  We discuss a number of problems associated with the circle compactification
of the bosonic tensile ambitwistor string with the asymmetric vacuum choice. By
considering the spectrum and physical state conditions, we show that the circle
radius plays a role as a tuning parameter which determines the low energy
effective field theory. At the self dual point, we construct the current
operators and compute OPEs between them. While the final outcome remains as yet
inconclusive, several new results are obtained. Through the current algebra
analysis we show that there is a subsector of the massless states where the
gauge symmetry is enhanced to $ISO(2)_L\times SU(2)_R$. Using the fact that the
one loop partition function is not modular invariant, we show that tensile
ambitwistor string partition function is exactly the same as a field theory
partition function. Our result proves that despite the existence of winding
modes, which is a typical characteristic of a string, the tensile ambitwistor
string behaves as a point particle theory.


  We present separability criteria for both bipartite and multipartite quantum
states. These criteria include the criteria based on the correlation matrix and
its generalized form as special cases. We show by detailed examples that our
criteria are more powerful than the positive partial transposition criterion,
the realignment criterion and the criteria based on the correlation matrices.


  We theoretically demonstrate dynamically selective bidirectional emission and
absorption of a single itinerant microwave photon in a waveguide. The proposed
device is an artificial molecule composed of two qubits coupled to a waveguide
a quarter-wavelength apart. By using simulations based on the input--output
theory, we show that upon preparing an appropriate entangled state of the two
qubits, a photon is emitted directionally as a result of the destructive
interference occurring either at the right or left of the qubits. Moreover, we
demonstrate that this artificial molecule possesses the capability of absorbing
and transmitting an incoming photon on-demand, a feature essential to the
creation of a fully inter-connected one-dimensional quantum network, in which
quantum information can be exchanged between any two given nodes.


  After finding the really self-consistent electromagnetic equations for a
plasma, we proceed in a similar fashion to find how the MHD equations have to
be modified accordingly. Substantially this is done by replacing the "Lorentz"
force equation by the correct (in our case) force equation. Formally we have to
use the vector potential instead of the magnetic field intensity.The appearance
of the formulae presented is the one of classical vector analysis. We thus find
a set of eight (8) equations in eight (8) unknowns, as previously known
concerning the tradditional MHD equations.


  The universality for the eigenvalue spacing statistics of generalized Wigner
matrices was established in our previous work \cite{EYY} under certain
conditions on the probability distributions of the matrix elements. A major
class of probability measures excluded in \cite{EYY} are the Bernoulli
measures. In this paper, we extend the universality result of \cite{EYY} to
include the Bernoulli measures so that the only restrictions on the probability
distributions of the matrix elements are the subexponential decay and the
normalization condition that the variances in each row sum up to one. The new
ingredient is a strong local semicircle law which improves the error estimate
on the Stieltjes transform of the empirical measure of the eigenvalues from the
order $(N \eta)^{-1/2}$ to $(N \eta)^{-1}$. Here $\eta$ is the imaginary part
of the spectral parameter in the definition of the Stieltjes transform and $N$
is the size of the matrix.


  Andreev bound states with opposite phase-inversion asymmetries are observed
in local and non-local tunneling spectra at the two ends of a
superconductor-semiconductor-superconductor planar Josephson junction in the
presence of a perpendicular magnetic field. Spectral signatures agree with a
theoretical model, yielding a physical picture in which phase textures in
superconducting leads localize and control the position of Andreev bound states
in the junction, demonstrating a simple means of controlling the position and
size of Andreev states within a planar junction.


  Let f(n) denote the smallest positive integer such that every set of $f(n)$
points in general position in the Euclidean plane contains a convex n-gon. In a
seminal paper published in 1935, Erd\H{o}s and Szekeres proved that f(n) exists
and provided an upper bound. In 1961, they also proved a lower bound, which
they conjectured is optimal. Their bounds are: $2^{n-2}+1 \leq f(n) \leq {2n -
4 \choose n-2}+1$. Since then, the upper bound has been improved by rougly a
factor of 2, to $f(n) \leq {2n - 5 \choose n-2}+1$. In the current paper, we
further improve the upper bound by proving that: $$
\limsup\limits_{n\rightarrow \infty} \frac{f(n)}{{2n-5 \choose n-2}} \leq
\frac{29}{32}$$


  The bunkbed conjecture was first posed by Kasteleyn. If $G=(V,E)$ is a finite
graph and $H$ some subset of $V$, then the bunkbed of the pair $(G,H)$ is the
graph $G\times\{1,2\}$ plus $|H|$ extra edges to connect for every $v\in H$ the
vertices $(v,1)$ and $(v,2)$. The conjecture asserts that $(v,1)$ is more
likely to connect with $(w,1)$ than with $(w,2)$ in the independent bond
percolation model for any $v,w\in V$. This is intuitive because $(v,1)$ is in
some sense closer to $(w,1)$ than it is to $(w,2)$. The conjecture has however
resisted several attempts of proof. This paper settles the conjecture in the
case of a constant percolation parameter and $G$ the complete graph.


  Extrasolar circumbinary planets are so called because they orbit two stars
instead of just one; to date, an increasing number of such planets have been
discovered with a variety of techniques. If the orbital frequency of the
hosting stellar pair is much higher than the planetary one, the tight stellar
binary can be considered as a matter ring current generating its own
post-Newtonian stationary gravitomagnetic field through its orbital angular
momentum. It affects the orbital motion of a relatively distant planet with
Lense-Thirring-type precessional effects which, under certain circumstances,
may amount to a significant fraction of the static, gravitoelectric ones,
analogous to the well known Einstein perihelion precession of Mercury,
depending only on the masses of the system's bodies. Instead, when the
gravitomagnetic field is due solely to the spin of each of the central star(s),
the Lense-Thirring shifts are several orders of magnitude smaller than the
gravitoelectric ones. In view of the growing interest in the scientific
community about the detection of general relativistic effects in exoplanets,
the perspectives of finding new scenarios for testing such a further
manifestation of general relativity might be deemed worth of further
investigations.


  Detecting H-antiH oscillations is intimately connected with the existence of
natural antiH. We detect natural H-antiH oscillations, generated by a classical
spin-free Coulomb quantum gap, which we calculate analytically without any
parameter. Oscillation times are much smaller than those predicted with the
Standard Model. These unprecedented results also remove the so-called problem
with matter-antimatter asymmetry in the Universe.


  Electron Spin Resonance and optical reflectivity measurements demonstrate a
metal-insulator transition in Na_2CsC_60 as the system passes from the low
temperature simple cubic to the high temperature {\it fcc} structure above 300
K. The non-conducting electronic state is especially unexpected in view of the
metallic character of other, apparently isostructural fullerides, like K_3C_60.
The occurence of this phase in Na_2CsC_60 suggests that alkali specific effects
can not be neglected in the description of the electronic properties of alkali
doped fullerides. We discuss the origin of the insulating state and the
relevance of our results for the anomaly observed in the magnitude of the
superconducting transition temperature of Na_2AC_60 fullerides.


  We consider the Higgs-dilaton(radion) system using the trace of
energy-momentum tensor ($T_{~\mu}^\mu$) with the full Standard Model (SM) gauge
symmetry $G_{\rm SM} \equiv SU(3)_c \times SU(2)_L \times U(1)_Y$, and find out
that the resulting phenomenology for the Higgs-dilaton(radion) system is
distinctly different from the earlier studies based on the $T_{~\mu}^\mu$ with
the unbroken subgroup $H_{\rm SM} \equiv SU(3)_c \times U(1)_{\rm em}$ of
$G_{\rm SM}$. After electroweak symmetry breaking (EWSB), the SM Higgs boson
and dilaton(radion) will mix with each other, and there appear two Higgs-like
scalar bosons and the Higgs-dilaton mixing changes the scalar phenomenology in
interesting ways. The signal strengths for the $gg$-initiated channels could be
modified significantly compared with the SM predictions due to the QCD scale
anomaly and the Higgs-dilaton(radion) mixing, whereas anomaly contributions are
almost negligible for other channels. We also discuss the self-couplings and
the signal strengths of the $126$ GeV scalar boson in various channels and
possible constraints from the extra light/heavy scalar boson. The
Higgs-dilaton(radion) system considered in this work has a number of
distinctive features that could be tested by the upcoming LHC running and at
the ILC.


  Let $d(\delta)$ denote the Hausdorff dimension of the Julia set of the
polynomial $f_\delta(z)=z^2-2+\delta$. In this paper we will study the
directional derivative of the function $d$ along directions landing at the
parameter $0$, which corresponds to $-2$ in the case of family $p_c(z)=z^2+c$.
We will consider all directions, except the one $\delta\in\mathbb{R}^+$, which
is inside the Mandelbrot set. We will prove asymptotic formula for the
directional derivative of $d$. Moreover, we will see that the derivative is
negative for all directions in the closed left half-plane. Computer
calculations show that it is negative except a cone (with opening angle
approximately $74^\circ$) around $\mathbb{R}^+$.


  The Weihrauch degrees are a tool to gauge the computational difficulty of
mathematical problems. Often, what makes these problems hard is their
discontinuity. We look at discontinuity in its purest form, that is, at
otherwise constant functions that make a single discontinuous step along each
dimension of their underlying space. This is an extension of previous work of
Kihara, Pauly, Westrick from a single dimension to multiple dimensions. Among
other results, we obtain strict hierarchies in the Weihrauch degrees, one of
which orders mathematical problems by the richness of the truth-tables
determining how discontinuous steps influence the output.


  We prove that the dynamics of the MBO scheme for data clustering converge to
a viscosity solution to mean curvature flow. The main ingredients are (i) a new
abstract convergence result based on quantitative estimates for heat operators
and (ii) the derivation of these estimates in the setting of random geometric
graphs. To implement the scheme in practice, two important parameters are the
number of eigenvalues for computing the heat operator and the step size of the
scheme. The results of the current paper give a theoretical justification for
the choice of these parameters in relation to sample size and interaction
width.


  We measured the effects of periodic surface holes, created using a focused
ion beam, on the phase diagram of the vortex matter in high-T_c
Bi_2Sr_2CaCu_2O_{8+\delta} crystals. Differential magneto-optical measurements
show that the irreversibility line is shifted to higher fields and
temperatures, with respect to the pristine melting line. The irreversibility
line displays weak field dependence between integer matching fields indicating
multiple-flux-quanta pinning at holes. We find reduced equilibrium
compressibility of the vortex matter at integer matching fields, which is
strong evidence for the existence of thermodynamic Mott insulator phases.
Shaking with a transverse ac field surprisingly reveals first-order melting
that is not shifted with respect to the pristine melting line and that seems to
occur within the Mott insulator regions. This melting is understood to be the
first-order transition in the bulk of the crystal beneath the surface holes.
The transition is visible at the surface, despite the reduced vortex
compressibility in the top layer.


  Answering a long standing question, we give an example of a Hilbert module
and a nonzero bounded right linear map having a kernel with trivial orthogonal
complement. In particular, this kernel is different from its own double
orthogonal complement.


  In this thesis we discuss three separate analysis of various phenomenological
aspects of heavy-ion collisions (HIC). The first one is a possible
generalization of the kinetic theory framework for dense systems. We
investigate its long-time behaviour and the properties of the equilibrium. The
second discussion is about the phenomenological analysis of the azimuthal
asymmetry of the particle yields in a HIC, where we link the initial stage
geometrical asymmetry to the particle yields and examine the possible
organizing mechanisms that could be responsible for such a relation. The third,
and also the most thorough part of the thesis is about the relation of the
spectral density of quasi-particle states and the macroscopic fluidity measure
(the ratio of shear viscosity and the entropy density) and other transport
properties of the system. We extensively study the liquid-gas crossover with
the help of model spectral functions. The main conclusion is that the relative
intensification of the continuum of the scattering states compared to the
quasi-particle peak makes the matter more fluent.


  This study comprehensively evaluates tuning methods for autofocal glasses
using virtual reality (VR), addressing the challenge of presbyopia. With aging,
presbyopia diminishes the eye's ability to focus on nearby objects, impacting
the quality of life for billions. Autofocals, employing focus-tunable lenses,
dynamically adjust optical power for each fixation, promising a more natural
visual experience than traditional bifocal or multifocal lenses. Our research
contrasts the most common tuning methods - manual, gaze-based, and vergence -
within a VR setup to mimic real-world scenarios. Utilizing the XTAL VR headset
equipped with eye-tracking, the study replicated autofocal scenarios, measuring
performance and usability through psychophysical tasks and NASA TLX surveys.
Results show varying strengths and weaknesses across methods, with gaze control
excelling in precision but not necessarily comfort and manual control providing
stability and predictability. The findings guide the selection of tuning
methods based on task requirements and user preferences, highlighting a balance
between precision and ease of use.


  We study algorithmic complexity of solving subtraction games in a~fixed
dimension with a finite difference set. We prove that there exists a game in
this class such that any algorithm solving the game runs in exponential time.
Also we prove an existence of a game in this class such that solving the game
is PSPACE-hard. The results are based on the construction introduced by Larsson
and W\"astlund. It relates subtraction games and cellular automata.


  The concept of agile process models has attained great popularity in software
(SW) development community in last few years. Agile models promote fast
development. Fast development has certain drawbacks, such as weak documentation
and performance for medium and large development projects. Fast development
also promotes use of agile process models in small-scale projects. This paper
modifies and evaluates Extreme Programming (XP) process model and proposes a
novel process model based on these modifications.


  Some open topics in the field of low energy photon-nucleon interactions are
discussed--which in my opinion are of interest both for obtaining new
information on nucleon structure as well as for precision tests of our
theoretical understanding of chiral dynamics. In particular, I discuss p-wave
multipoles in charged pion photoproduction off protons as well as the role of
spin-dependent effects in (unpolarized) Compton scattering off nucleons. There
the concept of dynamical spin polarizabilities is found to be essential for the
understanding of differential Compton cross sections above 120 MeV cms photon
energy.


  Distracted drivers are dangerous drivers. Equipping advanced driver
assistance systems (ADAS) with the ability to detect driver distraction can
help prevent accidents and improve driver safety. In order to detect driver
distraction, an ADAS must be able to monitor their visual attention. We propose
a model that takes as input a patch of the driver's face along with a crop of
the eye-region and classifies their glance into 6 coarse regions-of-interest
(ROIs) in the vehicle. We demonstrate that an hourglass network, trained with
an additional reconstruction loss, allows the model to learn stronger
contextual feature representations than a traditional encoder-only
classification module. To make the system robust to subject-specific variations
in appearance and behavior, we design a personalized hourglass model tuned with
an auxiliary input representing the driver's baseline glance behavior. Finally,
we present a weakly supervised multi-domain training regimen that enables the
hourglass to jointly learn representations from different domains (varying in
camera type, angle), utilizing unlabeled samples and thereby reducing
annotation cost.


  We construct a distorted Fourier transformation associated with the
multi-dimensional quantum walk. In order to avoid the complication of
notations, almost all of our arguments are restricted to two dimensional
quantum walks (2DQWs) without loss of generality. The distorted Fourier
transformation characterizes generalized eigenfunctions of the time evolution
operator of the QW. The 2DQW which will be considered in this paper has an
anisotropy due to the definition of the shift operator for the free QW. Then we
define an anisotropic Banach space as a modified Agmon-H\"{o}rmander's
$\mathcal{B}^*$ space and we derive the asymptotic behavior at infinity of
generalized eigenfunctions in these spaces. The scattering matrix appears in
the asymptotic expansion of generalized eigenfunctions.


  Brittle optimization has been observed to adversely impact model likelihoods
for regression and VAEs when simultaneously fitting neural network mappings
from a (random) variable onto the mean and variance of a dependent Gaussian
variable. Previous works have bolstered optimization and improved likelihoods,
but fail other basic posterior predictive checks (PPCs). Under the PPC
framework, we propose critiques to test predictive mean and variance
calibration and the predictive distribution's ability to generate sensible
data. We find that our attractively simple solution, to treat heteroscedastic
variance variationally, sufficiently regularizes variance to pass these PPCs.
We consider a diverse gamut of existing and novel priors and find our methods
preserve or outperform existing model likelihoods while significantly improving
parameter calibration and sample quality for regression and VAEs.


  We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime
where the norm closure of the Gibbs family fails due to discontinuities of the
maximum-entropy inference. The current discussion of maximum-entropy inference
and irreducible correlation in the area of quantum phase transitions is a major
motivation for this research. We extend a representation of the irreducible
correlation from finite temperatures to absolute zero.


  The local electronic and magnetic properties of superconducting FeSe have
been investigated by K$\beta$ x-ray emission (XES) and simultaneous x-ray
absorption spectroscopy (XAS) at the Fe K-edge at high pressure and low
temperature. Our results indicate a sluggish decrease of the local Fe spin
moment under pressure up to 7~GPa, in line with previous reports, followed by a
sudden increase at higher pressure which has been hitherto unobserved. The
magnetic surge is preceded by an abrupt change of the Fe local structure as
observed by the decrease of the XAS pre-edge region intensity and corroborated
by ab-initio simulations. This pressure corresponds to a structural transition,
previously detected by x-ray diffraction, from the $Cmma$ form to the denser
$Pbnm$ form with octahedral coordination of iron. Finally, the near-edge region
of the XAS spectra shows a change before this transition at 5~GPa,
corresponding well with the onset pressure of the previously observed
enhancement of $T_c$. Our results emphasize the delicate interplay between
structural, magnetic, and superconducting properties in FeSe under pressure.


  The BIX protocol is a blockchain-based protocol that allows distribution of
certificates linking a subject with his public key, hence providing a service
similar to that of a PKI but without the need of a CA. In this paper we analyze
the security of the BIX protocol in a formal way, in four steps. First, we
identify formal security assumptions which are well-suited to this protocol.
Second, we present some attack scenarios against the BIX protocol. Third, we
provide a formal security proof that some of these attacks are not feasible
under our previously established assumptions. Finally, we show how another
attack may be carried on.


  A recent study demonstrated the existence of oscillons -- extremely
long-lived localized configurations that undergo regular oscillations in time
-- in spontaneously broken SU(2) gauge theory with a fundamental Higgs particle
whose mass is twice the mass of the gauge bosons. This analysis was carried out
in a spherically symmetric ansatz invariant under combined spatial and isospin
rotations. We extend this result by considering a numerical simulation of the
the full bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in
3+1 dimensions, with no assumption of rotational symmetry, for a Higgs mass
equal to twice the $W^\pm$ boson mass. Within the limits of this numerical
simulation, we find that the oscillon solution from the pure SU(2) theory is
modified but remains stable in the full electroweak theory. The observed
oscillon solution contains total energy approximately 30 TeV localized in a
region of radius approximately 0.05 fm.


  In this paper, we propose a new joint dictionary learning method for
example-based image super-resolution (SR), using sparse representation. The
low-resolution (LR) dictionary is trained from a set of LR sample image
patches. Using the sparse representation coefficients of these LR patches over
the LR dictionary, the high-resolution (HR) dictionary is trained by minimizing
the reconstruction error of HR sample patches. The error criterion used here is
the mean square error. In this way we guarantee that the HR patches have the
same sparse representation over HR dictionary as the LR patches over the LR
dictionary, and at the same time, these sparse representations can well
reconstruct the HR patches. Simulation results show the effectiveness of our
method compared to the state-of-art SR algorithms.


  A periodically poled lithium niobate (PPLN) waveguide-based single-pixel
up-conversion infrared spectrometer was demonstrated. Sum-frequency generation
between a 1.5 micrometer band scanning pump laser and a 1.3 micrometer band
signal generated visible radiation which was detected by a silicon
single-photon detector. The noise equivalent power of the upconversion
spectrometer was two-orders-of-magnitude lower than that of a commercial
optical spectrum analyzer.


  Here I present the SiC-YiG Quantum Sensor, allowing electron paramagnetic
resonance (EPR) studies of monolayer or few nanometers thick chemical,
biological or physical samples located on the sensor surface. It contains two
parts, a 4H-SiC substrate with many paramagnetic silicon vacancies (V2) located
below its surface, and YIG ferrimagnetic nanostripes. Spins sensing properties
are based on optically detected double electron-electron spin resonance under
the strong magnetic field gradient of nanostripes. Here I describe fabrication,
magnetic, optical and spins sensing properties of this sensor. I show that the
target spins sensitivity is at least five orders of magnitude larger than the
one of standard X band EPR spectrometer, for which it constitutes, combined
with a fiber bundle, a powerful upgrade for sensitive surface EPR. This sensor
can determine the target spins planes EPR spectrum, their positions with a
nanoscale precision of +/- 1 nm, and their 2D concentration down to
1/(20nm.20nm).


  We study the equations of motion of the massive and massless particles in the
Schwarzschild geometry of general relativity by using the Laplace-Adomian
Decomposition Method, which proved to be extremely successful in obtaining
series solutions to a wide range of strongly nonlinear differential and
integral equations. After introducing a general formalism for the derivation of
the equations of motion in arbitrary spherically symmetric static geometries,
and of the general mathematical formalism of the Laplace-Adomian Decomposition
Method, we obtain the series solution of the geodesics equation in the
Schwarzschild geometry. The truncated series solution, containing only five
terms, can reproduce the exact numerical solution with a high precision. In the
first order of approximation we reobtain the standard expression for the
perihelion precession. We study in detail the bending angle of light by compact
objects in several orders of approximation. The extension of this approach to
more general geometries than the Schwarzschild one is also briefly discussed.


  The high energy limit of QCD is investigated in the generalized leading
logarithmic approximation. We study unitarity corrections to the BFKL Pomeron
containing t-channel states with up to six gluons. Special attention is given
to the field theory structure of the corresponding multi-gluon amplitudes. We
discuss the transition from two to six gluons in the t-channel.


  The simulation of quantum circuits using the tensor network method is very
computationally demanding and requires significant High Performance Computing
(HPC) resources to find an efficient contraction order and to perform the
contraction of the large tensor networks. In addition, the researchers want a
workflow that is easy to customize, reproduce and migrate to different HPC
systems. In this paper, we discuss the issues associated with the deployment of
the QuantEX quantum computing simulation software within containers on
different HPC systems. Also, we compare the performance of the containerized
software with the software running on bare metal.


  We consider the problem of Embodied Question Answering (EQA), which refers to
settings where an embodied agent such as a robot needs to actively explore an
environment to gather information until it is confident about the answer to a
question. In this work, we leverage the strong semantic reasoning capabilities
of large vision-language models (VLMs) to efficiently explore and answer such
questions. However, there are two main challenges when using VLMs in EQA: they
do not have an internal memory for mapping the scene to be able to plan how to
explore over time, and their confidence can be miscalibrated and can cause the
robot to prematurely stop exploration or over-explore. We propose a method that
first builds a semantic map of the scene based on depth information and via
visual prompting of a VLM - leveraging its vast knowledge of relevant regions
of the scene for exploration. Next, we use conformal prediction to calibrate
the VLM's question answering confidence, allowing the robot to know when to
stop exploration - leading to a more calibrated and efficient exploration
strategy. To test our framework in simulation, we also contribute a new EQA
dataset with diverse, realistic human-robot scenarios and scenes built upon the
Habitat-Matterport 3D Research Dataset (HM3D). Both simulated and real robot
experiments show our proposed approach improves the performance and efficiency
over baselines that do no leverage VLM for exploration or do not calibrate its
confidence. Webpage with experiment videos and code:
https://explore-eqa.github.io/


  While the disciplines of physics and engineering sciences in many cases have
taken advantage from accurate time-series prediction of system behaviour by
applying ordinary differential equation systems upon precise basic physical
laws such approach hardly could be adopted by other scientific disciplines
where precise mathematical basic laws are unknown. A new modelling schema, the
NMPC-graph, opens the possibility of interdisciplinary and generic nonlinear,
multivariate, dynamic, and recursive causal modelling in domains where basic
laws are only known as qualitative relationships among parameters while their
precise mathematical nature remains undisclosed at modelling time. The
symbolism of NMPC-graph is kept simple and suited for analysts without advanced
mathematical skills. This article presents the definition of the NMPC-graph
modelling method and its six component types. Further, it shows how to solve
the inverse problem of deriving a nonlinear ordinary differential equation
system from any NMPC-graph in conjunction with historic calibration data by
means of machine learning. This article further discusses how such a derived
NMPC-model can be used for hypothesis testing and time-series prediction with
the expectation of gaining prediction accuracy in comparison to conventional
prediction methods.


  We develop the theory of Berezin-Toeplitz operator on any compact symplectic
prequantizable manifold from scratch. Our main inspiration is the Boutet de
Monvel-Guillemin theory, that we simplify in several ways to obtain a concise
exposition. A comparison with the spin-c Dirac quantization is also included.


  We prove that the Poisson kernel
$P_{q,\beta}(t)=\sum\limits_{k=1}^{\infty}q^k\cos(kt-\dfrac{\beta\pi}{2})$,
${q\in(0,1)}$, $\beta\in\mathbb{R}$, satisfies Kushpel's condition $C_{y,2n}$
beginning with a number $n_q$ where $n_q$ is the smallest number $n\geq9$, for
which the following inequality is satisfied:
  $$ \dfrac{43}{10(1-q)}q^{\sqrt{n}}+\dfrac{160}{57(n-\sqrt{n})}\;
\dfrac{q}{(1-q)^2}\leq
(\dfrac{1}{2}+\dfrac{2q}{(1+q^2)(1-q)})(\dfrac{1-q}{1+q})^{\frac {4}{1-q^2}}.
$$
  As a consequence, for all $n\geq n_q$ we obtain lower bounds for Kolmogorov
widths in the space $C$ of classes $C_{\beta,\infty}^q$ of Poisson integrals of
functions that belong to the unit ball in the space $L_\infty$. The obtained
estimates coincide with the best uniform approximations by trigonometric
polynomials for these classes. As a result, we obtain exact values for widths
of classes $C_{\beta,\infty}^q$ and show that subspaces of trigonometric
polynomials of order $n-1$ are optimal for widths of dimension $2n$.


  We present a catalog of 110 variable stars within ~1' of Sgr A* based on
image subtraction of near-infrared (H and K) photometry. Our images were
obtained over 133 nights from 2000--2002 in H-band and over 134 nights from
2001--2002 in K-band; the typical FWHM is 1.4''. We match the catalog to other
near-infrared, X-ray, and radio (i.e., maser) data, and we discuss some of the
more interesting objects. The catalog includes 14 periodic sources, several
known long-period variables and three new LPV candidates. We associate IRS 10*
with OH, SiO, and H2O masers and a bright X-ray point source; this analysis
suggests IRS 10* is an AGB star with an accreting companion. Among the
approximately 90 newly discovered sources are a probable cataclysmic variable,
a potential edge-on contact 84 day period eclipsing binary, and a possible 41
day period pulsating variable.


  We prove optimal boundary regularity for bounded positive weak solutions of
fast diffusion equations in smooth bounded domains. This solves a problem
raised by Berryman and Holland in 1980 for these equations in the subcritical
and critical regimes. Our proof of the a priori estimates uses a geometric type
structure of the fast diffusion equations, where an important ingredient is an
evolution equation for a curvature-like quantity.


  We report Spitzer/IRAC photometry of the transiting giant exoplanet HAT-P-1b
during its secondary eclipse. This planet lies near the postulated boundary
between the pM and pL-class of hot Jupiters, and is important as a test of
models for temperature inversions in hot Jupiter atmospheres. We derive eclipse
depths for HAT-P-1b, in units of the stellar flux, that are: 0.080% +/-
0.008%,[3.6um], 0.135% +/- 0.022%,[4.5um],0.203% +/- 0.031%,[5.8um], and
$0.238% +/- 0.040%,[8.0um]. These values are best fit using an atmosphere with
a modest temperature inversion, intermediate between the archetype inverted
atmosphere (HD209458b) and a model without an inversion. The observations also
suggest that this planet is radiating a large fraction of the available stellar
irradiance on its dayside, with little available for redistribution by
circulation. This planet has sometimes been speculated to be inflated by tidal
dissipation, based on its large radius in discovery observations, and on a
non-zero orbital eccentricity allowed by the radial velocity data. The timing
of the secondary eclipse is very sensitive to orbital eccentricity, and we find
that the central phase of the eclipse is 0.4999 +/- 0.0005. The difference
between the expected and observed phase indicates that the orbit is close to
circular, with a 3-sigma limit of |e cosw| < 0.002.


  For most galaxies, the shutdown of star formation was a slow process that
took four billion years. An analysis of thousands of galaxies suggests that
'strangulation' by their environment was the most likely cause. See Letter on
page 192 of Peng, Maiolino and Cochrane (2015), Nature, vol. 521.


  The demise of Moore's Law has led to the rise of hardware acceleration.
However, the focus on accelerating stable algorithms in their entirety neglects
the abundant fine-grained acceleration opportunities available in broader
domains and squanders host processors' compute power. This paper presents Duet,
a scalable, manycore-FPGA architecture that promotes embedded FPGAs (eFPGA) to
be equal peers with processors through non-intrusive, bi-directionally
cache-coherent integration. In contrast to existing CPU-FPGA hybrid systems in
which the processors play a supportive role, Duet unleashes the full potential
of both the processors and the eFPGAs with two classes of post-fabrication
enhancements: fine-grained acceleration, which partitions an application into
small tasks and offloads the frequently-invoked, compute-intensive ones onto
various small accelerators, leveraging the processors to handle dynamic control
flow and less accelerable tasks; hardware augmentation, which employs
eFPGA-emulated hardware widgets to improve processor efficiency or mitigate
software overheads in certain execution models. An RTL-level implementation of
Duet is developed to evaluate the architecture with high fidelity. Experiments
using synthetic benchmarks show that Duet can reduce the processor-accelerator
communication latency by up to 82% and increase the bandwidth by up to 9.5x.
The RTL implementation is further evaluated with seven application benchmarks,
achieving 1.5-24.9x speedup.


  We study two related universal anomalies of the spectral function of
cuprates, so called waterfall and high-energy kink features, by a combined
cellular dynamical mean-field theory and angle-resolved photoemission study for
the oxychloride Na$_x$Ca$_{2-x}$CuO$_2$Cl$_2$ (Na-CCOC). Tracing their origin
back to an interplay of spin-polaron and local correlation effects both in
undoped and hole-doped (Na-)CCOC, we establish them as a universal crossover
between regions differing in the momentum dependence of the coupling and not
necessarily in the related quasiparticles' energies. The proposed scenario
extends to doping levels coinciding with the cuprate's superconducting dome and
motivates further investigations of the fate of spin-polarons in the
superconducting phase.


  Offline reinforcement learning is used to train policies in scenarios where
real-time access to the environment is expensive or impossible. As a natural
consequence of these harsh conditions, an agent may lack the resources to fully
observe the online environment before taking an action. We dub this situation
the resource-constrained setting. This leads to situations where the offline
dataset (available for training) can contain fully processed features (using
powerful language models, image models, complex sensors, etc.) which are not
available when actions are actually taken online. This disconnect leads to an
interesting and unexplored problem in offline RL: Is it possible to use a
richly processed offline dataset to train a policy which has access to fewer
features in the online environment? In this work, we introduce and formalize
this novel resource-constrained problem setting. We highlight the performance
gap between policies trained using the full offline dataset and policies
trained using limited features. We address this performance gap with a policy
transfer algorithm which first trains a teacher agent using the offline dataset
where features are fully available, and then transfers this knowledge to a
student agent that only uses the resource-constrained features. To better
capture the challenge of this setting, we propose a data collection procedure:
Resource Constrained-Datasets for RL (RC-D4RL). We evaluate our transfer
algorithm on RC-D4RL and the popular D4RL benchmarks and observe consistent
improvement over the baseline (TD3+BC without transfer). The code for the
experiments is available at https://github.com/JayanthRR/RC-OfflineRL.


  We observe that the dominant one loop contribution to the graviton propagator
in the theory of N (N>>1) light scalar fields \phi_a (with masses smaller than
M_{pl}/\sqrt{N}) minimally coupled to Einstein gravity is proportional to N
while that of graviton-scalar-scalar interaction vertex is N independent. We
use this to argue that the coefficient of the R\phi_a^2 term appearing at one
loop level is 1/N suppressed. This observation provides a resolution to the
\eta-problem, that the slow-roll parameter \eta receives order one quantum loop
corrections for inflationary models built within the framework of scalar fields
minimally coupled to Einstein gravity, for models involving large number of
fields. As particular examples, we employ this to argue in favor of the absence
of \eta-problem in M-flation and N-flation scenarios.


  The $n$-dimensional hypercube $Q_n$ is a graph with vertex set $\{0,1\}^n$
and there is an edge between two vertices if they differ in exactly one
coordinate. For any graph $H$, define $\text{ex}(Q_n,H)$ to be the maximum
number of edges of a subgraph of $Q_n$ without a copy of $H$. In this short
note, we prove that for any $n \in \mathbb{N}$ $$\text{ex}(Q_n, C_{10}) > 0.024
\cdot e(Q_n).$$ Our construction is strongly inspired by the recent
breakthrough work of Ellis, Ivan, and Leader, who showed that "daisy"
hypergraphs have positive Tur\'an density with an extremely clever and simple
linear-algebraic argument.


  We consider Schr\"odinger operator in dimension $d\ge 2$ with a singular
interaction supported by an infinite family of concentric spheres, analogous to
a system studied by Hempel and coauthors for regular potentials. The essential
spectrum covers a halfline determined by the appropriate one-dimensional
comparison operator; it is dense pure point in the gaps of the latter. If the
interaction is radially periodic, there are absolutely continuous bands; in
contrast to the regular case the measure of the p.p. segments does not vanish
in the high-energy limit.


  A rise in Advanced Persistent Threats (APTs) has introduced a need for
robustness against long-running, stealthy attacks which circumvent existing
cryptographic security guarantees. FlipIt is a security game that models
attacker-defender interactions in advanced scenarios such as APTs. Previous
work analyzed extensively non-adaptive strategies in FlipIt, but adaptive
strategies rise naturally in practical interactions as players receive feedback
during the game. We model the FlipIt game as a Markov Decision Process and
introduce QFlip, an adaptive strategy for FlipIt based on temporal difference
reinforcement learning. We prove theoretical results on the convergence of our
new strategy against an opponent playing with a Periodic strategy. We confirm
our analysis experimentally by extensive evaluation of QFlip against specific
opponents. QFlip converges to the optimal adaptive strategy for Periodic and
Exponential opponents using associated state spaces. Finally, we introduce a
generalized QFlip strategy with composite state space that outperforms a Greedy
strategy for several distributions including Periodic and Uniform, without
prior knowledge of the opponent's strategy. We also release an OpenAI Gym
environment for FlipIt to facilitate future research.


  The W-characteristic set of a polynomial ideal is the minimal triangular set
contained in the reduced lexicographical Groebner basis of the ideal. A pair
(G,C) of polynomial sets is a strong regular characteristic pair if G is a
reduced lexicographical Groebner basis, C is the W-characteristic set of the
ideal <G>, the saturated ideal sat(C) of C is equal to <G>, and C is regular.
In this paper, we show that for any polynomial ideal I with given generators
one can either detect that I is unit, or construct a strong regular
characteristic pair (G,C) by computing Groebner bases such that
I$\subseteq$sat(C)=<G> and sat(C) divides I, so the ideal I can be split into
the saturated ideal sat(C) and the quotient ideal I:sat(C). Based on this
strategy of splitting by means of quotient and with Groebner basis and ideal
computations, we devise a simple algorithm to decompose an arbitrary polynomial
set F into finitely many strong regular characteristic pairs, from which two
representations for the zeros of F are obtained: one in terms of strong regular
Groebner bases and the other in terms of regular triangular sets. We present
some properties about strong regular characteristic pairs and characteristic
decomposition and illustrate the proposed algorithm and its performance by
examples and experimental results.


  Explanation is a key component for the adoption of reinforcement learning
(RL) in many real-world decision-making problems. In the literature, the
explanation is often provided by saliency attribution to the features of the RL
agent's state. In this work, we propose a complementary approach to these
explanations, particularly for offline RL, where we attribute the policy
decisions of a trained RL agent to the trajectories encountered by it during
training. To do so, we encode trajectories in offline training data
individually as well as collectively (encoding a set of trajectories). We then
attribute policy decisions to a set of trajectories in this encoded space by
estimating the sensitivity of the decision with respect to that set. Further,
we demonstrate the effectiveness of the proposed approach in terms of quality
of attributions as well as practical scalability in diverse environments that
involve both discrete and continuous state and action spaces such as
grid-worlds, video games (Atari) and continuous control (MuJoCo). We also
conduct a human study on a simple navigation task to observe how their
understanding of the task compares with data attributed for a trained RL
policy. Keywords -- Explainable AI, Verifiability of AI Decisions, Explainable
RL.


  A \emph{Stick graph} is an intersection graph of axis-aligned segments such
that the left end-points of the horizontal segments and the bottom end-points
of the vertical segments lie on a `ground line,' a line with slope $-1$. It is
an open question to decide in polynomial time whether a given bipartite graph
$G$ with bipartition $A\cup B$ has a Stick representation where the vertices in
$A$ and $B$ correspond to horizontal and vertical segments, respectively. We
prove that $G$ has a Stick representation if and only if there are orderings of
$A$ and $B$ such that $G$'s bipartite adjacency matrix with rows $A$ and
columns $B$ excludes three small `forbidden' submatrices. This is similar to
characterizations for other classes of bipartite intersection graphs.
  We present an algorithm to test whether given orderings of $A$ and $B$ permit
a Stick representation respecting those orderings, and to find such a
representation if it exists. The algorithm runs in time linear in the size of
the adjacency matrix. For the case when only the ordering of $A$ is given, we
present an $O(|A|^3|B|^3)$-time algorithm. When neither ordering is given, we
present some partial results about graphs that are, or are not, Stick
representable.


  Stochastic effects in multi-field inflationary scenarios are investigated. A
hierarchy of diffusion equations is derived, the solutions of which yield
moments of the numbers of inflationary $e$-folds. Solving the resulting partial
differential equations in multi-dimensional field space is more challenging
than the single-field case. A few tractable examples are discussed, which show
that the number of fields is, in general, a critical parameter. When more than
two fields are present for instance, the probability to explore arbitrarily
large-field regions of the potential, otherwise inaccessible to single-field
dynamics, becomes non-zero. In some configurations, this gives rise to an
infinite mean number of $e$-folds, regardless of the initial conditions.
Another difference with respect to single-field scenarios is that multi-field
stochastic effects can be large even at sub-Planckian energy. This opens
interesting new possibilities for probing quantum effects in inflationary
dynamics, since the moments of the numbers of $e$-folds can be used to
calculate the distribution of primordial density perturbations in the
stochastic-$\delta N$ formalism.


  Consider an n-vertex graph G = (V,E) of maximum degree Delta, and suppose
that each vertex v \in V hosts a processor. The processors are allowed to
communicate only with their neighbors in G. The communication is synchronous,
i.e., it proceeds in discrete rounds. In the distributed vertex coloring
problem the objective is to color G with Delta + 1, or slightly more than Delta
+ 1, colors using as few rounds of communication as possible. (The number of
rounds of communication will be henceforth referred to as running time.)
Efficient randomized algorithms for this problem are known for more than twenty
years \cite{L86, ABI86}. Specifically, these algorithms produce a (Delta +
1)-coloring within O(log n) time, with high probability. On the other hand, the
best known deterministic algorithm that requires polylogarithmic time employs
O(Delta^2) colors. This algorithm was devised in a seminal FOCS'87 paper by
Linial \cite{L87}. Its running time is O(log^* n). In the same paper Linial
asked whether one can color with significantly less than Delta^2 colors in
deterministic polylogarithmic time. By now this question of Linial became one
of the most central long-standing open questions in this area. In this paper we
answer this question in the affirmative, and devise a deterministic algorithm
that employs \Delta^{1 +o(1)} colors, and runs in polylogarithmic time.
Specifically, the running time of our algorithm is O(f(Delta) log Delta log n),
for an arbitrarily slow-growing function f(Delta) = \omega(1). We can also
produce O(Delta^{1 + \eta})-coloring in O(log Delta log n)-time, for an
arbitrarily small constant \eta > 0, and O(Delta)-coloring in
O(Delta^{\epsilon} log n) time, for an arbitrarily small constant \epsilon > 0.


  The Colonel Blotto game is a renowned resource allocation problem with a
long-standing literature in game theory (almost 100 years). However, its scope
of application is still restricted by the lack of studies on the
incomplete-information situations where a learning model is needed. In this
work, we propose and study a regret-minimization model where a learner
repeatedly plays the Colonel Blotto game against several adversaries. At each
stage, the learner distributes her budget of resources on a fixed number of
battlefields to maximize the aggregate value of battlefields she wins; each
battlefield being won if there is no adversary that has higher allocation. We
focus on the bandit feedback setting. We first show that it can be modeled as a
path planning problem. It is then possible to use the classical COMBAND
algorithm to guarantee a sub-linear regret in terms of time horizon, but this
entails two fundamental challenges: (i) the computation is inefficient due to
the huge size of the action set, and (ii) the standard exploration distribution
leads to a loose guarantee in practice. To address the first, we construct a
modified algorithm that can be efficiently implemented by applying a dynamic
programming technique called weight pushing; for the second, we propose methods
optimizing the exploration distribution to improve the regret bound. Finally,
we implement our proposed algorithm and perform numerical experiments that show
the regret improvement in practice.


  The discovery of the optical counterpart, along with the gravitational waves
from GW170817, of the first binary neutron star merger, opened up a new era for
multi-messenger astrophysics. Combining the GW data with the optical
counterpart, also known as AT2017gfo, classified as a kilonova, has revealed
the nature of compact binary merging systems by extracting enriched information
about the total binary mass, the mass ratio, the system geometry, and the
equation of state. Even though the detection of kilonova brought about a
revolution in the domain of multi-messenger astronomy, since there has been
only one kilonova from a gravitational wave detected binary neutron star merger
event so far, this limits the exact understanding of the origin and propagation
of the kilonova. Here, we use a conditional variational autoencoder trained on
light curve data from two kilonova models having different temporal lengths,
and consequently, generate kilonova light curves rapidly based on physical
parameters of our choice with good accuracy. Once trained, the time scale for
light curve generation is of the order of a few milliseconds, thus speeding up
generating light curves by $1000$ times compared to the simulation. The mean
squared error between the generated and original light curves is typically
$0.015$ with a maximum of $0.08$ for each set of considered physical parameter;
while having a maximum of $\approx0.6$ error across the whole parameter space.
Hence, implementing this technique provides fast and reliably accurate results.


  A formal relationship between scattering amplitudes in critical bosonic
string theory and correlation functions of operators in topological string
theory is found.


  We lift the dynamical field of the $A_\infty$ superstring field theory to the
large Hilbert space by introducing a gauge invariance associated with the eta
zero mode. We then provide a field redefinition which relates the lifted field
to the dynamical field of Berkovits' superstring field theory in the large
Hilbert space. This generalizes the field redefinition in the small Hilbert
space described in earlier works, and gives some understanding of the relation
between the gauge symmetries of the theories. It also provides a new
perspective on the algebraic structure underlying gauge invariance of the
Wess-Zumino-Witten-like action.


  A nilpotent quandle is a quandle whose inner automorphism group is nilpotent.
Such quandles have been called reductive in previous works, but it turns out
that their behaviour is in fact very close to nilpotency for groups. In
particular, we show that it is easy to characterise generating sets of such
quandles, and that they have the Hopf property. We also show how to construct
free nilpotent quandles from free nilpotent groups. We then use the properties
of nilpotent quandles to describe a simple presentation of their associated
group, and we use this to recover the classification of abelian quandles by
Lebed and Mortier [LM21]. We also study reduced quandles, and we show that the
reduced fundamental quandle is equivalent, as an invariant of links, to the
reduced peripheral system, sharpening a previous result of Hughes [Hug11].
Finally, we give a characterisation of nilpotency in terms of the associated
invariants of braids.


  Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in
\mathbb{Z}^n$. We show under fairly general conditions that the non-uniform
Physarum dynamics \[ \dot{x}_e = a_e(x,t) \left(|q_e| - x_e\right) \] converges
to the optimum solution $x^*$ of the weighted basis pursuit problem minimize
$c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors
of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to
the constraints $A q = b$ and $\mathrm{supp}(q) \subseteq \mathrm{supp}(x)$,
and $a_e(x,t) > 0$ is the reactivity of edge $e$ to the difference $|q_e| -
x_e$ at time $t$ and in state $x$. Previously convergence was only shown for
the uniform case $a_e(x,t) = 1$ for all $e$, $x$, and $t$. We also show
convergence for the dynamics \[ \dot{x}_e = x_e \cdot \left( g_e
\left(\frac{|q_e|}{x_e}\right) - 1\right),\] where $g_e$ is an increasing
differentiable function with $g_e(1) = 1$. Previously convergence was only
shown for the special case of the shortest path problem on a graph consisting
of two nodes connected by parallel edges.


  In the present paper we extend the definition of slice-torus invariant to
links. We prove a few properties of the newly-defined slice-torus link
invariants: the behaviour under crossing change, a slice genus bound, an
obstruction to strong sliceness, and a combinatorial bound. Furthermore, we
provide an application to the computation of the splitting number. Finally, we
use the slice-torus link invariants, and the Whitehead doubling to define new
strong concordance invariants for links, which are proven to be independent
from the corresponding slice-torus link invariant.


  The RHIC high energy collision of species ranging from p+p, p(d)+A to A+A
provide access to the {small-x} component of the hadron wave function. The RHIC
program has brought renewed interest in that subject with its ability to reach
values of the parton momentum fraction smaller than 0.01 with studies of
particle production at high rapidity. Furthermore, the use of heavy nuclei in
the p(d)+A collisions facilitates the study of saturation effects in the
gluonic component of the nuclei because the appropriate scale for that regime
grows as A^1/3. We review the experimental results of the RHIC program that
have relevance to {small-x} emphasizing the physics extracted from d+Au
collisions and their comparison to p+p collisions at the same energy.


  High-frequency multi-messenger observations provide a powerful probe of
gamma-ray bursts (GRBs), pioneered by {\em BeppoSAX} in gamma-rays and
LIGO-Virgo in gravitational waves. Identifying the central engines - magnetars
or black holes - also promises to improve on GRBs as probes of cosmological
evolution. THESEUS' design is ideally suited to pursue both science objectives.
Here, we present a general-purpose {\em graphics processor units}
(GPU)-accelerated broadband search algorithm for long duration ascending and
descending chirps, post-merger or from core-collapse of massive stars, in
electromagnetic and gravitational radiation. It implements butterfly filtering
using banks of up to 8 million templates of 1 second duration at over one
million correlations per second by heterogeneous computing using a dozen
high-end GPUs. We demonstrate its application with the identification of
broadband Kolmogorov spectra in long GRBs and the long duration ascending chirp
in the merger GW170817. The first shows a noticeable absence of a high
frequency bump, otherwise expected from newly formed magnetar central engines.
The second illustrates the need for deep searches to identify GRB central
engines in descending chirps in gravitational waves, post-merger or from nearby
energetic core-collapse supernovae. A future catalogue of THESEUS' GRBs
covering a broad range of redshifts may probe the nature of the cosmological
vacuum and establish the de Sitter limit as a turning point in cosmological
evolution.


  Efficient driving in urban traffic scenarios requires foresight. The
observation of other traffic participants and the inference of their possible
next actions depending on the own action is considered cooperative prediction
and planning. Humans are well equipped with the capability to predict the
actions of multiple interacting traffic participants and plan accordingly,
without the need to directly communicate with others. Prior work has shown that
it is possible to achieve effective cooperative planning without the need for
explicit communication. However, the search space for cooperative plans is so
large that most of the computational budget is spent on exploring the search
space in unpromising regions that are far away from the solution. To accelerate
the planning process, we combined learned heuristics with a cooperative
planning method to guide the search towards regions with promising actions,
yielding better solutions at lower computational costs.


  Nonlinear response signatures are increasingly recognized as useful probes of
condensed matter systems, in particular for characterisation of topologically
non-trivial states. The circular photogalvanic effect (CPGE) is particularly
useful in study of topological semimetals, as the CPGE tensor quantises for
well-isolated topological degeneracies in strictly linearly-dispersing band
structures. Here, we study multiplicative Weyl semimetal band-structures, and
find that the multiplicative structure robustly protects the quantization of
the CPGE even in the case of non-linear dispersion. Computing phase diagrams as
a function of Weyl node tilting, we find a variety of quantised values for the
CPGE tensor, revealing that the CPGE is also a useful tool in detecting and
characterising parent topology of multiplicative topological states.


  We extend some recent work of D. McCarthy, proving relations among some
Fourier coefficients of a degree 2 Siegel modular form $F$ with arbitrary level
and character, provided there are some primes $q$ so that $F$ is an eigenform
for the Hecke operators $T(q)$ and $T_1(q^2)$.


  A numerical evidence for the dependence of the substructure abundance of
cluster halos on the orientation coherence of the surrounding tidal fields is
presented. Applying the adapted minimal spanning tree (MST) algorithm to the
cluster halos with $M\ge 10^{14}\,h^{-1}\,M_{\odot}$ from the Big
MultiDark-Planck Simulations, we identify primary MST stems composed of
multiple nodes as the filaments and measure their specific sizes (spatial
extents per node), which quantify the orientation coherence of the tidal field
on the cluster scales. Classifying the cluster halos into five samples by the
specific sizes of their host filaments and tallying the mass distributions of
the five samples, we investigate if and how the substructure abundance of the
cluster halos differs among the five samples. It is found that the cluster
halos embedded in the filaments with larger specific sizes tend to possess less
substructures. This anti-correlation is also shown robust against narrowing
down the formation epochs of the cluster halos as well as against fixing the
node number of the filaments. Given that the filaments with larger specific
sizes form at the regions where the surrounding tidal fields are coherent over
large scales in the orientations of their principal axes, we suggest that in
the filaments with larger specific sizes the satellite infall and matter
accretion onto the cluster halos should be obstructed due to the development of
the tangential velocities in the plane perpendicular to the elongated axes of
the filaments.


  Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was
originated for the goal of positive frequency representations of signals. It
achieved the goal and at the same time offered fast decompositions of signals.
There then arose several types of AFDs. AFD merged with the greedy algorithm
idea, and in particular, motivated the so-called pre-orthogonal greedy
algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm.
The cost of the advantages of the AFD type decompositions is, however, the high
computational complexity due to the involvement of maximal selections of the
dictionary parameters. The present paper offers one formulation of the 1-D AFD
algorithm by building the FFT algorithm into it. Accordingly, the algorithm
complexity is reduced, from the original $\mathcal{O}(M N^2)$ to $\mathcal{O}(M
N\log_2 N)$, where $N$ denotes the number of the discretization points on the
unit circle and $M$ denotes the number of points in $[0,1)$. This greatly
enhances the applicability of AFD. Experiments are carried out to show the high
efficiency of the proposed algorithm.


  A coarse-grained water model is developed using multistate iterative
Boltzmann inversion. Following previous work, the k-means algorithm is used to
dynamically map multiple water molecules to a single coarse-grained bead,
allowing the use of structure-based coarse-graining methods. The model is
derived to match the bulk and interfacial properties of liquid water and
improves upon previous work that used single state iterative Boltzmann
inversion. The model accurately reproduces the density and structural
correlations of water at 305 K and 1.0 atm, stability of a liquid droplet at
305 K, and shows little tendency to crystallize at physiological conditions.
This work also illustrates several advantages of using multistate iterative
Boltzmann inversion for deriving generally applicable coarse-grained
forcefields.


  So far, planetary surface exploration depends on various mobile robot
platforms. The autonomous navigation and decision-making of these mobile robots
in complex terrains largely rely on their terrain-aware perception,
localization and mapping capabilities. In this paper we release the TAIL-Plus
dataset, a new challenging dataset in deformable granular environments for
planetary exploration robots, which is an extension to our previous work, TAIL
(Terrain-Aware multI-modaL) dataset. We conducted field experiments on beaches
that are considered as planetary surface analog environments for diverse sandy
terrains. In TAIL-Plus dataset, we provide more sequences with multiple loops
and expand the scene from day to night. Benefit from our sensor suite with
modular design, we use both wheeled and quadruped robots for data collection.
The sensors include a 3D LiDAR, three downward RGB-D cameras, a pair of
global-shutter color cameras that can be used as a forward-looking stereo
camera, an RTK-GPS device and an extra IMU. Our datasets are intended to help
researchers developing multi-sensor simultaneous localization and mapping
(SLAM) algorithms for robots in unstructured, deformable granular terrains. Our
datasets and supplementary materials will be available at
\url{https://tailrobot.github.io/}.


  In this paper, we have made an accurate investigation of proton acceleration
in GRBs and we have predicted a possible signature of cosmic rays, in a
sufficiently baryon-loaded fireball, via GeV $\gamma$-ray emission produced by
$\pi^{0}$-meson decay. If two ungrounded assumptions are removed, namely,
Bohm's scaling and a slow magnetic field decrease, the usual Fermi processes
are unable to generate ultra high energy cosmic rays (UHECRs) in GRBs. We
propose to develop another scenario of relativistic Fermi acceleration in the
internal shock stage. We present the results of a realistic Monte-Carlo
simulation of a multi-front acceleration which clearly shows the possible
generation of UHECR. The amount of energy converted into UHECRs turns out to be
a sizeable fraction of the magnetic energy.


  Today's telecommunication networks have become sources of enormous amounts of
widely heterogeneous data. This information can be retrieved from network
traffic traces, network alarms, signal quality indicators, users' behavioral
data, etc. Advanced mathematical tools are required to extract meaningful
information from these data and take decisions pertaining to the proper
functioning of the networks from the network-generated data. Among these
mathematical tools, Machine Learning (ML) is regarded as one of the most
promising methodological approaches to perform network-data analysis and enable
automated network self-configuration and fault management. The adoption of ML
techniques in the field of optical communication networks is motivated by the
unprecedented growth of network complexity faced by optical networks in the
last few years. Such complexity increase is due to the introduction of a huge
number of adjustable and interdependent system parameters (e.g., routing
configurations, modulation format, symbol rate, coding schemes, etc.) that are
enabled by the usage of coherent transmission/reception technologies, advanced
digital signal processing and compensation of nonlinear effects in optical
fiber propagation. In this paper we provide an overview of the application of
ML to optical communications and networking. We classify and survey relevant
literature dealing with the topic, and we also provide an introductory tutorial
on ML for researchers and practitioners interested in this field. Although a
good number of research papers have recently appeared, the application of ML to
optical networks is still in its infancy: to stimulate further work in this
area, we conclude the paper proposing new possible research directions.


  We establish a local model for the moduli space of holomorphic symplectic
structures with logarithmic poles, near the locus of structures whose polar
divisor is normal crossings. In contrast to the case without poles, the moduli
space is singular: when the cohomology class of a symplectic structure
satisfies certain linear equations with integer coefficients, its polar divisor
can be partially smoothed, yielding adjacent irreducible components of the
moduli space that correspond to possibly non-normal crossings structures. These
components are indexed by combinatorial data we call smoothing diagrams, and
amenable to algorithmic classification. Applying the theory to four-dimensional
projective space, we obtain a total of 40 irreducible components of the moduli
space, most of which are new. Our main technique is a detailed analysis of the
relevant deformation complex (the Poisson cohomology) as an object of the
constructible derived category.


  Recently, data-driven predictive control of linear systems has received
wide-spread research attention. It hinges on the fundamental lemma by Willems
et al. In a previous paper, we have shown how this framework can be applied to
predictive control of linear time-invariant descriptor systems. In the present
paper, we present a case study wherein we apply data-driven predictive control
to a discrete-time descriptor model obtained by discretization of the
power-swing equations for a nine-bus system. Our results shows the efficacy of
the proposed control scheme and they underpin the prospect of the data-driven
framework for control of descriptor systems.


  Phase space method provides a novel way for deducing qualitative features of
nonlinear differential equations without actually solving them. The method is
applied here for analyzing stability of circular orbits of test particles in
various physically interesting environments. The approach is shown to work in a
revealing way in Schwarzschild spacetime. All relevant conclusions about
circular orbits in the Schwarzschild-de Sitter spacetime are shown to be
remarkably encoded in a single parameter. The analysis in the rotating Kerr
black hole readily exposes information as to how stability depends on the ratio
of source rotation to particle angular momentum. As a wider application, it is
exemplified how the analysis reveals useful information when applied to motion
in a refractive medium, for instance, that of optical black holes.


  We investigate temperature-dependent resonance fluorescence spectra obtained
from a single self-assembled quantum dot. A decrease of the Mollow triplet
sideband splitting is observed with increasing temperature, an effect we
attribute to a phonon-induced renormalisation of the driven dot Rabi frequency.
We also present first evidence for a non-perturbative regime of phonon
coupling, in which the expected linear increase in sideband linewidth as a
function of temperature is cancelled by the corresponding reduction in Rabi
frequency. These results indicate that dephasing in semiconductor quantum dots
may be less sensitive to changes in temperature than expected from a standard
weak-coupling analysis of phonon effects.


  We calculate Sudakov-type form factors for isolated spin-1/2 particles
(fermions) entering non-Abelian gauge-field systems. We consider both the on-
and the off-mass-shell case using a methodology which rests on a worldline
casting of field theories. The simplicity and utility of our approach derives
from the fact that we are in a position to make, a priori, a more transparent
separation (factorization), with respect to a given scale, between short- and
long-distance physics than diagramatic methods.


  In this paper we discuss the MHD flow of a second grade fluid, in particular
we prove the existence and uniqueness of a weak solution of a time-dependent
grade two fluid model in a two-dimensional Lipschitz domain. We follow the
methodology of Girault and Saadouni (Ref.[3]), i.e , we use a constructive
method which can be adapted to the numerical analysis of finite-element schemes
for solving this problem numerically.


  Suppose $T$ and $S$ are bounded adjointable operators between Hilbert
C*-modules admitting bounded Moore-Penrose inverse operators. Some necessary
and sufficient conditions are given for the reverse order law $(TS)^{ \dag}
=S^{ \dag} T^{ \dag}$ to hold. In particular, we show that the equality holds
if and only if $Ran(T^{\ast}TS) \subseteq Ran(S)$ and $Ran(SS^{\ast}T^{\ast})
\subseteq Ran(T^{\ast}),$ which was studied first by Greville [{\it SIAM Rev. 8
(1966) 518--521}] for matrices.


  This research investigates the multifaceted relationship underlying capital
structure dynamics along with financial performance as a result of mergers and
acquisitions, or M&As, in Indian banks. In the face of increasing competition,
banks have deliberately embraced M&A as a strategy of improving commercial
prospects and maintaining financial stability. The primary goal of this study
is to examine the changes in the capital framework and financial results of
banks before and after M&A transactions. The investigation, which employs a
paired t-test as a method of statistical analysis, is based on a review of
annual reports from selected banks over a two-year period before and after M&A
transactions. The paired t-test approach allows for a thorough statistical
analysis of interconnected datasets, revealing the subtle influence of M&A
attempts on both bank financial performance as well as capital structure
dynamics. The study's findings have the potential to add to the current body of
knowledge on organisational planning, managing finances, and capital structure
optimisation. The research has practical significance for financial companies,
legislators, and scholars interested in understanding the profound effects of
M&A inside the arena of financial institutions that operate within fiercely
competitive landscapes because it provides comprehensive insights regarding the
complex consequences of banking merger and acquisition (M&A) deals on capital
structure as well as financial performance. Finally, the goal of this research
is to provide the banking sector with educated decision-making capabilities and
strategic guidance to businesses facing heightened competition while coping
with the complexities of capital structure.


  Diabetes is considered a lifestyle disease and a well managed self-care plays
an important role in the treatment. Clinicians often conduct surveys to
understand the self-care behaviors in their patients. In this context, we
propose to use Self-Organising Maps (SOM) to explore the survey data for
assessing the self-care behaviors in Type-1 diabetic patients. Specifically,
SOM is used to visualize high dimensional similar patient profiles, which is
rarely discussed. Experiments demonstrate that our findings through SOM
analysis corresponds well to the expectations of the clinicians. In addition,
our findings inspire the experts to improve their understanding of the
self-care behaviors for their patients. The principle findings in our study
show: 1) patients who take correct dose of insulin, inject insulin at the right
time, 2) patients who take correct food portions undertake regular physical
activity and 3) patients who eat on time take correct food portions.


  We point out that some models with infinite additional dimension(s) of
Randall-Sundrum type predict the disappearance of orthopositronium (o-Ps) into
additional dimension(s). The experimental signature of this effect is the o-Ps
-> invisible decay of orthopositronium which may occur at a rate within three
orders of magnitude of the present experimental upper limit. This result
enhances existing motivations for a more sensitive search for this decay mode
and suggests additional directions for testing extra dimensions in non
accelerator experiments.


  We study a generic problem of dissipative quantum mechanics, a small local
quantum system with discrete states coupled in an arbitrary way (i.e. not
necessarily linear) to several infinitely large particle or heat reservoirs.
For both bosonic or fermionic reservoirs we develop a quantum field-theoretical
diagrammatic formulation in Liouville space by expanding systematically in the
reservoir-system coupling and integrating out the reservoir degrees of freedom.
As a result we obtain a kinetic equation for the reduced density matrix of the
quantum system. Based on this formalism, we present a formally exact
perturbative renormalization group (RG) method from which the kernel of this
kinetic equation can be calculated. It is demonstrated how the nonequilibrium
stationary state (induced by several reservoirs kept at different chemical
potentials or temperatures), arbitrary observables such as the transport
current, and the time evolution into the stationary state can be calculated.
Most importantly, we show how RG equations for the relaxation and dephasing
rates can be derived and how they cut off generically the RG flow of the
vertices. The method is based on a previously derived real-time RG technique
but formulated here in Laplace space and generalized to arbitrary
reservoir-system couplings. Furthermore, for fermionic reservoirs with flat
density of states, we make use of a recently introduced cutoff scheme on the
imaginary frequency axis which has several technical advantages. We demonstrate
the method by applying it to the nonequilibrium isotropic Kondo model in
1-loop. We present a systematic way to solve the RG equations analytically in
the weak-coupling limit and provide an outlook of the applicability to the
strong-coupling case.


  The type problem is the problem of deciding, for a simply connected Riemann
surface, whether it is conformally equivalent to the complex plane or to the
unit dic in the complex plane. We report on Teichm{\"u}ller's results on the
type problem from his two papers Eine Anwendung quasikonformer Abbildungen auf
das Typenproblem (An application of quasiconformal map-pings to the type
problem) (1937) and Untersuchungen{\"u}ber kon-forme und quasikonforme
Abbildungen (Investigations on con-formal and quasiconformal mappings) (1938).
They concern simply connected Riemann surfaces defined as branched covers of
the sphere. At the same time, we review the theory of line complexes, a
combinatorial device used by Teichm{\"u}ller and others to encode branched
coverings of the sphere. In the first paper, Teichm{\"u}ller proves that any
two simply connected Riemann surfaces which are branched coverings of the
Riemann sphere with finitely many branch values and which have the same line
complex are quasiconformally equivalent. For this purpose, he introduces a
technique for piecing together quasi-conformal mappings. He also obtains a
result on the extension of smooth orientation-preserving diffeomorphisms of the
circle to quasiconformal mappings of the disc which are conformal at the
boundary. In the second paper, using line complexes, Teichm{\"u}ller gives a
type criterion for a simply-connected surface which is a branched covering of
the sphere, in terms of an adequately defined measure of ramification, defined
by a limiting process. The result says that if the surface is ''sufficiently
ramified'' (in a sense to be made precise), then it is hyperbolic. In the same
paper, Te-ichm{\"u}ller answers by the negative a conjecture made by
Nevan-linna which states a criterion for parabolicity in terms of the value of
a (different) measure of ramification, defined by a limiting process.
Teichm{\"u}ller's results in his first paper are used in the proof of the
results of the second one.The final version of this paper will appear in Vol.
VII of the Handbook of Teichm{\"u}ller theory (European Mathematical Society
Publishing House, 2020).


  There is a growing need for unbiased clustering methods, ideally automated.
We have developed a topology-based analysis tool called Two-Tier Mapper (TTMap)
to detect subgroups in global gene expression datasets and identify their
distinguishing features. First, TTMap discerns and adjusts for highly variable
features in the control group and identifies outliers. Second, the deviation of
each test sample from the control group in a high-dimensional space is computed
and the test samples are clustered in a global and local network using a new
topological algorithm based on Mapper. Validation of TTMap on both synthetic
and biological datasets shows that it outperforms current clustering methods in
sensitivity and stability; clustering is not affected by removal of samples
from the control group, choice of normalization nor subselection of data. There
is no user induced bias because all parameters are data-driven. Datasets can
readily be combined into one analysis. TTMap reveals hitherto undetected gene
expression changes in mouse mammary glands related to hormonal changes during
the estrous cycle. This illustrates the ability to extract information from
highly variable biological samples and its potential for personalized medicine.


  Two recent experimental observations at the ATOMKI Institute of the Hungarian
Academy of Sciences (regarding the angular emission pattern of
electron-positron pairs from nuclear transitions from excited states in 8Be and
4He) indicate the possible existence of a particle of a rest mass energy of
roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the
process, preceding the emission of the electron-positron pair. Based on the
symmetry of the nuclear transitions ($1^+$ to $0^+$ and $0^-$ to $0^+$), the
X17 could either be a vector, or a pseudoscalar particle. Here, we calculate
the effective potentials generated by the X17, for hyperfine interactions in
simple atomic systems, for both the pseudoscalar as well as the vector X17
hypotheses. The effective Hamiltonians are obtained in a general form which is
applicable to both electronic as well as muonic bound systems. The effect of
virtual annihilation and its contribution to the hyperfine splitting also is
considered. Because of the short range of the X17-generated potentials, the
most promising pathway for the observation of the X17-mediated effects in bound
systems concerns hyperfine interactions, which, for $S$ states, are given by
modifications of short-range (Dirac-delta) potentials in coordinate space. For
the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between
the bound lepton and the nucleus exclusively leads to hyperfine effects, but
does not affect the Lamb shift. Effects due to the X17 are shown to be
drastically enhanced for muonic bound systems. Prospects for the detection of
hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium,
muonic hydrogen, muonium, true muonium ($\mu^+\mu^-$ bound system), and
positronium.


  Hyperspectral images (HSI) classification is a high technical remote sensing
tool. The main goal is to classify the point of a region. The HIS contains more
than a hundred bidirectional measures, called bands (or simply images), of the
same region called Ground Truth Map (GT). Unfortunately, some bands contain
redundant information, others are affected by the noise, and the high
dimensionalities of features make the accuracy of classification lower. All
these bands can be important for some applications, but for the classification
a small subset of these is relevant. In this paper we use mutual information
(MI) to select the relevant bands; and the Normalized Mutual Information
coefficient to avoid and control redundant ones. This is a feature selection
scheme and a Filter strategy. We establish this study on HSI AVIRIS 92AV3C.
This is effectiveness, and fast scheme to control redundancy. Index Terms:
Hyperspectral images, Classification, Feature Selection, Normalized Mutual
Information, Redundancy.


  We prove the local existence for the Water Waves equations with large
bathymetric variations on a time interval of size 1/\epsilon, where $\epsilon$
measures the amplitude of the wave. We just need the presence of surface
tension.


  We generalize Anderson's orthogonality determinant formula to describe the
statistics of work performed on generic disordered, non-interacting fermionic
nanograins during quantum quenches. The energy absorbed increases linearly with
time, while its variance exhibits a superdiffusive behavior due to Pauli's
exclusion principle. The probability of adiabatic evolution decays as a
stretched exponential. In slowly driven systems, work statistics exhibits
universal features, and can be understood in terms of fermion diffusion in
energy space, generated by Landau-Zener transitions. This diffusion is very
well captured by a Markovian symmetrical exclusion process, with the diffusion
constant identified as the energy absorption rate. The energy absorption rate
shows an anomalous frequency dependence at small energies, reflecting the
symmetry class of the underlying Hamiltonian. Our predictions can be
experimentally verified by calorimetric measurements performed on nanoscale
circuits.


  Single pseudoscalar and vector mesons hard semi-inclusive photoproduction
$\gamma h \to MX" via higher twist (HT) mechanism is calculated using the QCD
running coupling constant method. The structure of infrared renormalon
singularities of the HT subprocess cross section and the Borel sum for it are
found. The problem of normalization of HT process cross section in terms of the
meson elm form factor is discussed.


  Finding parameters in a deep neural network (NN) that fit training data is a
nonconvex optimization problem, but a basic first-order optimization method
(gradient descent) finds a global optimizer with perfect fit (zero-loss) in
many practical situations. We examine this phenomenon for the case of Residual
Neural Networks (ResNet) with smooth activation functions in a limiting regime
in which both the number of layers (depth) and the number of weights in each
layer (width) go to infinity. First, we use a mean-field-limit argument to
prove that the gradient descent for parameter training becomes a gradient flow
for a probability distribution that is characterized by a partial differential
equation (PDE) in the large-NN limit. Next, we show that under certain
assumptions, the solution to the PDE converges in the training time to a
zero-loss solution. Together, these results suggest that the training of the
ResNet gives a near-zero loss if the ResNet is large enough. We give estimates
of the depth and width needed to reduce the loss below a given threshold, with
high probability.


  Learning from the collective knowledge of data dispersed across private
sources can provide neural networks with enhanced generalization capabilities.
Federated learning, a method for collaboratively training a machine learning
model across remote clients, achieves this by combining client models via the
orchestration of a central server. However, current approaches face two
critical limitations: i) they struggle to converge when client domains are
sufficiently different, and ii) current aggregation techniques produce an
identical global model for each client. In this work, we address these issues
by reformulating the typical federated learning setup: rather than learning a
single global model, we learn N models each optimized for a common objective.
To achieve this, we apply a weighted distance minimization to model parameters
shared in a peer-to-peer topology. The resulting framework, Iterative Parameter
Alignment, applies naturally to the cross-silo setting, and has the following
properties: (i) a unique solution for each participant, with the option to
globally converge each model in the federation, and (ii) an optional
early-stopping mechanism to elicit fairness among peers in collaborative
learning settings. These characteristics jointly provide a flexible new
framework for iteratively learning from peer models trained on disparate
datasets. We find that the technique achieves competitive results on a variety
of data partitions compared to state-of-the-art approaches. Further, we show
that the method is robust to divergent domains (i.e. disjoint classes across
peers) where existing approaches struggle.


  As the Internet grows in importance, it is vital to develop methods and
techniques for educating end-users to improve their awareness of online
privacy. Web-based education tools have been proven effective in many domains
and have been increasingly adopted by many online professional and educational
services. However, the design and development of Web-based education tools for
online privacy is still in the early stage. The traditional solutions always
involve privacy experts who have sophisticated expertise. Such involvement can
make the tool development costly. Furthermore, it is not clear how inspiring
and effective these education tools are to general users of varying
backgrounds, specially to novice users who have rarely dealt with online
privacy issues before. In this paper, we design, develop, and evaluate a
game-based privacy learning system by leveraging the wisdom of a crowd of
non-experts on Amazon Mechanic Turk. Empirical study demonstrates that the
crowd can provide high-quality ideas of designing and developing a practical,
educational privacy learning game.


  A two-dimensional lattice gas of two species, driven in opposite directions
by an external force, undergoes a jamming transition if the filling fraction is
sufficiently high. Using Monte Carlo simulations, we investigate the growth of
these jams ("clouds"), as the system approaches a non-equilibrium steady state
from a disordered initial state. We monitor the dynamic structure factor
$S(k_x,k_y;t)$ and find that the $k_x=0$ component exhibits dynamic scaling, of
the form $S(0,k_y;t)=t^\beta \tilde{S}(k_yt^\alpha)$. Over a significant range
of times, we observe excellent data collapse with $\alpha=1/2$ and $\beta=1$.
The effects of varying filling fraction and driving force are discussed.


  In this paper, the performances of a type of the domestic THGEM (THick
Gaseous Electron Multiplier) working in the Ar/CO2 mixtures are reported in
details. This kind of single THGEM can provide the gain range from 100 to 1000,
which is very suitable for the application in the neutron detection. In order
to study its basic characteristics as the references for the development of
THGEM based neutron detector, the counting rate plateau, the energy resolution
and the gain of the THGEM have been measured in the different Ar/CO2 mixtures
with the change of the electrical fields. For the Ar/CO2(90%/10%) gas mixture,
a wide counting rate plateau is got from 720V to 770V with the plateau slope of
2.4% / 100 V and the excellent energy resolution about 22% is obtained at the
5.9keV full energy peak of the 55Fe X-ray source.


  The fundamental problem of the occurrence/removal of finite-time future
singularity in the universe evolution for coupled dark energy (DE) is
addressed. It is demonstrated the existence of the (instable or local minimum)
de Sitter space solution which may cure the Type II or Type IV future
singularity for DE coupled with DM as the result of tuning the initial
conditions. In case of phantom DE, the corresponding coupling may help to
resolve the coincidence problem but not the Big Rip (Type I) singularity issue.
We show that modified gravity of special form or inhomogeneous DE fluid may
offer the universal scenario to cure the Type I,II,III or IV future singularity
of coupled (fluid or scalar) DE evolution.


  The recent Pulsar Timing Arrays (PTAs) nano-Hz gravitational wave (GW)
background signal can be naturally induced by the annihilation of domain walls
(DWs) formed at a symmetry-breaking scale $f\simeq 200$~TeV in the clockwork
axion framework. Based on our first successful and precise prediction, we for
the first time suggest that the recent PTA observations strongly support the
novel mechanism of the QCD instanton-induced DW annihilation in the clockwork
axion framework. We also for the first time discover a novel correlation
between dark matter (DM) relic abundance and nano-Hz GW background, which in
turn indicates a natural connection between the axion decay constant and the
symmetry-breaking scale in the clockwork framework. We find that the GW signal
has a peak $h^2\Omega_{\rm GW}\simeq 10^{-6.6}-10^{-6.1}$ at about 50~nHz,
which is definite and testable for future PTA data at frequencies $\gtrsim
25$~nHz and CMB-S4 experiment. We also propose various phenomena that may
appear in PTAs and future GW interferometers.


  In this letter, we extend the recent black hole solution with spherical
symmetry [Phys. Lett. B \textbf{835} (2022), 137546], to a new class of black
hole solutions with different topology, namely, a torus-like black hole and a
black string in the presence of the cosmological constant. We have used the
regularized expressions for the gravitational and the electromagnetic
potentials, then we derived the corrections to the energy density and, finally,
the black hole solutions are obtained which are regular in the limit $r \to 0$.
Interestingly, it is found that the total mass of the black hole is corrected
due to the regularized self-energy of the electrostatic field. In the special
limit, we recover the well-known solutions in the literature.


  Knowledge graphs have been proven extremely useful in powering diverse
applications in semantic search and natural language understanding. In this
paper, we present GraphGen4Code, a toolkit to build code knowledge graphs that
can similarly power various applications such as program search, code
understanding, bug detection, and code automation. GraphGen4Code uses generic
techniques to capture code semantics with the key nodes in the graph
representing classes, functions, and methods. Edges indicate function usage
(e.g., how data flows through function calls, as derived from program analysis
of real code), and documentation about functions (e.g., code documentation,
usage documentation, or forum discussions such as StackOverflow). Our toolkit
uses named graphs in RDF to model graphs per program, or can output graphs as
JSON. We show the scalability of the toolkit by applying it to 1.3 million
Python files drawn from GitHub, 2,300 Python modules, and 47 million forum
posts. This results in an integrated code graph with over 2 billion triples. We
make the toolkit to build such graphs as well as the sample extraction of the 2
billion triples graph publicly available to the community for use.


  White dwarf stars are the most common end point of stellar evolution. Of
special interest are the ultramassive white dwarfs, as they are related to type
Ia Supernovae explosions, merger events, and Fast Radio Bursts. Ultramassive
white dwarfs are expected to harbour oxygen-neon (ONe) cores as a result of
single standard stellar evolution. However, a fraction of them could have
carbon-oxygen (CO) cores. Recent studies, based on the new observations
provided by the {\it Gaia} space mission, indicate that a small fraction of the
ultramassive white dwarfs experience a strong delay in their cooling, which
cannot be attributed only to the occurrence of crystallization, thus requiring
an unknown energy source able to prolong their life for long periods of time.
In this study we find that the energy released by $^{22}$Ne sedimentation in
the deep interior of ultramassive white dwarfs with CO cores and high $^{22}$Ne
content is consistent with the long cooling delay of these stellar remnants. On
the basis of a synthesis study of the white dwarf population, based on Monte
Carlo techniques, we find that the observations revealed by {\it Gaia} can be
explained by the existence of these prolonged youth ultramassive white dwarfs.
Although such a high $^{22}$Ne abundance is not consistent with the standard
evolutionary channels, our results provide sustain to the existence of CO-core
ultramassive white dwarfs and to the occurrence of $^{22}$Ne sedimentation.


  Pattern counting in graphs is a fundamental primitive for many network
analysis tasks, and a number of methods have been developed for scaling
subgraph counting to large graphs. Many real-world networks carry a natural
notion of strength of connection between nodes, which are often modeled by a
weighted graph, but existing scalable graph algorithms for pattern mining are
designed for unweighted graphs. Here, we develop a suite of deterministic and
random sampling algorithms that enable the fast discovery of the 3-cliques
(triangles) with the largest weight in a graph, where weight is measured by a
generalized mean of a triangle's edges. For example, one of our proposed
algorithms can find the top-1000 weighted triangles of a weighted graph with
billions of edges in thirty seconds on a commodity server, which is orders of
magnitude faster than existing "fast" enumeration schemes. Our methods thus
open the door towards scalable pattern mining in weighted graphs.


  Dedicated surveys using different detection pipelines are being carried out
at multiple observatories to find more Fast Radio Bursts (FRBs). Understanding
the efficiency of detection algorithms and the survey completeness function is
important to enable unbiased estimation of the underlying FRB population
properties. One method to achieve end-to-end testing of the system is by
injecting mock FRBs in the live data-stream and searching for them blindly.
Mock FRB injection is particularly effective for machine-learning-based
classifiers, for which analytic characterisation is impractical. We describe a
first-of-its-kind implementation of a real-time mock FRB injection system at
the upgraded Molonglo Observatory Synthesis Telescope (UTMOST) and present our
results for a set of 20,000 mock FRB injections. The injections have yielded
clear insight into the detection efficiencies and have provided a survey
completeness function for pulse width, fluence and DM. Mock FRBs are recovered
with uniform efficiency over the full range of injected DMs, however the
recovery fraction is found to be a strong function of the width and
Signal-to-Noise (SNR). For low widths ($\lesssim 20$ ms) and high SNR
($\gtrsim$ 9) the recovery is highly effective with recovery fractions
exceeding 90%. We find that the presence of radio frequency interference causes
the recovered SNR values to be systematically lower by up to 20% compared to
the injected values. We find that wider FRBs become increasingly hard to
recover for the machine-learning-based classifier employed at UTMOST. We
encourage other observatories to implement live injection set-ups for similar
testing of their surveys.


  Truck Factor (TF) is a metric proposed by the agile community as a tool to
identify concentration of knowledge in software development environments. It
states the minimal number of developers that have to be hit by a truck (or
quit) before a project is incapacitated. In other words, TF helps to measure
how prepared is a project to deal with developer turnover. Despite its clear
relevance, few studies explore this metric. Altogether there is no consensus
about how to calculate it, and no supporting evidence backing estimates for
systems in the wild. To mitigate both issues, we propose a novel (and
automated) approach for estimating TF-values, which we execute against a corpus
of 133 popular project in GitHub. We later survey developers as a means to
assess the reliability of our results. Among others, we find that the majority
of our target systems (65%) have TF <= 2. Surveying developers from 67 target
systems provides confidence towards our estimates; in 84% of the valid answers
we collect, developers agree or partially agree that the TF's authors are the
main authors of their systems; in 53% we receive a positive or partially
positive answer regarding our estimated truck factors.


  We show that the class QMA does not change even if we restrict Arthur's
computing ability to only Clifford gate operations (plus classical XOR gate).
The idea is to use the fact that the preparation of certain single-qubit
states, so called magic states, plus any Clifford gate operations are universal
for quantum computing. If Merlin is honest, he sends the witness plus magic
states to Arthur. If Merlin is malicious, he might send other states to Arthur,
but Arthur can verify the correctness of magic states by himself. We also
generalize the result to QIP[3]: we show that the class QIP[3] does not change
even if the computational power of the verifier is restricted to only Clifford
gate operations (plus classical XOR gate).