101, HMDB51, and Diving48 datasets, achieving up to +$4.9\%$
improvement compared to baseline methods.


  Although a discovery of wimps either at colliders or in direct experiments
would have enormous implications for our understanding of particle physics, it
would imply less than one would like about our understanding of the dark matter
in the universe or in the galactic halo: it surely is possible that the
discovered particles account for only a little of the total dark matter. To
establish the cosmological significance of a wimp discovery, their density must
be determined. We show that data from neither hadron colliders nor direct
detection experiments alone can be sufficient to determine the local or relic
density of discovered wimps, even allowing all needed assumptions about
cosmology and astrophysics. We provide examples of dark matter models where
nearly identical detector or collider signals correspond to very different
densities. We show, however, that it may be possible to determine the density
of wimps by combining data from both experiments; we present a general method
to do this in the case of supersymmetric dark matter, and describe how similar
studies could be made for other wimp candidates.


  We consider lepton flavor violations (LFV) mediated by photino as a result of
the nondiagonal slepton mass matrices in general supersymmetric models. Using
the experimental upper bounds on l \to l' + gamma and mu^- + Ti \to e^- + Ti as
constraints on the flavor changing slepton mass insertions, we predict the
possible ranges of the upper limits on the branching ratios of other LFV
processes such as l \to 3l', tau \to l_{i\neq 3} + pi^0 (or eta, rho^0, phi),
Z^0 \to l_i bar{l}_{j\neq i}, and muonium \to antimuonium conversion. Most of
these decays are expected to occur with small branching ratios far below the
current or future experimental search limits. We also derive constraints on the
flavor conserving mass insertions from the anomalous magnetic moments of
leptons.


  The project aimed to define the rules and develop a technological solution to
automatically identify a set of attributes within free-text clinical records
written in Portuguese. The first application developed and implemented on this
basis was a structured summary of a patient's clinical history, including
previous diagnoses and procedures, usual medication, and relevant
characteristics or conditions for clinical decisions, such as allergies, being
under anticoagulant therapy, etc. The project's goal was achieved by a
multidisciplinary team that included clinicians, epidemiologists, computational
linguists, machine learning researchers and software engineers, bringing
together the expertise and perspectives of a public hospital, the university
and the private sector. Relevant benefits to users and patients are related
with facilitated access to the patient's history, which translates into
exhaustiveness in apprehending the patient's clinical past and efficiency due
to time saving.


  Gauge unification in a five dimensional supersymmetric SO(10) model
compactified on an orbifold $S^1/(Z_2 \times Z_2^{\prime})$ is studied. One
orbifolding reduces N=2 supersymmetry to N=1, and the other breaks SO(10) to
the Pati-Salam gauge group $\ps$. Further breaking to the standard model gauge
group is made through the Higgs mechanism on one of the branes. The differences
of the three gauge couplings run logarithmically even in five dimensions and we
can keep the predictability for unification as in four dimensional gauge
theories. We obtain an excellent prediction for gauge coupling unification with
a cutoff scale $M_* \sim 3 \times 10^{17}$ GeV and a compactification scale
$M_c \sim 1.5 \times 10^{14}$ GeV. Finally, although proton decay due to
dimension 5 operators may be completely eliminated, the proton decay rate in
these models is sensitive to the placement of matter multiplets in the 5th
dimension, as well as to the unknown physics above the cutoff scale.


  The possibility of the mechanical detection of the Casimir friction using the
non-contact force microscope is discussed. On a SiO2 tip situated above a
graphene-covered SiO2 substrate will act the frictional drag force mediated by
a fluctuating electromagnetic field produced by a current in the graphene
sheet. This friction force will produce the bending of the cantilever, which
can be measured by state-of-art non-contact force microscope. Both the thermal
and quantum contributions to the Casimir frictional drag force can be studied
using this experimental setup. This result paves the ways for the mechanical
detection of the Casimir friction and for the application of the frictional
drag effect in micro- and nano- electromechanical devices (MEMS and NEMS).


  It was recently determined exactly through how many general points a
nondegenerate curve with nonspecial hyperplane section can pass. This gives
rise to a method of constructing reducible curves $C_1 \cup_\Gamma C_2 \to
\mathbb{P}^r$ with general nodes: We take a finite set $\Gamma \subset
\mathbb{P}^r$ of general points, and find nondegenerate nonspecial curves $C_1$
and $C_2$ in $\mathbb{P}^r$ of specified degrees and genera which pass through
$\Gamma$, and glue together along $\Gamma$. The goal of this paper is to show
that, subject to certain mild assumptions, stable maps constructed in this
manner lie in the closure of the locus of nondegenerate stable maps from curves
of general moduli, i.e. are BN-curves.
  As explained in arXiv:1809.05980, these results play a key role in the
author's proof of the Maximal Rank Conjecture.


  We formulate the spin foam representation of discrete SU(2) gauge theory as a
product of vertex amplitudes each of which is the spin network generating
function of the boundary graph dual to the vertex. In doing so the sums over
spins have been carried out. The boundary data of each n-valent node is
explicitly reduced with respect to the local gauge invariance and has a
manifest geometrical interpretation as a framed polyhedron of fixed total area.
Ultimately, sums over spins are traded for contour integrals over simple poles
and recoupling theory is avoided using generating functions.


  Death ligand mediated apoptotic activation is a mode of programmed cell death
that is widely used in cellular and physiological situations. Interest in
studying death ligand induced apoptosis has increased due to the promising role
of recombinant soluble forms of death ligands (mainly recombinant TRAIL) in
anti-cancer therapy. A clear elucidation of how death ligands activate the type
1 and type 2 apoptotic pathways in healthy and cancer cells may help develop
better chemotherapeutic strategies. In this work, we use kinetic Monte Carlo
simulations to address the problem of type 1/ type 2 choice in death ligand
mediated apoptosis of cancer cells. Our study provides insights into the
activation of membrane proximal death module that results from complex
interplay between death and decoy receptors. Relative abundance of death and
decoy receptors was shown to be a key parameter for activation of the initiator
caspases in the membrane module. Increased concentration of death ligands
frequently increased the type 1 activation fraction in cancer cells, and, in
certain cases changes the signaling phenotype from type 2 to type 1. Results of
this study also indicate that inherent differences between cancer and healthy
cells, such as in the membrane module, may allow robust activation of cancer
cell apoptosis by death ligand induction. At the same time, large cell-to-cell
variability through the type 2 pathway was shown to provide protection for
healthy cells. Such elucidation of selective activation of apoptosis in cancer
cells addresses a key question in cancer biology and cancer therapy.


  We have studied the adsorption of Li atoms at the hollow sites of graphene
nanoribbons (zigzag and armchair), graphene, and fullerenes by means of density
functional theory calculations including local and semilocal functionals. The
binding energy of a Li atom on armchair nanoribbons (of about 1.70 eV for LSDA
and 1.20 eV for PBE) is comparable to the corresponding value in graphene (1.55
and 1.04 eV for LSDA and PBE, respectively). Notably, the interaction between
Li and zigzag nanoribbons is much stronger. The binding energy of Li at the
edges of zigzag nanoribbons is about 50% stronger than in graphene for the
functionals studied here. While the charge transfer between the Li adatom and
the zigzag nanoribbon significantly affects the magnetic properties of the
latter providing an additional interaction mechanism that is not present in
two-dimensional graphene or armchair nanoribbons, we find that the morphology
of the edges, rather than magnetism, is responsible for the enhanced
Li-nanoribbon interaction.


  The AMTHA (Automatic Mapping Task on Heterogeneous Architectures) algorithm
for task-to-processors assignment and the MPAHA (Model of Parallel Algorithms
on Heterogeneous Architectures) model are presented. The use of AMTHA is
analyzed for multicore processor-based architectures, considering the
communication model among processes in use. The results obtained in the tests
carried out are presented, comparing the real execution times on multicores of
a set of synthetic applications with the predictions obtained with AMTHA.
Finally current lines of research are presented, focusing on clusters of
multicores and hybrid programming paradigms.


  Inspired by the recent measurements of the CMS collaboration, we report a QCD
study of dijet production in proton+lead collisions at the LHC involving
large-transverse-momentum jets, $p_T \gtrsim 100$ GeV. Examining the inherent
uncertainties of the next-to-leading order perturbative QCD calculations and
their sensitivity to the free proton parton distributions (PDFs), we observe a
rather small, typically much less than 5% clearance for the shape of the dijet
rapidity distribution within approximately 1.5 units around the midrapidity.
Even a more stable observable is the ratio between the yields in the positive
and negative dijet rapidity, for which the baseline uncertainty can be made
negligible by imposing a symmetric jet rapidity acceptance. Both observables
prove sensitive to the nuclear modifications of the gluon distributions, the
corresponding uncertainties clearly exceeding the estimated baseline
uncertainties from the free-proton PDFs and scale dependence. From a
theoretical point of view, these observables are therefore very suitable for
testing the validity of the collinear factorization and have a high potential
to provide precision constraints for the nuclear PDFs.


  We present a nonparametric construction for deep learning compatible modern
Hopfield models and utilize this framework to debut an efficient variant. Our
key contribution stems from interpreting the memory storage and retrieval
processes in modern Hopfield models as a nonparametric regression problem
subject to a set of query-memory pairs. Crucially, our framework not only
recovers the known results from the original dense modern Hopfield model but
also fills the void in the literature regarding efficient modern Hopfield
models, by introducing \textit{sparse-structured} modern Hopfield models with
sub-quadratic complexity. We establish that this sparse model inherits the
appealing theoretical properties of its dense analogue -- connection with
transformer attention, fixed point convergence and exponential memory capacity
-- even without knowing details of the Hopfield energy function. Additionally,
we showcase the versatility of our framework by constructing a family of modern
Hopfield models as extensions, including linear, random masked, top-$K$ and
positive random feature modern Hopfield models. Empirically, we validate the
efficacy of our framework in both synthetic and realistic settings.


  Highlights of the meeting include new insights into r and s-processes and an
explosion of interesting abundance data on stars in the Galactic halo and in
dwarf spheroidal galaxies. I include in this summary a few suggestions on the
chemical evolution of the Thick and Thin disks, and on the present and past
distribution of baryons and metals in the universe.


  In these notes we review emergent phenomena in complex systems, emphasizing
ways to identify potential underlying universal mechanisms that generates
complexity. The discussion is centered around the emergence of collective
behavior in dynamical systems when they are poised near a critical point of a
phase transition, either by tuning or by self-organization. We then argue the
rationale for our proposal that the brain is naturally poised near criticality
reviewing recent results as well as the implications of this view of the
functioning brain.


  We report the discovery of one unique cataclysmic variable drawn from the
Hamburg Quasar Survey, HS2331+3905. Follow-up observations obtained over three
years unveiled a very unusual picture. The large amplitude 3.5 h radial
velocity variations obtained from our optical spectroscopy is not the orbital
period of the system, as one would normally expect. Instead, extensive CCD
photometry strongly suggests that HS2331+3905 is a short orbital period
cataclysmic variable with Porb = 81.09 min, containing a cold white dwarf which
appears to exhibit ZZ Ceti pulsations.


  In public health applications, spatial data collected are often recorded at
different spatial scales and over different correlated variables. Spatial
change of support is a key inferential problem in these applications and have
become standard in univariate settings; however, it is less standard in
multivariate settings. There are several existing multivariate spatial models
that can be easily combined with multiscale spatial approach to analyze
multivariate multiscale spatial data. In this paper, we propose three new
models from such combinations for bivariate multiscale spatial data in a
Bayesian context. In particular, we extend spatial random effects models,
multivariate conditional autoregressive models, and ordered hierarchical models
through a multiscale spatial approach. We run simulation studies for the three
models and compare them in terms of prediction performance and computational
efficiency. We motivate our models through an analysis of 2015 Texas annual
average percentage receiving two blood tests from the Dartmouth Atlas Project.


  Instead of using current deep-learning segmentation models (like the UNet and
variants), we approach the segmentation problem using trained Convolutional
Neural Network (CNN) classifiers, which automatically extract important
features from images for classification. Those extracted features can be
visualized and formed into heatmaps using Gradient-weighted Class Activation
Mapping (Grad-CAM). This study tested whether the heatmaps could be used to
segment the classified targets. We also proposed an evaluation method for the
heatmaps; that is, to re-train the CNN classifier using images filtered by
heatmaps and examine its performance. We used the mean-Dice coefficient to
evaluate segmentation results. Results from our experiments show that heatmaps
can locate and segment partial tumor areas. But use of only the heatmaps from
CNN classifiers may not be an optimal approach for segmentation. We have
verified that the predictions of CNN classifiers mainly depend on tumor areas,
and dark regions in Grad-CAM's heatmaps also contribute to classification.


  In a recent Letter [PRL, 107, 047208 (2011)], Zorko et al. report on an
"unexpected inhomogeneous magnetism" related to "a peculiar fragility" of the
resonating-valence-bond (RVB) electronic state in the spin-1/2 quantum magnet
CuNCN. Here, we show that: i) the spin model of the anisotropic triangular
lattice (ATL), as proposed by Zorko et al., does not apply to CuNCN; ii) this
model does not support the proclaimed RVB ground state in the relevant
parameter range; iii) the magnetic state of CuNCN is not necessarily
inhomogeneous.


  Flexible loads are a resource for the Balancing Authority (BA) of the future
to aid in the balance of supply and demand in the power grid. Consequently, it
is of interest for a BA to know how much flexibility a collection of loads has,
so to successfully incorporate flexible loads into grid level resource
allocation. Loads' flexibility is limited by all their Quality of Service (QoS)
requirements. In this work we present a characterization of capacity for a
collection of flexible loads. This characterization is in terms of the Power
Spectral Density (PSD) of the reference signal. Two advantages of our
characterization are: (i) it easily allows for a BA to use the characterization
for resource allocation of flexible loads and (ii) it allows for precise
definitions of the power and energy capacity for a collection of flexible
loads.


  Adversarial Training (AT) and Virtual Adversarial Training (VAT) are the
regularization techniques that train Deep Neural Networks (DNNs) with
adversarial examples generated by adding small but worst-case perturbations to
input examples. In this paper, we propose xAT and xVAT, new adversarial
training algorithms, that generate \textbf{multiplicative} perturbations to
input examples for robust training of DNNs. Such perturbations are much more
perceptible and interpretable than their \textbf{additive} counterparts
exploited by AT and VAT. Furthermore, the multiplicative perturbations can be
generated transductively or inductively while the standard AT and VAT only
support a transductive implementation. We conduct a series of experiments that
analyze the behavior of the multiplicative perturbations and demonstrate that
xAT and xVAT match or outperform state-of-the-art classification accuracies
across multiple established benchmarks while being about 30\% faster than their
additive counterparts. Furthermore, the resulting DNNs also demonstrate
distinct weight distributions.


  A technique is introduced for estimating unknown parameters when time series
of only one variable from a multivariate nonlinear dynamical system is given.
The technique employs a combination of two different control methods, a linear
feedback for synchronizing system variables and an adaptive control. The
technique is shown to work even when the unknown parameter appears in the
evolution equations of the variables other than the one for which the time
series is given. The technique not only esablishes that explicit detailed
information about all system variables and parameters is contained in a scalar
time series, but also gives a way to exract it out under suitable conditions.
Illustrations are presented and effect of noise is studied.


  We present a $q_T$-resummed calculation of diphoton production at order
N$^3$LL$^\prime$+NNLO. To reach the primed level of accuracy we have
implemented the recently published three-loop $\mathcal{O}(\alpha_s^3)$ virtual
corrections in the $q\bar{q}$ channel and the three-loop transverse momentum
dependent beam functions and combined them with the existing infrastructure of
CuTe-MCFM, a code performing resummation at order N$^3$LL. While the primed
predictions are parametrically not more accurate, one typically observes from
lower orders and other processes that they are the dominant effect of the next
order. We include in both the $q\bar{q}$ and loop-induced $gg$ channel the hard
contributions consistently together at order $\alpha_s^3$ and find that the
resummed $q\bar{q}$ channel without matching stabilizes indeed. Due to large
matching corrections and large contributions and uncertainties from the $gg$
channel, the overall improvements are small though. We furthermore study the
effect of hybrid-cone photon isolation and hard-scale choice on our fully
matched results to describe the ATLAS 8 TeV data and find that the hybrid-cone
isolation destroys agreement at small $q_T$.


  We consider different generalizations of the honeycomb lattice to three
dimensional structures. We address the family of the hyper-honeycomb lattice,
which is made up of alternating layers of 2D honeycomb nano-ribbons, with each
layer rotated by $\pi/2$ with the layer below. When the orbitals of the lattice
sites are symmetric with respect to the planes of the trigonal links, these
structures can produce a Dirac loop, a closed line of Dirac nodes in momentum
space. For orbitals that break that symmetry, such as the carbon $p$-wave
orbitals, hyper-honeycomb lattices do not possess the loop structure. We also
consider a new structure, the screw hyper-honeycomb, in which the successive
layers of parallel units are rotated by $2\pi/3$. This structure has a Dirac
loop if reflection symmetry in the unit cell is imposed, regardless the
symmetry of the onsite orbitals. We discuss the implementation of those systems
in optical lattices.


  We focus on the study of $p$-Laplacian Dirichlet problem containing the left
and right fractional derivative operators. By using the genus properties in
critical point theory, we establish some new criteria to guarantee the
existence of infinitely many weak solutions for the considered problem.


  The fate of small particles in turbulent flows depends strongly on the
surrounding fluid's velocity gradient properties such as rotation and
strain-rates. For non-inertial (fluid) particles, the Restricted Euler model
provides a simple, low-dimensional dynamical system representation of
Lagrangian evolution of velocity gradients in fluid turbulence, at least for
short times. Here we derive a new restricted Euler dynamical system for the
velocity gradient evolution of inertial particles such as solid particles in a
gas or droplets and bubbles in turbulent liquid flows. The model is derived in
the limit of small (sub Kolmogorov scale) particles and low Stokes number. The
system exhibits interesting fixed points, stability and invariant properties.
Comparisons with data from Direct Numerical Simulations show that the model
predicts realistic trends such as the tendency of increased straining over
rotation along heavy particle trajectories and, for light particles such as
bubbles, the tendency of reduced self-stretching of strain-rate.


  The main result of this paper is a bijective proof showing that the
generating function for partitions with bounded differences between largest and
smallest part is a rational function. This result is similar to the closely
related case of partitions with fixed differences between largest and smallest
parts which has recently been studied through analytic methods by Andrews,
Beck, and Robbins. Our approach is geometric: We model partitions with bounded
differences as lattice points in an infinite union of polyhedral cones.
Surprisingly, this infinite union tiles a single simplicial cone. This
construction then leads to a bijection that can be interpreted on a purely
combinatorial level.


  In this paper we introduce and study several new Hilbert-type operators
acting between the weighted Fock spaces. We provide some sufficient and
necessary conditions for the boundedness and compactness of certain
Hilbert-type operators from one weighted Fock space to another.


  In this report we have made a systematic study of strangeness production in
proton-proton(pp),proton-nucleus(pA) and nucleus- nucleus(AA) collisions at
CERN Super Proton Synchroton energies, using$\,\,\, HIJING\,\,\, MONTE
\,\,\,CARLO \,\,\,MODEL $ \\ (version $HIJ.01$). Numerical results for mean
multiplicities of neutral strange particles ,as well as their ratios to
negatives hadrons($<h^{-}>$) for
p-p,nucleon-nucleon(N-N),\,\,p-S,\,\,p-Ag,\,\,p-Au('min. bias')collisions and
p-Au,\,\,S-S,\,\,S-Ag,\,\,S-Au ('central')collisions are compared to
experimental data available from CERN experiments and also with recent
theoretical estimations given by others models. Neutral strange particle
abundances are quite well described for p-p,N-N and p-A interactions ,but are
underpredicted by a factor of two in A-A interactions for
$\Lambda,\bar{\Lambda},
  K^{0}_{S}$ in symmetric collisions(S-S,\,\,Pb-Pb)and for
$\Lambda,\bar{\Lambda}\,\,$in asymmetric ones(S-Ag,\,\,S-Au,\,\,S-W). A
qualitative prediction for rapidity, transverse kinetic energy and transverse
momenta normalized distributions are performed at 200 GeV/Nucleon in
p-S,S-S,S-Ag and S-Au collisions in comparison with recent experimental data.
HIJING model predictions for coming experiments at CERN for S-Au, S-W and Pb-Pb
interactions are given. The theoretical calculations are estimated in a full
phase space.


  This paper models legislative decision-making with an agenda setter who can
propose policies sequentially, tailoring each proposal to the status quo that
prevails after prior votes. Voters are sophisticated and the agenda setter
cannot commit to her future proposals. Nevertheless, the agenda setter obtains
her favorite outcome in every equilibrium regardless of the initial default
policy. Central to our results is a new condition on preferences,
manipulability, that holds in rich policy spaces, including spatial settings
and distribution problems. Our results overturn the conventional wisdom that
voter sophistication alone constrains an agenda setter's power.


  Aharonov-Bohm (AB) interferences in the quantum Hall regime can be achieved,
provided that electrons are able to transmit between two edge channels in
nanostructures. Pioneering approaches include quantum point contacts in 2DEG
systems, bipolar graphene p-n junctions, and magnetic field heterostructures.
In this work, defect scattering is proposed as an alternative mechanism to
achieve AB interferences in polycrystalline graphene. Indeed, due to such
scattering, the extended defects across the sample can act as tunneling paths
connecting quantum Hall edge channels. Consequently, strong AB oscillations in
the conductance are predicted in polycrystalline graphene systems with two
parallel grain boundaries. In addition, this general approach is demonstrated
to be applicable to nano-systems containing two graphene barriers with
functional impurities and perspectively, can also be extended to similar
systems of 2D materials beyond graphene.


  Hands, one of the most dynamic parts of our body, suffer from blur due to
their active movements. However, previous 3D hand mesh recovery methods have
mainly focused on sharp hand images rather than considering blur due to the
absence of datasets providing blurry hand images. We first present a novel
dataset BlurHand, which contains blurry hand images with 3D groundtruths. The
BlurHand is constructed by synthesizing motion blur from sequential sharp hand
images, imitating realistic and natural motion blurs. In addition to the new
dataset, we propose BlurHandNet, a baseline network for accurate 3D hand mesh
recovery from a blurry hand image. Our BlurHandNet unfolds a blurry input image
to a 3D hand mesh sequence to utilize temporal information in the blurry input
image, while previous works output a static single hand mesh. We demonstrate
the usefulness of BlurHand for the 3D hand mesh recovery from blurry images in
our experiments. The proposed BlurHandNet produces much more robust results on
blurry images while generalizing well to in-the-wild images. The training codes
and BlurHand dataset are available at
https://github.com/JaehaKim97/BlurHand_RELEASE.


  Studying the impact of climate change on precipitation is constrained by
finding a way to evaluate the evolution of precipitation variability over time.
Classical approaches (feature-based) have shown their limitations for this
issue due to the intermittent and irregular nature of precipitation. In this
study, we present a novel variant of the Dynamic time warping method
quantifying the dissimilarity between two rainfall time series based on shapes
comparisons, for clustering annual time series recorded at daily scale. This
shape based approach considers the whole information (variability, trends and
intermittency). We further labeled each cluster using a feature-based approach.
While testing the proposed approach on the time series of Paris Montsouris, we
found that the precipitation variability increased over the years in Paris
area.


  We discuss spherically symmetric dynamical systems in the framework of a
general model of $f({\cal R})$ gravity, i.e. $f({\cal R})={\cal R}e^{\zeta
{\cal R}}$, where $\zeta$ is a dimensional quantity in squared length units
[L$^2$]. We initially assume that the internal structure of such systems is
governed by the Krori-Barua ansatz, alongside the presence of fluid anisotropy.
By employing astrophysical observations obtained from the pulsar {\textit SAX
J1748.9-2021}, derived from bursting X-ray binaries located within globular
clusters, we determine that $\zeta$ is approximately equal to $\pm 5$ km$^2$.
In particular, the model can create a stable configuration for {\textit SAX
J1748.9-2021}, encompassing its geometric and physical characteristics. In
$f({\cal R})$ gravity, the Krori-Barua approach links $p_r$ and $p_t$, which
represent the components of the pressures, to ($\rho$), representing the
density, semi-analytically. These relations are described as $p_r\approx v_r^2
(\rho-\rho_{I})$ and $p_t\approx v_t^2 (\rho-\rho_{II})$. Here, the expression
$v_r$ and $v_t$ represent the radial and tangential sound speeds, respectively.
Meanwhile, $\rho_I$ pertains to the surface density and $\rho_{II}$ is derived
using the parameters of the model. Notably, within the frame of $f({\cal R})$
gravity where $\zeta$ is negative, the maximum compactness, denoted as $C$, is
inherently limited to values that do not exceed the Buchdahl limit. This
contrasts with general relativity or with $f({\cal R})$ with positive $\zeta$,
where $C$ has the potential to reach the limit of the black hole
asymptotically. The predictions of such model suggest a central energy density
which largely exceeds the saturation of nuclear density, which has the value
$\rho_{\text{nuc}} = 3\times 10^{14}$ g/cm$^3$. Also, the density at the
surface $\rho_I$ surpasses $\rho_{\text{nuc}}$.


  We address the mechanism of early stages of growth and shape transition of
the unique nanowall network (NwN) nanostructure of GaN by experimentally
monitoring its controlled growth using PA-MBE and complementing it by
\textit{first-principles} calculations. Using electron microscopy, we observe
the formation of tetrahedron shaped (3 faced pyramid) islands at early stages
of growth, which later grows anisotropically along their edges of the
(20$\overline{2}$1) facets, to form the wall like structure. The mechanism of
this crystal growth is discussed in light of surface free energies of the
different surfaces, adsorption energy and diffusion barrier of Ga ad-atoms on
the (20$\overline{2}$1) facets. By \textit{first-principles} calculations, we
find that the diffusion barrier of ad-atoms decreases with decreasing width of
facets, and is responsible for the anisotropic growth and formation of the
nanowall network. This study suggest that formation of NwN is a archetype
example of structure dependent attachment kinetic (SDAK) instability induced
shape transition in thin film growth.


  Fourier integral operators with sufficiently smooth phase act on the
time-frequency content of functions. However time-frequency analysis has only
recently been used to analyze these operators. In this paper, we show that if a
Fourier integral operator has a smooth phase function and its symbol is
well-localized in time and frequency, then the operator is Schatten \( p
\)-class for \( p \in [1,2] \), with inclusion of the symbol in mixed
modulation spaces serving as the appropriate measure of time-frequency
localization. Our main results are sharp in the sense that larger mixed
modulation spaces necessarily contain symbols of Fourier integral operators
that are not Schatten \( p \)-class.


  Near infrared diffuse optical tomography (DOT) provides an imaging modality
for the oxygenation of tissue. In this paper, we propose a novel machine
learning algorithm based on time-domain radiative transfer equation. We use
temporal profiles of absorption measure for a two-dimensional model of target
tissue, which are calculated by solving time-domain radiative transfer
equation. Applying a long-short-term memory (LSTM) deep learning method, we
find that we can specify positions of cancer cells with high accuracy rates. We
demonstrate that the present algorithm can also predict multiple or extended
cancer cells.


  We construct a simple explicit local geometry providing a `bifid throat' for
5-brane axion monodromy. A bifid throat is a throat that splits into two
daughter throats in the IR, containing a homologous 2-cycle family reaching
down into each daughter throat. Our example consists of a deformed
$\mathbb{Z}_3\times\mathbb{Z}_2$ orbifold of the conifold, which provides us
with an explicit holographic dual of the bifid throat including D3-branes and
fractional 5-branes at the toric singularities of our setup. Having the
holographic description in terms of the dual gauge theory allows us to address
the effect of 5-brane-antibrane pair backreaction including the warping
effects. This leads to the size of the backreaction being small and
controllable after imposing proper normalization of the inflaton potential and
hence the warping scales.


  We have observed phase separation between the superfluid and the normal
component in a strongly interacting Fermi gas with imbalanced spin populations.
The in situ distribution of the density difference between two trapped spin
components is obtained using phase-contrast imaging and 3D image
reconstruction. A shell structure is clearly identified where the superfluid
region of equal densities is surrounded by a normal gas of unequal densities.
The phase transition induces a dramatic change in the density profiles as
excess fermions are expelled from the superfluid.


  This work concerns Artin's Conjecture on primitive roots and related problems
for number fields. Let $K$ be a number field and let $W_1$ to $W_n$ be finitely
generated subgroups of $K^\times$ of positive rank. We consider the index map,
which maps a prime $\mathfrak p$ of $K$ to the $n$-tuple of the indices of
$(W_i \bmod \mathfrak p)$. Conditionally under GRH, any preimage under the
index map admits a density, and the aim of this work is describing it. For
example, we express the density as a limit in various ways. We study in
particular the preimages of sets of $n$-tuples that are defined by prescribing
valuations for their entries. Under some mild assumptions we can express the
density as a multiple of a (suitably defined) Artin-type constant.


  Bosonic sector of d5 gauged supergravity with specific parametrization of
full scalar coset is considered (multi-dilaton gravity). Using holographic RG
in the form suggested by de Boer-Verlinde-Verlinde the holographic d4 conformal
anomaly (in the sector of curvature invariants) is found when bulk potential is
not constant. Its comparison with the earlier calculation done in the scheme
where expansion of metric and dilaton over radial coordinate of AdS space is
used demonstrates scheme dependence of holographic conformal anomaly. In
AdS/CFT correspondence where dilatons play role of coupling constants it
coincides with multi-loop conformal anomaly which depends on regularization
scheme in interacting dual QFT. Hence, scheme dependence of holographic
conformal anomaly is consistent with dual QFT expectations.


  We explore recurrence properties arising from dynamical approach to
combinatorial problems like the van der Waerden Theorem. We describe relations
between these properties, study their consequences for dynamics, and
demonstrate connections to combinatorial problems. In particular, we present a
measure-theoretical analog of a result of Glasner on multi-transitivity in
topological weakly mixing minimal maps. We also obtain a dynamical proof of the
existence of a C-set with zero Banach density.


  Recently, enhancement of the longitudinal magneto-electrical conductivity
(LMEC) has been observed in Bi$_{1-x}$Sb$_{x}$ around $x \sim 3\%$ under
$\bm{E} \parallel \bm{B}$ ($\bm{E}$: external electric field and $\bm{B}$:
external magnetic field) [Phys. Rev. Lett. {\bf 111}, 246603 (2013)], where an
enhancement factor proportional to $B^{2}$ is suggested to result from the
$\bm{E} \cdot \bm{B}$ term. In the present study, we show that this $B^{2}$
enhancement is not limited on the LMEC, where both the Seebeck and thermal
conductivities in the longitudinal setup ($\bm{E} \parallel \bm{B}$) are
predicted to show essentially the same enhancement proportional to $B^{2}$. In
particular, the $B^{2}$ enhancement factor of the LMEC turns out to differ from
that of the longitudinal thermal conductivity, responsible for breakdown of
Wiedemann-Franz (WF) law, which means that anomalous currents flowing through
the dissipationless channel differ from each other. Since the breakdown of the
WF law appears in spite of the existence of electron quasiparticles, regarded
to be a purely topological character (chiral anomaly), the Weyl metallic state
cannot be identified with the Landau's Fermi-liquid fixed point. We propose the
violation of the WF law as another hallmark of the Weyl metallic phase, which
originates from axion electrodynamics.


  In this paper, we study the nonlinear Schr\"odinger equation with focusing
point nonlinearity in dimension one. First, we establish a scattering criterion
for the equation based on Kenig-Merle's compactness-rigidity argument. Then we
prove the energy scattering below and above the mass-energy threshold. We also
describe the dynamics of solutions with data at the ground state threshold.
Finally, we prove a blow-up criteria for the equation with initial data with
arbitrarily large energy.


  Recent progress in the solution of Dyson-Schwinger equations of QCD allows
for a non perturbative evaluation of the One Gluon Exchange (OGE) interaction.
We calculate the interquark static potential for heavy mesons by assuming that
it is given by this OGE interaction and we apply it to the description of
charmonium.


  We consider finite-range effects when the scattering length goes to zero near
a magnetically controlled Feshbach resonance. The traditional effective-range
expansion is badly behaved at this point and we therefore introduce an
effective potential that reproduces the full T-matrix. To lowest order the
effective potential goes as momentum squared times a factor that is
well-defined as the scattering length goes to zero. The potential turns out to
be proportional to the background scattering length squared times the
background effective range for the resonance. We proceed to estimate the
applicability and relative importance of this potential for Bose-Einstein
condensates and for two-component Fermi gases where the attractive nature of
the effective potential can lead to collapse above a critical particle number
or induce instability toward pairing and superfluidity. For broad Feshbach
resonances the higher-order effect is completely negligible. However, for
narrow resonances in tightly confined samples signatures might be
experimentally accessible. This could be relevant for sub-optical wavelength
microstructured traps at the interface of cold atoms and solid-state surfaces.


  Let $\widetilde{K}$ be a two-periodic braid and let $K$ be its quotient. In
this paper we show there is a spectral sequence from the next-to-top winding
number grading of the sutured annular Khovanov homology of the closure of
$\widetilde{K}$ to the next-to-top winding number grading of the sutured
annular Khovanov homology of the closure of $K$.


  Graphene field-effect transistors exhibit negligible transconductance under
two scenarios: for any gate-to-source voltage when the drain-to-source voltage
is set to zero, and for an arbitrary drain-to-source voltage provided that the
gate-to-source voltage equals the Dirac voltage. Hence, extracting the channel
and the parasitic series resistances from S-parameters under these conditions
enables analyzing their dependence on the gate and drain biases. This is
fundamental to assess the portion of the output resistance that is controlled
by the gate. Besides, the drain bias dependence of the drain and source
resistances is also evidenced. Within the proposal, resistive components
accounting for the lossy nature of the gate capacitance are incorporated into
the model, which exhibits a broadband correlation with experimental data. This
avoids the series resistances to be considered as frequency dependent in the
model.


  We describe here two simple polytopes that have different Betti numbers and
whose moment-angle manifolds are diffeomorphic.


  We establish new conditions that prevent the existence of (weak) normal
integral bases in tame Galois extensions of number fields. This leads to the
following result: under appropriate technical hypotheses, the existence of a
normal integral basis in the upper layer of an abelian tower Q \subset K
\subset L forces the tower to be split in a very strong sense.


  Continuum dislocation dynamics models of mesoscale plasticity consist of
dislocation transport-reaction equations coupled with crystal mechanics
equations. The coupling between these two sets of equations is such that
dislocation transport gives rise to the evolution of plastic distortion
(strain), while the evolution of the latter fixes the stress from which the
dislocation velocity field is found via a mobility law. Earlier solutions of
these equations employed a staggered solution scheme for the two sets of
equations in which the plastic distortion was updated via time integration of
its rate, as found from Orowan's law. In this work, we show that such a direct
time integration scheme can suffer from accumulation of numerical errors. We
introduce an alternative scheme based on field dislocation mechanics that
ensures consistency between the plastic distortion and the dislocation content
in the crystal. The new scheme is based on calculating the compatible and
incompatible parts of the plastic distortion separately, and the incompatible
part is calculated from the current dislocation density field. Stress field and
dislocation transport calculations were implemented within a finite element
based discretization of the governing equations, with the crystal mechanics
part solved by a conventional Galerkin method and the dislocation transport
equations by the least squares method. A simple test is first performed to show
the accuracy of the two schemes for updating the plastic distortion, which
shows that the solution method based on field dislocation mechanics is more
accurate. This method then was used to simulate an austenitic steel crystal
under uniaxial loading and multiple slip conditions.


  We show that an A-infinity algebra structure can be transferred to a
projective resolution of the complex underlying any A-infinity algebra. Under
certain connectedness assumptions, this transferred structure is unique up to
homotopy. In contrast to the classical results on transfer of A-infinity
structures along homotopy equivalences, our result is of interest when the
ground ring is not a field. We prove an analog for A-infinity module
structures, and both transfer results preserve strict units.


  With the increased interest in integrating renewable energy sources (RES)
such as wind power and solar into the power systems owing to their zero
greenhouse gas emissions and the involvement of power converters for
integration in grid, the detection, classification and mitigation of power
quality events has become indispensable. For employing an appropriate
mitigation technique, it is a pre-requisite to correctly classify the various
types of disturbances in power quality. This paper, therefore, presents a
detailed research reviews on detection and classification of power quality
disturbances caused by the integration of renewable energy sources and
associated works present in literature till date. Attempts are also made to
highlight the current and future issues involved in the detection,
classification and mitigation of PQ disturbances. Best efforts have been made
to make this paper serve as a full-fledged reference for the future work in
this field. A list of 230 research publications on the subject is also appended
for quick reference.


  Tumor is heterogeneous - a tumor sample usually consists of a set of
subclones with distinct transcriptional profiles and potentially different
degrees of aggressiveness and responses to drugs. Understanding tumor
heterogeneity is therefore critical to precise cancer prognosis and treatment.
In this paper, we introduce BayCount, a Bayesian decomposition method to infer
tumor heterogeneity with highly over-dispersed RNA sequencing count data. Using
negative binomial factor analysis, BayCount takes into account both the
between-sample and gene-specific random effects on raw counts of sequencing
reads mapped to each gene. For posterior inference, we develop an efficient
compound Poisson based blocked Gibbs sampler. Through extensive simulation
studies and analysis of The Cancer Genome Atlas lung cancer and kidney cancer
RNA sequencing count data, we show that BayCount is able to accurately estimate
the number of subclones, the proportions of these subclones in each tumor
sample, and the gene expression profiles in each subclone. Our method
represents the first effort in characterizing tumor heterogeneity using RNA
sequencing count data that simultaneously removes the need of normalizing the
counts, achieves statistical robustness, and obtains biologically and
clinically meaningful insights.


  Majorana zero modes (MZMs) that obey the non-Abelian statistics have been
intensively investigated for potential applications in topological quantum
computing. The prevailing signals in tunneling experiments "fingerprinting" the
existence of MZMs are the zero-energy bound states (ZEBSs). However, nearly all
of the previously reported ZEBSs showing signatures of the MZMs are observed in
difficult-to-fabricate heterostructures at very low temperatures and
additionally require applied magnetic field. Here, by using in-situ scanning
tunneling spectroscopy, we detect the ZEBSs upon the interstitial Fe adatoms
deposited on two different high-temperature superconducting one-unit-cell-thick
iron chalcogenides on SrTiO3(001). The spectroscopic results resemble the
phenomenological characteristics of the MZMs inside the vortex cores of
topological superconductors. Our experimental findings may extend the MZM
explorations in connate topological superconductors towards an applicable
temperature regime and down to the two-dimensional limit. While a concrete
understanding of the observations is lacking, possible explanations involving
novel 2D superconducting states with spin-orbit coupling, spontaneous
nucleation of anomalous vortices at the magnetic sites, and noncoplanar
magnetic ordering may further stimulate theoretical understandings of the
scarcely captured ZEBSs in strongly correlated systems with multiband Cooper
pairing.


  We investigate the local structure of the space $\mathcal{M}$ consisting of
isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff
metric. We consider finite metric spaces of the same cardinality and suppose
that these spaces are in general position, i.e., all nonzero distances in each
of the spaces are distinct, and all triangle inequalities are strict. We show
that sufficiently small balls in $\mathcal{M}$ centered at these spaces and
having the same radii are isometric. As consequences, we prove that the cones
over such spaces (with the vertices at one-point space) are isometrical; the
isometry group of each sufficiently small ball centered at a general position
$n$-points space, $n\ge3$, contains a subgroup isomorphic to the group $S_n$ of
permutations of a set containing $n$ points.


  The research feld of magnonics proposes a low-energy wave-logic computation
technology based on spin waves to complement the established CMOS technology
and provide a basis for emerging unconventional computation architectures.
However, magnetic damping is a limiting factor for all-magnonic logic circuits
and multi-device networks, ultimately rendering mechanisms to effciently
manipulate and amplify spin waves a necessity. In this regard, parallel pumping
is a versatile tool since it allows to selectively generate and amplify spin
waves. While extensively studied in microscopic systems, nano-scaled systems
are lacking investigation to assess the feasibility and potential future use of
parallel pumping in magnonics. Here, we investigate a longitudinally magnetized
100 nm-wide magnonic nano-conduit using space and time-resolved micro-focused
Brillouin-light-scattering spectroscopy. Employing parallel pumping to generate
spin waves, we observe that the non-resonant excitation of dipolar spin waves
is favored over the resonant excitation of short wavelength exchange spin
waves. In addition, we utilize this technique to access the effective spin-wave
relaxation time of an individual nano-conduit, observing a large relaxation
time up to (115.0 +- 7.6) ns. Despite the significant decrease of the pumping
effciency in the investigated nano-conduit, a reasonably small threshold is
found rendering parallel pumping feasible on the nano-scale.


  In a fractional coloring, vertices of a graph are assigned measurable subsets
of the real line and adjacent vertices receive disjoint subsets; the fractional
chromatic number of a graph is at most $k$ if it has a fractional coloring in
which each vertex receives a subset of $[0, 1]$ of measure at least $1/k$. We
introduce and develop the theory of "fractional colorings with local demands"
wherein each vertex "demands" a certain amount of color that is determined by
local parameters such as its degree or the clique number of its neighborhood.
This framework provides the natural setting in which to generalize
degree-sequence type bounds on the independence number. Indeed, by Linear
Programming Duality, all of the problems we study have an equivalent
formulation as a problem concerning weighted independence numbers, and they
often imply new bounds on the independence number.
  Our results and conjectures are inspired by many of the most classical
results and important open problems concerning the independence number and the
chromatic number, often simultaneously. We conjecture a local strengthening of
both Shearer's bound on the independence number of triangle-free graphs and the
fractional relaxation of Molloy's recent bound on their chromatic number, as
well as a longstanding problem of Ajtai et al.\ on the independence number of
$K_r$-free graphs and the fractional relaxations of Reed's $\omega, \Delta,
\chi$ Conjecture and the Total Coloring Conjecture. We prove an approximate
version of the first two, and we prove "local demands" versions of Vizing's
Theorem and of some $\chi$-boundedness results.


  We study quantum phase transitions in the ground state of the two dimensional
hard-core boson Hubbard Hamiltonian. Recent work on this and related models has
suggested ``supersolid'' phases with simultaneous diagonal and off-diagonal
long range order. We show numerically that, contrary to the generally held
belief, the most commonly discussed ``checkerboard'' supersolid is
thermodynamically unstable. Furthermore, this supersolid cannot be stabilized
by next near neighbour interaction. We obtain the correct phase diagram using
the Maxwell construction. We demonstrate the ``striped'' supersolid is
thermodynamically stable and is separated from the superfluid phase by a
continuous phase transition.


  The quality of human capital is crucial for software companies to maintain
competitive advantages in knowledge economy era. Software companies recognize
superior talent as a business advantage. They increasingly recognize the
critical linkage between effective talent and business success. However,
software companies suffering from high turnover rates often find it hard to
recruit the right talents. There is an urgent need to develop a personnel
selection mechanism to find the talents who are the most suitable for their
software projects. Data mining techniques assures exploring the information
from the historical projects depending on which the project manager can make
decisions for producing high quality software. This study aims to fill the gap
by developing a data mining framework based on decision tree and association
rules to refocus on criteria for personnel selection. An empirical study was
conducted in a software company to support their hiring decision for project
members. The results demonstrated that there is a need to refocus on selection
criteria for quality objectives. Better selection criteria was identified by
patterns obtained from data mining models by integrating knowledge from
software project database and authors research techniques.


  We construct forward self-similar solutions (expanders) for the compressible
Navier-Stokes equations. Some of these self-similar solutions are smooth, while
others exhibit a singularity do to cavitation at the origin.


  Surveys of the Milky Way (MW) and M31 enable detailed studies of stellar
populations across ages and metallicities, with the goal of reconstructing
formation histories across cosmic time. These surveys motivate key questions
for galactic archaeology in a cosmological context: when did the main
progenitor of a MW/M31-mass galaxy form, and what were the galactic building
blocks that formed it? We investigate the formation times and progenitor
galaxies of MW/M31-mass galaxies using the FIRE-2 cosmological simulations,
including 6 isolated MW/M31-mass galaxies and 6 galaxies in Local Group
(LG)-like pairs at z = 0. We examine main progenitor "formation" based on two
metrics: (1) transition from primarily ex-situ to in-situ stellar mass growth
and (2) mass dominance compared to other progenitors. We find that the main
progenitor of a MW/M31-mass galaxy emerged typically at z ~ 3-4 (11.6-12.2 Gyr
ago), while stars in the bulge region (inner 2 kpc) at z = 0 formed primarily
in a single main progenitor at z < 5 (< 12.6 Gyr ago). Compared with isolated
hosts, the main progenitors of LG-like paired hosts emerged significantly
earlier (\Delta z ~ 2, \Delta t ~ 1.6 Gyr), with ~ 4x higher stellar mass at
all z > 4 (> 12.2 Gyr ago). This highlights the importance of environment in
MW/M31-mass galaxy formation, especially at early times. Overall, about 100
galaxies with M_star > 10^5 M_sun formed a typical MW/M31-mass system. Thus,
surviving satellites represent a highly incomplete census (by ~ 5x) of the
progenitor population.


  Let $n$ be an integer and $s$ be a real number such that $n > 2s \geq 2$.
Inspired by the perturbation approach initiated by F. Hang and P. Yang
(\textit{Int. Math. Res. Not. IMRN}, 2020), we are interested in non-negative,
smooth solution $v$ to the following higher-order fractional equation \[
{\mathbf P}_n^{2s}(v) = Q_n^{2s}(\varepsilon v+v^\alpha) \] on $\mathbf S^n$
with $0<\alpha \leq (n+2s)/(n-2s)$, and $\varepsilon \geq 0$. Here ${\mathbf
P}_n^{2s}$ is the fractional GJMS type operator of order $2s$ on $\mathbf S^n$
and $Q_n^{2s} ={\mathbf P}_n^{2s}(1)$ is constant. We show that if $\varepsilon
>0$ and $0<\alpha \leq (n+2s)/(n-2s)$, then any positive, smooth solution $v$
to the above equation must be constant. The same result remains valid if
$\varepsilon=0$ but with $0<\alpha < (n+2s)/(n-2s)$.As a by-product, with
$0<\alpha\leq (n+2s)/(n-2s)$, we compute the sharp constant of the
subcritical/critical Sobolev inequalities \[ \int_{\mathbf S^n} v {\mathbf
P}_n^{2s} (v) d\mu_{g_{\mathbf S^n}} \geq \frac{\Gamma (n/2 + s)}{\Gamma (n/2 -
s )} | \mathbf S^n|^\frac{\alpha-1}{\alpha+1} \Big( \int_{\mathbf S^n}
v^{\alpha+1} d\mu_{g_{\mathbf S^n}} \Big)^\frac{2}{\alpha+1}. \] for the GJMS
operator ${\mathbf P}_n^{2s}$ on $\mathbf S^n$ and for all non-negative
functions $v\in H^s(\mathbf S^n)$.


  We formulate a framework for discrete-time quantum walks, motivated by
classical random walks with memory. We present a specific representation of the
classical walk with memory 2 on which this is based. The framework has no need
for coin spaces, it imposes no constraints on the evolution operator other than
unitarity, and is unifying of other approaches. As an example we construct a
symmetric discrete-time quantum walk on the semi-infinite binary tree. The
generating function of the amplitude at the root is computed in closed-form, as
a function of time and the initial level n in the tree, and we find the
asymptotic and a full numerical solution for the amplitude. It exhibits a sharp
interference peak and a power law tail, as opposed to the exponentially
decaying tail of a broadly peaked distribution of the classical symmetric
random walk on a binary tree. The probability peak is orders of magnitude
larger than it is for the classical walk (already at small n). The quantum walk
shows a polynomial algorithmic speedup in n over the classical walk, which we
conjecture to be of the order 2/3, based on strong trends in data.


  The radially outward flow of fluid through a porous medium occurs in many
practical problems, from transport across vascular walls to the pressurisation
of boreholes in the subsurface. When the driving pressure is non-negligible
relative to the stiffness of the solid structure, the poromechanical coupling
between the fluid and the solid can control both the steady-state and the
transient mechanics of the system. Very large pressures or very soft materials
lead to large deformations of the solid skeleton, which introduce kinematic and
constitutive nonlinearity that can have a nontrivial impact on these mechanics.
Here, we study the transient response of a poroelastic cylinder to sudden fluid
injection. We consider the impacts of kinematic and constitutive nonlinearity,
both separately and in combination, and we highlight the central role of
driving method in the evolution of the response. We show that the various
facets of nonlinearity may either accelerate or decelerate the transient
response relative to linear poroelasticity, depending on the boundary
conditions and the initial geometry, and that an imposed fluid pressure leads
to a much faster response than an imposed fluid flux.


  Eliashberg theory provides a theoretical framework for understanding the
phenomenon of superconductivity when pairing between two electrons is mediated
by phonons, and retardation effects are fully accounted for. However, when a
direct Coulomb interaction between two electrons is also present, this
interaction is only partially accounted for. In this work we use a well-defined
Hamiltonian, the Hubbard-Holstein model, to examine this competition more
rigorously, using exact diagonalization on a two-site system. We find that the
direct electron-electron repulsion between two electrons has a significantly
more harmful effect on pairing than suggested through the standard treatment of
this interaction.


  For a closed oriented surface $ \Sigma $ we define its degenerations into
singular surfaces that are locally homeomorphic to wedges of disks. Let
$X_{\Sigma,n}$ be the set of isomorphism classes of orientation preserving
$n$-fold branched coverings $ \Sigma\rightarrow S^2 $ of the two-dimensional
sphere. We complete $X_{\Sigma,n}$ with the isomorphism classes of mappings
that cover the sphere by the degenerations of $ \Sigma $. In case $
\Sigma=S^2$, the topology that we define on the obtained completion
$\bar{X}_{\Sigma,n}$ coincides on $X_{S^2,n}$ with the topology induced by the
space of coefficients of rational functions $ P/Q $, where $ P,Q $ are
homogeneous polynomials of degree $ n $ on $ \mathbb{C}\mathrm{P}^1\cong S^2$.
  We prove that $\bar{X}_{\Sigma,n}$ coincides with the
Diaz-Edidin-Natanzon-Turaev compactification of the Hurwitz space
$H(\Sigma,n)\subset X_{\Sigma,n}$ consisting of isomorphism classes of branched
coverings with all critical values being simple.


  We study the entropic force by introducing a bound $S \le A^{3/4}$ between
entropy and area which was derived by imposing the non-gravitational collapse
condition. In this case, applying a modified entropic force to this system does
not lead to the Newtonian force law.


  Novel emergent phenomena are expected to occur under conditions exceeding the
QED critical electric field, where the vacuum becomes unstable to
electron-positron pair production. The required intensity to reach this regime,
$\sim10^{29}\,\mathrm{Wcm^{-2}}$, cannot be achieved even with the most intense
lasers now being planned/constructed without a sizeable Lorentz boost provided
by interactions with ultrarelativistic particles. Seeded laser-laser collisions
may access this strong-field QED regime at laser intensities as low as
$\sim10^{24}\,\mathrm{Wcm^{-2}}$. Counterpropagating e-beam--laser interactions
exceed the QED critical field at still lower intensities
($\sim10^{20}\,\mathrm{Wcm^{-2}}$ at $\sim10\,\mathrm{GeV}$). Novel emergent
phenomena are predicted to occur in the "QED plasma regime", where strong-field
quantum and collective plasma effects play off one another. Here the electron
beam density becomes a decisive factor. Thus, the challenge is not just to
exceed the QED critical field, but to do so with high quality, approaching
solid-density electron beams. Even though laser wakefield accelerators (LWFA)
represent a very promising research field, conventional accelerators still
provide orders of magnitude higher charge densities at energies
$\gtrsim10\,\mathrm{GeV}$. Co-location of extremely dense and highly energetic
electron beams with a multi-petawatt laser system would therefore enable
seminal research opportunities in high-field physics and laboratory
astrophysics. This white paper elucidates the potential scientific impact of
multi-beam capabilities that combine a multi-PW optical laser,
high-energy/density electron beam, and high-intensity x rays and outlines how
to achieve such capabilities by co-locating a 3-10 PW laser with a
state-of-the-art linear accelerator.


  The R Coronae Australis dark cloud is one of the closest star-forming regions
to the Sun. The cloud is known to be very active in star formation, harboring
many Herbig-Haro objects (HHs) and Molecular Hydrogen emission-line Objects
(MHOs). In this work we present results from molecular observations (a
$5.5^{'}\times5.5^{'}$ map of $^{12}$CO J$=3-2$ and HCO$^{+}$ J$=4-3$, and a
single spectrum of N$_{2}$H$^{+}$ J$=4-3$) obtained with the Atacama
Submillimeter Telescope Experiment (ASTE) towards the R CrA dark cloud with an
angular and spectral resolution of 22$^{"}$ and 0.11 km s$^{-1}$, respectively.
From the $^{12}$CO J$=3-2$ line we found kinematical spectral features strongly
suggesting the presence of outflows towards a region populated by several HHs
and MHOs. Moreover, most of these objects lie within an HCO$^{+}$ maximum,
suggesting that its emission arises from an increasement of its abundance due
to the chemistry triggered by the outflow activity. Additionally, we are
presenting the first reported detection of N$_{2}$H$^{+}$ in the J$=4-3$ line
towards the R CrA dark cloud.


  We present large deviations estimates in the supremum norm for a system of
independent random walks superposed with a birth-and-death dynamics evolving on
the discrete torus with $N$ sites. The scaling limit considered is the
so-called \textit{high density limit} (see the survey \cite{franco} on the
subject), where space, time and initial quantity of particles are rescaled. The
associated rate functional here obtained is a semi-linearised version of the
rate function of \cite{JonaLandimVares}, which dealt with large deviations of
exclusion processes superposed with birth-and-death dynamics. An ingredient in
the proof of large deviations consists in providing a limit of a suitable class
of perturbations of the original process. This is precisely one of the main
contributions of this work: a strategy to extend the original high density
approach (as in \cite{Arnold,blount2,blount,francogroisman,Kote2,KoteHigh1988})
to weakly asymmetric systems. Two cases are considered with respect to the
initial quantity of particles, the power law and the (at least) exponential
growth. In the first case, we present the lower bound only on a certain subset
of smooth profiles, while in the second case, additionally assuming concavity
of the birth and the death functions and a constant initial profile, we provide
a full large deviations principle.


  The aim of this paper is to investigate the use of close formula
approximation for pricing European mortgage options. Under the assumption of
logistic duration and normal mortgage rates the underlying price at the option
expiry is approximated by shifted lognormal or regular lognormal distribution
by matching moments. Once the price function is approximated by lognormal
distributions, the option price can be computed directly as an integration of
the distribution function over the payoff at the option expiry by using
Black-Scholes-Merton close formula. We will see that lower curvature levels
correspond to positively skewness price distributions and in this case
lognormal approximation leads to close parametric formula representation in
terms of all model parameters. The proposed methodologies are tested against
Monte Carlo approach under different market and contract parameters and the
tests confirmed that the close form approximation have a very good accuracy.


  The main idea of this ISO is to use StarGAN (A type of GAN model) to perform
training and testing on an emotion dataset resulting in a emotion recognition
which can be generated by the valence arousal score of the 7 basic expressions.
We have created an entirely new dataset consisting of 4K videos. This dataset
consists of all the basic 7 types of emotions: Happy, Sad, Angry, Surprised,
Fear, Disgust, Neutral. We have performed face detection and alignment followed
by annotating basic valence arousal values to the frames/images in the dataset
depending on the emotions manually. Then the existing StarGAN model is trained
on our created dataset after which some manual subjects were chosen to test the
efficiency of the trained StarGAN model.


  Due to the climate change debate, a lot of research and maps of external
climate parameters are available. However, maps of indoor climate performance
parameters are still lacking. This paper presents a methodology for obtaining
maps of performances of similar buildings that are virtually spread over whole
Europe. The produced maps are useful for analyzing regional climate influence
on building performance indicators such as energy use and indoor climate. This
is shown using the Bestest building as a reference benchmark. An important
application of the mapping tool is the visualization of potential building
measures over the EU. Also the performances of single building components can
be simulated and mapped. It is concluded that the presented method is efficient
as it takes less than 15 minutes to simulate and produce the maps on a
2.6GHz/4GB computer. Moreover, the approach is applicable for any type of
building.


  Functional regression is very crucial in functional data analysis and a
linear relationship between scalar response and functional predictor is often
assumed. However, the linear assumption may not hold in practice, which makes
the methods for linear models invalid. To gain more flexibility, we focus on
functional nonlinear models and aim to develop new method that requires no
strict constraint on the nonlinear structure. Inspired by the idea of the
kernel method in machine learning, we propose a kernel functional partial least
squares (KFPLS) method for the functional nonlinear models. The innovative
algorithm works on the prediction of the scalar response and is accompanied by
R package KFPLS for implementation. The simulation study demonstrates the
effectiveness of the proposed method for various types of nonlinear models.
Moreover, the real world application also shows the superiority of the proposed
KFPLS method.


  There has been tremendous progress in the degree of realism of
three-dimensional radiation magneto-hydrodynamic simulations of the solar
atmosphere in the past decades. Four of the most frequently used numerical
codes are Bifrost, CO5BOLD, MANCHA3D, and MURaM. Here we test and compare the
wave propagation characteristics in model runs from these four codes by
measuring the dispersion relation of acoustic-gravity waves at various heights.
We find considerable differences between the various models. The height
dependence of wave power, in particular of high-frequency waves, varies by up
to two orders of magnitude between the models, and the phase difference spectra
of several models show unexpected features, including $\pm180^\circ$ phase
jumps.


  Several finite element methods for simulating incompressible flows rely on
the streamline upwind Petrov-Galerkin stabilization (SUPG) term, which is
weighted by tau_SUPG. The conventional formulation of tau_SUPG includes a
constant that depends on the time step size, producing an overall method that
becomes exceedingly less accurate as the time step size approaches zero. In
practice, such method inconsistency introduces significant error in the
solution, especially in cardiovascular simulations, where small time step sizes
may be required. To overcome this issue, we propose a consistent method that is
based on a new definition of tau_SUPG. This method, which can be easily
implemented on top of an existing streamline upwind Petrov-Galerkin and
pressure stabilizing Petrov-Galerkin method, involves the replacement of the
time step size in tau_SUPG with a physical time scale. This time scale is
calculated in a simple operation once every time step for the entire
computational domain from the ratio of the L2-norm of the acceleration and the
velocity. The proposed method is compared against the conventional method using
four cases: a steady pipe flow, a blood flow through vascular anatomy, an
external flow over a square obstacle, and a fluid-structure interaction case.
These numerical experiments show that the proposed formulation eliminates the
inconsistency issue associated with the conventional formulation in all cases.
While the proposed method is slightly more costly than the conventional method,
it significantly reduces the error, particularly at small time step sizes. For
the pipe flow where an exact solution is available, we show the conventional
method can over-predict the pressure drop by a factor of three. This large
error is almost completely eliminated by the proposed formulation, dropping to
approximately 1% for all time step sizes and Reynolds numbers considered.


  The evolution of Artificial Intelligence (AI) has been significantly
accelerated by advancements in Large Language Models (LLMs) and Large
Multimodal Models (LMMs), gradually showcasing potential cognitive reasoning
abilities in problem-solving and scientific discovery (i.e., AI4Science) once
exclusive to human intellect. To comprehensively evaluate current models'
performance in cognitive reasoning abilities, we introduce OlympicArena, which
includes 11,163 bilingual problems across both text-only and interleaved
text-image modalities. These challenges encompass a wide range of disciplines
spanning seven fields and 62 international Olympic competitions, rigorously
examined for data leakage. We argue that the challenges in Olympic competition
problems are ideal for evaluating AI's cognitive reasoning due to their
complexity and interdisciplinary nature, which are essential for tackling
complex scientific challenges and facilitating discoveries. Beyond evaluating
performance across various disciplines using answer-only criteria, we conduct
detailed experiments and analyses from multiple perspectives. We delve into the
models' cognitive reasoning abilities, their performance across different
modalities, and their outcomes in process-level evaluations, which are vital
for tasks requiring complex reasoning with lengthy solutions. Our extensive
evaluations reveal that even advanced models like GPT-4o only achieve a 39.97%
overall accuracy, illustrating current AI limitations in complex reasoning and
multimodal integration. Through the OlympicArena, we aim to advance AI towards
superintelligence, equipping it to address more complex challenges in science
and beyond. We also provide a comprehensive set of resources to support AI
research, including a benchmark dataset, an open-source annotation platform, a
detailed evaluation tool, and a leaderboard with automatic submission features.


  Hyperspherical close-coupling method is used to calculate the elastic,
positronium formation and excitation cross sections for positron collisions
with atomic hydrogen at energies below the H(n=4) threshold for the J=2 partial
wave. The resonances below each inelastic threshold are also analyzed. The
adiabatic hyperspherical potential curves are used to identify the nature of
these resonances.