  In this work, we present optical space imaging using an unconventional yet
promising class of imaging devices known as neuromorphic event-based sensors.
These devices, which are modeled on the human retina, do not operate with
frames, but rather generate asynchronous streams of events in response to
changes in log-illumination at each pixel. These devices are therefore
extremely fast, do not have fixed exposure times, allow for imaging whilst the
device is moving and enable low power space imaging during daytime as well as
night without modification of the sensors. Recorded at multiple remote sites,
we present the first event-based space imaging dataset including recordings
from multiple event-based sensors from multiple providers, greatly lowering the
barrier to entry for other researchers given the scarcity of such sensors and
the expertise required to operate them. The dataset contains 236 separate
recordings and 572 labeled resident space objects. The event-based imaging
paradigm presents unique opportunities and challenges motivating the
development of specialized event-based algorithms that can perform tasks such
as detection and tracking in an event-based manner. Here we examine a range of
such event-based algorithms for detection and tracking. The presented methods
are designed specifically for space situational awareness applications and are
evaluated in terms of accuracy and speed and suitability for implementation in
neuromorphic hardware on remote or space-based imaging platforms.


  Celestial and momentum space amplitudes for massless particles are related to
each other by a change of basis provided by the Mellin transform. Therefore
properties of celestial amplitudes have counterparts in momentum space
amplitudes and vice versa. In this paper, we study the celestial avatar of dual
superconformal symmetry of $\mathcal{N}=4$ Yang-Mills theory. We also analyze
various differential equations known to be satisfied by celestial $n$-point
tree-level MHV amplitudes and identify their momentum space origins.


  It is well-known that the number of particles produced in cosmology, commonly
defined in the literature from the Fock space of the instantaneous hamiltonian
of the canonically normalized fields, is ambiguous. On the other hand, the
energy computed from the energy-momentum tensor should be physical. We compare
the corresponding Fock spaces and relate them through a Bogolyubov
transformation. We find that for particles of spin $0$, $1$ and $3/2$ the two
Fock spaces are different, whereas they are the same for spin $1/2$ fermions.
For spin $0$ and $1$, for particles of high momenta the two Fock spaces align,
as intuitively expected. For the spin $3/2$, one finds two puzzles. The first
one is that the two corresponding Fock spaces do not match even in the limit of
high momenta. The second is that whereas we provide evidence for the
equivalence theorem between longitudinal gravitinos and the goldstino in terms
of an exact matching between the lagrangians and the instantaneous hamiltonians
for the canonically normalized fields, the energy operator computed from the
Rarita--Schwinger action does not seem to be captured in a simple way by the
goldstino action. Our results suggest a re-analysis of non-thermal gravitino
production in cosmology.


  We report on an \textit{ab}-anisotropy of $J_{c \parallel b}/J_{c \parallel
a}% \cong 1.8$ and $I_{c}R_{n \parallel b}/I_{c}R_{n \parallel a}\cong 1.2$ in
ramp-edge junctions between untwinned YBa$_{2}$Cu$_{3}$O$_{7}$ and $s$% -wave
Nb. For these junctions, the angle $\theta $ with the YBa$_{2}$Cu$_{3}$O$_{7}$
crystal b-axis is varied as a single parameter. The
$R_{n}$A($\theta$)-dependence presents 2-fold symmetry. The minima in
$I_{c}R_{n}$ at $\theta \cong 50^{\circ}$ suggest a real s-wave subdominant
component and negligible $d_{xy}$-wave or imaginary s-wave admixtures. The
$I_{c}R_{n}$($\theta$)-dependence is well-fitted by 83% $d_{x^{2}-y^{2}}$-, 15%
isotropic $s$- and 2% anisotropic s-wave order parameter symmetry, consistent
with $\Delta_{b}/\Delta_{a} \cong 1.5$.


  We present a simple mechanism for generating a Higgs quartic in composite
Higgs models without a corresponding quadratic term. The extra quartic will
originate from a Higgs dependent kinetic mixing between additional fermionic
states. The mechanism can be naturally embedded to models with maximal symmetry
as well as Twin Higgs models. The resulting Twin Higgs models will have a fully
natural realistic Higgs potential, where the quartic mechanism will serve as
the only source for the $Z_2$ breaking, while the top and gauge sectors can
remain exactly $Z_2$ invariant.


  We study the Kapteyn series $% %TCIMACRO{\dsum \limits_{n=1}^{\infty}}%
%BeginExpansion {\displaystyle\sum\limits_{n=1}^{\infty}} %EndExpansion
t^{n}\mathrm{J}_{n}(nz) $. We find a series representation in powers of $z$ and
analyze its radius of convergence.


  The covariance matrix adaptation evolution strategy (CMA-ES) is an efficient
continuous black-box optimization method. The CMA-ES possesses many attractive
features, including invariance properties and a well-tuned default
hyperparameter setting. Moreover, several components to specialize the CMA-ES
have been proposed, such as noise handling and constraint handling. To utilize
these advantages in mixed-integer optimization problems, the CMA-ES with margin
has been proposed. The CMA-ES with margin prevents the premature convergence of
discrete variables by the margin correction, in which the distribution
parameters are modified to leave the generation probability for changing the
discrete variable. The margin correction has been applied to
($\mu/\mu_\mathrm{w}$,$\lambda$)-CMA-ES, while this paper introduces the margin
correction into (1+1)-CMA-ES, an elitist version of CMA-ES. The (1+1)-CMA-ES is
often advantageous for unimodal functions and can be computationally less
expensive. To tackle the performance deterioration on mixed-integer
optimization, we use the discretized elitist solution as the mean of the
sampling distribution and modify the margin correction not to move the elitist
solution. The numerical simulation using benchmark functions on mixed-integer,
integer, and binary domains shows that (1+1)-CMA-ES with margin outperforms the
CMA-ES with margin and is better than or comparable with several specialized
methods to a particular search domain.


  Whole and targeted sequencing of human genomes is a promising, increasingly
feasible tool for discovering genetic contributions to risk of complex
diseases. A key step is calling an individual's genotype from the multiple
aligned short read sequences of his DNA, each of which is subject to nucleotide
read error. Current methods are designed to call genotypes separately at each
locus from the sequence data of unrelated individuals. Here we propose
likelihood-based methods that improve calling accuracy by exploiting two
features of sequence data. The first is the linkage disequilibrium (LD) between
nearby SNPs. The second is the Mendelian pedigree information available when
related individuals are sequenced. In both cases the likelihood involves the
probabilities of read variant counts given genotypes, summed over the
unobserved genotypes. Parameters governing the prior genotype distribution and
the read error rates can be estimated either from the sequence data itself or
from external reference data. We use simulations and synthetic read data based
on the 1000 Genomes Project to evaluate the performance of the proposed
methods. An R-program to apply the methods to small families is freely
available at http://med.stanford.edu/epidemiology/PHGC/.


  The prospect of nonparametric reconstructions of cosmological parameters from
observational data sets has been a popular topic in the literature for a number
of years. This has mainly taken the form of a technique based on Gaussian
processes but this approach is exposed to several foundational issues ranging
from overfitting to kernel consistency problems. In this work, we explore the
possibility of using artificial neural networks (ANN) to reconstruct late-time
expansion and large scale structure cosmological parameters. We first show how
mock data can be used to design an optimal ANN for both parameters, which we
then use with real data to infer their respective redshift profiles. We further
consider cosmological null tests with the reconstructed data in order to
confirm the validity of the concordance model of cosmology, in which we observe
a mild deviation with cosmic growth data.


  Given a bipartite graph $G = (V_1,V_2,E)$ where edges take on {\it both}
positive and negative weights from set $\mathcal{S}$, the {\it maximum weighted
edge biclique} problem, or $\mathcal{S}$-MWEB for short, asks to find a
bipartite subgraph whose sum of edge weights is maximized. This problem has
various applications in bioinformatics, machine learning and databases and its
(in)approximability remains open. In this paper, we show that for a wide range
of choices of $\mathcal{S}$, specifically when $| \frac{\min\mathcal{S}} {\max
\mathcal{S}} | \in \Omega(\eta^{\delta-1/2}) \cap O(\eta^{1/2-\delta})$ (where
$\eta = \max\{|V_1|, |V_2|\}$, and $\delta \in (0,1/2]$), no polynomial time
algorithm can approximate $\mathcal{S}$-MWEB within a factor of $n^{\epsilon}$
for some $\epsilon > 0$ unless $\mathsf{RP = NP}$. This hardness result gives
justification of the heuristic approaches adopted for various applied problems
in the aforementioned areas, and indicates that good approximation algorithms
are unlikely to exist. Specifically, we give two applications by showing that:
1) finding statistically significant biclusters in the SAMBA model, proposed in
\cite{Tan02} for the analysis of microarray data, is
$n^{\epsilon}$-inapproximable; and 2) no polynomial time algorithm exists for
the Minimum Description Length with Holes problem \cite{Bu05} unless
$\mathsf{RP=NP}$.


  Deep Neural Networks (DNNs) are vulnerable to adversarial examples, which
causes serious threats to security-critical applications. This motivated much
research on providing mechanisms to make models more robust against adversarial
attacks. Unfortunately, most of these defenses, such as gradient masking, are
easily overcome through different attack means. In this paper, we propose
MUTEN, a low-cost method to improve the success rate of well-known attacks
against gradient-masking models. Our idea is to apply the attacks on an
ensemble model which is built by mutating the original model elements after
training. As we found out that mutant diversity is a key factor in improving
success rate, we design a greedy algorithm for generating diverse mutants
efficiently. Experimental results on MNIST, SVHN, and CIFAR10 show that MUTEN
can increase the success rate of four attacks by up to 0.45.


  In this paper, we investigate the convergence order in probability of a novel
ergodic numerical scheme for damped stochastic nonlinear Schr\"{o}dinger
equation with an additive noise. Theoretical analysis shows that our scheme is
of order one in probability under appropriate assumptions for the initial value
and noise. Meanwhile, we show that our scheme possesses the unique ergodicity
and preserves the discrete conformal multi-symplectic conservation law.
Numerical experiments are given to show the longtime behavior of the discrete
charge and the time average of the numerical solution, and to test the
convergence order, which verify our theoretical results.


  A toy model giving rise to long lived super heavy particles and an small
vacuum density energy, of the order of the one measured in the present
universe, is constructed. This model consists in hidden sector invariant under
an $SU(2)_L$ gauge symmetry, whose masses are provided by the standard Higgs
mechanism. It is assumed that the standard model particles are also charged
under this interaction. The hidden fermions and the hidden Higgs are
super-heavy, which mass values close to the GUT scale. In addition, there is an
spontaneously broken U(1) chiral symmetry, giving rise to a pseudoscalar
Goldstone boson which we refer as a "hidden axion". We model the vacuum energy
of the universe as the potential energy of this pseudoscalar, and this fixes
several scales of the model. In particular, it is shown that the interaction
between the hidden and the ordinary sector is very weak, of the order of the
gravitational one. The approach to the vacuum energy problem presented here is
a quintessence like mechanism, in which it is assumed that the true vacuum
density energy is zero for some unknown reason, except for the contribution of
the light axion. As consequence of the weakness of this interaction, the hidden
Higgs is long lived and may act as a super heavy component of the dark matter
at present times.


  By making use of the background field method, we derive a novel reformulation
of the Yang-Mills theory which was proposed recently by the author to derive
quark confinement in QCD. This reformulation identifies the Yang-Mills theory
with a deformation of a topological quantum field theory. The relevant
background is given by the topologically non-trivial field configuration,
especially, the topological soliton which can be identified with the magnetic
monopole current in four dimensions. We argue that the gauge fixing term
becomes dynamical and that the gluon mass generation takes place by a
spontaneous breakdown of the hidden supersymmetry caused by the dimensional
reduction. We also propose a numerical simulation to confirm the validity of
the scheme we have proposed. Finally we point out that the gauge fixing part
may have a geometric meaning from the viewpoint of global topology where the
magnetic monopole solution represents the critical point of a Morse function in
the space of field configurations.


  We approach autonomous drone-based reforestation with a collaborative
multi-agent reinforcement learning (MARL) setup. Agents can communicate as part
of a dynamically changing network. We explore collaboration and communication
on the back of a high-impact problem. Forests are the main resource to control
rising CO2 conditions. Unfortunately, the global forest volume is decreasing at
an unprecedented rate. Many areas are too large and hard to traverse to plant
new trees. To efficiently cover as much area as possible, here we propose a
Graph Neural Network (GNN) based communication mechanism that enables
collaboration. Agents can share location information on areas needing
reforestation, which increases viewed area and planted tree count. We compare
our proposed communication mechanism with a multi-agent baseline without the
ability to communicate. Results show how communication enables collaboration
and increases collective performance, planting precision and the risk-taking
propensity of individual agents.


  We investigate a top-down approach for modeling the dark energy where we fit
the luminosity distances directly rather than indirectly fitting the equation
of state.


  A slight incompatibility in recent low-energy and high-energy \alpha_s
measurements can be interpreted as evidence for new light colour degrees of
freedom. Assuming that these are the gluinos of a supersymmetric extension of
the Standard Model, we investigate to what extent they change the standard QCD
predictions for deep inelastic structure functions, and in particular whether
thay can be detected in such measurements at HERA. We present a modified set of
parton distributions which includes a light gluino distribution and which can
be used for further phenomenological investigations.


  The concept of informal mathematical proof considered in intuitionism is
apparently vulnerable to a version of the liar paradox. However, a careful
reevaluation of this concept reveals a subtle error whose correction blocks the
contradiction. This leads to a general resolution of the classical semantic
paradoxes. This paper is an expanded version of parts of my earlier paper
"Constructive truth and circularity" [arXiv:0905.1681].


  A non-potential quasi-static evolution model coupling the Sun's photospheric
and coronal magnetic fields is applied to the problem of filament chirality at
high latitudes. For the first time, we run a continuous 15 year simulation,
using bipolar active regions determined from US National Solar Observatory,
Kitt Peak magnetograms between 1996 and 2011. Using this simulation, we are
able to address the outstanding question of whether magnetic helicity transport
from active latitudes can overcome the effect of differential rotation at
higher latitudes. Acting alone, differential rotation would produce high
latitude filaments with opposite chirality to the majority type in each
hemisphere. We find that differential rotation can indeed lead to opposite
chirality at high latitudes, but only for around 5 years of the solar cycle
following the polar field reversal. At other times, including the rising phase,
transport of magnetic helicity from lower latitudes overcomes the effect of in
situ differential rotation, producing the majority chirality even on the polar
crowns at polar field reversal. These simulation predictions will allow for
future testing of the non-potential coronal model. The results indicate the
importance of long-term memory and helicity transport from active latitudes
when modeling the structure and topology of the coronal magnetic field at
higher latitudes.


  When the reduced twisted $C^*$-algebra $C^*_r(\mathcal{G}, c)$ of a
non-principal groupoid $\mathcal{G}$ admits a Cartan subalgebra, Renault's work
on Cartan subalgebras implies the existence of another groupoid description of
$C^*_r(\mathcal{G}, c)$. In an earlier paper, joint with Reznikoff and Wright,
we identified situations where such a Cartan subalgebra arises from a
subgroupoid $\mathcal{S}$ of $\mathcal{G}$. In this paper, we study the
relationship between the original groupoids $\mathcal{S}, \mathcal{G}$ and the
Weyl groupoid and twist associated to the Cartan pair. We first identify the
spectrum $\mathfrak{B}$ of the Cartan subalgebra $C^*_r(\mathcal{S}, c)$. We
then show that the quotient groupoid $\mathcal{G}/\mathcal{S}$ acts on
$\mathfrak{B}$, and that the corresponding action groupoid is exactly the Weyl
groupoid of the Cartan pair. Lastly we show that, if the quotient map
$\mathcal{G}\to\mathcal{G}/\mathcal{S}$ admits a continuous section, then the
Weyl twist is also given by an explicit continuous $2$-cocycle on
$\mathcal{G}/\mathcal{S} \ltimes \mathfrak{B}$.


  Autonomous assistance of people with motor impairments is one of the most
promising applications of autonomous robotic systems. Recent studies have
reported encouraging results using deep reinforcement learning (RL) in the
healthcare domain. Previous studies showed that assistive tasks can be
formulated as multi-agent RL, wherein there are two agents: a caregiver and a
care-receiver. However, policies trained in multi-agent RL are often sensitive
to the policies of other agents. In such a case, a trained caregiver's policy
may not work for different care-receivers. To alleviate this issue, we propose
a framework that learns a robust caregiver's policy by training it for diverse
care-receiver responses. In our framework, diverse care-receiver responses are
autonomously learned through trials and errors. In addition, to robustify the
care-giver's policy, we propose a strategy for sampling a care-receiver's
response in an adversarial manner during the training. We evaluated the
proposed method using tasks in an Assistive Gym. We demonstrate that policies
trained with a popular deep RL method are vulnerable to changes in policies of
other agents and that the proposed framework improves the robustness against
such changes.


  We consider a square-integrable semimartingale and investigate the convex
order relations between its discrete, continuous and predictable quadratic
variation. As the main results, we show that if the semimartingale has
conditionally independent increments and symmetric jump measure, then its
discrete realized variance dominates its quadratic variation in increasing
convex order. The results have immediate applications to the pricing of options
on realized variance. For a class of models including time-changed Levy models
and Sato processes with symmetric jumps our results show that options on
variance are typically underpriced, if quadratic variation is substituted for
the discretely sampled realized variance.


  We present observations of the known anomalous microwave emission region,
G159.6-18.5, in the Perseus molecular cloud at 16 GHz performed with the
Arcminute Microkelvin Imager Small Array. These are the highest angular
resolution observations of G159.6-18.5 at microwave wavelengths. By combining
these microwave data with infrared observations between 5.8 and 160 \mu m from
the Spitzer Space Telescope, we investigate the existence of a microwave -
infrared correlation on angular scales of ~2 arcmin. We find that the overall
correlation appears to increase towards shorter infrared wavelengths, which is
consistent with the microwave emission being produced by electric dipole
radiation from small, spinning dust grains. We also find that the microwave -
infrared correlation peaks at 24 \mu m (6.7\sigma), suggesting that the
microwave emission is originating from a population of stochastically heated
small interstellar dust grains rather than polycyclic aromatic hydrocarbons.


  We consider a two-level discrete-time control framework with real-time
constraints where a central controller issues setpoints to be implemented by
local controllers. The local controllers implement the setpoints with some
approximation and advertize a prediction of their constraints to the central
controller. The local controllers might not be able to implement the setpoint
exactly, due to prediction errors or because the central controller convexifies
the problem for tractability. In this paper, we propose to compensate for these
mismatches at the level of the local controller by using a variant of the error
diffusion algorithm. We give conditions under which the minimal (convex)
invariant set for the accumulated-error dynamics is bounded, and give a
computational method to construct this set. This can be used to compute a bound
on the accumulated error and hence establish convergence of the average error
to zero. We illustrate the approach in the context of real-time control of
electrical grids.


  This work addresses the problem of real-time rendering of photorealistic
human body avatars learned from multi-view videos. While the classical
approaches to model and render virtual humans generally use a textured mesh,
recent research has developed neural body representations that achieve
impressive visual quality. However, these models are difficult to render in
real-time and their quality degrades when the character is animated with body
poses different than the training observations. We propose an animatable human
model based on 3D Gaussian Splatting, that has recently emerged as a very
efficient alternative to neural radiance fields. The body is represented by a
set of gaussian primitives in a canonical space which is deformed with a coarse
to fine approach that combines forward skinning and local non-rigid refinement.
We describe how to learn our Human Gaussian Splatting (HuGS) model in an
end-to-end fashion from multi-view observations, and evaluate it against the
state-of-the-art approaches for novel pose synthesis of clothed body. Our
method achieves 1.5 dB PSNR improvement over the state-of-the-art on THuman4
dataset while being able to render in real-time (80 fps for 512x512
resolution).


  Results of a search for new phenomena in events with an energetic photon and
large missing transverse momentum with the ATLAS experiment at the Large Hadron
Collider are reported. The data were collected in proton--proton collisions at
a centre-of-mass energy of 13 TeV and correspond to an integrated luminosity of
3.2 $\rm fb^{-1}$. The observed data are in agreement with the Standard Model
expectations. Exclusion limits are presented in models of new phenomena
including pair production of dark matter candidates or large extra spatial
dimensions. In a simplified model of dark matter and an axial-vector mediator,
the search excludes mediator masses of up to 710 GeV for dark matter candidate
masses up to 150 GeV. In an effective theory of dark matter production, values
of the suppression scale $M_*$ up to 570 GeV are excluded and the effect of
truncation for various coupling values is reported. For the ADD large extra
spatial dimension model the search places more stringent limits than earlier
searches in the same event topology, excluding $M_{\rm D}$ up to about 2.3
(2.8) TeV for two (six) additional spatial dimensions; the limits are reduced
by 20--40% depending on the number of additional spatial dimensions when
applying a truncation procedure.


  Studies of the large $N$ behaviour of the topological properties of gauge
theories typically focused on the large $N$ scaling of the topological
susceptibility. A much more difficult task is the study of the behaviour of
higher cumulants of the topological charge in the large $N$ limit, which up to
now remained elusive. We will present first results confirming the expected
large $N$ scaling of the coefficient commonly denoted by $b_2$, related to the
kurtosis of the topological charge.


  We study the budgeted laminar matroid independent set problem. The input is a
ground set, where each element has a cost and a non-negative profit, along with
a laminar matroid over the elements and a budget. The goal is to select a
maximum profit independent set of the matroid whose total cost is bounded by
the budget. Several well known special cases, where we have, e.g., no matroid
constraint (the classic knapsack problem) or a uniform matroid constraint
(knapsack with a cardinality constraint), admit a fully polynomial-time
approximation scheme (FPTAS). In contrast, the budgeted matroid independent set
(BMI) problem with a general matroid has an efficient polynomial-time
approximation scheme (EPTAS) but does not admit an FPTAS. This implies an EPTAS
for our problem, which is the best known result prior to this work.
  We present an FPTAS for budgeted laminar matroid independent set, improving
the previous EPTAS for this matroid family and generalizing the FPTAS known for
knapsack with a cardinality constraint and multiple-choice knapsack. Our scheme
is based on a simple dynamic program which utilizes the tree-like structure of
laminar matroids.


  A new class of static plane symmetric solution of Einstein field equation,
which is judged as the source of Taub solution, was presented in our previous
work. In this letter the properties of geodesics of this solution are explored.
It is found that this solution can be an appropriate simulation to the field of
a uniformly accelerated observer in Newton mechanics. The essence of the source
is investigated. A phantom with dust and photon is suggested as the substance
of the source matter.


  Let f be a non-invertible holomorphic endomorphism of P^k having an
attracting set A. We show that, under some natural assumptions, A supports a
unique invariant positive closed current \tau, of the right bidegree and of
mass 1. Moreover, if R is a current supported in a small neighborhood of A then
its push-forwards by f^n converge to \tau exponentially fast. We also prove
that the equilibrium measure on A is hyperbolic.


  A (non-commutative) Ulam quasimorphism is a map $q$ from a group $\Gamma$ to
a topological group $G$ such that $q(xy)q(y)^{-1}q(x)^{-1}$ belongs to a fixed
compact subset of $G$. Generalizing the construction of Barge and Ghys, we
build a family of quasimorphisms on a fundamental group of a closed manifold
$M$ of negative sectional curvature, taking values in an arbitrary Lie group.
This construction, which generalizes the Barge-Ghys quasimorphisms, associates
a quasimorphism to any principal $G$-bundle with connection on $M$. Kapovich
and Fujiwara have shown that all quasimorphisms taking values in a discrete
group can be constructed from group homomorphisms and quasimorphisms taking
values in a commutative group. We construct Barge-Ghys type quasimorphisms
taking prescribed values on a given subset in $\Gamma$, producing
counterexamples to the Kapovich and Fujiwara theorem for quasimorphisms taking
values in a Lie group. Our construction also generalizes a result proven by D.
Kazhdan in his paper ``On $\epsilon$-representations''. Kazhdan has proved that
for any $\epsilon >0$, there exists an $\epsilon$-representation of the
fundamental group of a Riemann surface of genus 2 which cannot be
$1/10$-approximated by a representation. We generalize his result by
constructing an $\epsilon$-representation of the fundamental group of a closed
manifold of negative sectional curvature taking values in an arbitrary Lie
group.


  The distributions of the quark number and chiral condensate over the gauge
fields are computed for QCD in Euclidean space at nonzero quark chemical
potential. As both operators are non-hermitian the distributions are in the
complex plane. Moreover, because of the sign problem, the distributions are not
real and positive. The computations are carried out within leading order chiral
perturbation theory and give a direct insight into the delicate cancellations
that take place in contributions to the total baryon number and the chiral
condensate.


  The importance of many-body effects on electronic and magnetic properties and
stability of different structural phases was studied in novel iron oxide -
Fe$_2$O. It was found that while Hubbard repulsion hardly affects the
electronic spectrum of this material ($m^*/m \sim 1.2$), but it strongly
changes its phase diagram shifting critical pressures of structural transitions
to much lower values. Moreover, one of the previously obtained in the density
functional theory (DFT) structures (P$\bar 3$m1) becomes energetically unstable
if many-body effects are taken into consideration. It is shown that this is an
account of magnetic moment fluctuations in the DFT+DMFT approach, which
strongly contributes to modification of the phase diagram of Fe$_2$O.


  We have performed optical polarimetric observations of the SN2006aj
associated to the X-ray flash (XRF) of February 18, 2006, XRF060218 that
provide information on its expansion geometry. The data were acquired in the
R-band with the 0.7m telescope of Crimea, 2.5m Nordic Optical Telescope and the
2.2m of Calar Alto. We report the detection of linear polarization between 3
and 39 days after the gamma-ray event (t-t_0). This represents the first
polarization detection of a Ic supernova (SN) associated to an XRF. Our data
exhibit a degree of linear polarization (P) around P~4% at t-t_0 ~ 3-5 days,
followed by a constant polarization phase with P~1.4% at 13.7 < t-t_0 < 39
days. Our data suggest a decay in P, and more interestingly, show a position
angle (\theta) rotation of ~100 degrees comparing data taken before and after
the R-band lightcurve peak. The reported polarization measurements can be
explained by the evolution of an asymmetric SN expansion. We discuss on several
ingredients that could account for the observed \theta rotation.


  We discuss the binding energy E_b of impurities in semiconductors within
density functional theory (DFT) and the GW approximation, focusing on donors in
nanowires as an example. We show that DFT succeeds in the calculation of E_b
from the Kohn-Sham (KS) hamiltonian of the ionized impurity, but fails in the
calculation of E_b from the KS hamiltonian of the neutral impurity, as it
misses most of the interaction of the bound electron with the surface
polarization charges of the donor. We trace this deficiency back to the lack of
screened exchange in the present functionals.


  Momentum-transfer (q) dependent non-resonant inelastic x-ray scattering
measurements were made at the N4,5 edges for several rare earth compounds. With
increasing q, giant dipole resonances diminish, to be replaced by strong
multiplet lines at lower energy transfer. These multiplets result from two
different orders of multipole scattering and are distinct for systems with
simple 4f^0 and 4f^1 initial states. A many-body theoretical treatment of the
multiplets agrees well with the experimental data on ionic La and Ce phosphate
reference compounds. Comparing measurements on CeO2 and CeRh3 to the theory and
the phosphates indicates sensitivity to hybridization as observed by a
broadening of 4f^0-related multiplet features. We expect such strong, nondipole
features to be generic for NIXS from f-electron systems.


  B-mode ultrasound is commonly used to image musculoskeletal tissues, but one
major bottleneck is data interpretation, and analyses of muscle thickness,
pennation angle and fascicle length are often still performed manually. In this
study we trained deep neural networks (based on U-net) to detect muscle
fascicles and aponeuroses using a set of labelled musculoskeletal ultrasound
images. We then compared neural network predictions on new, unseen images to
those obtained via manual analysis and two existing semi/automated analysis
approaches (SMA and Ultratrack). With a GPU, inference time for a single image
with the new approach was around 0.7s, compared to 4.6s with a CPU. Our method
detects the locations of the superficial and deep aponeuroses, as well as
multiple fascicle fragments per image. For single images, the method gave
similar results to those produced by a non-trainable automated method (SMA;
mean difference in fascicle length: 1.1 mm) or human manual analysis (mean
difference: 2.1 mm). Between-method differences in pennation angle were within
1$^\circ$, and mean differences in muscle thickness were less than 0.2 mm.
Similarly, for videos, there was strong overlap between the results produced
with Ultratrack and our method, with a mean ICC of 0.73, despite the fact that
the analysed trials included hundreds of frames. Our method is fully automated
and open source, and can estimate fascicle length, pennation angle and muscle
thickness from single images or videos, as well as from multiple superficial
muscles. We also provide all necessary code and training data for custom model
development.


  In this contribution, we calculate the light deflection, perihelium shift,
time delay and gravitational redshift using an approximate metric that contains
the Kerr metric and an approximaction of the Erez-Rosen spacetime. The results
were obtained directly using Mathematica. The results agree with the ones
presented in the literature, but they are extended until second order terms of
mass, angular momentum and mass quadrupole.


  According to standard theory the magnetoresistance magnitude in ferromagnetic
manganites crucially depends on the electron-phonon coupling strength. We
showed that in La0.7Sr0.3MnO3 the phonon renormalization is strong, despite its
relatively small magnetoresistance. Here, we report results of a similar
inelastic neutron scattering investigation of a closely related compound,
La0.8Sr0.2MnO3, where the magnetoresistance is enhanced. We find similar phonon
renormalization and dynamic CE-type polaron correlations as in La0.7Sr0.3MnO3.
However, quantitative comparison of the results for the two samples shows that
only polaron lifetime is well correlated with the strength of the CMR.


  We minimize elastic energies on framed curves which penalize both curvature
and torsion. We also discuss critical points using the infinite dimensional
version of the Lagrange multipliers' method. Finally, some examples arising
from the applications are discussed and also numerical experiments are
presented.


  A new exact and analytic solution of non-relativistic fireball hydrodynamics
is presented. It describes an expanding triaxial ellipsoid that rotates around
one of its principal axes. The observables are calculated using simple analytic
formulas. Azimuthal oscillation of the off-diagonal Bertsch-Pratt radii of
Bose-Einstein correlations as well as rapidity dependent directed and third
flow measurements provide means to determine the magnitude of the rotation of
the fireball. Observing this rotation and its dependence on collision energy
may lead to new information on the equation of state of the strongly
interacting quark gluon plasma produced in high energy heavy ion collisions.


  As a contribution to the ongoing discussion of trajectories of spinless
particles in spaces with torsion we show that the geometry of such spaces can
be induced by embedding their curves in a euclidean space without torsion.
Technically speaking, we define the tangent (velocity) space of the embedded
space imposing non-holonomic constraints upon the tangent space of the
embedding space. Parallel transport in the embedded space is determined as an
induced parallel transport on the surface of constraints. Gauss' principle of
least constraint is used to show that autoparallels realize a constrained
motion that has a minimal deviation from the free, unconstrained motion, this
being a mathematical expression of the principle of inertia.


  We present ONeRF, a method that automatically segments and reconstructs
object instances in 3D from multi-view RGB images without any additional manual
annotations. The segmented 3D objects are represented using separate Neural
Radiance Fields (NeRFs) which allow for various 3D scene editing and novel view
rendering. At the core of our method is an unsupervised approach using the
iterative Expectation-Maximization algorithm, which effectively aggregates 2D
visual features and the corresponding 3D cues from multi-views for joint 3D
object segmentation and reconstruction. Unlike existing approaches that can
only handle simple objects, our method produces segmented full 3D NeRFs of
individual objects with complex shapes, topologies and appearance. The
segmented ONeRfs enable a range of 3D scene editing, such as object
transformation, insertion and deletion.


  We explore connections between the generalized multiplicities of square-free
monomial ideals and the combinatorial structure of the underlying hypergraphs
using methods of commutative algebra and polyhedral geometry. For instance, we
show the $j$-multiplicity is multiplicative over the connected components of a
hypergraph, and we explicitly relate the $j$-multiplicity of the edge ideal of
a properly connected uniform hypergraph to the Hilbert-Samuel multiplicity of
its special fiber ring. In addition, we provide general bounds for the
generalized multiplicities of the edge ideals and compute these invariants for
classes of uniform hypergraphs.


  According to \cite{Dvz}, we know that the class of all EMV-algebras,
$\mathsf{EMV}$, is not a variety, since it is not closed under the subalgebra
operator. The main aim of this work is to find the least variety containing
$\mathsf{EMV}$. For this reason, we introduced the variety $\mathsf{wEMV}$ of
wEMV-algebras of type $(2,2,2,2,0)$ induced by some identities. We show that,
adding a derived binary operation $\ominus$ to each EMV-algebra
$(M;\vee,\wedge,\oplus,0)$, we extend its language, so that
$(M;\vee,\wedge,\oplus,\ominus,0)$, called an associated wEMV-algebra, belongs
to $\mathsf{wEMV}$. Then using the congruence relations induced by the prime
ideals of a wEMV-algebra, we prove that each wEMV-algebra can be embedded into
an associated wEMV-algebra. We show that $\mathsf{wEMV}$ is the least
subvariety of the variety of wEMV-algebras containing $\mathsf{EMV}$. Finally,
we study Pierce sheaves of proper EMV-algebras.


  In this contribution we present the ionization structure in the enhanced wind
from the hot star in symbiotic binaries during active phases. Rotation of the
hot star leads to the compression of the outflowing material towards its
equatorial plane. As a result a neutral disk-like zone around the active hot
star near the orbital plane is created. We modelled the compression of the wind
using the wind compression model. Further, we calculated the neutral disk-like
zone in the enhanced wind from the hot star using the equation of the
photoionization equilibrium. The presence of such neutral disk-like zones was
also suggested on the basis of the modelling the spectral energy distribution
of symbiotic binaries. We confront the calculated ionization structures in the
enhanced wind from the hot star with the observations. We found that the
calculated column density of the neutral hydrogen atoms in the neutral
disk-like zone and the emission measure of the ionized part of the wind from
the hot star are in a good agreement with quantities derived from observations
during active phases. The presence of such neutral disk-like zones is
transient, being connected with the active phases of symbiotic binaries. During
quiescent phases, such neutral disk-like zones cannot be created, because of
insufficient mass loss rate of the hot star.


  We introduce CAPRI-Net, a neural network for learning compact and
interpretable implicit representations of 3D computer-aided design (CAD)
models, in the form of adaptive primitive assemblies. Our network takes an
input 3D shape that can be provided as a point cloud or voxel grids, and
reconstructs it by a compact assembly of quadric surface primitives via
constructive solid geometry (CSG) operations. The network is self-supervised
with a reconstruction loss, leading to faithful 3D reconstructions with sharp
edges and plausible CSG trees, without any ground-truth shape assemblies. While
the parametric nature of CAD models does make them more predictable locally, at
the shape level, there is a great deal of structural and topological
variations, which present a significant generalizability challenge to
state-of-the-art neural models for 3D shapes. Our network addresses this
challenge by adaptive training with respect to each test shape, with which we
fine-tune the network that was pre-trained on a model collection. We evaluate
our learning framework on both ShapeNet and ABC, the largest and most diverse
CAD dataset to date, in terms of reconstruction quality, shape edges,
compactness, and interpretability, to demonstrate superiority over current
alternatives suitable for neural CAD reconstruction.


  Code search is a common practice for developers during software
implementation. The challenges of accurate code search mainly lie in the
knowledge gap between source code and natural language (i.e., queries). Due to
the limited code-query pairs and large code-description pairs available, the
prior studies based on deep learning techniques focus on learning the semantic
matching relation between source code and corresponding description texts for
the task, and hypothesize that the semantic gap between descriptions and user
queries is marginal. In this work, we found that the code search models trained
on code-description pairs may not perform well on user queries, which indicates
the semantic distance between queries and code descriptions. To mitigate the
semantic distance for more effective code search, we propose QueCos, a
Query-enriched Code search model. QueCos learns to generate semantic enriched
queries to capture the key semantics of given queries with reinforcement
learning (RL). With RL, the code search performance is considered as a reward
for producing accurate semantic enriched queries. The enriched queries are
finally employed for code search. Experiments on the benchmark datasets show
that QueCos can significantly outperform the state-of-the-art code search
models.


  Knowledge distillation (KD) has emerged as a promising technique in deep
learning, typically employed to enhance a compact student network through
learning from their high-performance but more complex teacher variant. When
applied in the context of image super-resolution, most KD approaches are
modified versions of methods developed for other computer vision tasks, which
are based on training strategies with a single teacher and simple loss
functions. In this paper, we propose a novel Multi-Teacher Knowledge
Distillation (MTKD) framework specifically for image super-resolution. It
exploits the advantages of multiple teachers by combining and enhancing the
outputs of these teacher models, which then guides the learning process of the
compact student network. To achieve more effective learning performance, we
have also developed a new wavelet-based loss function for MTKD, which can
better optimize the training process by observing differences in both the
spatial and frequency domains. We fully evaluate the effectiveness of the
proposed method by comparing it to five commonly used KD methods for image
super-resolution based on three popular network architectures. The results show
that the proposed MTKD method achieves evident improvements in super-resolution
performance, up to 0.46dB (based on PSNR), over state-of-the-art KD approaches
across different network structures. The source code of MTKD will be made
available here for public evaluation.


  In this paper, we present an efficient implementation method of physical
layer of Y-00 which can support a secure communication and a quantum key
distribution (more generally key expansion) by IMDD(intensity modulation/direct
detection) or FSK(frequency shift keying)optical fiber communication network.
Although the general proof of the security is not yet given, a brief sketch of
security analysis is shown, which involve an entanglement attack.


  We study the multiple populations of $\omega$ Cen by using the abundances of
Fe, C, N, O, Mg, Al, Si, K, Ca, and Ce from the high-resolution, high
signal-to-noise (S/N$>$70) spectra of 982 red giant stars observed by the
SDSS-IV/APOGEE-2 survey. We find that the shape of the Al-Mg and N-C
anticorrelations changes as a function of metallicity, continuous for the
metal-poor groups, but bimodal (or unimodal) at high metallicities. There are
four Fe populations, similar to what has been found in previously published
investigations, but we find seven populations based on Fe, Al, and Mg
abundances. The evolution of Al in $\omega$ Cen is compared to its evolution in
the Milky Way and in five representative globular clusters. We find that the
distribution of Al in metal-rich stars of $\omega$ Cen closely follows what is
observed in the Galaxy. Other $\alpha-$elements and C, N, O, and Ce are also
compared to the Milky Way, and significantly elevated abundances are observed
over what is found in the thick disk for almost all elements. However, we also
find some stars with high metallicity and low [Al/Fe], suggesting that $\omega$
Cen could be the remnant core of a dwarf galaxy, but the existence of these
peculiar stars needs an independent confirmation. We also confirm the increase
in the sum of CNO as a function of metallicity previously reported in the
literature and find that the [C/N] ratio appears to show opposite correlations
between Al-poor and Al-rich stars as a function of metallicity.


  Neural networks have proven to be very powerful at computer vision tasks.
However, they often exhibit unexpected behaviours, violating known requirements
expressing background knowledge. This calls for models (i) able to learn from
the requirements, and (ii) guaranteed to be compliant with the requirements
themselves. Unfortunately, the development of such models is hampered by the
lack of datasets equipped with formally specified requirements. In this paper,
we introduce the ROad event Awareness Dataset with logical Requirements
(ROAD-R), the first publicly available dataset for autonomous driving with
requirements expressed as logical constraints. Given ROAD-R, we show that
current state-of-the-art models often violate its logical constraints, and that
it is possible to exploit them to create models that (i) have a better
performance, and (ii) are guaranteed to be compliant with the requirements
themselves.


  In this article we implement a method for the computation of a nonlinear
elliptic problem with nonstandard growth driven by the $p(x)-$Laplacian
operator. Our implementation is based in the {\em decomposition--coordination}
method that allows us, via an iterative process, to solve in each step a linear
differential equation and a nonlinear algebraic equation. Our code is
implemented in {\sc MatLab} in 2 dimensions and turns out to be extremely
efficient from the computational point of view.


  There is limited information about interaction strength of scalar dark matter
candidate with hadrons and leptons for scalar particle mass exceeding $10^{-3}$
eV while its interaction with photon is well-studied. The scalar-photon
coupling constant receives quantum corrections from one-loop Feynman diagrams
which involve the scalar-lepton, scalar-quark and scalar-W boson vertices. We
calculate these one-loop quantum corrections and find new limits on the scalar
particle interactions with electron, muon, tau, quarks, nucleons, gluons and W
boson for $m_{\phi}<15$ MeV by re-purposing the results of experiments
measuring the scalar-photon interaction. Limits on interactions with heavy
leptons and quarks have been obtained for the first time, limits on other
interactions in certain mass intervals are 2 to 15 orders of magnitude stronger
than those presented in previous publications.


  In an attempt to find a polynomial-time algorithm for the edge-clique cover
problem on cographs we tried to prove that the edge-clique graphs of cographs
have bounded rankwidth. However, this is not the case. In this note we show
that the edge-clique graphs of cocktail party graphs have unbounded rankwidth.


  The present paper is a continuation of author's paper arXiv:1909.00940
[math.AT] devoted to the lemmas of Alexander and Sperner, but is independent
from it. We begin by a step back from Alexander and Sperner to Lebesgue work on
the invariance of the dimension. In contrast with almost everybody else,
Lebesgue worked with cubes rather than with simplices. His methods were
developed by Hurewicz and Lusternik-Schnirelmann and then forgotten. In the
present paper these methods are recast in the language of cubical chains and
cochains.
  After this, we present a new approach to Lebesgue and Lusternik-Schnirelmann
theorems which is both conceptual and elementary. It is based on adaptation of
Serre's definition of products of singular cubical cochains to discrete
setting. The main results are new purely combinatorial "cubical lemmas". This
approach also clarifies the cubical versions of Sperner lemma of Kuhn and Ky
Fan. In particular, Ky Fan's lemma can be understood as a natural strengthening
of Lebesgue or Kuhn's results under a transversality assumption.
  The exposition does not assume any knowledge of algebraic topology.


  The fundamental ($f$-) mode gravitational waves from cold low-mass neutron
stars are systematically studied with various equations of state (EOSs)
characterized by the nuclear saturation parameters, especially focusing on the
phenomena of the avoided crossing with the first pressure ($p_1$-) mode. We
find that the $f$-mode frequency and the average density for the neutron star
at the avoided crossing can be expressed as a function of the parameter,
$\eta$, which is the specific combination of the nuclear saturation parameters.
Owing to these relations, we can derive the empirical formula expressing the
$f$-mode frequency for a low-mass neutron star, whose central density is larger
than that for the neutron star at the avoided crossing, as a function of $\eta$
and the square root of the stellar average density, $x$. On the other hand, we
also derive the empirical formula expressing the $f$-mode frequency for a
neutron star, whose central density is less than that for the neutron star at
the avoided crossing, as a function of $x$ independently of the adopted EOS.
Furthermore, adopting the empirical formula of $x$ as a function of $\eta$ and
$u_c$, which is the ratio of the stellar central density to the saturation
density, we can also rewrite our empirical formula for the $f$-mode frequency
to a function of $\eta$ and $u_c$. So, by observing the $f$-mode gravitational
wave from a low-mass neutron star, whose mass or gravitational redshift is
known, one could evaluate the values of $\eta$ and $u_c$, which enables us to
severely constrain the EOS for neutron star matter.


  We show from a simulations-based study of the TACTIC telescope that fractal
and wavelet analysis of Cerenkov images, recorded in a single imaging Cerenkov
telescope, enables almost complete segregation of isotropic gamma-ray initiated
events from the overwhelming background of cosmic-ray hadron-initiated events.
This presents a new method for measuring galactic and extragalactic gamma-ray
background above 1 TeV energy. Preliminary results based on this method are
reported here. Primary aim is to explore the possibility of using data recorded
by a single imaging atmospheric Cerenkov telescope(IACT) for making accurate
measurements of diffuse galactic and extragalactic gamma-ray flux above ~1 TeV
energy. Using simulated data of atmospheric Cerenkov images recorded in an
IACT, initiated both by cosmic ray protons and diffuse gamma-rays with energies
above 4 TeV and 2 TeV respectively, we identify the most efficient fractal
/wavelet parameters of the recorded images for primary identification. The
method is based on the pattern recognition technique and employs fractal and
wavelet analysis of the recorded Cerenkov images for gamma-hadron segregation.
We show that the value of wavelet dimension parameter B6 can segregate Cerenkov
images of hadronic origin from those of diffuse gamma-ray origin with almost
100% accuracy. We use the results to get a preliminary upper limit estimate of
the diffuse galactic gamma-ray flux within galactic range of |b|\leq -50 and
|l|\leq 2000 above 2TeV from a 36h data set recorded by the TACTIC telescope.


  We report the results of surveys we conducted in the US and Israel in 2020, a
time when many prices increased following the spread of the pandemic. To assess
respondents perceptions of price increases, we focus on goods whose prices have
increased during the pandemic, including some essential goods. Consistent with
the principle of dual entitlement, we find that respondents perceive price
increases as more acceptable if they are due to cost shocks than if they are
due to demand shocks. However, we also find large differences across the two
populations, as well as across goods.


  We consider a number of graph kernels and proximity measures including
commute time kernel, regularized Laplacian kernel, heat kernel, exponential
diffusion kernel (also called "communicability"), etc., and the corresponding
distances as applied to clustering nodes in random graphs and several
well-known datasets. The model of generating random graphs involves edge
probabilities for the pairs of nodes that belong to the same class or different
predefined classes of nodes. It turns out that in most cases, logarithmic
measures (i.e., measures resulting after taking logarithm of the proximities)
perform better while distinguishing underlying classes than the "plain"
measures. A comparison in terms of reject curves of inter-class and intra-class
distances confirms this conclusion. A similar conclusion can be made for
several well-known datasets. A possible origin of this effect is that most
kernels have a multiplicative nature, while the nature of distances used in
cluster algorithms is an additive one (cf. the triangle inequality). The
logarithmic transformation is a tool to transform the first nature to the
second one. Moreover, some distances corresponding to the logarithmic measures
possess a meaningful cutpoint additivity property. In our experiments, the
leader is usually the logarithmic Communicability measure. However, we indicate
some more complicated cases in which other measures, typically, Communicability
and plain Walk, can be the winners.


  Filaments are elongated structures that connect groups and clusters of
galaxies and are visually the striking feature in cosmological maps. In the
literature, typically filaments are defined only using galaxies, assuming that
these are good tracers of the dark matter distribution, despite the fact that
galaxies are a biased indicator. Here we apply the topological filament
extractor DisPerSE to the predictions of the semi-analytic code GAEA to
investigate the correspondence between the properties of $z=0$ filaments
extracted using the distribution of dark matter and the distribution of model
galaxies evolving within the same large-scale structure. We focus on filaments
around massive clusters with a mass comparable to Virgo and Coma, with the
intent of investigating the influence of massive systems and their feeding
filamentary structure on the physical properties of galaxies. We apply
different methods to compare the properties of filaments based on the different
tracers and study how the sample selection impacts the extraction. Overall,
filaments extracted using different tracers agree, although they never coincide
totally. We also find that the number of filaments ending up in the massive
clusters identified using galaxies distribution is typically underestimated
with respect to the corresponding dark matter filament extraction.


  Using the superfield approach we construct the n = 2 supersymmetric
lagrangian for the FRW Universe with perfect fluid as matter fields. The
obtained supersymmetric algebra allowed us to take the square root of the
Wheeler-DeWitt equation and solve the corresponding quantum constraint. This
model leads to the relation between the vacuum energy density and the energy
density of the dust matter.


  A large number of galactic binary systems emit gravitational waves (GW)
continuously with frequencies below $\sim$10 mHz. The LISA mission could
identify tens of thousands of binaries over years of observation and will be
subject to the confusion noise around 1 mHz yielded by the unresolved sources.
Beyond LISA, there are several missions have been proposed to observe GWs in
the sub-mHz range where the galactic foreground is expected to be overwhelming
the instrumental noises. In this study, we investigate the detectability of
sub-mHz GW missions to detect the galactic double white dwarf (DWD) binaries
and evaluate the confusion noise produced by the undistinguished DWDs. This
confusion noise could also be viewed as a stochastic GW foreground and be
effectively observed in the sub-mHz band. The parameter determinations for the
modeled foreground are examined by employing different detector sensitivities
and population models. By assuming the determined foregrounds could be
subtracted from the data, we evaluate the residuals which are expected to have
power spectral densities two orders of magnitude lower than the originals data.


  In this contribution, the latest ALICE results on charmed baryon production
are presented. In particular the measurements of $\Lambda_{\rm c}^{+}$-baryon
production in pp collisions at ${\sqrt{\rm s}}$ = 5.02 TeV and in p-Pb
collisions at $\sqrt{\rm s_{NN}}$ = 5.02 TeV are shown and compared with
previous measurements performed using pp and p-Pb data samples collected during
LHC Run 1. At mid-rapidity charmed baryons are reconstructed via their hadronic
decay and semileptonic decay channels, exploiting the high precision tracking,
excellent vertexing and particle identification capabilities offered by the
ALICE detector. The first measurement of $\Lambda_{\rm c}^{+}$-baryon
production in Pb-Pb collisions at $\sqrt{\rm s_{NN}}$ = 5.02 TeV is also shown.
Results are compared with theoretical expectations.


  A dual lattice vortex formulation of homogeneous turbulence is developed,
within the Martin-Siggia-Rose field theoretical approach. It consists of a
generalization of the usual dipole version of the Navier-Stokes equations,
known to hold in the limit of vanishing external forcing. We investigate, as a
straightforward application of our formalism, the dynamics of closed vortex
tubes, randomly stirred at large length scales by gaussian stochastic forces.
We find that besides the usual self-induced propagation, the vortex tube
evolution may be effectively modeled through the introduction of an additional
white-noise correlated velocity field background. The resulting
phenomenological picture is closely related to observations previously reported
from a wavelet decomposition analysis of turbulent flow configurations.


  Mamba, based on state space model (SSM) with its linear complexity and great
success in classification provide its superiority in 3D point cloud analysis.
Prior to that, Transformer has emerged as one of the most prominent and
successful architectures for point cloud analysis. We present PointABM, a
hybrid model that integrates the Mamba and Transformer architectures for
enhancing local feature to improve performance of 3D point cloud analysis. In
order to enhance the extraction of global features, we introduce a
bidirectional SSM (bi-SSM) framework, which comprises both a traditional token
forward SSM and an innovative backward SSM. To enhance the bi-SSM's capability
of capturing more comprehensive features without disrupting the sequence
relationships required by the bidirectional Mamba, we introduce Transformer,
utilizing its self-attention mechanism to process point clouds. Extensive
experimental results demonstrate that integrating Mamba with Transformer
significantly enhance the model's capability to analysis 3D point cloud.


  In this paper, we prove that if a finite group acts smoothly and effectively
on an integral homology six-sphere and the fixed point set has an odd Euler
characteristic, then the acting group is isomorphic to either the alternating
group on five letters, the symmetric group on five letters, or the Cartesian
product of the alternating group on five letters and a group of order 2 and the
fixed point set consists of precisely one point.


  The presence of a strong magnetic background can modify the nature and the
dynamics of the chiral phase transition at finite temperature. We compute the
modified effective potential in the linear sigma model with quarks to one loop
in the $\bar{MS}$ scheme for $N_{f}=2$. For fields $eB\sim 5 m_{\pi}^{2}$ and
larger a crossover is turned into a weak first-order transition. We discuss
possible implications for non-central heavy ion collisions at RHIC and LHC, and
for the primordial QCD transition.


  Dynamical descriptions and modeling of natural systems have generally focused
on fixed points, with saddles and saddle-based phase-space objects such as
heteroclinic channels/cycles being central concepts behind the emergence of
quasi-stable long transients. Reliable and robust transient dynamics observed
for real, inherently noisy systems is, however, not met by saddle-based
dynamics, as demonstrated here. Generalizing the notion of ghost states, we
provide a complementary framework that does not rely on the precise knowledge
or existence of (un)stable fixed points, but rather on slow directed flows
organized by ghost sets in ghost channels and ghost cycles. Moreover, we show
that appearance of these novel objects is an emergent property of a broad class
of models, typically used for description of natural systems.


  This paper reviews the effects of general relativity in an X-ray spectrum
reflected from a cold matter accreting onto a black hole. The spectrum consists
of the iron K$\alpha$ line and the Compton reflection. We sketch the overall
picture of radiative processes in the central parts of the accretion flow with
relation to the relativistic effects derived from the discrete features in the
X-ray spectrum. We discuss implications for detection of relativistic effects
and computational tools of spectral analysis.


  Explicit determination of the mean first-passage time (MFPT) for trapping
problem on complex media is a theoretical challenge. In this paper, we study
random walks on the Apollonian network with a trap fixed at a given hub node
(i.e. node with the highest degree), which are simultaneously scale-free and
small-world. We obtain the precise analytic expression for the MFPT that is
confirmed by direct numerical calculations. In the large system size limit, the
MFPT approximately grows as a power-law function of the number of nodes, with
the exponent much less than 1, which is significantly different from the
scaling for some regular networks or fractals, such as regular lattices,
Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is
the most efficient configuration for transport by diffusion among all
previously studied structure.


  This paper evaluates the utility of Rhetorical Structure Theory (RST) trees
and relations in discourse coherence evaluation. We show that incorporating
silver-standard RST features can increase accuracy when classifying coherence.
We demonstrate this through our tree-recursive neural model, namely
RST-Recursive, which takes advantage of the text's RST features produced by a
state of the art RST parser. We evaluate our approach on the Grammarly Corpus
for Discourse Coherence (GCDC) and show that when ensembled with the current
state of the art, we can achieve the new state of the art accuracy on this
benchmark. Furthermore, when deployed alone, RST-Recursive achieves competitive
accuracy while having 62% fewer parameters.


  We give an interpretation of the Riemann hypothesis in terms of complex and
topological dynamics. For example, the Riemann hypothesis is affirmative and
all zeros of the Riemann zeta function are simple if and only if a certain
meromorphic function has no attracting fixed point. To obtain this, we use
holomorphic index (residue fixed point index), which characterizes local
properties of fixed points in complex dynamics.


  The most popular tools for analysing the large scale distribution of galaxies
are second-order spatial statistics such as the two-point correlation function
or its Fourier transform, the power spectrum. In this review, we explain how
our knowledge of cosmic structures, encapsulated by these statistical
descriptors, has evolved since their first use when applied on the early galaxy
catalogues to the present generation of wide and deep redshift surveys,
incorporating the most challenging discovery in the study of the galaxy
distribution: the detection of Baryon Acoustic Oscillations.


  Nearest-neighbour clustering is a simple yet powerful machine learning
algorithm that finds natural application in the decoding of signals in
classical optical-fibre communication systems. Quantum k-means clustering
promises a speed-up over the classical k-means algorithm; however, it has been
shown to not currently provide this speed-up for decoding optical-fibre signals
due to the embedding of classical data, which introduces inaccuracies and
slowdowns. Although still not achieving an exponential speed-up for NISQ
implementations, this work proposes the generalised inverse stereographic
projection as an improved embedding into the Bloch sphere for quantum distance
estimation in k-nearest-neighbour clustering, which allows us to get closer to
the classical performance. We also use the generalised inverse stereographic
projection to develop an analogous classical clustering algorithm and benchmark
its accuracy, runtime and convergence for decoding real-world experimental
optical-fibre communication data. This proposed 'quantum-inspired' algorithm
provides an improvement in both the accuracy and convergence rate with respect
to the k-means algorithm. Hence, this work presents two main contributions.
Firstly, we propose the general inverse stereographic projection into the Bloch
sphere as a better embedding for quantum machine learning algorithms; here, we
use the problem of clustering quadrature amplitude modulated optical-fibre
signals as an example. Secondly, as a purely classical contribution inspired by
the first contribution, we propose and benchmark the use of the general inverse
stereographic projection and spherical centroid for clustering optical-fibre
signals, showing that optimizing the radius yields a consistent improvement in
accuracy and convergence rate.


  Light bosonic fields mediate long range forces between objects. If these
fields have self-interactions, i.e., non-quadratic terms in the potential, the
experimental constraints on such forces can be drastically altered due to a
screening (chameleon) or enhancement effect. We explore how technically natural
values for such self-interaction coupling constants modify the existing
constraints. We point out that assuming the existence of these natural
interactions leads to new constraints, contrary to the usual expectation that
screening leads to gaps in coverage. We discuss how screening can turn
fundamentally equivalence principle (EP)-preserving forces into EP-violating
ones. This means that when natural screening is present, searches for EP
violation can be used to constrain EP-preserving forces. We show how this
effect enables the recently discovered stellar triple system \textit{PSR
J0337$+$1715} to place a powerful constraint on EP-preserving fifth forces.
Finally, we demonstrate that technically natural cubic self-interactions modify
the vacuum structure of the scalar potential, leading to new constraints from
spontaneous and induced vacuum decay.


  We analyze electron paths in a solid-state double-slit interferometer based
on the two-dimensional electron gas and their mapping by the scanning gate
microscopy (SGM). A device with a quantum point source contact of a split exit
and a drain contact used for electron detection is considered. We study the SGM
maps of source-drain conductance ($G$) as functions of the probe position and
find that for a narrow drain the classical electron paths are clearly resolved
but without any trace of the double-slit interference. The latter is present in
the SGM maps of backscattering ($R$) probability only. The double-slit
interference is found in the $G$ maps for a wider drain contact but at the
expense of the loss of information on the electron trajectories. Stability of
$G$ and $R$ maps versus the geometry parameters of the scattering device is
also discussed. We discuss the interplay of the Young interference and
interference effects between various electron paths introduced by the tip and
the electron detector.


  We review the significant role played by red supergiants (RSGs) in stellar
populations, and some challenges and questions they raise for theoretical
stellar evolution. We present how metallicity and rotation modify the way stars
go to the red part of the Hertzsprung- Russell diagram or come back from it,
and how RSGs might keep a trace of their main-sequence evolution. We compare
theoretical popu- lation ratios with observed ones.


  We propose an approach of open-ended evolution via the simulation of swarm
dynamics. In nature, swarms possess remarkable properties, which allow many
organisms, from swarming bacteria to ants and flocking birds, to form
higher-order structures that enhance their behavior as a group. Swarm
simulations highlight three important factors to create novelty and diversity:
(a) communication generates combinatorial cooperative dynamics, (b) concurrency
allows for separation of timescales, and (c) complexity and size increases push
the system towards transitions in innovation. We illustrate these three
components in a model computing the continuous evolution of a swarm of agents.
The results, divided in three distinct applications, show how emergent
structures are capable of filtering information through the bottleneck of their
memory, to produce meaningful novelty and diversity within their simulated
environment.


  We use data from the first-year (Y1) observations of the DES collaboration to
measure the galaxy angular power spectrum (APS), and search for its BAO feature
using a template-fitting method. We test our methodology in a sample of 1800
DES Y1-like mock catalogs. The APS is measured with the pseudo-$C_\ell$ method,
using pixelized maps constructed from the mock catalogs and the DES mask. The
covariance matrix of the $C_\ell$'s in these tests are also obtained from the
mock catalogs. We use templates to model the measured spectra and estimate
template parameters firstly from the $C_\ell$'s of the mocks using two
different methods, a maximum likelihood estimator and a MCMC, finding
consistent results with a good reduced $\chi^2$. Robustness tests are performed
to estimate the impact of different choices of settings used in our analysis.
After these tests on mocks, we apply our method to a galaxy sample constructed
from DES Y1 data specifically for LSS studies. This catalog comprises galaxies
within an effective area of 1318 deg$^2$ and $0.6<z<1.0$. We fit the observed
spectra with our optimized templates, considering models with and without BAO
features. We find that the DES Y1 data favors a model with BAO at the
$2.6\,\sigma$ C.L. with a best-fit shift parameter of $\alpha=1.023\pm 0.047$.
However, the goodness-of-fit is somewhat poor, with $\chi^2/$(dof) = 1.49. We
identify a possible cause of this issue and show that using a theoretical
covariance matrix obtained from $C_\ell$'s that are better adjusted to data
results in an improved value of $\chi^2/$(dof) = 1.36 which is similar to the
value obtained with the real-space analysis. Our results correspond to a
distance measurement of $D_A(z_{\rm eff} = 0.81)/r_d = 10.65 \pm 0.49$,
consistent with the main DES BAO findings. This is a companion paper to the
main DES BAO article showing the details of the harmonic space analysis.


  We introduce and discuss a new approach to the phase retrieval of fields
radiated by continuous aperture sources having a circular support, which is of
interest in many applications including the detection of shape deformations on
reflector antennas. The approach is based on a decomposition of the actual 2-D
problem into a number of 1-D phase retrieval problems along diameters and
concentric rings of the visible part of the spectrum. In particular, the 1-D
problems are effectively solved by using the spectral factorization method,
while discrimination arguments at the crossing points allows to complete the
retrieval of the 2-D complex field. The proposed procedure, which just requires
a single set of far field amplitudes, takes advantage from up to now unexplored
field properties and it is assessed in terms of reflector aperture fields.


  While egocentric cameras like GoPro are gaining popularity, the videos they
capture are long, boring, and difficult to watch from start to end. Fast
forwarding (i.e. frame sampling) is a natural choice for faster video browsing.
However, this accentuates the shake caused by natural head motion, making the
fast forwarded video useless.
  We propose EgoSampling, an adaptive frame sampling that gives more stable
fast forwarded videos. Adaptive frame sampling is formulated as energy
minimization, whose optimal solution can be found in polynomial time.
  In addition, egocentric video taken while walking suffers from the left-right
movement of the head as the body weight shifts from one leg to another. We turn
this drawback into a feature: Stereo video can be created by sampling the
frames from the left most and right most head positions of each step, forming
approximate stereo-pairs.


  We give a self-contained presentation and comparison of two different
algorithms to explicitly solve quantum many body models of indistinguishable
particles moving on a circle and interacting with two-body potentials of
$1/\sin^2$-type. The first algorithm is due to Sutherland and well-known; the
second one is a limiting case of a novel algorithm to solve the elliptic
generalization of the Sutherland model. These two algorithms are different in
several details. We show that they are equivalent, i.e., they yield the same
solution and are equally simple.


  In this paper, we investigate the problem of including relevant information
as context in open-domain dialogue systems. Most models struggle to identify
and incorporate important knowledge from dialogues and simply use the entire
turns as context, which increases the size of the input fed to the model with
unnecessary information. Additionally, due to the input size limitation of a
few hundred tokens of large pre-trained models, regions of the history are not
included and informative parts from the dialogue may be omitted. In order to
surpass this problem, we introduce a simple method that substitutes part of the
context with a summary instead of the whole history, which increases the
ability of models to keep track of all the previous relevant information. We
show that the inclusion of a summary may improve the answer generation task and
discuss some examples to further understand the system's weaknesses.


  The extraction of process models from text refers to the problem of turning
the information contained in an unstructured textual process descriptions into
a formal representation,i.e.,a process model. Several automated approaches have
been proposed to tackle this problem, but they are highly heterogeneous in
scope and underlying assumptions,i.e., differences in input, target output, and
data used in their evaluation.As a result, it is currently unclear how well
existing solutions are able to solve the model-extraction problem and how they
compare to each other.We overcome this issue by comparing 10 state-of-the-art
approaches for model extraction in a systematic manner, covering both
qualitative and quantitative aspects.The qualitative evaluation compares the
analysis of the primary studies on: 1 the main characteristics of each
solution;2 the type of process model elements extracted from the input data;3
the experimental evaluation performed to evaluate the proposed framework.The
results show a heterogeneity of techniques, elements extracted and evaluations
conducted, that are often impossible to compare.To overcome this difficulty we
propose a quantitative comparison of the tools proposed by the papers on the
unifying task of process model entity and relation extraction so as to be able
to compare them directly.The results show three distinct groups of tools in
terms of performance, with no tool obtaining very good scores and also serious
limitations.Moreover, the proposed evaluation pipeline can be considered a
reference task on a well-defined dataset and metrics that can be used to
compare new tools. The paper also presents a reflection on the results of the
qualitative and quantitative evaluation on the limitations and challenges that
the community needs to address in the future to produce significant advances in
this area.


  In machine learning, a question of great interest is understanding what
examples are challenging for a model to classify. Identifying atypical examples
ensures the safe deployment of models, isolates samples that require further
human inspection and provides interpretability into model behavior. In this
work, we propose Variance of Gradients (VoG) as a valuable and efficient metric
to rank data by difficulty and to surface a tractable subset of the most
challenging examples for human-in-the-loop auditing. We show that data points
with high VoG scores are far more difficult for the model to learn and
over-index on corrupted or memorized examples. Further, restricting the
evaluation to the test set instances with the lowest VoG improves the model's
generalization performance. Finally, we show that VoG is a valuable and
efficient ranking for out-of-distribution detection.


  We study the passage of proton (H$^{+}$) through different five membered
aromatic ring systems by considering one dimensional motion of the proton along
a line perpendicular to the plane of the ring. The potential for the motion of
(H$^{+}$) from one side of the ring to the other through the center of the ring
is found to be a symmetric double well and such complexes are suggested as
molecular rattles which can exhibit a ring umbrella like inversion. Our study
reveals C$_{2}$H$_{2}$P$_{3}^{-}$ - H$^{+}$ to be a molecular rattle with a
barrier height of 44.277 kcal mol$^{-1}$ and exciting it to the third
vibrational level makes easy for the proton to go through the ring.


  Network data are observed in various applications where the individual
entities of the system interact with or are connected to each other, and often
these interactions are defined by their associated strength or importance.
Clustering is a common task in network analysis that involves finding groups of
nodes displaying similarities in the way they interact with the rest of the
network. However, most clustering methods use the strengths of connections
between entities in their original form, ignoring the possible differences in
the capacities of individual nodes to send or receive edges. This often leads
to clustering solutions that are heavily influenced by the nodes' capacities.
One way to overcome this is to analyse the strengths of connections in relative
rather than absolute terms, expressing each edge weight as a proportion of the
sending (or receiving) capacity of the respective node. This, however, induces
additional modelling constraints that most existing clustering methods are not
designed to handle. In this work we propose a stochastic block model for
composition-weighted networks based on direct modelling of compositional weight
vectors using a Dirichlet mixture, with the parameters determined by the
cluster labels of the sender and the receiver nodes. Inference is implemented
via an extension of the classification expectation-maximisation algorithm that
uses a working independence assumption, expressing the complete data likelihood
of each node of the network as a function of fixed cluster labels of the
remaining nodes. A model selection criterion is derived to aid the choice of
the number of clusters. The model is validated using simulation studies, and
showcased on network data from the Erasmus exchange program and a bike sharing
network for the city of London.


  Robustness against image perturbations bounded by a $\ell_p$ ball have been
well-studied in recent literature. Perturbations in the real-world, however,
rarely exhibit the pixel independence that $\ell_p$ threat models assume. A
recently proposed Wasserstein distance-bounded threat model is a promising
alternative that limits the perturbation to pixel mass movements. We point out
and rectify flaws in previous definition of the Wasserstein threat model and
explore stronger attacks and defenses under our better-defined framework.
Lastly, we discuss the inability of current Wasserstein-robust models in
defending against perturbations seen in the real world. Our code and trained
models are available at https://github.com/edwardjhu/improved_wasserstein .


  We give lower bounds for the Gordian distance and the unknotting number of
handlebody-knots by using Alexander biquandle colorings. We construct
handlebody-knots with Gordian distance $n$ and unknotting number $n$ for any
positive integer $n$.


  In this paper we prove the existence of small-amplitude quasi-periodic
solutions with Sobolev regularity, for the $d$-dimensional forced Kirchhoff
equation with periodic boundary conditions. This is the first result of this
type for a quasi-linear equations in high dimension. The proof is based on a
Nash-Moser scheme in Sobolev class and a regularization procedure combined with
a multiscale analysis in order to solve the linearized problem at any
approximate solution.


  In the simplest model of horizontal U(1) symmetry with one singlet added to
the supersymmetric standard model, we systematically reconstruct quark mass
matrices from the low-energy data to prove that there are only two mass
matrices found by Binetruy et.~al.. The same U(1) symmetry constrains the
hierarchical structure of L-violating couplings, from which we build radiative
neutrino mass matrices accommodating the solar and hot dark matter neutrino
masses and mixing. We find a few patterns of acceptable charged lepton and
neutrino mass matrices, most of which are consistent with large $\tan\beta
\simeq m_t/m_b$ only.


  An efficient joint source-channel (S/C) decoder based on the side information
of the source and on the MN-Gallager Code over Galois fields, $q$, is
presented. The dynamical posterior probabilities are derived either from the
statistical mechanical approach for calculation of the entropy for the
correlated sequences, or by the Markovian joint S/C algorithm. The Markovian
joint S/C decoder has many advantages over the statistical mechanical approach,
among them: (a) there is no need for the construction and the diagonalization
of a $q \times q$ matrix and for a solution to saddle point equations in $q$
dimensions; (b) a generalization to a joint S/C coding of an array of
two-dimensional bits (or higher dimensions) is achievable; (c) using parametric
estimation, an efficient joint S/C decoder with the lack of side information is
discussed. Besides the variant joint S/C decoders presented, we also show that
the available sets of autocorrelations consist of a convex volume, and its
structure can be found using the Simplex algorithm.


  Any observable with finite eigenvalue spectrum can be measured using a
multiport apparatus realizing an appropriate unitary transformation and an
array of detector instruments, where each detector operates as an indicator of
one possible value of the observable. The study of this setup in the frame of
von Neumann's quantum mechanical measurement process has a remarkable result:
already after the interaction of the measured system with the detector array
without collapse, exactly one detector is indicating a detection. Each single
detector indicates either 0 or 1 detection, and no superposition can be
attributed to it.


  We propose a novel visual place recognition approach, VOP, that efficiently
addresses occlusions and complex scenes by shifting from traditional reliance
on global image similarities and local features to image overlap prediction.
The proposed method enables the identification of visible image sections
without requiring expensive feature detection and matching. By focusing on
obtaining patch-level embeddings by a Vision Transformer backbone and
establishing patch-to-patch correspondences, our approach uses a voting
mechanism to assess overlap scores for potential database images, thereby
providing a nuanced image retrieval metric in challenging scenarios. VOP leads
to more accurate relative pose estimation and localization results on the
retrieved image pairs than state-of-the-art baselines on a number of
large-scale, real-world datasets. The code is available at
https://github.com/weitong8591/vop.


  We use the Gurevich-Pitaevskii approach based on the Whitham averaging method
for studying the formation of dispersive shock waves in an intense light pulse
propagating through a saturable nonlinear medium. Although the Whitham
modulation equations cannot be diagonalized in this case, the main
characteristics of the dispersive shock can be derived by means of an analysis
of the properties of these equations at the boundaries of the shock. Our
approach generalizes a previous analysis of step-like initial intensity
distributions to a more realistic type of initial light pulse and makes it
possible to determine, in a setting of experimental interest, the value of
measurable quantities such as the wave-breaking time or the position and light
intensity of the shock edges.


  Biological growth is often driven by mechanical cues, such as changes in
external pressure or tensile loading. Moreover, it is well known that many
living tissues actively maintain a preferred level of mechanical internal
stress, called the mechanical homeostasis. The tissue-level feedback mechanism
by which changes of the local mechanical stresses affect growth is called a
growth law within the theory of morphoelasticity, a theory for understanding
the coupling between mechanics and geometry in growing and evolving biological
materials. The goal of this article is to develop mathematical techniques to
analyze growth laws and to explore issues of heterogeneity and growth
stability. We discuss the growth dynamics of tubular structures, which are very
common in biology (e.g. arteries, plant stems, airways) and model the
homeostasis-driven growth dynamics of tubes which produces spatially
inhomogeneous residual stress. We show that the stability of the homeostatic
state depends nontrivially on the anisotropy of the growth response. The key
role of anisotropy may provide a foundation for experimental testing of
homeostasis-driven growth laws.


  It is shown for all local fields $\mathbb{F}$ which are of characteristic
different from $2$ that any distribution on $GL_{n+1}(\mathbb{F})$ which is
invariant under conjugation by $GL_n(\mathbb{F})$ is also invariant under
transposition. In this paper we give an adaptation of the proof of this theorem
to fields of characteristic 2.


  In this study, we propose a big data pipeline for cotton bloom detection
using a Lambda architecture, which enables real-time and batch processing of
data. Our proposed approach leverages Azure resources such as Data Factory,
Event Grids, Rest APIs, and Databricks. This work is the first to develop and
demonstrate the implementation of such a pipeline for plant phenotyping through
Azure's cloud computing service. The proposed pipeline consists of data
preprocessing, object detection using a YOLOv5 neural network model trained
through Azure AutoML, and visualization of object detection bounding boxes on
output images. The trained model achieves a mean Average Precision (mAP) score
of 0.96, demonstrating its high performance for cotton bloom classification. We
evaluate our Lambda architecture pipeline using 9000 images yielding an
optimized runtime of 34 minutes. The results illustrate the scalability of the
proposed pipeline as a solution for deep learning object detection, with the
potential for further expansion through additional Azure processing cores. This
work advances the scientific research field by providing a new method for
cotton bloom detection on a large dataset and demonstrates the potential of
utilizing cloud computing resources, specifically Azure, for efficient and
accurate big data processing in precision agriculture.


  Decaying magnetohydrodynamic (MHD) turbulence is important in various
astrophysical contexts, including early universe magnetic fields, star
formation, turbulence in galaxy clusters, magnetospheres and solar corona.
Previously known in the nonhelical case of magnetically dominated decaying
turbulence, we show that magnetic reconnection is important also in the fully
helical case and is likely the agent responsible for the inverse transfer of
energy. Again, in the fully helical case, we find that there is a similarity in
power law decay exponents in both 2.5D and 3D simulations. To understand this
intriguing similarity, we investigate the possible quasi-two-dimensionalization
of the 3D system. We perform Minkowski functional analysis and find that the
characteristic length scales of a typical magnetic structure in the system are
widely different, suggesting the existence of local anisotropies. Finally, we
provide a quasi-two-dimensional hierarchical merger model which recovers the
relevant power law scalings. In the nonhelical case, we show that a
helicity-based invariant cannot constrain the system, and the best candidate is
still anastrophy or vector potential squared, which is consistent with the
quasi-two-dimensionalization of the system.


  In the current models of galaxy formation and evolution, AGN feedback is
crucial to reproduce galaxy luminosity function, colour-magnitude relation and
M-sigma relation. However, if AGN-feedback can indeed expel and heat up
significant amount of cool molecular gas and consequently quench star
formation, is yet to be demonstrated observationally. Only in four cases so far
(Cen A, NGC 3801, NGC 6764 and Mrk 6), X-ray observations have found evidences
of jet-driven shocks heating the ISM. We chose the least-explored galaxy, NGC
3801, and present the first ultraviolet imaging and stellar population
analysisis of this galaxy from GALEX data. We find this merger-remnant
early-type galaxy to have an intriguing spiral-wisp of young star forming
regions (age ranging from 100--500 Myr). Taking clues from dust/PAH, HI and CO
emission images we interpret NGC 3801 to have a kinamatically decoupled core or
an extremely warped gas disk. From the HST data we also show evidence of
ionised gas outflow similar to that observed in HI and molecular gas (CO) data,
which may have caused the decline of star formation leading to the red optical
colour of the galaxy. However, from these panchromatic data we interpret that
the expanding shock shells from the young ($\sim$2.4 million years) radio jets
are yet to reach the outer gaseous regions of the galaxy. It seems, we observe
this galaxy at a rare stage of its evolutionary sequence where post-merger star
formation has already declined and new powerful jet feedback is about to affect
the gaseous star forming outer disk within the next 10 Myr, to further
transform it into a red-and-dead early-type galaxy.


  For a real Hilbert space $H_{\mathbb{R}}$ and $-1 < q < 1$ Bozejko and
Speicher introduced the C$^\ast$-algebra $A_q(H_{\mathbb{R}})$ and von Neumann
algebra $M_q(H_{\mathbb{R}})$ of $q$-Gaussian variables. We prove that if
$\dim(H_{\mathbb{R}}) = \infty$ and $-1 < q < 1, q \not = 0$ then
$M_q(H_{\mathbb{R}})$ does not have the Akemann-Ostrand property with respect
to $A_q(H_{\mathbb{R}})$. It follows that $A_q(H_{\mathbb{R}})$ is not
isomorphic to $A_0(H_{\mathbb{R}})$. This gives an answer to the
C$^\ast$-algebraic part of Question 1.1 and Question 1.2 in [NeZe18].


  A conjecture of Riley about the relationship between real parabolic
representations and signatures of two-bridge knots is verified for double twist
knots.


  With the advancements of artificial intelligence (AI), we're seeing more
scenarios that require AI to work closely with other agents, whose goals and
strategies might not be known beforehand. However, existing approaches for
training collaborative agents often require defined and known reward signals
and cannot address the problem of teaming with unknown agents that often have
latent objectives/rewards. In response to this challenge, we propose teaming
with unknown agents framework, which leverages kernel density Bayesian inverse
learning method for active goal deduction and utilizes pre-trained,
goal-conditioned policies to enable zero-shot policy adaptation. We prove that
unbiased reward estimates in our framework are sufficient for optimal teaming
with unknown agents. We further evaluate the framework of redesigned
multi-agent particle and StarCraft II micromanagement environments with diverse
unknown agents of different behaviors/rewards. Empirical results demonstrate
that our framework significantly advances the teaming performance of AI and
unknown agents in a wide range of collaborative scenarios.


  We present a new method for calculating the merger history of matter halos in
hierarchical clustering cosmologies. The linear density field is smoothed on a
range of scales, these are then ordered in decreasing density and a merger tree
constructed. The method is similar in many respects to the block model of Cole
\& Kaiser but has a number of advantages: (i) it retains information about the
spatial correlations between halos, (ii) it uses a series of overlapping grids
and is thereby much better at finding rare, high-mass halos, (iii) it is not
limited to halos whose mass ratios are powers of two, and (iv) it is based on
an actual realization of the density field and so can be tested against N-body
simulations. The major disadvantages are (i) the minimum halo mass is eight
times the unit cell with a corresponding loss of dynamic range, and (ii)
occasionally the relative location of halos in the tree does not reflect the
correct ordering of their collapse times, as computed from the mean halo
density. We show that our model exhibits the required scaling behaviour when
tested on power-law spectra of density perturbations, but that it predicts far
more massive halos than does the Press-Schechter formalism for flat spectra. We
suggest reasons why this should be so.


  The holomorphic anomaly equations describe B-model closed topological strings
in Calabi-Yau geometries. Having been used to construct perturbative
expansions, it was recently shown that they can also be extended past
perturbation theory by making use of resurgent transseries. These yield formal
nonperturbative solutions, showing integrability of the holomorphic anomaly
equations at the nonperturbative level. This paper takes such constructions one
step further by working out in great detail the specific example of topological
strings in the mirror of the local CP2 toric Calabi-Yau background, and by
addressing the associated (resurgent) large-order analysis of both perturbative
and multi-instanton sectors. In particular, analyzing the asymptotic growth of
the perturbative free energies, one finds contributions from three different
instanton actions related by Z_3 symmetry, alongside another action related to
the Kahler parameter. Resurgent transseries methods then compute, from the
extended holomorphic anomaly equations, higher instanton sectors and it is
shown that these precisely control the asymptotic behavior of the perturbative
free energies, as dictated by resurgence. The asymptotic large-order growth of
the one-instanton sector unveils the presence of resonance, i.e., each
instanton action is necessarily joined by its symmetric contribution. The
structure of different resurgence relations is extensively checked at the
numerical level, both in the holomorphic limit and in the general
nonholomorphic case, always showing excellent agreement with transseries data
computed out of the nonperturbative holomorphic anomaly equations. The
resurgence relations further imply that the string free energy displays an
intricate multi-branched Borel structure, and that resonance must be properly
taken into account in order to describe the full transseries solution.


  The exact charged rotating solution of 2+1 Einstein-Maxwell equations with
$\Lambda$ term is obtained and its properties outlined. It generalizes the
Cataldo-Cruz-del Campo-Garc{\'\i}a relativistic charged massive black hole on
the 2+1 anti-de Sitter cosmological background. We show that rotating solutions
correspond to inhomogeneous field equations, thus presence of sources in 2+1
Maxwell's equations cannot be identified with existence of a charge
distribution. Instead, these sources are related to the 2+1 Machian 2-form
field, and the overall Lagrangian structure of the rotating system is
reconstructed.


  Temperature can be responsible for strengthening effective couplings between
quantum states, determining a hierarchy of interactions, and making it possible
to establish such dynamical regimes known as Zeno dynamics, wherein a strong
coupling can hinder the effects of a weak one. The relevant physical mechanisms
which connect the structure of a thermal state with the appearance of special
dynamical regimes are analyzed in depth.