  In the context of control of smart structures, we present an approach for
state estimation of adaptive buildings with active load-bearing elements. For
obtaining information on structural deformation, a system composed of a digital
camera and optical emitters affixed to selected nodal points is introduced as a
complement to conventional strain gauge sensors. Sensor fusion for this novel
combination of sensors is carried out using a Kalman filter that operates on a
reduced-order structure model obtained by modal analysis. Signal delay caused
by image processing is compensated for by an out-of-sequence measurement update
which provides for a flexible and modular estimation algorithm. Since the
camera system is very precise, a self-tuning algorithm that adjusts model along
with observer parameters is introduced to reduce discrepancy between system
dynamic model and actual structural behavior. We further employ optimal sensor
placement to limit the number of sensors to be placed on a given structure and
examine the impact on estimation accuracy. A laboratory scale model of an
adaptive high-rise with actuated columns and diagonal bracings is used for
experimental demonstration of the proposed estimation scheme.


  One of the key concepts in testing is that of adequate test sets. A test
selection criterion decides which test sets are adequate. In this paper, a
language schema for specifying a large class of test selection criteria is
developed; the schema is based on two operations for building complex criteria
from simple ones. Basic algebraic properties of the two operations are derived.
  In the second part of the paper, a simple language-an instance of the general
schema-is studied in detail, with the goal of generating small adequate test
sets automatically. It is shown that one version of the problem is intractable,
while another is solvable by an efficient algorithm. An implementation of the
algorithm is described.


  We present an analysis of the environment of six QSO triplets at 1 $\lesssim$
z $\lesssim$ 1.5 by analyzing multiband (r,i,z, or g,r,i) images obtained with
Megacam at the CFHT telescope, aiming to investigate whether they are
associated or not with galaxy protoclusters. This was done by using photometric
redshifts trained using the high accuracy photometric redshifts of the
COSMOS2015 catalogue. To improve the quality of our photometric redshift
estimation, we included in our analysis near-infrared photometry (3.6 and 4.5
$\mu m$) from the unWISE survey available for our fields and the COSMOS survey.
This approach allowed us to obtain good photometric redshifts with dispersion,
as measured with the robust Sigma NMAD statistics of $\sim$ 0.04 for our six
fields. Our analysis setup was reproduced on lightcones constructed from the
Millennium Simulation data and the latest version of the L-GALAXIES
semi-analytic model to verify the protocluster detectability in such
conditions. The density field in a redshift slab containing each triplet was
then analyzed with a Gaussian kernel density estimator. We did not find any
significant evidence of the triplets inhabiting dense structures, such as a
massive galaxy cluster or protocluster.


  Using a magnetocapacitance technique, we determine the magnetic field of the
spin transition, B*, at filling factor nu=2/3 in the 2D electron system in
GaAs/AlGaAs heterojunctions. The field B* is found to decrease appreciably as
the wave function extent controlled by back gate voltage is increased. Our
calculations show that the contributions to the shift of B* from the change of
the Coulomb energy and the g factor change due to nonparabolicity are
approximately the same. The observed relative shift of B* is described with no
fitting parameters.


  The majority of the statisticians concluded many decades ago that fiducial
inference was nonsensical to them. Hannig et al. (2016) and others have,
however, contributed to a renewed interest and focus. Fiducial inference is
similar to Bayesian analysis, but without requiring a prior. The prior
information is replaced by assuming a particular data generating equation.
Berger (1985) explains that Bayesian analysis and statistical decision theory
are in harmony. Taraldsen and Lindqvist (2013) show that fiducial theory and
statistical decision theory also play well together. The purpose of this text
is to explain and exemplify this together with recent mathematical results.


  We introduce a two-dimensional Chern insulator in proximity to a $d$-wave
pseudogap state of the high-T$_c$ superconducting material as an effective
platform to realize the higher order topological system. The proximity-induced
$d$-density-wave (DDW) order in the Chern insulator layer serves as an
effective mass. The edge states will be fully gapped by this DDW order. In the
real space, the sign of the DDW order parameter changes at the system corners
due to the $d$-wave factor, leading to the gapless corner states, indicating
that this system may be in a higher order topological state. The higher order
topology in this coupled system is confirmed based on the calculation of the
edge polarization and the quadrupole moment. In the superconducting state where
the superconducting order and the DDW order coexist, the Majorana corner states
emerge.


  The AI for social good movement has now reached a state in which a large
number of one-off demonstrations have illustrated that partnerships of AI
practitioners and social change organizations are possible and can address
problems faced in sustainable development. In this paper, we discuss how moving
from demonstrations to true impact on humanity will require a different course
of action, namely open platforms containing foundational AI capabilities to
support common needs of multiple organizations working in similar topical
areas. We lend credence to this proposal by describing three example patterns
of social good problems and their AI-based solutions: natural language
processing for making sense of international development reports, causal
inference for providing guidance to vulnerable individuals, and
discrimination-aware classification for supporting unbiased allocation
decisions. We argue that the development of such platforms will be possible
through convenings of social change organizations, AI companies, and
grantmaking foundations.


  We demonstrate that the critical magnetic Reynolds number $Rm_c$ for a
turbulent non-helical dynamo in the low magnetic Prandtl number $Pm$ limit
(i.e. $Pm = Rm/Re \ll 1$) can be significantly reduced if the flow is submitted
to global rotation. Even for moderate rotation rates the required energy
injection rate can be reduced by a factor more than $10^3$. This strong
decrease of the onset is attributed to the reduction of the turbulent
fluctuations that makes the flow to have a much larger cut-off length-scale
compared to a non-rotating flow of the same Reynolds number. The dynamo thus
behaves as if it is driven by laminar behaviour (i.e. high $Pm$ behaviour) even
at high values of the Reynolds number (i.e. at low values of $Pm$). Our finding
thus points into a new paradigm for the design of new liquid metal dynamo
experiments.


  Communication efficiency is of importance for wireless federated learning
systems. In this paper, we propose a communication-efficient strategy for
federated learning over multiple-input multiple-output (MIMO) multiple access
channels (MACs). The proposed strategy comprises two components. When sending a
locally computed gradient, each device compresses a high dimensional local
gradient to multiple lower-dimensional gradient vectors using block
sparsification. When receiving a superposition of the compressed local
gradients via a MIMO-MAC, a parameter server (PS) performs a joint MIMO
detection and the sparse local-gradient recovery. Inspired by the turbo
decoding principle, our joint detection-and-recovery algorithm accurately
recovers the high-dimensional local gradients by iteratively exchanging their
beliefs for MIMO detection and sparse local gradient recovery outputs. We then
analyze the reconstruction error of the proposed algorithm and its impact on
the convergence rate of federated learning. From simulations, our gradient
compression and joint detection-and-recovery methods diminish the communication
cost significantly while achieving identical classification accuracy for the
case without any compression.


  We explore protoneutron star matter in the framework of cold and dense QCD
using the state-of-the-art perturbative equation of state including neutrinos
fixed by a lepton fraction that is appropriate for this environment.
Furthermore, we calculate the modifications in the lepton-rich equation of
state showing that stable strange quark matter has a more restricted parameter
space.


  Correlation clustering is a well-known unsupervised learning setting that
deals with positive and negative pairwise similarities. In this paper, we study
the case where the pairwise similarities are not given in advance and must be
queried in a cost-efficient way. Thereby, we develop a generic active learning
framework for this task that benefits from several advantages, e.g.,
flexibility in the type of feedback that a user/annotator can provide,
adaptation to any correlation clustering algorithm and query strategy, and
robustness to noise. In addition, we propose and analyze a number of novel
query strategies suited to this setting. We demonstrate the effectiveness of
our framework and the proposed query strategies via several experimental
studies.


  The min-max optimization problem, also known as the saddle point problem, is
a classical optimization problem which is also studied in the context of
zero-sum games. Given a class of objective functions, the goal is to find a
value for the argument which leads to a small objective value even for the
worst case function in the given class. Min-max optimization problems have
recently become very popular in a wide range of signal and data processing
applications such as fair beamforming, training generative adversarial networks
(GANs), and robust machine learning, to just name a few. The overarching goal
of this article is to provide a survey of recent advances for an important
subclass of min-max problem, where the minimization and maximization problems
can be non-convex and/or non-concave. In particular, we will first present a
number of applications to showcase the importance of such min-max problems;
then we discuss key theoretical challenges, and provide a selective review of
some exciting recent theoretical and algorithmic advances in tackling
non-convex min-max problems. Finally, we will point out open questions and
future research directions.


  We measure the time-dependent $C\!P$ violation parameters in $B^{0} \to
K^{0}_{S}K^{0}_{S}K^{0}_{S}$ decays using $772 \times 10^6$ $B {\mkern
1.5mu\overline{\mkern-1.5mu B \mkern-0.1mu}\mkern 0.1mu}$ pairs collected at
the $\Upsilon (4S)$ resonance with the Belle detector at the KEKB
asymmetric-energy $e^+ e^-$ collider. The obtained mixing-induced and direct
$C\!P$ asymmetries are $-0.71 \pm 0.23~{\rm(stat)} \pm 0.05~{\rm(syst)}$ and
$0.12 \pm 0.16~{\rm(stat)} \pm 0.05~{\rm(syst)}$, respectively. These values
are consistent with the Standard Model predictions. The significance of $C\!P$
violation differs from zero by 2.5 standard deviations.


  This chapter introduces the thermal conductivity of a novel one-dimensional
carbon nanostructure - diamond nanothread. It starts by introducing the family
of the diamond nanothread as acquired from density functional theory
calculations and also its successful experimental synthesisation. It then
briefs the mechanical properties of the diamond nanothreads as a fundamental
for their engineering applications. After that, it focuses on the thermal
transport properties of the diamond nanothreads by examining the influences
from various parameters such as size, geometry, and temperature. Then, the
application of diamond nanothread as reinforcements for nanocomposites is
discussed. By the end of the chapter, future directions and their potential
applications are discussed.


  The purpose of this paper is to obtain sufficient conditions for the
existence of a unique fixed point of T-Kannan type mappings on complete cone
metric spaces depended on another function.


  We show in a rigorous way that Crum's result on equal eigenvalue spectrum of
Sturm-Liouville problems can be obtained iteratively by successive Darboux
transformations. It can be shown that all neighbouring Darboux-transformed
potentials of higher order, u_{k} and u_{k+1}, satisfy the condition of shape
invariance provided the original potential u does. We use this result to proof
that under the condition of shape invariance the n-th iteration of the original
Sturm-Liouville problem defined through shape invariance is equal to the n-th
Crum transformation


  Face detection serves as a fundamental research topic for many applications
like face recognition. Impressive progress has been made especially with the
recent development of convolutional neural networks. However, the issue of
large scale variations, which widely exists in high resolution images/videos,
has not been well addressed in the literature. In this paper, we present a
novel algorithm called SFace, which efficiently integrates the anchor-based
method and anchor-free method to address the scale issues. A new dataset called
4K-Face is also introduced to evaluate the performance of face detection with
extreme large scale variations. The SFace architecture shows promising results
on the new 4K-Face benchmarks. In addition, our method can run at 50 frames per
second (fps) with an accuracy of 80% AP on the standard WIDER FACE dataset,
which outperforms the state-of-art algorithms by almost one order of magnitude
in speed while achieves comparative performance.


  In Bayesian inference, making deductions about a parameter of interest
requires one to sample from or compute an integral against a posterior
distribution. A popular method to make these computations cheaper in
high-dimensional settings is to replace the posterior with its Laplace
approximation (LA), a Gaussian distribution. In this work, we derive a leading
order decomposition of the LA error, a powerful technique to analyze the
accuracy of the approximation more precisely than was possible before. It
allows us to derive the first ever skew correction to the LA which provably
improves its accuracy by an order of magnitude in the high-dimensional regime.
Our approach also enables us to prove both tighter upper bounds on the standard
LA and the first ever lower bounds in high dimensions. In particular, we prove
that $d^2\ll n$ is in general necessary for accuracy of the LA, where $d$ is
dimension and $n$ is sample size. Finally, we apply our theory in two example
models: a Dirichlet posterior arising from a multinomial observation, and
logistic regression with Gaussian design. In the latter setting, we prove high
probability bounds on the accuracy of the LA and skew-corrected LA in powers of
$d/\sqrt n$ alone.


  Let F be a differential field with field of constants C. We assume C to be
algebraically closed and of characteristic 0. The complete Picard--Vessiot
closure of F is a differential field extension of F with the same constants C
as F, which has no Picard--Vessiot extensions, and is minimal over F with these
properties. There is a correspondence between subfields of the complete
Picard--Vessiot closure and subgroups of its differential automorphism group,
which arises because the complete Picard--Vessiot closure comes from F via
repeated Picard--Vessiot extensions. This correspondence also obtains for
certain normal subfields of the complete Picard--Vessiot closure, fields which
can be characterized independently of their embedding in the complete
Picard--Vessiot closure.


  In this paper, a novel label fusion method is proposed for brain magnetic
resonance image segmentation. This label fusion method is formulated on a
graph, which embraces both label priors from atlases and anatomical priors from
target image. To represent a pixel in a comprehensive way, three kinds of
feature vectors are generated, including intensity, gradient and structural
signature. To select candidate atlas nodes for fusion, rather than exact
searching, randomized k-d tree with spatial constraint is introduced as an
efficient approximation for high-dimensional feature matching. Feature
Sensitive Label Prior (FSLP), which takes both the consistency and variety of
different features into consideration, is proposed to gather atlas priors. As
FSLP is a non-convex problem, one heuristic approach is further designed to
solve it efficiently. Moreover, based on the anatomical knowledge, parts of the
target pixels are also employed as graph seeds to assist the label fusion
process and an iterative strategy is utilized to gradually update the label
map. The comprehensive experiments carried out on two publicly available
databases give results to demonstrate that the proposed method can obtain
better segmentation quality.


  We study $B_{1g}$ Raman intensity $R(\Omega)$ and the density of states
$N(\omega)$ in isotropic 2D d-wave superconductors. For an ideal gas,
$R(\Omega)$ and $N(\omega)$ have sharp peaks at $\Omega =2\Delta$ and $\omega
=\Delta$, respectively, where $\Delta$ is the maximum value of the gap.
  We study how the peak positions are affected by the fermionic damping due to
impurity scattering.
  We show that while the damping generally shifts the peak positions to larger
frequencies, the peak in $R(\Omega)$ still occurs at almost twice the peak
position in $N(\omega)$ and therefore cannot account for the experimentally
observed downturn shift of the peak frequency in $R(\Omega)$ in underdoped
cuprates compared to twice that in $N(\omega)$. We also discuss how the
fermionic damping affects the dynamical spin susceptibility.


  Consider the one-dimensional stochastic Helmholtz equation where the source
is assumed to be driven by the white noise. This paper concerns the stability
analysis of the inverse random source problem which is to reconstruct the
statistical properties of the source such as the mean and variance. Our results
show that increasing stability can be obtained for the inverse problem by using
suitable boundary data with multi-frequencies.


  In the iron-based superconductors, both nematic and magnetic fluctuations are
expected to enhance superconductivity and may originate from a quantum critical
point hidden beneath the superconducting dome. The behavior of the
non-superconducting state can be an important piece of the puzzle, motivating
in this paper the use of high magnetic fields to suppress superconductivity and
measure the nematic susceptibility of the normal state at low temperatures. We
describe experimental advances which make it possible to measure a resistive
gauge factor (which is a proxy for the nematic susceptibility) in the
field-induced normal state in a 65 T pulsed magnet, and report measurements of
the gauge factor of a micromachined single crystal of
Ba(Fe$_{0.926}$Co$_{0.074}$)$_2$As$_2$ at temperatures down to 1.2 K. The
nematic susceptibility increases monotonically in the field-induced normal
state as the temperature decreases, consistent with the presence of a quantum
critical point nearby in composition.


  We present a detailed statistical analysis of the alignment of polarizations
of radio sources at high redshift.
  We use the JVAS/CLASS 8.4-GHz surveys for our study. This study is motivated
by the puzzling signal of alignment of polarizations from distant quasars at
optical frequencies. We explore several different cuts on the polarization flux
for our analysis. We find that the entire data shows a very significant signal
of alignment on very large distance scales of order 500 Mpc. The alignment
starts to decay only at much larger distances of order Gpc. If we only consider
data with polarization flux greater than 1 mJy, we find alignment at distance
scales less than 150 Mpc. We also find that data with polarization flux less
than 0.5 mJy does not show significant alignment. Similar results are seen for
data with degree of polarization less than 0.01, although here a mild signal of
alignment is observed for a narrow range of angular separations. We argue that
the signal cannot be explained in terms of bias due to systematic errors in
removal of instrumental polarization. We also find that the degree of
polarization shows a strong negative correlation with the total flux. The data
appears to fall into two classes, one of which shows such a correlation. The
remaining set, which has total flux greater than 100 mJy and degree of
polarization lying between 0.01 and 0.1, shows a more random behaviour. The
latter set is also found to show no alignment whereas the first set shows a
very strong polarization alignment.


  We aim at studying automorphic forms of bounded analytic conductor in the
division quaternion algebra setting. We prove the equidistribution of the
universal family with respect to an explicit and geometrically meaningful
measure. It leads to answering the Sato-Tate conjectures in this case, and
contains the counting law of the universal family, with a power savings error
term in the totally definite case.


  Committing to a version control system means submitting a software change to
the system. Each commit can have a message to describe the submission. Several
approaches have been proposed to automatically generate the content of such
messages. However, the quality of the automatically generated messages falls
far short of what humans write. In studying the differences between
auto-generated and human-written messages, we found that 82% of the
human-written messages have only one sentence, while the automatically
generated messages often have multiple lines. Furthermore, we found that the
commit messages often begin with a verb followed by an direct object. This
finding inspired us to use a "verb+object" format in this paper to generate
short commit summaries. We split the approach into two parts: verb generation
and object generation. As our first try, we trained a classifier to classify a
diff to a verb. We are seeking feedback from the community before we continue
to work on generating direct objects for the commits.


  Most current recommender systems primarily focus on what to recommend,
assuming users always require personalized recommendations. However, with the
widely spread of ChatGPT and other chatbots, a more crucial problem in the
context of conversational systems is how to minimize user disruption when we
provide recommendation services for users. While previous research has
extensively explored different user intents in dialogue systems, fewer efforts
are made to investigate whether recommendations should be provided. In this
paper, we formally define the recommendability identification problem, which
aims to determine whether recommendations are necessary in a specific scenario.
First, we propose and define the recommendability identification task, which
investigates the need for recommendations in the current conversational
context. A new dataset is constructed. Subsequently, we discuss and evaluate
the feasibility of leveraging pre-trained language models (PLMs) for
recommendability identification. Finally, through comparative experiments, we
demonstrate that directly employing PLMs with zero-shot results falls short of
meeting the task requirements. Besides, fine-tuning or utilizing soft prompt
techniques yields comparable results to traditional classification methods. Our
work is the first to study recommendability before recommendation and provides
preliminary ways to make it a fundamental component of the future
recommendation system.


  We study static, spherically symmetric vacuum solutions to Quadratic Gravity,
extending considerably our previous Rapid Communication [Phys. Rev. D 98,
021502(R) (2018)] on this topic. Using a conformal-to-Kundt metric ansatz, we
arrive at a much simpler form of the field equations in comparison with their
expression in the standard spherically symmetric coordinates. We present
details of the derivation of this compact form of two ordinary differential
field equations for two metric functions. Next, we apply analytical methods and
express their solutions as infinite power series expansions. We systematically
derive all possible cases admitted by such an ansatz, arriving at six main
classes of solutions, and provide recurrent formulas for all the series
coefficients. These results allow us to identify the classes containing the
Schwarzschild black hole as a special case. It turns out that one class
contains only the Schwarzschild black hole, three classes admit the
Schwarzschild solution as a special subcase, and two classes are not compatible
with the Schwarzschild solution at all since they have strictly nonzero Bach
tensor. In our analysis, we naturally focus on the classes containing the
Schwarzschild spacetime, in particular on a new family of the
Schwarzschild-Bach black holes which possesses one additional non-Schwarzschild
parameter corresponding to the value of the Bach tensor invariant on the
horizon. We study its geometrical and physical properties, such as basic
thermodynamical quantities and tidal effects on free test particles induced by
the presence of the Bach tensor. We also compare our results with previous
findings in the literature obtained using the standard spherically symmetric
coordinates.


  We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa
matrix element $|V_{cb}|$ using the decay $B\to D\ell\nu_\ell$ ($\ell=e,\mu$)
based on 711 fb$^{-1}$ of $e^+e^-\to \Upsilon(4S)$ data recorded by the Belle
detector and containing $772 \times 10^6$ $B\bar{B}$ pairs. One $B$ meson in
the event is fully reconstructed in a hadronic decay mode while the other, on
the signal side, is partially reconstructed from a charged lepton and either a
$D^+$ or $D^0$ meson in a total of 23 hadronic decay modes. The
isospin-averaged branching fraction of the decay $B\to D\ell\nu_\ell$ is found
to be $\mathcal{B}(B^0 \to D^- \ell^+ \nu_{\ell})=(2.31\pm
0.03(\mathrm{stat})\pm 0.11(\mathrm{syst}))\%$. Analyzing the differential
decay rate as a function of the hadronic recoil with the parameterization of
Caprini, Lelouch and Neubert and using the form-factor prediction
$\mathcal{G}(1)=1.0541\pm 0.0083$ calculated by FNAL/MILC, we obtain
$\eta_\mathrm{EW}|V_{cb}|=(40.12\pm 1.34)\times 10^{-3}$, where
$\eta_\mathrm{EW}$ is the electroweak correction factor. Alternatively,
assuming the model-independent form-factor parameterization of Boyd, Grinstein
and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD
collaborations, we find $\eta_\mathrm{EW}|V_{cb}|=(41.10 \pm 1.14)\times
10^{-3}$.


  We consider the a posteriori error estimation for an atomistic-to-continuum
cou- pling scheme for a generic one-dimensional many-body
next-nearest-neighbour interaction model in 1D. We derive and rigorously prove
the efficiency of the residual type estimator. We prove the equivalence between
the residual type and the gradient recovery type estima- tor in the continuum
region and propose a (novel) hybrid a a posteriori error estimator by combining
the two types of estimators. Our numerical experiments illustrate the optimal
con- vergence rate of the adaptive algorithms using these estimators whose
efficiency factors are also presented.


  Consider the random quadratic form $T_n=\sum_{1 \leq u < v \leq n} a_{uv} X_u
X_v$, where $((a_{uv}))_{1 \leq u, v \leq n}$ is a $\{0, 1\}$-valued symmetric
matrix with zeros on the diagonal, and $X_1,$ $X_2, \ldots, X_n$ are i.i.d.
$\mathrm{Ber}(p_n)$. In this paper, we prove various characterization theorems
about the limiting distribution of $T_n$, in the sparse regime, where $0 < p_n
\ll 1$ such that $\mathbb E(T_n)=O(1).$ The main result is a decomposition
theorem showing that distributional limits of $T_n$ is the sum of three
components: a mixture which consists of a quadratic function of independent
Poisson variables; a linear Poisson mixture, where the mean of the mixture is
itself a (possibly infinite) linear combination of independent Poisson random
variables; and another independent Poisson component. This is accompanied with
a universality result which allows us to replace the Bernoulli distribution
with a large class of other discrete distributions. Another consequence of the
general theorem is a necessary and sufficient condition for Poisson
convergence, where an interesting second moment phenomenon emerges.


  We study pattern formation in planar fluid systems driven by intermolecular
cohesion (which manifests as a line tension) and dipole-dipole repulsion which
are observed in physical systems including ferrofluids in Hele-Shaw cells and
Langmuir layers. When the dipolar repulsion is sufficiently strong, domains
undergo forked branching reminiscent of viscous fingering. A known difficulty
with these models is that the energy associated with dipole-dipole interactions
is singular at small distances. Following previous work, we demonstrate how to
ameliorate this singularity and show that in the macroscopic limit, only the
relative scale of the microscopic details of a system are relevant, and develop
an expression for the system energy that depends only on a generalized line
tension, {\Lambda}, that in turn depends logarithmically on that scale. We
conduct numerical studies that use energy minimization to find equilibrium
states. Following the subcritical bifurcations from the circle, we find a few
highly symmetric stable shapes, but nothing that resembles the observed
diversity of experimental and dynamically simulated domains. The application of
a weak random background to the energy landscape stabilizes a sm\"org\r{a}sbord
of domain morphologies recovering the diversity observed experimentally. With
this technique, we generate a large sample of qualitatively realistic shapes
and use them to create an empirical model for extracting {\Lambda} using only a
shape's perimeter and morphology with high accuracy.


  The traditional statistical inference is static, in the sense that the
estimate of the quantity of interest does not affect the future evolution of
the quantity. In some sequential estimation problems however, the future values
of the quantity to be estimated depend on the estimate of its current value.
This type of estimation problems has been formulated as the dynamic inference
problem. In this work, we formulate the Bayesian learning problem for dynamic
inference, where the unknown quantity-generation model is assumed to be
randomly drawn according to a random model parameter. We derive the optimal
Bayesian learning rules, both offline and online, to minimize the inference
loss. Moreover, learning for dynamic inference can serve as a meta problem,
such that all familiar machine learning problems, including supervised
learning, imitation learning and reinforcement learning, can be cast as its
special cases or variants. Gaining a good understanding of this unifying meta
problem thus sheds light on a broad spectrum of machine learning problems as
well.


  Wavelets, known to be useful in non-linear multi-scale processes and in
multi-resolution analysis, are shown to have a q-deformed algebraic structure.
The translation and dilation operators of the theory associate with any scaling
equation a non-linear, two parameter algebra. This structure can be mapped onto
the quantum group $su_{q}(2)$ in one limit, and approaches a Fourier series
generating algebra, in another limit. A duality between any scaling function
and its corresponding non-linear algebra is obtained. Examples for the Haar and
B-wavelets are worked out in detail.


  This paper discusses the efficiency of Hybrid Primal-Dual (HPD) type
algorithms to approximate solve discrete Optimal Transport (OT) and Wasserstein
Barycenter (WB) problems, with and without entropic regularization. Our first
contribution is an analysis showing that these methods yield state-of-the-art
convergence rates, both theoretically and practically. Next, we extend the HPD
algorithm with linesearch proposed by Malitsky and Pock in 2018 to the setting
where the dual space has a Bregman divergence, and the dual function is
relatively strongly convex to the Bregman's kernel. This extension yields a new
method for OT and WB problems based on smoothing of the objective that also
achieves state-of-the-art convergence rates. Finally, we introduce a new
Bregman divergence based on a scaled entropy function that makes the algorithm
numerically stable and reduces the smoothing, leading to sparse solutions of OT
and WB problems. We complement our findings with numerical experiments and
comparisons.


  We numerically examine the ordering, pinning and flow of superconducting
vortices interacting with a Santa Fe artificial ice pinning array. We find that
as a function of magnetic field and pinning density, a wide variety of vortex
states occur, including ice rule obeying states and labyrinthine patterns. In
contrast to square pinning arrays, we find no sharp peaks in the critical
current due to the inherent frustration effect imposed by the Santa Fe ice
geometry; however, there are some smoothed peaks when the number of vortices
matches the number of pinning sites. For some fillings, the Santa Fe array
exhibits stronger pinning than the square array due to the suppression of
one-dimensional flow channels when the vortex motion in the Santa Fe lattice
occurs through the formation of both longitudinal and transverse flow channels.


  Image Quality Assessment (IQA) has long been a research hotspot in the field
of image processing, especially No-Reference Image Quality Assessment (NR-IQA).
Due to the powerful feature extraction ability, existing Convolution Neural
Network (CNN) and Transformers based NR-IQA methods have achieved considerable
progress. However, they still exhibit limited capability when facing unknown
authentic distortion datasets. To further improve NR-IQA performance, in this
paper, a novel supervised contrastive learning (SCL) and Transformer-based
NR-IQA model SaTQA is proposed. We first train a model on a large-scale
synthetic dataset by SCL (no image subjective score is required) to extract
degradation features of images with various distortion types and levels. To
further extract distortion information from images, we propose a backbone
network incorporating the Multi-Stream Block (MSB) by combining the CNN
inductive bias and Transformer long-term dependence modeling capability.
Finally, we propose the Patch Attention Block (PAB) to obtain the final
distorted image quality score by fusing the degradation features learned from
contrastive learning with the perceptual distortion information extracted by
the backbone network. Experimental results on seven standard IQA datasets show
that SaTQA outperforms the state-of-the-art methods for both synthetic and
authentic datasets. Code is available at
https://github.com/I2-Multimedia-Lab/SaTQA


  We consider a chaotic many-body system (i.e., one that satisfies the
eigenstate thermalization hypothesis) that is split into two subsystems, with
an interaction along their mutual boundary, and study the entanglement
properties of an energy eigenstate with nonzero energy density. When the two
subsystems have nearly equal volumes, we find a universal correction to the
entanglement entropy that is proportional to the square root of the system's
heat capacity (or a sum of capacities, if there are conserved quantities in
addition to energy). This phenomenon was first noted by Vidmar and Rigol in a
specific system; our analysis shows that it is generic, and expresses it in
terms of thermodynamic properties of the system. Our conclusions are based on a
refined version of a model of a chaotic eigenstate originally due to Deutsch,
and analyzed more recently by Lu and Grover.


  We study a simple dark matter model given by two interacting real singlet
scalars, with only one of them coupled to the Higgs. The model therefore
presents a minimal assisted-freeze-out framework: both scalars contribute to
the dark matter relic density, but only one of them takes part in the elastic
scattering with nuclei. This reduces the expected interaction rate in direct
detection experiments in such a way that the model in some regions of the
parameter space may evade XENON1T constraints. We explore the model under
theoretical (perturbativity, stability potential and unitarity) and
experimental constraints (Higgs to invisible, relic density, direct detection),
with the use of the narrow-width-approximation near the Higgs resonance to
calculate the average annihilation cross section. We show that the model is
viable in the Higgs resonance region and for scalar singlets masses of hundreds
of GeV, although the model becomes highly constrained at high energies.


  We construct an effective Lagrangian for interacting pions with
non-relativistic energies. The coupling constants can be expressed in terms of
the different scattering lengths and slopes. When used in the calculation of
the pionium decay rate, the scattering slope contribution gives a correction of
about 8% compared with the lowest order contribution coming from the scattering
lengths alone.


  Crystalline silicon has been proposed as a new test mass material in third
generation gravitational wave detectors such as the Einstein Telescope (ET).
Birefringence can reduce the interferometric contrast and can produce dynamical
disturbances in interferometers. In this work we use the method of
polarisation-dependent resonance frequency analysis of Fabry-Perot-cavities
containing silicon as a birefringent medium. Our measurements show a
birefringence of silicon along the (111) axis of the order of $\Delta\, n
\approx 10^{-7}$ at a laser wavelength of 1550nm and room temperature. A model
is presented that explains the results of different settings of our
measurements as a superposition of elastic strains caused by external stresses
in the sample and plastic strains possibly generated during the production
process. An application of our theory on the proposed ET test mass geometry
suggests no critical effect on birefringence due to elastic strains.


  We study the uniqueness, existence, and properties of bounded distributional
solutions of the initial value problem problem for the anomalous diffusion
equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$
can be any nonlocal symmetric degenerate elliptic operator including the
fractional Laplacian and numerical discretizations of this operator. The
function $\varphi:\mathbb{R} \to \mathbb{R}$ is only assumed to be continuous
and nondecreasing. The class of equations include nonlocal (generalized) porous
medium equations, fast diffusion equations, and Stefan problems. In addition to
very general uniqueness and existence results, we obtain $L^1$-contraction and
a priori estimates. We also study local limits, continuous dependence, and
properties and convergence of a numerical approximation of our equations.


  The interactions between elementary excitations such as phonons, plasmons,
magnons, or particle-hole pairs, drive emergent functionalities and electronic
instabilities such as multiferroic behaviour, anomalous thermoelectric
properties, polar order, or superconductivity. Whereas various hybrid
excitations have been studied extensively, the feed-back of prototypical
elementary excitations on the crystal electric fields (CEF), defining the
environment in which the elementary excitations arise, has been explored for
very strong coupling only. We report high-resolution neutron spectroscopy and
ab-initio phonon calculations of {\ceaual}, an archetypal fluctuating valence
compound. The high resolution of our data allows us to quantify the energy
scales of three coupling mechanisms between phonons, CEF-split localized 4f
electron states, and conduction electrons. Although these interactions do not
appear to be atypically strong for this class of materials, we resolve, for the
first time, a profound renormalization of low-energy quasiparticle excitations
on all levels. The key anomalies of the spectrum we observe comprise (1) the
formation of a CEF-phonon bound state with a comparatively low density of
acoustic phonons reminiscent of vibronic modes observed in other materials,
where they require a pronounced abundance of optical phonons, (2) an
anti-crossing of CEF states and acoustic phonons, and (3) a strong broadening
of CEF states due to the hybridization with more itinerant excitations. The
fact that all of these features are well resolved in CeAuAl$_3$ suggests that
similar hybrid excitations should also be dominant in a large family of related
materials. This promises a predictive understanding towards the discovery of
new magneto-elastic functionalities and instabilities.


  System-of-systems (SoS) approach is often used for simulating disruptions to
business and infrastructure system networks allowing for integration of several
models into one simulation. However, the integration is frequently challenging
as each system is designed individually with different characteristics, such as
time granularity. Understanding the impact of time granularity on propagation
of disruptions between businesses and infrastructure systems and finding the
appropriate granularity for the SoS simulation remain as major challenges. To
tackle these, we explore how time granularity, recovery time, and disruption
size affect the propagation of disruptions between constituent systems of an
SoS simulation. To address this issue, we developed a High Level Architecture
(HLA) simulation of 3 networks and performed a series of simulation
experiments. Our results revealed that time granularity and especially recovery
time have huge impact on propagation of disruptions. Consequently, we developed
a model for selecting an appropriate time granularity for an SoS simulation
based on expected recovery time. Our simulation experiments show that time
granularity should be less than 1.13 of expected recovery time. We identified
some areas for future research centered around extending the experimental
factors space.


  The question of neutrino mass is one of the major riddles in particle
physics. Recently, strong evidence that neutrinos have nonzero masses has been
found. While tiny, these masses could be large enough to contribute
significantly to the mass density of the universe. The evidence for
nonvanishing neutrino masses is based on the apparent observation of neutrino
oscillation -- the transformation of a neutrino of one type or "flavor" into
one of another. We explain the physics of neutrino oscillation, and review and
weigh the evidence that it actually occurs in nature. We also discuss the
constraints on neutrino mass from cosmology and from experiments with negative
results. After presenting illustrative neutrino mass spectra suggested by the
present data, we consider how near- and far-future experiments can further
illuminate the nature of neutrinos and their masses.


  Domain walls in correlated charge density wave compounds such as 1T-TaS2 can
have distinct localized states which govern physical properties and
functionalities of emerging quantum phases. However, detailed atomic and
electronic structures of domain walls have largely been elusive. We identify
using scanning tunneling microscope and density functional theory calculations
the atomic and electronic structures for a plethora of discommensuration domain
walls in 1T-TaS2 quenched metastably with nanoscale domain wall networks. The
domain walls exhibit various in-gap states within the Mott gap but metallic
states appear in only particular types of domain walls. A systematic
understanding of the domain-wall electronic property requests not only the
electron counting but also including various intertwined interactions such as
structural relaxation, electron correlation, and charge transfer. This work
guides the domain wall engineering of the functionality in correlated van der
Waals materials.


  We develop a novel formulation of the hadron-resonance gas model which,
besides a hard-core repulsion, explicitly accounts for the surface tension
induced by the interaction between the particles. Such an equation of state
allows us to go beyond the Van der Waals approximation for any number of
different hard-core radii. A comparison with the Carnahan-Starling equation of
state shows that the new model is valid for packing fractions 0.2-0.22, while
the usual Van der Waals model is inapplicable at packing fractions above
0.1-0.11. Moreover, it is shown that the equation of state with induced surface
tension is softer than the one of hard spheres and remains causal at higher
particle densities. The great advantage of our model is that there are only two
equations to be solved and it does not depend on the various values of the
hard-core radii used for different hadronic resonances. Using this novel
equation of state we obtain a high-quality fit of the ALICE hadron
multiplicities measured at center-of-mass energies of 2.76 TeV per nucleon.
Furthermore, using the traditional hadron-resonance gas model with
multi-component hard-core repulsion and the novel one we investigate the
recently suggested model in which the proper volume of a hadron is proportional
to its mass. We find that the high-temperature maximum of $\chi^2/ndf$ observed
in the latter model always appears in the region located far above the limit of
its applicability.


  A. Capelli gave a necessary and sufficient condition for the reducibility of
$x^n-a$ over $\Q$. In this article, we are providing an alternate elementary
proof for the same.


  We derive the properties of polaritons in single-$\Lambda$ and
double-$\Lambda$ media using a microscopic equation-of-motion technique. In
each case, the polaritonic dispersion relation and composition arise from a
matrix eigenvalue problem for arbitrary control field strengths. We show that
the double-$\Lambda$ medium can be used to up- or down-convert single photons
while preserving quantum coherence. The existence of a dark-state polariton
protects this single-photon four-wave mixing effect against incoherent decay of
the excited atomic states. The efficiency of this conversion is limited mainly
by the sample size and the lifetime of the metastable state.


  This paper considers the problem of symbol detection in massive
multiple-input multiple-output (MIMO) wireless communication systems. We
consider hard-thresholding preceeded by two variants of the regularized least
squares (RLS) decoder; namely the unconstrained RLS and the RLS with box
constraint. For all schemes, we focus on the evaluation of the mean squared
error (MSE) and the symbol error probability (SEP) for M-ary pulse amplitude
modulation (M-PAM) symbols transmitted over a massive MIMO system when the
channel is estimated using linear minimum mean squared error (LMMSE) estimator.
Under such circumstances, the channel estimation error is Gaussian which allows
for the use of the convex Gaussian min-max theorem (CGMT) to derive asymptotic
approximations for the MSE and SER when the system dimensions and the coherence
duration grow large with the same pace. The obtained expressions are then
leveraged to derive the optimal power distribution between pilot and data under
a total transmit energy constraint. In addition, we derive an asymptotic
approximation of the goodput for all schemes which is then used to jointly
optimize the number of training symbols and their associated power. Numerical
results are presented to support the accuracy of the theoretical results.


  Let $\lambda_{max}$ be a shifted maximal real eigenvalue of a random $N\times
N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix') in the
$N\to\infty$ limit. It was shown by Poplavskyi, Tribe, Zaboronski \cite{PZT}
that the limiting distribution of the maximal real eigenvalue has $s\to-\infty$
asymptotics $$\mathbb{P} [ \lambda_{max} < s ] = {\rm
e}^{\frac{1}{2\sqrt{2\pi}} \zeta(\frac32)s + \mathcal{O}(1)},$$ where $\zeta$
is the Riemann zeta-function. This limiting distribution was expressed by Baik,
Bothner \cite{BB18} in terms of the solution $q(x)$ of a certain
Zakharov-Shabat inverse scattering problem, and the asymptotics was extended to
the form $$\mathbb{P} [ \lambda_{max} < s ] = {\rm
e}^{\frac{1}{2\sqrt{2\pi}}\zeta(\frac32)t} c(1+_\mathcal{O}(1)),\
s\to-\infty.$$ We show that $q(x)$ is a smooth function, which behaves as
$\frac{1}{x}$ as $x\to-\infty.$ Second, we show that the error term in the
asymptotics is subexponential, i.e. smaller that ${\rm e}^{-C|s|}$ for any $C.$
Third, we identify the constant $c$ as a conserved quantity of a certain fast
decaying solution $u(x,t)$ of the Korteweg-de Vries equation. This, in
principle, gives a way to determine $c$ via the known long-time $t\to+\infty$
asymptotics of $u(x,t).$ We also conjecture a representation for the $c$ in
terms of an integral of the Hastings-MacLeod solution of Painlev\'e II
equation.


  We prove that 2-dimensional simplicial complexes whose first homology group
is trivial have topological embeddings in 3-space if and only if there are
embeddings of their link graphs in the plane that are compatible at the edges
and they are simply connected.


  The ontological model framework provides a rigorous approach to address the
question of whether the quantum state is ontic or epistemic. When considering
only conventional projective measurements, auxiliary assumptions are always
needed to prove the reality of the quantum state in the framework. For example,
the Pusey-Barrett-Rudolph theorem is based on an additional preparation
independence assumption. In this paper, we give a new proof of psi-ontology in
terms of protective measurements in the ontological model framework. The proof
does not rely on auxiliary assumptions, and also applies to deterministic
theories such as the de Broglie-Bohm theory. In addition, we give a simpler
argument for psi-ontology beyond the framework, which is only based on
protective measurements and a weaker criterion of reality. The argument may be
also appealing for those people who favor an anti-realist view of quantum
mechanics.


  We prove a characterization for the Peetre type $K$-functional on
$\mathbb{M}$, a compact two-point homogeneous space, in terms the rate of
approximation of a family of multipliers operator defined to this purpose. This
extends the well known results on the spherical setting. The characterization
is employed to show that an abstract H\"{o}lder condition or finite order of
differentiability condition imposed on kernels generating certain operators
implies a sharp decay rates for their eigenvalues sequences. The latest is
employed to obtain estimates for the Kolmogorov $n$-width of unit balls in
Reproducing Kernel Hilbert Space (RKHS).


  Modern disease mapping draws upon a wealth of high resolution spatial data
products reflecting environmental and/or socioeconomic factors as covariates,
or `features', within a geostatistical framework to improve predictions of
disease risk. Feature selection is an important step in building these models,
helping to reduce overfitting and computational complexity, and to improve
model interpretability. Selecting only features that have a causal relationship
with the response variable could potentially improve predictions and
generalisability, but identifying these causal features from
non-interventional, spatiotemporal data is a challenging problem. Here we
examine the performance of a causal feature selection procedure with regard to
estimating malaria incidence in Madagascar. The studied procedure designed for
this task combines the PC algorithm with spatiotemporal prewhitening and
kernel-based independence tests extended to accommodate aggregated data. This
case study reveals a clear advantage for causal feature selection in terms of
the out-of-sample predictive accuracy in a forward temporal estimation task,
but not in a spatiotemporal interpolation task, in comparison with thresholded
spike-and-slab, for both linear and non-linear regression models. Compared to
no feature selection, causal feature selection was most beneficial in settings
wherein the volume of available data was low relative to the model complexity.


  The MultiNoC system implements a programmable on-chip multiprocessing
platform built on top of an efficient, low area overhead intra-chip
interconnection scheme. The employed interconnection structure is a Network on
Chip, or NoC. NoCs are emerging as a viable alternative to increasing demands
on interconnection architectures, due to the following characteristics: (i)
energy efficiency and reliability; (ii) scalability of bandwidth, when compared
to traditional bus architectures; (iii) reusability; (iv) distributed routing
decisions. An external host computer feeds MultiNoC with application
instructions and data. After this initialization procedure, MultiNoC executes
some algorithm. After finishing execution of the algorithm, output data can be
read back by the host. Sequential or parallel algorithms conveniently adapted
to the MultiNoC structure can be executed. The main motivation to propose this
design is to enable the investigation of current trends to increase the number
of embedded processors in SoCs, leading to the concept of "sea of processors"
systems.


  We present results from cryogenic tests of Volume-Phase Holographic(VPH)
gratings at 100 K. The aims of these tests are to see whether the diffraction
efficiency as a function of wavelength is significantly different at a low
temperature from that at room temperature and to see how the performance of a
VPH grating is affected by a number of thermal cycles. We have completed 10
cycles between room temperature and 100 $K$, and find no clear evidence that
the diffraction efficiency changes with temperature or with successive thermal
cycle.


  Two chaotic systems which interact by mutually exchanging a signal built from
their delayed internal variables, can synchronize. A third unit may be able to
record and to manipulate the exchanged signal. Can the third unit synchronize
to the common chaotic trajectory, as well? If all parameters of the system are
public, a proof is given that the recording system can synchronize as well.
However, if the two interacting systems use private commutative filters to
generate the exchanged signal, a driven system cannot synchronize. It is shown
that with dynamic private filters the chaotic trajectory even cannot be
calculated. Hence two way (interaction) is more than one way (drive). The
implication of this general result to secret communication with chaos
synchronization is discussed.


  We present a new measurement of the systemic proper motion of the Small
Magellanic Cloud (SMC), based on an expanded set of 30 fields containing
background quasars and spanning a $\sim$3 year baseline, using the
\textit{Hubble Space Telescope} (\textit{HST}) Wide Field Camera 3. Combining
this data with our previous 5 \textit{HST} fields, and an additional 8
measurements from the \textit{Gaia}-Tycho Astrometric Solution Catalog, brings
us to a total of 43 SMC fields. We measure a systemic motion of $\mu_{W}$ =
$-0.82$ $\pm$ 0.02 (random) $\pm$ 0.10 (systematic) mas yr$^{-1}$ and $\mu_{N}$
= $-1.21$ $\pm$ 0.01 (random) $\pm$ 0.03 (systematic) mas yr$^{-1}$. After
subtraction of the systemic motion, we find little evidence for rotation, but
find an ordered mean motion radially away from the SMC in the outer regions of
the galaxy, indicating that the SMC is in the process of tidal disruption. We
model the past interactions of the Clouds with each other based on the measured
present-day relative velocity between them of $103 \pm 26$ km s$^{-1}$. We find
that in 97\% of our considered cases, the Clouds experienced a direct collision
$147 \pm 33$ Myr ago, with a mean impact parameter of $7.5 \pm 2.5$ kpc.


  Previous top-performing methods for 3D instance segmentation often maintain
inter-task dependencies and the tendency towards a lack of robustness. Besides,
inevitable variations of different datasets make these methods become
particularly sensitive to hyper-parameter values and manifest poor
generalization capability. In this paper, we address the aforementioned
challenges by proposing a novel query-based method, termed as 3D-QueryIS, which
is detector-free, semantic segmentation-free, and cluster-free. Specifically,
we propose to generate representative points in an implicit manner, and use
them together with the initial queries to generate the informative instance
queries. Then, the class and binary instance mask predictions can be produced
by simply applying MLP layers on top of the instance queries and the extracted
point cloud embeddings. Thus, our 3D-QueryIS is free from the accumulated
errors caused by the inter-task dependencies. Extensive experiments on multiple
benchmark datasets demonstrate the effectiveness and efficiency of our proposed
3D-QueryIS method.


  Oblique contributions from vector particles that are strongly coupled to the
known gauge bosons are calculated for the case of various observables at a 1
TeV $e^+e^-$ collider. Constraints provided by LEP 1 results are taken into
account in a model-independent way through a dispersion relation technique.
Depending on the assumed theoretical properties, mass limits of several TeV
should be observable.


  According to the experimental evidence damage induced by densely ionizing
radiation in mammalian cells is distributed along the DNA molecule in the form
of clusters. The most critical constituent of DNA damage are double-strand
breaks (DSBs) which are formed when the breaks occur in both DNA strands and
are directly opposite or separated by only a few base pairs. The paper
discusses a model of clustered DSB formation viewed in terms of compound
Poisson process along with the predictive assay of the formalism in application
to experimental data.


  In bounce inflation scenario, the inflation is singularity-free, while the
advantages of inflation are reserved. We analytically calculate the power
spectrum of its primordial gravitational waves (GWs), and show a universal
result including the physics of the bounce phase. The spectrum acquires a
cutoff at large scale, while the oscillation around the cutoff scale is quite
drastic, which is determined by the details of bounce. Our work highlights that
the primordial GWs at large scale may encode the physics of the bounce ever
happened at about $\sim 60$ efolds before inflation.


  Dynamic metasurface antennas (DMAs) provide a new paradigm to realize
large-scale antenna arrays for future wireless systems. In this paper, we study
the downlink millimeter wave (mmWave) DMA systems with limited number of radio
frequency (RF) chains. By using a specific DMA structure, an equivalent mmWave
channel model is first explicitly characterized. Based on that, we propose an
effective joint microstrip selection and beamforming scheme to accommodate for
the limited number of RF chains. A low-complexity digital beamforming solution
with channel gain-based microstrip selection is developed, while the analog
beamformer is obtained via a coordinate ascent method. The proposed scheme is
numerically shown to approach the performance of DMAs without RF chain
reduction, verifying the effectiveness of the proposed schemes.


  We present a new string SMT solver, Z3str3, that is faster than its
competitors Z3str2, Norn, CVC4, S3, and S3P over a majority of three
industrial-strength benchmarks, namely Kaluza, PISA, and IBM AppScan. Z3str3
supports string equations, linear arithmetic over length function, and regular
language membership predicate. The key algorithmic innovation behind the
efficiency of Z3str3 is a technique we call theory-aware branching, wherein we
modify Z3's branching heuristic to take into account the structure of theory
literals to compute branching activities. In the traditional DPLL(T)
architecture, the structure of theory literals is hidden from the DPLL(T) SAT
solver because of the Boolean abstraction constructed over the input theory
formula. By contrast, the theory-aware technique presented in this paper
exposes the structure of theory literals to the DPLL(T) SAT solver's branching
heuristic, thus enabling it to make much smarter decisions during its search
than otherwise. As a consequence, Z3str3 has better performance than its
competitors.


  We describe a two-player non-local game, with a fixed small number of
questions and answers, such that an $\epsilon$-close to optimal strategy
requires an entangled state of dimension $2^{\Omega(\epsilon^{-1/8})}$. Our
non-local game is inspired by the three-player non-local game of Ji, Leung and
Vidick [arXiv:1802.04926]. It reduces the number of players from three to two,
as well as the question and answer set sizes. Moreover, it provides an
(arguably) elementary proof of the non-closure of the set of quantum
correlations, based on embezzlement and self-testing. In contrast, previous
proofs involved representation theoretic machinery for finitely-presented
groups and $C^*$-algebras.


  This paper establishes a new combinatorial framework for the study of coarse
median spaces, bridging the worlds of asymptotic geometry, algebra and
combinatorics. We introduce a simple and entirely algebraic notion of coarse
median algebra which simultaneously generalises the concepts of bounded
geometry coarse median spaces and classical discrete median algebras. We study
the coarse median universe from the perspective of intervals, with a particular
focus on cardinality as a proxy for distance. In particular we prove that the
metric on a quasi-geodesic coarse median space of bounded geometry can be
constructed up to quasi-isometry using only the coarse median operator. Finally
we develop a concept of rank for coarse median algebras in terms of the
geometry of intervals and show that the notion of finite rank coarse median
algebra provides a natural higher dimensional analogue of Gromov's concept of
$\delta$-hyperbolicity.


  Panoramic X-ray is a simple and effective tool for diagnosing dental diseases
in clinical practice. When deep learning models are developed to assist dentist
in interpreting panoramic X-rays, most of their performance suffers from the
limited annotated data, which requires dentist's expertise and a lot of time
cost. Although self-supervised learning (SSL) has been proposed to address this
challenge, the two-stage process of pretraining and fine-tuning requires even
more training time and computational resources. In this paper, we present a
self-supervised auxiliary detection (SSAD) framework, which is plug-and-play
and compatible with any detectors. It consists of a reconstruction branch and a
detection branch. Both branches are trained simultaneously, sharing the same
encoder, without the need for finetuning. The reconstruction branch learns to
restore the tooth texture of healthy or diseased teeth, while the detection
branch utilizes these learned features for diagnosis. To enhance the encoder's
ability to capture fine-grained features, we incorporate the image encoder of
SAM to construct a texture consistency (TC) loss, which extracts image
embedding from the input and output of reconstruction branch, and then enforces
both embedding into the same feature space. Extensive experiments on the public
DENTEX dataset through three detection tasks demonstrate that the proposed SSAD
framework achieves state-of-the-art performance compared to mainstream object
detection methods and SSL methods. The code is available at
https://github.com/Dylonsword/SSAD


  How can we induce social media users to be discerning when sharing
information during a pandemic? An experiment on Facebook Messenger with users
from Kenya (n = 7,498) and Nigeria (n = 7,794) tested interventions designed to
decrease intentions to share COVID-19 misinformation without decreasing
intentions to share factual posts. The initial stage of the study incorporated:
(i) a factorial design with 40 intervention combinations; and (ii) a contextual
adaptive design, increasing the probability of assignment to treatments that
worked better for previous subjects with similar characteristics. The second
stage evaluated the best-performing treatments and a targeted treatment
assignment policy estimated from the data. We precisely estimate null effects
from warning flags and related article suggestions, tactics used by social
media platforms. However, nudges to consider information's accuracy reduced
misinformation sharing relative to control by 4.9% (estimate = -2.3 pp, s.e. =
1.0 , Z = -2.31, p = 0.021, 95% CI = [-4.2 , -0.35]). Such low-cost scalable
interventions may improve the quality of information circulating online.


  In this article a complete description is given of the simple representations
of a 3-dimensional Sklyanin algebra associated to a torsion point. In order to
determine these irreducible representations, a review is given of classical
results regarding representation theory of graded rings with excellent
homological and algebraic properties.


  In quantum information theory, entropic inequalities act as the necessary and
sufficient conditions to noncontextuality. Here, we first experimentally
demonstrate the violation of the entropic noncontextual inequality in a
four-level quantum system, by using the five-qubit IBM quantum computer. The
experimental result disproves the existence of a local realist model.


  Ar XIII is found to be unique with new features in electron-ion recombination
not seen in any other ion. The ion has been studied with the unified method
which provides a theoretically self-consistent set of atomic parameters for the
inverse processes of photoionization and total electron-ion recombination. The
unified method subsumes both the radiative recombination (RR) and dielectronic
recombination (DR) within the framework of close-coupling formulations using
the R-matrix method. A set of four DR "bumps", two in the low and two in the
high temperature regions, is found to exist in the recombination rates of Ar
XIV + e $\to$ Ar XIII. This is in contrast to two typical DR "bumps", one at
high temperature common for most ions and one at low temperature depending on
the presence of near threshold autoionizing resonances in the bound-free
process. The large scale ab initio calculations for Ar XIII employ
eigenfunction expansion of 37 core Ar XIV states from n = 2 and 3 complexes.
This enables core excitations of type $\Delta n$ = 0 and 1. Ar XIII exhibits
more extensive resonant structures and wider PEC (photoexitation-of-core)
resonances for n = 3 core states than those of n = 2 states. Hence the high
energy region of photoionization and recombination are dominated by these
structures. Total and partial photoionization cross sections of all bound
states, state-specific recombinaion rates of 561 bound states and total
recombination rate coefficients are presented.


  The influence of the tip-substrate bias induced electric field in a
scanning-tunneling-spectroscopy experiment on charged InAs nanocrystals is
studied. Calculating the ground and first excited many-particle state for five
electrons occupying the quantum dot reveals a Stark-induced reordering of
states by increasing the electric field strength. It is shown that this
reordering of states is accompanied by a symmetry change of the local density
of states (LDOS), which in principal is observable in a wave-function mapping
experiment. Since in the usually performed experiments the electric field can
not be directly controlled, we investigate the crystal size dependence of the
5-electron LDOS symmetry. It is found that the symmetry changes from spherical
to torus-like by increasing the nanocrystal radius.


  Quasi-elliptic cohomology is conjectured by Sati and Schreiber as a
particularly suitable approximation to equivariant 4-th Cohomotopy, which
classifies the charges carried by M-branes in M-theory in a way that is
analogous to the traditional idea that complex K-theory classifies the charges
of D-branes in string theory. In this paper we compute quasi-elliptic
cohomology of 4-spheres under the action by some finite subgroups that are the
most interesting isotropy groups where the M5-branes may sit.


  A quantum walk model which reflects the $2$-cell embedding on the orientable
closed surface of a graph in the dynamics is introduced. We show that the
scattering matrix is obtained by finding the faces on the underlying surface
which have the overlap to the boundary and the stationary state is obtained by
counting two classes of the rooted spanning subgraphs of the dual graph on the
underlying embedding.


  We compute the drag force experienced by a heavy quark that moves through
plasma in a gauge theory whose dual description involves arbitrary metric and
dilaton fields. As a concrete application, we consider the cascading gauge
theory at temperatures high above the deconfining scale, where we obtain a drag
force with a non-trivial velocity dependence. We compare our results with the
jet-quenching parameter for the same theory, and find qualitative agreement
between the two approaches. Conversely, we calculate the jet-quenching
parameter for N=4 super-Yang-Mills with an R-charge density (or equivalently, a
chemical potential), and compare our result with the corresponding drag force.


  A main disadvantage of many high-order methods for hyperbolic conservation
laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear
in the solution. Due to the Gibbs-Wilbraham phenomenon, the numerical
approximation will be polluted by spurious oscillations, which produce
unphysical numerical solutions and might finally blow up the computation. In
this work, we propose a new shock capturing procedure to stabilise high-order
spectral element approximations. The procedure consists of going over from the
original (polluted) approximation to a convex combination of the original
approximation and its Bernstein reconstruction, yielding a stabilised
approximation. The coefficient in the convex combination, and therefore the
procedure, is steered by a discontinuity sensor and is only activated in
troubled elements. Building up on classical Bernstein operators, we are thus
able to prove that the resulting Bernstein procedure is total variation
diminishing and preserves monotone (shock) profiles. Further, the procedure can
be modified to not just preserve but also to enforce certain bounds for the
solution, such as positivity. In contrast to other shock capturing methods,
e.g. artificial viscosity methods, the new procedure does not reduce the time
step or CFL condition and can be easily and efficiently implemented into any
existing code. Numerical tests demonstrate that the proposed shock-capturing
procedure is able to stabilise and enhance spectral element approximations in
the presence of shocks.


  Using data samples collected with the BESIII detector at the BEPCII collider,
we measure the Born cross section of $e^{+}e^{-}\rightarrow p\bar{p}$ at 12
center-of-mass energies from 2232.4 to 3671.0 MeV. The corresponding effective
electromagnetic form factor of the proton is deduced under the assumption that
the electric and magnetic form factors are equal $(|G_{E}|= |G_{M}|)$. In
addition, the ratio of electric to magnetic form factors, $|G_{E}/G_{M}|$, and
$|G_{M}|$ are extracted by fitting the polar angle distribution of the proton
for the data samples with larger statistics, namely at $\sqrt{s}=$ 2232.4 and
2400.0 MeV and a combined sample at $\sqrt{s}$ = 3050.0, 3060.0 and 3080.0 MeV,
respectively. The measured cross sections are in agreement with recent results
from BaBar, improving the overall uncertainty by about 30\%. The
$|G_{E}/G_{M}|$ ratios are close to unity and consistent with BaBar results in
the same $q^{2}$ region, which indicates the data are consistent with the
assumption that $|G_{E}|=|G_{M}|$ within uncertainties.


  We study the properties of heavy probes moving in strongly coupled plasmas at
finite chemical potential. Using the gauge/gravity duality we consider large
classes of gravity models consisting in deformed AdS5 spacetimes endowed with
Reissner-Nordstr\"om-type black holes. We report on our analysis of the
screening distance of a quark-antiquark pair, its free energy, and the running
coupling. These observables show a certain insensitivity as to which model and
deformation is used, pointing to strong-coupling universal behavior. Thus, the
results may be relevant for modeling heavy quarkonia traversing a quark-gluon
plasma at finite net baryon density, and their suppression by melting.


  What is the probability for a number field of composite degree $d$ to have a
nontrivial subfield? As the reader might expect the answer heavily depends on
the interpretation of probability. We show that if the fields are enumerated by
the smallest height of their generators the probability is zero, at least if
$d>6$. This is in contrast to what one expects when the fields are enumerated
by the discriminant. The main result of this article is an estimate for the
number of algebraic numbers of degree $d=e n$ and bounded height which generate
a field that contains an unspecified subfield of degree $e$. If
$n>\max\{e^2+e,10\}$ we get the correct asymptotics as the height tends to
infinity.


  In this paper, we establish a new volume comparison theorem for a complete
manifold with a function $\rho(x)$ as the lower bound of the Bakry-Emery Ricci
curvature. As applications, we obtain a new volume rigidity result of the
gradient Ricci almost solitons. Furthermore, we extend the results of Cao and
Zhou \cite{CZ} to shrinking gradient Ricci almost solitons and get the rigidity
result with respect to the maximal volume growth.


  A lower bound on the amount of noise that must be added to a GHZ-like
entangled state to make it separable (also called the random robustness) is
found using the transposition condition. The bound is applicable to arbitrary
numbers of subsystems, and dimensions of Hilbert space, and is shown to be
exact for qubits. The new bound is compared to previous such bounds on this
quantity, and found to be stronger in all cases. It implies that increasing the
number of subsystems, rather than increasing their Hilbert space dimension is a
more effective way of increasing entanglement. An explicit decomposition into
an ensemble of separable states, when the state is not entangled,is given for
the case of qubits.


  Creating 4D fields of Gaussian Splatting from images or videos is a
challenging task due to its under-constrained nature. While the optimization
can draw photometric reference from the input videos or be regulated by
generative models, directly supervising Gaussian motions remains underexplored.
In this paper, we introduce a novel concept, Gaussian flow, which connects the
dynamics of 3D Gaussians and pixel velocities between consecutive frames. The
Gaussian flow can be efficiently obtained by splatting Gaussian dynamics into
the image space. This differentiable process enables direct dynamic supervision
from optical flow. Our method significantly benefits 4D dynamic content
generation and 4D novel view synthesis with Gaussian Splatting, especially for
contents with rich motions that are hard to be handled by existing methods. The
common color drifting issue that happens in 4D generation is also resolved with
improved Guassian dynamics. Superior visual quality on extensive experiments
demonstrates our method's effectiveness. Quantitative and qualitative
evaluations show that our method achieves state-of-the-art results on both
tasks of 4D generation and 4D novel view synthesis. Project page:
https://zerg-overmind.github.io/GaussianFlow.github.io/


  We present the results of a radial velocity (RV) survey of 46 subdwarf B
(sdB) and 23 helium-rich subdwarf O (He-sdO) stars. We detected 18 (39%) new
sdB binary systems, but only one (4%) He-sdO binary. Orbital parameters of nine
sdB and sdO binaries, derived from follow-up spectroscopy, are presented. Our
results are compared with evolutionary scenarios and previous observational
investigations.


  We propose two new techniques for training Generative Adversarial Networks
(GANs). Our objectives are to alleviate mode collapse in GAN and improve the
quality of the generated samples. First, we propose neighbor embedding, a
manifold learning-based regularization to explicitly retain local structures of
latent samples in the generated samples. This prevents generator from producing
nearly identical data samples from different latent samples, and reduces mode
collapse. We propose an inverse t-SNE regularizer to achieve this. Second, we
propose a new technique, gradient matching, to align the distributions of the
generated samples and the real samples. As it is challenging to work with
high-dimensional sample distributions, we propose to align these distributions
through the scalar discriminator scores. We constrain the difference between
the discriminator scores of the real samples and generated ones. We further
constrain the difference between the gradients of these discriminator scores.
We derive these constraints from Taylor approximations of the discriminator
function. We perform experiments to demonstrate that our proposed techniques
are computationally simple and easy to be incorporated in existing systems.
When Gradient matching and Neighbour embedding are applied together, our GN-GAN
achieves outstanding results on 1D/2D synthetic, CIFAR-10 and STL-10 datasets,
e.g. FID score of $30.80$ for the STL-10 dataset. Our code is available at:
https://github.com/tntrung/gan


  The interplay of star formation and supernova (SN) feedback in galaxy
formation is a key element for understanding galaxy evolution. Since these
processes occur at small scales, it is necessary to have sub-grid models that
recover their evolution and environmental effects at the scales reached by
cosmological simulations. We simulate the same spiral galaxy inhabiting a Milky
Way (MW) size halo in a cosmological environment changing the sub-grid models
for SN feedback and star formation. We test combinations of the Schmidt law and
a multi-freefall based star formation with delayed cooling feedback or
mechanical feedback. We reach a resolution of 35 pc in a zoom-in box of 36 Mpc.
For this, we use the code RAMSES with the implementation of gas turbulence in
time and trace the local hydrodynamical features of the star-forming gas.
Finally, we compare the galaxies at redshift 0 with global and interstellar
medium observations in the MW and local spiral galaxies. The simulations show
successful comparisons with observations. Nevertheless, diverse galactic
morphologies are obtained from different numerical implementations. We
highlight the importance of detailed modelling of the star formation and
feedback processes, especially when increasing the resolution of simulations.
Future improvements could alleviate the degeneracies exhibited in our simulated
galaxies under different sub-grid models.


  Most of the existing visual SLAM methods heavily rely on a static world
assumption and easily fail in dynamic environments. Some recent works eliminate
the influence of dynamic objects by introducing deep learning-based semantic
information to SLAM systems. However such methods suffer from high
computational cost and cannot handle unknown objects. In this paper, we propose
a real-time semantic RGB-D SLAM system for dynamic environments that is capable
of detecting both known and unknown moving objects. To reduce the computational
cost, we only perform semantic segmentation on keyframes to remove known
dynamic objects, and maintain a static map for robust camera tracking.
Furthermore, we propose an efficient geometry module to detect unknown moving
objects by clustering the depth image into a few regions and identifying the
dynamic regions via their reprojection errors. The proposed method is evaluated
on public datasets and real-world conditions. To the best of our knowledge, it
is one of the first semantic RGB-D SLAM systems that run in real-time on a
low-power embedded platform and provide high localization accuracy in dynamic
environments.


  Dust growth and settling considerably affect the spectral energy
distributions (SEDs) of protoplanetary disks. We investigated dust growth and
settling in protoplanetary disks through numerical simulations to examine
time-evolution of the disk optical thickness and SEDs. In the present paper, we
considered laminar disks as a first step of a series of papers. As a result of
dust growth and settling, a dust layer forms around the mid-plane of a gaseous
disk. After the formation of the dust layer, small dust grains remain floating
above the layer. Although the surface density of the floating small grains is
much less than that of the dust layer, they govern the disk optical thickness
and the emission. The floating small grains settle onto the dust layer in a
long time scale compared with the formation of the dust layer. Rapid grain
growth in the inner part of disks makes the radial distribution of the disk
optical thickness less steep than that of the disk surface density. At t >
10^6yr, the optical thickness of the inner disk (> a few AU) almost vanishes,
which may correspond to disk inner holes observed by Spitzer Space Telescope.
Furthermore, we examined time-evolution of disk SEDs, using our numerical
results and the two-layer model. The grain growth and settling decrease the
magnitude of the SEDs especially. Our results indicate that grain growth and
settling can explain the decrease in observed energy fluxes at
millimeter/sub-millimeter wavelengths with time scales of 10^{6-7}yr without
depletion of the disks.


  In an influential paper, Eppley and Hannah argued that gravity must
necessarily be quantized, by proposing a thought experiment involving classical
gravitational waves interacting with quantum matter. They argue the interaction
must either violate the uncertainty principle or allow superluminal signalling.
The feasibility of implementing their experiment in our universe has been
challenged by Mattingly, and other limitations of the argument have been noted
by Huggett and Callender and by Albers et al.. However, these critiques do not
directly refute the claim that coupling quantum theories with a Copenhagen
collapse postulate to unentanglable classical gravitational degrees of freedom
leads to contradiction. I note here that if the gravitational field interacts
with matter via the local quantum state, the Eppley-Hannah argument evidently
fails. This seems a plausibly natural feature of a hybrid theory, whereas the
alternative considered by Eppley-Hannah is evidently inconsistent with
relativity.


  We review strangeness as signature of quark gluon plasma (QGP) and the
hadronization process of a QGP fireball formed in relativistic heavy-ion
collisions in the entire range of today accessible reaction energies. We
discuss energy dependence of the statistical hadronization parameters within
the context of fast QGP hadronization. We find that QGP breakup occurs for all
energies at the universal hadronization pressure $P = 80\pm
3\,\mathrm{MeV/fm}^3 $.


  Using as ingredients the non-perturbative solutions of various QCD Green's
function obtained from Schwinger-Dyson equations (SDEs), we study two versions
of the QCD effective charge. The first one obtained from the pinch technique
gluon self-energy, and the second from the ghost-gluon vertex. Despite the
distinct nature of their buildings blocks, the two effectives charges are
almost identical in the entire range of momenta, due to a fundamental identity
relating the ghost dressing function with the two form factors of Green's
function, which is of central importance in the PT-BFM formalism. In this talk,
we outline how to derive this crucial identity from the SDEs of the
aforementioned Green's functions. The renormalization procedure that preserves
the validity of this identity is discussed in detail. Most importantly, we show
that due to the infrared finiteness of the gluon propagator, the QCD charge
obtained with either definition freezes in the deep infrared, in agreement with
theoretical and phenomenological expectations.


  Drawing independent samples from a probability distribution is an important
computational problem with applications in Monte Carlo algorithms, machine
learning, and statistical physics. The problem can in principle be solved on a
quantum computer by preparing a quantum state that encodes the entire
probability distribution followed by a projective measurement. We investigate
the complexity of adiabatically preparing such quantum states for the Gibbs
distributions of various classical models including the Ising chain,
hard-sphere models on different graphs, and a model encoding the unstructured
search problem. By constructing a parent Hamiltonian, whose ground state is the
desired quantum state, we relate the asymptotic scaling of the state
preparation time to the nature of transitions between distinct quantum phases.
These insights enable us to identify adiabatic paths that achieve a quantum
speedup over classical Markov chain algorithms. In addition, we show that
parent Hamiltonians for the problem of sampling from independent sets on
certain graphs can be naturally realized with neutral atoms interacting via
highly excited Rydberg states.


  In an N-level quantum mechanical system, the problem of unitary feedback
stabilization of mixed density operators to periodic orbits admits a natural
Lyapunov-based time-varying feedback design. A global description of the domain
of attraction of the closed-loop system can be provided based on a
``root-space''-like structure of the space of density operators. This convex
set foliates as a complex flag manifold where each leaf is identified with the
coadjoint orbit of the eigenvalues of the density operator. The converging
conditions are time-independent but depend from the topology of the flag
manifold: it is shown that the closed loop must have a number of equilibria at
least equal to the Euler characteristic of the manifold, thus imposing
obstructions of topological nature to global stabilizability.


  In a nucleus which has two Hartree states deformed in quadrupole symmetry,
i.e., prolate state and oblate state, the nuclear residual interaction derived
in the present theory beyond the Hartree approximation acts as the restoring
force for the spherical symmetry of the nuclear system to be recovered so that
the deformed nucleus makes collective tunneling transitions between prolate
states and oblate states. We derive the Hamiltonian that is effective not only
for the Hartree states but also for the collective tunneling transitions
between the Hartree states. Solving the secular equation for the effective
Hamiltonian on the basis states expressed in terms of SU(5) algebra, we analyze
the nuclear collective tunneling transitions between a prolate state and an
oblate state in the real-time description. The collective tunneling transitions
are discussed to proceed through tri-axially asymmetric deformed states.


  Quantum magnetism is a fundamental phenomenon of nature. As of late, it has
garnered a lot of interest because experiments with ultracold atomic gases in
optical lattices could be used as a simulator for phenomena of magnetic
systems. A paradigmatic example is the time evolution of a domain-wall state of
a spin-1/2 Heisenberg chain, the so-called domain-wall melting. The model can
be implemented by having two species of bosonic atoms with unity filling and
strong on-site repulsion U in an optical lattice. In this paper, we study the
domain-wall melting in such a setup on the basis of the time-dependent density
matrix renormalization group (tDMRG). We are particularly interested in the
effects of defects that originate from an imperfect preparation of the initial
state. Typical defects are holes (empty sites) and flipped spins. We show that
the dominating effects of holes on observables like the spatially resolved
magnetization can be taken account of by a linear combination of spatially
shifted observables from the clean case. For sufficiently large U, further
effects due to holes become negligible. In contrast, the effects of spin flips
are more severe as their dynamics occur on the same time scale as that of the
domain-wall melting itself. It is hence advisable to avoid preparation schemes
that are based on spin-flips.


  We study the topological entropy of a two-parameter family of maps related to
(a,b)-continued fraction algorithms and prove that it is constant on a square
within the parameter space (two vertices of this square correspond to
well-studied continued fraction algorithms). The proof uses conjugation to maps
of constant slope. We also present experimental evidence that the topological
entropy is flexible (i.e., takes any value in a range) on the whole parameter
space.


  Psychologists have long known that an expert in a field not only knows
significantly more individual facts/skills than a novice but also has these
facts/skills organized into a mental hierarchy that links the individual facts
(at the bottom of the hierarchy) together with larger more-encompassing ideas
(at the top of the hierarchy). In the Spring quarter of 2012, UC Davis offered
4 sections (about 180 students each) of the first quarter of introductory
physics, Physics 9A, covering Newtonian mechanics. One of these sections is a
"treatment" group and had the entire 10-week quarter's set of ideas introduced,
largely qualitatively, in the first 6 weeks followed by the 4 weeks where
students learn to use those ideas to solve the algebraically complicated
problems that physicists prize. The other three sections were organized as
usual. The treatment group and one of the other sections were taught by the
author and were identical (same homework, discussion, lecture, and lab) except
for the organization of the content. After controlling for GPA as well as Force
Concept Inventory pretest scores, the treatment group was found, with better
than 99% confidence, to score higher on the final exam. Some curricular details
of the treatment class are discussed in this paper.


  An example of a cold massive core, JCMT 18354-0649S, a possible high mass
analogue to a low mass star forming core is studied. Line and continuum
observations from JCMT, Mopra Telescope and Spitzer are presented and modelled
in detail using a 3D molecular line radiative transfer code. In almost every
way JCMT 18354-0649S is a scaled-up version of a typical low mass core with
similar temperatures, chemical abundances and densities. The difference is that
both the infall velocity and the turbulent width of the line profiles are an
order of magnitude larger. While the higher infall velocity is expected due to
the large mass of JCMT 18354-0649S, we suggest that the dissipation of this
highly supersonic turbulence may lead to the creation of dense clumps of gas
that surround the high mass core.


  We present a set of $UBVRIzJHK_s$ photometry for 745 $J+H$ band selected
objects in a $22.5' \times 29.2'$ region centered on the core of the Coma
cluster. This includes 516 galaxies and is at least 80% complete to H=16, with
a spectroscopically complete sample of 111 cluster members (nearly all with
morphological classification) for $H < 14.5$. For each object we present total
\cite{kron80} magnitudes and aperture photometry. As an example, we use these
data to derive color-magnitude relations for Coma early-type galaxies, measure
the intrinsic scatter of these relations and its dependence on galaxy mass, and
address the issue of color gradients. We find that the color gradients are mild
and that the intrinsic scatter about the color-magnitude relation is small
($\sim 0.05$ mag in $U-V$ and less than $\sim 0.03$ in $B-R$, $V-I$ or $J-K$).
There is no evidence that the intrinsic scatter varies with galaxy luminosity,
suggesting that the cluster red sequence is established at early epochs over a
range of $\sim 100$ in stellar mass.


  A simple algorithm to calculate the group theory factor entering in anomalies
at four and six dimensions for SU(N) and SO(N) groups in terms of the Casimir
invariants of their subgroups is presented. Explicit examples of some of the
lower dimensional representations of $SU(n), n \leq 5$ and SO(10) groups are
presented, which could be used for model building in four and six dimensions.


  We present a model of supersymmetry breaking in which the contributions from
gravity/modulus, anomaly, and gauge mediation are all comparable. We term this
scenario "deflected mirage mediation," which is a generalization of the
KKLT-motivated mirage mediation scenario to include gauge mediated
contributions. These contributions deflect the gaugino mass unification scale
and alter the pattern of soft parameters at low energies. In some cases, this
results in a gluino LSP and light stops; in other regions of parameter space,
the LSP can be a well-tempered neutralino. We demonstrate explicitly that
competitive gauge-mediated terms can naturally appear within phenomenological
models based on the KKLT setup by addressing the stabilization of the gauge
singlet field which is responsible for the masses of the messenger fields. For
viable stabilization mechanisms, the relation between the gauge and anomaly
contributions is identical in most cases to that of deflected anomaly
mediation, despite the presence of the Kahler modulus. Turning to TeV scale
phenomenology, we analyze the renormalization group evolution of the
supersymmetry breaking terms and the resulting low energy mass spectra. The
approach sets the stage for studies of such mixed scenarios of supersymmetry
breaking at the LHC.


  We review and expand on recent advances in theory and experiments concerning
the problem of wavefunction uncollapse: Given an unknown state that has been
disturbed by a generalized measurement, restore the state to its initial
configuration. We describe how this is probabilistically possible with a
subsequent measurement that involves erasing the information extracted about
the state in the first measurement. The general theory of abstract measurements
is discussed, focusing on quantum information aspects of the problem, in
addition to investigating a variety of specific physical situations and
explicit measurement strategies. Several systems are considered in detail: the
quantum double dot charge qubit measured by a quantum point contact (with and
without Hamiltonian dynamics), the superconducting phase qubit monitored by a
SQUID detector, and an arbitrary number of entangled charge qubits.
Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and
the optical polarization qubit are also reviewed. For each of these systems the
physics of the continuous measurement process, the strategy required to ideally
uncollapse the wavefunction, as well as the statistical features associated
with the measurement is discussed. We also summarize the recent experimental
realization of two of these systems, the phase qubit and the polarization
qubit.


  We report the first observation of cations, dications and trications of large
clusters of adamantane. Cluster formation was initiated near 0 K in helium
droplets and ionization was achieved with one or more collisions with energetic
He species (He$^{\star}$, He$^{+}$ or He$^{\star}$$^{-}$). The occurrence of
Coulomb explosion appeared to discriminate against the formation of small
multiply charged clusters. High resolution mass spectrometry revealed the
presence of "magic number" m/z peaks that can be attributed to the packing of
adamantane molecules into cluster structures of special stability involving
preferred arrangements of these molecules. These abundance anomalies were seen
to be independent of charge state. While some dehydrogenation of adamantane and
its clusters was seen as well, no major transformations into adamantoids or
microdiamonds were observed.


  We study multiplicative Dirac structures on Lie groups. We show that the
characteristic foliation of a multiplicative Dirac structure is given by the
cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf
space inherits the structure of a Poisson-Lie group. We also describe
multiplicative Dirac structures on Lie groups infinitesimally.


  We present an efficient proposal for error-rejecting quantum computing with
quantum dots (QD) embedded in single-sided optical microcavities based on the
interface between the circularly polarized photon and QDs. An almost unity
fidelity of the quantum entangling gate (EG) can be implemented with a
detectable error that leads to a recycling EG procedure, which improves further
the efficiency of our proposal along with the robustness to the errors involved
in imperfect input-output processes. Meanwhile, we discuss the performance of
our proposal for the EG on two solid-state spins with currently achieved
experiment parameters, showing that it is feasible with current experimental
technology. It provides a promising building block for solid-state quantum
computing and quantum networks.


  In this article we study the Gevrey regularization effect for the spatially
inhomogeneous Boltzmann equation without angular cutoff. This equation is
partially elliptic in the velocity direction and degenerates in the spatial
variable. We consider the nonlinear Cauchy problem for the fluctuation around
the Maxwellian distribution and prove that any solution with mild regularity
will become smooth in Gevrey class at positive time, with Gevrey index
depending on the angular singularity. Our proof relies on the symbolic calculus
for the collision operator and the global subelliptic estimate for the Cauchy
problem of linearized Boltzmann operator.


  The limitations of centralized optimization methods in managing power
distribution systems operations motivate distributed control and optimization
algorithms. However, the existing distributed optimization algorithms are
inefficient in managing fast varying phenomena, resulting from highly variable
distributed energy resources (DERs). Related online distributed control methods
are equally limited in their applications. They require thousands of time-steps
to track the network-level optimal solutions, resulting in slow performance. We
have previously developed an online distributed controller that leverages the
system's radial topology to achieve network-level optimal solutions within a
few time steps. However, it requires solving a node-level nonlinear programming
problem at each time step. This paper analyzes the solution space for the
node-level optimization problem and derives the analytical closed-form
solutions for the decision variables. The theoretical analysis of the
node-level optimization problem and obtained closed-form optimal solutions
eliminate the need for embedded optimization solvers at each distributed agent
and significantly reduce the computational time and optimization costs.