  In this paper we investigate some basic properties of fractional powers. In
this regard, we show that for any rational number $1\leq {2r+1\over 2s+1}<
og(G)$, $G^{{2r+1\over 2s+1}}\longrightarrow H$ if and only if
$G\longrightarrow H^{-{2s+1\over 2r+1}}.$ Also, for two rational numbers
${2r+1\over 2s+1} < {2p+1\over 2q+1}$ and a non-bipartite graph $G$, we show
that $G^{2r+1\over 2s+1} < G^{2p+1\over 2q+1}$. In the sequel, we introduce an
equivalent definition for circular chromatic number of graphs in terms of
fractional powers. We also present a sufficient condition for equality of
chromatic number and circular chromatic number.


  We study a frequency-dependent damping model of hyper-diffusion within the
generalized Langevin equation. The model allows for the colored noise defined
by its spectral density, assumed to be proportional to $\omega^{\delta-1}$ at
low frequencies with $0<\delta<1$ (sub-Ohmic damping) or $1<\delta<2$
(super-Ohmic damping), where the frequency-dependent damping is deduced from
the noise by means of the fluctuation-dissipation theorem. It is shown that for
super-Ohmic damping and certain parameters, the diffusive process of the
particle in a titled periodic potential undergos sequentially four
time-regimes: thermalization, hyper-diffusion, collapse and asymptotical
restoration. For analysing transition phenomenon of multi-diffusive states, we
demonstrate that the first exist time of the particle escaping from the locked
state into the running state abides by an exponential distribution. The concept
of equivalent velocity trap is introduced in the present model, moreover,
reformation of ballistic diffusive system is also considered as a marginal
situation, however there does not exhibit the collapsed state of diffusion.


  We recalculate in a systematic and pedagogical way one of the most important
results of Bosonic open string theory in the light-cone formulation, namely the
[J^{-i},J^{-j}] commutators, which together with Lorentz covariance, famously
yield the critical dimension D=26 and the normal order constant a=1. We use
traditional transverse oscillator mode expansions (avoiding the elegant but
more advanced language of operator product expansions). We streamline the proof
by introducing a novel bookkeeping/regularization parameter \kappa to avoid
splitting into creation and annihilation parts, and to avoid sandwiching
between bras and kets.


  We present results of a method for an automatic search for HI shells in 3D
data cubes and apply it to the Leiden-Dwingeloo HI survey of the northern Milky
Way. In the 2nd Galactic quadrant, where identifications of structures are not
substantially influenced by overlapping, we find nearly 300 structures. The
Galactic distribution of shells has an exponential profile in the radial
direction with a scale length of 3 kpc. In the z direction, one half of the
shells are found at distances smaller than 500 pc. We also calculate the
energies necessary to create the shells: there are several structures with
energies greater than 10 E_SN but only one with an energy exceeding 100 E_SN.
Their size distribution, corrected for distance effects, is approximated by a
power-law with an index 2.1. Our identifications provide a lower limit to the
filling factor of shells in the outer Milky Way: f_2D = 0.4 and f_3D = 0.05.


  In this series we introduce and investigate the concept of connectoids, which
captures the connectivity structure of various discrete objects like undirected
graphs, directed graphs, bidirected graphs, hypergraphs or finitary matroids.
  In this paper we develop a universal end space theory based on connectoids:
the end spaces of connectoids unify the existing end spaces of undirected and
directed graphs and establish end spaces for bidirected graphs, hypergraphs and
finitary matroids.
  The main result shows that the tangle-like description of ends in undirected
graphs, called directions, extends to connectoids: there is a one-to-one
correspondence between the directions of a connectoid and its ends.
Furthermore, we generalise normal trees of undirected graphs to connectoids and
show that normal trees represent the ends of a connectoid as they do for
undirected graphs.


  In the last few years the hydrodynamic formulation of quantum mechanics,
equivalent to the Bohmian equations of motion, has been used to obtain
numerical solutions of the Schrodinger equation. Problems, however, have been
experienced near wave function nodes (or low probability regions). Here we
attempt to compute wave functions and Bohmian trajectories for the interference
of one particle or of two identical particles. It turns out that the large
number of nodes (i.e. interference minima) makes the hydrodynamic equations
impractical, whereas a more straightforward solution of the Schrodinger
equation gives very good results.


  Nuclear modification factors of inclusive prompt photon production in d-Au
collisions at RHIC and p-Pb collisions at the LHC are provided at different
rapidities. The calculations are performed at NLO accuracy using the EPS09 NLO
nuclear parton distribution functions (nPDFs) and their error sets. The results
are compared to the ones obtained with the nDS and HKN07 NLO nPDFs, and to the
corresponding nuclear modification factors of neutral pion production in these
collisions. The sensitivity of these results to the scale choice is also
investigated. Interestingly, the predictions using the different nPDF sets
differ from each other to the extent that this observable can be expected to
become very useful for probing nPDFs over a wide range of Bjorken-x. In order
to obtain a perturbative QCD baseline in heavy-ion collisions, calculations are
carried out for minimum bias Au-Au collisions at RHIC and Pb-Pb collisions at
the LHC. We also estimate the maximal possible suppression which the produced
QCD matter can be expected to have on inclusive prompt photon production due to
the quenching of the fragmentation component. The nuclear modification factor
for prompt photon production is thus suggested to be used for gauging both the
cold and the hot nuclear matter effects on other hard processes which are
expected to be affected by quark-gluon plasma formation, such as large-pT
hadron and jet production.


  We consider the tiling of an $n$-board (a board of size $n\times1$) with
squares of unit width and $(1,1)$-fence tiles. A $(1,1)$-fence tile is composed
of two unit-width square subtiles separated by a gap of unit width. We show
that the number of ways to tile an $n$-board using unit-width squares and
$(1,1)$-fence tiles is equal to a Fibonacci number squared when $n$ is even and
a golden rectangle number (the product of two consecutive Fibonacci numbers)
when $n$ is odd. We also show that the number of tilings of boards using $n$
such square and fence tiles is a Jacobsthal number. Using combinatorial
techniques we prove identities involving sums of Fibonacci and Jacobsthal
numbers in a straightforward way. Some of these identities appear to be new. We
also construct and obtain identities for a known Pascal-like triangle (which
has alternating ones and zeros along one side) whose $(n,k)$th entry is the
number of tilings using $n$ tiles of which $k$ are fence tiles. There is a
simple relation between this triangle and the analogous one for tilings of an
$n$-board. Connections between the triangles and Riordan arrays are also
demonstrated. With the help of the triangles, we express the Fibonacci numbers
squared, golden rectangle numbers, and Jacobsthal numbers as double sums of
products of two binomial coefficients.


  We studied the timing and spectral properties of the Be/X-ray pulsar Swift
J1626.6-5156 using the \emph{NICER} observations of its 2021 outburst. The most
important observation is the positive correlation of the centroid energy of the
fundamental cyclotron line with the luminosity. This observation agrees with
the usual positive correlation of the centroid energy cyclotron line with
luminosity in the sub-critical regime. The correlation between the two
quantities is verified using two different continuum models. The photon index
decreases with an increase in flux. Thus, the spectrum is softer when the flux
is low, which may be due to a decrease in the optical depth of the accretion
column with a decrease in the flux.


  The spectrum of curvature perturbation generated during inflation is studied
in the case the inflation-driving scalar field (inflaton) $\phi$ crosses over
its potential extremum. It is shown that the nondecaying mode of perturbation
has a finite value and a proper formula is given. The result is also extended
to more general cases where $\ddot{\phi}$ is non-negligible.


  We introduce the notion of index of summability for pairs of Banach spaces;
for Banach spaces E; F, this index plays the role of a kind of measure of how
the m-homogeneous polynomials from E to F are far from being absolutely
summing. In some cases the optimal index of summability is computed.


  The main goal of this paper is to give explicit descriptions of two maximal
cones in the Gr\"obner fan of the Pl\"ucker ideal. These cones correspond to
the monomial ideals given by semistandard and PBW-semistandard Young tableaux.
For the first cone, as an intermediate result we obtain the description of a
maximal cone in the Gr\"obner fan of any Hibi ideal. For the second, we
generalize the notion of Hibi ideals by associating an ideal with every
interpolating polytope. This is a family of polytopes that generalizes the
order and chain polytopes of a poset (\`a la Fang--Fourier--Litza--Pegel). We
then describe a maximal cone in the Gr\"obner fan of each of these ideals. We
also establish some useful facts concerning PBW-semistandardness, in
particular, we prove that it provides a new Hodge algebra structure on the
Pl\"ucker algebra.


  We report on ROSAT and ASCA observations of the LINER NGC1052, which is the
first one where broad optical lines in polarized light have been observed. The
2-10 keV spectrum is very flat, with an observed photon index (Gamma) ~0.1. A
model where a nuclear source is - partly or totally - obscured by a screen of
matter with column density ~10^23 atom/cm/cm is the most convincing explanation
for the observed flatness. This agrees with the hypothesis that the LINERs are
a population of low-luminosity AGN, to which the Seyfert unification scenario
applies. The intrinsic spectral index is still rather flat (1.0-1.4), as
observed in a few type-2 Seyferts so far or predicted if the accretion occurs
in an advection-dominated flow.


  We study the occurrence of spectroscopic binaries in young star-forming
regions using the INfrared Spectroscopy of Young Nebulous Clusters(IN-SYNC)
survey, carried out in SDSS-III with the APOGEE spectrograph. Multi-epoch
observations of thousands of low-mass stars in Orion A, NGC 2264, NGC 1333, IC
348, and the Pleiades have been carried out, yielding H-band spectra with a
nominal resolution of R=22,500 for sources with H $\le$ 12 mag. Radial velocity
precisions of $\sim$0.3 $km\:s^{-1}$ were achieved, which we use to identify
radial velocity variations indicative of undetected companions. We use Monte
Carlo simulations to assess the types of spectroscopic binaries to which we are
sensitive, finding sensitivity to binaries with orbital periods $< 10^{4}$ d,
for stars with $2500 {\rm K} \le T_\mathrm{eff} \le 6000 {\rm K}$ and $\it{v}
\sin \it{i}$ $\le$ 100 $km\:s^{-1}$. Using Bayesian inference, we find evidence
for a decline in the spectroscopic binary fraction, by a factor of 3-4 from the
age of our pre-main-sequence sample to the Pleiades age . The significance of
this decline is weakened if spot-induced radial-velocity jitter is strong in
the sample, and is only marginally significant when comparing any one of the
pre-main-sequence clusters against the Pleiades. However, the same decline in
both sense and magnitude is found for each of the five pre-main-sequence
clusters, and the decline reaches statistical significance of greater than 95%
confidence when considering the pre-main-sequence clusters jointly. Our results
suggest that dynamical processes disrupt the widest spectroscopic binaries
($P_{\rm orb} \approx 10^3 - 10^4$ d) as clusters age, indicating that this
occurs early in the stars' evolution, while they still reside within their
nascent clusters.


  In this study, we consider curves of generalized AW(k)-type of Euclidean
n-space. We give curvature conditions of these kind of curves.


  We study the relationship between free curves and periodic points for torus
homeomorphisms in the homotopy class of the identity. By free curve we mean a
homotopically nontrivial simple closed curve that is disjoint from its image.
We prove that every rational point in the rotation set is realized by a
periodic point provided that there is no free curve and the rotation set has
empty interior. This gives a topological version of a theorem of Franks. Using
this result, and inspired by a theorem of Guillou, we prove a version of the
Poincar\'e-Birkhoff Theorem for torus homeomorphisms: in the absence of free
curves, either there is a fixed point or the rotation set has nonempty
interior.


  With quantum resources a precious commodity, their efficient use is highly
desirable. Quantum autoencoders have been proposed as a way to reduce quantum
memory requirements. Generally, an autoencoder is a device that uses machine
learning to compress inputs, that is, to represent the input data in a
lower-dimensional space. Here, we experimentally realize a quantum autoencoder,
which learns how to compress quantum data using a classical optimization
routine. We demonstrate that when the inherent structure of the data set allows
lossless compression, our autoencoder reduces qutrits to qubits with low error
levels. We also show that the device is able to perform with minimal prior
information about the quantum data or physical system and is robust to
perturbations during its optimization routine.


  We study 4-dimensional higher-derivative conformal higher spin (CHS) fields
generalising Weyl graviton and conformal gravitino. They appear, in particular,
as "induced" theories in the AdS/CFT context. We consider their partition
function on curved Einstein-space backgrounds like (A)dS or sphere and
Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition
function appears to be given by a product of partition functions of the
standard 2nd-derivative "partially massless" spin s fields, generalising the
previously known expression for the 1-loop Weyl graviton (s=2) partition
function. We compute the corresponding spin s Weyl anomaly coefficients a_s and
c_s. Our result for a_s reproduces the expression found recently in
arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the
partition function of a CHS field on S^4 to a ratio of known partition
functions of massless higher spin field in AdS_5 with alternate boundary
conditions). We also obtain similar results for the fermionic CHS fields. In
this half-integer spin s case the CHS partition function on (A)dS background is
given by a product of squares of "partially massless" spin s partition
functions and one extra factor corresponding to a special massive conformally
invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the
bosonic a_s coefficients over all spins s is zero when computed using the
zeta-function regularization, and we observe that the same property is true
also in the fermionic case, suggesting that the corresponding conformal higher
spin theory may be consistent at the quantum level.


  Background: Long-baseline experiments such as the planned Deep Underground
Neutrino Experiment (DUNE) require theoretical descriptions of the complete
event in a neutrino-nucleus reaction. Since nuclear targets are used this
requires a good understanding of neutrino-nucleus interactions.
  Purpose: Develop a consistent theory and code framework for the description
of lepton-nucleus interactions that can be used to describe not only inclusive
cross sections, but also the complete final state of the reaction.
  Methods: The Giessen-Boltzmann-Uehling-Uhlenbeck (GiBUU) implementation of
quantum-kinetic transport theory is used, with improvements in its treatment of
the nuclear ground state and of 2p2h interactions. For the latter an empirical
structure function from electron scattering data is used as a basis.
  Results: Results for electron-induced inclusive cross sections are given as a
necessary check for the overall quality of this approach. The calculated
neutrino-induced inclusive double-differential cross sections show good
agreement with data from neutrino- and antineutrino reactions for different
neutrino flavors at MiniBooNE and T2K. Inclusive double-differential cross
sections for MicroBooNE, NOvA, MINERvA and LBNF/DUNE are given.
  Conclusions: Based on the GiBUU model of lepton-nucleus descriptions a good
theoretical description of inclusive electron-, neutrino- and
antineutrino-nucleus data over a wide range of energies, different neutrino
flavors and different experiments is now possible. Since no tuning is involved
this theory and code should be reliable also for new energy regimes and target
masses. \end{description}


  In this article, we develop an intuitive and efficient, numerical technique
to solve the quantum evolution equation of generic lattice-refined models in
loop quantum cosmology. As an application of this method, we extensively study
the solutions of the recently introduced, lattice-refined anisotropic model of
the Schwarzschild interior geometry. Our calculations suggest that the results
obtained from the approach are accurate, robust and are in complete agreement
with the expectations from the von Neumann stability analysis of the model.


  We prove an escape rate result for special semi-flows over non-invertible
subshifts of finite type. Our proofs are based on a discretisation of the flow
and an application of an escape rate result for conformal repellers.


  We present data on the Baikal water luminescence collected with the
Baikal-GVD neutrino telescope. This three-dimensional array of photo-sensors
allows the observation of time and spatial variations of the ambient light
field. We report on annual increase of luminescence activity in years
2018-2020. We observed a unique event of a highly luminescent layer propagating
upwards with a maximum speed of 28 m/day for the first time.


  The field enhancement factor (FEF) is an important quantity in field emission
calculations since the tunneling electron current depends very sensitively on
its magnitude. The exact dependence of FEF on the emitter height $h$, the
radius of curvature at the apex $R_a$, as well as the shape of the emitter base
is still largely unknown. In this work, a universal formula for the field
enhancement factor is derived. It depends on the ratio $h/R_a$ and has the form
$\gamma_a = (2h/R_a)/[\alpha_1 \log(4h/R_a) - \alpha_2 ]$ where $\alpha_1$,
$\alpha_2$ depend on the charge distribution on the emitter. Numerical results
show that a simpler form $\gamma_a = (2h/R_a)/[\log(4h/R_a) - \alpha]$ is
equally valid with $\alpha$ depending on the class of emitter and indicative of
the shielding by the emitter-base. For the hyperboloid, conical and ellipsoid
emitters, the value of $\alpha$ is $0, 0.88$ and $2$ while for the cylindrical
base where shielding is minimum, $\alpha \simeq 2.6$.


  Photorealistic style transfer aims to transfer the artistic style of an image
onto an input image or video while keeping photorealism. In this paper, we
think it's the summary statistics matching scheme in existing algorithms that
leads to unrealistic stylization. To avoid employing the popular Gram loss, we
propose a self-supervised style transfer framework, which contains a style
removal part and a style restoration part. The style removal network removes
the original image styles, and the style restoration network recovers image
styles in a supervised manner. Meanwhile, to address the problems in current
feature transformation methods, we propose decoupled instance normalization to
decompose feature transformation into style whitening and restylization. It
works quite well in ColoristaNet and can transfer image styles efficiently
while keeping photorealism. To ensure temporal coherency, we also incorporate
optical flow methods and ConvLSTM to embed contextual information. Experiments
demonstrates that ColoristaNet can achieve better stylization effects when
compared with state-of-the-art algorithms.


  Weak lensing has become an increasingly important tool in cosmology and the
use of galaxy shapes to measure cosmic shear has become routine. The
weak-lensing distortion tensor contains two other effects in addition to the
two components of shear: the convergence and rotation. The rotation mode is not
measurable using the standard cosmic shear estimators based on galaxy shapes,
as there is no information on the original shapes of the images before they
were lensed. Due to this, no estimator has been proposed for the rotation mode
in cosmological weak-lensing surveys, and the rotation mode has never been
constrained. Here, we derive an estimator for this quantity, which is based on
the use of radio polarisation measurements of the intrinsic position angles of
galaxies. The rotation mode can be sourced by physics beyond $\Lambda$CDM, and
also offers the chance to perform consistency checks of $\Lambda$CDM and of
weak-lensing surveys themselves. We present simulations of this estimator and
show that, for the pedagogical example of cosmic string spectra, this estimator
could detect a signal that is consistent with the constraints from Planck. We
examine the connection between the rotation mode and the shear $B$-modes and
thus how this estimator could help control systematics in future radio
weak-lensing surveys.


  In the context of one-dimensional fermionic systems, helical Luttiger liquids
are not only characterized by intriguing spin properties, but also by the
possibility to be manipulated by means of electrostatic gates, exploiting
finite Rashba coupling. We use this property to show that a heterostructure
composed of a helical Luttinger liquid, contacted to two metallic leads and
supplemented by top gates, can be used as a tunable thermal valve. By relying
on bosonization techniques and scattering of plasmonic modes, we investigate
the performance of this valve with respect to electron-electron interactions,
temperature, and properties of the gates. The maximal modulation of the thermal
conductance that the proposed device can achieve is, for experimentally
relevant parameters, around $7 \%$. Such variation can be both positive or
negative. Moreover, a modification in the geometry of the gate can lead to
particular temperature dependencies related to interference effects. We also
argue that the effects we predict can be used to establish the helical nature
of the edge states in two-dimensional topological insulators.


  Global optimization techniques are increasingly preferred over human-driven
methods in the design of electromagnetic structures such as metasurfaces, and
careful construction and parameterization of the physical structure is critical
in ensuring computational efficiency and convergence of the optimization
algorithm to a globally optimal solution. While many design variables in
physical systems take discrete values, optimization algorithms often benefit
from a continuous design space. This work demonstrates the use of level set
functions as a continuous basis for designing material distributions for
metasurface arrays and introduces an improved parameterization which is termed
the periodic level set function. We explore the use of alternate norms in the
definition of the level set function and define a new pseudo-inverse technique
for upsampling basis coefficients with these norms. The level set method is
compared to the fragmented parameterization and shows improved electromagnetic
responses for two dissimilar cost functions: a narrowband objective and a
broadband objective. Finally, we manufacture an optimized level set metasurface
and measure its scattering parameters to demonstrate real-world performance.


  Under a certain scaling, the electron densities of finite systems become both
large and slowly-varying, so that the gradient expansions of the density
functionals for the Kohn-Sham kinetic and exchange energies become
asymptotically exact to order $\nabla^2$. Neutral atoms of large $Z$ scale
similarly, but a cusp correction at the nucleus requires generalizing the
gradient expansion for exchange, producing the wrong gradient coefficient in
the slowly-varying limit. Meta-generalized gradient approximations (meta-GGA's)
recover both the slowly-varying and large-$Z$ limits. GGA correlation energies
of large-Z atoms are found to be accurate.


  Networks are a natural representation of complex systems across the sciences,
and higher-order dependencies are central to the understanding and modeling of
these systems. However, in many practical applications such as online social
networks, networks are massive, dynamic, and naturally streaming, where
pairwise interactions among vertices become available one at a time in some
arbitrary order. The massive size and streaming nature of these networks allow
only partial observation, since it is infeasible to analyze the entire network.
Under such scenarios, it is challenging to study the higher-order structural
and connectivity patterns of streaming networks. In this work, we consider the
fundamental problem of estimating the higher-order dependencies using adaptive
sampling. We propose a novel adaptive, single-pass sampling framework and
unbiased estimators for higher-order network analysis of large streaming
networks. Our algorithms exploit adaptive techniques to identify edges that are
highly informative for efficiently estimating the higher-order structure of
streaming networks from small sample data. We also introduce a novel
James-Stein shrinkage estimator to reduce the estimation error. Our approach is
fully analytic, computationally efficient, and can be incrementally updated in
a streaming setting. Numerical experiments on large networks show that our
approach is superior to baseline methods.


  With this work we try to analyse the agglomeration process in the Portuguese
regions, using the New Economic Geography models. In these models the base idea
is that where has increasing returns to scale in the manufactured industry and
low transport costs, there is agglomeration. Of referring, as summary
conclusion, that with this work the existence of increasing returns to scale
and low transport cost, in the Portuguese regions, was proven and as such the
existence of agglomeration in Portugal.


  Consider a triangle $ABC$ with given lengths $l_a,l_b,l_c$ of its internal
angle bisectors. We prove that in general, it is impossible to construct a
square of the same area as $ABC$ using a ruler and compass. Moreover, it is
impossible to express the area of $ABC$ in radicals of $l_a,l_b,l_c$.


  We introduce a new neural network-based continual learning algorithm, dubbed
as Uncertainty-regularized Continual Learning (UCL), which builds on
traditional Bayesian online learning framework with variational inference. We
focus on two significant drawbacks of the recently proposed
regularization-based methods: a) considerable additional memory cost for
determining the per-weight regularization strengths and b) the absence of
gracefully forgetting scheme, which can prevent performance degradation in
learning new tasks. In this paper, we show UCL can solve these two problems by
introducing a fresh interpretation on the Kullback-Leibler (KL) divergence term
of the variational lower bound for Gaussian mean-field approximation. Based on
the interpretation, we propose the notion of node-wise uncertainty, which
drastically reduces the number of additional parameters for implementing
per-weight regularization. Moreover, we devise two additional regularization
terms that enforce stability by freezing important parameters for past tasks
and allow plasticity by controlling the actively learning parameters for a new
task. Through extensive experiments, we show UCL convincingly outperforms most
of recent state-of-the-art baselines not only on popular supervised learning
benchmarks, but also on challenging lifelong reinforcement learning tasks. The
source code of our algorithm is available at https://github.com/csm9493/UCL.


  A Gaussian interference channel (IC) with a relay is considered. The relay is
assumed to operate over an orthogonal band with respect to the underlying IC,
and the overall system is referred to as IC with an out-of-band relay (IC-OBR).
The system can be seen as operating over two parallel interference-limited
channels: The first is a standard Gaussian IC and the second is a Gaussian
relay channel characterized by two sources and destinations communicating
through the relay without direct links. We refer to the second parallel channel
as OBR Channel (OBRC). The main aim of this work is to identify conditions
under which optimal operation, in terms of the capacity region of the IC-OBR,
entails either signal relaying and/or interference forwarding by the relay,
with either a separable or non-separable use of the two parallel channels, IC
and OBRC. Here "separable" refers to transmission of independent information
over the two constituent channels. For a basic model in which the OBRC consists
of four orthogonal channels from sources to relay and from relay to
destinations (IC-OBR Type-I), a condition is identified under which signal
relaying and separable operation is optimal. When this condition is not
satisfied, various scenarios are identified in which interference forwarding
and non-separable operation are necessary to achieve optimal performance. In
these scenarios, the system exploits the "excess capacity" on the OBRC via
interference forwarding to drive the IC-OBR system in specific interference
regimes (strong or mixed). The analysis is then turned to a more complex
IC-OBR, in which the OBRC consists of only two orthogonal channels, one from
sources to relay and one from relay to destinations (IC-OBR Type-II). For this
channel, some capacity resuls are derived that parallel the conclusions for
IC-OBR Type-I.


  This two-part paper considers strategic topology switching for security in
the second-order multi-agent system. In Part II, we propose a strategy on
switching topologies to detect zero-dynamics attack (ZDA), whose
attack-starting time is allowed to be not the initial time. We first
characterize the sufficient and necessary condition for detectability of ZDA,
in terms of the network topologies to be switched to and the set of agents to
be monitored. We then propose an attack detection algorithm based on the
Luenberger observer, using the characterized detectability condition. Employing
the strategy on switching times proposed in Part I and the strategy on
switching topologies proposed here, a strategic topology-switching algorithm is
derived. Its primary advantages are threefold: (i) in achieving consensus in
the absence of attacks, the control protocol does not need velocity
measurements and the algorithm has no constraint on the magnitudes of coupling
weights; (ii) in tracking system in the absence of attacks, the Luenberger
observer has no constraint on the magnitudes of observer gains and the number
of monitored agents, i.e., only one monitored agent's output is sufficient;
(iii) in detecting ZDA, the algorithm allows the defender to have no knowledge
of the attack-starting time and the number of misbehaving agents (i.e., agents
under attack). Simulations are provided to verify the effectiveness of the
strategic topology-switching algorithm.


  The logic of information flows (LIF) has recently been proposed as a general
framework in the field of knowledge representation. In this framework, tasks of
procedural nature can still be modeled in a declarative, logic-based fashion.
In this paper, we focus on the task of query processing under limited access
patterns, a well-studied problem in the database literature. We show that LIF
is well-suited for modeling this task. Toward this goal, we introduce a variant
of LIF called "forward" LIF (FLIF), in a first-order setting. FLIF takes a
novel graph-navigational approach; it is an XPath-like language that
nevertheless turns out to be equivalent to the "executable" fragment of
first-order logic defined by Nash and Lud\"ascher. One can also classify the
variables in FLIF expressions as inputs and outputs. Expressions where inputs
and outputs are disjoint, referred to as io-disjoint FLIF expressions, allow a
particularly transparent translation into algebraic query plans that respect
the access limitations. Finally, we show that general FLIF expressions can
always be put into io-disjoint form.


  Quantum simulation involves engineering devices to implement different
Hamiltonians and measuring their quantized spectra to study quantum many-body
systems. Recent developments in topological photonics have shown the
possibility of studying novel quantum phenomena by controlling the topological
properties of such devices. Here, using coupled arrays of upto 16 high Q
nano-cavities we experimentally realize quantum photonic baths which are
analogs of the Su-Schrieffer-Heeger model. We investigate the effect of
fabrication induced disorder on these baths by probing individual super-modes
and demonstrate the design mitigation steps required to overcome the disorder
effects on the quantum phenomena.


  We present the results of a pilot XMM-$Newton$ and $Chandra$ program aimed at
studying the diffuse intragroup medium (DIM) of optically-selected nearby
groups from the Zurinch ENvironmental Study (ZENS) catalog. The groups are in a
narrow mass range about $10^{13}M_\odot$, a mass scale at which the interplay
between the DIM and the group member galaxies is still largely unprobed. X-ray
emission from the DIM is detected in the energy band 0.5--2 keV with flux $\le
10^{-14}$ erg cm$^{-1}$ s$^{-1}$, which is one order of magnitude fainter than
for typical ROSAT groups (RASS). For many groups we set upper limits to the
X-ray luminosity, indicating that the detections are likely probing the upper
envelope of the X-ray emitting groups. We find evidence for our optically
selected groups to be under-luminous with respect to predictions from X-ray
scaling relations. X-ray mass determinations are in best agreement with those
based on the member galaxies bulge luminosity, followed by their total optical
luminosity and velocity dispersion. We measure a stellar mass fraction with a
median value of about 1$\%$, with a contribution from the most massive galaxies
between 30 to 50 \%. Optical and X-ray data give often complementary answers
concerning the dynamical state of the groups, and are essential for a complete
picture of the system. Extending this pilot program to a larger sample of
groups is mandatory to unveil any imprint of interaction between member
galaxies and DIM in halo potentials of key importance for
environmentally-driven galactic evolution.


  We analyse the spectrum of additive finite-rank deformations of $N \times N$
Wigner matrices $H$. The spectrum of the deformed matrix undergoes a
transition, associated with the creation or annihilation of an outlier, when an
eigenvalue $d_i$ of the deformation crosses a critical value $\pm 1$. This
transition happens on the scale $|d_i| - 1 \sim N^{-1/3}$. We allow the
eigenvalues $d_i$ of the deformation to depend on $N$ under the condition
$|\abs{d_i} - 1| \geq (\log N)^{C \log \log N} N^{-1/3}$. We make no
assumptions on the eigenvectors of the deformation. In the limit $N \to
\infty$, we identify the law of the outliers and prove that the non-outliers
close to the spectral edge have a universal distribution coinciding with that
of the extremal eigenvalues of a Gaussian matrix ensemble.
  A key ingredient in our proof is the \emph{isotropic local semicircle law},
which establishes optimal high-probability bounds on the quantity $< v,[(H -
z)^{-1} - m(z) 1] w >$, where $m(z)$ is the Stieltjes transform of Wigner's
semicircle law and $v, w$ are arbitrary deterministic vectors.


  Recent Vision-Language Pretrained (VLP) models have become the backbone for
many downstream tasks, but they are utilized as frozen model without learning.
Prompt learning is a method to improve the pre-trained VLP model by adding a
learnable context vector to the inputs of the text encoder. In a few-shot
learning scenario of the downstream task, MLE training can lead the context
vector to over-fit dominant image features in the training data. This
overfitting can potentially harm the generalization ability, especially in the
presence of a distribution shift between the training and test dataset. This
paper presents a Bayesian-based framework of prompt learning, which could
alleviate the overfitting issues on few-shot learning application and increase
the adaptability of prompts on unseen instances. Specifically, modeling
data-dependent prior enhances the adaptability of text features for both seen
and unseen image features without the trade-off of performance between them.
Based on the Bayesian framework, we utilize the Wasserstein Gradient Flow in
the estimation of our target posterior distribution, which enables our prompt
to be flexible in capturing the complex modes of image features. We demonstrate
the effectiveness of our method on benchmark datasets for several experiments
by showing statistically significant improvements on performance compared to
existing methods. The code is available at https://github.com/youngjae-cho/APP.


  We study the value of information in sequential compressed sensing by
characterizing the performance of sequential information guided sensing in
practical scenarios when information is inaccurate. In particular, we assume
the signal distribution is parameterized through Gaussian or Gaussian mixtures
with estimated mean and covariance matrices, and we can measure compressively
through a noisy linear projection or using one-sparse vectors, i.e., observing
one entry of the signal each time. We establish a set of performance bounds for
the bias and variance of the signal estimator via posterior mean, by capturing
the conditional entropy (which is also related to the size of the uncertainty),
and the additional power required due to inaccurate information to reach a
desired precision. Based on this, we further study how to estimate covariance
based on direct samples or covariance sketching. Numerical examples also
demonstrate the superior performance of Info-Greedy Sensing algorithms compared
with their random and non-adaptive counterparts.


  Autonomous operation of UAVs in a closed environment requires precise and
reliable pose estimate that can stabilize the UAV without using external
localization systems such as GNSS. In this work, we are concerned with
estimating the pose from laser scans generated by an inexpensive and
lightweight LIDAR. We propose a localization system for lightweight (under
200g) LIDAR sensors with high reliability in arbitrary environments, where
other methods fail. The general nature of the proposed method allows deployment
in wide array of applications. Moreover, seamless transitioning between
different kinds of environments is possible.
  The advantage of LIDAR localization is that it is robust to poor
illumination, which is often challenging for camera-based solutions in dark
indoor environments and in the case of the transition between indoor and
outdoor environment. Our approach allows executing tasks in poorly-illuminated
indoor locations such as historic buildings and warehouses, as well as in the
tight outdoor environment, such as forest, where vision-based approaches fail
due to large contrast of the scene, and where large well-equipped UAVs cannot
be deployed due to the constrained space.


  Future optical clock networks will require free-space optical time-frequency
transfer between flying clocks. However, simple one-way or standard two-way
time transfer between flying clocks will completely break down because of the
time-of-flight variations and Doppler shifts associated with the strongly
time-varying optical link distances. Here, we demonstrate an advanced,
comb-based optical two-way time-frequency transfer that can successfully
synchronize the optical timescales at two sites connected via a time-varying
turbulent air path. The link between the two sites is established using either
a quadcopter-mounted retroreflector or a swept delay line at speeds up to 24
m/s. Despite 50-ps breakdown in time-of-flight reciprocity, the sites'
timescales are synchronized to < 1 fs in time deviation. The corresponding
sites' frequencies agree to $\sim$ $10^{-18}$ despite $10^{-7}$ Doppler shifts.
This work demonstrates comb-based O-TWTFT can enable free-space optical
networks between airborne or satellite-borne optical clocks for precision
navigation, timing and probes of fundamental science.


  Optical vortices are the electromagnetic analogue of fluid vortices studied
in hydrodynamics. In both cases the traveling wavefront, either made of light
or fluid, is twisted like a corkscrew around its propagation axis - an analogy
that inspired also the first proposition of the concept of optical vortex. Even
though vortices are one of the most fundamental topological excitations in
nature, they are rarely found in their electromagnetic form in natural systems,
for the exception of energetic sources in astronomy, such as pulsars, quasars
and black holes. Mostly optical vortices are artificially created in the
laboratory by a rich variety of approaches. Here we provide our perspective on
a technology that shook-up optics in the last decade - metasurfaces, planar
nanostructured metamaterials - with a specific focus on its use for molding and
controlling optical vortices.


  We introduce spaces of test functions $\mathbf{G}^{\alpha}_{\alpha}(\mathbb R
^d_+)$ and $\mathbf{g}^{\alpha}_{\alpha}(\mathbb R ^d_+)$, $\alpha > 0$, by
using the iterates of the Laguerre operator, and show that these spaces
represent a natural counterpart of global Pilipovi\'c spaces on $\mathbb R ^d$.
Moreover, we show that $\mathbf{G}^{\alpha}_{\alpha}(\mathbb R^d_+)$ and
$\mathbf{g}^{\alpha}_{\alpha}(\mathbb R ^d_+)$ coincide with $G-$type spaces
when $\alpha \geq 1$, and $\alpha > 1$, respectively. We also consider the
associated spaces of ultradistributions. The main tool in our study is the use
of sequence spaces $\ell_{\alpha}(\mathbb N_0 ^d)$ and $\ell_{0,\alpha}(\mathbb
N_0 ^d)$ arising from the corresponding Laguerre expansions. In addition, by
considering sequence spaces $ \ell_{\flat_{\sigma}}(\mathbb N^d_0) $ and
$\ell_{0,\flat_{\sigma}}(\mathbb N^d_0)$, we introduce and study flat
Pilipovi\'c spaces on orthants.


  Assuming non-ideal circuit power consumption at the energy harvesting (EH)
nodes, we propose two practical protocols that optimize the performance of the
harvest-then-transmit wireless powered communication networks (WPCNs) under two
different objectives: (1) proportional fair (PF) resource allocation, and (2)
sum rate maximization. These objectives lead to optimal allocations for the
transmit power by the base station (BS), which broadcasts RF radiation over the
downlink, and optimal durations of the EH phase and the uplink information
transmission phases within the dynamic time-division multiple access (TDMA)
frame. Compared to the max-sum-rate protocol, the PF protocol attains a higher
level of system fairness at the expense of the sum rate degradation. The PF
protocol is advantageous over the max-sum-rate protocol in terms of system
fairness regardless of the circuit power consumption, whereas the uplink sum
rates of both protocols converge when this power consumption increases.


  We develop a reduction procedure which provides an equivalence from an
arbitrary block of the BGG category for the queer Lie superalgebra
$\mathfrak{q}(n)$ to a "$\mathbb{Z}\pm s$-weights" ($s\in \mathbb{C}$) block of
a BGG category for finite direct sum of queer Lie superalgebras. We give
descriptions of blocks. We also establish equivalences between certain maximal
parabolic subcategories for $\mathfrak{q}(n)$ and blocks of atypicality-one of
the category of finite-dimensional modules for $\mathfrak{gl}(\ell|n-\ell)$.


  In the first part of this paper, we present general results concerning the
colorability of torus knots using conjugation quandles over any abstract group.
Subsequently, we offer a numerical characterization for the colorability of
torus knots using conjugation quandles over some particular groups, such as the
matrix groups $GL(2,q)$ and $SL(2,q)$, the dihedral group, and the symmetric
group.


  An innovative field-particle correlation technique is proposed that uses
single-point measurements of the electromagnetic fields and particle velocity
distribution functions to investigate the net transfer of energy from fields to
particles associated with the collisionless damping of turbulent fluctuations
in weakly collisional plasmas, such as the solar wind. In addition to providing
a direct estimate of the local rate of energy transfer between fields and
particles, it provides vital new information about the distribution of that
energy transfer in velocity space. This velocity-space signature can
potentially be used to identify the dominant collisionless mechanism
responsible for the damping of turbulent fluctuations in the solar wind. The
application of this novel field-particle correlation technique is illustrated
using the simplified case of the Landau damping of Langmuir waves in an
electrostatic 1D-1V Vlasov-Poisson plasma, showing that the procedure both
estimates the local rate of energy transfer from the electrostatic field to the
electrons and indicates the resonant nature of this interaction. Modifications
of the technique to enable single-point spacecraft measurements of fields and
particles to diagnose the collisionless damping of turbulent fluctuations in
the solar wind are discussed, yielding a method with the potential to transform
our ability to maximize the scientific return from current and upcoming
spacecraft missions, such as the Magnetospheric Multiscale (MMS) and Solar
Probe Plus missions.


  We present Herschel/HIFI observations of the fundamental rotational
transitions of ortho- and para-H$_2^{16}$O and H$_2^{18}$O in absorption
towards Sagittarius~B2(M) and W31C. The ortho/para ratio in water in the
foreground clouds on the line of sight towards these bright continuum sources
is generally consistent with the statistical high-temperature ratio of 3,
within the observational uncertainties. However, somewhat unexpectedly, we
derive a low ortho/para ratio of $2.35 \pm 0.35$, corresponding to a spin
temperature of $\sim$27~K, towards Sagittarius~B2(M) at velocities of the
expanding molecular ring. Water molecules in this region appear to have formed
with, or relaxed to, an ortho/para ratio close to the value corresponding to
the local temperature of the gas and dust.


  This paper reviews a recent non-Landau-Ginzburg-Wilson (LGW) approach to
superfluid to Mott insulator transitions in two dimensional bosonic lattice
systems, using a dual vortex field theory (cond-mat/0408329). The physical
interpretation of conventional LGW theory of quantum criticality is re-examined
and similarities and differences with the vortex picture are discussed. The
``unification'' of various competing (insulating) orders, and the coincidence
of these orders with the Mott transition are readily understood in this
formulation. Some aspects of the recent theory of ``deconfined'' quantum
criticality, which are to an extent subsumed in this approach, are discussed. A
pedagogical presentation of the ``nuts and bolts'' of boson-vortex duality at
the hamiltonian level is included, tailored to a condensed matter audience.


  In this paper we show, using scanning tunneling spectroscopy (STS), the
existence of static striped density of electronic states in nearly optimally
doped $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$ in zero field. The observed modulation
is strongest at roughly half the superconducting gap energy and is aligned with
the Cu-O bonds, with a periodicity of four lattice constants, exhibiting
features characteristic of a two-dimensional system of line objects. These
features also exhibit asymmetries between the two orthogonal directions
locally, pointing to a possible broken symmetry state (i. e., stripe phase). We
further show that the density of states modulation manifests itself as a shift
of states from above to below the superconducting gap. The fact that a single
energy scale (i. e., the gap) appears for both superconductivity and stripes
suggests that these two effects have the same microscopic origin.


  We have already derived the Criteria for thermal stability of charged
rotating quantum black holes, for horizon areas that are large relative to the
Planck area. The derivation is done by using results of loop quantum gravity
and equilibrium statistical mechanics of the Grand Canonical ensemble. It is
also shown that in four dimensional spacetime, quantum ADS Kerr-Newman Black
hole is thermally stable within certain range of its' parameters. In this
paper, the expectation values of fluctuations and correlations among horizon
area, charge and angular momentum of stable quantum ADS black hole are
calculated within the range of stability. Interestingly, it is found that
leading order fluctuations of charge and angular momentum, in large horizon
area limit, are independent of the values of charge and angular momentum at
equilibrium.


  We investigate the influence of a Markovian environment on the dynamics of
interacting spinful fermionic atoms in a lattice. In order to explore the
physical phenomena occurring at short times, we develop a method based on a
slave-spin representation of fermions which is amenable to the investigation of
the dynamics of dissipative systems. We apply this approach to two different
dissipative couplings which can occur in current experiments: a coupling via
the local density and a coupling via the local double occupancy. We complement
our study based on this novel method with results obtained using the adiabatic
elimination technique and with an exact study of a two-site model. We uncover
that the decoherence is slowed down by increasing either the interaction
strength or the dissipative coupling (the Zeno effect). We also find, for the
coupling to the local double occupancy, that the final steady state can sustain
single-particle coherence.


  Hall, resistivity, magnetization, and thermoelectric power measurements were
performed on single crystals of the highly anisotropic layered metal LaSb2. A
100-fold linear magnetoresistance (MR) was observed in fields up to 45 T, with
no indication of saturation. We show that the MR is associated with a
magnetic-field-dependent holelike carrier density, n(H) \propto 1/H. The effect
is orbital, depending upon the component of the magnetic field normal to the
layers. At low temperature, a field of 9 T reduces the carrier density by more
than an order of magnitude.


  We introduce the notion of Fermi flow for hypersurfaces in Riemannian
manifolds. It turns out that this is a powerful tool to study the geometry of
distance surfaces about a given initial hypersurface. Some of the results in
this paper are known in one form or another, however the aim is to demonstrate
how they can all be derived by the same method and proved in a very simple
manner. In addition we obtain some new results and results that are stronger
than those stated in the literature.


  Bootstrap is a useful tool for making statistical inference, but it may
provide erroneous results under complex survey sampling. Most studies about
bootstrap-based inference are developed under simple random sampling and
stratified random sampling. In this paper, we propose a unified bootstrap
method applicable to some complex sampling designs, including Poisson sampling
and probability-proportional-to-size sampling. Two main features of the
proposed bootstrap method are that studentization is used to make inference,
and the finite population is bootstrapped based on a multinomial distribution
by incorporating the sampling information. We show that the proposed bootstrap
method is second-order accurate using the Edgeworth expansion. Two simulation
studies are conducted to compare the proposed bootstrap method with the
Wald-type method, which is widely used in survey sampling. Results show that
the proposed bootstrap method is better in terms of coverage rate especially
when sample size is limited.


  Let $G$ be the right-angled Artin group associated to the flag complex
$\Sigma$ and let $\pi:G\to\Z$ be its canonical height function. We investigate
the presentation theory of the groups $\Gamma_n=\pi^{-1}(n\Z)$ and construct an
algorithm that, given $n$ and $\Sigma$, outputs a presentation of optimal
deficiency on a minimal generating set, provided $\Sigma$ is triangle-free; the
deficiency tends to infinity as $n\to\infty$ if and only if the corresponding
Bestvina-Brady kernel $\bigcap_n\Gamma_n$ is not finitely presented, and the
algorithm detects whether this is the case. We explain why there cannot exist
an algorithm that constructs finite presentations with these properties in the
absence of the triangle-free hypothesis. We explore what is possible in the
general case, describing how to use the configuration of 2-simplices in
$\Sigma$ to simplify presentations and giving conditions on $\Sigma$ that
ensure that the deficiency goes to infinity with $n$. We also prove, for
general $\Sigma$, that the abelianized deficiency of $\Gamma_n$ tends to
infinity if and only if $\Sigma$ is 1-acyclic, and discuss connections with the
relation gap problem.


  We present a new model for LT codes which simplifies the analysis of the
error probability of decoding by belief propagation. For any given degree
distribution, we provide the first rigorous expression for the limiting error
probability as the length of the code goes to infinity via recent results in
random hypergraphs [Darling-Norris 2005]. For a code of finite length, we
provide an algorithm for computing the probability of error of the decoder.
This algorithm improves the one of [Karp-Luby-Shokrollahi 2004] by a linear
factor.


  Face presentation attack detection (fPAD) plays a critical role in the modern
face recognition pipeline. The generalization ability of face presentation
attack detection models to unseen attacks has become a key issue for real-world
deployment, which can be improved when models are trained with face images from
different input distributions and different types of spoof attacks. In reality,
due to legal and privacy issues, training data (both real face images and spoof
images) are not allowed to be directly shared between different data sources.
In this paper, to circumvent this challenge, we propose a Federated Test-Time
Adaptive Face Presentation Attack Detection with Dual-Phase Privacy
Preservation framework, with the aim of enhancing the generalization ability of
fPAD models in both training and testing phase while preserving data privacy.
In the training phase, the proposed framework exploits the federated learning
technique, which simultaneously takes advantage of rich fPAD information
available at different data sources by aggregating model updates from them
without accessing their private data. To further boost the generalization
ability, in the testing phase, we explore test-time adaptation by minimizing
the entropy of fPAD model prediction on the testing data, which alleviates the
domain gap between training and testing data and thus reduces the
generalization error of a fPAD model. We introduce the experimental setting to
evaluate the proposed framework and carry out extensive experiments to provide
various insights about the proposed method for fPAD.


  Many object pose estimation algorithms rely on the analysis-by-synthesis
framework which requires explicit representations of individual object
instances. In this paper we combine a gradient-based fitting procedure with a
parametric neural image synthesis module that is capable of implicitly
representing the appearance, shape and pose of entire object categories, thus
rendering the need for explicit CAD models per object instance unnecessary. The
image synthesis network is designed to efficiently span the pose configuration
space so that model capacity can be used to capture the shape and local
appearance (i.e., texture) variations jointly. At inference time the
synthesized images are compared to the target via an appearance based loss and
the error signal is backpropagated through the network to the input parameters.
Keeping the network parameters fixed, this allows for iterative optimization of
the object pose, shape and appearance in a joint manner and we experimentally
show that the method can recover orientation of objects with high accuracy from
2D images alone. When provided with depth measurements, to overcome scale
ambiguities, the method can accurately recover the full 6DOF pose successfully.


  Several structural results for the set of competitive equilibria in trading
networks with frictions are established: The lattice theorem, the rural
hospitals theorem, the existence of side-optimal equilibria, and a
group-incentive-compatibility result hold with imperfectly transferable utility
and in the presence of frictions. While our results are developed in a trading
network model, they also imply analogous (and new) results for exchange
economies with combinatorial demand and for two-sided matching markets with
transfers.


  Anderson localization is a consequence of coherent interference of multiple
scattering events in the presence of disorder, which leads to an exponential
suppression of the transmission. The decay of the transmission is typically
probed at a given energy or frequency. Here we show that this decay affects the
dynamics of a qubit coupled to the disordered system and we express the
relaxation rate of the qubit in terms of the localization properties.
Conversely, adding static disorder to a channel coupled to a qubit will reduce
the decoherence rate of the qubit. Hence, when designing electrodes that couple
to qubits it is possible to improve their performance by adding impurities to
the channel.


  Nanostructured electronic devices, such as those based on graphene, are
typically grown on top of the insulator SiO2. Their exposure to a flux of small
size-selected silver nanoparticles has revealed remarkably selective adhesion:
the graphene channel can be made fully metallized while the insulating
substrate remains coverage-free. This conspicuous contrast derives from the low
binding energy between the metal nanoparticles and a contaminant-free
passivated silica surface. In addition to providing physical insight into
nanoparticle adhesion, this effect may be of value in applications involving
deposition of metallic layers on device working surfaces: it eliminates the
need for masking the insulating region and the associated extensive and
potentially deleterious pre- and postprocessing.


  Benchmarks, such as COCO, play a crucial role in object detection. However,
existing benchmarks are insufficient in scale variation, and their protocols
are inadequate for fair comparison. In this paper, we introduce the
Universal-Scale object detection Benchmark (USB). USB has variations in object
scales and image domains by incorporating COCO with the recently proposed Waymo
Open Dataset and Manga109-s dataset. To enable fair comparison and inclusive
research, we propose training and evaluation protocols. They have multiple
divisions for training epochs and evaluation image resolutions, like weight
classes in sports, and compatibility across training protocols, like the
backward compatibility of the Universal Serial Bus. Specifically, we request
participants to report results with not only higher protocols (longer training)
but also lower protocols (shorter training). Using the proposed benchmark and
protocols, we conducted extensive experiments using 15 methods and found
weaknesses of existing COCO-biased methods. The code is available at
https://github.com/shinya7y/UniverseNet .


  Using a new form of density functional theory for the {\em ab initio}
description of electronic systems in contact with a dielectric environment, we
present the first detailed study of the impact of a solvent on the surface
chemistry of Cr$_2$O$_3$, the passivating layer of stainless steel alloys.
Compared to vacuum, we predict that the presence of water has little impact on
the adsorption of chloride ions to the oxygen-terminated surface but a dramatic
effect on the binding of hydrogen to that surface. These results indicate that
the dielectric screening properties of water are important to the passivating
effects of the oxygen-terminated surface.


  The growth rate of the filamentation instability triggered when a diluted
cold electron beam passes through a cold plasma is evaluated using the quantum
hydrodynamic equations. Compared with a cold fluid model, quantum effects
reduce both the unstable wave vector domain and the maximum growth rate.
Stabilization of large wave vector modes is always achieved, but significant
reduction of the maximum growth rate depends on a dimensionless parameter that
is provided. Although calculations are extended to the relativistic regime,
they are mostly relevant to the non-relativistic one.


  The average matter density within the turnaround scale, which demarcates
where galaxies shift from clustering around a structure to joining the
expansion of the Universe, is an important cosmological probe. However, a
measurement of the mass enclosed by the turnaround radius is difficult.
Analyses of the turnaround scale in simulated galaxy clusters place the
turnaround radius at about three times the virial radius in a \(\Lambda CDM\)
universe and at a (present-day) density contrast with the background matter
density of the Universe of \(\delta \sim 11\). Assessing the mass at such
extended distances from a cluster's center is a challenge for current mass
measurement techniques. Consequently, there is a need to develop and validate
new mass-scaling relations, to connect observable masses at cluster interiors
with masses at greater distances. Our research aims to establish an analytical
framework for the most probable mass profile of galaxy clusters, leading to
novel mass scaling relations, allowing us to estimate masses at larger scales.
We derive such analytical mass profiles and compare them with those from
cosmological simulations. We use excursion set theory, which provides a
statistical framework for the density and local environment of dark matter
halos, and complement it with the spherical collapse model to follow the
non-linear growth of these halos. The profile we developed analytically shows a
good agreement (better than 30\%, and dependent on halo mass) with the mass
profiles of simulated galaxy clusters. Mass scaling relations are obtained from
the analytical profile with offset better than 15\% from the simulated ones.
This level of precision highlights the potential of our model for probing
structure formation dynamics at the outskirts of galaxy clusters.


  Minimum Bayes Risk (MBR) decoding is a text generation technique that has
been shown to improve the quality of machine translations, but is expensive,
even if a sampling-based approximation is used. Besides requiring a large
number of sampled sequences, it requires the pairwise calculation of a utility
metric, which has quadratic complexity. In this paper, we propose to
approximate pairwise metric scores with scores calculated against aggregated
reference representations. This changes the complexity of utility estimation
from $O(n^2)$ to $O(n)$, while empirically preserving most of the quality gains
of MBR decoding. We release our source code at https://github.com/ZurichNLP/mbr


  Cloud computing is steadily growing and, as IaaS vendors have started to
offer pay-as-you-go billing policies, it is fundamental to achieve as much
elasticity as possible, avoiding over-provisioning that would imply higher
costs. In this paper, we briefly analyse the orchestration characteristics of
PaaSSOA, a proposed architecture already implemented for Jolie microservices,
and Kubernetes, one of the various orchestration plugins for Docker; then, we
outline similarities and differences of the two approaches, with respect to
their own domain of application. Furthermore, we investigate some ideas to
achieve a federation of the two technologies, proposing an architectural
composition of Jolie microservices on Docker Container-as-a-Service layer.


  Let $\mu_{q, b}$ be the Cantor measure associated with the iterated function
system $f_i(x)=x/b+i/q, 0\le i\le q-1$, where $2\le q, b/q\in \Z$. In this
paper, we consider spectra and maximal orthogonal sets of the Cantor measure
$\mu_{q, b}$ and their rational rescaling. We introduce a quantity to measure
level difference between a branch and its subbranch for the labeling tree
corresponding to a maximal orthogonal set of the Cantor measure $\mu_{q, b}$,
and use certain boundedness property of that quantity as sufficient and
necessary conditions for a maximal orthogonal set of the Cantor measure
$\mu_{q, b}$ to be its spectrum. We show that the integrally rescaled set
$K\Lambda$ is still a spectrum if it is a maximal orthogonal set, and we
provide a simple characterization for the integrally rescaled set to be a
maximal orthogonal set. As an application of the above characterization, we
find all integers $K$ such that $K\Lambda_4$ are spectra of the Cantor measure
$\mu_{2, 4}$, where $\Lambda_4:=\{\sum_{n=0}^\infty d_n 4^n: d_n\in \{0,
1\}\}\subset \Z$ is the first known spectrum for the Cantor measure $\mu_{2,
4}$. Finally we discuss rescaling spectra rationally and construct a spectrum
$\Lambda$ for the Cantor measure $\mu_{q, b}$ such that $\Lambda/(b-1)$ is a
maximal orthogonal set but not a spectrum.


  Topological Data Analysis (TDA) is the collection of mathematical tools that
capture the structure of shapes in data. Despite computational topology and
computational geometry, the utilization of TDA in time series and signal
processing is relatively new. In some recent contributions, TDA has been
utilized as an alternative to the conventional signal processing methods.
Specifically, TDA is been considered to deal with noisy signals and time
series. In these applications, TDA is used to find the shapes in data as the
main properties, while the other properties are assumed much less informative.
In this paper, we will review recent developments and contributions where
topological data analysis especially persistent homology has been applied to
time series analysis, dynamical systems and signal processing. We will cover
problem statements such as stability determination, risk analysis, systems
behaviour, and predicting critical transitions in financial markets.


  We study the entanglement dynamics of two atoms coupled to their own
Jaynes-Cummings cavities in single-excitation space. Here we use the
concurrence to measure the atomic entanglement. And the partial Bell states as
initial states are considered. Our analysis suggests that there exist collapses
and recovers in the entanglement dynamics. The physical mechanism behind the
entanglement dynamics is the periodical information and energy exchange between
atoms and light fields. For the initial Partial Bell states, only if the ratio
of two atom-cavity coupling strengths is a rational number, the evolutionary
periodicity of the atomic entanglement can be found. And whether there is time
translation between two kinds of initial partial Bell state cases depends on
the odd-even number of the coupling strength ratio.


  A high level of physical detail in a molecular model improves its ability to
perform high accuracy simulations, but can also significantly affect its
complexity and computational cost. In some situations, it is worthwhile to add
additional complexity to a model to capture properties of interest; in others,
additional complexity is unnecessary and can make simulations computationally
infeasible. In this work we demonstrate the use of Bayes factors for molecular
model selection, using Monte Carlo sampling techniques to evaluate the evidence
for different levels of complexity in the two-centered Lennard-Jones +
quadrupole (2CLJQ) fluid model. Examining three levels of nested model
complexity, we demonstrate that the use of variable quadrupole and bond length
parameters in this model framework is justified only sometimes. We also explore
the effect of the Bayesian prior distribution on the Bayes factors, as well as
ways to propose meaningful prior distributions. This Bayesian Markov Chain
Monte Carlo (MCMC) process is enabled by the use of analytical surrogate models
that accurately approximate the physical properties of interest. This work
paves the way for further atomistic model selection work via Bayesian inference
and surrogate modeling


  We present a search for RR Lyrae variable stars from archival observations of
the Southern Edgeworth-Kuiper Belt Object survey. The survey covers 1675 square
degrees along the ecliptic to a mean depth of V=19.5, i.e. a heliocentric
distance of ~50kpc for RR Lyrae stars. The survey reveals 2016 RR Lyrae
candidates. Follow-up photometric monitoring of a subset of these candidates
shows (24+/-12)% contamination by non-RR Lyrae variables. We derive a map of
over-density of RR Lyraes in the halo that reveals a series of structures
coincident with the leading and trailing arms of debris from the Sagittarius
dwarf galaxy. One of the regions of over-density is found on the trailing arm,
200 deg. from the main body of the Sagittarius dwarf at a distance of ~45kpc.
This distant detection of the stellar population of the outer trailing arm of
Sagittarius offers a tight constraint on the motion of the dwarf galaxy. A
distinctly separate region of over-density is seen towards the Virgo Over
Density.


  In this paper, we study the clustering properties of the Spatial Preferential
Attachment (SPA) model. This model naturally combines geometry and preferential
attachment using the notion of spheres of influence. It was previously shown in
several research papers that graphs generated by the SPA model are similar to
real-world networks in many aspects. Also, this model was successfully used for
several practical applications. However, the clustering properties of the SPA
model were not fully analyzed. The clustering coefficient is an important
characteristic of complex networks which is tightly connected with its
community structure. In the current paper, we study the behaviour of C(d),
which is the average local clustering coefficient for the vertices of degree d.
It was empirically shown that in real-world networks C(d) usually decreases as
1/d^a for some a>0 and it was often observed that a=1. We prove that in the SPA
model C(d) decreases as 1/d. Furthermore, we are also able to prove that not
only the average but the individual local clustering coefficient of a vertex v
of degree $d$ behaves as 1/d if d is large enough. The obtained results further
confirm the suitability of the SPA model for fitting various real-world complex
networks.


  Preprocessing a 2D image often produces a noisy cloud of interest points. We
study the problem of counting holes in unorganized clouds in the plane. The
holes in a given cloud are quantified by the topological persistence of their
boundary contours when the cloud is analyzed at all possible scales. We design
the algorithm to count holes that are most persistent in the filtration of
offsets (neighborhoods) around given points. The input is a cloud of $n$ points
in the plane without any user-defined parameters. The algorithm has $O(n\log
n)$ time and $O(n)$ space. The output is the array (number of holes, relative
persistence in the filtration). We prove theoretical guarantees when the
algorithm finds the correct number of holes (components in the complement) of
an unknown shape approximated by a cloud.


  Room temperature single photon emitters are very important resources for
photonics and emerging quantum technologies. In this work we study single
photon emission from defect centers in 20 nm zinc oxide (ZnO) nanoparticles.
The emitters exhibit bright broadband fluorescence in the red spectral range
centered at 640 nm with polarized excitation and emission. The studied emitters
showed continuous blinking, however, bleaching can be suppressed using a
polymethyl methacrylate (PMMA) coating. Furthermore, hydrogen termination
increased the density of single photon emitters. Our results will contribute to
the identification of quantum systems in ZnO.


  In rapidly-evolving domains such as autonomous driving, the use of multiple
sensors with different modalities is crucial to ensure high operational
precision and stability. To correctly exploit the provided information by each
sensor in a single common frame, it is essential for these sensors to be
accurately calibrated. In this paper, we leverage the ability of Neural
Radiance Fields (NeRF) to represent different sensors modalities in a common
volumetric representation to achieve robust and accurate spatio-temporal sensor
calibration. By designing a partitioning approach based on the visible part of
the scene for each sensor, we formulate the calibration problem using only the
overlapping areas. This strategy results in a more robust and accurate
calibration that is less prone to failure. We demonstrate that our approach
works on outdoor urban scenes by validating it on multiple established driving
datasets. Results show that our method is able to get better accuracy and
robustness compared to existing methods.


  We investigate the open string propagation in the weakly curved background
with the Kalb-Ramond field containing an infinitesimal part, linear in
coordinate. Solving the Neumann boundary conditions, we find the expression for
the space-time coordinates in terms of the effective ones. So, the initial
theory reduces to the effective one. This effective theory is defined on the
nongeometric doubled space $(q^\mu,\tilde{q}_\mu)$, where $q^\mu$ is the
effective coordinate and $\tilde{q}_\mu$ is its T-dual. The effective metric
depends on the coordinate $q^\mu$ and there exists non-trivial effective
Kalb-Ramond field which depends on the T-dual coordinate $\tilde{q}_\mu$. The
fact that $\tilde{q}_\mu$ is $\Omega$-odd leads to the nonvanishing effective
Kalb-Ramond field.


  Unmanned aerial vehicle (UAV) tracking is of great significance for a wide
range of applications, such as delivery and agriculture. Previous benchmarks in
this area mainly focused on small-scale tracking problems while ignoring the
amounts of data, types of data modalities, diversities of target categories and
scenarios, and evaluation protocols involved, greatly hiding the massive power
of deep UAV tracking. In this work, we propose WebUAV-3M, the largest public
UAV tracking benchmark to date, to facilitate both the development and
evaluation of deep UAV trackers. WebUAV-3M contains over 3.3 million frames
across 4,500 videos and offers 223 highly diverse target categories. Each video
is densely annotated with bounding boxes by an efficient and scalable
semiautomatic target annotation (SATA) pipeline. Importantly, to take advantage
of the complementary superiority of language and audio, we enrich WebUAV-3M by
innovatively providing both natural language specifications and audio
descriptions. We believe that such additions will greatly boost future research
in terms of exploring language features and audio cues for multimodal UAV
tracking. In addition, a fine-grained UAV tracking-under-scenario constraint
(UTUSC) evaluation protocol and seven challenging scenario subtest sets are
constructed to enable the community to develop, adapt and evaluate various
types of advanced trackers. We provide extensive evaluations and detailed
analyses of 43 representative trackers and envision future research directions
in the field of deep UAV tracking and beyond. The dataset, toolkits and
baseline results are available at \url{https://github.com/983632847/WebUAV-3M}.


  Considered is the standard 4-dimensional ${\cal N}=1\,\,SU(N_c)$ SQCD with
$1\leq N_F\leq N_c$ quark flavors with masses $m_{Q,i}$. {\bf The gauge
invariant order parameter $\rho$ is introduced in \cite{ch1} distinguishing
confinement (with $\rho=0$) and higgs (with $\rho\neq 0$) phases}. Using a
number of independent arguments for different variants of transition between
the confinement and higgs regimes in these theories, it is shown that {\bf
transitions between these regimes are not crossovers but the phase
transitions}.
  In \cite{FS} the very special $SU(N_c)$ QCD theory with $N_F=N_c$ defective
scalar "quarks" was considered by E.Fradkin and S.H.Shenker. The conclusion of
\cite{FS} was that {\bf the transition between the confinement and higgs
regimes is the analytic crossover}. And although the theory considered in
\cite{FS} was very specific, the experience shows that up to now there is a
widely spread opinion that this conclusion has general applicability.
  This model \cite{FS} is criticized in \cite{ch1},\cite{ch2} as incompatible
with and very different from the standard non-SUSY $SU(N_c)\,\,N_F=N_c$ QCD
theory with standard scalar quarks with all their physical degrees of freedom.
It is emphasized that this model \cite{FS} is really {\bf the Stuckelberg
$SU(N_c)$ YM-theory with no dynamical electric quarks and massive all $N_c^2-1$
electric gluons with fixed by hands nonzero masses}. There is no genuine
confinement in this theory, it stays permanently in the completely higgsed
(i.e. condensed) by hands phase only. And this is a reason for a crossover in
this theory. While in the theory with standard scalar quarks there is the phase
transition between the confinement (at $0 < |v|\ll \Lambda_{QCD}$) and higgs
(at $|v|\gg\Lambda_{QCD}$) regimes.


  Flares overlaid on the smooth power-law decay of Swift X-ray afterglows are
rather common, appearing in roughly half the observed light curves. They are a
manifestation of the late time activity of the inner engine, since their
temporal evolution is too fast to be linked to activity taking place in the
external shock blastwave. In this paper we show that the energy emitted in the
form of flares decreases with time as a power-law. We discuss several
possibilities in which the flares can be powered and the source of the observed
variability. We show that late time accretion from a disk can provide the
necessary energy input in both classes of short duration and long duration
gamma-ray bursts.


  Magnetic van der Waals (vdW) materials have been heavily pursued for
fundamental physics as well as for device design. Despite the rapid advances,
so far magnetic vdW materials are mainly insulating or semiconducting, and none
of them possesses a high electronic mobility - a property that is rare in
layered vdW materials in general. The realization of a magnetic high-mobility
vdW material would open the possibility for novel magnetic twistronic or
spintronic devices. Here we report very high carrier mobility in the layered
vdW antiferromagnet GdTe3. The electron mobility is beyond 60,000 cm2 V-1 s-1,
which is the highest among all known layered magnetic materials, to the best of
our knowledge. Among all known vdW materials, the mobility of bulk GdTe3 is
comparable to that of black phosphorus, and is only surpassed by graphite. By
mechanical exfoliation, we further demonstrate that GdTe3 can be exfoliated to
ultrathin flakes of three monolayers, and that the magnetic order and
relatively high mobility is retained in approximately 20-nm-thin flakes.


  We give an asymptotic formula for the $2k$th moment of a sum of
multiplicative Steinhaus variables. This was recently computed independently by
Harper, Nikeghbali and Radziwi\l\l. We also compute the $2k$th moment of a
truncated characteristic polynomial of a unitary matrix. This provides an
asymptotic equivalence with the moments of Steinhaus variables. Similar results
for multiplicative Rademacher variables are given.


  An axis-parallel $d$--dimensional box is a Cartesian product $R_1 \times R_2
\times ... \times R_d$ where $R_i$ (for $1 \le i \le d$) is a closed interval
of the form $[a_i, b_i]$ on the real line. For a graph $G$, its \emph{boxicity}
$\boxi(G)$ is the minimum dimension $d$, such that $G$ is representable as the
intersection graph of (axis--parallel) boxes in $d$--dimensional space. The
concept of boxicity finds applications in various areas such as ecology,
operation research etc. We show that for any graph $G$ with maximum degree
$\Delta$, $\boxi(G) \le 2 \Delta^2 + 2$. That the bound does not depend on the
number of vertices is a bit surprising considering the fact that there are
highly connected bounded degree graphs such as expander graphs. Our proof is
very short and constructive. We conjecture that $\boxi(G)$ is $O(\Delta)$.


  It is explained how field-theoretic methods and the dynamic renormalisation
group (RG) can be applied to study the universal scaling properties of systems
that either undergo a continuous phase transition or display generic scale
invariance, both near and far from thermal equilibrium. Part 1 introduces the
response functional field theory representation of (nonlinear) Langevin
equations. The RG is employed to compute the scaling exponents for several
universality classes governing the critical dynamics near second-order phase
transitions in equilibrium. The effects of reversible mode-coupling terms,
quenching from random initial conditions to the critical point, and violating
the detailed balance constraints are briefly discussed. It is shown how the
same formalism can be applied to nonequilibrium systems such as driven
diffusive lattice gases. Part 2 describes how the master equation for
stochastic particle reaction processes can be mapped onto a field theory
action. The RG is then used to analyse simple diffusion-limited annihilation
reactions as well as generic continuous transitions from active to inactive,
absorbing states, which are characterised by the power laws of (critical)
directed percolation. Certain other important universality classes are
mentioned, and some open issues are listed.


  Incremental few-shot semantic segmentation (IFSS) aims to incrementally
extend a semantic segmentation model to novel classes according to only a few
pixel-level annotated data, while preserving its segmentation capability on
previously learned base categories. This task faces a severe semantic-aliasing
issue between base and novel classes due to data imbalance, which makes
segmentation results unsatisfactory. To alleviate this issue, we propose the
Semantic-guided Relation Alignment and Adaptation (SRAA) method that fully
considers the guidance of prior semantic information. Specifically, we first
conduct Semantic Relation Alignment (SRA) in the base step, so as to
semantically align base class representations to their semantics. As a result,
the embeddings of base classes are constrained to have relatively low semantic
correlations to categories that are different from them. Afterwards, based on
the semantically aligned base categories, Semantic-Guided Adaptation (SGA) is
employed during the incremental learning stage. It aims to ensure affinities
between visual and semantic embeddings of encountered novel categories, thereby
making the feature representations be consistent with their semantic
information. In this way, the semantic-aliasing issue can be suppressed. We
evaluate our model on the PASCAL VOC 2012 and the COCO dataset. The
experimental results on both these two datasets exhibit its competitive
performance, which demonstrates the superiority of our method.


  Joint estimation of grasped object pose and extrinsic contacts is central to
robust and dexterous manipulation. In this paper, we propose a novel
state-estimation algorithm that jointly estimates contact location and object
pose in 3D using exclusively proprioception and tactile feedback. Our approach
leverages two complementary particle filters: one to estimate contact location
(CPFGrasp) and another to estimate object poses (SCOPE). We implement and
evaluate our approach on real-world single-arm and dual-arm robotic systems. We
demonstrate that by bringing two objects into contact, the robots can infer
contact location and object poses simultaneously. Our proposed method can be
applied to a number of downstream tasks that require accurate pose estimates,
such as tool use and assembly. Code and data can be found at
https://github.com/MMintLab/scope.


  Several prominent proposals have suggested that spins of localized electrons
could serve as quantum computer qubits. The exchange interaction has been
invoked as a means of implementing two qubit gates. In this paper, we analyze
the strength and form of the exchange interaction under relevant conditions. We
find that, when several spins are engaged in mutual interactions, the
quantitative strengths or even qualitative forms of the interactions can
change. It is shown that the changes can be dramatic within a Heitler-London
model. Hund-Mulliken calculations are also presented, and support the
qualititative conclusions from the Heitler-London model. The effects need to be
considered in spin-based quantum computer designs, either as a source of gate
error to be overcome or a new interaction to be exploited.


  For propagation of surface shallow-water waves on irrotational flows, we
derive a new two-component system. The system is obtained by a variational
approach in the Lagrangian formalism. The system has a non-canonical
Hamiltonian formulation. We also find its exact solitary-wave solutions.


  Thermal transport in the mixed state of a d-wave superconductor is considered
within the weak-field regime. We express the thermal conductivity,
$\kappa_{xx}$, and the thermal Hall conductivity, $\kappa_{xy}$, in terms of
the cross section for quasiparticle scattering from a single vortex. Solving
for the cross section (neglecting the Berry phase contribution and the
anisotropy of the gap nodes), we obtain $\kappa_{xx}(H,T)$ and
$\kappa_{xy}(H,T)$ in surprisingly good agreement with the qualitative features
of the experimental results for YBa$_{2}$Cu$_{3}$O$_{6.99}$. In particular, we
show that the simple, yet previously unexpected, weak-field behavior,
$\kappa_{xy}(H,T) \sim T\sqrt{H}$, is that of thermally-excited nodal
quasiparticles, scattering primarily from impurities, with a small skew
component provided by vortex scattering.


  Ride-pooling systems, despite being an appealing urban mobility mode, still
struggle to gain momentum. While we know the significance of critical mass in
reaching system sustainability, less is known about the spatiotemporal patterns
of system performance. Here, we use 1.5 million NYC taxi trips (sampled over a
six-month period) and experiment to understand how well they could be served
with pooled services. We use a utility-driven ride-pooling algorithm and
observe the pooling potential with six performance indicators: mileage
reductions, travellers' utility gains, share of pooled rides, occupancy,
detours, and potential fleet reduction. We report distributions and temporal
profiles of about 35 thousand experiments covering weekdays, weekends,
evenings, mornings, and nights. We report complex spatial patterns, with gains
concentrated in the core of the network and costs concentrated on the
peripheries. The greatest potential shifts from the North in the morning to the
Central and South in the afternoon. Offering pooled rides at the fare 32% lower
than private ride-hailing seems to be sufficient to attract pooling yet
dynamically adjusting it to the demand level and spatial pattern may be
efficient. The patterns observed in NYC were replicated on smaller datasets in
Chicago and Washington, DC, the occupancy grows with the demand with similar
trends.


  Momentum transfer due to electron-electron interaction (Coulomb drag) between
two quantum wells, separated by a distance $d$, in the presence of a
perpendicular magnetic field, is studied at low temperatures. We find besides
the well known Shubnikov-de Haas oscillations, which also appear in the drag
effect, the momentum transfer is markedly enhanced by the magnetic field.


  In the purely affine formulation of gravity, the gravitational field is
represented by the symmetric part of the Ricci tensor of the affine connection.
The classical electromagnetic field can be represented in this formulation by
the second Ricci tensor of the connection. Such a construction is dynamically
equivalent to the sourceless Einstein-Maxwell equations. We generalize this
construction to the case with sources, represented by the derivative of the
affine Lagrangian density with respect to the connection. We show that the
Maxwell equations with sources emerge for the simplest affine Lagrangian for
matter, while the Einstein and Lorentz equations arise if mass has
electromagnetic origin. We also show that the Maxwell equations replace the
unphysical constraint imposed by the projective invariance of purely affine
Lagrangians that depend explicitly on the connection.


  We study a hybrid optomechanical system consisting of a Bose-Einstein
condensate (BEC) trapped inside a single-mode optical cavity with a moving
end-mirror. The intracavity light field has a dual role: it excites a momentum
side-mode of the condensate, and acts as a nonlinear spring that couples the
vibrating mirror to that collective density excitation. We present the dynamics
in a regime where the intracavity optical field, the mirror, and the side-mode
excitation all display bistable behavior. In this regime we find that the
dynamics of the system exhibits Hamiltonian chaos for appropriate initial
conditions.


  The line profile variability and photometric variability of the O9.5 Vp star
HD93521 are examined in order to establish the properties of the non-radial
pulsations in this star. Fourier techniques are used to characterize the
modulations of the He I 5876, 6678 and H-alpha lines in several spectroscopic
time series and to search for variations in a photometric time series. Our
spectroscopic data confirm the existence of two periods of 1.75 and 2.89 hr.
The line profiles, especially those affected by emission wings, exhibit also
modulations on longer time scales, but these are epoch-dependent and change
from line to line. Unlike previous claims, we find no unambiguous signature of
the rotational period in our data, nor of a third pulsation period
(corresponding to a frequency of 2.66 day$^{-1}$). HD 93521 very likely
exhibits non-radial pulsations with periods of 1.75 and 2.89 hr with $l \simeq
8 \pm 1$ and $l \simeq 4 \pm 1$ respectively. No significant signal is found in
the first harmonics of these two periods. The 2.89 hr mode is seen at all
epochs and in all lines investigated, while the visibility of the 1.75 hr mode
is clearly epoch dependent. Whilst light variations are detected, their
connection to these periodicities is not straightforward.


  At the LHC we are colliding protons, but it is not the protons that are doing
the interacting. It is their constituents the quarks, antiquarks and
gluons-collectively known as partons. We need to know how what fractional
momentum of the proton each of these partons takes at the energy scale of LHC
collisions, in order to understand LHC physics. Such parton momentum
distributions are known as PDFs (Parton Distribution Functions) and are a field
of study in their own right. However, it is now the case that the uncertainties
on PDFs are a major contributor to the background to the discovery of physics
Beyond the Standard Model (BSM). Firstly in searches at the highest energy
scales of a few TeV and secondly in precision measurements of Standard Model
(SM) parameters such as the mass of the W-boson, $m_W$, or the weak mixing
angle, $sin^2\theta_W$, which can provide indirect evidence for BSM physics in
their deviations from SM values.


  The notion of degree and related notions concerning recurrence and transience
for a class of L'evy processes on metric Abelian groups are studied. The case
of random walks on a hierarchical group is examined with emphasis on the role
of the ultrametric structure of the group and on analogies and differences with
Euclidean random walks. Applications to separation of time scales and
occupation times of multilevel branching systems are discussed.


  Randomized rumor spreading processes diffuse information on an undirected
graph and have been widely studied. In this work, we present a generic
framework for analyzing a broad class of such processes on regular graphs. Our
analysis is protocol-agnostic, as it only requires the expected proportion of
newly informed vertices in each round to be bounded, and a natural negative
correlation property.
  This framework allows us to analyze various protocols, including PUSH, PULL,
and PUSH-PULL, thereby extending prior research. Unlike previous work, our
framework accommodates message failures at any time $t\geq 0$ with a
probability of $1-q(t)$, where the credibility $q(t)$ is any function of time.
This enables us to model real-world scenarios in which the transmissibility of
rumors may fluctuate, as seen in the spread of ``fake news'' and viruses.
Additionally, our framework is sufficiently broad to cover dynamic graphs.


  The angular and temperature (10-250 K) variation of the Knight shift of
single-crystalline U(Pt0.95Pd0.05)3 has been measured in transverse field
(B=0.6 T) mSR experiments. By analysing the temperature variation of the Knight
shift with a modified Curie-Weiss expression the muon localization site in this
hexagonal material is determined at (0,0,0).


  We study generalized Killing spinors on the standard sphere $\mathbb{S}^3$,
which turn out to be related to Lagrangian embeddings in the nearly K\"ahler
manifold $S^3\times S^3$ and to great circle flows on $\mathbb{S}^3$. Using our
methods we generalize a well known result of Gluck and Gu concerning
divergence-free geodesic vector fields on the sphere and we show that the space
of Lagrangian submanifolds of $S^3\times S^3$ has at least three connected
components.


  Unsupervised learning of discrete representations in neural networks (NNs)
from continuous ones is essential for many modern applications. Vector
Quantisation (VQ) has become popular for this, in particular in the context of
generative models, such as Variational Auto-Encoders (VAEs), where the
exponential moving average-based VQ (EMA-VQ) algorithm is often used. Here, we
study an alternative VQ algorithm based on Kohonen's learning rule for the
Self-Organising Map (KSOM; 1982). EMA-VQ is a special case of KSOM. KSOM is
known to offer two potential benefits: empirically, it converges faster than
EMA-VQ, and KSOM-generated discrete representations form a topological
structure on the grid whose nodes are the discrete symbols, resulting in an
artificial version of the brain's topographic map. We revisit these properties
by using KSOM in VQ-VAEs for image processing. In our experiments, the speed-up
compared to well-configured EMA-VQ is only observable at the beginning of
training, but KSOM is generally much more robust, e.g., w.r.t. the choice of
initialisation schemes.


  We show that in general holographic stress tensor may contain a new term of
divergence of a spacelike unit normal acceleration. Then, it is shown that in
contrast to previous descriptions, a new stress tensor for Kerr-AdS solutions
can be a traceless one. Interestingly, this prescription entails a local
failure on the IR-UV connection.


  In this paper, we address a novel task, namely weakly-supervised
spatio-temporally grounding natural sentence in video. Specifically, given a
natural sentence and a video, we localize a spatio-temporal tube in the video
that semantically corresponds to the given sentence, with no reliance on any
spatio-temporal annotations during training. First, a set of spatio-temporal
tubes, referred to as instances, are extracted from the video. We then encode
these instances and the sentence using our proposed attentive interactor which
can exploit their fine-grained relationships to characterize their matching
behaviors. Besides a ranking loss, a novel diversity loss is introduced to
train the proposed attentive interactor to strengthen the matching behaviors of
reliable instance-sentence pairs and penalize the unreliable ones. Moreover, we
also contribute a dataset, called VID-sentence, based on the ImageNet video
object detection dataset, to serve as a benchmark for our task. Extensive
experimental results demonstrate the superiority of our model over the baseline
approaches.


  The antiferromagnetic (AFM) state has been investigated in the three
heavy-fermion compounds URu2Si2, UPd2Al3, and UNi2Al3 by measuring dV/dI(V)
curves of point contacts at different temperatures (1.5-20 K) and magnetic
fields (0-28 T). The zero-bias maximum in dV/dI(V) for URu2Si2 points to a
partially gapped Fermi-surface related to the itinerant nature of the AFM state
contrary to UPd2Al3 where analogous features have not been found. The AFM state
in UNi2Al3 has more similarities with URu2Si2. For URu2Si2, the same critical
field of about 40 T along the easy c axis is found for all features in dV/dI(V)
corresponding to the Neel temperature, the gap in the electronic density of
states, and presumably the ordered moments.


  In recent years, there has been increasing attention to the spatial
dimensions of residential segregation, such as the spatial arrangement of
segregated neighborhoods and the geographic scale or relative size of
segregated areas. However, the methods used to measure segregation do not
incorporate features of the built environment, such as the road connectivity
between locations or the physical barriers that divide groups. This article
introduces the Spatial Proximity and Connectivity (SPC) method for measuring
and analyzing segregation. The SPC method addresses the limitations of current
approaches by taking into account how the physical structure of the built
environment affects the proximity and connectivity of locations. In this
article, I describe the method and its application for studying segregation and
spatial inequality more broadly. I demonstrate one such application-analyzing
the impact of physical barriers on residential segregation-with a stylized
example and an empirical analysis of racial segregation in Pittsburgh, PA. The
SPC method contributes to scholarship on residential segregation by capturing
the effect of an important yet understudied mechanism of segregation-the
connectivity, or physical barriers, between locations-on the level and spatial
pattern of segregation, and enables further consideration of the role of the
built environment in segregation processes.