  Many scientific and engineering challenges can be formulated as optimization
problems which are constrained by partial differential equations (PDEs). These
include inverse problems, control problems, and design problems. As a major
challenge, the associated optimization procedures are inherently large-scale.
To ensure computational tractability, the design of efficient and robust
iterative methods becomes imperative. To meet this challenge, this paper
introduces a fast and memory-efficient preconditioned iterative scheme for a
class of distributed optimal control problems governed by
convection-diffusion-reaction (CDR) equations. As an alternative to low-order
discretizations and Schur-complement block preconditioners, the scheme combines
a high-order spectral Galerkin method with an efficient preconditioner tailored
specifically for the CDR application. The preconditioner is matrix-free and can
be applied within linear complexity where the proportionality constant is
small. Numerical results demonstrate that the preconditioner is ideal in the
sense that appropriate Krylov subspace methods converge within a low number of
iterations, independently of the problem size and the Tikhonov regularization
parameter.


  We study pure exploration in bandits, where the dimension of the feature
representation can be much larger than the number of arms. To overcome the
curse of dimensionality, we propose to adaptively embed the feature
representation of each arm into a lower-dimensional space and carefully deal
with the induced model misspecification. Our approach is conceptually very
different from existing works that can either only handle low-dimensional
linear bandits or passively deal with model misspecification. We showcase the
application of our approach to two pure exploration settings that were
previously under-studied: (1) the reward function belongs to a possibly
infinite-dimensional Reproducing Kernel Hilbert Space, and (2) the reward
function is nonlinear and can be approximated by neural networks. Our main
results provide sample complexity guarantees that only depend on the effective
dimension of the feature spaces in the kernel or neural representations.
Extensive experiments conducted on both synthetic and real-world datasets
demonstrate the efficacy of our methods.


  Using the population synthesis binary evolution code StarTrack, we present
theoretical rates and delay times of Type Ia supernovae arising from various
formation channels. These channels include binaries in which the exploding
white dwarf reaches the Chandrasekhar mass limit (DDS, SDS, and helium-rich
donor scenario) as well as the sub-Chandrasekhar mass scenario, in which a
white dwarf accretes from a helium-rich companion and explodes as a SN Ia
before reaching the Chandrasekhar mass limit. We find that using a common
envelope parameterization employing energy balance with alpha=1 and lambda=1,
the supernova rates per unit mass (born in stars) of sub-Chandrasekhar mass SNe
Ia exceed those of all other progenitor channels at epochs t=0.7 - 4 Gyr for a
burst of star formation at t=0. Additionally, the delay time distribution of
the sub-Chandrasekhar model can be divided in to two distinct evolutionary
channels: the `prompt' helium-star channel with delay times < 500 Myr, and the
`delayed' double white dwarf channel with delay times > 800 Myr spanning up to
a Hubble time. These findings are in agreement with recent
observationally-derived delay time distributions which predict that a large
number of SNe Ia have delay times < 1 Gyr, with a significant fraction having
delay times < 500 Myr. We find that the DDS channel is also able to account for
the observed rates of SNe Ia. However, detailed simulations of white dwarf
mergers have shown that most of these mergers will not lead to SNe Ia but
rather to the formation of a neutron star via accretion-induced collapse. If
this is true, our standard population synthesis model predicts that the only
progenitor channel which can account for the rates of SNe Ia is the
sub-Chandrasekhar mass scenario, and none of the other progenitors considered
can fully account for the observed rates.


  We demonstrate that any physical object, as long as its volume is conserved
when coupled with suitable operations, provides a sophisticated decision-making
capability. We consider the problem of finding, as accurately and quickly as
possible, the most profitable option from a set of options that gives
stochastic rewards. These decisions are made as dictated by a physical object,
which is moved in a manner similar to the fluctuations of a rigid body in a
tug-of-war game. Our analytical calculations validate statistical reasons why
our method exhibits higher efficiency than conventional algorithms.


  Quantum annealing has the potential to find low energy solutions of NP-hard
problems that can be expressed as quadratic unconstrained binary optimization
problems. However, the hardware of the quantum annealer manufactured by D-Wave
Systems, which we consider in this work, is sparsely connected and moderately
sized (on the order of thousands of qubits), thus necessitating a
minor-embedding of a logical problem onto the physical qubit hardware. The
combination of relatively small hardware sizes and the necessity of a
minor-embedding can mean that solving large optimization problems is not
possible on current quantum annealers. In this research, we show that a hybrid
approach combining parallel quantum annealing with graph decomposition allows
one to solve larger optimization problem accurately. We apply the approach on
the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.


  We investigate, assess, and suggest possibilities for a measurement of the
local spin susceptibility of a conducting low-dimensional electron system. The
basic setup of the experiment we envisage is a source-probe one. Locally
induced spin density (e.g. by a magnetized atomic force microscope tip) extends
in the medium according to its spin susceptibility. The induced magnetization
can be detected as a dipolar magnetic field, for instance, by an
ultra-sensitive nitrogen-vacancy center based detector, from which the spatial
structure of the spin susceptibility can be deduced. We find that
one-dimensional systems, such as semiconducting nanowires or carbon nanotubes,
are expected to yield a measurable signal. The signal in a two-dimensional
electron gas is weaker, though materials with high enough $g$-factor (such as
InGaAs) seem promising for successful measurements.


  Iris recognition systems are vulnerable to the presentation attacks, such as
textured contact lenses or printed images. In this paper, we propose a
lightweight framework to detect iris presentation attacks by extracting
multiple micro-stripes of expanded normalized iris textures. In this procedure,
a standard iris segmentation is modified. For our presentation attack detection
network to better model the classification problem, the segmented area is
processed to provide lower dimensional input segments and a higher number of
learning samples. Our proposed Micro Stripes Analyses (MSA) solution samples
the segmented areas as individual stripes. Then, the majority vote makes the
final classification decision of those micro-stripes. Experiments are
demonstrated on five databases, where two databases (IIITD-WVU and Notre Dame)
are from the LivDet-2017 Iris competition. An in-depth experimental evaluation
of this framework reveals a superior performance compared with state-of-the-art
algorithms. Moreover, our solution minimizes the confusion between textured
(attack) and soft (bona fide) contact lens presentations.


  We consider the optimization problem of minimizing
$\int_{\mathbb{R}^n}|\nabla u|^2\,\mathrm{d}x$ with double obstacles $\phi\leq
u\leq\psi$ a.e. in $D$ and a constraint on the volume of
$\{u>0\}\setminus\overline{D}$, where $D\subset\mathbb{R}^n$ is a bounded
domain. By studying a penalization problem that achieves the constrained volume
for small values of penalization parameter, we prove that every minimizer is
$C^{1,1}$ locally in $D$ and Lipschitz continuous in $\mathbb{R}^n$ and that
the free boundary $\partial\{u>0\}\setminus\overline{D}$ is smooth. Moreover,
when the boundary of $D$ has a plane portion, we show that the minimizer is
$C^{1,\frac{1}{2}}$ up to the plane portion.


  Actively monitoring machine learning models during production operations
helps ensure prediction quality and detection and remediation of unexpected or
undesired conditions. Monitoring models already deployed in big data
environments brings the additional challenges of adding monitoring in parallel
to the existing modelling workflow and controlling resource requirements. In
this paper, we describe (1) a framework for monitoring machine learning models;
and, (2) its implementation for a big data supply chain application. We use our
implementation to study drift in model features, predictions, and performance
on three real data sets. We compare hypothesis test and information theoretic
approaches to drift detection in features and predictions using the
Kolmogorov-Smirnov distance and Bhattacharyya coefficient. Results showed that
model performance was stable over the evaluation period. Features and
predictions showed statistically significant drifts; however, these drifts were
not linked to changes in model performance during the time of our study.


  In \cite{Bia97} Biane proposed a new statistic on set partitions which he
called \emph{restricted crossings}. In a series of papers
\cite{Ans01,Ans04,Ans04b,Ans05} Anshelevich showed that this statistic is an
essential tool to investigate stochastic processes on $q$-Fock space. In
particular, Anshelevich constructed operators whose moments count restricted
crossings and used these operators to develop a beautiful theory of
noncommutative $q$-L\'{e}vy processes. In the present paper following
Anshelevich we define gauge operators on $(\alpha,q)$-Fock and cumulants which
are governed by statistics on partitions of type B. In addition we investigate
this construction in the context of a model of Blitvi{\'c} model \cite{B12},
where some related but different combinatorial structures appear, and we
explain their relation with $t$-free probability.


  We prove here some dimension free Poincar\'e-type inequalities on Hamming
cube for functions with different spectral properties and for fractional
Laplacians. In this note the main attention is paid to estimates in $L^1$ norm
on Hamming cube. We build the examples showing that our assumptions on spectral
properties of functions cannot be dropped in general.


  We investigate the problem of learning discrete, undirected graphical models
in a differentially private way. We show that the approach of releasing noisy
sufficient statistics using the Laplace mechanism achieves a good trade-off
between privacy, utility, and practicality. A naive learning algorithm that
uses the noisy sufficient statistics "as is" outperforms general-purpose
differentially private learning algorithms. However, it has three limitations:
it ignores knowledge about the data generating process, rests on uncertain
theoretical foundations, and exhibits certain pathologies. We develop a more
principled approach that applies the formalism of collective graphical models
to perform inference over the true sufficient statistics within an
expectation-maximization framework. We show that this learns better models than
competing approaches on both synthetic data and on real human mobility data
used as a case study.


  In this work we report the opening of an energy gap at the filling factor
$\nu=3+1/3$, firmly establishing the ground state as a fractional quantum Hall
state. This and other odd-denominator states unexpectedly break particle-hole
symmetry. Specifically, we find that the relative magnitudes of the energy gaps
of the $\nu=3+1/3$ and $3+1/5$ states from the upper spin branch are reversed
when compared to the $\nu=2+1/3$ and $2+1/5$ counterpart states in the lower
spin branch. Our findings raise the possibility that the former states have a
non-conventional origin.


  In two-dimensional superconductors, Yu-Shiba-Rusinov bound states, induced by
the magnetic impurities, extend over long distances giving rise to a long-range
hopping model supporting a large number of topological phases with distinct
Chern numbers. Here, we study how the electron-electron interactions affect on
a mean-field level the selection of the realized Chern numbers and the
magnitudes of the topological energy gaps in this model. We find that in the
case of an individual choice of the model parameters the interactions can
enhance or reduce the topological gap as well as cause topological phase
transitions because of the complex interplay of superconductivity, magnetism,
and large spatial extent of the Yu-Shiba-Rusinov states. By sampling a large
number of realizations of Yu-Shiba-Rusinov lattice models with different model
parameters, we show that statistically the interactions have no effect on the
realized Chern numbers and typical magnitudes of the topological gaps. However,
the interactions substantially increase the likelihood of the largest
topological gaps in the tails of the energy gap distribution in comparison to
the non-interacting case.


  Background and Objective: Vital sign monitoring in the Intensive Care Unit
(ICU) is crucial for enabling prompt interventions for patients. This
underscores the need for an accurate predictive system. Therefore, this study
proposes a novel deep learning approach for forecasting Heart Rate (HR),
Systolic Blood Pressure (SBP), and Diastolic Blood Pressure (DBP) in the ICU.
  Methods: We extracted $24,886$ ICU stays from the MIMIC-III database which
contains data from over $46$ thousand patients, to train and test the model.
The model proposed in this study, Transformer-based Diffusion Probabilistic
Model for Sparse Time Series Forecasting (TDSTF), merges Transformer and
diffusion models to forecast vital signs. The TDSTF model showed
state-of-the-art performance in predicting vital signs in the ICU,
outperforming other models' ability to predict distributions of vital signs and
being more computationally efficient. The code is available at
https://github.com/PingChang818/TDSTF.
  Results: The results of the study showed that TDSTF achieved a Standardized
Average Continuous Ranked Probability Score (SACRPS) of $0.4438$ and a Mean
Squared Error (MSE) of $0.4168$, an improvement of $18.9\%$ and $34.3\%$ over
the best baseline model, respectively. The inference speed of TDSTF is more
than $17$ times faster than the best baseline model.
  Conclusion: TDSTF is an effective and efficient solution for forecasting
vital signs in the ICU, and it shows a significant improvement compared to
other models in the field.


  Objective: To develop and evaluate FastContext, an efficient, scalable
implementation of the ConText algorithm suitable for very large-scale clinical
natural language processing. Background: The ConText algorithm performs with
state-of-art accuracy in detecting the experiencer, negation status, and
temporality of concept mentions in clinical narratives. However, the speed
limitation of its current implementations hinders its use in big data
processing. Methods: We developed FastContext through hashing the ConText's
rules, then compared its speed and accuracy with JavaConText and
GeneralConText, two widely used Java implementations. Results: FastContext ran
two orders of magnitude faster and was less decelerated by rule increase than
the other two implementations used in this study for comparison. Additionally,
FastContext consistently gained accuracy improvement as the rules increased
(the desired outcome of adding new rules), while the other two implementations
did not. Conclusions: FastContext is an efficient, scalable implementation of
the popular ConText algorithm, suitable for natural language applications on
very large clinical corpora.


  Aldous-Broder algorithm is a famous algorithm used to sample a uniform
spanning tree of any finite connected graph $G$, but it is more general: given
an irreducible and reversible Markov chain $M$ on $G$ started at $r$, the tree
rooted at $r$ formed by the first entrance steps in each node (different from
the root) has a probability proportional to $\prod_{e=(e^-,e^+)\in {\sf
Edges}(t,r)} M_{e^{-},e^+}$, where the edges are directed toward $r$. In this
paper we give proofs of Aldous-Broder theorem in the general case, where the
kernel $M$ is irreducible but not assumed to be reversible (this generalized
version appeared recently in Hu, Lyons and Tang )


  We present an analytic $\mathcal O(\alpha_s)$ calculation of cross sections
in deep inelastic scattering (DIS) dependent on an event shape, 1-jettiness,
that probes final states with one jet plus initial state radiation. This is the
first entirely analytic calculation for a DIS event shape cross section at this
order. We present results for the differential and cumulative 1-jettiness cross
sections, and express both in terms of structure functions dependent not only
on the usual DIS variables $x$, $Q^2$ but also on the 1-jettiness $\tau$.
Combined with previous results for log resummation, predictions are obtained
over the entire range of the 1-jettiness distribution.


  Let A(x) be a holomorphic family of bounded self-adjoint operators on a
separable Hilbert space H and let A(x)_n be the orthogonal compressions of A(x)
to the span of first n elements of an orthonormal basis of H. The problem
considered here is to approximate the spectrum of A(x) using the sequence of
eigenvalues of A(x)_n. We show that the bounds of the essential spectrum and
the discrete spectral values outside the bounds of essential spectrum of A(x)
can be approximated uniformly on all compact subsets by the sequence of
eigenvalue functions of A(x)_n. The known results for a bounded selfadjoint
operator, are translated into the case of a holomorphic family of operators.
Also an attempt is made to predict the existence of spectral gaps that may
occur between the bounds of essential spectrum of A(0) = A and study the effect
of holomorphic perturbation of operators in the prediction of spectral gaps. As
an example, gap issues of some block Toeplitz-Laurent operators are discussed.
The pure linear algebraic approach is the main advantage of the results here.


  We present new Keck/DEIMOS spectroscopic observations of hundreds of
individual stars along the sightline to Andromeda's first three discovered
dwarf spheroidal galaxies (dSphs) - And I, II, and III, and leverage recent
observations by our team of three additional dSphs, And VII, X, and XIV, as a
part of the SPLASH Survey. Member stars of each dSph are isolated from
foreground Milky Way dwarf and M31 field contamination using a variety of
photometric and spectroscopic diagnostics. Our final spectroscopic sample of
member stars in each dSph, for which we measure accurate radial velocities with
a median uncertainty (random plus systematic errors) of 4 - 5 km/s, includes 80
red giants in And I, 95 in And II, 43 in And III, 18 in And VII, 22 in And X,
and 38 in And XIV. The sample of confirmed members in the six dSphs are used to
derive each system's mean radial velocity, intrinsic central velocity
dispersion, mean abundance, abundance spread, and dynamical mass. This combined
data set presents us with a unique opportunity to perform the first systematic
comparison of the global properties (e.g., metallicities, sizes, and dark
matter masses) of one-third of Andromeda's total known dSph population with
Milky Way counterparts of the same luminosity. We discuss both the
luminosity-metallicity relation and the luminosity-size relation of these
satellites, and find that the chemical evolution histories of each host's
satellites is similar. The dynamical mass estimates of M31's dSphs are similar
or smaller than Milky Way dSphs of the same luminosity despite their sizes
being similar or larger, suggesting M31 dSphs are less dense than Milky Way
counterparts. The implications of these results for general understanding of
galaxy formation and evolution is summarized. Abridged.


  Fermilab experiment E791 studied weak decays of D+, D_s, and D^0 mesons
produced in collisions of 500 GeV/c negative pions with Pt and C targets. The
experiment collected over 200,000 fully reconstructed charm decays. Four recent
results are discussed here: (a) measurement of the form factor ratios V/A_1,
A_2/A_1, and A_3/A_1 in D->K*-l-nu and Ds->phi-l-nu decays; (b) measurement of
the difference in decay widths $\Delta\Gamma$ between the two D^0/D^0-bar mass
eigenstates; (c) search for rare and forbidden D decays to dilepton final
states; and (d) search for a ``Pentaquark,'' a bound state of c-bar-suud.


  Food occupies a central position in every culture and it is therefore of
great interest to understand the evolution of food culture. The advent of the
World Wide Web and online recipe repositories has begun to provide
unprecedented opportunities for data-driven, quantitative study of food
culture. Here we harness an online database documenting recipes from various
Chinese regional cuisines and investigate the similarity of regional cuisines
in terms of geography and climate. We found that the geographical proximity,
rather than climate proximity is a crucial factor that determines the
similarity of regional cuisines. We develop a model of regional cuisine
evolution that provides helpful clues to understand the evolution of cuisines
and cultures.


  The number of positive and negative carries in the addition of two
independent random signed digit expansions of given length is analyzed
asymptotically for the $(q, d)$-system and the symmetric signed digit
expansion. The results include expectation, variance, covariance between the
positive and negative carries and a central limit theorem.
  Dependencies between the digits require determining suitable transition
probabilities to obtain equidistribution on all expansions of given length. A
general procedure is described to obtain such transition probabilities for
arbitrary regular languages.
  The number of iterations in von Neumann's parallel addition method for the
symmetric signed digit expansion is also analyzed, again including expectation,
variance and convergence to a double exponential limiting distribution. This
analysis is carried out in a general framework for sequences of generating
functions.


  We derive the exact dual representation of the bosonic Hubbard model which
takes the form of conserved current loops. The hardcore limit, which
corresponds to the quantum spin-${1\over 2}$ Heisenberg antiferromagnet, is
also obtained. In this limit, the dual partition function takes a particularly
simple form which is very amenable to numerical simulations. In addition to the
usual quantities that we can measure (energy, density-density correlation
function and superfluid density) we can with this new algorithm measure
efficiently the order parameter correlation function, $<a_i a_j^{\dagger}>,
|i-j|\ge 1$. We demonstrate this with numerical tests in one dimension.


  This paper presents the design, analysis, and performance evaluation of an
omnidirectional transformable wheel-leg robot called OmniWheg. We design a
novel mechanism consisting of a separable omni-wheel and 4-bar linkages,
allowing the robot to transform between omni-wheeled and legged modes smoothly.
In wheeled mode, the robot can move in all directions and efficiently adjust
the relative position of its wheels, while it can overcome common obstacles in
legged mode, such as stairs and steps. Unlike other articles studying whegs,
this implementation with omnidirectional wheels allows the correction of
misalignments between right and left wheels before traversing obstacles, which
effectively improves the success rate and simplifies the preparation process
before the wheel-leg transformation. We describe the design concept, mechanism,
and the dynamic characteristic of the wheel-leg structure. We then evaluate its
performance in various scenarios, including passing obstacles, climbing steps
of different heights, and turning/moving omnidirectionally. Our results confirm
that this mobile platform can overcome common indoor obstacles and move
flexibly on the flat ground with the new transformable wheel-leg mechanism,
while keeping a high degree of stability.


  We consider the Dirac equation in cylindrically symmetric magnetic fields and
find its normal modes as eigenfunctions of a complete set of commuting
operators. This set consists of the Dirac operator itself, the $z$-components
of the linear and the total angular momenta, and of one of the possible spin
polarization operators. The spin structure of the solution is completely fixed
independently of the radial distribution of the magnetic field which influences
only the radial modes. We solve explicitly the radial equations for the uniform
magnetic field inside a solenoid of a finite radius and consider in detail the
scattering of scalar and Dirac particles in this field. For particles with low
energy the scattering cross section coincides with the Aharonov-Bohm scattering
cross section. We work out the first order corrections to this result caused by
the fact that the solenoid radius is finite. At high energies we obtain the
classical result for the scattering cross section.


  (abridged) NGC 1569 is a nearby dwarf irregular galaxy which underwent an
intense burst of star formation 10 to 40 Myr ago. We present observations that
reach surface brightnesses two to eighty times fainter than previous radio
continuum observations and the first radio continuum polarization observations.
These observations allow us to probe the relationship of the magnetic field of
NGC 1569 to the rest of its interstellar medium. We confirm the presence of an
extended radio continuum halo at 20 cm and see for the first time the radio
continuum feature associated with the western Halpha arm at wavelengths shorter
than 20cm. The spectral index trends in this galaxy support the theory that
there is a convective wind at work in this galaxy. We derive a total magnetic
field strength of 38 microG in the central regions and 10-15 microG in the
halo. The magnetic field is largely random in the center of the galaxy; the
uniform field is ~3-9 microG and is strongest in the halo. We find that the
magnetic pressure is the same order of magnitude but, in general, a factor of a
few less than the other components of the interstellar medium in this galaxy.
The uniform magnetic field in NGC 1569 is closely associated with the Halpha
bubbles and filaments. We suggest that a supernova-driven dynamo may be
operating in this galaxy. The outflow of hot gas from NGC 1569 is clearly
shaping the magnetic field, but the magnetic field in turn may be aiding the
outflow by channeling gas out of the disk of the galaxy. Dwarf galaxies with
extended radio continuum halos like that of NGC 1569 may play an important role
in magnetizing the intergalactic medium.


  The shear signal required for weak lensing analyses is small, so any
detector-level effects which distort astronomical images can contaminate the
inferred shear. The Nancy Grace Roman Space Telescope (Roman) will fly a focal
plane with 18 Teledyne H4RG-10 near infrared (IR) detector arrays; these have
never been used for weak lensing and they present unique instrument calibration
challenges. A pair of previous investigations (Hirata & Choi 2020; Choi &
Hirata 2020) demonstrated that spatiotemporal correlations of flat fields can
effectively separate the brighter-fatter effect (BFE) and interpixel
capacitance (IPC). Later work (Freudenburg et al. 2020) introduced a
Fourier-space treatment of these correlations which allowed the authors to
expand to higher orders in BFE, IPC, and classical nonlinearity (CNL). This
work expands the previous formalism to include quantum yield and charge
diffusion. We test the updated formalism on simulations and show that we can
recover input characterization values. We then apply the formalism to visible
and IR flat field data from three Roman flight candidate detectors. We fit a 2D
Gaussian model to the charge diffusion at 0.5 $\mu$m wavelength, and find
variances of $C_{11} = 0.1066\pm 0.0011$ pix$^2$ in the horizontal direction,
$C_{22} = 0.1136\pm 0.0012$ pix$^2$ in the vertical direction, and a covariance
of $C_{12} = 0.0001\pm 0.0007$ pix$^2$ (stat) for SCA 20829. Last, we convert
the asymmetry of the charge diffusion into an equivalent shear signal, and find
a contamination of the shear correlation function to be $\xi_+ \sim 10^{-6}$
for each detector. This exceeds Roman's allotted error budget for the
measurement by a factor of $\mathcal{O}(10)$ in power (amplitude squared) but
can likely be mitigated through standard methods for fitting the point spread
function (PSF) since charge diffusion can be treated as a contribution to the
PSF.


  We introduce a simple model for an engine based on the Nernst effect. In the
presence of a magnetic field, a vertical heat current can drive a horizontal
particle current against a chemical potential. For a microscopic model invoking
classical particle trajectories subject to the Lorentz force, we prove a
universal bound 3-2*sqrt(2) simeq 0.172 for the ratio between maximum
efficiency and Carnot efficiency. This bound, as the slightly lower one 1/6 for
efficiency at maximum power, can indeed be saturated for large magnetic field
and small fugacity irrespective of the aspect ratio.


  We extend Barwick's and Haugseng's construction of the double
$\infty$-category of spans in a pullback-complete $\infty$-category
$\mathfrak{C}$ to more general shapes: for a large class of algebraic patterns
$\mathfrak{P}$, we define a $\mathfrak{P}$-monoidal $\infty$-category of
$\mathfrak{P}$-shaped spans in $\mathfrak{C}$, and we identify monads in it
with Segal $\mathfrak{P}$-objects in $\mathfrak{C}$. For the cell pattern
$\Theta^{\mathrm{op}}$, this recovers a homotopical reformulation of Batanin's
original definition of weak $\omega$-categories, and in general can be seen as
a variant of the generalised multicategories of Burroni, Hermida, Leinster and
Cruttwell-Shulman.


  The behavior of the simplex algorithm is a widely studied subject.
Specifically, the question of the existence of a polynomial pivot rule for the
simplex algorithm is of major importance. Here, we give exponential lower
bounds for three history-based pivot rules. Those rules decide their next step
based on memory of the past steps. In particular, we study Zadeh's least
entered rule, Johnson's least-recently basic rule and Cunningham's
least-recently considered (or round-robin) rule. We give exponential lower
bounds on Acyclic Unique Sink Orientations (AUSO) of the abstract cube, for all
of these pivot rules. For Johnson's rule our bound is the first superpolynomial
one in any context; for Zadeh's it is the first one for AUSO. Those two are our
main results.


  In amorphous solids at finite temperatures the particles follow chaotic
trajectories which, at temperatures sufficiently lower than the glass
transition, are trapped in "cages". Averaging their positions for times shorter
than the diffusion time, one can define a time-averaged configuration. Under
strain or stress, these {\em average} configurations undergo sharp plastic
instabilities. In athermal glasses the understanding of plastic instabilities
is furnished by the Hessian matrix, its eigenvalues and eigenfunctions. Here we
propose an uplifting of Hessian methods to thermal glasses, with the aim of
understanding the plastic responses in the time-averaged configuration. We
discuss a number of potential definitions of Hessians and identify which of
these can provide eigenvalues and eigenfunctions which can explain and predict
the instabilities of the time-averaged configurations. The conclusion is that
the non-affine changes in the average configurations during an instability is
accurately predicted by the eigenfunctions of the low-lying eigenvalues of the
chosen Hessian.


  How to make unsupervised language pre-training more efficient and less
resource-intensive is an important research direction in NLP. In this paper, we
focus on improving the efficiency of language pre-training methods through
providing better data utilization. It is well-known that in language data
corpus, words follow a heavy-tail distribution. A large proportion of words
appear only very few times and the embeddings of rare words are usually poorly
optimized. We argue that such embeddings carry inadequate semantic signals,
which could make the data utilization inefficient and slow down the
pre-training of the entire model. To mitigate this problem, we propose Taking
Notes on the Fly (TNF), which takes notes for rare words on the fly during
pre-training to help the model understand them when they occur next time.
Specifically, TNF maintains a note dictionary and saves a rare word's
contextual information in it as notes when the rare word occurs in a sentence.
When the same rare word occurs again during training, the note information
saved beforehand can be employed to enhance the semantics of the current
sentence. By doing so, TNF provides better data utilization since
cross-sentence information is employed to cover the inadequate semantics caused
by rare words in the sentences. We implement TNF on both BERT and ELECTRA to
check its efficiency and effectiveness. Experimental results show that TNF's
training time is $60\%$ less than its backbone pre-training models when
reaching the same performance. When trained with the same number of iterations,
TNF outperforms its backbone methods on most of downstream tasks and the
average GLUE score. Source code is attached in the supplementary material.


  The review is devoted to a relativistic formulation of the first Dirac
quantization of QED (1927) and its generalization to the non-Abelian theories
(Yang-Mills and QCD) with the topological degeneration of initial data. Using
the Dirac variables we give a systematic description of relativistic nonlocal
bound states in QED with a choice of the time axis of quantization along the
eigenvectors of their total momentum operator.
  We show that the Dirac variables of the non-Abelian fields are topologically
degenerated, and there is a pure gauge Higgs effect in the sector of the zero
winding number that leads to a nonperturbative physical vacuum in the form of
the Wu-Yang monopole. Phases of the topological degeneration in the new
perturbation theory are determined by an equation of the Gribov ambiguity of
the constraint-shell gauge defined as an integral of the Gauss equation with
zero initial data. The constraint-shell non-Abelian dynamics includes zero mode
of the Gauss law differential operator, and a rising potential of the
instantaneous interaction, that rearranges the perturbation series and changes
the assymptotic freedom formula.
  The Dirac variables in QCD with the topological degeneration of initial data
describe constituent gluon, and quark masses, the spontaneous chiral symmetry
breaking, color confinement in the form of quark-hadron duality as a
consequence of summing over the Gribov copies. A solution of U(1)-problem is
given by mixing the zero mode with $\eta_0$ - meson. We discuss reasons why all
these physical effects disappear for arbitrary gauges of physical sources in
the standard Faddeev-Popov integral.


  We consider the examples of partial functional differential equations with
delay in the Laplacian. First of these equations is linear parabolic equation,
the second one is linear hyperbolic equation, third equation is perturbed
hyperbolic equation with delay. We show that there are the sequence of
eigenvalues in both cases with real parts tends to plus infinity.


  This report analyzes the Google search results from more than 1,500 volunteer
data donors who, in the five weeks leading up to the federal election on
September 24th, 2017, automatically searched Google for 16 predefined names of
political parties and politicians every four hours. It is based on an adjusted
database consisting of more than 8,000,000 data records, which were generated
in the context of the research project "#Datenspende: Google und die
Bundestagswahl 2017" and sent to us for evaluation. The #Datenspende project
was commissioned by six state media authorities. Spiegel Online acted as a
media partner. Focal points of the present study are, i.a., the question of the
degree of personalization of search results, the proportion of regionalization
and the risk of algorithm-based filter bubble formation or reinforcement by the
leader in the search engine market.


  We have applied the real space quantum renormalization group approach to
study the topological quantum phase transition in the one-dimensional chain of
a spinless p-wave superconductor. We investigate the behavior of local
compressibility and ground-state fidelity of the Kitaev chain. We show that the
topological phase transition is signaled by the maximum of local
compressibility at the quantum critical point tuned by the chemical potential.
Moreover, a sudden drop of the ground-state fidelity and the divergence of
fidelity susceptibility at the topological quantum critical point have been
used as a proper indicators for the topological quantum phase transition, which
signals the appearance of Majorana fermions. We also present the scaling
analysis of ground-state fidelity near the critical point that manifests the
universal information about the topological phase transition.


  Understanding carrier trapping in solids has proven key to semiconductor
technologies but observations thus far have relied on ensembles of point
defects, where the impact of neighboring traps or carrier screening is often
important. Here, we investigate the capture of photo-generated holes by an
individual negatively-charged nitrogen-vacancy (NV) center in diamond at room
temperature. Using an externally gated potential to minimize space-charge
effects, we find the capture probability under electric fields of variable sign
and amplitude shows an asymmetric-bell-shaped response with maximum at zero
voltage. To interpret these observations, we run semi-classical Monte Carlo
simulations modeling carrier trapping through a cascade process of phonon
emission, and obtain electric-field-dependent capture probabilities in good
agreement with experiment. Since the mechanisms at play are insensitive to the
trap characteristics, the capture cross sections we observe - largely exceeding
those derived from ensemble measurements - should also be present in materials
platforms other than diamond.


  We report the results of muon-spin relaxation measurements on the
low-dimensional antiferromagnet Rb4Cu(MoO4)3. No long-range magnetic order is
observed down to 50 mK implying a ratio T_N/J<0.005 (where J is the principal
exchange strength along the spin chains) and an effective ratio of interchain
to intrachain exchange of |J_perp/J|<2 x 10^-3, making the material an
excellent realization of a one-dimensional quantum Heisenberg antiferromagnet.
We probe the persistent spin excitations at low temperatures and find that
ballistic spin transport dominates the excitations detected below 0.3 K.


  We present the first high resolution UV spectra toward Herschel 36, a
Trapezium-like system of high-mass stars contained within the Lagoon Nebula
(M8, NGC 6523). The spectra reveal extreme ro-vibrational excitation of
molecular hydrogen in material at a single velocity or very small range of
velocities, with this component presumably lying near the star system and
undergoing fluorescent excitation. The overall H$_2$ excitation is similar to,
but apparently larger than, that seen towards HD 37903 which previously showed
the largest vibrationally excited H$_2$ column densities seen in UV absorption
spectra. While the velocities of the highly excited H$_2$ lines are consistent
within each observation, it appears that they underwent a $\sim$60 km s$^{-1}$
redshift during the 3.6 years between observations. In neither case does the
velocity of the highly excited material match the velocity of the bulk of the
line-of-sight material which appears to mostly be in the foreground of M8.
Recent work shows unusually excited CH and CH$^{+}$ lines and several unusually
broad Diffuse Interstellar Bands towards Herschel 36. Along with the H$_2$
excitation, all of these findings appear to be related to the extreme
environment within $\sim$0.1 pc of the massive young stellar system.


  In this paper, we obtain stability results for backward stochastic
differential equations with jumps (BSDEs) in a very general framework. More
specifically, we consider a convergent sequence of standard data, each
associated to their own filtration, and we prove that the associated sequence
of (unique) solutions is also convergent. The current result extends earlier
contributions in the literature of stability of BSDEs and unifies several
frameworks for numerical approximations of BSDEs and their implementations.


  In this paper, we study the complexity factor of a static anisotropic sphere
in the context of self-interacting Brans-Dicke theory. We split the Riemann
tensor using Bel's approach to obtain structure scalars relating to comoving
congruence and Tolman mass in the presence of a scalar field. We then define
the complexity factor with the help of these scalars to demonstrate the complex
nature of the system. We also evaluate the vanishing complexity condition to
obtain solutions for two stellar models. It is concluded that the complexity of
the system increases with the inclusion of the scalar field and potential
function.


  Elucidating the spatial dynamic and core constituents of the microbial
communities found in association with arthropod hosts is of crucial importance
for insects that may vector human or agricultural pathogens. The hematophagous
Cimex lectularius, known as the common bed bug, has made a recent resurgence in
North America, as well as worldwide, potentially owing to increased travel and
resistance to insecticides. A comprehensive survey of the bed bug microbiome
has not been performed to date, nor has an assessment of the spatial dynamics
of its microbiome. Here we present a survey of bed bug microbial communities by
amplifying the V4-V6 hypervariable region of the 16S rDNA gene region followed
by 454 Titanium sequencing using 31 individuals from eight natural populations
collected from residences in Cincinnati, OH. Across all samples, 97% of the
microbial community is made up of two dominant OTUs identified as the
{\alpha}-proteobacterium Wolbachia and an unnamed {\gamma}-proteobacterium from
the Enterobacteriaceae. Microbial communities varied among host populations for
measures of community diversity and exhibited significant population structure.
We also uncovered a strong negative correlation in the abundance of the two
dominant OTUs, suggesting they may fulfill similar roles as nutritional
mutualists. This broad survey represents the most comprehensive assessment, to
date, of the microbes that associate with bed bugs, and uncovers evidence for
potential antagonism between the two dominant members of the bed bug
microbiome.


  I review the phenomenological and cosmological constraints on the parameter
space associated with the Constrained Minimal Supersymmetric Standard Model
(CMSSM). The effect of the recent WMAP determination of the cold dark matter
density will be discussed. A very constrained model (based on minimal
supergravity relations between the bi- and tri-linear supersymmetry breaking
mass terms) will be outlined.


  Two years ago, Conlon and Gowers, and Schacht proved general theorems that
allow one to transfer a large class of extremal combinatorial results from the
deterministic to the probabilistic setting. Even though the two papers solve
the same set of long-standing open problems in probabilistic combinatorics, the
methods used in them vary significantly and therefore yield results that are
not comparable in certain aspects. The theorem of Schacht can be applied in a
more general setting and yields stronger probability estimates, whereas the one
of Conlon and Gowers also implies random versions of some structural statements
such as the famous stability theorem of Erdos and Simonovits. In this paper, we
bridge the gap between these two transference theorems. Building on the
approach of Schacht, we prove a general theorem that allows one to transfer
deterministic stability results to the probabilistic setting that is somewhat
more general and stronger than the one obtained by Conlon and Gowers. We then
use this theorem to derive several new results, among them a random version of
the Erdos-Simonovits stability theorem for arbitrary graphs. The main new idea,
a refined approach to multiple exposure when considering subsets of binomial
random sets, may be of independent interest.


  Majorana modes and fractional fermions are two types of edge zero modes
appearing separately in topological superconductors and dimerized chains. Here
we reveal how to harvest both types of edge modes simultaneously in an exotic
chain. Such modes are naturally spin-charge separated, and are protected by the
inversion and spin-parity symmetries. We construct a lattice model to
illustrate the nature of these edge modes, utilizing fermionic functional
renormalization group, mean-field theory and bosonization. We also elucidate
that the four-fold degenerate ground states with edge-spinons in the Haldane
phase of spin-$1$ chain may be reinterpreted as our spin-charge separated edge
modes in an equivalent spin-$1/2$ fermionic model.


  Objects interact with each other in various ways, including containment,
contact, or maintaining fixed distances. Ensuring these topological
interactions is crucial for accurate modeling in many scenarios. In this paper,
we propose a novel method to refine 3D object representations, ensuring that
their surfaces adhere to a topological prior. Our key observation is that the
object interaction can be observed via a stochastic approximation method: the
statistic of signed distances between a large number of random points to the
object surfaces reflect the interaction between them. Thus, the object
interaction can be indirectly manipulated by using choosing a set of points as
anchors to refine the object surfaces. In particular, we show that our method
can be used to enforce two objects to have a specific contact ratio while
having no surface intersection. The conducted experiments show that our
proposed method enables accurate 3D reconstruction of human hearts, ensuring
proper topological connectivity between components. Further, we show that our
proposed method can be used to simulate various ways a hand can interact with
an arbitrary object.


  In the framework of hierarchical structure formation ellipticals can form
from merging of smaller disk galaxies. The nearby interacting 'Antennae' galaxy
pair (NGC 4038/39) is one of the best-studied local systems of merging spirals,
thus presenting us with an ideal laboratory for the study of galaxy evolution
models. The Antennae are believed to be in a state prior to their final
encounter with rapid subsequent merging, which puts them in the first position
of the Toomre (1977) merger sequence. Here we present first numerical
high-resolution, self-consistent, smoothed particle hydrodynamics (SPH)
simulations of the Antennae system, including star formation and stellar
feedback, and compare our results to VLA HI observations by Hibbard et al.
(2001). We are able to obtain a close, but not yet perfect match to the
observed morphology and kinematics of the system.


  The measurement of D meson production provides key tests for parton
energy-loss models, which predict that charm quarks should experience less
in-medium energy loss than light quarks and gluons. The ALICE experiment has
measured the production of prompt D^(0), D^(+) and D^(*+) mesons in pp and
Pb-Pb collisions at the LHC at sqrt(s) = 7 and 2.76 TeV and at sqrt(s_NN) =
2.76 TeV, respectively, via the exclusive reconstruction of their hadronic
decay. The pT-differential production yields in the range 2 < pT < 16 GeV/c at
central rapidity, |y| < 0.5, were used to calculate the nuclear modification
factor. A suppression of a factor 3 to 4 for transverse momenta larger than 5
GeV/c in the 20% most central collisions was observed. Preliminary results in
an extended pT-range, using the data sample collected during the 2011 Pb-Pb
run, together with the first measurement of D^(+)_(s) nuclear modification
factor will be shown.


  In this paper we discuss geodesic Witten diagrams in generic holographic
conformal field theories with boundary or defect. Boundary CFTs allow two
different decompositions of two-point functions into conformal blocks: boundary
channel and ambient channel. Building on earlier work, we derive a holographic
dual of the boundary channel decomposition in terms of bulk-to-bulk propagators
on lower dimensional AdS slices. In the situation in which we can treat the
boundary or defect as a perturbation around pure AdS spacetime, we obtain the
leading corrections to the two-point function both in boundary and ambient
channel in terms of geodesic Witten diagrams which exactly reproduce the
decomposition into corresponding conformal blocks on the field theory side.


  We study the problem of efficiently summarizing a short video into several
keyframes, leveraging recent progress in fast graph sampling. Specifically, we
first construct a similarity path graph (SPG) $\mathcal{G}$, represented by
graph Laplacian matrix $\mathbf{L}$, where the similarities between adjacent
frames are encoded as positive edge weights. We show that maximizing the
smallest eigenvalue $\lambda_{\min}(\mathbf{B})$ of a coefficient matrix
$\mathbf{B} = \text{diag}(\mathbf{a}) + \mu \mathbf{L}$, where $\mathbf{a}$ is
the binary keyframe selection vector, is equivalent to minimizing a worst-case
signal reconstruction error. We prove that, after partitioning $\mathcal{G}$
into $Q$ sub-graphs $\{\mathcal{G}^q\}^Q_{q=1}$, the smallest Gershgorin circle
theorem (GCT) lower bound of $Q$ corresponding coefficient matrices -- $\min_q
\lambda^-_{\min}(\mathbf{B}^q)$ -- is a lower bound for
$\lambda_{\min}(\mathbf{B})$. This inspires a fast graph sampling algorithm to
iteratively partition $\mathcal{G}$ into $Q$ sub-graphs using $Q$ samples
(keyframes), while maximizing $\lambda^-_{\min}(\mathbf{B}^q)$ for each
sub-graph $\mathcal{G}^q$. Experimental results show that our algorithm
achieves comparable video summarization performance as state-of-the-art
methods, at a substantially reduced complexity.


  We present detailed NLTE synthetic spectra of hydrodynamic SNe Ia models. We
make no assumptions about the form of the spectrum at the inner boundary. We
calculate both Chandrasekhar-mass deflagration models and sub-Chandrasekhar
``helium detonators.'' Gamma-ray deposition is handled in a simple, accurate
manner. We have parameterized the storage of energy that arises from the time
dependent deposition of radioactive decay energy in a reasonable manner, that
spans the expected range. We find that the Chandrasekhar-mass deflagration
model W7 of Nomoto etal shows good agreement with the observed spectra of SN
1992A and SN 1994D, particularly in the UV, where our models are expected to be
most accurate. The sub-Chandrasekhar models do not reproduce the UV deficit
observed in normal SNe Ia. They do bear some resemblance to sub-luminous SNe
Ia, but the shape of the spectra (i.e. the colors) are opposite to that of the
observed ones and the intermediate mass element lines such as Si II, and Ca II
are extremely weak, which seems to be a generic difficulty of the models.
Although the sub-Chandrasekhar models have a significant helium abundance
(unlike Chandrasekhar-mass models), helium lines are not prominent in the
spectra near maximum light and thus do not act as a spectral signature for the
progenitor.


  Let $k$ a field of characteristic zero. Let $X$ be a smooth, projective,
geometrically rational $k$-surface. Let $\mathcal{T}$ be a universal torsor
over $X$ with a $k$-point et $\mathcal{T}^c$ a smooth compactification of
$\mathcal{T}$. There is an open question: is $\mathcal{T}^c$ $k$-birationally
equivalent to a projective space? We know that the unramified cohomology groups
of degree 1 and 2 of $\mathcal{T}$ and $\mathcal{T}^c$ are reduced to their
constant part. For the analogue of the third cohomology groups, we give a
sufficient condition using the Galois structure of the geometrical Picard group
of $X$. This enables us to show that
$H^{3}_{nr}(\mathcal{T}^{c},\mathbb{Q}/\mathbb{Z}(2))/H^3(k,\mathbb{Q}/\mathbb{Z}(2))$
vanishes if $X$ is a generalised Ch\^atelet surface and that this group is
reduced to its $2$-primary part if $X$ is a del Pezzo surface of degree at
least 2.


  We are grateful to all discussants of our re-visitation for their strong
support in our enterprise and for their overall agreement with our perspective.
Further discussions with them and other leading statisticians showed that the
legacy of Theory of Probability is alive and lasting. [arXiv:0804.3173]


  We theoretically study the effects of elastic collisions on the determination
of frequency standards via Ramsey fringe spectroscopy in optical-lattice atom
clocks. Interparticle interactions of bosonic atoms in multiply-occupied
lattice sites can cause a linear frequency shift, as well as generate
asymmetric Ramsey fringe patterns and reduce fringe visibility due to
interparticle entanglement. We propose a method of reducing these collisional
effects in an optical lattice by introducing a phase difference of $\pi$
between the Ramsey driving fields in adjacent sites. This configuration
suppresses site to site hopping due to interference of two tunneling pathways,
without degrading fringe visibility. Consequently, the probability of double
occupancy is reduced, leading to cancellation of collisional shifts.


  Giant planet formation in the core accretion (CA) paradigm is predicated by
the formation of a core, assembled by the coagulation of grains and later by
planetesimals within a protoplanetary disc. In contrast, in the disc
instability paradigm, giant planet formation is believed to be independent of
core formation: massive self-gravitating gas fragments cool radiatively and
collapse as a whole. We show that giant planet formation in the disc
instability model may be also enhanced by core formation for reasons physically
very similar to the CA paradigm. In the model explored here, efficient grain
sedimentation within an initial fragment (rather than the disc) leads to the
formation of a core composed of heavy elements. We find that massive
atmospheres form around cores and undergo collapse as a critical core mass is
exceeded, analogous to CA theory. The critical mass of the core to initiate
such a collapse depends on the fragment mass and metallicity, as well as core
luminosity, but ranges from less than 1 to as much as $\sim80$ Earth masses. We
therefore suggest that there are two channels for the collapse of a gaseous
fragment to planetary scales within the disc instability model: (i) H$_2$
dissociative collapse of the entire gaseous clump, and (ii) core-assisted gas
capture, as presented here. We suggest that the first of these two is favoured
in metal-poor environments and for fragments more massive than $\sim 5-10$
Jupiter masses, whereas the second is favored in metal-rich environments and
fragments of lower mass. [Abridged]


  We study the Maker-Breaker game on the hypergraph of chains of fixed size in
a poset. In a product of chains, the maximum size of a chain that Maker can
guarantee building is $k-\lfloor r/2\rfloor$, where $k$ is the maximum size of
a chain in the product, and $r$ is the maximum size of a factor chain. We also
study a variant in which Maker must follow the chain in order, called the {\it
Walker-Blocker game}. In the poset consisting of the bottom $k$ levels of the
product of $d$ arbitrarily long chains, Walker can guarantee a chain that hits
all levels if $d\ge14$; this result uses a solution to Conway's Angel-Devil
game. When d=2, the maximum that Walker can guarantee is only 2/3 of the
levels, and 2/3 is asymptotically achievable in the product of two equal
chains.


  Monosubstituted nitrotoluenes serve as important model compounds for
nitroaromatic energetic molecules such as trinitrotoluene. This work
investigates the ultrafast nuclear dynamics of 3- and 4-nitrotoluene radical
cations using femtosecond pump-probe measurements and the results of density
functional theory calculations. Strong-field adiabatic ionization of 3- and
4-nitrotoluene using 1500 nm, 18 fs pulses produces radical cations in the
ground electronic state with distinct coherent vibrational excitations. In both
nitrotoluene isomers, a one-photon excitation with the probe pulse results in
\ce{NO2} loss to form \ce{C7H7+}, which exhibits out-of-phase oscillations in
yield with the parent molecular ion. The oscillations in 4-nitrotoluene with a
period of 470 fs are attributed to the torsional motion of the \ce{NO2} group
based on theoretical results showing that the dominant relaxation pathway in
4-nitrotoluene radical cation involves the rotation of the \ce{NO2} group away
from the planar geometry. The distinctly faster oscillation period of 216 fs in
3-nitrotoluene is attributed to an in-plane bending motion of the \ce{NO2} and
\ce{CH3} moieties based on analysis of the normal modes. These results
demonstrate that coherent nuclear motions determine the probability of
\ce{C-NO2} homolysis in the nitrotoluene radical cations upon optical
excitation within several hundred femtoseconds of the initial ionization event.


  Combined relativistic configuration interaction and many-body perturbation
calculations are performed for the 359 fine-structure levels of the $2s^2
2p^3$, $2s 2p^4$, $2p^5$, $2s^2 2p^2 3l$, $2s 2p^3 3l$, $2p^4 3l$, and $2s^2
2p^2 4l$ configurations in N-like ions from Ar XII to Zn XXIV. A complete and
consistent data set of energies, wavelengths, radiative rates, oscillator
strengths, and line strengths for all possible electric dipole, magnetic
dipole, electric quadrupole, and magnetic quadrupole transitions among the 359
levels are given for each ion. The present work significantly increases the
amount of accurate data for ions in the nitrogen-like sequence, and the
accuracy of the energy levels is high enough to serve identification and
interpretation of observed spectra involving the $n=3,4$ levels, for which the
experimental values are largely scarce. Meanwhile, the results should be of
great help in modeling and diagnosing astrophysical and fusion plasmas.


  We investigate the "theta-deformed spheres" C(S^{3}_{theta}) and
C(S^{4}_{theta}), where theta is any real number. We show that all
finitely-generated projective modules over C(S^{3}_{theta}) are free, and that
C(S^{4}_{theta}) has the cancellation property. We classify and construct all
finitely-generated projective modules over C(S^{4}_{\theta}) up to isomorphism.
An interesting feature is that if theta is irrational then there are nontrivial
"rank-1" modules over C(S^{4}_{\theta}). In that case, every finitely-generated
projective module over C(S^{4}_{\theta}) is a sum of a rank-1 module and a free
module. If theta is rational, the situation mirrors that for the commutative
case theta=0.


  Gravitational waves were copiously produced in the early Universe whenever
the processes taking place were sufficiently violent. The spectra of several of
these gravitational wave backgrounds on subhorizon scales have been extensively
studied in the literature. In this paper we analyze the shape and amplitude of
the gravitational wave spectrum on scales which are superhorizon at the time of
production. Such gravitational waves are expected from the self ordering of
randomly oriented scalar fields which can be present during a thermal phase
transition or during preheating after hybrid inflation. We find that, if the
gravitational wave source acts only during a small fraction of the Hubble time,
the gravitational wave spectrum at frequencies lower than the expansion rate at
the time of production behaves as $\Omega_{\rm GW}(f) \propto f^3$ with an
amplitude much too small to be observable by gravitational wave observatories
like LIGO, LISA or BBO. On the other hand, if the source is active for a much
longer time, until a given mode which is initially superhorizon ($k\eta_* \ll
1$), enters the horizon, for $k\eta \gtrsim 1$, we find that the gravitational
wave energy density is frequency independent, i.e. scale invariant. Moreover,
its amplitude for a GUT scale scenario turns out to be within the range and
sensitivity of BBO and marginally detectable by LIGO and LISA. This new
gravitational wave background can compete with the one generated during
inflation, and distinguishing both may require extra information.


  3D anomaly detection is an emerging and vital computer vision task in
industrial manufacturing (IM). Recently many advanced algorithms have been
published, but most of them cannot meet the needs of IM. There are several
disadvantages: i) difficult to deploy on production lines since their
algorithms heavily rely on large pre-trained models; ii) hugely increase
storage overhead due to overuse of memory banks; iii) the inference speed
cannot be achieved in real-time. To overcome these issues, we propose an easy
and deployment-friendly network (called EasyNet) without using pre-trained
models and memory banks: firstly, we design a multi-scale multi-modality
feature encoder-decoder to accurately reconstruct the segmentation maps of
anomalous regions and encourage the interaction between RGB images and depth
images; secondly, we adopt a multi-modality anomaly segmentation network to
achieve a precise anomaly map; thirdly, we propose an attention-based
information entropy fusion module for feature fusion during inference, making
it suitable for real-time deployment. Extensive experiments show that EasyNet
achieves an anomaly detection AUROC of 92.6% without using pre-trained models
and memory banks. In addition, EasyNet is faster than existing methods, with a
high frame rate of 94.55 FPS on a Tesla V100 GPU.


  Recovering a function from its spherical Radon transform with centers of
spheres of integration restricted to a hypersurface is at the heart of several
modern imaging technologies, including SAR, ultrasound imaging, and photo- and
thermoacoustic tomography. In this paper we study an inversion of the spherical
Radon transform with centers of integration restricted to cylindrical surfaces
of the form $\Gamma \times \mathbb{R}^m$, where $\Gamma$ is a hypersurface in
$\mathbb{R}^n$. We show that this transform can be decomposed into two lower
dimensional spherical Radon transforms, one with centers on $\Gamma$ and one
with a planar center-set in $\mathbb{R}^{m+1}$. Together with explicit
inversion formulas for the spherical Radon transform with a planar center-set
and existing algorithms for inverting the spherical Radon transform with a
center-set $\mathbb{R}$, this yields reconstruction procedures for general
cylindrical domains. In the special case of spherical or elliptical cylinders
we obtain novel explicit inversion formulas. For three spatial dimensions,
these inversion formulas can be implemented efficiently by backprojection type
algorithms only requiring $\mathcal O(N^{4/3})$ floating point operations,
where $N$ is the total number of unknowns to be recovered. We present numerical
results demonstrating the efficiency of the derived algorithms.


  Probabilistic programming languages (PPLs) are powerful modelling tools which
allow to formalise our knowledge about the world and reason about its inherent
uncertainty. Inference methods used in PPL can be computationally costly due to
significant time burden and/or storage requirements; or they can lack
theoretical guarantees of convergence and accuracy when applied to large scale
graphical models. To this end, we present the Universal Marginaliser (UM), a
novel method for amortised inference, in PPL. We show how combining samples
drawn from the original probabilistic program prior with an appropriate
augmentation method allows us to train one neural network to approximate any of
the corresponding conditional marginal distributions, with any separation into
latent and observed variables, and thus amortise the cost of inference.
Finally, we benchmark the method on multiple probabilistic programs, in Pyro,
with different model structure.


  Contrastive Language-Image Pre-Training (CLIP) has shown impressive
performance in short-term Person Re-Identification (ReID) due to its ability to
extract high-level semantic features of pedestrians, yet its direct application
to Cloth-Changing Person Re-Identification (CC-ReID) faces challenges due to
CLIP's image encoder overly focusing on clothes clues. To address this, we
propose a novel framework called CLIP-Driven Cloth-Agnostic Feature Learning
(CCAF) for CC-ReID. Accordingly, two modules were custom-designed: the
Invariant Feature Prompting (IFP) and the Clothes Feature Minimization (CFM).
These modules guide the model to extract cloth-agnostic features positively and
attenuate clothes-related features negatively. Specifically, IFP is designed to
extract fine-grained semantic features unrelated to clothes from the raw image,
guided by the cloth-agnostic text prompts. This module first covers the clothes
in the raw image at the pixel level to obtain the shielding image and then
utilizes CLIP's knowledge to generate cloth-agnostic text prompts.
Subsequently, it aligns the raw image-text and the raw image-shielding image in
the feature space, emphasizing discriminative clues related to identity but
unrelated to clothes. Furthermore, CFM is designed to examine and weaken the
image encoder's ability to extract clothes features. It first generates text
prompts corresponding to clothes pixels. Then, guided by these clothes text
prompts, it iteratively examines and disentangles clothes features from
pedestrian features, ultimately retaining inherent discriminative features.
Extensive experiments have demonstrated the effectiveness of the proposed CCAF,
achieving new state-of-the-art performance on several popular CC-ReID
benchmarks without any additional inference time.


  In this paper, we consider initial-boundary value problems for two-component
nonlinear systems of time-fractional diffusion equations with the homogeneous
Neumann boundary condition and non-negative initial values. The main results
are the existence of solutions global in time and the blow-up. Our approach
involves the truncation of the nonlinear terms, which enables us to handle all
local Lipschitz continuous nonlinear terms, provided their sum is less than or
equal to zero. By employing a comparison principle for the corresponding linear
system, we establish also the non-negativity of the nonlinear system.


  A measurement of the groomed jet mass in PbPb and pp collisions at a
nucleon-nucleon center-of-mass energy of 5.02 TeV with the CMS detector at the
LHC is presented. Jet grooming is a recursive procedure which sequentially
removes soft constituents of a jet until a pair of hard subjets is found. The
resulting groomed jets can be used to study modifications to the parton shower
evolution in the presence of the hot and dense medium created in heavy ion
collisions. Predictions of groomed jet properties from the PYTHIA and HERWIG++
event generators agree with the measurements in pp collisions. When comparing
the results from the most central PbPb collisions to pp data, a hint of an
increase of jets with large jet mass is observed, which could originate from
additional medium-induced radiation at a large angle from the jet axis.
However, no modification of the groomed mass of the core of the jet is observed
for all PbPb centrality classes. The PbPb results are also compared to
predictions from the JEWEL and Q-PYTHIA event generators, which predict a large
modification of the groomed mass not observed in the data.


  This paper presents a numerical study of flow through static random
assemblies of monodisperse, spherical particles. A lattice Boltzmann approach
based on a two relaxation time collision operator is used to obtain reliable
predictions of the particle drag by direct numerical simulation. From these
predictions a closure law $F(Re, {\varphi})$ of the drag force relationship to
the bed density ${\varphi}$ and the particle Reynolds number $Re$ is derived.
The present study includes densities ${\varphi}$ ranging from $0.01$ to $0.35$
with Re ranging up to $300$, that is compiled into a single drag correlation
valid for the whole range. The corelation has a more compact expression
compared to others previously reported in literature. At low particle
densities, the new correlation is close to the widely used Wen & Yu -
correlation. Recently, there has been reported a discrepancy between results
obtained using different numerical methods, namely the comprehensive lattice
Boltzmann study of Beetstra et al. (2007) and the predictions based on an
immersed boundary - pseudo-spectral Navier-Stokes approach (Tenneti et al.,
2011). The present study excludes significant finite resolution effects, which
have been suspected to cause the reported deviations, but does not coincide
exactly with either of the previous studies. This indicates the need for yet
more accurate simulation methods in the future.


  Memories are stored, retained, and recollected through complex, coupled
processes operating on multiple timescales. To understand the computational
principles behind these intricate networks of interactions we construct a broad
class of synaptic models that efficiently harnesses biological complexity to
preserve numerous memories. The memory capacity scales almost linearly with the
number of synapses, which is a substantial improvement over the square root
scaling of previous models. This was achieved by combining multiple dynamical
processes that initially store memories in fast variables and then
progressively transfer them to slower variables. Importantly, the interactions
between fast and slow variables are bidirectional. The proposed models are
robust to parameter perturbations and can explain several properties of
biological memory, including delayed expression of synaptic modifications,
metaplasticity, and spacing effects.


  The quantum measurement problem as formalised by Bassi and Ghirardi [Phys.
Lett. A 275 (2000)373] without taking recourse to sharp apparatus observables
is extended to cover impure initial states.


  In human locomotion, sensorimotor synchronization of gait consists of the
coordination of stepping with rhythmic auditory cues (auditory cueing, AC). AC
changes the long-range correlations among consecutive strides (fractal
dynamics) into anti-correlations. Visual cueing (VC) is the alignment of step
lengths with marks on the floor. The effects of VC on the fluctuation structure
of walking have not been investigated. Therefore, the objective was to compare
the effects of AC and VC on the fluctuation pattern of basic spatiotemporal
gait parameters. Thirty-six healthy individuals walked 3 x 500 strides on an
instrumented treadmill with augmented reality capabilities. The conditions were
no cueing (NC), AC, and VC. AC included an isochronous metronome. In VC,
projected stepping stones were synchronized with the treadmill speed. Detrended
fluctuation analysis assessed the correlation structure. The coefficient of
variation (CV) was also assessed. The results showed that AC and VC similarly
induced a strong anti-correlated pattern in the gait parameters. The CVs were
similar between the NC and AC conditions but substantially higher in the VC
condition. AC and VC probably mobilize similar motor control pathways and can
be used alternatively in gait rehabilitation. However, the increased gait
variability induced by VC should be considered.


  We study the capabilities of future electron-positron Linear Colliders, with
centre-of-mass energy at the TeV scale, in accessing the parameter space of a
$Z'$ boson within the minimal $B-L$ model. We carry out a detailed comparison
between the discovery regions mapped over a two-dimensional configuration space
($Z'$ mass and coupling) at the Large Hadron Collider and possible future
Linear Colliders for the case of di-muon production. As known in the literature
for other $Z'$ models, we confirm that leptonic machines, as compared to the
CERN hadronic accelerator, display an additional potential in discovering a
$Z'$ boson as well as in allowing one to study its properties at a level of
precision well beyond that of any of the existing colliders.


  Clarification questions are an essential dialogue tool to signal
misunderstanding, ambiguities, and under-specification in language use. While
humans are able to resolve uncertainty by asking questions since childhood,
modern dialogue systems struggle to generate effective questions. To make
progress in this direction, in this work we take a collaborative dialogue task
as a testbed and study how model uncertainty relates to human uncertainty -- an
as yet under-explored problem. We show that model uncertainty does not mirror
human clarification-seeking behavior, which suggests that using human
clarification questions as supervision for deciding when to ask may not be the
most effective way to resolve model uncertainty. To address this issue, we
propose an approach to generating clarification questions based on model
uncertainty estimation, compare it to several alternatives, and show that it
leads to significant improvements in terms of task success. Our findings
highlight the importance of equipping dialogue systems with the ability to
assess their own uncertainty and exploit in interaction.


  We present the first set of definitive trigonometric parallaxes and proper
motions from the Cerro Tololo Inter-American Observatory Parallax Investigation
(CTIOPI). Full astrometric reductions for the program are discussed, including
methods of reference stars selection, differential color refraction
corrections, and conversion of relative to absolute parallax. Using data
acquired at the 0.9-m at CTIO, full astrometric solutions and $VRIJHK_s$
photometry are presented for 36 red and white dwarf stellar systems with proper
motions faster than 1\farcs0/yr. Of these, thirty three systems have the first
ever trigonometric parallaxes, which comprise 41% of MOTION systems (those with
proper motions greater than 1\farcs0/yr) south of $\delta$ $=$ 0 that have no
parallaxes. Four of the systems are new members of the RECONS 10 pc sample for
which the first accurate trigonometric parallaxes are published here: DENIS
J1048-3956 (4.04 $\pm$ 0.03 pc), GJ 1128 (LHS 271, 6.53 $\pm$ 0.10 pc), GJ 1068
(LHS 22, 6.97 $\pm$ 0.09 pc), and GJ 1123 (LHS 263, 9.02 $\pm$ 0.16 pc). In
addition, two red subdwarf-white dwarf pairs, LHS 193AB and LHS 300AB, are
identified. The white dwarf secondaries fall in a previously uncharted region
of the HR diagram.


  We discuss various lifting and reduction problems for bundles and gerbes in
the context of a strict Lie 2-group. We obtain a geometrical formulation (and a
new proof) for the exactness of Breen's long exact sequence in non-abelian
cohomology. We use our geometrical formulation in order to define a
transgression map in non-abelian cohomology. This transgression map relates the
degree one non-abelian cohomology of a smooth manifold (represented by
non-abelian gerbes) with the degree zero non-abelian cohomology of the free
loop space (represented by principal bundles). We prove several properties for
this transgression map. For instance, it reduces - in case of a Lie 2-group
with a single object - to the ordinary transgression in ordinary cohomology. We
describe applications of our results to string manifolds: first, we obtain a
new comparison theorem for different notions of string structures. Second, our
transgression map establishes a direct relation between string structures and
spin structure on the loop space.


  Some aspects of the rotating three-dimensional Einstein-Anti-de-Sitter black
hole solution, constructed recently by Banados, Teitelboim and Zanelli are
discussed. It is shown explicitly that this black hole represents the most
general black hole type solution of the Einstein-Anti-de-Sitter theory. The
interpretation of one of the integrals of motion as the spin is discussed. Its
physics relies on the topological structure of the black hole manifold, and the
notion of simultaneity of space-like separated intervals. The relationship of
the black hole solution to string theory on a $2 + 1$ dimensional target space
is examined, and it is shown that the black hole can be understood as a part of
the full axion-dilaton-gravity, realized as a WZWN $\sigma $ model. In
conclusion, the pertinence of this solution to four-dimensional black strings
and topologically massive gravity is pointed out.


  An improved SOI-MAPS (Silicon On Insulator Monolithic Active Pixel Sensor)
for ionizing radiation based on thick-film High Voltage SOI technology (HV-SOI)
has been developed. Similar to existing Fully Depleted SOI-based (FD-SOI) MAPS,
a buried silicon oxide inter-dielectric (BOX) layer is used to separate the
CMOS electronics from the handle wafer which is used as a depleted charge
collection layer. FD-SOI MAPS suffer from radiation damage such as transistor
threshold voltage shifts due to charge traps in the oxide layers and charge
states created at the silicon oxide boundaries (back gate effect). The X-FAB
180-nm HV-SOI technology offers an additional isolation by deep non-depleted
implant between the BOX layer and the active circuitry witch mitigates this
problem. Therefore we see in this technology a high potential to implement
radiation-tolerant MAPS with fast charge collection property. The design and
measurement results from a first prototype are presented including charge
collection in neutron irradiated samples.


  We study the electronic structure and the magnetic properties of epitaxial
(Ni1-xCox)Fe2O4(111) layers (x = 0 - 1) with thicknesses d = 1.7 - 5.2 nm grown
on Al2O3(111)/Si(111) structures, to achieve a high value of inversion
parameter y, which is the inverse-to-normal spinel-structure ratio, and hence
to obtain good magnetic properties even when the thickness is thin enough for
electron tunneling as a spin filter. We revealed the crystallographic
(octahedral Oh or tetrahedral Td) sites and the valences of the Fe, Co, and Ni
cations using experimental soft X-ray absorption spectroscopy and X-ray
magnetic circular dichroism spectra and configuration-interaction cluster-model
calculation. In all the (Ni1-xCox)Fe2O4 layers with d = about 4 nm, all Ni
cations occupy the Ni2+ (Oh) site, whereas Co cations occupy the three
different Co2+ (Oh), Co2+ (Td), and Co3+ (Oh) sites with constant occupancies.
According to these features, the occupancy of the Fe3+ (Oh) cations decreases
and that of the Fe3+ (Td) cations increases with decreasing x. Consequently, we
obtained a systematic increase of y with decreasing x and achieved the highest
y value of 0.91 for the NiFe2O4 layer with d = 3.5 nm. From the d dependences
of y and magnetization in the d range of 1.7 - 5.2 nm, a magnetically dead
layer is present near the NiFe2O4/Al2O3 interface, but its influence on the
magnetization was significantly suppressed compared with the case of CoFe2O4
layers reported previously [Y. K. Wakabayasi et al., Phys. Rev. B 96, 104410
(2017)], due to the high site selectivity of the Ni cations. Since our
epitaxial NiFe2O4 layer with d = 3.5 nm has a high y values (0.91) and a
reasonably large magnetization (180 emu/cc), it is expected to exhibit a strong
spin filter effect, which can be used for efficient spin injection into Si.


  The sequential multiple assignment randomized trial (SMART) is the gold
standard trial design to generate data for the evaluation of multi-stage
treatment regimes. As with conventional (single-stage) randomized clinical
trials, interim monitoring allows early stopping; however, there are few
methods for principled interim analysis in SMARTs. Because SMARTs involve
multiple stages of treatment, a key challenge is that not all enrolled
participants will have progressed through all treatment stages at the time of
an interim analysis. Wu et al. (2021) propose basing interim analyses on an
estimator for the mean outcome under a given regime that uses data only from
participants who have completed all treatment stages. We propose an estimator
for the mean outcome under a given regime that gains efficiency by using
partial information from enrolled participants regardless of their progression
through treatment stages. Using the asymptotic distribution of this estimator,
we derive associated Pocock and O'Brien-Fleming testing procedures for early
stopping. In simulation experiments, the estimator controls type I error and
achieves nominal power while reducing expected sample size relative to the
method of Wu et al. (2021). We present an illustrative application of the
proposed estimator based on a recent SMART evaluating behavioral pain
interventions for breast cancer patients.


  The spontaneous fluorescence rates of single-molecule emitters are typically
on the order of nanoseconds. However coupling them with plasmonic
nanostructures can substantially increase their fluorescence yields. The
confinement between the tip and sample of a scanning tunneling microscope
creates a tunable nanocavity, an ideal platform for exploring the yields and
excitation decay rates of single-molecule emitters depending on the coupling
strength to the nanocavity. With this setup we estimate the excitation
lifetimes from the direct time-resolved measurements of the fluorescence decays
of phthalocyanine adsorbates, decoupled from the metal substrates by ultrathin
NaCl layers. It is found that nanosecond-range lifetimes prevail for the
emitters away from the nanocavity, whereas for the tip approached to a
molecule, we find a substantial effect of the nanocavity coupling, which
reduces the lifetimes to a few picoseconds. An analysis is performed to
investigate the crossover between the far-field and tip-enhanced
photoluminescence regimes. This approach overcomes the drawbacks associated
with the estimation of lifetimes for single molecules from their respective
emission linewidths.


  The modeling and simulation of dynamical systems is a necessary step for many
control approaches. Using classical, parameter-based techniques for modeling of
modern systems, e.g., soft robotics or human-robot interaction, is often
challenging or even infeasible due to the complexity of the system dynamics. In
contrast, data-driven approaches need only a minimum of prior knowledge and
scale with the complexity of the system. In particular, Gaussian process
dynamical models (GPDMs) provide very promising results for the modeling of
complex dynamics. However, the control properties of these GP models are just
sparsely researched, which leads to a "blackbox" treatment in modeling and
control scenarios. In addition, the sampling of GPDMs for prediction purpose
respecting their non-parametric nature results in non-Markovian dynamics making
the theoretical analysis challenging. In this article, we present approximated
GPDMs which are Markov and analyze their control theoretical properties. Among
others, the approximated error is analyzed and conditions for boundedness of
the trajectories are provided. The outcomes are illustrated with numerical
examples that show the power of the approximated models while the the
computational time is significantly reduced.


  This paper proposes a sparse regression strategy for discovery of ordinary
and partial differential equations from incomplete and noisy data. Inference is
performed over both equation parameters and state variables using a
statistically motivated likelihood function. Sparsity is enforced by a
selection algorithm which iteratively removes terms and compares models using
statistical information criteria. Large scale optimization is performed using a
second-order variant of the Levenberg-Marquardt method, where the gradient and
Hessian are computed via automatic differentiation. Illustrations involving
canonical systems of ordinary and partial differential equations are used to
demonstrate the flexibility and robustness of the approach. Accurate
reconstruction of systems is found to be possible even in extreme cases of
limited data and large observation noise.


  The COVID-19 epidemics, started in China in January 2020, was recognized to
have reached Italy around February 20; recent estimates show that most probably
the virus circulated in the country already in January, but was not recognized.
Data for the early dynamics of COVID-19 in Northern Italy are analyzed.


  We use the NewHorizon simulation to study the redshift evolution of bar
properties and fractions within galaxies in the stellar masses range $M_{\star}
= 10^{7.25} - 10^{11.4} \ \rm{M}_{\odot}$ over the redshift range $z = 0.25 -
1.3$. We select disc galaxies using stellar kinematics as a proxy for galaxy
morphology. We employ two different automated bar detection methods, coupled
with visual inspection, resulting in observable bar fractions of $f_{\rm bar} =
0.070_{{-0.012}}^{{+0.018}}$ at $z\sim$ 1.3, decreasing to $f_{\rm bar} =
0.011_{{-0.003}}^{{+0.014}}$ at $z\sim$ 0.25. Only one galaxy is visually
confirmed as strongly barred in our sample. This bar is hosted by the most
massive disk and only survives from $z=1.3$ down to $z=0.7$. Such a low bar
fraction, in particular amongst Milky Way-like progenitors, highlights a
missing bars problem, shared by literally all cosmological simulations with
spatial resolution $<$100 pc to date. The analysis of linear growth rates,
rotation curves and derived summary statistics of the stellar, gas and dark
matter components suggest that galaxies with stellar masses below
$10^{9.5}-10^{10} \ \rm{M}_{\odot}$ in NewHorizon appear to be too dominated by
dark matter to form a bar, while more massive galaxies typically have formed
large bulges that prevent bar persistence at low redshift. This investigation
confirms that the evolution of the bar fraction puts stringent constraints on
the assembly history of baryons and dark matter onto galaxies.


  With six recorded nova outbursts, the prototypical recurrent nova T Pyxidis
is the ideal cataclysmic variable system to assess the net change of the white
dwarf mass within a nova cycle. Recent estimates of the mass ejected in the
2011 outburst ranged from a few 1.E-5 sollar mass to 3.3E-4 sollar mass, and
assuming a mass accretion rate of 1.E-8 to 1.E-7 Sollar mass/yr for 44yrs, it
has been concluded that the white dwaf in T Pyx is actually losing mass. Using
NLTE disk modeling spectra to fit our recently obtained Hubble Space Telescope
(HST) COS and STIS spectra, we find a mass accretion rate of up to two orders
of magnitude larger than previously estimated. Our larger mass accretion rate
is due mainly to the newly derived distance of T Pyx (4.8kpc; Sokoloski et al.
2013, larger than the previous 3.5kpc estimate), our derived reddening of
E(B-V)=0.35 (based on combined IUE and GALEX spectra) and NLTE disk modeling
(compared to black body and raw flux estimates in earlier works). We find that
for most values of the reddening (0.25 < E(B-V) < 0.50) and white dwaf mass
(0.70 to 1.35 Sollar mass) the accreted mass is larger than the ejected mass.
Only for a low reddening (0.25 and smaller) combined with a large white dwaf
mass (0.9 sollar mass and larger) is the ejected mass larger than the accreted
one. However, the best spectral fitting results are obtained for a larger value
of the reddening.


  We report on a direct search for scalar field dark matter using data from
LIGO's third observing run. We analyse the coupling of size oscillations of the
interferometer's beamsplitter and arm test masses that may be caused by scalar
field dark matter. Using new efficient search methods to maximise sensitivity
for signatures of such oscillations, we set new upper limits for the coupling
constants of scalar field dark matter as a function of its mass, which improve
upon bounds from previous direct searches by several orders of magnitude in a
frequency band from 10 Hz to 180 Hz.


  The accessible information acc(E) of an ensemble E is the maximum mutual
information between a random variable encoded into quantum states, and the
probabilistic outcome of a quantum measurement of the encoding. Accessible
information is extremely difficult to characterize analytically; even bounds on
it are hard to place. The celebrated Holevo bound states that accessible
information cannot exceed chi(E), the quantum mutual information between the
random variable and its encoding. However, for general ensembles, the gap
between the acc(E) and chi(E) may be arbitrarily large.
  We consider the special case of a binary random variable, which often serves
as a stepping stone towards other results in information theory and
communication complexity. We give explicit lower bounds on the the accessible
information acc(E) of an ensemble E = {(p, rho_0), (1-p, rho_1)}, with 0 <= p
<= 1, as functions of p and chi(E). The bounds are incomparable in the sense
that they surpass each other in different parameter regimes.
  Our bounds arise by measuring the ensemble according to a complete orthogonal
measurement that preserves the fidelity of the states rho_0,rho_1. As an
intermediate step, therefore, we give new relations between the two quantities
acc(E), chi(E) and the fidelity B(rho_0,rho_1).


  We present a new physically-motivated model for estimating the molecular line
emission in active galaxies. The model takes into account (i) the internal
density structure of giant molecular clouds (GMCs), (ii) the heating associated
both to stars and to the active galactic nuclei (AGN), respectively producing
photodissociation regions (PDRs) and X-ray dominated regions (XDRs) within the
GMCs, and (iii) the mass distribution of GMCs within the galaxy volume. The
model needs, as input parameters, the radial profiles of molecular mass, far-UV
flux and X-ray flux for a given galaxy, and it has two free parameters: the
CO-to-H2 conversion factor $\alpha_{CO}$, and the X-ray attenuation column
density $N_H$. We test this model on a sample of 24 local ($z \leq 0.06$)
AGN-host galaxies, simulating their carbon monoxide spectral line energy
distribution (CO SLED). We compare the results with the available observations
and calculate, for each galaxy, the best ($\alpha_{CO}$, $N_H$) with a Markov
chain Monte Carlo algorithm, finding values consistent with those present in
the literature. We find a median $\alpha_{CO} = 4.8$ M$_{\odot}$ (K km s$^{-1}$
pc$^{2}$)$^{-1}$ for our sample. In all the modelled galaxies, we find the XDR
component of the CO SLED to dominate the CO luminosity from $J_{\text{upp}}
\geq 4$. We conclude that, once a detailed distribution of molecular gas
density is taken into account, PDR emission at mid-/high-$J$ becomes negligible
with respect to XDR.


  Individual participants in human society collectively exhibit aggregation
behavior. In this study, we present a simple microscopic model of labor force
migration by employing the active Brownian particles framework. Through
agent-based simulations, we find that our model produces clusters of agents
from a random initial distribution. Furthermore, two empirical regularities
called Zipf's and Okun's laws were observed in our model. To reveal the
mechanism underlying the reproduced agglomeration phenomena, we derived an
extended Keller-Segel system, a classic model that describes the aggregation
behavior of biological organisms called "taxis," from our microscopic model.
The obtained macroscopic system indicates that the agglomeration of the
workforce in real world can be accounted for through a new type of taxis
central to human behavior, which highlights the relevance of urbanization to
blow-up phenomena in the derived PDE system. We term it "econotaxis."


  Exploring the characterization of singular black hole spacetimes, we study
the relation between energy density, curvature invariants, and geodesic
completeness using a quadratic $f(R)$ gravity theory coupled to an anisotropic
fluid. Working in a metric-affine approach, our models and solutions represent
minimal extensions of General Relativity (GR) in the sense that they rapidly
recover the usual Reissner-Nordstr\"{o}m solution from near the inner horizon
outwards. The anisotropic fluid helps modify only the innermost geometry.
Depending on the values and signs of two parameters on the gravitational and
matter sectors, a breakdown of the correlations between the
finiteness/divergence of the energy density, the behavior of curvature
invariants, and the (in)completeness of geodesics is obtained. We find a
variety of configurations with and without wormholes, a case with a de Sitter
interior, solutions that mimic non-linear models of electrodynamics coupled to
GR, and configurations with up to four horizons. Our results raise questions
regarding what infinities, if any, a quantum version of these theories should
regularize.


  The main objective of the RET workshop was to explore the interaction of
Requirements Engineering (RE) and Testing, i.e. RET, in research and industry,
and the challenges that result from this interaction. While much work has been
done in the respective fields of requirements engineering and testing, there
exists much more than can be done to understand the connection between the
processes of RE and of testing.


  The degree of alignment between a star's spin axis and the orbital plane of
its planets (the stellar obliquity) is related to interesting and poorly
understood processes that occur during planet formation and evolution. Hot
Jupiters orbiting hot stars ($\gtrsim$6250 K) display a wide range of
obliquities, while similar planets orbiting cool stars are preferentially
aligned. Tidal dissipation is expected to be more rapid in stars with thick
convective envelopes, potentially explaining this trend. Evolved stars provide
an opportunity to test the damping hypothesis, particularly stars that were hot
on the main sequence and have since cooled and developed deep convective
envelopes. We present the first systematic study of the obliquities of hot
Jupiters orbiting subgiants that recently developed convective envelopes using
Rossiter-McLaughlin observations. Our sample includes two newly discovered
systems in the Giants Transiting Giants Survey (TOI-6029 b, TOI-4379 b). We
find that the orbits of hot Jupiters orbiting subgiants that have cooled below
$\sim$6250 K are aligned or nearly aligned with the spin-axis of their host
stars, indicating rapid tidal realignment after the emergence of a stellar
convective envelope. We place an upper limit for the timescale of realignment
for hot Jupiters orbiting subgiants at $\sim$500 Myr. Comparison with a
simplified tidal evolution model shows that obliquity damping needs to be
$\sim$4 orders of magnitude more efficient than orbital period decay to damp
the obliquity without destroying the planet, which is consistent with recent
predictions for tidal dissipation from inertial waves excited by hot Jupiters
on misaligned orbits.


  Recently, much progress has been made for self-supervised action recognition.
Most existing approaches emphasize the contrastive relations among videos,
including appearance and motion consistency. However, two main issues remain
for existing pre-training methods: 1) the learned representation is neutral and
not informative for a specific task; 2) multi-task learning-based pre-training
sometimes leads to sub-optimal solutions due to inconsistent domains of
different tasks. To address the above issues, we propose a novel action
recognition pre-training framework, which exploits human-centered prior
knowledge that generates more informative representation, and avoids the
conflict between multiple tasks by using task-dependent representations.
Specifically, we distill knowledge from a human parsing model to enrich the
semantic capability of representation. In addition, we combine knowledge
distillation with contrastive learning to constitute a task-dependent
multi-task framework. We achieve state-of-the-art performance on two popular
benchmarks for action recognition task, i.e., UCF101 and HMDB51, verifying the
effectiveness of our method.


  We investigate galactic winds driven by supernova (SN) explosions in an
isolated dwarf galaxy using high-resolution (particle mass $m_{\rm gas} = 1{\rm
M_\odot}$, number of neighbor $N_{\rm ngb} = 100$) smoothed-particle
hydrodynamics simulations that include non-equilibrium cooling and chemistry,
individual star formation, stellar feedback and metal enrichment. Clustered SNe
lead to the formation of superbubbles which break out of the disk and vent out
hot gas, launching the winds. We find much weaker winds than what cosmological
simulations typically adopt at this mass scale. At the virial radius, the
time-averaged loading factors of mass, momentum and energy are 3, 1 and 0.05,
respectively, and the metal enrichment factor is 1.5. Winds that escape the
halo consist of two populations that differ in their launching temperatures.
Hot gas acquires enough kinetic energy to escape when launched while warm gas
does not. However, warm gas can be further accelerated by the ram pressure of
the subsequently launched hot gas and eventually escape. The strong
interactions between different temperature phases highlight the caveat of
extrapolating properties of warm gas to large distances based on its local
conditions (e.g. the Bernoulli parameter). Our convergence study finds that
wind properties converge when the cooling masses of individual SNe are
resolved, which corresponds to $m_{\rm gas}=5 {\rm M_\odot}$ with an injection
mass of $500 {\rm M_\odot}$. The winds weaken dramatically once the SNe become
unresolved. We demonstrate that injecting the terminal momentum of SNe, a
popular sub-grid model in the literature, fails to capture SN winds
irrespective of the inclusion of residual thermal energy.


  In this work, we prove the existence of a third embedded minimal hypersurface
spanning a closed submanifold $\gamma$ contained in the boundary of a compact
Riemannian manifold with convex boundary, when it is known a priori the
existence of two strictly stable minimal hypersurfaces that bound $\gamma$. In
order to do so, we develop min-max methods similar to those of De Lellis and
Ramic, references in the paper, adapted to the discrete setting of Almgren and
Pitts.