  In this paper we present BeppoSax and XMM observations of two long Gamma-ray
bursts, the X-ray rich event of December 11, 2001 (GRB011211) and the hard and
very bright event of November 21, 2001 (GRB011121). In both events we find
evidence of a late X-ray burst, taking place several minutes after the prompt
emission. The temporal and spectral behaviour of this phenomenon suggest that
it represents the onset of the afterglow. Broad band spectral modelling of the
afterglow indicate that the fireball evolution in the December burst takes
place in a ISM environment. On the contrary in the November burst the wind case
is revealed by an X-ray decay slower than that observed in the optical
($\delta_{\rm X}=1.29\pm0.04$ vs $\delta_{\rm O}=1.66\pm0.06$). The wind
profile should change into a constant density profile at large radii, in order
to reconcile late-time radio data with a jet. Two other results are obtained
for this burst. An X-ray burst is preceding by about 30 s the much harder GRB.
Contrary to the prediction of simple models of precursor activity for
collapsars, its spectrum is not consistent with a black body. Finally, a
substantial absorption column ($\NH=(7\pm2)\times10^{22}$ cm$^{-2}$) is
detected during the early part of the prompt emission. This is much greater
than that of the wind, and it is thus likely associated with the region
surrounding the burst.


  This paper summarizes the main results of our recent study of the non-Blazhko
RR Lyrae stars observed with the Kepler space telescope. These stars offer the
opportunity for studying the stability of the pulsations of RR Lyrae stars and
for providing a reference against which the Blazhko RR Lyrae stars can be
compared. Of particular interest is the stability of the low-dispersion (sigma
< 1mmag) light curves constructed from ~18,000 long-cadence (30-min) and (for
FN Lyr and AW Dra) the ~150,000 short-cadence (1-min) photometric data points.
Fourier-based [Fe/H] values and other physical characteristics are also
derived. When the observed periods are compared with periods computed with the
Warsaw non-linear convective pulsation code better agreement is achieved
assuming pulsational L and M values rather than the (higher) evolutionary L and
M values.


  We study pseudoholomorphic discs with boundaries attached to a real
hypersurface in an almost complex manifold of dimension 2. We prove that if the
hypersurface contains no discs, then they fill a one sided neighborhood of the
hypersurface.


  We derive, via the Hardy-Littlewood method, an asymptotic formula for the
number of integral zeros of a particular class of weighted quartic forms under
the assumption of non-singular local solubility. Our polynomials $F({\mathbf
x},{\mathbf y}) \in \mathbb{Z}[x_1,\ldots,x_{s_1},y_1,\ldots,y_{s_2}]$ satisfy
the condition that $F(\lambda^2 {\mathbf x}, \lambda {\mathbf y}) = \lambda^4
F({\mathbf x},{\mathbf y})$. Our conclusions improve on those that would follow
from a direct application of the methods of Birch. For example, we show that in
many circumstances the expected asymptotic formula holds when $s_1 \ge 2$ and
$2s_1 + s_2 > 8$.


  We reveal how the vector field links are untied under the influence of
anti-parity-time-symmetric couplings in a dissipative sublattice-symmetric
topological photonic crystal lattice. The topology of the quasi-one-dimensional
two-band system is encoded in the geometric topology of the vector fields
associated with the Bloch Hamiltonian. The linked vector fields reflect the
topology of the nontrivial phase. The topological phase transition occurs
concomitantly with the untying of the vector field link at the exceptional
points. Counterintuitively, more dissipation constructively creates a
nontrivial topology. The linking number predicts the number of topological
photonic zero modes.


  Computing the viability kernel is key in providing guarantees of safety and
proving existence of safety-preserving controllers for constrained dynamical
systems. Current numerical techniques that approximate this construct suffer
from a complexity that is exponential in the dimension of the state. We study
conditions under which a linear time-invariant (LTI) system can be suitably
decomposed into lower-dimensional subsystems so as to admit a conservative
computation of the viability kernel in a decentralized fashion in subspaces. We
then present an isomorphism that imposes these desired conditions, particularly
on two-time-scale systems. Decentralized computations are performed in the
transformed coordinates, yielding a conservative approximation of the viability
kernel in the original state space. Significant reduction of complexity can be
achieved, allowing the previously inapplicable tools to be employed for
treatment of higher-dimensional systems. We show the results on two examples
including a 6D system.


  We apply quantum statistics to our quantized versions of Schwarzschild-AdS
and Kerr-AdS black holes and also to the quantized globally hyperbolic
spacetimes having an asymptotically Euclidean Cauchy hypersurface by first
proving, for the temporal Hamiltonian $H_0$, that $e^{-\beta H_0}$, $\beta>0$,
is of trace class and then, that this result is also valid for the spatial
Hamiltonian $H_1$, which has the same eigenvalues but with larger
multiplicities. Since the lowest eigenvalue is strictly positive the extension
of $e^{-\beta H_1}$ to the corresponding symmetric Fock space is also of trace
class and we are thus able to define a partition function $Z$, the operator
density $\rho$, the entropy $S$, and the average energy $E$. We prove that $S$
and $E$ tend to infinity if the cosmological constant $\Lambda$ tends to $0$
and vanish if $|\Lambda|$ tends to infinity. We also conjecture that $E$ is the
source of the dark matter and that the dark energy density is a multiple of the
eigenvalue of $\rho$ with respect to the vacuum vector which is $Z^{-1}$.


  We study the following Brezis-Nirenberg problem of Kirchhoff type $$
\left\{\aligned &-(a+b\int_{\Omega}|\nabla u|^2dx)\Delta u = \lambda|u|^{q-2}u
+ \delta |u|^{2}u, &\quad \text{in}\ \Omega, \\ &u=0,& \text{on}\
\partial\Omega, \endaligned \right. $$ where $\Omega\subset \bbr^4$ is a
bounded domain with the smooth boundary $\partial\Omega$, $2\leq q<4$ and $a$,
$b$, $\lambda$, $\delta$ are positive parameters. We obtain some new existence
and nonexistence results, depending on the values of the above parameters,
which improves some known results. The asymptotical behaviors of the solutions
are also considered in this paper.


  This paper investigates the robustness of a novel high-dimensional
continuification control method for complex multi-agent systems. We begin by
formulating a partial differential equation describing the spatio-temporal
density dynamics of swarming agents. A stable control action for the density is
then derived and validated under nominal conditions. Subsequently, we
discretize this macroscopic strategy into actionable velocity inputs for the
system's agents. Our analysis demonstrates the robustness of the approach
beyond idealized assumptions of unlimited sensing and absence of perturbations.


  Data-driven approaches for modelling contact-rich tasks address many of the
difficulties that analytical models bear. For real-world scenarios, the
hardware capabilities constrain the available measurements and consequently,
every step of the problem's formulation. In this work, we propose a formulation
that encapsulates knowledge from a baseline controller for the contact-rich
task of food-cutting. Based on this formulation, we employ deep networks to
model the dynamics within a model predictive controller. We design a training
process based on curriculum training with learning rate decay for multi-step
predictions, which are essential for receding horizon control. Experimental
results demonstrate that even with a simple architecture, our model achieves
consistently good predictive performance on known and unknown object classes
and exhibits a good understanding of the long term dynamics.


  In this paper, we propose a novel method for detecting DeepFakes, enhancing
the generalization of detection through semantic decoupling. There are now
multiple DeepFake forgery technologies that not only possess unique forgery
semantics but may also share common forgery semantics. The unique forgery
semantics and irrelevant content semantics may promote over-fitting and hamper
generalization for DeepFake detectors. For our proposed method, after
decoupling, the common forgery semantics could be extracted from DeepFakes, and
subsequently be employed for developing the generalizability of DeepFake
detectors. Also, to pursue additional generalizability, we designed an adaptive
high-pass module and a two-stage training strategy to improve the independence
of decoupled semantics. Evaluation on FF++, Celeb-DF, DFD, and DFDC datasets
showcases our method's excellent detection and generalization performance. Code
is available at: https://anonymous.4open.science/r/DFS-GDD-0F42.


  We study the Hawking radiation in field theories which break Lorentz
invariance via dissipative effects above a certain energy scale. We assume that
the additional degrees of freedom which cause dissipation are Gaussian and
freely falling. The asymptotic spectrum and the correlations are extracted from
the anticommutator of the radiation field. The singular behavior of the Green
function found for relativistic fields as one point crosses the horizon is
completely suppressed by dissipation. Yet, when the dissipative frequency scale
is much larger than the surface gravity of the black hole, we show that the
asymptotic observables acquire their standard (relativistic) vacuum expectation
values. We explicitly compute the effects of dissipation on the spectrum and on
the nonseparable character of the correlations when varying the dissipative
scale, the extension of the near-horizon geometry, and the temperature of the
environment.


  In this article, we extend the conventional framework of
convolutional-Restricted-Boltzmann-Machine to learn highly abstract features
among abitrary number of time related input maps by constructing a layer of
multiplicative units, which capture the relations among inputs. In many cases,
more than two maps are strongly related, so it is wise to make multiplicative
unit learn relations among more input maps, in other words, to find the optimal
relational-order of each unit. In order to enable our machine to learn
relational order, we developed a reinforcement-learning method whose optimality
is proven to train the network.


  The shift of atomic energy levels due to hadronic vacuum polarization is
evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen.
A parametric hadronic polarization function obtained from experimental cross
sections of $e^-e^+$ annihilation into hadrons is applied to derive an
effective relativistic Uehling potential. The energy corrections originating
from hadronic vacuum polarization are calculated for low-lying levels using
analytical Dirac-Coulomb wave functions, as well as bound wave functions
accounting for the finite nuclear size. Closed formulas for the hadronic
Uehling potential of an extended nucleus as well as for the relativistic energy
shift in case of a point-like nucleus are derived. These results are compared
to existing analytic formulas from non-relativistic theory.


  In 1981 Hong and Kung proved a lower bound on the amount of communication
needed to perform dense, matrix-multiplication using the conventional $O(n^3)$
algorithm, where the input matrices were too large to fit in the small, fast
memory. In 2004 Irony, Toledo and Tiskin gave a new proof of this result and
extended it to the parallel case. In both cases the lower bound may be
expressed as $\Omega$(#arithmetic operations / $\sqrt{M}$), where M is the size
of the fast memory (or local memory in the parallel case). Here we generalize
these results to a much wider variety of algorithms, including LU
factorization, Cholesky factorization, $LDL^T$ factorization, QR factorization,
algorithms for eigenvalues and singular values, i.e., essentially all direct
methods of linear algebra. The proof works for dense or sparse matrices, and
for sequential or parallel algorithms. In addition to lower bounds on the
amount of data moved (bandwidth) we get lower bounds on the number of messages
required to move it (latency). We illustrate how to extend our lower bound
technique to compositions of linear algebra operations (like computing powers
of a matrix), to decide whether it is enough to call a sequence of simpler
optimal algorithms (like matrix multiplication) to minimize communication, or
if we can do better. We give examples of both. We also show how to extend our
lower bounds to certain graph theoretic problems.
  We point out recently designed algorithms for dense LU, Cholesky, QR,
eigenvalue and the SVD problems that attain these lower bounds; implementations
of LU and QR show large speedups over conventional linear algebra algorithms in
standard libraries like LAPACK and ScaLAPACK. Many open problems remain.


  We analyze different holographic complexity proposals for black holes that
include corrections from bulk quantum fields. The specific setup is the quantum
BTZ black hole, which encompasses in an exact manner the effects of conformal
fields with large central charge in the presence of the black hole, including
the backreaction corrections to the BTZ metric. Our results show that Volume
Complexity admits a consistent quantum expansion and correctly reproduces known
limits. On the other hand, the generalized Action Complexity picks up large
contributions from the singularity, which is modified due to quantum
backreaction, with the result that Action Complexity does not reproduce the
expected classical limit. Furthermore, we show that the doubly-holographic
setup allows computing the complexity coming purely from quantum fields - a
notion that has proven evasive in usual holographic setups. We find that in
holographic induced-gravity scenarios the complexity of quantum fields in a
black hole background vanishes to leading order in the gravitational strength
of CFT effects.


  In this paper we study a singular limit problem in the context of partially
dissipative first order quasilinear systems. This problem arises in multiphase
fluid mechanics. More precisely, taking into account dissipative effects for
the velocity, we show that the so-called Kapilla system is obtained as a
relaxation limit from the Baer-Nunziato (BN) system and derive the convergence
rate of this process. The main problem we encounter is that the (BN)-system
does not verify the celebrated (SK) condition due to Shizuta and Kawashima. It
turns out that we can rewrite the (BN)-system in terms of new variables such as
to highlight a subsystem for which the linearized does verify the (SK)
condition which is coupled through lower-order terms with a transport equation.
We construct an appropriate weighted energy-functional which allows us to
tackle the lack of symmetry of the system, provides decay information and
allows us to close the estimate uniformly with respect to the relaxation
parameter.


  We extend the theory and the algorithms of Border Bases to systems of Laurent
polynomial equations, defining "toric" roots. Instead of introducing new
variables and new relations to saturate by the variable inverses, we propose a
more efficient approach which works directly with the variables and their
inverse. We show that the commutation relations and the inversion relations
characterize toric border bases. We explicitly describe the first syzygy module
associated to a toric border basis in terms of these relations. Finally, a new
border basis algorithm for Laurent polynomials is described and a proof of its
termination is given for zero-dimensional toric ideals.


  We set up a hydrodynamic description of the non-equilibrium dynamics of
sine-Gordon quantum field theory for generic coupling. It is built upon an
explicit form of the Bethe Ansatz description of general thermodynamic states,
with the structure of the resulting coupled integral equations encoded in terms
of graphical diagrams. The resulting framework is applied to derive results for
the Drude weights of charge and energy. Quantities associated with the charge
universally have fractal dependence on the coupling, which is notably absent
from those associated with energy, a feature explained by the different roles
played by reflective scattering in transporting these quantities. We then
present far-from-equilibrium results, including explicit time evolution
starting from bipartite initial states and dynamical correlation functions. Our
framework can be applied to explore numerous other aspects of non-equilibrium
dynamics, which opens the way to a wide array of theoretical studies and
potential novel experimental predictions.


  With silicon being the go-to material for spin qubits, and motivated by the
demand of a scalable quantum computer architecture for fast and reliable
quantum information transfer on-chip, we study coherent electron transport in a
silicon double quantum dot. We first examine the valley-orbital dynamics in a
silicon double dot, and discuss how to properly measure the tunnel couplings as
well as the valley phase difference between two quantum dots. We then focus on
possible phase and spin flip errors during spin transport across a silicon
double dot. In particular, we clarify correction on the effective $g$-factor
for the electron spin from the double dot confinement potential, and quantify
the resulting phase error. We then study spin fidelity loss due to spin-valley
mixing, which is a unique feature of silicon quantum dots. We show that a small
phase correction between valleys can cause a significant coherence loss. We
also investigate spin flip errors caused by either an external inhomogeneous
magnetic field or the intrinsic spin-orbit coupling. We show that the presence
of valleys makes it possible to have much broader (in terms of interdot
detuning) level anti-crossings compared to typical anti-crossings in, for
example, a GaAs double dot, and such broad anti-crossings lead to amplification
of spin flip errors. Lastly, we design a pulse sequence to suppress various
possible spin flip errors by taking advantage of the multiple level
anti-crossings in a silicon double dot and employing Landau-Zener transitions.


  We prove tight upper bounds for the number of vertices of a simple polygon
that is the union or the intersection of two simple polygons with given numbers
of convex and concave vertices. The similar question on graphs of the lower (or
upper) envelope of two continuous piecewise linear functions is considered.


  Lipschitz equivalence of self-similar sets is an important area in the study
of fractal geometry. It is known that two dust-like self-similar sets with the
same contraction ratios are always Lipschitz equivalent. However, when
self-similar sets have touching structures the problem of Lipschitz equivalence
becomes much more challenging and intriguing at the same time. So far the only
known results only cover self-similar sets in $\bR$ with no more than 3
branches. In this study we establish results for the Lipschitz equivalence of
self-similar sets with touching structures in $\bR$ with arbitrarily many
branches. Key to our study is the introduction of a geometric condition for
self-similar sets called {\em substitutable}.


  We present a new simulation setup using the MURaM radiative
Magnetohydrodynamic (MHD) code that allows to study the formation of
collisional polarity inversion lines (cPILs) in the photosphere and the coronal
response including flares. In this scheme we start with a bipolar sunspot
configuration and set the spots on collision course by imposing the appropriate
velocity field at the footpoints in the subphotospheric boundary. We produce
different setups with the same initial spot separation by varying physical
parameters such as the collision speed and minimum collision distance. While
all setups lead to the formation of an EUV and X-ray sigmoid structure, only
the cases with a close passing of the spots cause flares and mass eruptions.
The energy release is in the $1-2 \times 10^{31}$ erg range, putting the
simulated flares into the upper C-class to lower M-class range of GOES X-ray
1-8 A flux. While the setup with the more distant passing of the spots does not
lead to a flare, the corona is nonetheless substantially heated, suggesting
non-eruptive energy release mechanisms. We focus our discussion on two
particular setups that differ in spot coherence and resulting cPIL length
persistence. We find different timings in the transition from a sheared
magnetic arcade (SMA) to magnetic flux rope (MFR); the setup with a large
length but shorter duration cPIL produces a MFR during the eruption, while the
MFR is pre-existing in the setup with a large length and longer duration cPIL.
While both result in flares of comparable strength and the eruption of a CME,
the setup with pre-existing MFR (and embedded filament) leads to an MFR
eruption with a larger mass content.


  We show that a sequence of stochastic spatial Lotka-Volterra models, suitably
rescaled in space and time, converges weakly to super-Brownian motion with
drift. The result includes both long range and nearest neighbor models, the
latter for dimensions three and above. These theorems are special cases of a
general convergence theorem for perturbations of the voter model.


  Many robotic tasks, such as human-robot interactions or the handling of
fragile objects, require tight control and limitation of appearing forces and
moments alongside sensible motion control to achieve safe yet high-performance
operation. We propose a learning-supported model predictive force and motion
control scheme that provides stochastic safety guarantees while adapting to
changing situations. Gaussian processes are used to learn the uncertain
relations that map the robot's states to the forces and moments. The model
predictive controller uses these Gaussian process models to achieve precise
motion and force control under stochastic constraint satisfaction. As the
uncertainty only occurs in the static model parts -- the output equations -- a
computationally efficient stochastic MPC formulation is used. Analysis of
recursive feasibility of the optimal control problem and convergence of the
closed loop system for the static uncertainty case are given. Chance constraint
formulation and back-offs are constructed based on the variance of the Gaussian
process to guarantee safe operation. The approach is illustrated on a
lightweight robot in simulations and experiments.


  Atomically thin transition metal dichalcogenide crystals (TMDCs) have
extraordinary optical properties that make them attractive for future
optoelectronic applications. Integration of TMDCs into practical all-dielectric
heterostructures hinges on the ability to passivate and protect them against
necessary fabrication steps on large scales. Despite its limited scalability,
encapsulation of TMDCs in hexagonal boron nitride (hBN) currently has no viable
alternative for achieving high performance of the final device. Here, we show
that the novel, ultrathin Ga$_2$O$_3$ glass is an ideal centimeter-scale
coating material that enhances optical performance of the monolayers and
protects them against further material deposition. In particular, Ga$_2$O$_3$
capping of commercial grade WS$_2$ monolayers outperforms hBN in both
scalability and optical performance at room temperature. These properties make
Ga$_2$O$_3$ highly suitable for large scale passivation and protection of
monolayer TMDCs in functional heterostructures.


  For every Gaussian kernel density estimator $f(x)=\sum_i a_i \exp(-\lVert
x-x_i\rVert^2/2h^2)$ associated to a point cloud
$\mathcal{D}=\{x_1,...,x_N\}\subset \mathbb{R}^d$, we define a nested family of
closed subspaces $\mathcal{S}(a)\subset\mathbb{R}^d$, which we interpret as a
continuous version of an alpha shape. Using arguments based on Fenchel duality,
we prove that $\mathcal{S}(a)$ is homotopy equivalent to the superlevel set
$\mathcal{L}(a)=f^{-1}[e^{-a},\infty)$, and that $\mathcal{L}(a)$ can be
realized as the union of a certain power-shifted covering by balls with centers
in $\mathcal{S}(a)$. By extracting finite alpha complexes with vertices in
$\mathcal{S}(a)$, we obtain refined geometric models of noisy point clouds, as
well as density-filtered persistent homology calculations. In order to compute
alpha complexes in higher dimension, we used a recent algorithm due to the
present authors based on the duality principle.


  We develop a version of Cichon's diagram for cardinal invariants on the
generalized Cantor space 2^kappa or the generalized Baire space kappa^kappa
where kappa is an uncountable regular cardinal. For strongly inaccessible
kappa, many of the ZFC-results about the order relationship of the cardinal
invariants which hold for omega generalize; for example we obtain a natural
generalization of the Bartoszynski-Raisonnier-Stern Theorem. We also prove a
number of independence results, both with <kappa-support iterations and
kappa-support iterations and products, showing that we consistently have strict
inequality between some of the cardinal invariants.


  Repeated asymptomatic screening for SARS-CoV-2 promises to control spread of
the virus but would require too many resources to implement at scale. Group
testing is promising for screening more people with fewer test resources:
multiple samples tested together in one pool can be excluded with one negative
test result. Existing approaches to group testing design for SARS-CoV-2
asymptomatic screening, however, do not consider dilution effects: that false
negatives become more common with larger pools. As a consequence, they may
recommend pool sizes that are too large or misestimate the benefits of
screening. Modeling dilution effects, we derive closed-form expressions for the
expected number of tests and false negative/positives per person screened under
two popular group testing methods: the linear and square array methods. We find
that test error correlation induced by a common viral load across an
individual's samples results in many fewer false negatives than would be
expected from less realistic but more widely assumed independent errors. This
insight also suggests that false positives can be controlled through repeated
tests without significantly increasing false negatives. Using these closed-form
expressions to trace a Pareto frontier over error rates and tests, we design
testing protocols for repeated asymptomatic screening of a large population. We
minimize disease prevalence by optimizing a time-varying pool sizes and
screening frequency constrained by daily test capacity and a false positive
limit. This provides a testing protocol practitioners can use for mitigating
COVID-19. In a case study, we demonstrate the effectiveness of this methodology
in controlling spread.


  A complete classification is presented of quantum and classical
superintegrable systems in $E_2$ that allow the separation of variables in
polar coordinates and admit an additional integral of motion of order three in
the momentum. New quantum superintegrable systems are discovered for which the
potential is expressed in terms of the sixth Painlev\'e transcendent or in
terms of the Weierstrass elliptic function.


  This survey article is the written version of a talk given at the Bourbaki
seminar in April 2021. We give an introduction to Zagier's conjecture on
special values of Dedekind zeta functions, and its relation to $K$-theory of
fields and the theory of motives. We survey recent progress on the conjecture
and in particular the proof of the $n=4$ case of the conjecture by Goncharov
and Rudenko.


  In this paper, we study the dynamics of a test particle around a regular
black hole (BH) in a non-minimal Einstein Yang Mills (EYM) theory and examine
the BH shadow. The EYM theory is a non-minimally coupled theory in which
curvature couples to non-Abelian gauge fields. We investigate particle motion
with parameters in EYM BH for massless and massive particles. This work
provides the horizon structure, photon radius and inner stable circular orbit
(ISCO) of a mass particle with EYM BH parameters. An analysis is provided of
the effective potential as well as the possible orbits for test particles under
various EYM BH parameters values. In timelike radial geodesics, we find that
for smaller values of magnetic charge, particles following a timelike radial
geodesic are hastier in EYM BH, and hence arrive at the center faster than
those traveling a Schwarzschild BH geodesic. However, at larger values of the
magnetic charge, the inverse effect is observed. The effect of model parameters
is investigated in order to study the ISCO, photon radius, orbit stability
(Lyapunov exponent), and effective force on particles for the BH in the EYM
theory. Finally, we investigate the BH shadow. We find that higher magnetic
charge values and non-minimal coupling parameters result in smaller shadow
radius values.


  Here we introduce a new model of natural textures based on the feature spaces
of convolutional neural networks optimised for object recognition. Samples from
the model are of high perceptual quality demonstrating the generative power of
neural networks trained in a purely discriminative fashion. Within the model,
textures are represented by the correlations between feature maps in several
layers of the network. We show that across layers the texture representations
increasingly capture the statistical properties of natural images while making
object information more and more explicit. The model provides a new tool to
generate stimuli for neuroscience and might offer insights into the deep
representations learned by convolutional neural networks.


  In a previous work we obtained exact solutions for the proper time quantum
mechanics of a thin dust shell, collapsing in a vacuum. We extend these results
to the quantum collapse of a dust shell surrounding a pre-existing black hole.
In lieu of exact solutions, which have so far proved difficult to obtain for
this system, we establish the essential features of the quantum shell through a
Wentzel-Kramers-Brillouin (WKB) approximation, which is valid only when the
mass of the shell is much greater than the Planck mass. There are many
similarities with the vacuum collapse: only bound states exist and the proper
energy spectrum of the shell is unaffected by the presence of the central black
hole to this order. There are no peculiar or distinguishing features of the
wave function near the black hole horizon. It vanishes at the center and
oscillates between the origin and the classically forbidden region, beyond
which it decays exponentially.


  In interactive information retrieval, researchers consider the user behavior
towards systems and search tasks in order to adapt search results by analyzing
their past interactions. In this paper, we analyze the user behavior towards
Marcia Bates' search stratagems such as 'footnote chasing' and 'citation
search' in an academic search engine. We performed a preliminary analysis of
their frequency and stage of use in the social sciences search engine sowiport.
In addition, we explored the impact of these stratagems on the whole search
process performance. We can conclude that the appearance of these two search
features in real retrieval sessions lead to an improvement of the precision in
terms of positive interactions with 16% when using footnote chasing and 17% for
the citation search stratagem.


  Following our previous work on fractional spin symmetries (FSS) \cite{6, 7},
we consider here the construction of field theoretical models that are
invariant under the $D=2(1/3,1/3)$ supersymmetric algebra.


  Moran's index is a basic measure of spatial autocorrelation, which has been
applied to varied fields of both natural and social sciences. A good measure
should have clear boundary values or critical value. However, for Moran's
index, both boundary values and critical value are controversial. In this
paper, a novel method is proposed to derive the boundary values of Moran's
index. The key lies in finding conditional extremum based on quadratic form of
defining Moran's index. As a result, two sets of boundary values are derived
naturally for Moran's index. One is determined by the eigenvalues of spatial
weight matrix, and the other is determined by the quadratic form of spatial
autocorrelation coefficient (-1<Moran's I<1). The intersection of these two
sets of boundary values gives four possible numerical ranges of Moran's index.
A conclusion can be reached that the bounds of Moran's index is determined by
size vector and spatial weight matrix, and the basic boundary values are -1 and
1. The eigenvalues of spatial weight matrix represent the maximum extension
length of the eigenvector axes of n geographical elements at different
directions. This work solves one of the fundamental problems of spatial
autocorrelation analysis.


  In this paper, practically computable low-order approximations of potentially
high-dimensional differential equations driven by geometric rough paths are
proposed and investigated. In particular, equations are studied that cover the
linear setting, but we allow for a certain type of dissipative nonlinearity in
the drift as well. In a first step, a linear subspace is found that contains
the solution space of the underlying rough differential equation (RDE). This
subspace is associated to covariances of linear Ito-stochastic differential
equations which is shown exploiting a Gronwall lemma for matrix differential
equations. Orthogonal projections onto the identified subspace lead to a first
exact reduced order system. Secondly, a linear map of the RDE solution
(quantity of interest) is analyzed in terms of redundant information meaning
that state variables are found that do not contribute to the quantity of
interest. Once more, a link to Ito-stochastic differential equations is used.
Removing such unnecessary information from the RDE provides a further dimension
reduction without causing an error. Finally, we discretize a linear parabolic
rough partial differential equation in space. The resulting large-order RDE is
subsequently tackled with the exact reduction techniques studied in this paper.
We illustrate the enormous complexity reduction potential in the corresponding
numerical experiments.


  In this paper, we represent a methodology of a graph embeddings algorithm
that is used to transform labeled property graphs obtained from a Building
Information Model (BIM). Industrial Foundation Classes (IFC) is a standard
schema for BIM, which is utilized to convert the building data into a graph
representation. We used node2Vec with biased random walks to extract semantic
similarities between different building components and represent them in a
multi-dimensional vector space. A case study implementation is conducted on a
net-zero-energy building located at the National University of Singapore
(SDE4). This approach shows promising machine learning applications in
capturing the semantic relations and similarities of different building
objects, more specifically, spatial and spatio-temporal data.


  Magnetic Fr\'eedericksz transition was studied in ferronematics based on the
nematic liquid crystal 4-(trans-4'-n-hexylcyclohexyl)-isothiocyanatobenzene
(6CHBT). 6CHBT was doped with rod-like magnetic particles of different size and
volume concentration. The volume concentrations of magnetic particles in the
prepared ferronematics were $\phi_1$ = 10$^{-4}$ and $\phi_2$ = 10$^{-3}$. The
structural changes were observed by capacitance measurements that demonstrate a
significant influence of the concentration, the shape anisotropy, and/or the
size of the magnetic particles on the magnetic response of these ferronematics.


  Modeling the ideological perspectives of political actors is an essential
task in computational political science with applications in many downstream
tasks. Existing approaches are generally limited to textual data and voting
records, while they neglect the rich social context and valuable expert
knowledge for holistic ideological analysis. In this paper, we propose
\textbf{PAR}, a \textbf{P}olitical \textbf{A}ctor \textbf{R}epresentation
learning framework that jointly leverages social context and expert knowledge.
Specifically, we retrieve and extract factual statements about legislators to
leverage social context information. We then construct a heterogeneous
information network to incorporate social context and use relational graph
neural networks to learn legislator representations. Finally, we train PAR with
three objectives to align representation learning with expert knowledge, model
ideological stance consistency, and simulate the echo chamber phenomenon.
Extensive experiments demonstrate that PAR is better at augmenting political
text understanding and successfully advances the state-of-the-art in political
perspective detection and roll call vote prediction. Further analysis proves
that PAR learns representations that reflect the political reality and provide
new insights into political behavior.


  The Ising antiferromagnet on a face-centered cubic (fcc) lattice with
nearest-neighbor interaction only is well known to exhibit a macroscopic
(exponential in the system size $L$) ground-state degeneracy. With increasing
temperature, this degeneracy is expected to be lifted and the model undergoes a
first-order phase transition. For a model with an exponential degeneracy in the
whole low-temperature phase, it was recently found that the finite-size scaling
behavior is governed by leading correction terms $\sim L^{-2}$ instead of $\sim
L^{-3}$ as usual. To test the conjecture that such a transmuted behavior may
effectively persist also for the fcc antiferromagnet up to some crossover
system size, we have performed parallel multicanonical Monte Carlo simulations
for lattices of linear size $L \le 18$ with periodic boundary conditions and
determined various inverse pseudo phase transition temperatures, as well as the
extremal values of the specific heat and the energetic Binder parameter. We
indeed find that, for the simulated lattice sizes, the conjectured transmuted
finite-size scaling ansatz fits the data better than the standard ansatz. On
this basis, we extrapolate for the transition temperature an estimate of $T_0 =
1.735047(46)$.


  In this note, we consider the problem of existence of adaptive confidence
bands in the fixed design regression model, adapting ideas in Hoffmann and
Nickl (2011) to the present case. In the course of the proof, we show that
sup-norm adaptive estimators exist as well in regression.


  We propose an efficient inverse design approach for multifunctional optical
elements based on adaptive deep diffractive neural networks (a-D$^2$NNs).
Specifically, we introduce a-D$^2$NNs and design two-layer diffractive devices
that can selectively focus incident radiation over two well-separated spectral
bands at desired distances. We investigate focusing efficiencies at two
wavelengths and achieve targeted spectral lineshapes and spatial point-spread
functions (PSFs) with optimal focusing efficiency. In particular, we
demonstrate control of the spectral bandwidths at separate focal positions
beyond the theoretical limit of single-lens devices with the same aperture
size. Finally, we demonstrate devices that produce super-oscillatory focal
spots at desired wavelengths. The proposed method is compatible with current
diffractive optics and doublet metasurface technology for ultracompact
multispectral imaging and lensless microscopy applications.


  We investigate the bounds on light pseudoscalars that arise from a variety of
collider searches. Special attention is thereby devoted to the mass regions
$[3, 5] \, {\rm GeV}$ and $[9,11] \, {\rm GeV}$, in which a meaningful
theoretical description has to include estimates of non-perturbative effects
such as the mixing of the pseudoscalar with QCD bound states. A compendium of
formulas that allows to deal with the relevant corrections is provided. It
should prove useful for the interpretation of future LHC searches for light
CP-odd spin-0 states.


  Modified gravity theories can introduce modifications to the Poisson equation
in the Newtonian limit. As a result, we expect to see interesting features of
these modifications inside stellar objects. White dwarf stars are one of the
most well studied stars in stellar astrophysics. We explore the effect of
modified gravity theories inside white dwarfs. We derive the modified stellar
structure equations and solve them to study the mass-radius relationships for
various modified gravity theories. We also constrain the parameter space of
these theories from observations.


  Many applications require efficient management of large sets of intervals
because many objects are associated with intervals (e.g., time and price
intervals). In such interval management systems, range search is a primitive
operator for retrieving and analysis tasks. As dataset sizes are growing
nowadays, range search results are also becoming larger, which may overwhelm
users and incur long computation time. Because applications are usually
satisfied with a subset of the result set, it is desirable to efficiently
obtain only small samples from the result set.We therefore address the problem
of independent range sampling on interval data, which outputs $s$ random
samples that overlap a given query interval and are independent of the samples
of all previous queries. To efficiently solve this problem theoretically and
practically, we propose a variant of an interval tree, namely the augmented
interval tree (or AIT), and we show that there exists an exact algorithm that
needs $O(n \log n)$ space and $O(\log^{2} n + s)$ time, where $n$ is the
dataset size. The simple structure of an AIT provides flexible extensions: (i)
its time and space complexities respectively become $O(\log^{2} n + s)$
expected and $O(n)$ by bucketing intervals and (ii) it can deal with weighted
intervals and outputs $s$ weighted random samples in $O(\log^{2} n+s\log n)$
time. We conduct extensive experiments on real datasets, and the results
demonstrate that our algorithms significantly outperform competitors.


  We prove an algorithmic hardness result for finding low-energy states in the
so-called \emph{continuous random energy model (CREM)}, introduced by Bovier
and Kurkova in 2004 as an extension of Derrida's \emph{generalized random
energy model}. The CREM is a model of a random energy landscape $(X_v)_{v \in
\{0,1\}^N}$ on the discrete hypercube with built-in hierarchical structure, and
can be regarded as a toy model for strongly correlated random energy landscapes
such as the family of $p$-spin models including the Sherrington--Kirkpatrick
model. The CREM is parameterized by an increasing function $A:[0,1]\to[0,1]$,
which encodes the correlations between states.
  We exhibit an \emph{algorithmic hardness threshold} $x_*$, which is explicit
in terms of $A$. More precisely, we obtain two results: First, we show that a
renormalization procedure combined with a greedy search yields for any
$\varepsilon > 0$ a linear-time algorithm which finds states $v \in \{0,1\}^N$
with $X_v \ge (x_*-\varepsilon) N$. Second, we show that the value $x_*$ is
essentially best-possible: for any $\varepsilon > 0$, any algorithm which finds
states $v$ with $X_v \ge (x_*+\varepsilon)N$ requires exponentially many
queries in expectation and with high probability. We further discuss what
insights this study yields for understanding algorithmic hardness thresholds
for random instances of combinatorial optimization problems.


  Memory effects can be studied through a conditional past-future correlation,
which measures departure with respect to a conditional past-future independence
valid in a memoryless Markovian regime. In a quantum regime this property leads
to an operational definition of quantum non-Markovianity based on three
consecutive system measurement processes and postselection [Budini, Phys. Rev.
Lett. 121, 240401 (2018)]. Here, we study the conditional past-future
correlation for a qubit system coupled to different dephasing environments.
Exact solutions are obtained for a quantum spin bath as well as for classically
fluctuating random Hamiltonian models. The developing of memory effects and
departures from Born-Markov or white-noise approximations are related to a
measurement back action that changes the system dynamics between consecutive
measurements. It is shown that this effect may develop even when the former
system evolution is given by a time-independent Lindblad equation. This unusual
non-Markovian case arises when the characteristic parameters of the dynamics
become Lorentzian random distributed variables.


  We present weak-lensing measurements using the first-year data from the Hyper
Suprime-Cam Strategic Survey Program on the Subaru telescope for eight galaxy
clusters selected through their thermal Sunyaev-Zel'dovich (SZ) signal measured
at 148 GHz with the Atacama Cosmology Telescope Polarimeter experiment. The
overlap between the two surveys in this work is 33.8 square degrees, before
masking bright stars. The signal-to-noise ratio of individual cluster lensing
measurements ranges from 2.2 to 8.7, with a total of 11.1 for the stacked
cluster weak-lensing signal. We fit for an average weak-lensing mass
distribution using three different profiles, a Navarro-Frenk-White profile, a
dark-matter-only emulated profile, and a full cosmological hydrodynamic
emulated profile. We interpret the differences among the masses inferred by
these models as a systematic error of 10\%, which is currently smaller than the
statistical error. We obtain the ratio of the SZ-estimated mass to the
lensing-estimated mass (the so-called hydrostatic mass bias $1-b$) of
$0.74^{+0.13}_{-0.12}$, which is comparable to previous SZ-selected clusters
from the Atacama Cosmology Telescope and from the {\sl Planck} Satellite. We
conclude with a discussion of the implications for cosmological parameters
inferred from cluster abundances compared to cosmic microwave background
primary anisotropy measurements.


  Given a prime $p$, let $P(t)$ be a non-constant monic polynomial in $t$ over
the ring $\mathbb{Z}_{p}$ of $p$-adic integers. Let $X_{n}$ be an $n \times n$
random matrix over $\mathbb{Z}_{p}$ with independent entries that lie in any
residue class modulo $p$ with probability at most $1 - \epsilon$ for a fixed
real number $0 < \epsilon < 1$. We prove that as $n \rightarrow \infty$, the
distribution of the cokernel $\mathrm{cok}(P(X_{n}))$ of $P(X_{n})$ converges
to the distribution given by a finite product of some explicit measures that
resemble Cohen--Lenstra measures. For example, the random matrix $X_{n}$ can be
taken as a Haar-random matrix or a uniformly random $(0,1)$-matrix. We consider
the distribution of $\mathrm{cok}(P(X_{n}))$ as a distribution of modules over
$\mathbb{Z}_{p}[t]/(P(t))$, which gives us a clearer formulation in comparison
to considering the distribution as that of abelian groups. For the proof, we
first reduce our problem into a problem over $\mathbb{Z}/p^{k}\mathbb{Z}$, for
large enough positive integer $k$, in place of $\mathbb{Z}_{p}$. Then we use a
result of Sawin and Wood to reduce our problem into another problem of
computing the limit of the expected number of surjective
$(\mathbb{Z}/p^{k}\mathbb{Z})[t]/(P(t))$-linear maps from
$\mathrm{cok}(P(X_{n}))$ modulo $p^{k}$ to a fixed finite size
$(\mathbb{Z}/p^{k}\mathbb{Z})[t]/(P(t))$-module $G$. To estimate the expected
number and compute the desired limit, we carefully adopt subtle techniques
developed by Wood, which were originally used to compute the asymptotic
distribution of the $p$-part of the sandpile group of a random graph.


  There are the results of gamma-ray bursts observations obtained using the
MASTER robotic telescope in 2007 - 2009. We observed 20 error-boxes of
gamma-ray bursts this period.The limits on their optical brightnesses have been
derived. There are 5 prompt observations among them, obtained at our very wide
field cameras. Also we present the results of the earliest observations of the
optical emission of the gamma-ray bursts GRB 050824 and GRB 060926.


  Despite the enormous theoretical and experimental progress made so far in
quantum key distribution (QKD), the security of most existing QKD
implementations is not rigorously established yet. A critical obstacle is that
almost all existing security proofs make ideal assumptions on the QKD devices.
Problematically, such assumptions are hard to satisfy in the experiments, and
therefore it is not obvious how to apply such security proofs to practical QKD
systems. Fortunately, any imperfections and security-loopholes in the
measurement devices can be perfectly closed by measurement-device-independent
QKD (MDI-QKD), and thus we only need to consider how to secure the source
devices. Among imperfections in the source devices, correlations between the
sending pulses are one of the principal problems. In this paper, we consider a
setting-choice-independent correlation (SCIC) framework in which the sending
pulses can present arbitrary correlations but they are independent of the
previous setting choices such as the bit, the basis and the intensity settings.
Within the framework of SCIC, we consider the dominant fluctuations of the
sending states, such as the relative phases and the intensities, and provide a
self-contained information theoretic security proof for the loss-tolerant QKD
protocol in the finite-key regime. We demonstrate the feasibility of secure
quantum communication within a reasonable number of pulses sent, and thus we
are convinced that our work constitutes a crucial step toward guaranteeing
implementation security of QKD.


  We report a search for CP violation in the decay \tau- -> \pi - \K^0_S (>= 0
\pi 0) \nu_\tau\ using a dataset of 437 million \tau\ lepton pairs,
corresponding to an integrated luminosity of 476 fb^{-1}, collected with the
BABAR detector at the PEP-II asymmetric energy e+e- storage rings. The
CP-violating decay-rate asymmetry is determined to be (-0.45 +/- 0.24 +/-
0.11)%, approximately three standard deviations from the Standard Model
prediction of (0.33 +/- 0.01)%.


  In many quantum technologies adiabatic processes are used for coherent
quantum state operations, offering inherent robustness to errors in the control
parameters. The main limitation is the long operation time resulting from the
requirement of adiabaticity. The superadiabatic method allows for faster
operation, by applying counterdiabatic driving that corrects for excitations
resulting from the violation of the adiabatic condition. In this article we
show how to construct the counterdiabatic Hamiltonian in a system with
forbidden transitions by using two-photon processes and how to correct for the
resulting time-dependent ac-Stark shifts in order to enable population transfer
with unit fidelity. We further demonstrate that superadiabatic stimulated Raman
passage can realize a robust unitary NOT-gate between the ground state and the
second excited state of a three-level system. The results can be readily
applied to a three-level transmon with the ladder energy level structure.


  In the last decade it became clear that methods and techniques based on
supersymmetry provide deep insights in quantum chromodynamics and other
supersymmetric and non-supersymmetric gauge theories at strong coupling. In
this review we summarize major advances in the critical
(Bogomol'nyi-Prasad-Sommerfeld-saturated, BPS for short) solitons in
supersymmetric theories and their implications for understanding basic
dynamical regularities of non-supersymmetric theories. After a brief
introduction in the theory of critical solitons (including a historical
introduction) we focus on three topics: (i) non-Abelian strings in N=2 and
confined monopoles; (ii) reducing the level of supersymmetry; and (iii) domain
walls as D brane prototypes.


  Non-Gaussianity may exist in the CDM isocurvature perturbation. We provide
general expressions for the bispectrum and trispectrum of both adiabatic and
isocurvature pertubations. We apply our result to the QCD axion case, and found
a consistency relation between the coefficients of the bispectrum and
trispectrum : tau_{NL}^(iso)~10^3 [f_{NL}^(iso)]^{4/3}, if the axion is
dominantly produced by quantum fluctuation. Thus future observations of the
trispectrum, as well as the bispectrum, will be important for understanding the
origin of the CDM and baryon asymmetry.


  We consider massive Dirac equations on asymptotically static spacetimes with
a Cauchy surface of bounded geometry. We prove that the associated quantized
Dirac field admits in and out states, which are asymptotic vacuum states when
some time coordinate tends to $\mp\infty$. We also show that the in /out states
are Hadamard states.(new version with some typos corrected).


  Eulerian cosmological codes are especially suited to properly describe the
low density regions. This property makes this class of codes excellent tools to
study the formation and evolution of cosmic voids. Following such ideas, we
present the results of an Eulerian adaptive mesh refinement (AMR)
hydrodynamical and N-body simulation, that contrary to the common practice, has
been designed to refine the computational grid in the underdense regions of the
simulated volume. Thus, the void regions are better described due to the
combined effect of the Eulerian character of the numerical technique and the
use of high numerical resolution from the AMR approach. To analyse the outcome
of this simulation, we have constructed a new void finder optimally suited to
find the hierarchy of voids in AMR simulations. The algorithm identifies voids
starting from the cells with least density and highest velocity divergence and
then expanding the underdense volume until reaching the void walls, defined
from the steepness of the density gradient. At redshift z=0, in a cosmological
box of comoving side length 100 Mpc/h, we identify hundreds of voids with sizes
up to 17 Mpc/h and typical density contrast of -0.8, which show a complex
morphology and an intricate hierarchy of nested structures. The analysis of
their mass density profile leads to the conclusion that a universal density
profile can be applied to voids of any size, density, morphology and redshift.


  Federated learning (FL) is a distributed deep learning method which enables
multiple participants, such as mobile phones and IoT devices, to contribute a
neural network model while their private training data remains in local
devices. This distributed approach is promising in the edge computing system
where have a large corpus of decentralized data and require high privacy.
However, unlike the common training dataset, the data distribution of the edge
computing system is imbalanced which will introduce biases in the model
training and cause a decrease in accuracy of federated learning applications.
In this paper, we demonstrate that the imbalanced distributed training data
will cause accuracy degradation in FL. To counter this problem, we build a
self-balancing federated learning framework call Astraea, which alleviates the
imbalances by 1) Global data distribution based data augmentation, and 2)
Mediator based multi-client rescheduling. The proposed framework relieves
global imbalance by runtime data augmentation, and for averaging the local
imbalance, it creates the mediator to reschedule the training of clients based
on Kullback-Leibler divergence (KLD) of their data distribution. Compared with
FedAvg, the state-of-the-art FL algorithm, Astraea shows +5.59% and +5.89%
improvement of top-1 accuracy on the imbalanced EMNIST and imbalanced CINIC-10
datasets, respectively. Meanwhile, the communication traffic of Astraea can be
82% lower than that of FedAvg.


  We refine two results in the paper entitled "Sofic mean dimension" by Hanfeng
Li, improving two inequalities with two equalities, respectively, for sofic
mean dimension of typical actions. On the one hand, we study sofic mean
dimension of full shifts, for which, Li provided an upper bound which however
is not optimal. We prove a more delicate estimate from above, which is optimal
for sofic mean dimension of full shifts over arbitrary alphabets (i.e. compact
metrizable spaces). Our refinement, together with the techniques (in relation
to an estimate from below) in the paper entitled "Mean dimension of full
shifts" by Masaki Tsukamoto, eventually allows us to get the exact value of
sofic mean dimension of full shifts over any finite dimensional compact
metrizable spaces. On the other hand, we investigate finite group actions. In
contrast to the case that the acting group is infinite (and amenable), Li
showed that if a finite group acts continuously on a finite dimensional compact
metrizable space, then sofic mean dimension may be different from (strictly
less than) the classical (i.e. amenable) mean dimension (an explicitly known
value in this case). We strengthen this result by proving a sharp lower bound,
which, combining with the upper bound, gives the exact value of sofic mean
dimension for all the actions of finite groups on finite dimensional compact
metrizable spaces. Furthermore, this equality leads to a satisfactory
comparison theorem for those actions, deciding when sofic mean dimension would
coincide with classical mean dimension. Moreover, our two results, in
particular, verify for a typical class of sofic group actions that sofic mean
dimension does not depend on sofic approximation sequences.


  In data-driven SHM, the signals recorded from systems in operation can be
noisy and incomplete. Data corresponding to each of the operational,
environmental, and damage states are rarely available a priori; furthermore,
labelling to describe the measurements is often unavailable. In consequence,
the algorithms used to implement SHM should be robust and adaptive, while
accommodating for missing information in the training-data -- such that new
information can be included if it becomes available. By reviewing novel
techniques for statistical learning (introduced in previous work), it is argued
that probabilistic algorithms offer a natural solution to the modelling of SHM
data in practice. In three case-studies, probabilistic methods are adapted for
applications to SHM signals -- including semi-supervised learning, active
learning, and multi-task learning.


  The atomic structure of Ni64.5Zr35.5 metallic glass has been investigated by
molecular dynamics (MD) simulations. The calculated structure factors from the
MD glassy sample at room temperature agree well with the X-ray diffraction
(XRD) and neutron diffraction (ND) experimental data. Using the pairwise
cluster alignment and clique analysis methods, we show that there are three
types dominant short-range order (SRO) motifs around Ni atoms in the glass
sample of Ni64.5Zr35.5, i.e., Mixed-Icosahedron(ICO)-Cube, Twined-Cube and
icosahedron-like clusters. Furthermore, chemical order and medium-range order
(MRO) analysis show that the Mixed-ICO-Cube and Twined-Cube clusters exhibit
the characteristics of the crystalline B2 phase. Our simulation results suggest
that the weak glass-forming ability (GFA) of Ni64.5Zr35.5 can be attributed to
the competition between the glass forming ICO SRO and the crystalline
Mixed-ICO-Cube and Twined-Cube motifs.


  An important aspect of astrophysical MHD turbulence research is developing
diagnostics to connect simulations with the observable universe. Turbulent
systems are by definition structurally complex in all fluid variables (density,
velocity, and magnetic field), such that they must be described statistically.
By developing and applying diagnostic tools to simulation data, it is possible
to interpret empirical laws for the statistical properties of observed systems
in terms of fundamental dynamical processes, and to identify and calibrate
robust probes of physical parameters that cannot be measured directly. Using
several different examples, I describe how structural diagnostic analyses have
already yielded significant insights into the nature of turbulent molecular
clouds. I review results from several different groups, and discuss directions
for future diagnostics to enhance our understanding of cloud structure and
constrain models of the evolutionary course that governs star formation.


  We study all-charm tetraquarks in the front form of Hamiltonian dynamics
using the many-body basis function approach known as basis light-front
quantization. The model Hamiltonian contains transverse and longitudinal
confining potentials and a one-gluon-exchange effective potential. We calculate
masses of two-charm-two-anticharm states focusing on the lowest state. We also
calculate two-quark and four-quark estimates of meson-meson breakup threshold.
The results suggest that the lowest two-charm-two-anticharm state is not a
tightly bound tetraquark. We discuss implications of the cluster decomposition
principle for theories formulated on the light front and present our treatment
of identical particles together with color-singlet restrictions on the space of
quantum states.


  In many professional sports leagues, teams from opposing leagues/conferences
compete against one another, playing inter-league games. This is an example of
a bipartite tournament. In this paper, we consider the problem of reducing the
total travel distance of bipartite tournaments, by analyzing inter-league
scheduling from the perspective of discrete optimization. This research has
natural applications to sports scheduling, especially for leagues such as the
National Basketball Association (NBA) where teams must travel long distances
across North America to play all their games, thus consuming much time, money,
and greenhouse gas emissions. We introduce the Bipartite Traveling Tournament
Problem (BTTP), the inter-league variant of the well-studied Traveling
Tournament Problem. We prove that the 2n-team BTTP is NP-complete, but for
small values of n, a distance-optimal inter-league schedule can be generated
from an algorithm based on minimum-weight 4-cycle-covers. We apply our
theoretical results to the 12-team Nippon Professional Baseball (NPB) league in
Japan, producing a provably-optimal schedule requiring 42950 kilometres of
total team travel, a 16% reduction compared to the actual distance traveled by
these teams during the 2010 NPB season. We also develop a nearly-optimal
inter-league tournament for the 30-team NBA league, just 3.8% higher than the
trivial theoretical lower bound.


  We collect and analyze the data for working time, life expectancy, and the
pair output and infrastructure of industrializing nations. During S-functional
recovery from disaster the pair's time shifts yield 25 years for the
infrastructure's physical lifetime. At G7 level the per capita outputs converge
and the time shifts identify a heritable quantity with a reaction time of 62
years. It seems to control demand and the spare time required for enjoying G7
affluence. The sum of spare and working time is fixed by the universal flow of
time. This yields analytic solutions for equilibrium, recovery, and long-term
evolution for all six variables with biologically stabilized parameters.


  Alloy disorder in II-VI diluted magnetic semiconductors (DMS) is typically
reduced when the local magnetic spins align in an applied magnetic field. An
important and untested expectation of current models of alloy disorder,
however, is that alloy fluctuations in many DMS compounds should increase again
in very large magnetic fields of order 100 tesla. Here we measure the disorder
potential in a Zn$_{.70}$Cd$_{.22}$Mn$_{.08}$Se quantum well via the low
temperature photoluminescence linewidth, using a new magnet system to 89 T.
Above 70 T, the linewidth is observed to increase again, in accord with a
simple model of alloy disorder.


  We demonstrate all-optical demultiplexing at 160 Gigabits per second in the
C-band, based on nonlinear optics using four-wave mixing (FWM) in a silicon
nanowire. We achieve error-free operation with a penalty of ~ 3.9dB.


  Due to color confinement, hadrons are inseparable when studying strong
interactions. The paper mainly studies the scattering in the background field,
especially the scattering of quarks in the hadronic background field. We
discovered that the coupling constant within the background field is made up of
the distribution function of background field. The finding provides a
foundational comprehension of coupling constants, which significantly
contributes to our understanding of running coupling constant and the
perturbative nature of theory.


  We observed two secondary eclipses of the exoplanet WASP-12b using the
Infrared Array Camera on the Spitzer Space Telescope. The close proximity of
WASP-12b to its G-type star results in extreme tidal forces capable of inducing
apsidal precession with a period as short as a few decades. This precession
would be measurable if the orbit had a significant eccentricity, leading to an
estimate of the tidal Love number and an assessment of the degree of central
concentration in the planetary interior. An initial ground-based secondary
eclipse phase reported by Lopez-Morales et al. (0.510 +/- 0.002) implied
eccentricity at the 4.5 sigma level. The spectroscopic orbit of Hebb et al. has
eccentricity 0.049 +/- 0.015, a 3 sigma result, implying an eclipse phase of
0.509 +/- 0.007. However, there is a well documented tendency of spectroscopic
data to overestimate small eccentricities. Our eclipse phases are 0.5010 +/-
0.0006 (3.6 and 5.8 microns) and 0.5006 +/- 0.0007 (4.5 and 8.0 microns). An
unlikely orbital precession scenario invoking an alignment of the orbit during
the Spitzer observations could have explained this apparent discrepancy, but
the final eclipse phase of Lopez-Morales et al. (0.510 -0.006 / +0.007) is
consistent with a circular orbit at better than 2 sigma. An orbit fit to all
the available transit, eclipse, and radial-velocity data indicates precession
at <1 sigma; a non-precessing solution fits better. We also comment on analysis
and reporting for Spitzer exoplanet data in light of recent re-analyses.


  Extreme environmental phenomena such as major precipitation events manifestly
exhibit spatial dependence. Max-stable processes are a class of
asymptotically-justified models that are capable of representing spatial
dependence among extreme values. While these models satisfy modeling
requirements, they are limited in their utility because their corresponding
joint likelihoods are unknown for more than a trivial number of spatial
locations, preventing, in particular, Bayesian analyses. In this paper, we
propose a new random effects model to account for spatial dependence. We show
that our specification of the random effect distribution leads to a max-stable
process that has the popular Gaussian extreme value process (GEVP) as a
limiting case. The proposed model is used to analyze the yearly maximum
precipitation from a regional climate model.


  We report numerical results which show the achievement of net transport of
self-propelled particles (SPP) in the presence of a two-dimensional regular
array of convex, either symmetric or asymmetric, rigid obstacles. The repulsive
inter-particle (soft disks) and particle-obstacle interactions present no
alignment rule. We find that SPP present a vortex-type motion around convex
symmetric obstacles even in the absence of hydrodynamic effects. Such a motion
is not observed for a single SPP, but is a consequence of the collective motion
of SPP around the obstacles. An steady particle current is spontaneously
established in an array of non-symmetric convex obstacle (which presents no
cavity in which particles may be trapped in), and in the absence of an external
field. Our results are mainly a consequence of the tendency of the
self-propelled particles to attach to solid surfaces.


  We present results for the photon spectrum emitted in non-linear Compton
scattering of pulsed ultra-strong laser fields off relativistic electrons for
intensities up to $a_0\gtrsim 100$ and pulse lengths of a few laser cycles. At
ultrahigh laser intensity, it is appropriate to average over the sub-
structures of the differential photon spectrum. Supplementing this procedure
with a stationary phase approximation one can evaluate the total emission
probability. We find the photon yield in pulsed fields to be up to a factor of
ten larger than results obtained from a monochromatic wave calculation.


  Chimera states for the one-dimensional array of nonlocally coupled phase
oscillators in the continuum limit are assumed to be stationary states in most
studies, but a few studies report the existence of breathing chimera states. We
focus on multichimera states with two coherent and incoherent regions, and
numerically demonstrate that breathing multichimera states, whose global order
parameter oscillates temporally, can appear. Moreover, we show that the system
exhibits a Hopf bifurcation from a stationary multichimera to a breathing one
by the linear stability analysis for the stationary multichimera.


  This study is aimed at investigating the physicochemical properties of low
rank Nigerian coals. The coal samples were examined using bomb calorimetry,
ultimate and proximate analyses to determine the heating value, elemental
composition and physicochemical properties. The calorific values of the coals
were; 23.74 MJ/kg for GMG; 27.34 MJ/kg for SKJ and 30.52 MJ/kg for AFZ. The
results of elemental analysis showed high C, H, O and low N, and S content for
the coals. The GMG coal displayed the lowest N, and S values emphasizing its
low pollutant emission potential. The highest VM (51.16 %) and M (5.28 %)
content was observed for GMG; AFZ coal displayed the highest ash content at
30.99 %; and SKJ the highest FC content. Consequently, the reactivity and
maturity of the low rank Nigerian coals investigated increases in the order;
GMG > SKJ > AFZ.
  Keywords: Physicochemical, Characterization, Low rank, Nigeria, Coal, Energy


  We introduce a novel approach for scalable domain adaptation in cloud
robotics scenarios where robots rely on third-party AI inference services
powered by large pre-trained deep neural networks. Our method is based on a
downstream proposal-refinement stage running locally on the robots, exploiting
a new lightweight DNN architecture, R2SNet. This architecture aims to mitigate
performance degradation from domain shifts by adapting the object detection
process to the target environment, focusing on relabeling, rescoring, and
suppression of bounding-box proposals. Our method allows for local execution on
robots, addressing the scalability challenges of domain adaptation without
incurring significant computational costs. Real-world results on mobile service
robots performing door detection show the effectiveness of the proposed method
in achieving scalable domain adaptation.


  The Heisenberg product is an associative product defined on symmetric
functions which interpolates between the usual product and the Kronecker
product. In 1938, Murnaghan discovered that the Kronecker product of two Schur
functions stabilizes. We prove an analogous result for the Heisenberg product
of Schur functions.


  We investigate test particle trajectories in warped spacetimes with a thick
brane warp factor, a cosmological on--brane line element and a time dependent
extra dimension. The geodesic equations are reduced to a first order autonomous
dynamical system. Using analytical methods, we arrive at some useful general
conclusions regarding possible trajectories. Oscillatory motion, suggesting
confinement about the location of the thick brane, arises for a growing warp
factor. On the other hand, we find runaway trajectories (exponential-like) for
a decaying warp factor. Variations of the extra dimensional scale factor yield
certain quantitative differences. Results obtained from explicit numerical
evaluations match well with the qualitative conclusions obtained from the
dynamical systems analysis.


  Given a very ample line bundle on a smooth projective variety, the variation
of Hodge structure associated to the universal family of hyperplane sections
can be thought of as a $D$-module with action generated by the Gauss-Manin
connection. The decomposition theorem for a projective morphism and results
similar to the Lefschetz hyperplane theorem tell us that the only nontrivial
part of this VHS occurs in the middle degree corresponding to the vanishing
cohomology of the hyperplane sections. We use Nori's connectivity theorem to
give an explicit description of the cohomology sheaves of the de Rham complex
of this $D$-module in terms of the vanishing cohomology of the original
variety.


  This is largely an exposition article that expands the author's talk at the
Xiamen International Conference on Geometric Analysis in June 2021. We first
survey the author's joint work with Jiyuan Han on the Yau-Tian-Donaldson (YTD)
conjecture for $g$-weighted K\"{a}hler-Ricci solitons ($g$-solitons). We then
review recent works of Apostolov-Canderbank-Jubert-Lahdili which establish a
connection between a particular $g$-soliton equation with Ricci-flat K\"{a}hler
cone metrics (or equivalently Sasaki-Einstein metrics). The main interest in
this connection is the transformation of a possibly irregular Sasaki-Einstein
metric to a particular $g$-soliton equation on any quasi-regular quotient. We
will revisit this transformation by understanding how the corresponding
transversal complex Monge-Amp\`{e}re equations are transformed under the
deformation of Reeb vector fields. Finally we explain how this
PDE/pluripotential point of view allows one to prove the YTD conjecture for
general Fano cones by combining the YTD conjecture for $g$-solitons on log Fano
pairs and the above transformation.


  We describe some interesting graded rings which are generated by degree-3
elements inside the Sklyanin algebra S, and prove that they have many good
properties. Geometrically, these rings R correspond to blowups of the Sklyanin
P^2 at 7 or fewer points. We show that the rings R are exactly those
degree-3-generated subrings of S which are maximal orders in the quotient ring
of the 3-Veronese of S.


  The energy source has remained to be the great mystery in understanding of
the gamma-ray bursts (GRBs) if the events are placed at cosmological distances
as indicated by a number of recent observations. The currently popular models
include (1)the merger of two neutron stars or a neutron star and a black hole
binary and (2)the hypernova scenario of the collapse of a massive member in a
close binary. Since a neutron star will inevitably collapse into a black hole
if its mass exceeds the limit $M_{max}\approx3M_{\odot}$, releasing a total
binding gravitational energy of $\sim10^{54}$ erg, we explore semi-empirically
the possibility of attributing the energy source of GRB to the accretion-
induced collapse of a neutron star (AICNS) in a massive X-ray binary system
consisting of a neutron star and a type O/B companion. This happens because a
significant mass flow of $\sim10^{-3}$--$10^{-4}M_{\odot}$ yr$^{-1}$ may be
transferred onto the neutron star through the Roche-lobe overflow and primarily
during the spiral-in phase when it plunges into the envelope of the companion,
which may eventually lead to the AICNS before the neutron star merges with the
core of the companion. In this scenario, a ``dirty'' fireball with a moderate
amount of beaming is naturally expected because of the nonuniformity of the
stellar matter surrounding the explosion inside the companion, and a small
fraction ($\sim0.1%$) of the energy is sufficient to create the observed GRBs.
In addition, the bulk of the ejecting matter of the companion star with a
relatively slow expansion rate may act as the afterglow. Assuming a
non-evolutionary model for galaxies, we estimate that the birthrate of the
AICNS events is about 2 per day within a volume to redshift $z=1$ for an
$\Omega_0=1$ universe, consistent with the reported GRB rate.


  (Abridged) We show that sizeable fractions of incident ionizing radiation
from stochastic astrophysical sources can be redistributed to biologically and
chemically important UV wavelengths, a significant fraction of which can reach
the surface. This redistribution is mediated by secondary electrons, resulting
from Compton scattering and X-ray photoabsorption, with energies low enough to
excite atmospheric molecules and atoms, resulting in a rich aurora-like
spectrum. We calculate the fraction of energy redistributed into biologically
and chemically important wavelength regions for spectra characteristic of
stellar flares and supernovae using a Monte-Carlo transport code written for
this problem and then estimate the fraction of this energy that is transmitted
from the atmospheric altitudes of redistribution to the surface for a few
illustrative cases. Redistributed fractions are found to be of order 1%, even
in the presence of an ozone shield. This result implies that planetary
organisms will be subject to mutationally significant, if intermittent,
fluences of UV-B and harder radiation even in the presence of a narrow-band UV
shield like ozone. We also calculate the surficial transmitted fraction of
ionizing radiation and redistributed ultraviolet radiation for two illustrative
evolving Mars atmospheres whose initial surface pressures were 1 bar. Our
results suggest that coding organisms on planets orbiting low-mass stars (and
on the early Earth) may evolve very differently than on contemporary Earth,
with diversity and evolutionary rate controlled by a stochastically varying
mutation rate and frequent hypermutation episodes.


  Matrix factorization (MF) has been widely used to discover the low-rank
structure and to predict the missing entries of data matrix. In many real-world
learning systems, the data matrix can be very high-dimensional but sparse. This
poses an imbalanced learning problem, since the scale of missing entries is
usually much larger than that of observed entries, but they cannot be ignored
due to the valuable negative signal. For efficiency concern, existing work
typically applies a uniform weight on missing entries to allow a fast learning
algorithm. However, this simplification will decrease modeling fidelity,
resulting in suboptimal performance for downstream applications.
  In this work, we weight the missing data non-uniformly, and more generically,
we allow any weighting strategy on the missing data. To address the efficiency
challenge, we propose a fast learning method, for which the time complexity is
determined by the number of observed entries in the data matrix, rather than
the matrix size. The key idea is two-fold: 1) we apply truncated SVD on the
weight matrix to get a more compact representation of the weights, and 2) we
learn MF parameters with element-wise alternating least squares (eALS) and
memorize the key intermediate variables to avoid repeating computations that
are unnecessary. We conduct extensive experiments on two recommendation
benchmarks, demonstrating the correctness, efficiency, and effectiveness of our
fast eALS method.


  Inference in the presence of outliers is an important field of research as
outliers are ubiquitous and may arise across a variety of problems and domains.
Bayesian optimization is method that heavily relies on probabilistic inference.
This allows outstanding sample efficiency because the probabilistic machinery
provides a memory of the whole optimization process. However, that virtue
becomes a disadvantage when the memory is populated with outliers, inducing
bias in the estimation. In this paper, we present an empirical evaluation of
Bayesian optimization methods in the presence of outliers. The empirical
evidence shows that Bayesian optimization with robust regression often produces
suboptimal results. We then propose a new algorithm which combines robust
regression (a Gaussian process with Student-t likelihood) with outlier
diagnostics to classify data points as outliers or inliers. By using an
scheduler for the classification of outliers, our method is more efficient and
has better convergence over the standard robust regression. Furthermore, we
show that even in controlled situations with no expected outliers, our method
is able to produce better results.


  In this paper we introduce a new neural network architecture designed to use
in embedded vision applications. It merges the best working practices of
network architectures like MobileNets and ResNets to our named RMNet
architecture. We also focus on key moments of building mobile architectures to
carry out in the limited computation budget. Additionally, to demonstrate the
effectiveness of our architecture we evaluate the RMNet backbone on Person
Re-identification task. The proposed approach is in top 3 of state of the art
solutions on Market-1501 challenge, however our method significantly
outperforms them by the inference speed.


  We use the Belle data on the $K^- p$ mass distribution of the $\Lambda_c^+
\to p K^- \pi^+$ reaction near the $\eta \Lambda$ threshold to determine the
$\eta \Lambda $ scattering length and effective range. We show that from these
data alone we can determine the value of $a$ with better precision than so far
determined, and the value of $r_0$ for the first time. The addition of the $K^-
p \to \eta \Lambda$ data allows us to improve the precision of these
magnitudes, with errors smaller than $15\%$. We also determine with high
precision the pole position of the $\Lambda(1670)$.


  Near-Earth small-body mission targets 162173 Ryugu, 101955 Bennu, and 25143
Itokawa produce gravity fields around 4 orders of magnitude below that of Earth
and their irregular shapes, combined with rotational effects produce varying
surface potentials. Still, we observe familiar geologic textures and landforms
that are the result of the granular physical processes that take place on their
surfaces. The nature of these landforms, however, their origins, and how these
surfaces react to interrogation by probes, landers, rovers, and penetrators,
remain largely unknown, and therefore landing on an asteroid and manipulating
its surface material remains a daunting challenge. The AOSAT+ design is a 12U
CubeSat that will be in Low-Earth Orbit (LEO) and that will operate as a
spinning on-orbit centrifuge. Part of this 12U CubeSat will contain a
laboratory that will recreate asteroid surface conditions using crushed
meteorite as a regolith proxy. The spinning of the laboratory will simulate the
surface gravity of asteroids 2 km and smaller. The result is a bed of realistic
regolith, the environment that landers and diggers and maybe astronauts will
interact with. A crucial component of this mission involves the reproduction of
the experimental results in numerical simulation in order to extract the
material parameters of the regolith and its behavior in a sustained, very low
but nonzero-gravity environment.


  A tunneling spectroscopy study is presented of superconducting MoN and
Nb$_{0.8}$Ti$_{0.2}$N thin films grown by atomic layer deposition (ALD). The
films exhibited a superconducting gap of 2meV and 2.4meV respectively with a
corresponding critical temperature of 11.5K and 13.4K, among the highest
reported $T_c$ values achieved by the ALD technique. Tunnel junctions were
obtained using a mechanical contact method with a Au tip. While the native
oxides of these films provided poor tunnel barriers, high quality tunnel
junctions with low zero bias conductance (below $\sim$10%) were obtained using
an artificial tunnel barrier of Al$_2$O$_3$ on the film's surface grown
$\textit{ex situ}$ by ALD. We find a large critical current density on the
order of $4\times 10^6$A/cm$^2$ at $T=0.8T_c$ for a 60nm MoN film and
demonstrate conformal coating capabilities of ALD onto high aspect ratio
geometries. These results suggest the ALD technique offers significant promise
for thin film superconducting device applications.


  Using Levi-Civita's theory of ideal fluids, we derive the complex Korteweg-de
Vries (KdV) equation, describing the complex velocity of a shallow fluid up to
first order. We use perturbation theory, and the long wave, slowly varying
velocity approximations for shallow water. The complex KdV equation describes
the nontrivial dynamics of all water particles from the surface to the bottom
of the water layer. A crucial new step made in our work is the proof that a
natural consequence of the complex KdV theory is that the wave elevation is
described by the real KdV equation. The complex KdV approach in the theory of
shallow fluids is thus more fundamental than the one based on the real KdV
equation. We demonstrate how it allows direct calculation of the particle
trajectories at any point of the fluid, and that these results agree well with
numerical simulations of other authors.


  Strongly correlated materials that exhibit an insulator-metal transition are
key candidates in the search for new computing platforms. Understanding the
pathways and timescales underlying the electrically-driven insulator-metal
transition is crucial for uncovering the fundamental limits of device
operation. Using stroboscopic electron diffraction, we perform synchronized
time-resolved measurements of atomic motions and electronic transport in
operating vanadium dioxide switches. We discover an electrically-triggered,
isostructural state that forms transiently on microsecond timescales,
stabilized by local heterogeneities and interfacial interactions between the
equilibrium phases. This metastable phase bears striking similarity to that
formed under photoexcitation within picoseconds, suggesting a universal
transformation pathway across eight orders of magnitude of timescale. Our
results establish a new route for uncovering non-equilibrium and metastable
phases in correlated materials, and open avenues for engineering novel
dynamical behavior in nanoelectronics.


  We investigate a generalized Lagrange multiplier system in a Banach space,
called a mixed variational-hemivariational inequality (MVHVI, for short), which
contains a hemivariational inequality and a variational inequality. First, we
employ the Minty technique and a monotonicity argument to establish an
equivalence theorem, which provides three different equivalent formulations of
the inequality problem. Without compactness for one of operators in the
problem, a general existence theorem for (MVHVI) is proved by using the
Fan-Knaster-Kuratowski-Mazurkiewicz principle combined with methods of
nonsmooth analysis. Furthermore, we demonstrate several crucial properties of
the solution set to (MVHVI) which include boundedness, convexity, weak
closedness, and continuity. Finally, a uniqueness result with respect to the
first component of the solution for the inequality problem is proved by using
the Ladyzhenskaya-Babuska-Brezzi (LBB) condition. All results are obtained in a
general functional framework in reflexive Banach spaces.


  The silhouette cast by the horizon of the supermassive black hole in M87 can
now be resolved with the emerging millimeter very-long baseline interferometry
(VLBI) capability. Despite being ~2000 times farther away than SgrA* (the
supermassive black hole at the center of the Milky-Way and the primary target
for horizon-scale imaging), M87's much larger black hole mass results in a
horizon angular scale roughly half that of SgrA*'s, providing another practical
target for direct imaging. However, unlike SgrA*, M87 exhibits a powerful radio
jet, providing an opportunity to study jet formation physics on horizon scales.
We employ a simple, qualitatively correct force-free jet model to explore the
expected high-resolution images of M87 at wavelengths of 1.3mm and 0.87mm
(230GHz and 345GHz), for a variety of jet parameters. We show that future VLBI
data will be able to constrain the size of the jet footprint, the jet
collimation rate, and the black hole spin. Polarization will further probe the
structure of the jet's magnetic field and its effect on the emitting gas.
Horizon-scale imaging of M87 and SgrA* will enable for the first time the
empirical exploration of the relationship between the mass and spin of a black
hole and the characteristics of the gas inflow/outflow around it.


  Attention mechanisms take an expectation of a data representation with
respect to probability weights. This creates summary statistics that focus on
important features. Recently, (Martins et al. 2020, 2021) proposed continuous
attention mechanisms, focusing on unimodal attention densities from the
exponential and deformed exponential families: the latter has sparse support.
(Farinhas et al. 2021) extended this to use Gaussian mixture attention
densities, which are a flexible class with dense support. In this paper, we
extend this to two general flexible classes: kernel exponential families and
our new sparse counterpart kernel deformed exponential families. Theoretically,
we show new existence results for both kernel exponential and deformed
exponential families, and that the deformed case has similar approximation
capabilities to kernel exponential families. Experiments show that kernel
deformed exponential families can attend to multiple compact regions of the
data domain.


  Quantum-gravity corrections to the probability of emission of a particle from
a black hole in the Parikh-Wilczek tunneling framework are studied. We consider
the effects of zero-point quantum fluctuations of the metric on the emission
probability for a tunneling shell. Quantum properties of the geometry are
responsible for the formation of a "quantum egosphere" whose effects on the
emission probability can be related to the emergence of a logarithmic
correction to the Bekenstein-Hawking entropy-area formula.


  Aims: Today, large ground-based instruments, like VISIR on the VLT, providing
diffraction-limited (about 0.3 arcsec) images in the mid-infrared where strong
PAH features appear enable us to see the flaring structure of the disks around
Herbig Ae stars.
  Although great progress has been made in modelling the disk with radiative
transfer models able to reproduce the spectral energy distribution (SED) of
Herbig Ae stars, the constraints brought by images have not been yet fully
exploited. Here, we are interested in checking if these new observational
imaging constraints can be accounted for by predictions based on existing
models of passive centrally irradiated hydrostatic disks made to fit the SEDs
of the Herbig Ae stars.
  Methods: The images taken by VISIR in the 8.6 and 11.3 microns aromatic
features reveal a large flaring disk around HD97048 inclined to the line of
sight. In order to analyse the spatial distribution of these data, we use a
disk model which includes the most up to date understanding of disk structure
and physics around Herbig Ae stars with grains in thermal equilibrium in
addition to transiently-heated PAHs.
  Results: We compare the observed spatial distribution of the PAH emission
feature and the adjacent continuum emission with predictions based on existing
full disk models. Both SED and spatial distribution are in very good agreement
with the model predictions for common disk parameters.
  Conclusions: We take the general agreement between observations and
predictions as a strong support for the physical pictures underlying our flared
disk model.


  Foundation models have impressive performance and generalization capabilities
across a wide range of applications. The increasing size of the models
introduces great challenges for the training. Tensor parallelism is a critical
technique that is currently used in almost all foundation model training and
has a significant impact on overall training performance. However, current
tensor parallelism in machine learning frameworks misses optimization
opportunities in fitting various interconnection topologies. In this work, we
present ATP, an adaptive tensor parallelism framework for foundation models,
which can automatically select the optimal parallel strategy on different
interconnections. We propose column- and row-first tensor parallelism based on
2D device meshes and construct a search space. Combined with the hierarchical
communication matrix, ATP can identify the optimal strategy in the search
space. We also propose chunk-based overlapping to reduce communication
overhead. Our evaluations show ATP consistently outperforms the
state-of-the-art approaches for various model sizes and interconnects,
achieving end-to-end training performance improvements of up to 37-64% on
specific interconnects. Based on our theoretical model, the communication
overhead of ATP decreases with scaling, indicating a qualitative leap forward.


  In part I, spectral moments and kurtosis were established as parameters in
analytic models of correlation and spectral density functions for dynamic
reverberation fields. In this part II, several practical limitations affecting
the accuracy of estimating these parameters from measured stir sweep data are
investigated. For sampled fields, the contributions of finite differencing and
aliasing are evaluated. Finite differencing results in a negative bias that
depends, to leading order, quadratically on the product of the sampling time
interval and the stir bandwidth. Numerical estimates of moments extracted
directly from sampled stir sweeps show good agreement with values obtained by
an autocovariance method. The effects of data decimation and noise-to-stir
ratios of RMS amplitudes are determined and experimentally verified. In
addition, the dependencies on the noise-to-stir-bandwidth ratio, EMI, and
unstirred energy are characterized.


  Whether to attract viewer attention to a particular object, give the
impression of depth or simply reproduce human-like scene perception, shallow
depth of field images are used extensively by professional and amateur
photographers alike. To this end, high quality optical systems are used in DSLR
cameras to focus on a specific depth plane while producing visually pleasing
bokeh. We propose a physically motivated pipeline to mimic this effect from
all-in-focus stereo images, typically retrieved by mobile cameras. It is
capable to change the focal plane a posteriori at 76 FPS on KITTI images to
enable real-time applications. As our portmanteau suggests, SteReFo
interrelates stereo-based depth estimation and refocusing efficiently. In
contrast to other approaches, our pipeline is simultaneously fully
differentiable, physically motivated, and agnostic to scene content. It also
enables computational video focus tracking for moving objects in addition to
refocusing of static images. We evaluate our approach on the publicly available
datasets SceneFlow, KITTI, CityScapes and quantify the quality of architectural
changes.


  Krylov subspace recycling is a powerful tool for solving long series of
large, sparse linear systems that change slowly. In PDE constrained shape
optimization, these appear naturally, as hundreds or more optimization steps
are needed with only small changes in the geometry. In this setting, however,
applying Krylov subspace recycling can be difficult. As the geometry evolves,
so does the finite element mesh, especially if re-meshing is needed. As a
result, the number of algebraic degrees of freedom in the system may change
from one optimization step to the next, and with it the size of the finite
element system matrix. Changes in the mesh also lead to structural changes in
the matrices. In the case of remeshing, even if the geometry changes only a
little, the corresponding mesh might differ substantially from the previous
one. This prevents any straightforward mapping of the approximate invariant
subspace of the linear system matrix (the focus of recycling in this paper)
from one step to the next; similar problems arise for other selected subspaces.
We present an algorithm for general meshes to map an approximate invariant
subspace of the system matrix for the previous optimization step to an
approximate invariant subspace of the system matrix for the current
optimization step. We exploit the map from coefficient vectors to finite
element functions on the mesh combined with function approximation on the
finite element mesh. In addition, we develop a straightforward warm-start
adaptation of the Krylov-Schur algorithm [G.W. Stewart, SIAM J. Matrix Anal.
Appl. 23, 2001] to improve the approximate invariant subspace at the start of a
new optimization step if needed. We demonstrate the effectiveness of our
approach numerically with several proof of concept studies for a specific
meshing technique.


  In this paper, we consider a fully nonlinear curvature flow of a convex
hypersurface in the Euclidean n-space. This flow involves k-th elementary
symmetric function for principal curvature radii and a function of support
function. Under some appropriate assumptions, we prove the long-time existence
and convergence of this flow. As an application, we give the existence of
smooth solutions to the Orlicz-Christoffel-Minkowski problem.


  We propose a mathematical model for computing drug release from multi-layer
capsules. The diffusion problem in such heterogeneous layer-by-layer composite
medium is described by a system of coupled partial differential equations,
which we solve analytically using separation of variables. In addition to the
conventional interlayer continuous mass transfer boundary conditions, we
consider also the case of finite mass transfer resistance, which corresponds to
the case of a coated capsule. The drug concentration in the core and through
all layers, as well as in the external release medium, is then given in terms
of a Fourier series that we compute numerically to characterize the drug
release mechanism.


  The determination of the speed of travelling fronts of the scalar reaction
diffusion equation has been the subject of much study. Using different
approaches seemingly disconnected variational principles have been established.
The purpose of this work is to show the connection between them. For monostable
reaction terms, we prove that a principle established by Hadeler and Rothe in
1975 and a second one by Benguria and Depassier in 1996 are logically
equivalent, that is, either can be derived from the other. Two variational
principles, formulated for arbitrary reaction terms, are shown to be related by
a suitable change of variables. Finally a variational principle proven for
monostable reaction terms is shown to be a formulation of the two previous ones
in yet another independent variable.