  Quantum key distribution (QKD) aims to generate secure private keys shared by
two remote parties. With its security being protected by principles of quantum
mechanics, some technology challenges remain towards practical application of
QKD. The major one is the distance limit, which is caused by the fact that a
quantum signal cannot be amplified while the channel loss is exponential with
the distance for photon transmission in optical fiber. Here using the
3-intensity sending-or-not-sending protocol with the
actively-odd-parity-pairing method, we demonstrate a fiber-based twin-field QKD
over 1002 km. In our experiment, we developed a dual-band phase estimation and
ultra-low noise superconducting nanowire single-photon detectors to suppress
the system noise to around 0.02 Hz. The secure key rate is $9.53\times10^{-12}$
per pulse through 1002 km fiber in the asymptotic regime, and
$8.75\times10^{-12}$ per pulse at 952 km considering the finite size effect.
Our work constitutes a critical step towards the future large-scale quantum
network.


  Signature of heavier charged Higgs boson, much above the top quark mass, is
investigated at the LHC Run 2 experiments, following its decay mode via top and
bottom quark focusing on both hadronic and leptonic signal final states. The
generic two Higgs doublet model framework is considered with a special emphasis
on supersymmetry motivated Type II model. The signal is found to heavily
affected by the huge irreducible backgrounds due to the top pair production and
QCD events. The jet substructure technique is used to tag moderately boosted
top jets in order to reconstruct charged Higgs mass. The simple cut based
analysis is performed optimizing various kinematic selections, and the signal
sensitivity is found to be reasonable for only lower range of charged Higgs
masses for very high luminosity 3000 fb$^{-1}$ option. However, employing the
multi-variate analysis(MVA) technique, a remarkable improvement in signal
sensitivity is achieved. We find, the charged Higgs signal for the mass range
about $300-600$ is observable with 1000 fb$^{-1}$ luminosity option. However,
for more high luminosity option 3000 fb$^{-1}$, the discovery potential can be
extended to $700-800$ GeV.


  We prove the existence of correlations between the equilibrium states at
different temperatures of the multi-$p$-spin spherical spin-glass models with
continuous replica symmetry breaking: there is no chaos in temperature in these
models. Furthermore, the overlaps satisfy ultrametric relations. As a
consequence the Parisi tree is essentially the same at all temperatures with
lower branches developing when lowering the temperature. We conjecture that the
reference free energies of the clusters are also fixed at all temperatures as
in the generalized random-energy model.


  In this work, we describe our method for tackling the valence-arousal
estimation challenge from ABAW FG-2020 Competition. The competition organizers
provide an in-the-wild Aff-Wild2 dataset for participants to analyze affective
behavior in real-life settings. We use MIMAMO Net \cite{deng2020mimamo} model
to achieve information about micro-motion and macro-motion for improving video
emotion recognition and achieve Concordance Correlation Coefficient (CCC) of
0.415 and 0.511 for valence and arousal on the reselected validation set.


  Motivated by the work of J.K.~Jang et al., Nat.~Commun.~{\bf 6}, 7370 (2015),
where the authors experimentally tweeze cavity solitons in a passive loop of
optical fiber, we study the amenability to tweezing of cavity solitons as the
properties of a localized tweezer are varied. The system is modeled by the
Lugiato-Lefever equation, a variant of the complex Ginzburg-Landau equation. We
produce an effective, localized, trapping tweezer potential by assuming a
Gaussian phase-modulation of the holding beam. The potential for tweezing is
then assessed as the total (temporal) displacement and speed of the tweezer are
varied, and corresponding phase diagrams are presented. As the relative speed
of the tweezer is increased we find two possible dynamical scenarios:
successful tweezing and release of the cavity soliton. We also deploy a
non-conservative variational approximation (NCVA) based on a Lagrangian
description which reduces the original dissipative partial differential
equation to a set of coupled ordinary differential equations for the cavity
soliton parameters. We illustrate the ability of the NCVA to accurately predict
the separatrix between successful and failed tweezing. This showcases the
versatility of the NCVA to provide a low-dimensional description of the
experimental realization of the temporal tweezing.


  Let $\Gamma$ be a countable abelian group and $f \in \Z[\Gamma]$, where
$\Z[\Gamma]$ denotes the integral group ring of $\Gamma$. Consider the
Pontryagin dual $X_f$ of the cyclic $\Z[\Gamma]$-module $\Z[\Gamma]/\Z[\Gamma]
f$ and suppose that the natural action of $\Gamma$ on $X_f$ is expansive and
that $X_f$ is connected. We prove that if $\tau \colon X_f \to X_f$ is a
$\Gamma$-equivariant continuous map, then $\tau$ is surjective if and only if
the restriction of $\tau$ to each $\Gamma$-homoclinicity class is injective.
This is an analogue of the classical Garden of Eden theorem of Moore and Myhill
for cellular automata with finite alphabet over $\Gamma$.


  We present a tutorial on the principles of crystal growth of intermetallic
and oxide compounds from molten solutions, with an emphasis on the fundamental
principles governing the underlying phase equilibria and phase diagrams of
multicomponent systems.


  The Dirac equation describes the motion of electrons in electromagnetic
field, but it considers spin as intrinsic property without any real motion. We
postulate spin as the intrinsic feature of vacuum, in which the incident
electromagnetic radiation can create vortices with well defined spinning
frequency and completely undefined axis of rotation. The vortices have finite
surface determined by the spinning frequency that makes the peripheral speed
equal to the velocity of light. According to the Lorentz equations of special
relativity, the product of radius and mass of rotating objects is independent
of the frequency of rotation and it is equal to 3/4h/2pic for all fermions.
This invariance explains how the light with infinite spatial dimension and zero
mass can produce finite mass and size for the particles in the pair-creation
processes. The vortex model interprets the rest energy as the kinetic energy of
spinning motion. The isotropic character of spinning can be represented by
helical motion with right or left-handed chirality corresponding to the duality
of matter and anti-matter. Conservation rule is proposed for the chirality
explaining the electron-positron annihilation and the pair-creation processes.
The vortex induced field rotation around the particle can reproduce the
gravitational formula if the curvature of field is derived from the Lorentz
contraction on the surface of rotating sphere. Generalized Hamiltonian is
suggested for the fermions describing the spinning motion in the internal frame
of particles, it reproduces the Dirac equation, when the rest energy is
predominant.


  We select a sample of 70378 E/S0 (early-type) galaxies at 0<z<0.36 from the
Sloan Digital Sky Survey, excluding disk and star-forming galaxies. We estimate
g and r magnitudes in the observer- and rest-frames directly from the SDSS DR6
spectra; this provides an object-by-object estimate of the k-correction. We use
the k-corrections from the spectra to study the evolution of the rest-frame
colour-magnitude relation (CMR) and colour-sigma (velocity dispersion) relation
(CsigmaR). The evolution is very sensitive to the k-correction. Both the CMR
and CsigmaR evolve blueward with increasing redshift, approximately in
agreement with passive evolution models with age approx. 12 Gyr. The slope and
zero-point of the CMR depend on whether colours were defined in fixed physical
or angular apertures, a consequence of the fact that the centers of these
objects tend to be redder: the relation is steeper for fixed angular apertures.
One the other hand, the CsigmaR slope does not show this dependence on the
aperture in which the colour was defined, suggesting that colour gradients are
correlated with residuals from the sigma-M_r relation. As these residuals are
age indicators, our findings suggest that colour gradients correlate with the
age of the stellar population.


  We study the nature of the globular cluster (GC) candidates FSR 1603 and FSR
1755 selected from the catalogue of \citet{FSRcat}. Their properties are
investigated with 2MASS field-star decontaminated photometry, which is used to
build colour-magnitude diagrams (CMDs), and stellar radial density profiles
(RDPs). FSR 1603 has the open cluster (OC) Ruprecht 101 as optical counterpart,
and we show it to be a massive intermediate age cluster (IAC). Relevant
parameters of FSR 1603 are the age $\approx1$ Gyr, distance from the Sun
$\ds\approx2.7$ kpc, Galactocentric distance $\dgc\approx6.4$ kpc, core radius
$\rc\approx1.1$ pc, mass function slope $\chi\approx1.8$, observed stellar mass
(for stars with mass in the range $\rm 1.27 \ms\leq m\leq2.03 \ms$)
$\mObs\approx500 \ms$, and a total (extrapolated to $\rm m=0.08 \ms$) stellar
mass $\mTot\approx2300 \ms$. FSR 1755, on the other hand, is not a populous
cluster. It may be a sparse young cluster embedded in the H II region Sh2-3,
subject to an absorption $\aV\approx4.1$, located at $\ds\approx1.3$ kpc.
Important field-star contamination, spatially-variable heavy dust obscuration,
even in \ks, and gas emission characterise its field. A nearly vertical, sparse
blue stellar sequence shows up in the CMDs.


  Audio tagging aims to detect the types of sound events occurring in an audio
recording. To tag the polyphonic audio recordings, we propose to use
Connectionist Temporal Classification (CTC) loss function on the top of
Convolutional Recurrent Neural Network (CRNN) with learnable Gated Linear Units
(GLU-CTC), based on a new type of audio label data: Sequentially Labelled Data
(SLD). In GLU-CTC, CTC objective function maps the frame-level probability of
labels to clip-level probability of labels. To compare the mapping ability of
GLU-CTC for sound events, we train a CRNN with GLU based on Global Max Pooling
(GLU-GMP) and a CRNN with GLU based on Global Average Pooling (GLU-GAP). And we
also compare the proposed GLU-CTC system with the baseline system, which is a
CRNN trained using CTC loss function without GLU. The experiments show that the
GLU-CTC achieves an Area Under Curve (AUC) score of 0.882 in audio tagging,
outperforming the GLU-GMP of 0.803, GLU-GAP of 0.766 and baseline system of
0.837. That means based on the same CRNN model with GLU, the performance of CTC
mapping is better than the GMP and GAP mapping. Given both based on the CTC
mapping, the CRNN with GLU outperforms the CRNN without GLU.


  We find that the local galactic extinction towards the field of gamma-ray
burst GRB970228 is $A_V=1.09^{+0.10}_{-0.20}$, which implies a substantial
dimming and change in the spectral slope of the intrinsic GRB970228 afterglow.
We measure a color $(V_{606}-I_{814})_{ST} = -0.18^{+0.51}_{-0.61}$ for the
extended source coincident with the afterglow. Taking into account our
measurement of the extinction toward this field, this color implies that the
extended source is most likely a galaxy undergoing star formation, in agreement
with our earlier conclusion (\cite{CL98}). In a separate analysis, we find that
the inferred intrinsic spectrum of the GRB 980329 afterglow is consistent with
the predictions of the simplest relativistic fireball model. We also find that
the intrinsic spectrum of the afterglow is extincted both by dust (source frame
$A_V \ga 1$ mag), and that the shape of the extinction curve is typical of
young star-forming regions like the Orion Nebula but is not typical of older
star-forming or starburst regions. The $\approx$ 2 mag drop between the $R$ and
the $I$ bands can be explained by the far-ultraviolet non-linear component of
the extinction curve if $3 \la z \la 4$, and by the 2175 \AA\ bump if $z
\approx 2$; other redshifts are not consistent with the observational data,
given our general model.


  We extend the ab initio no-core shell model/resonating-group method to
include three-nucleon (3N) interactions for the description of nucleon-nucleus
collisions. We outline the formalism, give algebraic expressions for the
3N-force integration kernels, and discuss computational aspects of two
alternative implementations. The extended theoretical framework is then applied
to nucleon-4He scattering using similarity-renormalization-group (SRG) evolved
nucleon-nucleon plus three-nucleon potentials derived from chiral effective
field theory. We analyze the convergence properties of the calculated phase
shifts and explore their dependence upon the SRG evolution parameter. We
include up to six excited states of the 4He target and find significant effects
from the inclusion of the chiral 3N force, e.g., it enhances the spin-orbit
splitting between the 3/2- and 1/2- resonances and leads to an improved
agreement with the phase shifts obtained from an accurate R-matrix analysis of
the five-nucleon experimental data. We find remarkably good agreement with
measured differential cross sections at various energies, while analyzing
powers manifest larger deviations from experiment for certain energies and
angles.


  We cross-correlate the recent CMB WMAP 1 year data with the diffuse soft
X-ray background map of ROSAT. We look for common signatures due to galaxy
clusters (SZ effect in CMB, bremsstrahlung in X-rays) by cross-correlating the
two maps in real and in Fourier space. We do not find any significant
correlation and we explore the different reasons for this lack of correlation.
The most likely candidates are the possibility that we live in a low $\sigma
_8$ universe ($\sigma_8 < 0.9$) and/or systematic effects in the data
especially in the diffuse X-ray maps which may suffer from significant cluster
signal subtraction during the point source removal process.


  We revisit the issue of mixing matrix renormalization in theories that
include Dirac or Majorana fermions. We show how a gauge-variant on-shell
renormalized mixing matrix can be related to a manifestly gauge-independent one
within a generalized ${\bar {\rm MS}}$ scheme of renormalization. This
scheme-dependent relation is a consequence of the fact that in any scheme of
renormalization, the gauge-dependent part of the mixing-matrix counterterm is
ultra-violet safe and has a pure dispersive form. Employing the unitarity
properties of the theory, we can successfully utilize the afore-mentioned
scheme-dependent relation to preserve basic global or local symmetries of the
bare Lagrangian through the entire process of renormalization. As an immediate
application of our study, we derive the gauge-independent renormalization-group
equations of mixing matrices in a minimal extension of the Standard Model with
isosinglet neutrinos.


  We discuss two conjectures by Francesco Severi and Joe Harris about the
irreducibility and the dimension of the Hilbert scheme parameterizing smooth
projective curves of given degree and genus.


  The group of continuous binary operations on a topological space is studied;
its relationship with the group of homeomorphisms is established. The category
of binary $G$-spaces and bi-equivariant maps is constructed, which is a natural
extension of the category of $G$-spaces and equivariant maps. Results related
to the foundations of the theory of binary $G$-spaces are obtained.


  Spins and oscillators are foundational to much of physics and applied
sciences. For quantum information, a spin 1/2 exemplifies the most basic unit,
a qubit. High angular momentum spins and harmonic oscillators provide
multi-level manifolds (e.g., qudits) which have the potential for
hardware-efficient protected encodings of quantum information and simulation of
many-body quantum systems. In this work, we demonstrate a new quantum control
protocol that conceptually merges these disparate hardware platforms. Namely,
we show how to modify a harmonic oscillator on-demand to implement a continuous
range of generators associated to resonant driving of a harmonic qudit, and
then specifically design a harmonic multi-level spin degree of freedom. The
synthetic spin is verified by demonstration of spin coherent (SU(2)) rotations
and comparison to other manifolds like simply-truncated oscillators. Our scheme
allows universal control of the qudit, and, for the first time, we use linear,
harmonic operations to accomplish four logical gates on a harmonic qudit
encoding. Our results show how motion on a closed Hilbert space can be useful
for quantum information processing and opens the door to superconducting
circuit simulations of higher angular momentum quantum magnetism.


  We consider the Neumann eigenvalue problem for Laplacian on a bounded
multi-connected domain contained in simply connected space forms. Under certain
symmetry assumptions on the domain, we prove Szeg\"{o}-Weinberger type
inequalities for the first $n$ positive Neumann eigenvalues.


  We study the quantum many-body ground states of electrons on the half-filled
honeycomb lattice with short- and long-ranged density-density interactions as a
model for graphene. To this end, we employ the recently developed
truncated-unity functional renormalization group (TU-fRG) approach which allows
for a high resolution of the interaction vertex' wavevector dependence. We
connect to previous lattice quantum Monte Carlo (QMC) results which predict a
stabilization of the semimetallic phase for realistic \emph{ab initio}
interaction parameters and confirm that the application of a finite biaxial
strain can induce a quantum phase transition towards an ordered ground state.
In contrast to lattice QMC simulations, the TU-fRG is not limited in the choice
of tight-binding and interaction parameters to avoid the occurrence of a sign
problem. Therefore, we also investigate a range of parameters relevant to the
realistic graphene material which are not accessible by numerically exact
methods. Although a plethora of charge density waves arise under medium-range
interactions, we find the antiferromagnetic spin-density wave to be the
prevailing instability for long-range interactions. We further explore the
impact of an extended tight-binding Hamiltonian with second-nearest neighbor
hopping and a finite chemical potential for a more accurate description of the
band structure of graphene's $p_z$ electrons.


  We study the profile of a thin disk configuration as described by an
axisymmetric ideal magnetohydrodynamics steady equilibrium. We consider the
disk like a differentially rotating system dominated by the Keplerian term, but
allowing for a non-zero radial and vertical matter flux. As a result, the
steady state allows for the existence of local peaks for the vertical velocity
of the plasma particles, though it prevents the radial matter accretion rate.
This ideal magnetohydrodynamics scheme is therefore unable to solve the angular
momentum-transport problem, but we suggest that it provides a mechanism for the
generation of matter-jet seeds.


  Upcoming WiFi-based localization systems for indoor environments face a
conflict of privacy interests: Server-side localization violates location
privacy of the users, while localization on the user's device forces the
localization provider to disclose the details of the system, e.g.,
sophisticated classification models. We show how Secure Two-Party Computation
can be used to reconcile privacy interests in a state-of-the-art localization
system. Our approach provides strong privacy guarantees for all involved
parties, while achieving room-level localization accuracy at reasonable
overheads.


  Above a certain density a granular material jams. This property can be
controlled by either tuning a global property, such as the packing fraction or
by applying shear strain, or at the micro-scale by tuning grain shape,
inter-particle friction or externally controlled organization. Here, we
introduce a novel way to change a local granular property by adding a weak
anisotropic magnetic interaction between particles. We measure the evolution of
the pressure, $P$, and coordination number, $Z$, for a packing of 2D
photo-elastic disks, subject to uniaxial compression. Some of the particles
have embedded cuboidal magnets. The strength of the magnetic interactions
between particles are too weak to have a strong direct effect on $P$ or $Z$
when the system is jammed. However, the magnetic interactions play an important
role in the evolution of latent force networks when systems containing a large
enough fraction of the particles with magnets are driven through unjammed
states. In this case, a statistically stable network of magnetic chains
self-organizes and overlaps with force chains, strengthening the granular
medium. We believe this property can be used to reversibly control mechanical
properties of granular materials.


  We show that the statistics of the charge transfer of non-interacting
fermions through a two-lead contact is generalized binomial, at any temperature
and for any form of the scattering matrix: an arbitrary charge-transfer process
can be decomposed into independent single-particle events. This result
generalizes previous studies of adiabatic pumping at zero temperature and of
transport induced by bias voltage.


  Dataflow/mapping decides the compute and energy efficiency of DNN
accelerators. Many mappers have been proposed to tackle the intra-layer
map-space. However, mappers for inter-layer map-space (aka layer-fusion
map-space), have been rarely discussed. In this work, we propose a mapper,
DNNFuser, specifically focusing on this layer-fusion map-space. While existing
SOTA DNN mapping explorations rely on search-based mappers, this is the first
work, to the best of our knowledge, to propose a one-shot inference-based
mapper. We leverage Transformer as our DNN architecture to learn layer-fusion
optimization as a sequence modeling problem. Further, the trained DNNFuser can
generalize its knowledge and infer new solutions for unseen conditions. Within
one inference pass, DNNFuser can infer solutions with compatible performance to
the ones found by a highly optimized search-based mapper while being 66x-127x
faster.


  Identifying optimal basic feasible solutions to linear programming problems
is a critical task for mixed integer programming and other applications. The
crossover method, which aims at deriving an optimal extreme point from a
suboptimal solution (the output of a starting method such as interior-point
methods or first-order methods), is crucial in this process. This method,
compared to the starting method, frequently represents the primary
computational bottleneck in practical applications. We propose approaches to
overcome this bottleneck by exploiting problem characteristics and implementing
customized strategies. For problems arising from network applications and
exhibiting network structures, we take advantage of the graph structure of the
problem and the tree structure of the optimal solutions. Based on these
structures, we propose a tree-based crossover method, aiming to recovering
basic solutions by identifying nearby spanning tree structures. For general
linear programs, we propose recovering an optimal basic solution by identifying
the optimal face and employing controlled perturbations based on the suboptimal
solution provided by interior-point methods. We prove that an optimal solution
for the perturbed problem is an extreme point, and its objective value is at
least as good as that of the initial interior point solution. Computational
experiments show significant speed-ups achieved by our methods compared to
state-of-the-art commercial solvers on classical linear programming problem
benchmarks, network flow problem benchmarks, and optimal transport problems.


  Despite the identification of a great number of Jupiter-like and Earth-like
planets at close-in orbits, the number of "hot Neptunes" - the planets with
0.6-18 times of Neptune mass and orbital periods less than 3 days - turned out
to be very small. The corresponding region in the mass-period distribution was
assigned as the "short-period Neptunian desert". The common explanation of this
fact is that the gaseous planet with few Neptune masses would not survive in
the vicinity of host star due to intensive atmosphere outflow induced by
heating from stellar radiation. To check this hypothesis we performed numerical
simulations of atmosphere dynamics for a hot Neptune. We adopt the previously
developed self-consistent 1D model of hydrogen-helium atmosphere with
suprathermal electrons accounted. The mass-loss rates as a function of orbital
distances and stellar ages are presented. We conclude that the desert of
short-period Neptunes could not be entirely explained by evaporation of planet
atmosphere caused by the radiation from a host star. For the less massive
Neptune-like planet, the estimated upper limits of the mass loss may be
consistent with the photo-evaporation scenario, while the heavier Neptune-like
planets could not lose the significant mass through this mechanism. We also
found the significant differences between our numerical results and widely used
approximate estimates of the mass loss.


  We report the discovery of a young massive stellar cluster and infrared
nebula in the direction of the CS molecular cloud associated to the IRAS point
source 16132-5039. The analysis of the mid-infrared images from the more
accurate MSX catalog, reveled that there are two independent components
associated with the IRAS source. The integral of the spectral energy
distribution for these components, between 8.28 $\mu$m and 100 $\mu$m, gave
lower limits for the bolometric luminosity of the embedded objects of $8.7
\times 10^4 L_\odot$ and $9 \times 10^3 L_\odot$, which corresponds to ZAMS O8
and B0.5 stars, respectively. The number of Lyman continuum photons expected
from the stars that lie along the reddening line for early-type stars is about
1.7 $ \times$ 10$^{49}$ s$^{-1}$, enough to produce the detected flux densities
at 5 GHz. The NIR spectrum of the nebula increases with frequency, implying
that free-free emission cannot be the main source of the extended luminosity,
from which we conclude that the observed emission must be mainly dust scattered
light. A comparison of the cluster described in this paper with the young
stellar cluster associated with the IRAS source 16177-5018, which is located at
the same distance and direction, shows that the mean visual absorption of the
newly discovered cluster is about 10 magnitudes smaller and it contains less
massive stars, suggesting that it was formed from a less massive molecular
cloud.


  Accretion is a common phenomenon associated with any astrophysical compact
object, which is best described by plasma, a state of matter composed of
electrons and heavy ions. In this paper, we analyze the linear dynamics of
electromagnetic (EM) fields propagating through the accreting plasma around a
static and spherically symmetric horizon-less, exotic compact object (ECO). The
general equations governing the propagation of EM waves in such a background
exhibits quasi-bound states, with a characteristic oscillation around the BH
values, for both the axial and the polar modes, as well as for homogeneous and
inhomogeneous plasma distributions. The amplitude of these oscillations depend
on the non-zero reflectivity of the surface of the compact object, while the
oscillation length depends on its compactness. This results into slower decay
of the quasi-bound states with time for certain parameter space of the plasma
frequency, compared to BHs, making these ECOs more prone to instabilities.


  In this paper we make the connection between semi-classical string
quantization and exact conformal field theory quantization of strings in 2+1
Anti de Sitter spacetime. More precisely, considering the WZWN model
corresponding to SL(2,R) and its covering group, we construct quantum {\it
coherent} string states, which generalize the ordinary coherent states of
quantum mechanics, and show that in the classical limit they correspond to
oscillating circular strings. After quantization, the spectrum is found to
consist of two parts: A continuous spectrum of low mass states (partly
tachyonic) fulfilling the standard spin-level condition necessary for unitarity
|j|< k/2, and a discrete spectrum of high mass states with asymptotic behaviour
m^2\alpha'\propto N^2 (N positive integer). The quantization condition for the
high mass states arises from the condition of finite positive norm of the
coherent string states, and the result agrees with our previous results
obtained using semi-classical quantization. In the k\to\infty limit, all the
usual properties of coherent or {\it quasi-classical} states are recovered. It
should be stressed that we consider the circular strings only for simplicity
and clarity, and that our construction can easily be used for other string
configurations too. We also compare our results with those obtained in the
recent preprint hep-th/0001053 by Maldacena and Ooguri.


  We show that a construction by Aanderaa and Cohen used in their proof of the
Higman Embedding Theorem preserves torsion length. We give a new construction
showing that every finitely presented group is the quotient of some $C'(1/6)$
finitely presented group by the subgroup generated by its torsion elements. We
use these results to show there is a finitely presented group with infinite
torsion length which is $C'(1/6)$, and thus word-hyperbolic and virtually
torsion-free.


  Telephone-cord patterns have been recently observed in smectic liquid crystal
capillaries. In this paper we analyse the effects that may induce them. As long
as the capillary keeps its linear shape, we show that a nonzero chiral
cholesteric pitch favors the SmA*-SmC* transition. However, neither the
cholesteric pitch nor the presence of an intrinsic bending stress are able to
give rise to a curved capillary shape.
  The key ingredient for the telephone-cord instability is spontaneous
polarization. The free energy minimizer of a spontaneously polarized SmA* is
attained on a planar capillary, characterized by a nonzero curvature. More
interestingly, in the SmC* phase the combined effect of the molecular tilt and
the spontaneous polarization pushes towards a helicoidal capillary shape, with
nonzero curvature and torsion.


  This paper presents our models for WNUT 2020 shared task2. The shared task2
involves identification of COVID-19 related informative tweets. We treat this
as binary text classification problem and experiment with pre-trained language
models. Our first model which is based on CT-BERT achieves F1-score of 88.7%
and second model which is an ensemble of CT-BERT, RoBERTa and SVM achieves
F1-score of 88.52%.


  We demonstrate an efficient method to engineer the quantum confinement in a
system of two quantum dots grown in a vertical stack. We achieve this by using
materials with a different lattice constant for the growth of the outer and
inner barriers. We monitor the resulting dot morphology with transmission
electron microscopy studies and correlate the results with ensemble quantum dot
photoluminescence. Furthermore, we embed the double quantum dots into diode
structures and study photoluminescence as a function of bias voltage. We show
that in properly engineered structures, it is possible to achieve a resonance
of the hole states by tuning the energy levels with electric field. At the
resonance, we observe signatures of a formation of a molecular state,
hybridized over the two dots.


  The elegant `no short hair' theorem states that, if a spherically-symmetric
static black hole has hair, then this hair must extend beyond 3/2 the horizon
radius. In the present paper we provide evidence for the failure of this
theorem beyond the regime of spherically-symmetric static black holes. In
particular, we show that rotating black holes can support extremely short-range
stationary scalar configurations (linearized scalar `clouds') in their exterior
regions. To that end, we solve analytically the Klein-Gordon-Kerr-Newman wave
equation for a linearized massive scalar field in the regime of large scalar
masses.


  MIRC-X is a six telescope beam combiner at the CHARA array that works in J
and H wavelength bands and provides an angular resolution equivalent to a
$B$=331m diameter telescope. The legacy MIRC combiner has delivered outstanding
results in the fields of stellar astrophysics and binaries. However, we
required higher sensitivity to make ambitious scientific measurements of faint
targets such as young stellar objects, binary systems with exoplanets, and
active galactic nuclei. For that purpose, MIRC-X is built and is offered to the
community since mid-2017. MIRC-X has demonstrated up to two magnitudes of
improved faint magnitude sensitivity with the best-case H <= 8. Here we present
a review of the instrument and present early science results, and highlight
some of our ongoing science programs.


  In the present paper, we consider two applications of the pentagon equation.
The first deals with actions of flips on edges of triangulations labelled by
rational functions in some variables. The second can be formulated as a system
of linear equations with variables corresponding to triangles of a
triangulation. The general method says that if there is some general {\em data}
(say, edge lengths or areas) associated with {\em states} (say, triangulations)
and a general {\em data transformation rule} (say, how lengths or areas are
changed under flips) then after returning to the initial state we recover the
initial data.


  We report on observations made with the Cosmic Origins Spectrograph (COS) on
the Hubble Space Telescope (HST) using background QSOs to probe the
circum-galactic medium (CGM) around 17 low-redshift galaxies that are
undergoing or have recently undergone a strong starburst (the COS-Burst
program). The sightlines extend out to roughly the virial radius of the galaxy
halo. We construct control samples of normal star-forming low-redshift galaxies
from the COS/HST archive that match the starbursts in terms of galaxy stellar
mass and impact parameter.
  We find clear evidence that the CGM around the starbursts differs
systematically compared to the control galaxies. The Ly$\alpha$, Si III, C IV,
and possibly O VI absorption-lines are stronger as a function of impact
parameter, and the ratios of the equivalent widths of C IV/Ly$\alpha$ and Si
III/Ly$\alpha$ are both larger than in normal star-forming galaxies. We also
find that the widths and the velocity offsets (relative to $v_{sys}$) of the
Ly$\alpha$ absorption-lines are significantly larger in the CGM of the
starbursts, implying velocities of the absorbing material that are roughly
twice the halo virial velocity.
  We show that these properties can be understood as a consequence of the
interaction between a starburst-driven wind and the pre-existing CGM. These
results underscore the importance of winds driven from intensely star-forming
galaxies in helping drive the evolution of galaxies and the intergalactic
medium. They also offer a new probe of the properties of starburst-driven winds
and of the CGM itself.


  We study the thin-shell conjecture for the Schatten classes. In particular,
we establish the conjecture for the operator norm; we also improve on the best
known bound for the Schatten classes, due to Barthe and Cordero-Erausquin [F.
Barthe and D. Cordero-Erausquin, "Invariances in variance estimates",
Proceedings of the London Mathematical Society 106 (2013): 33-64], for a few
more cases. Moreover, we show that a necessary condition for the conjecture to
be true for any of the Schatten classes is a rather strong negative correlation
property: this implies of course that, for the cases for which we already have
the conjecture (as for example for the operator norm), but in fact also for all
the cases for which we can get a better estimate than the one in [F. Barthe and
D. Cordero-Erausquin, "Invariances in variance estimates"], this negative
correlation property follows. For the proofs, our starting point is techniques
that were employed for the Schatten classes with regard to other problems in
[H. K\"onig, M. Meyer and A. Pajor, "The isotropy constants of the Schatten
classes are bounded", Mathematische Annalen 312 (1998): 773-783] and [O.
Gu\'edon and G. Paouris, "Concentration of mass on the Schatten classes",
Annales de l'Institut Henri Poincar\'e, Probabilit\'e et Statistiques 43
(2007): 87-99].


  Most recent measurements of open charm and beauty production in high energy
ep collisions at HERA are reviewed. The measurements explored the different
aspects of quantum chromodynamics involved in the process of heavy flavor
production. The results are compared with perturbative theoretical calculations
at next-to-leading order.


  Extrasolar debris disks are detected by observing dust, which is thought to
be released during planetesimal collisions. This implies that planetesimals are
dynamically excited ("stirred"), such that collisions are sufficiently common
and violent. The most frequently considered stirring mechanisms are
self-stirring by disk self-gravity, and planet-stirring via secular
interactions. However, these models face problems when considering disk mass,
self-gravity, and planet eccentricity, leading to the possibility that other,
unexplored mechanisms instead stir debris. We hypothesize that planet-stirring
could be more efficient than the traditional secular model implies, due to two
additional mechanisms. First, a planet at the inner edge of a debris disk can
scatter massive bodies onto eccentric, disk-crossing orbits, which then excite
debris ("projectile stirring"). Second, a planet can stir debris over a wide
region via broad mean-motion resonances, both at and between nominal resonance
locations ("resonant stirring"). Both mechanisms can be effective even for
low-eccentricity planets, unlike secular-planet-stirring. We run N-body
simulations across a broad parameter space, to determine the viability of these
new stirring mechanisms. We quantify stirring levels using a bespoke program
for assessing Rebound debris simulations, which we make publicly available. We
find that even low-mass projectiles can stir disks, and verify this with a
simple analytic criterion. We also show that resonant stirring is effective for
planets above ~0.5 MJup. By proving that these mechanisms can increase
planet-stirring efficiency, we demonstrate that planets could still be stirring
debris disks even in cases where conventional (secular) planet-stirring is
insufficient.


  We perform the momentum-space quantization of a spin-less particle moving on
the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by
using a non-canonical method entirely based on symmetry grounds. To achieve
this task, non-standard (contact) symmetries are required as already shown in a
previous article where the configuration-space quantization was given. The
Hilbert space in the momentum space representation turns out to be made of a
subset of (oscillatory) solutions of the Helmholtz equation in four dimensions.
The most relevant result is the fact that both the scalar product and the
generalized Fourier transform between configuration and momentum spaces deviate
notably from the naively expected expressions, the former exhibiting now a
non-trivial kernel, under a double integral, traced back to the non-trivial
topology of the phase space, even though the momentum space as such is flat. In
addition, momentum space itself appears directly as the carrier space of an
irreducible representation of the symmetry group, and the Fourier transform as
the unitary equivalence between two unitary irreducible representations.


  The Nagel-Schreckenberg model is a simple cellular automaton for a realistic
description of single-lane traffic on highways. For the case $v_{max}=1$ the
properties of the stationary state can be obtained exactly. For the more
relevant case $v_{max}>1$, however, one has to rely on Monte Carlo simulations
or approximative methods. Here we study several analytical approximations and
compare with the results of computer simulations. The role of the braking
parameter $p$ is emphasized. It is shown how the local structure of the
stationary state depends on the value of $p$. This is done by combining the
results of computer simulations with those of the approximative methods.


  We study the Higgs boson $(h)$ decay to two light jets at the 14 TeV
High-Luminosity-LHC (HL-LHC), where a light jet ($j$) represents any non-flavor
tagged jet from the observational point of view. The decay mode $h\to gg$ is
chosen as the benchmark since it is the dominant channel in the Standard Model
(SM), but the bound obtained is also applicable to the light quarks
$(j=u,d,s)$. We estimate the achievable bounds on the decay branching fractions
through the associated production $Vh\ (V=W^\pm,Z)$. Events of the Higgs boson
decaying into heavy (tagged) or light (un-tagged) jets are correlatively
analyzed. We find that with 3000 fb$^{-1}$ data at the HL-LHC, we should expect
approximately $1\sigma$ statistical significance on the SM $Vh(gg)$ signal in
this channel. This corresponds to a reachable upper bound ${\rm BR}(h\to jj)
\leq 4~ {\rm BR}^{SM}(h\to gg)$ at $95\%$ confidence level. A consistency fit
also leads to an upper bound ${\rm BR}(h\to cc) < 15~ {\rm BR}^{SM}(h\to cc)$
at $95\%$ confidence level. The estimated bound may be further strengthened by
adopting multiple variable analyses, or adding other production channels.


  We refine Cohen and Lustig's description of centralisers of Dehn twists of
free groups. We show that the centraliser of a Dehn twist of a free group has a
subgroup of finite index that has a finite classifying space. We describe an
algorithm to find a presentation of the centraliser. We use this algorithm to
give an explicit presentation for the centraliser of a Nielsen automorphism in
Aut(F_n). This gives restrictions to actions of Aut(F_n) on CAT(0) spaces.


  We investigate first-passage statistics of an ensemble of N noninteracting
random walks on a line. Starting from a configuration in which all particles
are located in the positive half-line, we study S_n(t), the probability that
the nth rightmost particle remains in the positive half-line up to time t. This
quantity decays algebraically, S_n (t) ~ t^{-beta_n}, in the long-time limit.
Interestingly, there is a family of nontrivial first-passage exponents,
beta_1<beta_2<...<beta_{N-1}; the only exception is the two-particle case where
beta_1=1/3. In the N-->infinity limit, however, the exponents attain a scaling
form, beta_n(N)--> beta(z) with z=(n-N/2)/sqrt{N}. We also demonstrate that the
smallest exponent decays exponentially with N. We deduce these results from
first-passage kinetics of a random walk in an N-dimensional cone and confirm
them using numerical simulations. Additionally, we investigate the family of
exponents that characterizes leadership statistics of multiple random walks and
find that in this case, the cone provides an excellent approximation.


  Realizing axion insulator state with a uniform magnetization considerably
facilitates experimental explorations of the intriguing topological
magnetoelectric effect, a hallmark of three-dimensional (3D) topological
insulators (TIs). Through density functional theory calculations and four-band
model studies, we find that magnetic ions Cr3+ in monolayer CrI3 and Mn2+ in
septuple-layer MnBi2Se4 have opposite exchange couplings to the topological
surface states of 3D TI Bi2Se3. As an exciting result of such opposite exchange
couplings, axion insulator state is realized by a uniform magnetization in
CrI3/Bi2Se3/MnBi2Se4 heterostructure. Our work opens up opportunities for
exploring topological magnetoelectric effect realized by the uniform
magnetization induced axion insulator state in heterostructures of 3D TIs and
two-dimensional van der Waals ferromagnetic insulators.


  We study the dynamics of finite-gap solutions in classical string theory on R
x S^3. Each solution is characterised by a spectral curve, \Sigma, of genus g
and a divisor, \gamma, of degree g on the curve. We present a complete
reconstruction of the general solution and identify the corresponding
moduli-space, M^(2g)_R, as a real symplectic manifold of dimension 2g. The
dynamics of the general solution is shown to be equivalent to a specific
Hamiltonian integrable system with phase-space M^(2g)_R. The resulting
description resembles the free motion of a rigid string on the Jacobian torus
J(\Sigma). Interestingly, the canonically-normalised action variables of the
integrable system are identified with certain filling fractions which play an
important role in the context of the AdS/CFT correspondence.


  We consider some long multiplets describing bulk massive excitations of
M-theory two-branes and IIB string three-branes which correspond to ``non
chiral'' primary operators of the boundary OSp(8/4) and SU(2,2/4)
superconformal field theories. Examples of such multiplets are the ``radial''
modes on the branes, including up to spin 4 excitations, which may be then
considered as prototypes of states which are not described by the K-K spectrum
of the corresponding supergravity theories on AdS_4 x S_7 and AdS_5 x S_5
respectively.


  The recent progress in the optimization of two-dimensional tensor networks
[H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X ${\bf 9}$, 031041
(2019)] based on automatic differentiation opened the way towards precise and
fast optimization of such states and, in particular, infinite projected
entangled-pair states (iPEPS) that constitute a generic-purpose ${\it Ansatz}$
for lattice problems governed by local Hamiltonians. In this work, we perform
an extensive study of a paradigmatic model of frustrated magnetism, the
$J_1-J_2$ Heisenberg antiferromagnet on the square lattice. By using advances
in both optimization and subsequent data analysis, through finite
correlation-length scaling, we report accurate estimations of the magnetization
curve in the N\'eel phase for $J_2/J_1 \le 0.45$. The unrestricted iPEPS
simulations reveal an $U(1)$ symmetric structure, which we identify and impose
on tensors, resulting in a clean and consistent picture of antiferromagnetic
order vanishing at the phase transition with a quantum paramagnet at $J_2/J_1
\approx 0.46(1)$. The present methodology can be extended beyond this model to
study generic order-to-disorder transitions in magnetic systems.


  Temperature is a major source of inaccuracy in high-sensitivity
accelerometers and gravimeters. Active thermal control systems require power
and may not be ideal in some contexts such as airborne or spaceborne
applications. We propose a solution that relies on multiple thermometers placed
within the accelerometer to measure temperature and thermal gradient
variations. Machine Learning algorithms are used to relate the temperatures to
their effect on the accelerometer readings. However, obtaining labeled data for
training these algorithms can be difficult. Therefore, we also developed a
training platform capable of replicating temperature variations in a laboratory
setting. Our experiments revealed that thermal gradients had a significant
effect on accelerometer readings, emphasizing the importance of multiple
thermometers. The proposed method was experimentally tested and revealed a
great potential to be extended to other sources of inaccuracy, such as
rotations, as well as to other types of measuring systems, such as
magnetometers or gyroscopes.


  We discuss the thermal and magnetic entanglement in the one-dimensional Kondo
necklace model. Firstly, we show how the entanglement naturally present at zero
temperature is distributed among pairs of spins according to the strength of
the two couplings of the chain, namely, the Kondo exchange interaction and the
hopping energy. The effect of the temperature and the presence of an external
magnetic field is then investigated, being discussed the adjustment of these
variables in order to control the entanglement available in the system. In
particular, it is indicated the existence of a critical magnetic field above
which the entanglement undergoes a sharp variation, leading the ground state to
a completely unentangled phase.


  We describe phase-retrieval holography measurements of the 100-m diameter
Green Bank Telescope using astronomical sources and an astronomical receiver
operating at a wavelength of 7 mm. We use the technique with parameterization
of the aperture in terms of Zernike polynomials and employing a large defocus,
as described by Nikolic, Hills & Richer (2006). Individual measurements take
around 25 minutes and from the resulting beam maps (which have peak signal to
noise ratios of 200:1) we show that it is possible to produce low-resolution
maps of the wavefront errors with accuracy around a hundredth of a wavelength.
  Using such measurements over a wide range of elevations, we have calculated a
model for the wavefront-errors due to the uncompensated gravitational
deformation of the telescope. This model produces a significant improvement at
low elevations, where these errors are expected to be the largest; after
applying the model, the aperture efficiency is largely independent of
elevation. We have also demonstrated that the technique can be used to measure
and largely correct for thermal deformations of the antenna, which often exceed
the uncompensated gravitational deformations during daytime observing.
  We conclude that the aberrations induced by gravity and thermal effects are
large-scale and the technique used here is particularly suitable for measuring
such deformations in large millimetre wave radio telescopes.


  In set theory without the axiom of regularity, we consider a game in which
two players choose in turn an element of a given set, an element of this
element, etc.; a player wins if its adversary cannot make any next move. Sets
that are winning, i.e. have a winning strategy for a player, form a natural
hierarchy with levels indexed by ordinals. We show that the class of
hereditarily winning sets is an inner model containing all well-founded sets,
and that all four possible relationships between the universe, the class of
hereditarily winning sets, and the class of well-founded sets are consistent.
We describe classes of ordinals for which it is consistent that winning sets
without minimal elements are exactly in the levels indexed by ordinals of this
class. For consistency results, we propose a new method for getting
non-well-founded models. Finally, we establish a probability result by showing
that on hereditarily finite well-founded sets the first player wins almost
always.


  In this work we report the results concerning calculations for
quantum-mechanical rotational transitions in molecular hydrogen, H$_2$, induced
by an ultra-cold ground state anti-hydrogen atom $\bar{H}_{1s}$. The
calculations are accomplished using a non-reactive close-coupling
quantum-mechanical approach. The H$_2$ molecule is treated as a rigid rotor.
The total elastic scattering cross section $\sigma_{el}(\epsilon)$ at energy
$\epsilon$, state-resolved rotational transition cross sections
$\sigma_{jj'}(\epsilon)$ between states $j$ and $j'$ and corresponding thermal
rate coefficients $k_{jj'}(T)$ are computed in the temperature range 0.004 K $
\lesssim T \lesssim$ 4 K. Satisfactory agreement with other calculations
(variational) has been obtained for $\sigma_{el}(\epsilon)$.


  The PDPTW is an optimization vehicles routing problem which must meet
requests for transport between suppliers and customers satisfying precedence,
capacity and time constraints. We present, in this paper, a genetic algorithm
for optimization of a multi pickup and delivery problem with time windows
(m-PDPTW). We purposes a brief literature review of the PDPTW, present an
approach based on genetic algorithms to give a satisfying solution to the
m-PDPTW minimizing the total travel cost.


  We derive two-sided bounds for expected values of suprema of canonical
processes based on random variables with moments growing regularly. We also
discuss a Sudakov-type minoration principle for canonical processes.


  Gabriel F. Calvo and Antonio Picon defined a class of operators, for use in
quantum communication, that allows arbitrary manipulations of the three lowest
two-dimensional Hermite-Gaussian modes {|0,0>,|1,0>,|0,1>}. Our paper continues
the study of those operators, and our results fall into two categories. For
one, we show that the generators of the operators have infinite deficiency
indices, and we explicitly describe all self-adjoint realizations. And secondly
we investigate semiclassical approximations of the propagators. The basic
method is to start from a semiclassical Fourier integral operator ansatz and
then construct approximate solutions of the corresponding evolution equations.
In doing so, we give a complete description of the Hamilton flow, which in most
cases is given by elliptic functions. We find that the semiclassical
approximation behaves well when acting on sufficiently localized initial
conditions, for example, finite sums of semiclassical Hermite-Gaussian modes,
since near the origin the Hamilton trajectories trace out the bounded
components of elliptic curves.


  The Casimir effect, arising from vacuum quantum fluctuations, plays a
fundamental role in the development of modern quantum electrodynamics. In
parallel, the field of condensed matter has flourished through the discovery of
various materials exhibiting broken symmetries, often connected to topology and
characterized by magneto-electric coupling. Here, we calculate the Casimir
forces between materials with time-reversal symmetry and/or parity symmetry
breaking. Remarkably, we obtain a universal phase diagram governing the sign of
symmetry-breaking-induced Casimir forces, contributing to a comprehensive
understanding on the sign of Casimir force for linear optical materials. The
discovered phase diagram serves as a roadmap for searching repulsive Casimir
forces, a subject bearing both theoretical interest and practical significance.


  Network coding has the potential to improve the overall throughput of a
network by combining different streams of data and forwarding them. In wireless
networks, the wireless channel provide an excellent medium for physical layer
network coding as signals from different transmitters are combined
automatically by the wireless channel. In such scenarios, it would be
interesting to investigate protocols and algorithms which can optimally relay
information. In this paper, we look at a four-node two-way or bidirectional
relay network, and propose a relay protocol which can relay information
efficiently in this network.


  In the continuation of a preceding work, we derive a new expression for the
metric in the near zone of an isolated matter system in post-Newtonian
approximations of general relativity. The post-Newtonian metric, a solution of
the field equations in harmonic coordinates, is formally valid up to any order,
and is cast in the form of a particular solution of the wave equation, plus a
specific homogeneous solution which ensures the asymptotic matching to the
multipolar expansion of the gravitational field in the exterior of the system.
The new form provides some insights on the structure of the post-Newtonian
expansion in general relativity and the gravitational radiation reaction terms
therein.


  In this article, we study an almost contact metric structure on a
$G_2$-manifold constructed by Arikan, Cho and Salur in via the classification
of almost contact metric structures given by Chinea and Gonzalez. In
particular, we characterize when this almost contact metric structure is
cosymplectic and narrow down the possible classes in which this almost contact
metric structure could lie. Finally, we show that any closed $G_2$-manifold
admits an almost contact metric $3$-structure by constructing it explicitly and
characterize when this almost contact metric $3$-structure is $3$-cosymplectic.


  Sgr A* is the unique 1 Jy flat spectrum radio point source located at the
dynamical center of the Galaxy and in the very center of the central star
cluster. Due to its unusual appearance it has long been speculated that this
source is powered by a supermassive black hole. The enormous increase in
observational data obtained for Sgr A* in recent years has enabled us to
develop, compare and constrain a variety of models for the emission
characteristics of this source. Because of its relative proximity and further
observational input to come Sgr A* may therefore become one of the best
laboratories for studying supermassive black hole candidates and basic AGN
physics. This paper briefly summarizes our current understanding of this
enigmatic radio source and compares various models, i.e. disk/jet and
wind-accretion models.


  Vertical convection is the fluid motion that is induced by the heating and
cooling of two opposed vertical boundaries of a rectangular cavity (see e.g.
Wang et al. 2021). We consider the linear stability of the steady
two-dimensional flow reached at Rayleigh numbers of O($10^8$).
  As a function of the Prandtl number, $Pr$, and the height-to-width aspect
ratio of the domain, $A$, the base flow of each case is computed numerically
and linear simulations are used to obtain the properties of the leading linear
instability mode. Flow regimes depend on the presence of a circulation in the
entire cavity, detachment of the thermal layer from the boundary or the corner
regions, and on the oscillation frequency relative to the natural frequency of
oscillation in the stably temperature-stratified interior, allowing for the
presence of internal waves or not. Accordingly the regime is called slow or
fast, respectively. Either the global circulation or internal waves in the
interior may couple the top and bottom buoyancy currents, while their absence
implies asymmetry in their perturbation amplitude.
  Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq
A \leq 2$. For $Pr \lessapprox 0.4 $ and $A>1$ the base flow is driven by a
large circulation in the entire cavity. For $Pr \gtrapprox 0.7$ the thermal
boundary layers are thin and the instability is driven by the motion along the
wall and the detached boundary layer. A transition between these regimes is
marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm0.15$ and
$A <2$.


  Geometry of relativistic jets in active galaxies provides important
information about mechanisms of launching, collimation and acceleration of
plasma flow. We propose a new method to probe a boundary shape of a jet on
parsec scales -- in the vicinity of its radio core. Apparent speed of an
outflow is derived from variability time delays and core shifts measured at the
same jet region, providing a self-consistent estimate of the Lorentz factor
$\Gamma$. We link together the distance along the jet $z$ with its transverse
size assuming a constant flow acceleration. Our results indicate that jets have
parabolic shape and sustain an effective acceleration in the core region,
consistent with the Lorentz factor dependency $\Gamma\propto z^{0.5}$. The
proposed method can be applied to the sources observed at small viewing angles
as well as to the distant sources when direct measurements are impossible due
to a limited angular resolution.


  The ANTAREX project relies on a Domain Specific Language (DSL) based on
Aspect Oriented Programming (AOP) concepts to allow applications to enforce
extra functional properties such as energy-efficiency and performance and to
optimize Quality of Service (QoS) in an adaptive way. The DSL approach allows
the definition of energy-efficiency, performance, and adaptivity strategies as
well as their enforcement at runtime through application autotuning and
resource and power management. In this paper, we present an overview of the key
outcome of the project, the ANTAREX DSL, and some of its capabilities through a
number of examples, including how the DSL is applied in the context of the
project use cases.


  High-accuracy microwave sensing is widely demanded in various fields, ranging
from cosmology to microwave quantum technology. Quantum receivers based on
inorganic solid-state spin systems are promising candidates for such purpose
because of the stability and compatibility, but their best sensitivity is
currently limited to a few pT/$\sqrt{\rm{Hz}}$. Here, by utilising an enhanced
readout scheme with the state-of-the-art solid-state maser technology, we
develop a robust microwave quantum receiver functioned by organic molecular
spins at ambient conditions. Owing to the maser amplification, the sensitivity
of the receiver achieves 6.14 $\pm$ 0.17 fT/$\sqrt{\rm{Hz}}$ which exceeds
three orders of magnitude than that of the inorganic solid-state quantum
receivers. The heterodyne detection without additional local oscillators
improves bandwidth of the receiver and allows frequency detection. The scheme
can be extended to other solid-state spin systems without complicated control
pulses and thus enables practical applications such as electron spin resonance
spectroscopy, dark matter searches, and astronomical observations.


  We present a reflexive Banach space with an unconditional basis which is
quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list
within the framework of Gowers' classification program of Banach spaces, but
contrary to the recently constructed space of type (4) also tight with
constants, thus essentially extending the list of known examples in Gowers
classification program. The space is defined on the base on a boundedly
modified mixed Tsirelson space with use of a special coding function.


  Nowadays much is written about how to manage projects, but too little on what
really happens in project actuality. Project Actuality came out in the
Rethinking Project Management (RPM) agenda in 2006 and it aims at understanding
what really happens at project context. To be able to understand project
actuality phenomenon, we first need to get a better comprehension on its
definition and discover how to observe it and analyse it. This paper presents
the results of the systematic review conducted to collect evidence on Project
Actuality. The research focused on four search engines, in publications from
1994 to 2013. Among others, the study concludes that project actuality has been
analysed by several methods and techniques, mostly on large organization and
public sectors, in Northern Europe. The most common definitions, techniques,
and tips were identified as well as the intent of transforming the results in
knowledge.


  The microstructure of a second-generation nickel base superalloy is studied
using X-ray computed tomography (XCT) and scanning electron microscopy (SEM).
The as-cast material contains 0.15 (+-0.001) vol% voids and these are
distributed in the inter-dendritic region. The volume fraction of the voids
increases to 0.21 (+-0.001) vol% after tensile deformation. Surface
observations show evidence of dislocation emissions from the void surface, a
mechanism possibly facilitates the expansion of the voids and contributes to
the increased void volume fraction. Phenomenological parameters such as stress
triaxiality, often believed to control void growth, are investigated through
crystal plasticity simulation and compared with literature reported data. The
results indicate weak correlation between stress triaxiality and void growth,
but this may be possibly due to the lack of data at higher level of plastic
deformation, which is limited by the ductility of the material. The
distribution of the stress triaxiality field within the sample is heterogeneous
and the peak of the triaxiality field is a function of the ratio between notch
diameter and sample width. A smaller notch diameter to sample width ratio tend
to distribute the triaxiality peaks towards the centre of the sample but also
lead to higher strain localisation, an effect that results in early sample
failure.


  We consider the problem of identifying people on the basis of their walk
(gait) pattern. Classical approaches to tackle this problem are based on, e.g.,
video recordings or piezoelectric sensors embedded in the floor. In this work,
we rely on acoustic and vibration measurements, obtained from a microphone and
a geophone sensor, respectively. The contribution of this work is twofold.
First, we propose a feature extraction method based on an (untrained) shallow
scattering network, specially tailored for the gait signals. Second, we
demonstrate that fusing the two modalities improves identification in the
practically relevant open set scenario.


  Let p be an odd prime and let P be a p-group. We examine the order complex of
the poset of elementary abelian subgroups of P having order at least p^2. S.
Bouc and J. Th\'evenaz showed that this complex has the homotopy type of a
wedge of spheres. We show that, for each nonnegative integer l, the number of
spheres of dimension l in this wedge is controlled by the number of
extraspecial subgroups X of P having order p^{2l+3} and satisfying
Omega_1(C_P(X))=Z(X). We go on to provide a negative answer to a question
raised by Bouc and Th\'evenaz concerning restrictions on the homology groups of
the given complex.


  Diffusion models have the ability to generate high quality images by
denoising pure Gaussian noise images. While previous research has primarily
focused on improving the control of image generation through adjusting the
denoising process, we propose a novel direction of manipulating the initial
noise to control the generated image. Through experiments on stable diffusion,
we show that blocks of pixels in the initial latent images have a preference
for generating specific content, and that modifying these blocks can
significantly influence the generated image. In particular, we show that
modifying a part of the initial image affects the corresponding region of the
generated image while leaving other regions unaffected, which is useful for
repainting tasks. Furthermore, we find that the generation preferences of pixel
blocks are primarily determined by their values, rather than their position. By
moving pixel blocks with a tendency to generate user-desired content to
user-specified regions, our approach achieves state-of-the-art performance in
layout-to-image generation. Our results highlight the flexibility and power of
initial image manipulation in controlling the generated image.


  We study the dynamics of a quantum superconducting circuit which consists of
a Josephson charge qubit, coupled capacitively to a current biased Josephson
junction. Under certain conditions, the eigenstates of the qubit and the
junction become entangled. We obtain the time evolution of these states in the
limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous
emission and re-absorption of a single oscillation quantum in the junction. We
discuss a possible way to experimentally determine the quantum state of the
junction and hence observe the Rabi oscillations.


  We analyze theoretically the propagation of surface plasmon polaritons about
a metallic corner with a finite bend radius, using a one-dimensional model
analogous to the scattering from a finite-depth potential well. We obtain
expressions for the energy reflection and transmission coefficients in the
short wavelength limit, as well as an upper bound for the transmittance. In
certain cases we find that propagation on non-planar interfaces may result in
lower losses than on flat surfaces, contrary to expectation. In addition, we
also find that the maximum transmittance depends non-monotonously on the bend
radius, allowing increased transmission with decreasing radius.


  So far, Brillouin scattering and cavity optomechanics were mostly
disconnected branches of research -- although both deal with photon-phonon
coupling. This begs for the development of a broader theory that contains both
fields. Here, we derive the dynamics of optomechanical cavities from that of
Brillouin-active waveguides. This explicit transition elucidates the link
between phenomena such as Brillouin amplification and electromagnetically
induced transparency. It proves that effects familiar from cavity optomechanics
all have traveling-wave partners, but not vice versa. We reveal a close
connection between two parameters of central importance in these fields: the
Brillouin gain coefficient and the zero-point optomechanical coupling rate.
This enables comparisons between systems as diverse as ultracold atom clouds,
plasmonic Raman cavities and nanoscale silicon waveguides. In addition,
back-of-the-envelope calculations show that unobserved effects, such as
photon-assisted amplification of traveling phonons, are now accessible in
existing systems. Finally, we formulate both circuit- and cavity-oriented
optomechanics in terms of vacuum coupling rates, cooperativities and gain
coefficients, thus reflecting the similarities in the underlying physics.


  In past work (Onokpasa, Wild, Wong, DCC 2023), we showed that (a) for joint
compression of RNA sequence and structure, stochastic context-free grammars are
the best known compressors and (b) that grammars which have better compression
ability also show better performance in ab initio structure prediction.
Previous grammars were manually curated by human experts. In this work, we
develop a framework for automatic and systematic search algorithms for
stochastic grammars with better compression (and prediction) ability for RNA.
We perform an exhaustive search of small grammars and identify grammars that
surpass the performance of human-expert grammars.


  Monte Carlo Tree Search (MCTS) is a best-first sampling method employed in
the search for optimal decisions. The effectiveness of MCTS relies on the
construction of its statistical tree, with the selection policy playing a
crucial role. A selection policy that works particularly well in MCTS is the
Upper Confidence Bounds for Trees, referred to as UCT. The research community
has also put forth more sophisticated bounds aimed at enhancing MCTS
performance on specific problem domains. Thus, while MCTS UCT generally
performs well, there may be variants that outperform it. This has led to
various efforts to evolve selection policies for use in MCTS. While all of
these previous works are inspiring, none have undertaken an in-depth analysis
to shed light on the circumstances in which an evolved alternative to MCTS UCT
might prove advantageous. Most of these studies have focused on a single type
of problem. In sharp contrast, this work explores the use of five functions of
different natures, ranging from unimodal to multimodal and deceptive functions.
We illustrate how the evolution of MCTS UCT can yield benefits in multimodal
and deceptive scenarios, whereas MCTS UCT is robust in all of the functions
used in this work.


  Several recent studies have shown that very wide binary stars can potentially
provide an interesting test for modified-gravity theories which attempt to
emulate dark matter; these systems should be almost Newtonian according to
standard dark-matter theories, while the predictions for MOND-like theories are
distinctly different, if the various observational issues can be overcome. Here
we explore an observational application of the test from the recent GAIA DR2
data release: we select a large sample of $\sim 24,000$ candidate wide binary
stars with distance $< 200$ parsec and magnitudes $G < 16$ from GAIA DR2, and
estimated component masses using a main-sequence mass-luminosity relation. We
then compare the frequency distribution of pairwise relative projected velocity
(relative to circular-orbit value) as a function of projected separation; these
distributions show a clear peak at a value close to Newtonian expectations,
along with a long `tail' which extends to much larger velocity ratios; the
`tail' is considerably more numerous than in control samples constructed from
DR2 with randomised positions, so its origin is unclear. Comparing the velocity
histograms with simulated data, we conclude that MOND-like theories without an
external field effect are strongly inconsistent with the observed data since
they predict a peak-shift in clear disagreement with the data; testing
MOND-like theories with an external field effect is not decisive at present,
but has good prospects to become decisive in future with improved modelling or
understanding of the high-velocity tail, and additional spectroscopic data.


  Rapid emergence of the multimodal imaging in scanning probe, electron, and
optical microscopies have brought forth the challenge of understanding the
information contained in these complex data sets, targeting both the intrinsic
correlations between different channels and further exploring the underpinning
causal physical mechanisms. Here, we develop such analysis framework for the
Piezoresponse Force Microscopy. We argue that under certain conditions, we can
bootstrap experimental observations with the prior knowledge of materials
structure to get information on certain non-observed properties, and
demonstrate linear causal analysis for PFM observables. We further demonstrate
that this approach can be extended to complex descriptors using the deep kernel
learning (DKL) model. In this DKL analysis, we use the prior information on
domain structure within the image to predict the physical properties. This
analysis demonstrates the correlative relationships between morphology,
piezoresponse, elastic property, etc. at nanoscale. The prediction of
morphology and other physical parameters illustrates a mutual interaction
between surface condition and physical properties in ferroelectric materials.
This analysis is universal and can be extended to explore the correlative
relationships of other multi-channel datasets.


  Irreducible Artin groups of finite type can be parametrized via their
associated Coxeter diagrams into six sporadic examples and four infinite
families, each of which is further parametrized by the natural numbers. Within
each of these four infinite families, we investigate the relationship between
elementary equivalence and isomorphism. For three out of the four families, we
show that two groups in the same family are equivalent if and only if they are
isomorphic; a positive, but weaker, result is also attained for the fourth
family. In particular, we show that two braid groups are elementarily
equivalent if and only if they are isomorphic.
  As a consequence of our work, we prove that there are infinitely many
elementary equivalence classes of irreducible Artin groups of finite type. We
also show that mapping class groups of closed surfaces - a geometric analogue
of braid groups - are elementarily equivalent if and only if they are
isomorphic.


  Without positional information, attention-based Transformer neural networks
are permutation-invariant. Absolute or relative positional embeddings are the
most popular ways to feed Transformer models with positional information.
Absolute positional embeddings are simple to implement, but suffer from
generalization issues when evaluating on sequences longer than seen at training
time. Relative positions are more robust to input length change, but are more
complex to implement and yield inferior model throughput due to extra
computational and memory costs. In this paper, we propose an augmentation-based
approach (CAPE) for absolute positional embeddings, which keeps the advantages
of both absolute (simplicity and speed) and relative positional embeddings
(better generalization). In addition, our empirical evaluation on
state-of-the-art models in machine translation, image and speech recognition
demonstrates that CAPE leads to better generalization performance as well as
increased stability with respect to training hyper-parameters.


  It is currently believed that the ``standard'' accretion disk theory
under-predicts the observed X-ray luminosity from Soft X-ray Transients (SXT)
in quiescence by as much as 4 to 6 orders of magnitude. This failure of the
standard model is considered to be an important argument for the existence of
the alternative mode of accretion -- Advection Dominated Accretion Flows (ADAF)
in astrophysics, since these flows allow a much higher level of X-ray emission
in quiescence, in agreement with the observations. Here we point out that, in
stark contrast to steady-state standard disks, such disks in quiescence (being
non-steady) produce most of the X-ray emission very far from the last stable
orbit. Taking this into account, these disks can accommodate the observed X-ray
luminosities of SXTs rather naturally. Our theory predicts that Fe K-alpha
lines from standard accretion disks in quiescence should be narrow even though
the cold disk goes all the way down to the last stable orbit.


  The one parameter family of Jack(alpha) measures on partitions is an
important discrete analog of Dyson's beta ensembles of random matrix theory.
Except for special values of alpha=1/2,1,2 which have group theoretic
interpretations, the Jack(alpha) measure has been difficult if not intractable
to analyze. This paper proves a central limit theorem (with an error term) for
Jack(alpha) measure which works for arbitrary values of alpha. For alpha=1 we
recover a known central limit theorem on the distribution of character ratios
of random representations of the symmetric group on transpositions. The case
alpha=2 gives a new central limit theorem for random spherical functions of a
Gelfand pair. The proof uses Stein's method and has interesting ingredients: an
intruiging construction of an exchangeable pair, properties of Jack
polynomials, and work of Hanlon relating Jack polynomials to the Metropolis
algorithm.


  There is a recent surge in the development of spatio-temporal forecasting
models in the transportation domain. Long-range traffic forecasting, however,
remains a challenging task due to the intricate and extensive spatio-temporal
correlations observed in traffic networks. Current works primarily rely on road
networks with graph structures and learn representations using graph neural
networks (GNNs), but this approach suffers from over-smoothing problem in deep
architectures. To tackle this problem, recent methods introduced the
combination of GNNs with residual connections or neural ordinary differential
equations (ODE). However, current graph ODE models face two key limitations in
feature extraction: (1) they lean towards global temporal patterns, overlooking
local patterns that are important for unexpected events; and (2) they lack
dynamic semantic edges in their architectural design. In this paper, we propose
a novel architecture called Graph-based Multi-ODE Neural Networks (GRAM-ODE)
which is designed with multiple connective ODE-GNN modules to learn better
representations by capturing different views of complex local and global
dynamic spatio-temporal dependencies. We also add some techniques like shared
weights and divergence constraints into the intermediate layers of distinct
ODE-GNN modules to further improve their communication towards the forecasting
task. Our extensive set of experiments conducted on six real-world datasets
demonstrate the superior performance of GRAM-ODE compared with state-of-the-art
baselines as well as the contribution of different components to the overall
performance. The code is available at https://github.com/zbliu98/GRAM-ODE


  Continuous-variable quantum key distribution (CV-QKD) has many practical
advantages including compatibility with current optical communication
technology. Implementation using heterodyne measurements is particularly
attractive since it eliminates the need for active phase locking of the remote
pair of local oscillators, but the full security of CV QKD with discrete
modulation was only proved for a protocol using homodyne measurements. Here we
propose an all-heterodyne CV-QKD protocol with binary modulation and prove its
security against general attacks in the finite-key regime. Although replacing a
homodyne measurement with a heterodyne measurement would be naively expected to
incur a 3-dB penalty in the rate-distance curve, our proof achieves a key rate
with only a 1-dB penalty.


  Score tests have the advantage of requiring estimation alone of the model
restricted by the null hypothesis, which often is much simpler than models
defined under the alternative hypothesis. This is typically so when the
alternative hypothesis involves inequality constraints. However, existing score
tests address only jointly testing all parameters of interest; a leading
example is testing all ARCH parameters or variances of random coefficients
being zero or not. In such testing problems rejection of the null hypothesis
does not provide evidence on rejection of specific elements of parameter of
interest. This paper proposes a class of one-sided score tests for testing a
model parameter that is subject to inequality constraints. Proposed tests are
constructed based on the minimum of a set of $p$-values. The minimand includes
the $p$-values for testing individual elements of parameter of interest using
individual scores. It may be extended to include a $p$-value of existing score
tests. We show that our tests perform better than/or perform as good as
existing score tests in terms of joint testing, and has furthermore the added
benefit of allowing for simultaneously testing individual elements of parameter
of interest. The added benefit is appealing in the sense that it can identify a
model without estimating it. We illustrate our tests in linear regression
models, ARCH and random coefficient models. A detailed simulation study is
provided to examine the finite sample performance of the proposed tests and we
find that our tests perform well as expected.


  Shock wave reflection from a rigid wall has been thoroughly studied in the
Newtonian limit, simplifying the problem by analyzing it in a steady-state
frame, $S'$, where the point $P$ of the shock's intersection with the wall is
at rest. However, a "super-luminal" regime emerges when the velocity of point
$P$ ($v_p$) exceeds the speed of light ($v_p>c$), where no steady-state frame
$S'$ exists. It occurs predominantly in the relativistic regime, relevant in
astrophysics, where it encompasses nearly all of the shock incidence angles. To
study this regime, we introduce a new approach. We formulate integral
conservation laws in the lab frame $S$ (where the unshocked fluid is at rest)
for regular reflection (RR), using two methods: a. fixed volume analysis and b.
fixed fluid analysis. We show the equivalence between the two methods, and also
to the steady-state oblique shock jump conditions in frame $S'$ in the
sub-luminal regime ($v_p<c$). Applying this framework, we find that both the
weak and strong shock RR solutions are bounded in the parameter space by the
detachment line on the higher incidence angles side. The strong shock solution
is also bounded by the luminal line on the lower incidence angles side, and
exists only between these two critical lines, in the sub-luminal attachment
region.


  We show that the way inference is performed in few-shot segmentation tasks
has a substantial effect on performances -- an aspect often overlooked in the
literature in favor of the meta-learning paradigm. We introduce a transductive
inference for a given query image, leveraging the statistics of its unlabeled
pixels, by optimizing a new loss containing three complementary terms: i) the
cross-entropy on the labeled support pixels; ii) the Shannon entropy of the
posteriors on the unlabeled query-image pixels; and iii) a global KL-divergence
regularizer based on the proportion of the predicted foreground. As our
inference uses a simple linear classifier of the extracted features, its
computational load is comparable to inductive inference and can be used on top
of any base training. Foregoing episodic training and using only standard
cross-entropy training on the base classes, our inference yields competitive
performances on standard benchmarks in the 1-shot scenarios. As the number of
available shots increases, the gap in performances widens: on PASCAL-5i, our
method brings about 5% and 6% improvements over the state-of-the-art, in the 5-
and 10-shot scenarios, respectively. Furthermore, we introduce a new setting
that includes domain shifts, where the base and novel classes are drawn from
different datasets. Our method achieves the best performances in this more
realistic setting. Our code is freely available online:
https://github.com/mboudiaf/RePRI-for-Few-Shot-Segmentation.


  Inner-approximate reachability analysis involves calculating subsets of
reachable sets, known as inner-approximations. This analysis is crucial in the
fields of dynamic systems analysis and control theory as it provides a reliable
estimation of the set of states that a system can reach from given initial
states at a specific time instant. In this paper, we study the
inner-approximate reachability analysis problem based on the set-boundary
reachability method for systems modelled by ordinary differential equations, in
which the computed inner-approximations are represented with zonotopes. The
set-boundary reachability method computes an inner-approximation by excluding
states reached from the initial set's boundary. The effectiveness of this
method is highly dependent on the efficient extraction of the exact boundary of
the initial set. To address this, we propose methods leveraging boundary and
tiling matrices that can efficiently extract and refine the exact boundary of
the initial set represented by zonotopes. Additionally, we enhance the
exclusion strategy by contracting the outer-approximations in a flexible way,
which allows for the computation of less conservative inner-approximations. To
evaluate the proposed method, we compare it with state-of-the-art methods
against a series of benchmarks. The numerical results demonstrate that our
method is not only efficient but also accurate in computing
inner-approximations.


  This is a review on the two first parts of our work on $p$-adic multiple zeta
values at $N$-th roots of unity ($p$MZV$\mu_{N}$'s), the $p$-adic periods of
the crystalline pro-unipotent fundamental groupoid of $\mathbb{P}^{1} -
\{0,\mu_{N},\infty\}$ (where $N$ and $p$ are coprime). We restrict for
simplicity the review to the case of $N=1$, i.e. the case of $p$-adic multiple
zeta values ($p$MZV's). The main tools are new objects which we call $p$-adic
pro-unipotent harmonic actions. These are continuous group actions on a space
containing the non-commutative generating series of weighted multiple harmonic
sums, they are related to the motivic Galois action on
$\pi_{1}^{\un}(\mathbb{P}^{1} - \{0,1,\infty\})$ and to the Poisson-Ihara
bracket, and interrelated by some maps. They are defined in \cite{J2} and
\cite{J3} ; the definition relies on a simplification of the differential
equation of the Frobenius, proved as a preliminary technical fact by \cite{J1}.
Part I (\cite{J1},\cite{J2},\cite{J3}) is an explicit computation of the
Frobenius of $\pi_{1}^{\un,\crys}(\mathbb{P}^{1} - \{0,1,\infty\})$, and in
particular of $p$MZV's. We give formulas which keep a track of the motivic
Galois action. Part II (\cite{J4},\cite{J5},\cite{J6}) is a study of the
algebraic properties of $p$MZV's brought together with the formulas of part I.
We state an explicit elementary version of the Galois theory of $p$MZV's.


  In order to remain adaptable to a dynamic environment, neural activity must
be simultaneously both sensitive and stable. To solve this problem, the brain
has been hypothesised to sit near a critical boundary. Yet, precisely how
criticality and these opposing information processing modes are implemented in
the brain remains elusive. A potential solution to this problem involves
modulating intrinsically nonlinear neurons within the cerebral cortex with
neuromodulatory neurotransmitters such as noradrenaline, a highly-conserved
chemical released from the pontine locus coeruleus. Here we confirm that
neuronal spiking in mice is poised close to the critical point of a branching
process and that time-varying signatures of criticality fluctuate with
neuromodulatory tone, as assessed by dynamic alterations in pupil diameter. We
explore these results theoretically by creating a dual-compartment model of
non-linear pyramidal neurons - capable of both regular spike and bursting modes
- that replicates our main empirical findings of slightly subcritical dynamics.
We then probe our model at a resolution impossible in vivo to demonstrate that
noradrenaline differentially alters spiking- and bursting-criticality to
facilitate sensitive and stable dynamics following an inverted-U profile that
peaks at intermediate noradrenergic tone. Finally, we demonstrate that this
intermediate noradrenergic regime displays burst avalanches with power-law size
and duration distributions and scaling relationship belonging to the
universality class of self-organized criticality. Our results confirm that the
noradrenergic ascending arousal system acts as a control parameter for emergent
critical dynamics in the brain. This methodology could be extended to explore
other neuromodulators as control parameters of the brain.


  We study different aspects of a U-duality recently presented by Maldacena and
Martelli and apply it to non-extremal backgrounds. In particular, starting from
new non-extremal wrapped D5 branes we generate new non-extremal generalizations
of the Baryonic Branch of the Klebanov-Strassler solution. We also elaborate on
different conceptual aspects of these U-dualities, like its action on (extremal
and non-extremal) Dp branes, dual models for Yang-Mills-like theories, generic
asymptotics and decoupling limit of the generated solutions.


  A general formalism for computing only the rational parts of oneloop QCD
amplitudes is developed. Starting from the Feynman integral representation of
the one-loop amplitude, we use tensor reduction and recursive relations to
compute the rational parts directly. Explicit formulas for the rational parts
are given for all bubble and triangle integrals. Formulas are also given for
box integrals up to two-masshard boxes which are the needed ingredients to
compute up to 6-gluon QCD amplitudes. We use this method to compute explicitly
the rational parts of the 5- and 6-gluon QCD amplitudes in two accompanying
papers.


  We study the local limit of the fixed-point forest, a tree structure
associated to a simple sorting algorithm on permutations. This local limit can
be viewed as an infinite random tree that can be constructed from a Poisson
point process configuration on $[0,1]^\mathbb{N}$. We generalize this random
tree, and compute the expected size and expected number of leaves of a random
rooted subtree in the generalized version. We also obtain bounds on the
variance of the size.


  In modern society, the trading methods and strategies used in financial
market have gradually changed from traditional on-site trading to electronic
remote trading, and even online automatic trading performed by a pre-programmed
computer programs because the continuous development of network and computer
computing technology. The quantitative trading, which the main purpose is to
automatically formulate people's investment decisions into a fixed and
quantifiable operation logic that eliminates all emotional interference and the
influence of subjective thoughts and applies this logic to financial market
activities in order to obtain excess profits above average returns, has led a
lot of attentions in financial market. The development of self-adjustment
programming algorithms for automatically trading in financial market has
transformed a top priority for academic research and financial practice. Thus,
a new flexible grid trading model combined with the Simplified Swarm
Optimization (SSO) algorithm for optimizing parameters for various market
situations as input values and the fully connected neural network (FNN) and
Long Short-Term Memory (LSTM) model for training a quantitative trading model
to automatically calculate and adjust the optimal trading parameters for
trading after inputting the existing market situation is developed and studied
in this work. The proposed model provides a self-adjust model to reduce
investors' effort in the trading market, obtains outperformed investment return
rate and model robustness, and can properly control the balance between risk
and return.


  We establish topological local rigidity for uniform lattices in compactly
generated groups, extending the result of Weil from the realm of Lie groups. We
generalize the classical local rigidity theorem of Selberg, Calabi and Weil to
irreducible uniform lattices in $\text{Isom}(X)$ where $X$ is a proper
$\text{CAT}(0)$ space with no Euclidian factors, not isometric to the
hyperbolic plane. We deduce an analog of Wang's finiteness theorem for certain
non-positively curved metric spaces.


  In 1967, Kadison asked "if $N$ is a subfactor of the factor $M$ for which $N'
\cap M$ consists of scalars, will some maximal abelian *-subalgebra of $N$ be a
maximal abelian subalgebra of $M$?". Generalizing a theorem of Popa in the type
$\mathrm{II}$ case (1981), we solve Kadison's problem for all subfactors with
expectation $N \subset M$ where $N$ is either a type $\mathrm{III}_\lambda$
factor with $0 \leq \lambda < 1$ or a type $\mathrm{III}_1$ factor that
satisfies Connes's bicentralizer conjecture. Our solution is based on a new
explicit formula for the bicentralizer algebras of arbitrary inclusions. This
formula implies a type $\mathrm{III}$ analog of Popa's local quantization
principle. We generalize Haaegrup's theorem from 1984 by connecting the
relative bicentralizer conjecture to the Dixmier property. Finally, we prove
this conjecture for a large class of inclusions and we prove an ergodicity
theorem for the bicentralizer flow. We also give applications of our methods to
$\mathrm{II}_1$ factors, including a new characterization of Ozawa's
W*-Akemann-Ostrand property.


  A word $\sigma=\sigma_1...\sigma_n$ over the alphabet $[k]=\{1,2,...,k\}$ is
said to be {\em smooth} if there are no two adjacent letters with difference
greater than 1. A word $\sigma$ is said to be {\em smooth cyclic} if it is a
smooth word and in addition satisfies $|\sigma_n-\sigma_1|\le 1$. We find the
explicit generating functions for the number of smooth words and cyclic smooth
words in $[k]^n$, in terms of {\it Chebyshev polynomials of the second kind}.
Additionally, we find explicit formula for the numbers themselves, as
trigonometric sums. These lead to immediate asymptotic corollaries. We also
enumerate smooth necklaces, which are cyclic smooth words that are not
equivalent up to rotation.


  Pedestrian trajectory prediction is an essential component in a wide range of
AI applications such as autonomous driving and robotics. Existing methods
usually assume the training and testing motions follow the same pattern while
ignoring the potential distribution differences (e.g., shopping mall and
street). This issue results in inevitable performance decrease. To address this
issue, we propose a novel Transferable Graph Neural Network (T-GNN) framework,
which jointly conducts trajectory prediction as well as domain alignment in a
unified framework. Specifically, a domain-invariant GNN is proposed to explore
the structural motion knowledge where the domain-specific knowledge is reduced.
Moreover, an attention-based adaptive knowledge learning module is further
proposed to explore fine-grained individual-level feature representations for
knowledge transfer. By this way, disparities across different trajectory
domains will be better alleviated. More challenging while practical trajectory
prediction experiments are designed, and the experimental results verify the
superior performance of our proposed model. To the best of our knowledge, our
work is the pioneer which fills the gap in benchmarks and techniques for
practical pedestrian trajectory prediction across different domains.


  We study the dynamics of a point particle in a periodic array of spherical
scatterers, and construct a stochastic process that governs the time evolution
for random initial data in the limit of low scatterer density (Boltzmann-Grad
limit). A generic path of the limiting process is a piecewise linear curve
whose consecutive segments are generated by a Markov process with memory two.


  Since their discovery in 1896, x-rays have had a profound impact on science,
medicine and technology. Here we show that the x-rays from a novel tabletop
source of bright coherent synchrotron radiation can be applied to phase
contrast imaging of biological specimens, yielding superior image quality and
avoiding the need for scarce or expensive conventional sources.


  We propose a useful method for mapping large-scale velocity fields in the
solar photosphere. It is based on the local correlation tracking algorithm when
tracing supergranules in full-disc dopplergrams. The method was developed using
synthetic data. The data processing the data are transformed during the data
processing into a suitable coordinate system, the noise is removed, and finally
the velocity field is calculated. Resulting velocities are compared with the
model velocities and the calibration is done. From our results it becomes clear
that this method could be applied to full-disc dopplergrams acquired by the
Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory
(SoHO).


  A mechanism for orientation of bilayer classical Wigner crystals in a
piezoelectric medium is considered. For the GaAs system the piezoelectric
correction to the electrostatic interaction between electrons is calculated. It
is shown that taking into account the correction due to the piezoelectric
effect leads to a dependence of the total energy of the electron crystal on its
orientation with respect to the crystallographic axes of the surrounding
matrix. A generalization of Ewald's method is obtained for calculating the
anisotropic interaction between electrons in a Wigner crystal. The method is
used to calculate the energy of bilayer Wigner crystals in electron layers
parallel to the crystallographic planes (001), (0-11), and (111) as a function
of their orientation and the distance between layers, and the energetically
most favorable orientation for all types of electron lattices in a bilayer
system is found. It is shown that phase transitions between structures with
different lattice symmetry in a Wigner crystal can be accompanied by a change
of its orientation.