  Predicting the 3D structure of a macromolecule, such as a protein or an RNA
molecule, is ranked top among the most difficult and attractive problems in
bioinformatics and computational biology. Its importance comes from the
relationship between the 3D structure and the function of a given protein or
RNA. 3D structures also help to find the ligands of the protein, which are
usually small molecules, a key step in drug design. Unfortunately, there is no
shortcut to accurately obtain the 3D structure of a macromolecule. Many
physical measurements of macromolecular 3D structures cannot scale up, due to
their large labor costs and the requirements for lab conditions.
  In recent years, computational methods have made huge progress due to advance
in computation speed and machine learning methods. These methods only need the
sequence information to predict 3D structures by employing various mathematical
models and machine learning methods. The success of computational methods is
highly dependent on a large database of the proteins and RNA with known
structures.
  However, the performance of computational methods are always expected to be
improved. There are several reasons for this. First, we are facing, and will
continue to face sparseness of data.Secondly, the 3D structure space is too
large for our computational capability.
  The two obstacles can be removed by knowledge-based methods, which combine
knowledge learned from the known structures and biologists' knowledge of the
folding process of protein or RNA. In the dissertation, I will present my
results in building a knowledge-based method by using machine learning methods
to tackle this problem. My methods include the knowledge constraints on
intermediate states, which can highly reduce the solution space of a protein or
RNA, in turn increasing the efficiency of the structure folding method and
improving its accuracy.


  We extend to curved backgrounds all flat-space scalar field models that obey
purely second-order equations, while maintaining their second-order dependence
on both field and metric. This extension simultaneously restores to second
order the, originally higher derivative, stress tensors as well. The process is
transparent and uniform for all dimensions.


  It has been noticed that all the known binary sequences having the asymptotic
merit factor $\ge 6$ are the modifications to the real primitive characters. In
this paper, we give a new modification of the character sequences at length
$N=p_1p_2\dots p_r$, where $p_i$'s are distinct odd primes and $r$ is finite.
Based on these new modifications, for $N=p_1p_2\dots p_r$ with $p_i$'s distinct
odd primes, we can construct a binary sequence of length $2N$ with asymptotic
merit factor $6.0$


  Optical frequency combs can potentially provide an efficient light source for
multi-terabit-per-second optical superchannels. However, as the bandwidth of
these multi-wavelength light sources is increased, it can result in low
per-line power. Optical amplifiers can be used to overcome power limitations,
but the accompanying spontaneous optical noise can degrade performance in
optical systems. To overcome this, we demonstrate wideband noise reduction for
comb lines using a high-Q microring resonator whose resonances align with the
comb lines, providing tight optical filtering of multiple combs lines at the
same time. By distilling an optical frequency comb in this way, we are able to
reduce the required comb line OSNR when these lines are used in a coherent
optical communications system. Through performance tests on a 19.45-GHz-spaced
comb generating 71 lines, using 18 Gbaud, 64-QAM sub-channels at a spectral
efficiency of 10.6 b/s/Hz, we find that noise-corrupted comb lines can reduce
the optical signal-to-noise ratio required for the comb by ~ 9 dB when used as
optical carriers at the transmitter side, and by ~ 12 dB when used as a local
oscillator at the receiver side. This demonstration provides a method to enable
low power optical frequency combs to be able to support high bandwidth and
high-capacity communications.


  Helical configurations of inhomogeneous symmetric rods with non-constant
bending and twisting stiffness are studied within the framework of the
Kirchhoff rod model. From the static Kirchhoff equations, we obtain a set of
differential equations for the curvature and torsion of the centerline of the
rod and the Lancret's theorem is used to find helical solutions. We obtain a
free standing helical solution for an inhomogeneous rod whose curvature and
torsion depend on the form of variation of the bending coefficient along the
rod. These results are obtained for inhomogeneous rods without intrinsic
curvature, and for a particular case of intrinsic curvature.


  We report on the observation of Bragg scattering of an ultracold Fermi gas of
6Li atoms at a dynamic optical potential. The momentum states produced in this
way oscillate in the trap for time scales on the order of seconds, nearly
unperturbed by collisions, which are absent for ultracold fermions due to the
Pauli principle. In contrast, interactions in a mixture with 87Rb atoms lead to
rapid damping. The coherence of these states is demonstrated by Ramsey-type
matter wave interferometry. The signal is improved using an echo pulse
sequence, allowing us to observe coherence times longer than 100 mus. Finally
we use Bragg spectroscopy to measure the in-situ momentum distribution of the
6Li cloud. Signatures for the degeneracy of the Fermi gas can be observed
directly from the momentum distribution of the atoms inside the trap.


  Videos often have to be transmitted and stored at low bitrates due to poor
network connectivity during adaptive bitrate streaming. Designing optimal
bitrate ladders that would select the perceptually-optimized resolution,
frame-rate, and compression level for low-bitrate videos for adaptive streaming
across the internet is therefore a task of great interest. Towards that end, we
conducted the first large-scale study of medium and low-bitrate videos from
live sports for two codecs (Elemental AVC and HEVC) and created the Amazon
Prime Video Low-Bitrate Sports (APV LBS) dataset. The study involved 94
participants and 742 videos, with more than 23,000 human opinion scores
collected in total. We analyzed the data obtained and we also conducted an
extensive evaluation of objective Video Quality Assessment (VQA) algorithms and
benchmarked their performance, and make recommendations on bitrate ladder
design. We're making the metadata and VQA features available at
https://github.com/JoshuaEbenezer/lbmfr-public.


  We revisit the previously unsolved problems of ensuring Lorentz invariance
and non-perturbative unitarity in Lee-Wick theories. We base our discussion on
an ultraviolet completion of QED by Lee-Wick ghost fields, which is argued to
be asymptotically safe. We argue that as long as the state space is based upon
a suitable choice of distributions of a type invented by Gel'fand and Shilov,
the Lee-Wick ghosts can be eliminated while preserving Lorentz invariance to
produce a unitary theory. The method for eliminating ghosts is in principle
non-perturbatively well-defined, in contrast with some previous proposals. We
also point out a second, independent mechanism for producing a unitary theory,
based on a covariant constraint on the maximum four-momentum, which would imply
an amusing connection, based on naturalness, between the coupling constant and
the hierarchy of scales in the theory. We further emphasize that the resulting
theory is causal, and point out some analogies between between the behaviour of
Lee-Wick ghost degrees of freedom and black holes.


  The principal aim of this project is to determine the structural parameters
of the rapidly pulsating subdwarf B star PG 0911+456 from asteroseismology. Our
work forms part of an ongoing programme to constrain the internal
characteristics of hot B subdwarfs with the long-term goal of differentiating
between the various formation scenarios proposed for these objects. First
comparisons of asteroseismic values with evolutionary theory look promising,
however it is clear that more targets are needed for meaningful statistics to
be derived. The observational pulsation periods of PG 0911+456 were extracted
from rapid time-series photometry using standard Fourier analysis techniques.
Supplemented by spectroscopic estimates of the star's mean atmospheric
parameters, they were used as a basis for the "forward modelling" approach in
asteroseismology. The latter culminates in the identification of one or more
"optimal" models that can accurately reproduce the observed period spectrum.
This naturally leads to an identification of the oscillations detected in terms
of degree l and radial order k, and infers the structural parameters of the
target. From the photometry it was possible to extract 7 independent pulsation
periods in the 150-200 s range with amplitudes between 0.05 and 0.8 % of the
star's mean brightness. An asteroseismic search of parameter space identified
several models that matched the observed properties of PG 0911+456 well, one of
which was isolated as the "optimal" model on the basis of spectroscopic and
mode identification considerations. All the observed pulsations are identified
with low-order acoustic modes with degree indices l=0,1,2 and 4, and match the
computed periods with a dispersion of only ~0.26 %.


  Many real-world datasets live on high-dimensional Stiefel and Grassmannian
manifolds, $V_k(\mathbb{R}^N)$ and $Gr(k, \mathbb{R}^N)$ respectively, and
benefit from projection onto lower-dimensional Stiefel (respectively,
Grassmannian) manifolds. In this work, we propose an algorithm called Principal
Stiefel Coordinates (PSC) to reduce data dimensionality from $
V_k(\mathbb{R}^N)$ to $V_k(\mathbb{R}^n)$ in an $O(k)$-equivariant manner ($k
\leq n \ll N$). We begin by observing that each element $\alpha \in
V_n(\mathbb{R}^N)$ defines an isometric embedding of $V_k(\mathbb{R}^n)$ into
$V_k(\mathbb{R}^N)$. Next, we optimize for such an embedding map that minimizes
data fit error by warm-starting with the output of principal component analysis
(PCA) and applying gradient descent. Then, we define a continuous and
$O(k)$-equivariant map $\pi_\alpha$ that acts as a ``closest point operator''
to project the data onto the image of $V_k(\mathbb{R}^n)$ in
$V_k(\mathbb{R}^N)$ under the embedding determined by $\alpha$, while
minimizing distortion. Because this dimensionality reduction is
$O(k)$-equivariant, these results extend to Grassmannian manifolds as well.
Lastly, we show that the PCA output globally minimizes projection error in a
noiseless setting, but that our algorithm achieves a meaningfully different and
improved outcome when the data does not lie exactly on the image of a linearly
embedded lower-dimensional Stiefel manifold as above. Multiple numerical
experiments using synthetic and real-world data are performed.


  We consider a class of stochastic processing networks. Assume that the
networks satisfy a complete resource pooling condition. We prove that each
maximum pressure policy asymptotically minimizes the workload process in a
stochastic processing network in heavy traffic. We also show that, under each
quadratic holding cost structure, there is a maximum pressure policy that
asymptotically minimizes the holding cost. A key to the optimality proofs is to
prove a state space collapse result and a heavy traffic limit theorem for the
network processes under a maximum pressure policy. We extend a framework of
Bramson [Queueing Systems Theory Appl. 30 (1998) 89--148] and Williams
[Queueing Systems Theory Appl. 30 (1998b) 5--25] from the multiclass queueing
network setting to the stochastic processing network setting to prove the state
space collapse result and the heavy traffic limit theorem. The extension can be
adapted to other studies of stochastic processing networks.


  We study the fragmentation of the b quark in top decay in NLO QCD, within the
framework of perturbative fragmentation, which allows one to resum large
logarithms $\sim\log (m_t^2/m_b^2)$. We show the b-energy distribution, which
we compare with the exact ${\cal O} (\alpha_S)$ result for a massive b quark.
We use data from $e^+e^-$ machines in order to describe the b-quark
hadronization and make predictions for the energy spectrum of b-flavoured
hadrons in top decay. We also investigate the effect of NLL soft-gluon
resummation in the initial condition of the perturbative fragmentation function
on parton- and hadron-level energy distributions.


  Given a holomorphic selfmap f of the complex projective plane of algebraic
degree at least 2, we give sufficient conditions on a positive closed (1,1)
current S of unit mass under which the normalized pullbacks of S under iterates
of f converge to the Green current T.
  In particular, we completely characterize the plane algebraic curves whose
normalized pullbacks converge weakly to T.


  Core helium burning is the dominant source of energy of extreme horizontal
branch stars, as the hydrogen envelope is too small to contribute to the
nuclear energy output. The evolution of each mass in the HR diagram occurs
along vertical tracks that, when the core helium is consumed, evolve to higher
Teff and then to the white dwarf stage. The larger is the mass, the smaller is
the Teff of the models, so that the zero age horizontal branch (ZAHB) is
"horizontal". In this paper we show that, if the helium mass fraction (Y) of
the envelope is larger than Y~0.5, the shape of the tracks changes completely:
the hydrogen burning becomes efficient again also for very small envelope
masses, thanks to the higher molecular weight and to the higher temperatures of
the hydrogen shell. The larger is Y, the smaller is the envelope mass that
provides strong H-shell burning. These tracks have a curled shape, are located
at a Teff following the approximate relation Teff=8090+ 32900xY, and become
more luminous for larger envelope masses. Consequently, the ZAHB of the very
high helium models is "vertical" in the HR diagram. Synthetic models based on
these tracks nicely reproduce the location and shape of the "blue hook" in the
globular cluster wCen, best fit by a very high Teff (bluer) sequence with
Y=0.80 and a cooler (redder) one with Y=0.65. Although these precise values of
Y may depend on the color-Teff conversions, we know that the helium content of
the progenitors of the blue hook stars can not be larger than Y~0.38-0.40, if
they are descendants of the cluster blue main sequence. Consequently, this
interpretation implies that all these objects must in fact be progeny of the
blue main sequence, but they have all suffered further deep mixing, that has
largely and uniformly increased their surface helium abundance, during the red
giant branch evolution. A late helium flash can not be the cause of this deep
mixing, as the models we propose have hydrogen rich envelopes much more massive
than those required for a late flash. We discuss different models of deep
mixing proposed in the literature, and conclude that our interpretation of the
blue hook can not be ruled out, but requires a much deeper investigation before
it can be accepted.


  Consider a selfadjoint unbounded operator D on a Hilbert space H and a one
parameter norm continuous family of selfadjoint bounded operators {A(t)}
parametrized by the real line. Then under certain conditions \cite{RS95} that
include the assumption that the operators {D(t)= D+A(t)} all have discrete
spectrum then the spectral flow along the path { D(t)} can be shown to be equal
to the index of d/dt+D(t) when the latter is an unbounded Fredholm operator on
L^2(R, H). In \cite{GLMST11} an investigation of the index=spectral flow
question when the operators in the path may have some essential spectrum was
started but under restrictive assumptions that rule out differential operators
in general. In \cite{CGPST14a} the question of what happens when the Fredholm
condition is dropped altogether was investigated. In these circumstances the
Fredholm index is replaced by the Witten index.
  In this paper we take the investigation begun in \cite{CGPST14a} much
further. We show how to generalise a formula known from the setting of the L^2
index theorem to the non-Fredholm setting. Our main theorem gives a trace
formula relating the homological index of \cite{CaKa:TIH} to an integral
formula that is known, for a path of selfadjoint Fredholms with compact
resolvent and with unitarily equivalent endpoints, to compute spectral flow.
Our formula however, applies to paths of selfadjoint non-Fredholm operators. We
interpret this as indicating there is a generalisation of spectral flow to the
non-Fredholm setting.


  In a context of non-uniformly expanding maps, possibly with the presence of a
critical set, we prove the existence of finitely many ergodic equilibrium
states for hyperbolic potentials. Moreover, the equilibrium states are
expanding measures. This generalizes a result due to Ramos and Viana, where
analytical methods are used for maps with no critical sets. The strategy here
consists in using a finite number of inducing schemes with a Markov structure
in infinitely many symbols to code the dynamics, to obtain an equilibrium state
for the associated symbolic dynamics and then projecting it to obtain an
equilibrium state for the original map. We apply our results to the important
class of multidimensional Viana maps.


  We propose an efficient procedure to obtain Green's functions by combining
the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with
the nonequilibrium Green's function (NEGF) method based on a real-space
finite-difference (RSFD) approach. The bottleneck of the computation in the
NEGF scheme is matrix inversion of the Hamiltonian including the self-energy
terms of electrodes to obtain perturbed Green's function in the transition
region. This procedure first computes unperturbed Green's functions and
calculates perturbed Green's functions from the unperturbed ones using a
mathematically strict relation. Since the matrices to be inverted to obtain the
unperturbed Green's functions are sparse, complex-symmetric and shifted for a
given set of sampling energy points, we can use the shifted COCG method, in
which once the Green's function for a reference energy point has been
calculated, the Green's functions for the other energy points can be obtained
with a moderate computational cost. We calculate the transport properties of a
C$_{60}$@(10,10) carbon nanotube (CNT) peapod suspended by (10,10)CNTs as an
example of a large-scale transport calculation. The proposed scheme opens the
possibility of performing large-scale RSFD-NEGF transport calculations using
massively parallel computers without the loss of accuracy originating from the
incompleteness of the localized basis set.


  We propose here a new mechanism of droplet coarsening in phase-separating
fluid mixtures. In contrast to the conventional understanding that there are no
interactions between droplets in the late stage of spinodal decomposition, we
demonstrate the existence of interactions between droplets that is caused by
the coupling between diffuse concentration change around droplets. We show the
possibility that this mechanism plays an important role in droplet phase
separation together with Brownian-coagulation mechanism. We also discuss the
coupling between hydrodynamic and diffusion modes, namely, "collision-induced
collision" phenomena.


  We consider the problem of constructing quantum operations or channels, if
they exist, that transform a given set of quantum states $\{\rho_1, \dots,
\rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other
words, we must find a {\em completely positive linear map}, if it exists, that
maps a given set of density matrices to another given set of density matrices.
This problem, in turn, is an instance of a positive semi-definite feasibility
problem, but with highly structured constraints. The nature of the constraints
makes projection based algorithms very appealing when the number of variables
is huge and standard interior point-methods for semi-definite programming are
not applicable. We provide emperical evidence to this effect. We moreover
present heuristics for finding both high rank and low rank solutions. Our
experiments are based on the \emph{method of alternating projections} and the
\emph{Douglas-Rachford} reflection method.


  Gravitational wave memory effects arise from non-oscillatory components of
gravitational wave signals, and they are predictions of general relativity in
the nonlinear regime that have close connections to the asymptotic properties
of isolated gravitating systems. There are many types of memory effects that
have been studied in the literature. In this paper we focus on the
"displacement" and "spin" memories, which are expected to be the largest of
these effects from sources such as the binary black hole mergers which have
already been detected by LIGO and Virgo. The displacement memory is a change in
the relative separation of two initially comoving observers due to a burst of
gravitational waves, whereas the spin memory is a portion of the change in
relative separation of observers with initial relative velocity. As both of
these effects are small, LIGO, Virgo, and KAGRA can only detect memory effects
from individual events that are much louder (and thus rarer) than those that
have been detected so far. By combining data from multiple events, however,
these effects could be detected in a population of binary mergers. In this
paper, we present new forecasts for how long current and future detectors will
need to operate in order to measure these effects from populations of binary
black hole systems that are consistent with the populations inferred from the
detections from LIGO and Virgo's first three observing runs. We find that a
second-generation detector network of LIGO, Virgo, and KAGRA operating at the
O4 ("design") sensitivity for 1.5 years and then operating at the O5 ("plus")
sensitivity for an additional year can detect the displacement memory. For
Cosmic Explorer, we find that displacement memory could be detected for
individual loud events, and that the spin memory could be detected in a
population within 2 years of observation time.


  This paper is concerned with non-parametric estimation of the entropy in
ranked set sampling. Theoretical properties of the proposed estimator are
studied. The proposed estimator is compared with the rival estimator in simple
random sampling. The applications of the proposed estimator to the mutual
information estimation as well as estimation of the Kullback-Leibler divergence
are provided. Several Monte-Carlo simulation studies are conducted to examine
the performance of the estimator. The results are applied to the long-leaf pine
(pinus palustris) trees and the body fat percentage data sets to illustrate
applicability of theoretical results.


  Dynamic functional connectivity is an effective measure for the brain's
responses to continuous stimuli. We propose an inferential method to detect the
dynamic changes of brain networks based on time-varying graphical models.
Whereas most existing methods focus on testing the existence of change points,
the dynamics in the brain network offer more signals in many neuroscience
studies. We propose a novel method to conduct hypothesis testing on changes in
dynamic brain networks. We introduce a bootstrap statistic to approximate the
supreme of the high-dimensional empirical processes over dynamically changing
edges. Our simulations show that this framework can capture the change points
with changed connectivity. Finally, we apply our method to a brain imaging
dataset under a natural audio-video stimulus and illustrate that we are able to
detect temporal changes in brain networks. The functions of the identified
regions are consistent with specific emotional annotations, which are closely
associated with changes inferred by our method.


  In this paper we study the zero energy solutions of the Dirac equation in the
background of a $Z_2$ vortex of a non-Abelian gauge model with three charged
scalar fields. We determine the number of the fermionic zero modes giving their
explicit form for two specific Ansatze.


  In this paper we will develop a very general approach which shows that
critical relations of holomorphic maps on the complex plane unfold
transversally in a positively oriented way. We will mainly illustrate this
approach to obtain transversality for a wide class of one-parameter families of
interval maps, for example maps with flat critical points, piecewise linear
maps, maps with discontinuities but also for families of maps with complex
analytic extensions such as certain polynomial-like maps.


  The large $n$ behaviour of the hypergeometric polynomial
  $$\FFF{-n}{\sfrac12}{\sfrac12}{\sfrac12-n}{\sfrac12-n}{-1}$$ is considered by
using integral representations of this polynomial. This ${}_3F_2$ polynomial is
associated with the Catalan-Larcombe-French sequence. Several other
representations are mentioned, with references to the literature, and another
asymptotic method is described by using a generating function of the sequence.
The results are similar to those obtained by Clark (2004) who used a binomial
sum for obtaining an asymptotic expansion.


  The purpose of this work is to show that there exists an additional
invariance of the $\beta$-function equations of string theory on
$d+1$-dimensional targets with $d$ toroidal isometries. It corresponds to a
shift of the dilaton field and a scaling of the lapse function, and is
reminiscent of string field redefinitions. While it preserves the form of the
$\beta$-function equations, it changes the effective action and the solutions.
Thus it can be used as a solution generating technique. It is particularly
interesting to note that there are field redefinitions which map solutions with
non-zero string cosmological constant to those with zero cosmological constant.
Several simple examples involving two- and three-dimensional black holes and
black strings are provided to illustrate the role of such field redefinitions.


  This paper studies the tension between throughput and decoding delay
performance of two widely-used network coding schemes: random linear network
coding (RLNC) and instantly decodable network coding (IDNC). A single-hop
broadcasting system model is considered that aims to deliver a block of packets
to all receivers in the presence of packet erasures. For a fair and
analytically tractable comparison between the two coding schemes, the
transmission comprises two phases: a systematic transmission phase and a
network coded transmission phase which is further divided into rounds. After
the systematic transmission phase and given the same packet reception state,
three quantitative metrics are proposed and derived in each scheme: 1) the
absolute minimum number of transmissions in the first coded transmission round
(assuming no erasures), 2) probability distribution of extra coded
transmissions in a subsequent round (due to erasures), and 3) average packet
decoding delay. This comparative study enables application-aware adaptive
selection between IDNC and RLNC after systematic transmission phase.
  One contribution of this paper is to provide a deep and systematic
understanding of the IDNC scheme, to propose the notion of packet diversity and
an optimal IDNC encoding scheme for minimizing metric 1. This is generally
NP-hard, but nevertheless required for characterizing and deriving all the
three metrics. Analytical and numerical results show that there is no clear
winner between RLNC and IDNC if one is concerned with both throughput and
decoding delay performance. IDNC is more preferable than RLNC when the number
of receivers is smaller than packet block size, and the case reverses when the
number of receivers is much greater than the packet block size. In the middle
regime, the choice can depend on the application and a specific instance of the
problem.


  The pursuit of the progenitors of short duration-hard spectrum gamma-ray
bursts (SHBs) draws strongly upon similar quests for the origin of supernovae
(SNe) and long duration-soft spectrum GRBs(LSBs). Indeed the notion that, in
the absence of smoking guns, the progenitors of cosmic explosions betray their
identities both on the global and local scale, motivates the study of SHB
redshifts, host galaxies, and locations with respect to hosts. To this end, we
suggest both a historical and emergent physical analogy of GRBs with SNe:
long-soft GRBs are to core-collapsed supernovae as short-hard GRBs are to Type
Ia supernovae ("LSB:CC::SHB:Ia''). Still, the SHB progenitor pursuit is just
beginning and we caution that while there are some substantive differences
between observations of LSBs and SHBs on large-scales, particularly in host
demographics, neither the offset nor the redshift distributions of SHBs are
statistically inconsistent with those of LSBs.


  We show that for a sofic shift Lambda, Matsumoto's C*-algebra O_Lambda is
isomorphic to the Cuntz-Krieger algebra of the left Krieger cover graph of
Lambda.


  At high area fractions, monolayers of colloidal dimer particles form a
degenerate crystal (DC) structure in which the particle lobes occupy triangular
lattice sites while the particles are oriented randomly along any of the three
lattice directions. We report that dislocation glide in DCs is blocked by
certain particle orientations. The mean number of lattice constants between
such obstacles is 4.6 +/- 0.2 in experimentally observed DC grains and 6.18 +/-
0.01 in simulated monocrystalline DCs. Dislocation propagation beyond these
obstacles is observed to proceed through dislocation reactions. We estimate
that the energetic cost of dislocation pair separation via such reactions in an
otherwise defect free DC grows linearly with final separation, hinting that the
material properties of DCs may be dramatically different from those of 2-D
crystals of spheres.


  We prove that for "most" closed 3-dimensional manifolds $M$, the existence of
a closed non singular one-form in a given cohomology class $u\in H^1 (M,\bf R)$
is equivalent to the fact that every twisted Alexander polynomial
$\Delta^H(M,u) \in {\bf Z}[G/\ker u]$ associated to a normal subgroup with
finite index $H < \pi_1(M)$ has a unitary $u$-minimal term.


  This paper is concerned with diffuse-interface approximations of the Willmore
flow. We first present numerical results of standard diffuse-interface models
for colliding one dimensional interfaces. In such a scenario evolutions towards
interfaces with corners can occur that do not necessarily describe the adequate
sharp-interface dynamics.
  We therefore propose and investigate alternative diffuse-interface
approximations that lead to a different and more regular behavior if interfaces
collide. These dynamics are derived from approximate energies that converge to
the $L^1$-lower-semicontinuous envelope of the Willmore energy, which is in
general not true for the more standard Willmore approximation.


  Spectroscopic features revealing the coherent interaction of a degenerate
two-level atomic system with two optical fields are examined. A model for the
numerical calculation of the response of a degenerate two-level system to the
action of an arbitrarily intense resonant pump field and a weak probe in the
presence of a magnetic field is presented. The model is valid for arbitrary
values of the total angular momentum of the lower and upper levels and for any
choice of the polarizations of the optical waves. Closed and open degenerate
two-level systems are considered. Predictions for probe absorption and
dispersion, field generation by four-wave-mixing, population modulation and
Zeeman optical pumping are derived. On all these observables, sub-natural-width
coherence resonances are predicted and their spectroscopic features are
discussed. Experimental spectra for probe absorption and excited state
population modulation in the D2 line of Rb vapor are presented in good
agreement with the calculations


  A threefold degenerate electronic state is Jahn-Teller unstable with respect
to symmetry lowering distortions, which transform as the five quadrupolar
modes. The solution of the corresponding vibronic Hamiltonian is constructed
using the analytical method introduced by Bargmann, as an alternative to
existing group-theoretical methods based on coefficients of fractional
parentage. It involves the construction of an Ansatz which incorporates SO(5)
to SO(3) symmetry breaking. The resulting Jahn-Teller equations are derived,
and solved in terms of radial polynomials and Gegenbauer functions.


  Composed image retrieval is a type of image retrieval task where the user
provides a reference image as a starting point and specifies a text on how to
shift from the starting point to the desired target image. However, most
existing methods focus on the composition learning of text and reference images
and oversimplify the text as a description, neglecting the inherent structure
and the user's shifting intention of the texts. As a result, these methods
typically take shortcuts that disregard the visual cue of the reference images.
To address this issue, we reconsider the text as instructions and propose a
Semantic Shift network (SSN) that explicitly decomposes the semantic shifts
into two steps: from the reference image to the visual prototype and from the
visual prototype to the target image. Specifically, SSN explicitly decomposes
the instructions into two components: degradation and upgradation, where the
degradation is used to picture the visual prototype from the reference image,
while the upgradation is used to enrich the visual prototype into the final
representations to retrieve the desired target image. The experimental results
show that the proposed SSN demonstrates a significant improvement of 5.42% and
1.37% on the CIRR and FashionIQ datasets, respectively, and establishes a new
state-of-the-art performance. Codes will be publicly available.


  We propose a novel mechanism for photogeneration of multiexcitons by single
photons (carrier multiplication) in semiconductor nanocrystals. In this
mechanism, the Coulomb interaction between two valence-band electrons involving
their transfer to the conduction band creates a virtual biexciton from vacuum
that is then converted into a real biexciton by photon absorption on an
intraband optical transition. This mechanism is inactive in bulk semiconductors
as momentum conservation suppresses intraband absorption. However, it becomes
highly efficient in zero-dimensional nanocrystals and can provide a significant
contribution to carrier multiplication in these materials.


  We employ \textit{ab initio} methods of quantum chemistry to investigate
spin-1/2 fermions interacting via a two-body contact potential in a
one-dimensional harmonic trap. The convergence of the total energy with the
size of the one-particle basis set is analytically investigated for the
two-body problem and the same form of the convergence formula is numerically
confirmed to be valid for the many-body case. Benchmark calculations for two to
six fermions with the full configuration interaction method equivalent to the
exact diagonalization approach, and the coupled cluster method including
single, double, triple, and quadruple excitations are presented. The
convergence of the correlation energy with the level of excitations included in
the coupled cluster model is analyzed. The range of the interaction strength
for which single-reference coupled cluster methods work is examined. Next, the
coupled cluster method restricted to single, double, and noniterative triple
excitations, CCSD(T), is employed to study a two-component Fermi gas composed
of 6 to 80 atoms in a one-dimensional harmonic trap. The density profiles of
trapped atomic clouds are also reported. Finally, a comparison with
experimental results for few-fermion systems is presented. Upcoming possible
applications and extensions of the presented approach are discussed.


  We have observed resonant energy transfer between cold Rydberg atoms in
spatially separated cylinders. Resonant dipole-dipole coupling excites the 49s
atoms in one cylinder to the 49p state while the 41d atoms in the second
cylinder are transferred down to the 42p state. We have measured the production
of the 49p state as a function of separation of the cylinders (0 - 80 um) and
the interaction time (0 - 25 us). In addition we measured the width of the
electric field resonances. A full many-body quantum calculation reproduces the
main features of the experiments.


  The course of non-thermal electron ejection in relativistic unmagnetized
electron-ion shocks is investigated by performing self-consistent
particle-in-cell simulations. The shocks are excited through the injection of
relativistic jet into ambient plasma, leading to two distinct shocks (named as
the trailing shock and leading shock) and a contact discontinuity. The
Weibel-like instabilities heat the electrons up to approximately half of ion
kinetic energy. The double layers formed in the trailing and leading edges then
accelerated the electrons by the ion kinetic energy. The electron distribution
function in the leading edge shows a clear non-thermal power-law tail which
contains $\sim1\%$ of electrons and $\sim8\%$ of electron energy. Its power-law
index is -2.6. The acceleration efficiency is $\sim23\%$ by number and
$\sim50\%$ by energy and the power-law index is -1.8 for electron distribution
function in the trailing edge. The effect of the dimensionality is examined by
comparing results of 3D simulation with 2D ones. It exhibits that the electron
acceleration is more efficient in 2D.


  In this study, we propose a novel scene descriptor for visual place
recognition. Unlike popular bag-of-words scene descriptors which rely on a
library of vector quantized visual features, our proposed descriptor is based
on a library of raw image data, such as publicly available photo collections
from Google StreetView and Flickr. The library images need not to be associated
with spatial information regarding the viewpoint and orientation of the scene.
As a result, these images are cheaper than the database images; in addition,
they are readily available. Our proposed descriptor directly mines the image
library to discover landmarks (i.e., image patches) that suitably match an
input query/database image. The discovered landmarks are then compactly
described by their pose and shape (i.e., library image ID, bounding boxes) and
used as a compact discriminative scene descriptor for the input image. We
evaluate the effectiveness of our scene description framework by comparing its
performance to that of previous approaches.


  A survey of recent results concerning cardinal invariants of measure and
category.
  Submitted as a chapter of the upcoming Handbook of Set Theory.


  This paper describes how to determine the parameter values of the chaotic
Lorenz system from one of its variables waveform. The geometrical properties of
the system are used firstly to reduce the parameter search space. Then, a
synchronization-based approach, with the help of the same geometrical
properties as coincidence criteria, is implemented to determine the parameter
values with the wanted accuracy. The method is not affected by a moderate
amount of noise in the waveform. As way of example of its effectiveness, the
method is applied to figure out directly from the ciphertext the secret keys of
two-channel chaotic cryptosystems using the variable $z$ as a synchronization
signal, based on the ultimate state projective chaos synchronization.


  Galaxies migrate from the blue cloud to the red sequence when their star
formation is quenched. Here, we report on galaxies quenched by environmental
effects and not by mergers or strong AGN as often invoked: They form stars at a
reduced rate which is optically even less conspicuous, and manifest a
transition population of blue spirals evolving into S0 galaxies. These
'optically passive' or 'red spirals' are found in large numbers in the STAGES
project (and by Galaxy Zoo) in the infall region of clusters and groups.


  We find exact states of graphene quasiparticles under a time-dependent
deformation (sound wave), whose propagation velocity is smaller than the Fermi
velocity. To solve the corresponding effective Dirac equation, we adapt the
Volkov-like solutions for relativistic fermions in a medium under a plane
electromagnetic wave. The corresponding electron-deformation quasiparticle
spectrum is determined by the solutions of a Mathieu equation resulting in band
tongues warped in the surface of the Dirac cones. This leads to a collimation
effect of electron conduction due to strain waves.


  Following the general theory of categorified quantum groups developed by the
author previously (arxiv:2304.07398), we construct the 2-Drinfel'd double
associated to a finite group $N=G_0$. For $N=\mathbb{Z}_2$, we explicitly
compute the braided 2-categories of 2-representations of certain version of
this 2-Drinfel'd double, and prove that they characterize precisely the 4d
toric code and its spin-$\mathbb{Z}_2$ variant. This result relates the two
descriptions (categorical vs. field theoretical) of 4d gapped topological
phases in existing literature and, perhaps more strikingly, displays the first
ever instances of higher Tannakian duality for braided 2-categories. In
particular, we show that particular twists of the underlying 2-Drinfel'd double
is responsible for much of the higher-structural properties that arise in 4d
topological orders.


  We describe the development of artificial neural networks (ANN) for the
prediction of the properties of ceramic materials. The ceramics studied here
include polycrystalline, inorganic, non-metallic materials and are investigated
on the basis of their dielectric and ionic properties. Dielectric materials are
of interest in telecommunication applications where they are used in tuning and
filtering equipment. Ionic and mixed conductors are the subjects of a concerted
effort in the search for new materials that can be incorporated into efficient,
clean electrochemical devices of interest in energy production and greenhouse
gas reduction applications. Multi-layer perceptron ANNs are trained using the
back-propagation algorithm and utilise data obtained from the literature to
learn composition-property relationships between the inputs and outputs of the
system. The trained networks use compositional information to predict the
relative permittivity and oxygen diffusion properties of ceramic materials. The
results show that ANNs are able to produce accurate predictions of the
properties of these ceramic materials which can be used to develop materials
suitable for use in telecommunication and energy production applications.


  In this paper we consider a star-shaped hypersurface flow by mean curvature.
Without any assumption on the convexity, we give a new proof of gradient
estimate for a short time. As an application, we also give a lower bound for
the blowing up time.


  We propose a simple scenario in which dark matter (DM) emerges as a stable
neutral hadronic thermal relics, its stability following from an exact
$\operatorname{U}(1)_D$ symmetry. Neutrinos pick up radiatively induced
Majorana masses from the exchange of colored DM constituents. There is a common
origin for both dark matter and neutrino mass, with a lower bound for
neutrinoless double beta decay. Direct DM searches at nuclear recoil
experiments will test the proposal, which may also lead to other
phenomenological signals at future hadron collider and lepton flavour violation
experiments.


  Let $K$ be a field of characteristic different from $2$, $\bar{K}$ its
algebraic closure. Let $n \ge 3$ be an odd integer. Let $f(x)$ and $h(x)$ be
degree $n$ polynomials with coefficients in $K$ and without repeated roots. Let
us consider genus $(n-1)/2$ hyperelliptic curves $C_f: y^2=f(x)$ and $C_h:
y^2=h(x)$, and their jacobians $J(C_f)$ and $J(C_h)$, which are
$(n-1)/2$-dimensional abelian varieties defined over $K$.
  Suppose that one of the polynomials is irreducible and the other splits
completely over $K$. We prove that if $J(C_f)$ and $J(C_h)$ are isogenous over
$\bar{K}$ then there is an (odd) prime $\ell$ dividing $n$ such that the
endomorphism algebras of both $J(C_f)$ and $J(C_h)$ contain a subfield that is
isomorphic to the field of $\ell$th roots of $1$.


  We investigate the effect of the Plume/Interplume Lane (PIPL) structure of
the solar Polar Coronal Hole (PCH) on the propagation characteristics of
ion-cyclotron waves (ICW). The gradients of physical parameters determined by
SOHO and TRACE satellites both parallel and perpendicular to the magnetic field
are considered with the aim of determining how the efficiency of the ICR
process varies along the PIPL structure of PCH. We construct a model based on
the kinetic theory by using quasi-linear approximation. We solve the Vlasov
equation for O VI ions and obtain the dispersion relation of ICW. The resonance
process in the interplume lanes is much more effective than in the plumes,
agreeing with the observations which show the source of fast solar wind is
interplume lanes. The solution of the Vlasov equation in PIPL structure of PCH,
the physical parameters of which display gradients along and perpendicular
direction to the external magnetic field, is thus obtained in a more general
form than the previous investigations.


  Using a recently developed method for calculating series expansions of the
excitation spectra of quantum lattice models, we obtain the spin-wave spectra
for square lattice, $S=1/2$ Heisenberg-Ising antiferromagnets. The calculated
spin-wave spectrum for the Heisenberg model is close to but noticeably
different from a uniformly renormalized classical (large-$S$) spectrum with the
renormalization for the spin-wave velocity of approximately $1.18$. The
relative weights of the single-magnon and multi-magnon contributions to neutron
scattering spectra are obtained for wavevectors throughout the Brillouin zone.


  We present an accurate determination of the refractive index of hydrogen,
helium, H2O and neon up to 35 GPa at ambient temperature. The experimental
method is based on the combination of two interferometric signals of the
Fabry-Perot cavity containing the sample in the diamond anvil cell. The data
are put in perspective through the variation of the molecular polarisability
with density. Significant electronic changes are observed. Interesting
possibilities of the method are also illustrated: the high precision to finely
probe phase transition; the simultaneous measurement of the volume to obtain
the equation of state of transparent media with around 1 % accuracy.


  Let $f:T^2\to\mathbb{R}$ be a Morse function on a 2-torus, $\mathcal{S}(f)$
and $\mathcal{O}(f)$ be its stabilizer and orbit with respect to the right
action of the group $\mathcal{D}(T^2)$ of diffeomorphisms of $T^2$,
$\mathcal{D}_{\mathrm{id}}(T^2)$ be the identity path component of
$\mathcal{D}(T^2)$, and $\mathcal{S}'(f) = \mathcal{S}(f) \cap
\mathcal{D}_{\mathrm{id}}(T^2)$. We give sufficient conditions under which $$
\pi_1\mathcal{O}_f(f) \ \cong \ \pi_1\mathcal{D}(T^2) \times \pi_0
\mathcal{S}'(f) \ \equiv \ \mathbb{Z}^2 \times \pi_0 \mathcal{S}'(f).$$ In fact
this result holds for a larger class of smooth functions $f:T^2\to\mathbb{R}$
having the following property: for every critical point $z$ of $f$ the germ of
$f$ at $z$ is smothly equivalent to a homogeneous polynomial $\mathbb{R}^2\to
\mathbb{R}$ without multiple factors.


  Low values of the fusion cross sections and very short half-lives of nuclei
with Z$>$120 put obstacles in synthesis of new elements. Different nuclear
reactions (fusion of stable and radioactive nuclei, multi-nucleon transfers and
neutron capture), which could be used for the production of new isotopes of
superheavy (SH) elements, are discussed in the paper. The gap of unknown SH
nuclei, located between the isotopes which were produced earlier in the cold
and hot fusion reactions, can be filled in fusion reactions of $^{48}$Ca with
available lighter isotopes of Pu, Am, and Cm. Cross sections for the production
of these nuclei are predicted to be rather large, and the corresponding
experiments can be easily performed at existing facilities. For the first time,
a narrow pathway is found to the middle of the island of stability owing to
possible $\beta^+$-decay of SH isotopes which can be formed in ordinary fusion
reactions of stable nuclei. Multi-nucleon transfer processes at near barrier
collisions of heavy (and very heavy, U-like) ions are shown to be quite
realistic reaction mechanism allowing us to produce new neutron enriched heavy
nuclei located in the unexplored upper part of the nuclear map. Neutron capture
reactions can be also used for the production of the long-living neutron rich
SH nuclei. Strong neutron fluxes might be provided by pulsed nuclear reactors
and by nuclear explosions in laboratory conditions and by supernova explosions
in nature. All these possibilities are discussed in the paper.


  In a type I Dirac or Weyl semimetal, the low energy states are squeezed to a
single point in momentum space when the chemical potential Ef is tuned
precisely to the Dirac/Weyl point. Recently, a type II Weyl semimetal was
predicted to exist, where the Weyl states connect hole and electron bands,
separated by an indirect gap. This leads to unusual energy states, where hole
and electron pockets touch at the Weyl point. Here we present the discovery of
a type II topological Weyl semimetal (TWS) state in pure MoTe2, where two sets
of WPs (W2+-, W3+-) exist at the touching points of electron and hole pockets
and are located at different binding energies above Ef. Using ARPES, modeling,
DFT and calculations of Berry curvature, we identify the Weyl points and
demonstrate that they are connected by different sets of Fermi arcs for each of
the two surface terminations. We also find new surface "track states" that form
closed loops and are unique to type II Weyl semimetals. This material provides
an exciting, new platform to study the properties of Weyl fermions.


  Red novae are optical transients erupting at luminosities typically higher
than those of classical novae. Their outbursts are believed to be caused by
stellar mergers. We present millimeter/submillimeter-wave observations with
ALMA and SMA of the three best known Galactic red novae, V4332 Sgr, V1309 Sco,
and V838 Mon. The observations were taken 22, 8, and 14 yr after their
respective eruptions and reveal the presence of molecular gas at excitation
temperatures of 35-200 K. The gas displays molecular emission in rotational
transitions with very broad lines (full width $\sim$400 km\s). We found
emission of CO, SiO, SO, SO$_2$ (in all three red novae), H$_2$S (covered only
in V838 Mon) and AlO (present in V4332 Sgr and V1309 Sco). No anomalies were
found in the isotopic composition of the molecular material and the chemical
(molecular) compositions of the three red novae appear similar to those of
oxygen-rich envelopes of classical evolved stars (RSGs, AGBs, post-AGBs). The
minimum masses of the molecular material that most likely was dispersed in the
red-nova eruptions are 0.1, 0.01, and 10$^{-4}$ M$_{\odot}$ for V838 Mon, V4332
Sgr, and V1309 Sco, respectively. The molecular outflows in V4332 Sgr and V1309
Sco are spatially resolved and appear bipolar. The kinematic distances to V1309
Sco and V4332 Sgr are 2.1 and 4.2 kpc, respectively. The kinetic energy stored
in the ejecta of the two older red-nova remnants of V838 Mon and V4332 Sgr is
of order $10^{46}$ erg, similar to values found for some post-AGB (pre-PN)
objects whose bipolar ejecta were also formed in a short-duration eruption. Our
observations strengthen the link between these post-AGB objects and red novae
and support the hypothesis that some of the post-AGB objects were formed in a
common-envelope ejection event or its most catastrophic outcome, a merger.


  We prove that Hori--Vafa mirror models for smooth Fano complete intersections
in weighted projective spaces admit an interpretation as Laurent polynomials.


  In this paper, we apply the attention mechanism to autonomous driving for
steering angle prediction. We propose the first model, applying the recently
introduced sparse attention mechanism to visual domain, as well as the
aggregated extension for this model. We show the improvement of the proposed
method, comparing to no attention as well as to different types of attention.


  In this paper we present simulated observations of massive self-gravitating
circumstellar discs using the Atacama Large Millimetre/sub-millimetre Array
(ALMA). Using a smoothed particle hydrodynamics model of a $0.2M_{\odot}$ disc
orbiting a $1M_{\odot}$ protostar, with a cooling model appropriate for discs
at temperatures below $\sim 160$K and representative dust opacities, we have
constructed maps of the expected emission at sub-mm wavelengths. We have then
used the CASA ALMA simulator to generate simulated images and visibilities with
various array configurations and observation frequencies, taking into account
the expected thermal noise and atmospheric opacities. We find that at 345 GHz
(870 $\mu$m) spiral structures at a resolution of a few AU should be readily
detectable in approximately face-on discs out to distances of the Taurus-Auriga
star-forming complex.


  Recently, we are witnessing the remarkable progress and widespread adoption
of sensing technologies in autonomous driving, robotics, and metaverse.
Considering the rapid advancement of computer vision (CV) technology to analyze
the sensing information, we anticipate a proliferation of wireless applications
exploiting the sensing and CV technologies in 6G. In this article, we provide a
holistic overview of the sensing and CV-aided wireless communications (SVWC)
framework for 6G. By analyzing the high-resolution sensing information through
the powerful CV techniques, SVWC can quickly and accurately understand the
wireless environments and then perform the wireless tasks. To demonstrate the
efficacy of SVWC, we design the whole process of SVWC including the sensing
dataset collection, DL model training, and execution of realistic wireless
tasks. From the numerical evaluations on 6G communication scenarios, we show
that SVWC achieves considerable performance gains over the conventional 5G
systems in terms of positioning accuracy, data rate, and access latency.


  Diffusion Monte Carlo calculations on the adsorption of $^4$He in open-ended
single walled (10,10) nanotubes are presented. We have found a first order
phase transition separating a low density liquid phase in which all $^4$He
atoms are adsorbed close to the tube wall and a high density arrangement
characterized by two helium concentric layers. The energy correction due to the
presence of neighboring tubes in a bundle has also been calculated, finding it
negligible in the density range considered.


  Database fingerprinting have been widely adopted to prevent unauthorized
sharing of data and identify the source of data leakages. Although existing
schemes are robust against common attacks, like random bit flipping and subset
attack, their robustness degrades significantly if attackers utilize the
inherent correlations among database entries. In this paper, we first
demonstrate the vulnerability of existing database fingerprinting schemes by
identifying different correlation attacks: column-wise correlation attack,
row-wise correlation attack, and the integration of them. To provide robust
fingerprinting against the identified correlation attacks, we then develop
mitigation techniques, which can work as post-processing steps for any
off-the-shelf database fingerprinting schemes. The proposed mitigation
techniques also preserve the utility of the fingerprinted database considering
different utility metrics. We empirically investigate the impact of the
identified correlation attacks and the performance of mitigation techniques
using real-world relational databases. Our results show (i) high success rates
of the identified correlation attacks against existing fingerprinting schemes
(e.g., the integrated correlation attack can distort 64.8\% fingerprint bits by
just modifying 14.2\% entries in a fingerprinted database), and (ii) high
robustness of the proposed mitigation techniques (e.g., with the mitigation
techniques, the integrated correlation attack can only distort $3\%$
fingerprint bits).


  Microbial dormancy is an evolutionary trait that has emerged independently at
various positions across the tree of life. It describes the ability of a
microorganism to switch to a metabolically inactive state that can withstand
unfavorable conditions. However, maintaining such a trait requires additional
resources that could otherwise be used to increase e.g. reproductive rates. In
this paper, we aim for gaining a basic understanding under which conditions
maintaining a seed bank of dormant individuals provides a "fitness advantage"
when facing resource limitations and competition for resources among
individuals (in an otherwise stable environment). In particular, we wish to
understand when an individual with a "dormancy trait" can invade a resident
population lacking this trait despite having a lower reproduction rate than the
residents.
  To this end, we follow a stochastic individual-based approach employing
birth-and-death processes, where dormancy is triggered by competitive pressure
for resources. In the large-population limit, we identify a necessary and
sufficient condition under which a complete invasion of mutants has a positive
probability. Further, we explicitly determine the limiting probability of
invasion and the asymptotic time to fixation of mutants in the case of a
successful invasion. In the proofs, we observe the three classical phases of
invasion dynamics in the guise of Coron et al. (2017, 2019).


  We introduce a new quasi-isometry invariant of metric spaces called the
hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic
dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension,
however, unlike the asymptotic dimension, the hyperbolic dimension of any
Euclidean space R^n is zero (while asdim R^n=n.) This invariant possesses usual
properties of dimension like monotonicity and product theorems. Our main result
says that the hyperbolic dimension of any Gromov hyperbolic space X (with mild
restrictions) is at least the topological dimension of the boundary at infinity
plus 1. As an application we obtain that there is no quasi-isometric embedding
of the real hyperbolic space H^n into the (n-1)-fold metric product of metric
trees stabilized by any Euclidean factor.


  Let $p$ be a real number greater than one and let $X$ be a locally compact,
noncompact metric measure space that satisfies certain conditions. The
$p$-Royden and $p$-harmonic boundaries of $X$ are constructed by using the
$p$-Royden algebra of functions on $X$ and a Dirichlet type problem is solved
for the $p$-Royden boundary. We also characterize the metric measure spaces
whose $p$-harmonic boundary is empty.


  We have unambiguously established the dynamical source of the mass scale
parameter (the mass gap) responsible for the large scale structure of the true
QCD vacuum. At the microscopic, Lagrangian level it is the nonlinear
fundamental four-gluon interaction. At the level of the corresponding equation
of motion for the full gluon propagator, it is all the skeleton loop
contributions into the gluon self-energy, which contain the four-gluon
vertices. The key role of the four-gluon interaction is determined by the fact
that this interaction survivies when all the gluon momenta involved go to zero,
while the three-gluon vertex vanishes in this limit. The mass gap and the
corresponding infrared singularities are "hidden" in these terms, and they show
up explicitly when the gluon momentum $q$ goes to zero. The general iteration
solution (i.e., when the relevant skeleton loop integrals have to be iterated)
for the full gluon propagator unavoidably becomes the exact sum of the two
terms. The first term is the Laurent expansion in the inverse powers of the
gluon momentum squared, starting necessarily from the simplest one $1/(q^2)^2$.
Each severe (i.e., more singular than $1/q^2$) power-type IR singularity is
accompanied by the corresponding powers of the mass gap. The standard second
term is always as much singular as $1/q^2$, otherwise remaining undetermined.
The inevitable existence of the first term makes just the principal difference
between non-Abelian QCD and Abelian QED. Moreover, the infrared renormalization
program of the theory leads to the gluon confinement criterion in the
gauge-invariant way.


  In this paper we review and extend some results in the literature pertaining
to spacetime topology while naturally utilizing properties of the codimension 2
null cut locus. Our results fall into two classes, depending on whether or not
one assumes the presence of horizons. Included among the spacetimes we consider
are those that apply to the asymptotically (locally) AdS setting.


  In this paper, we study the strong asymptotic for the orthogonal polynomials
and universality associated with singularly perturbed Pollaczek-Jacobi type
weight $$w_{p_J2}(x,t)=e^{-\frac{t}{x(1-x)}}x^\alpha(1-x)^\beta, $$ where $t
\ge 0$, $\alpha >0$, $\beta >0$ and $x \in [0,1].$ Our main results obtained
here include two aspects:
  { I. Strong asymptotics:} We obtain the strong asymptotic expansions for the
monic Pollaczek-Jacobi type orthogonal polynomials in different interval
$(0,1)$ and outside of interval $\mathbb{C}\backslash (0,1)$, respectively; Due
to the effect of $\frac{t}{x(1-x)}$ for varying $t$, different asymptotic
behaviors at the hard edge $0$ and $1$ were found with different scaling
schemes. Specifically, the uniform asymptotic behavior can be expressed as a
Airy function in the neighborhood of point $1$ as $\zeta= 2n^2t \to \infty,
n\to \infty$, while it is given by a Bessel function as $\zeta \to 0, n \to
\infty$.
  { II. Universality:} We respectively calculate the limit of the eigenvalue
correlation kernel in the bulk of the spectrum and at the both side of hard
edge, which will involve a $\psi$-functions associated with a particular
Painlev$\acute{e}$ \uppercase\expandafter{\romannumeral3} equation near $x=\pm
1$. Further, we also prove the $\psi$-funcation can be approximated by a Bessel
kernel as $\zeta \to 0$ compared with a Airy kernel as $\zeta \to \infty$. Our
analysis is based on the Deift-Zhou nonlinear steepest descent method for the
Riemann-Hilbert problems.


  In the post-Newtonian (PN) expansion, we extend the determination of
quasicircular orbital parameters to be used by subsequent full numerical
simulations to the 3.5PN order, and find that this leads to lower
eccentricities, $e$, than with our previous method that used up to 3PN order.
We also supplement the computation of the radial infall due to radiation
reaction and the location of the center of mass to 3.5PN order, providing
explicit formulas. In addition, we consider the small mass ratio limit by
explicitly including the Schwarzschild and Kerr limits, the later in
quasi-isotropic as well as in our standard use of ADMTT coordinates. We evolve
binaries with a $q=1/16$ mass ratio by using 3PN, 3.5PN, 3.5PN+Schwarzschild,
3.5PN+KerrQISO and 3.5PN+KerrADMTT quasicircular data for three different
configurations where the larger hole intrinsic spins are $\chi^z=-0.8$, $-0.4$
and $+0.8$. Using different measures of eccentricity from the black hole
trajectories and from the waveform amplitudes and phases, we determine a
systematic reduction of eccentricities with respect to the 3PN initial values
by factors of up to an order of magnitude, and reaching the desired
$e\sim10^{-3}$ threshold.


  In this paper, we get the 1D approximate analytical solution of the plasma
electrostatic wake driven by the laser, and get the oscillating frequency of
the wake modified by the nonlinear high order terms, and find that the
frequency depends on the oscillating amplitudes of the wake and the laser which
is the general nonlinear phenomenon. Finally we analyze the longitudinal beam
dynamics in this electrostatic wake, and find that the high order terms don't
change the topology of the longitudinal phase space.


  The possible existence of warm ($T_{\rm eff}\sim19\,000$ K) pulsating DA
white dwarf (WD) stars, hotter than ZZ Ceti stars, was predicted in theoretical
studies more than 30 yr ago. However, to date, no pulsating warm DA WD has been
discovered. We re-examine the pulsational predictions for such WDs on the basis
of new full evolutionary sequences. We analyze all the warm DAs observed by
TESS satellite up to Sector 9 in order to search for the possible pulsational
signal. We compute WD evolutionary sequences with H content in the range $-14.5
\lesssim \log(M_{\rm H}/M_{\star}) \lesssim -10$, appropriate for the study of
warm DA WDs. We use a new full-implicit treatment of time-dependent element
diffusion. Non-adiabatic pulsations were computed in the effective temperature
range of $30\,000-10\,000$ K, focusing on $\ell= 1$ $g$ modes with periods in
the range $50-1500$ s. We find that extended He/H transition zones inhibit the
excitation of $g$ modes due to partial ionization of He below the H envelope,
and only in the case that the H/He transition is assumed much more abrupt,
models do exhibit pulsational instability. In this case, instabilities are
found only in WD models with H envelopes in the range of $-14.5 \lesssim
\log(M_{\rm H}/M_{\star}) \lesssim -10$ and at effective temperatures higher
than those typical of ZZ Ceti stars, in agreement with previous studies. None
of the 36 warm DAs observed so far by TESS satellite are found to pulsate. Our
study suggests that the non-detection of pulsating warm DAs, if WDs with very
thin H envelopes do exist, could be attributed to the presence of a smooth and
extended H/He transition zone. This could be considered as an indirect proof
that element diffusion indeed operates in the interior of WDs.


  The appearance of the time derivative of the acceleration in the equation of
motion (EOM) of an electric charge is studied. It is shown that when an
electric charge is accelerated, a stress force exists in the curved electric
field of the accelerated charge, and this force is proportional to the
acceleration. This stress force acts as a reaction force which is responsible
for the creation of the radiation (instead of the "radiation reaction force"
that actually does not exist at low velocities). Thus the initial acceleration
should be supplied as an initial condition for the solution of the EOM of an
electric charge. It is also shown that in certain cases, like periodic motions
of an electric charge, the term that includes the time derivative of the
acceleration, represents the stress reaction force.


  Recent progress in the dynamical analysis of elliptical galaxy kinematics is
reviewed. Results reported briefly include (i) the surprisingly uniform
anisotropy structure of luminous ellipticals, (ii) their nearly flat (to $\sim
2R_e$) circular velocity curves, (iii) the Tully-Fisher and $M/L - L$ relations
and the connection to the Fundamental Plane, and (iv) the large halo mass
densities implied by the dynamical models.


  Stimulated emission by black holes is discussed in light of the analogue
gravity program. We first consider initial quantum states containing a definite
number of particles, and then we take into account the case where the initial
state is a coherent state. The latter case is particularly significant in the
case where Hawking radiation is studied in dielectric black holes, and the
emission is stimulated by a laser probe. We are particularly interested in the
case of the electromagnetic field, for which stimulated radiation is calculated
too.


  In this paper, we prove Gukov-Pei-Putrov-Vafa's conjecture that the
Witten-Reshetikhin-Turaev invariants are radial limits of homological blocks,
which are $ q $-series introduced by them for plumbed $ 3 $-manifolds with
negative definite linking matrices. In our previous work, the author attributed
this conjecture to the holomorphy of certain rational functions by developing
an asymptotic formula based on the Euler-Maclaurin summation formula. However,
it is challenging to prove holomorphy for general plumbed manifolds. In this
paper, we address this challenge using induction on a sequence of trees
obtained by repeating "pruning trees."


  We revisit the line of non-unitary theories that interpolate between the
Virasoro minimal models. Numerical bootstrap applications have brought about
interest in the four-point function involving the scalar primary of lowest
dimension. Using recent progress in harmonic analysis on the conformal group,
we prove the conjecture that global conformal blocks in this correlator appear
with positive coefficients. We also compute many such coefficients in the
simplest mixed correlator system. Finally, we comment on the status of using
global conformal blocks to isolate the truly unitary points on this line.


  Federated learning has faced performance and network communication
challenges, especially in the environments where the data is not independent
and identically distributed (IID) across the clients. To address the former
challenge, we introduce the federated-centralized concordance property and show
that the federated single-mini-batch training approach can achieve comparable
performance as the corresponding centralized training in the Non-IID
environments. To deal with the latter, we present the federated
multi-mini-batch approach and illustrate that it can establish a trade-off
between the performance and communication efficiency and outperforms federated
averaging in the Non-IID settings.


  We compare the response of five different models of two interacting electrons
in a quantum dot to an external short lived radial excitation that is strong
enough to excite the system well beyond the linear response regime. The models
considered describe the Coulomb interaction between the electrons in different
ways ranging from mean-field approaches to configuration interaction (CI)
models, where the two-electron Hamiltonian is diagonalized in a large truncated
Fock space. The radially symmetric excitation is selected in order to severely
put to test the different approaches to describe the interaction and
correlations of an electron system in a nonequilibrium state. As can be
expected for the case of only two electrons none of the mean-field models can
in full details reproduce the results obtained by the CI model. Nonetheless,
some linear and nonlinear characteristics are reproduced reasonably well. All
the models show activation of an increasing number of collective modes as the
strength of the excitation is increased. By varying slightly the confinement
potential of the dot we observe how sensitive the properties of the excitation
spectrum are to the Coulomb interaction and its correlation effects. In order
to approach closer the question of nonlinearity we solve one of the mean-field
models directly in a nonlinear fashion without resorting to iterations.


  This paper deals with the quasistatic crack growth of a homogeneous elastic
brittle thin film. It is shown that the quasistatic evolution of a
three-dimensional cylinder converges, as its thickness tends to zero, to a
two-dimensional quasistatic evolution associated with the relaxed model.
Firstly, a $\Gamma$-convergence analysis is performed with a surface energy
density which does not provide weak compactness in the space of Special
Functions of Bounded Variation. Then, the asymptotic analysis of the
quasistatic crack evolution is presented in the case of bounded solutions that
is with the simplifying assumption that every minimizing sequence is uniformly
bounded in $L^\infty$.


  Recently, with the rise of web images, managing and understanding large-scale
image datasets has become increasingly important. Vision Large Language Models
(VLLMs) have recently emerged due to their robust vision-understanding
capabilities. However, training these models requires vast amounts of data,
posing challenges to efficiency, effectiveness, data quality, and privacy. In
this paper, we introduce SynthVLM, a novel data synthesis pipeline for VLLMs.
Unlike existing methods that generate captions from images, SynthVLM employs
advanced diffusion models and high-quality captions to automatically generate
and select high-resolution images from captions, creating precisely aligned
image-text pairs. Leveraging these pairs, we achieve state-of-the-art (SoTA)
performance on various vision question answering tasks, maintaining high
alignment quality and preserving advanced language abilities. Moreover,
SynthVLM surpasses traditional GPT-4 Vision-based caption generation methods in
performance while significantly reducing computational overhead. Crucially, our
method's reliance on purely generated data ensures the preservation of privacy,
achieving SoTA performance with just 100k data points (only 18% of the official
dataset size).


  S17 near zero energy was calculated without using the effective expansion of
the S factor or the asymptotic wave functions. Variations of the nuclear
potential parameters scarcely affect the d-wave capture cross section below 0.1
MeV, but the s-wave capture cross section near zero energy is affected strongly
by the shape of the nuclear potential in our calculations. This result is
contrary to the existing assumption that the value of the S factor near zero
energy depends on the asymptotic wave function (or asymptotic normalization
coefficient). We showed that although the s-wave contribution is dominant near
zero energy, the d-wave contribution is not negligible.


  Recent advances in text-to-music generation models have opened new avenues in
musical creativity. However, music generation usually involves iterative
refinements, and how to edit the generated music remains a significant
challenge. This paper introduces a novel approach to the editing of music
generated by such models, enabling the modification of specific attributes,
such as genre, mood and instrument, while maintaining other aspects unchanged.
Our method transforms text editing to \textit{latent space manipulation} while
adding an extra constraint to enforce consistency. It seamlessly integrates
with existing pretrained text-to-music diffusion models without requiring
additional training. Experimental results demonstrate superior performance over
both zero-shot and certain supervised baselines in style and timbre transfer
evaluations. Additionally, we showcase the practical applicability of our
approach in real-world music editing scenarios.


  All-carbon heterostructures have been produced recently via focused ion beam
patterning of single layer graphene. Amorphized graphene is similar to a
graphene sheet in which some hexagons are replaced by a combination of
pentagonal, heptagonal and octagonal rings. The present investigation provides
a general view regarding phonon and load transfer along amorphous graphene. The
developed models for the evaluation of mechanical and thermal conductivity
properties yield accurate results for pristine graphene and acquired findings
for amorphized graphene films are size independent. Our atomistic results show
that amorphous graphene sheets could exhibit a remarkably high elastic modulus
of ~500 GPa and tensile strengths of ~50 GPa at room temperature. However, our
results show that mechanical properties of amorphous graphene decline at higher
temperatures. Furthermore, we show that amorphized graphene present a low
thermal conductivity ~15 W/mK which is two orders of magnitude smaller than
pristine graphene, and we verify that its thermal conductivity is almost
insensitive to temperature since it is dominated by phonon-defect scattering
rather than phonon-phonon scattering. Finally, our results show that amorphized
graphene structures present a remarkably high elastic modulus and mechanical
strength, along with a low thermal conductivity, which is an unusual
combination for carbon-based materials.


  Predicting distant future trajectories of agents in a dynamic scene is not an
easy problem because the future trajectory of an agent is affected by not only
his/her past trajectory but also the scene contexts. To tackle this problem, we
propose a model based on recurrent neural networks (RNNs) and a novel method
for training the model. The proposed model is based on an encoder-decoder
architecture where the encoder encodes inputs (past trajectories and scene
context information) while the decoder produces a trajectory from the context
vector given by the encoder. We train the networks of the proposed model to
produce a future trajectory, which is the closest to the true trajectory, while
maximizing a reward from a reward function. The reward function is also trained
at the same time to maximize the margin between the rewards from the
ground-truth trajectory and its estimate. The reward function plays the role of
a regularizer for the proposed model so the trained networks are able to better
utilize the scene context information for the prediction task. We evaluated the
proposed model on several public datasets. Experimental results show that the
prediction performance of the proposed model is much improved by the
regularization, which outperforms the-state-of-the-arts in terms of accuracy.
The implementation codes are available at
https://github.com/d1024choi/traj-pred-irl/.


  The Fermi surface topologies of underdoped samples the high-Tc superconductor
Bi2212 have been measured with angle resolved photoemission. By examining
thermally excited states above the Fermi level, we show that the Fermi surfaces
in the pseudogap phase of underdoped samples are actually composed of fully
enclosed hole pockets. The spectral weight of these pockets is vanishingly
small at the anti-ferromagnetic zone boundary, which creates the illusion of
Fermi "arcs" in standard photoemission measurements. The area of the pockets as
measured in this study is consistent with the doping level, and hence carrier
density, of the samples measured. Furthermore, the shape and area of the
pockets is well reproduced by a phenomenological model of the pseudogap phase
as a spin liquid.


  We study strong equilibria in network creation games. These form a classical
and well-studied class of games where a set of players form a network by buying
edges to their neighbors at a cost of a fixed parameter $\alpha$. The cost of a
player is defined to be the cost of the bought edges plus the sum of distances
to all the players in the resulting graph.
  We identify and characterize various structural properties of strong
equilibria, which lead to a characterization of the set of strong equilibria
for all $\alpha$ in the range $(0,2)$. For $\alpha > 2$, Andelman et al. (2009)
prove that a star graph in which every leaf buys one edge to the center node is
a strong equilibrium, and conjecture that in fact any star is a strong
equilibrium. We resolve this conjecture in the affirmative. Additionally, we
show that when $\alpha$ is large enough ($\geq 2n$) there exist non-star trees
that are strong equilibria. For the strong price of anarchy, we provide precise
expressions when $\alpha$ is in the range $(0,2)$, and we prove a lower bound
of $3/2$ when $\alpha \geq 2$.
  Lastly, we aim to characterize under which conditions (coalitional)
improvement dynamics may converge to a strong equilibrium. To this end, we
study the (coalitional) finite improvement property and (coalitional) weak
acyclicity property. We prove various conditions under which these properties
do and do not hold. Some of these results also hold for the class of pure Nash
equilibria.


  In this article we investigate the time evolution of the adiabatic(curvature)
and isocurvature (entropy) spectral indices after end of inflation for all
cosmological scales and two different initial conditions. For this purpose,we
first extract an explicit equation for the time evolution of the comoving
curvature perturbation (which may be known as the generalized Mukhanov-Sasaki
equation). It shall be manifested that the evolution of adibatic spectral index
severely depends on the intial conditions and just for the super-Hubble scales
and adiabatic initial conditions is constat as be expected.Moreover,it shall be
clear that the adiabatic spectral index after recombination approach to a
constant value for the isocurvature perturbations.Finally,we re-investgate the
Sachs-Wolfe effect and show that the fudge factor 1/3 in the adiabatic ordinary
Sachs-Wolfe formula must be replaced by 0.4.


  Given a 0-dimensional scheme X in a n-dimensional projective space P^n_K over
an arbitrary field K, we use Liaison theory to characterize the
Cayley-Bacharach property of X. Our result extends the result for sets of
K-rational points given in [7]. In addition, we examine and bound the Hilbert
function and regularity index of the Dedekind different of X when X has the
Cayley-Bacharach property.


  This report details the generation and use of tree node ordering keys in a
single relational database table. The keys for each node are calculated from
the keys of its parent, in such a way that the sort order places every node in
the tree before all of its descendants and after all siblings having a lower
index. The calculation from parent keys to child keys is simple, and reversible
in the sense that the keys of every ancestor of a node can be calculated from
that node's keys without having to consult the database.
  Proofs of the above properties of the key encoding process and of its
correspondence to a finite continued fraction form are provided.


  How a galaxy regulates its SNe energy into different
interstellar/circumgalactic medium components strongly affects galaxy
evolution. Based on the JVLA D-configuration C- (6 GHz) and L-band (1.6 GHz)
continuum observations, we perform statistical analysis comparing
multi-wavelength properties of the CHANG-ES galaxies. The high-quality JVLA
data and edge-on orientation enable us for the first time to include the halo
into the energy budget for a complete radio-flux-limited sample. We find tight
correlations of $L_{\rm radio}$ with the mid-IR-based SFR. The normalization of
our $I_{\rm 1.6GHz}/{\rm W~Hz^{-1}}-{\rm SFR}$ relation is $\sim$2-3 times of
those obtained for face-on galaxies, probably a result of enhanced IR
extinction at high inclination. We also find tight correlations between $L_{\rm
radio}$ and the SNe energy injection rate $\dot{E}_{\rm SN(Ia+CC)}$, indicating
the energy loss via synchrotron radio continuum accounts for $\sim0.1\%$ of
$\dot{E}_{\rm SN}$, comparable to the energy contained in CR electrons. The
integrated C-to-L-band spectral index is $\alpha\sim0.5-1.1$ for non-AGN
galaxies, indicating a dominance by the diffuse synchrotron component. The
low-scatter $L_{\rm radio}-{\rm SFR}$/$L_{\rm radio}-\dot{E}_{\rm SN (Ia+CC)}$
relationships have super-linear logarithmic slopes at $\sim2~\sigma$ in L-band
($1.132\pm0.067$/$1.175\pm0.102$) while consistent with linear in C-band
($1.057\pm0.075$/$1.100\pm0.123$). The super-linearity could be naturally
reproduced with non-calorimeter models for galaxy disks. Using Chandra halo
X-ray measurements, we find sub-linear $L_{\rm X}-L_{\rm radio}$ relations.
These results indicate that the observed radio halo of a starburst galaxy is
close to electron calorimeter, and a galaxy with higher SFR tends to distribute
an increased fraction of SNe energy into radio emission (than X-ray).


  For any countable graph $E$, we investigate the relationship between the
Leavitt path algebra $L_{\C}(E)$ and the graph C*-algebra $C^*(E)$. For graphs
$E$ and $F$, we examine ring homomorphisms, ring *-homomorphisms, algebra
homomorphisms, and algebra *-homomorphisms between $L_{\C}(E)$ and $L_{\C}(F)$.
We prove that in certain situations isomorphisms between $L_{\C}(E)$ and
$L_{\C}(F)$ yield *-isomorphisms between the corresponding C*-algebras $C^*(E)$
and $C^*(F)$. Conversely, we show that *-isomorphisms between $C^*(E)$ and
$C^*(F)$ produce isomorphisms between $L_{\C}(E)$ and $L_{\C}(F)$ in specific
cases. The relationship between Leavitt path algebras and graph C*-algebras is
also explored in the context of Morita equivalence.


  Secret sharing allows a user to split a secret into many shares so that the
secret can be recovered if, and only if, an authorized set of shares is
collected. Although secret sharing typically does not require any computational
hardness assumptions, its security does require that an adversary cannot
collect an authorized set of shares. Over long periods of time where an
adversary can benefit from multiple data breaches, this may become an
unrealistic assumption.
  We initiate the systematic study of secret sharing with certified deletion in
order to achieve security even against an adversary that eventually collects an
authorized set of shares. In secret sharing with certified deletion, a
(classical) secret is split into quantum shares which can be verifiably
destroyed. We define two natural notions of security: no-signaling security and
adaptive security.
  Next, we show how to construct (i) a secret sharing scheme with no-signaling
certified deletion for any monotone access structure, and (ii) a threshold
secret sharing scheme with adaptive certified deletion. Our first construction
uses Bartusek and Khurana's (CRYPTO 2023) 2-out-of-2 secret sharing scheme with
certified deletion as a building block, while our second construction is built
from scratch and requires several new technical ideas. For example, we
significantly generalize the ``XOR extractor'' of Agarwal, Bartusek, Khurana,
and Kumar (EUROCRYPT 2023) in order to obtain high rate seedless extraction
from certain quantum sources of entropy.


  In three-dimensional turbulent flows, the flux of energy from large to small
scales breaks time symmetry. We show here that this irreversibility can be
quantified by following the relative motion of several Lagrangian tracers. We
find by analytical calculation, numerical analysis and experimental observation
that the existence of the energy flux implies that, at short times, two
particles separate temporally slower forwards than backwards, and the
difference between forward and backward dispersion grows as $t^3$. We also find
the geometric deformation of material volumes, surrogated by four points
spanning an initially regular tetrahedron, to show sensitivity to the
time-reversal with an effect growing linearly in $t$. We associate this with
the structure of the strain rate in the flow.


  Defect detection plays a vital role in the manufacturing process of
integrated circuits (ICs). Die attachment and wire bonding are two steps of the
manufacturing process that determine the power and signal transmission quality
and dependability in an IC. This paper presents a survey or literature review
of the methods used for detecting these defects based on different sensing
modalities used including optical, radiological, acoustical, and infrared
thermography. A discussion of the detection methods used is provided in this
survey. Both conventional and deep learning approaches for detecting die
attachment and wire bonding defects are considered along with challenges and
future research directions.


  Axion-like particles (ALPs) are predicted to mediate exotic interactions
between spin and mass. We propose an ALP-searching experiment based on the
levitated micromechanical oscillator, which is one of the most sensitive
sensors for spin-mass forces at a short distance. The proposed experiment tests
the spin-mass resonant interaction between the polarized electron spins and a
diamagnetically levitated microsphere. By periodically flipping the electron
spins, the contamination from nonresonant background forces can be eliminated.
The levitated microoscillator can prospectively enhance the sensitivity by
nearly $10^3$ times over current experiments for ALPs with mass in the range 4
meV to 0.4 eV.


  We study reproducing kernels, and associated reproducing kernel Hilbert
spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In
this setting we analyze in detail the distributions of the corresponding Dirac
point-masses of $V$. Illustrations include certain models from neural networks:
An Extreme Learning Machine (ELM) is a neural network-configuration in which a
hidden layer of weights are randomly sampled, and where the object is then to
compute resulting output. For RKHSs $\mathscr{H}$ of functions defined on a
prescribed countable infinite discrete set $V$, we characterize those which
contain the Dirac masses $\delta_{x}$ for all points $x$ in $V$. Further
examples and applications where this question plays an important role are: (i)
discrete Brownian motion-Hilbert spaces, i.e., discrete versions of the
Cameron-Martin Hilbert space; (ii) energy-Hilbert spaces corresponding to
graph-Laplacians where the set $V$ of vertices is then equipped with a
resistance metric; and finally (iii) the study of Gaussian free fields.


  With the possible spacial association to the Fermi/LAT source 3FGL
J1330.0-3818, TOL 1326-379 may be the first one that is identified as a
gamma-ray emitting Fanaroff-Riley type 0 radio galaxy (FR0 RG). We analyze the
~12 yr Fermi/LAT observation data of this gamma-ray source and examine its
association to TOL 1326-379. We show that the gamma-ray source (named as
J1331.0-3818) is tentatively detected with a TS value of 28.7, 3FGL
J1330.0-3818 is out of the 95% containment of J1331.0-3818, and their positions
are spatially separated ~0.2 degr. 4FGL J1331.3-3818 falls into the 68%
containment of J1331.0-3818, suggesting that our result agrees with that
reported in the Fourth Fermi LAT Source Catalog. TOL 1326-379 is out of the 95%
containment of J1331.0-3818, and their positions are spatially separated ~0.4
degr, indicating that the association between J1331.0-3818 and TOL 1326-379 is
quite ambiguous. However, we do not find other possible potential radio or
X-ray counterpart within the circle centered at J1331.0-3818 with a radius of
0.4 degr. The spectral energy distribution (SED) of TOL 1326-379 shows a
bimodal feature as seen in the gamma-ray emitting RGs. We fit the SED with the
one-zone leptonic model and find that the average energy spectrum of
J1331.0-3818 agrees with the model prediction. Assuming that J1331.0-3818 is an
unidentified gamma-ray source, we derive the upper-limit of the gamma-ray flux
for TOL 1326-379. It is not tight enough to exclude this possibility with the
SED modeling. Based on these results, we cautiously argue that the gamma-ray
source J1331.0-3818 is associated with TOL 1326-379 and its jet radiation
physic is similar to those gamma-ray emitting RGs.


  Algebraic quantization has been applied on the class of globally hyperbolic
spacetime for many decades, leading to remarkable results. Nonetheless, the
presence of a boundary calls for a separate treatment, since, in general, it
breaks global hyperbolicity and it requires the introduction of boundary
conditions to the field equation. Although a general theory for such situations
is lacking, we develop an explicit construction of the algebraic quantization
of a massless scalar field on two prototypical geometries, by exploiting the
method of images. This well known technique gives a way to relate solutions of
the boundary value problem to solution of the field equation on Minkowski
spacetime, filling the gap with the standard theory. At the same time, we point
out some limits of reliability of this scheme.


  A ternary inclusion-exclusion polynomial is a polynomial of the form \[
Q_{{p,q,r}}=\frac{(z^{pqr}-1)(z^p-1)(z^q-1)(z^r-1)}
{(z^{pq}-1)(z^{qr}-1)(z^{rp}-1)(z-1)}, \] where $p$, $q$, and $r$ are integers
$\ge3$ and relatively prime in pairs. This class of polynomials contains, as
its principle subclass, the ternary cyclotomic polynomials corresponding to
restricting $p$, $q$, and $r$ to be distinct odd prime numbers. Our object here
is to continue the investigation of the relationship between the coefficients
of $Q_{{p,q,r}}$ and $Q_{{p,q,s}}$, with $r\equiv s\pmod{pq}$. More
specifically, we consider the case where $1\le s<\max(p,q)<r$, and obtain a
recursive estimate for the function $A(p,q,r)$--the function that gives the
maximum of the absolute values of the coefficients of $Q_{{p,q,r}}$. A simple
corollary of our main result is the following absolute estimate. If $s\ge1$ and
$r\equiv\pm s\pmod{pq}$, then $A(p,q,r)\le s$.


  In this paper we consider the Brauer groups of algebraic stacks and GIT
quotients: the only algebraic stacks we consider in this paper are quotient
stacks [X/G], where X is a smooth scheme of finite type over a field k, and G
is a linear algebraic group over k and acting on X, as well as various moduli
stacks of principal G-bundles on a smooth projective curve X, associated to a
reductive group G. We also consider the Brauer groups of the corresponding
coarse moduli spaces, which most often identify with the corresponding
GIT-quotients. One conclusion that we seem to draw then is that the Brauer
groups (or their $\ell$-primary torsion parts, for a fixed prime $\ell$
different from char(k)) of the corresponding stacks and coarse moduli spaces
depend strongly on the Brauer group of the given scheme X.


  We investigate the influence of step edge diffusion (SED) and desorption on
Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the
solid-on-solid (SOS) model. Based on these investigations we propose two
strategies to optimize MBE growth. The strategies are applicable in different
growth regimes: During layer-by-layer growth one can exploit the presence of
desorption in order to achieve smooth surfaces. By additional short high flux
pulses of particles one can increase the growth rate and assist layer-by-layer
growth. If, however, mounds are formed (non-layer-by-layer growth) the SED can
be used to control size and shape of the three-dimensional structures. By
controlled reduction of the flux with time we achieve a fast coarsening
together with smooth step edges.


  In this work, we study constant-roll inflation driven by a scalar field with
non-minimal derivative coupling to gravity, via the Einstein tensor. This model
contains a free parameter, $\eta$, which quantifies the non-minimal derivative
coupling and a parameter $\alpha$ which characterize the constant-roll
condition. In this scenario, using the Hamilton-Jacobi-like formalism, an
ansatz for the Hubble parameter (as a function of the scalar field) and some
restrictions on the model parameters, we found new exact solutions for the
inflaton potential which include power-law, de Sitter, quadratic hilltop and
natural inflation, among others. Additionally, a phase space analysis was
performed and it is shown that the exact solutions associated to natural
inflation and a "$\cosh$-type" potential, are attractors.


  We investigate terahertz emission from two-color fs-laser-induced
microplasmas. Under strongest focusing conditions, microplasmas are shown to
act as point-sources for broadband terahertz-to-far-infrared radiation, where
the emission bandwidth is determined by the plasma density. Semi-analytical
modeling allows us to identify scaling laws with respect to important laser
parameters. In particular, we find that the optical-to-THz conversion
efficiency crucially depends on the focusing conditions. We use this insight to
demonstrate by means of Maxwell-consistent 3D simulations, that for only
10-$\mu$J laser energy a conversion efficiency well above $10^{-4}$ can be
achieved.


  We present a few ways of using conformal maps in the reconstruction of
two-dimensional conductivities in electrical impedance tomography. First, by
utilizing the Riemann mapping theorem, we can transform any simply connected
domain of interest to the unit disk where the D-bar method can be implemented
most efficiently. In particular, this applies to the open upper half-plane.
Second, in the unit disk we may choose a region of interest that is magnified
using a suitable M\"obius transform. To facilitate the efficient use of
conformal maps, we introduce input current patterns that are named conformally
transformed truncated Fourier basis; in practice, their use corresponds to
positioning the available electrodes close to the region of interest. These
ideas are numerically tested using simulated continuum data in bounded domains
and simulated point electrode data in the half-plane. The connections to
practical electrode measurements are also discussed.


  Let $C$ be an extremal self-dual binary code of length 72 and $g\in \Aut(C) $
be an automorphism of order 2. We show that $C$ is a free $\F_2<g>$ module and
use this to exclude certain subgroups of order 8 of $\Aut (C)$. We also show
that $\Aut(C)$ does not contain an element of order 10.


  Since DARPA Grand Challenges (rural) in 2004/05 and Urban Challenges in 2007,
autonomous driving has been the most active field of AI applications. Almost at
the same time, deep learning has made breakthrough by several pioneers, three
of them (also called fathers of deep learning), Hinton, Bengio and LeCun, won
ACM Turin Award in 2019. This is a survey of autonomous driving technologies
with deep learning methods. We investigate the major fields of self-driving
systems, such as perception, mapping and localization, prediction, planning and
control, simulation, V2X and safety etc. Due to the limited space, we focus the
analysis on several key areas, i.e. 2D and 3D object detection in perception,
depth estimation from cameras, multiple sensor fusion on the data, feature and
task level respectively, behavior modelling and prediction of vehicle driving
and pedestrian trajectories.


  Transitions between different charge density wave (CDW) states in
quasi-two-dimensional materials may be accompanied also by changes in the
inter-layer stacking of the CDW. Using MeV ultrafast electron diffraction, the
out-of-plane stacking order dynamics in the quasi-two-dimensional
dichalcogenide 1T-TaS$_2$ is investigated for the first time. From the
intensity of the CDW satellites aligned around the commensurate $l$ = 1/6
characteristic stacking order, it is found out that this phase disappears with
a 0.5 ps time constant. Simultaneously, in the same experiment, the emergence
of the incommensurate phase, with a slightly slower 2.0 ps time constant, is
determined from the intensity of the CDW satellites aligned around the
incommensurate $l$ = 1/3 characteristic stacking order. These results might be
of relevance in understanding the metallic character of the laser-induced
metastable "hidden" state recently discovered in this compound.