  We investigate the quantum evolution of the universe in the presence of two
types of dark energies. First, we consider the phantom class ($\omega<-1$)
which would be responsible for a super-accelerated cosmic expansion, and then
we apply the procedure to an ordinary $\Lambda>0$ vacuum ($\omega=-1$). This is
done by analytically solving the Wheeler-DeWitt equation with ordering term
(WdW) in the cosmology of Friedmann-Robertson-Walker. In this paper, we find
exact solutions in the scale factor $a$ and the ordering parameter $q$. For
$q=1$ it is shown that the universe has a high probability of evolving from a
big bang singularity. On the other hand, for $q = 0$ the solution indicates
that an initial singularity is unlikely. Instead, the universe has maximal
probability of starting with a finite well-defined size which we compute
explicitly at primordial times. We also study the time evolution of the scale
factor by means of the Hamilton-Jacobi equation and show that an ultimate big
rip singularity emerges explicitly from our solutions. The phantom scenario
thus predicts a dramatic end in which the universe would reach an infinite
scale factor in a finite cosmological time as pointed by Caldwell et al. in a
classical setup. Finally, we solve the WdW equation with ordinary constant dark
energy and show that in this case the universe does not rip apart in a finite
era.


  We study spin transport in nonitinerant one-dimensional quantum spin chains.
Motivated by possible applications in spintronics, we consider rectification
effects in both ferromagnetic and antiferromagnetic systems. We find that the
crucial ingredients in designing a system that displays a nonzero rectification
current are an anisotropy in the exchange interaction of the spin chain
combined with an offset magnetic field. For both ferromagnetic and
antiferromagnetic systems we can exploit the gap in the excitation spectrum
that is created by a bulk anisotropy to obtain a measurable rectification
effect at realistic magnetic fields. For antiferromagnetic systems we also find
that we can achieve a similar effect by introducing a magnetic impurity,
obtained by altering two neighboring bonds in the spin Hamiltonian.


  This paper tackles the problem of making complex resource-constrained
cyber-physical systems (CPS) resilient to sensor anomalies. In particular, we
present a framework for checkpointing and roll-forward recovery of
state-estimates in nonlinear, hierarchical CPS with anomalous sensor data. We
introduce three checkpointing paradigms for ensuring different levels of
checkpointing consistency across the hierarchy. Our framework has algorithms
implementing the consistent paradigm to perform accurate recovery in a
time-efficient manner while managing the tradeoff with system resources and
handling the interplay between diverse anomaly detection systems across the
hierarchy. Further in this work, we detail bounds on the recovered
state-estimate error, maximum tolerable anomaly duration and the
accuracy-resource gap that results from the aforementioned tradeoff. We explore
use-cases for our framework and evaluate it on a case study of a simulated
ground robot to show that it scales to multiple hierarchies and performs better
than an extended Kalman filter (EKF) that does not incorporate a checkpointing
procedure during sensor anomalies. We conclude the work with a discussion on
extending the proposed framework to distributed systems.


  The distribution of trade sizes and trading volumes are investigated based on
the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen
Stock Exchange in the whole year 2003. We observe that the size distribution of
trades for individual stocks exhibits jumps, which is caused by the number
preference of traders when placing orders. We analyze the applicability of the
"$q$-Gamma" function for fitting the distribution by the Cram\'{e}r-von Mises
criterion. The empirical PDFs of trading volumes at different timescales
$\Delta{t}$ ranging from 1 min to 240 min can be well modeled. The
applicability of the $q$-Gamma functions for multiple trades is restricted to
the transaction numbers $\Delta{n}\leqslant8$. We find that all the PDFs have
power-law tails for large volumes. Using careful estimation of the average tail
exponents $\alpha$ of the distribution of trade sizes and trading volumes, we
get $\alpha>2$, well outside the L{\'e}vy regime.


  We argue that the homogeneous distribution of spins in the spin-spiral state
of orthorhombic manganites is deformed by the relativistic spin-orbit
interaction. The thus induced spin-spiral inhomogeneity gives rise to the
ferroelectric response of the purely electronic origin in even-periodic
magnetic structures. The mechanism is generic and explains the appearance of
ferroelectricity in the twofold periodic structure of HoMnO3 as well as the
fourfold periodic structure of TbMnO3. Nevertheless, odd-periodic magnetic
structures preserve the inversion symmetry and thus are not ferroelectric. Our
analysis is based on the low-energy model derived from the first-principles
electronic structure calculations and the Berry-phase formalism for the
electronic polarization.


  EK Draconis (HD 129333: G1.5 V) is a well-known young (50 Myr) solar analog.
In 2012, Hubble Space Telescope returned to EK Dra to follow up a
far-ultraviolet (FUV) SNAPshot visit by Cosmic Origins Spectrograph (COS) two
years earlier. The brief SNAP pointing had found surprisingly redshifted,
impulsively variable subcoronal "hot-line" emission of Si IV 140 nm (T~ 80,000
K). Serendipitously, the 2012 follow-on program witnessed one of the largest
FUV flares ever recorded on a sunlike star, which again displayed strong
redshifts (downflows) of 30-40 km/s, even after compensating for small
systematics in the COS velocity scales, uncovered through a cross-calibration
by Space Telescope Imaging Spectrograph (STIS). The (now reduced, but still
substantial) ~10 km/s hot-line redshifts outside the flaring interval did not
vary with rotational phase, so cannot be caused by "Doppler Imaging" (bright
surface patches near a receding limb). Density diagnostic O IV] 140 nm
multiplet line ratios of EK Dra suggest log(Ne)~ 11, an order of magnitude
larger than in low-activity solar twin Alpha Centauri A, but typical of
densities inferred in large stellar soft X-ray events. The self-similar FUV
hot-line profiles between the flare decay and the subsequent more quiet
periods, and the unchanging but high densities, reinforce a long-standing idea
that the coronae of hyperactive dwarfs are flaring all the time, in a
scale-free way; a "flare-ona" if you will. In this picture, the subsonic
hot-line downflows probably are a byproduct of the post-flare cooling process,
something like "coronal rain" on the Sun. All in all, the new STIS/COS program
documents a complex, energetic, dynamic outer atmosphere of the young sunlike
star.


  In this paper, we discuss Hochschild chain models for some of the string
topology operations. We use these models to simplify the proofs and
computations of some of the results in string topology. Along the way we also
make some new observations. We further discuss how nonnilpotent local level
homology classes with respect to the Chas-Sullivan and the Goresky-Hingston
product detect closed geodesics with optimal index growth rates.


  Despite the presence of strong fluctuations, many turbulent systems such as
Rayleigh-B\'{e}nard convection and Taylor-Couette flow display self-organized
large-scale flow patterns. How do small-scale turbulent fluctuations impact the
emergence and stability of such large-scale flow patterns? Here, we approach
this question conceptually by investigating a class of pattern forming systems
in the presence of random advection by a Kraichnan-Kazantsev velocity field.
Combining tools from pattern formation with statistical theory and simulations,
we show that random advection shifts the onset and the wave number of emergent
patterns. As a simple model for pattern formation in convection, the effects
are demonstrated with a generalized Swift-Hohenberg equation including random
advection. We also discuss the implications of our results for the large-scale
flow of turbulent Rayleigh-B\'{e}nard convection.


  Knowledge of the midplane temperature of protoplanetary disks is one of the
key ingredients in theories of dust growth and planet formation. However,
direct measurement of this quantity is complicated, and often depends on the
fitting of complex models to the data. In this paper we demonstrate a method to
directly measure the midplane gas temperature from an optically thick molecular
line, if the disk is moderately inclined. The only model assumption that enters
is that the line is very optically thick, also in the midplane region where we
wish to measure the temperature. Freeze-out of the molecule onto dust grains
could thwart this. However, in regions that are expected to be warm enough to
avoid freeze-out, this method should work. We apply the method to the CO 2-1
line channel maps of the disk around HD 163296. We find that the midplane
temperature between 100 and 400 au drops only mildly from 25 K down to 18 K.
While we see no direct evidence of the midplane being optically thin due to
strong CO depletion by freeze-out, we cannot rule it out either. The fact that
the inferred temperatures are close to the expected CO freeze-out temperature
could be an indication of this. Incidently, for the disk around HD 163296 we
also find dynamic evidence for a rather abrupt outer edge of the disk,
suggestive of outside-in photoevaporation or truncation by an unseen companion.


  The interplay between the Hamilton-Jacobi theory of orthogonal separation of
variables and the theory of group actions is investigated based on concrete
examples.


  Aims. We report on simultaneous observations and modeling of mid-infrared
(MIR), near-infrared (NIR), and submillimeter (submm) emission of the source
Sgr A* associated with the supermassive black hole at the center of our Galaxy.
Our goal was to monitor the activity of Sgr A* at different wavelengths in
order to constrain the emitting processes and gain insight into the nature of
the close environment of Sgr A*. Methods. We used the MIR instrument VISIR in
the BURST imaging mode, the adaptive optics assisted NIR camera NACO, and the
sub-mm antenna APEX to monitor Sgr A* over several nights in July 2007.
Results. The observations reveal remarkable variability in the NIR and sub-mm
during the five nights of observation. No source was detected in the MIR, but
we derived the lowest upper limit for a flare at 8.59 microns (22.4 mJy with
A_8.59mu = 1.6+/- 0.5). This observational constraint makes us discard the
observed NIR emission as coming from a thermal component emitting at sub-mm
frequencies. Moreover, comparison of the sub-mm and NIR variability shows that
the highest NIR fluxes (flares) are coincident with the lowest sub-mm levels of
our five-night campaign involving three flares. We explain this behavior by a
loss of electrons to the system and/or by a decrease in the magnetic field, as
might conceivably occur in scenarios involving fast outflows and/or magnetic
reconnection.


  We consider anisotropies in the Cosmic Microwave Background (CMB) generated
by spatially limited seeds; these objects could correspond to relics of high
energy symmetry breaking in the early universe. It is shown how the CMB
perturbation propagate beyond the size of the seed in the form of waves
traveling with the CMB sound velocity. Moreover, these waves are the
substantial part of the signal, both for polarization and temperature. The
explanation of this phenomenology in terms of the CMB equations is given.
  Observationally, this effect is threefold promising. First, it enlarges the
signal from a seed intersecting the last scattering surface to the scale of the
CMB sound horizon at decoupling, that is roughly one degree in the sky. Second,
it offers cross correlation possibilities between the polarization and
temperature signals. Third, it allows to unambiguously distinguish these
structures from point-like astrophysical sources.


  The cloud computing literature provides various ways to utilise cloud
services, each with a different viewpoint, focus, and mostly using
heterogeneous technical-centric terms. This hinders efficient and consistent
knowledge flow across the community. Little, if any, research has aimed on
developing an integrated process model which captures core domain concepts and
ties them together to provide an overarching view of migrating legacy systems
to cloud platforms that is customisable for a given context. We adopt design
science research guidelines in which we use a metamodeling approach to develop
a generic process model and then evaluate and refine the model through three
case studies and domain expert reviews. This research benefits academics and
practitioners alike by underpinning a substrate for constructing,
standardising, maintaining, and sharing bespoke cloud migration models that can
be applied to given cloud adoption scenarios.


  We deal with the black hole information loss paradox by showing that the
stimulated emission component of the black hole radiation contains information
about the initial state of the system. The nonlocal behaviour that allows the
recovery of information about the matter that falls behind the horizon appears
in a natural way. We calculate the expectation value and probability
distribution of particles at ${\cal J}^+$ for a non-vacuum initial state. The
entropy of the final state is compared to that of a thermal state with the same
energy per mode. We find that the information recovered about the initial state
increases with the number $r$ of the initially incoming particles, reaching for
example over 30\% for $r = 1000$. We point out that recovering information
about the initial state, nevertheless, does not automatically imply the purity
of the final state.


  Normalization techniques have become a basic component in modern
convolutional neural networks (ConvNets). In particular, many recent works
demonstrate that promoting the orthogonality of the weights helps train deep
models and improve robustness. For ConvNets, most existing methods are based on
penalizing or normalizing weight matrices derived from concatenating or
flattening the convolutional kernels. These methods often destroy or ignore the
benign convolutional structure of the kernels; therefore, they are often
expensive or impractical for deep ConvNets. In contrast, we introduce a simple
and efficient "Convolutional Normalization" (ConvNorm) method that can fully
exploit the convolutional structure in the Fourier domain and serve as a simple
plug-and-play module to be conveniently incorporated into any ConvNets. Our
method is inspired by recent work on preconditioning methods for convolutional
sparse coding and can effectively promote each layer's channel-wise isometry.
Furthermore, we show that our ConvNorm can reduce the layerwise spectral norm
of the weight matrices and hence improve the Lipschitzness of the network,
leading to easier training and improved robustness for deep ConvNets. Applied
to classification under noise corruptions and generative adversarial network
(GAN), we show that the ConvNorm improves the robustness of common ConvNets
such as ResNet and the performance of GAN. We verify our findings via numerical
experiments on CIFAR and ImageNet.


  In this paper we describe in some detail the representation of the
topological $CP^1$ model in terms of a matrix integral which we have introduced
in a previous article. We first discuss the integrable structure of the $CP^1$
model and show that it is governed by an extension of the 1-dimensional Toda
hierarchy. We then introduce a matrix model which reproduces the sum over
holomorphic maps from arbitrary Riemann surfaces onto $CP^1$. We compute
intersection numbers on the moduli space of curves using geometrical method and
show that the results agree with those predicted by the matrix model. We also
develop a Landau-Ginzburg (LG) description of the $CP^1$ model using a
superpotential $e^X+e^{t_{0,Q}}e^{-X}$ given by the Lax operator of the Toda
hierarchy ($X$ is the LG field and $t_{0,Q}$ is the coupling constant of the
K\"ahler class). The form of the superpotential indicates the close connection
between $CP^1$ and $N=2$ supersymmetric sine-Gordon theory which was noted some
time ago by several authors. We also discuss possible generalizations of our
construction to other manifolds and present a LG formulation of the topological
$CP^2$ model.


  This paper centers around a simple yet crucial question for everyday users:
How should one choose their delegated validators within proof-of-stake (PoS)
protocols, particularly in the context of Ethereum 2.0? This has been a
long-overlooked gap, as existing studies have primarily focused on
inter-committee (validator set) behaviors and activities, while neglecting the
dynamic formation of committees, especially for individual stakeholders seeking
reliable validators. Our study bridges this gap by diving into the delegation
process (normal users delegate their small-value tokens to delegatees who later
act as validators) before entering an actual consensus phase.
  We propose a Bayesian model to quantify normal users' trust in delegatees,
which we further incorporate into a game-theoretical model to simulate users'
reactions against a set of critical factors identified through extensive
research (including 10+ staking service provider as well as 30+ PoS
blockchains). Our results reveal that users tend to choose their delegatees and
utilize their tokens by carefully weighing the delegation cost, the behaviors
of other users, and the reputation of delegatees, ultimately reaching a Nash
equilibrium. Unfortunately, the collective trend significantly increases the
likelihood of token concentration on a small number of delegatees.


  A bulk polycrystalline sample of YBa_{2}Cu_{3}O_{7-\delta} (\delta \approx
0.1) has been irradiated by \gamma-rays with ^{60}Co source. Non-monotonic
behavior of T_c (defined as the temperature at which normal resistance is
halved) with increasing irradiation dose \Phi (up to about 220 MR) is observed:
T_c decreases at low doses (\Phi \leq 50 MR) from initial value (\approx 93 K)
by about 2 K and then rises, forming minimum. At highest doses (\Phi \geq 120
MR) T_c goes down again. The temperature width, \delta T_c, of resistive
transition increases rather sharp with dose below 75 MR and somewhat drops at
higher dose. We believe that this effect is revealed for the first time at
\gamma-irradiation of high-T_c superconductor. The cross section for the
displacement of lattice atoms in YBCO by \gamma-rays due to the Compton process
were calculated, and possible dpa values were estimated. The results obtained
are discussed taking into account that the sample is granular superconductor
and, hence, the observed variations of superconducting properties should be
connected primarily with the influence of \gamma-rays on intergrain Josephson
coupling.


  The recent results from the Fermilab muon $g-2$ experiment, as well as the
persisting hints of lepton flavor universality violation in $B$-meson decays,
present a very strong case for flavor-nonuniversal new physics beyond the
Standard Model. We assert that a minimal $R$-parity violating supersymmetric
scenario with relatively light third-generation sfermions (dubbed as 'RPV3')
provides a natural, well-motivated framework for the simultaneous explanation
of all flavor anomalies, while being consistent with a multitude of low-energy
flavor constraints, as well as with limits from high-energy collider searches.
We further propose complementary tests and distinct signatures of this scenario
in the high-$p_T$ searches at current and future colliders. Specifically, we
find that an sbottom in the mass range of 2-12 TeV accounts for $R_{D^{(*)}}$
and $R_{K^{(*)}}$ flavor anomalies and it only plays a minor role in the
$(g-2)_\mu$ anomaly, whereas a sneutrino with mass between 0.7-1 TeV is the
dominant player for $(g-2)_\mu$. In this context, we propose specific collider
signatures of sbottom via its decays to $ \overline{ t}(t) \mu^+ \mu^-$, and of
sneutrino pairs with their decays leading to a highly distinctive and
spectacular four-muon final state, which can be used to completely probe the
RPV3 parameter space of interest.


  We study the generalization capacity of group convolutional neural networks.
We identify precise estimates for the VC dimensions of simple sets of group
convolutional neural networks. In particular, we find that for infinite groups
and appropriately chosen convolutional kernels, already two-parameter families
of convolutional neural networks have an infinite VC dimension, despite being
invariant to the action of an infinite group.


  A candidate explanation of the good empirical performance of deep neural
networks is the implicit regularization effect of first order optimization
methods. Inspired by this, we prove a convergence theorem for nonconvex
composite optimization, and apply it to a general learning problem covering
many machine learning applications, including supervised learning. We then
present a deep multilayer perceptron model and prove that, when sufficiently
wide, it $(i)$ leads to the convergence of gradient descent to a global optimum
with a linear rate, $(ii)$ benefits from the implicit regularization effect of
gradient descent, $(iii)$ is subject to novel bounds on the generalization
error, $(iv)$ exhibits the lazy training phenomenon and $(v)$ enjoys learning
rate transfer across different widths. The corresponding coefficients, such as
the convergence rate, improve as width is further increased, and depend on the
even order moments of the data generating distribution up to an order depending
on the number of layers. The only non-mild assumption we make is the
concentration of the smallest eigenvalue of the neural tangent kernel at
initialization away from zero, which has been shown to hold for a number of
less general models in contemporary works. We present empirical evidence
supporting this assumption as well as our theoretical claims.


  We present a multisymplectic formulation of the Yang--Mills equations. The
connections are represented by normalized equivariant 1-forms on the total
space of a principal bundle, with values in a Lie algebra. Within the
multisymplectic framework we realize that, under reasonable hypotheses, it is
not necessary to assume the equivariance condition a priori, since this
condition is a consequence of the dynamical equations.


  Rings comprising chemically bonded atoms are essential topological motifs for
the structural ordering of network-forming materials. Quantification of such
larger motifs beyond short-range pair correlation is essential for
understanding the linkages between the orderings and macroscopic behaviors.
Here, we propose two quantitative analysis methods based on rings. The first
method quantifies rings by two geometric indicators: roundness and roughness.
These indicators reveal the linkages between highly symmetric rings and crystal
symmetry in silica and that the structure of amorphous silica mainly consists
of distorted rings. The second method quantifies a spatial correlation function
that describes three-dimensional atomic densities around rings. A comparative
analysis among the functions for different degrees of ring symmetries reveals
that symmetric rings contribute to the local structural order in amorphous
silica. Another analysis of amorphous models with different orderings reveals
anisotropy of the local structural ordering around rings; this contributes to
building the intermediate-range ordering.


  Quantum codes typically rely on large numbers of degrees of freedom to
achieve low error rates. However each additional degree of freedom introduces a
new set of error mechanisms. Hence minimizing the degrees of freedom that a
quantum code utilizes is helpful. One quantum error correction solution is to
encode quantum information into one or more bosonic modes. We revisit
rotation-invariant bosonic codes, which are supported on Fock states that are
gapped by an integer $g$ apart, and the gap $g$ imparts number shift resilience
to these codes. Intuitively, since phase operators and number shift operators
do not commute, one expects a trade-off between resilience to number-shift and
rotation errors. Here, we obtain results pertaining to the non-existence of
approximate quantum error correcting $g$-gapped single-mode bosonic codes with
respect to Gaussian dephasing errors. We show that by using arbitrarily many
modes, $g$-gapped multi-mode codes can yield good approximate quantum error
correction codes for any finite magnitude of Gaussian dephasing and amplitude
damping errors.


  From a stable vector of a stable grading on a simple Lie algebra, Yun defined
a rigid automorphic datum that encodes a epipelagic representation, and also an
irregular connection on the projective line called $\theta$-connection. We show
that under geometric Langlands correspondence, $\theta$-connection corresponds
to the Hecke eigensheaf attached the rigid automorphic datum, assuming the
stable grading is inner and its Kac coordinate $s_0$ is positive. We provide
numerous applications of the main result including physical and cohomological
rigidity of $\theta$-connections, global oper structures, and a de Rham analog
of Reeder-Yu's predictions on epipelagic Langlands parameters.


  Doppler laser cooling of a three-level ladder system using two near-resonant
laser fields is analyzed in the case of the intermediate level being metastable
while the upper level is short-lived. Analytical as well as numerical results
for e.g. obtainable scattering rates and achievable temperatures are presented.
When appropriate, comparisons with two-level single photon Doppler laser
cooling is made. These results are relevant to recent experimental Doppler
laser cooling investigations addressing intercombination lines in alkali-earth
metal atoms and quadrupole transitions in alkali-earth metal ions.


  We analyze self-dual polyhedral cones and prove several properties about
their slack matrices. In particular, we show that self-duality is equivalent to
the existence of a positive semidefinite (PSD) slack. Beyond that, we show that
if the underlying cone is irreducible, then the corresponding PSD slacks are
not only doubly nonnegative matrices (DNN) but are extreme rays of the cone of
DNN matrices, which correspond to a family of extreme rays not previously
described. More surprisingly, we show that, unless the cone is simplicial, PSD
slacks not only fail to be completely positive matrices but they also lie
outside the cone of completely positive semidefinite matrices. Finally, we show
how one can use semidefinite programming to probe the existence of self-dual
cones with given combinatorics. Our results are given for polyhedral cones but
we also discuss some consequences for negatively self-polar polytopes.


  Massive stars play an important role in the Universe. Unlike low-mass stars,
the formation of these objects located at great distances is still unclear. It
is expected to be governed by some combination of self-gravity, turbulence, and
magnetic fields. Our aim is to study of the chemical and physical conditions of
dense clumps in several high-mass star-forming regions. We performed
observations towards 5 high-mass star-forming regions (L1287, S187, S231,
DR21(OH), NGC7538) with the IRAM 30 m telescope. We covered the 2-3 and 4 mm
wavelength band and analyzed the lines of HCN, HNC, HCO$^+$, HC$_3$N, HNCO,
OCS, CS, SiO, SO$_2$ and SO. Using astrodendro algorithm on the 850 $\mu$m dust
emission data from the SCUBA Legacy catalogue, we identified dense gas clumps
and determined their masses, H$_2$ column densities and sizes. Furthermore, the
kinetic temperatures, molecular abundances and dynamical state were obtained.
The Red Midcourse Space Experiment Source survey (RMS) was used to determine
the clump types. We identified $\sim$20 clumps. We found no significant
correlation between line width and size, but the linewidth-mass and mass-size
relationships are strongly correlated. Virial analysis indicated that the
clumps with HII regions and young stellar objects (YSOs) are gravitationally
bound. Furthermore, it was suggested that significant magnetic fields provide
additional support for clump stability. The molecular abundances decrease from
YSOs to submm and HII regions.


  A hidden symmetry of the nonlinear wave equation is exploited to analyse the
propagation of paraxial and uniform atom-laser beams in time-independent,
quadratic and cylindrical potentials varying smoothly along the propagation
axis. The quality factor and the paraxial ABCD formalism are generalized to
account exactly for mean-field interaction effects in such beams. Using an
approach based on moments, these theoretical tools provide a very simple and
yet exact picture of the interacting beam profile evolution. Guided atom laser
experiments are discussed. This treatment addresses simultaneously optical and
atomic beams in a unified manner, exploiting the formal analogy between
nonlinear optics and nonlinear paraxial atom optics.


  The "Perpendicular Bisectors Construction" is a natural way to seek a
replacement for the circumcenter of a noncyclic quadrilateral in the plane. In
this paper, we generalize this iterative construction to a construction on
polytopes with $n$ vertices in $(n-2)$-dimensional Euclidean, Hyperbolic and
Elliptic geometries. We then show that a number of nice properties concerning
this iterative construction continue to hold in these geometries. We also
introduce an analogue of the isoptic point of a quadrilateral, which is the
limit point of the Perpendicular Bisectors Construction, in $\mathbb{R}^{n}$
and prove some of its properties.


  We propose and design photonic crystal cavities (PCCs) in hexagonal boron
nitride (hBN) for diverse photonic and quantum applications. Two dimensional
(2D) hBN flakes contain quantum emitters which are ultra-bright and photostable
at room temperature. To achieve optimal coupling of these emitters to optical
resonators, fabrication of cavities from monolithic hBN is therefore required,
to maximize the overlap between cavity optical modes and the emitters. Here, we
design 2D and 1D PCCs using anisotropic indices of hBN. The influence of
underlying substrates and material absorption are investigated, and spontaneous
emission rate enhancements are calculated. Our results are promising for future
quantum photonic experiments with hBN.


  In order to convey the most content in their limited space, advertisements
embed references to outside knowledge via symbolism. For example, a motorcycle
stands for adventure (a positive property the ad wants associated with the
product being sold), and a gun stands for danger (a negative property to
dissuade viewers from undesirable behaviors). We show how to use symbolic
references to better understand the meaning of an ad. We further show how
anchoring ad understanding in general-purpose object recognition and image
captioning improves results. We formulate the ad understanding task as matching
the ad image to human-generated statements that describe the action that the ad
prompts, and the rationale it provides for taking this action. Our proposed
method outperforms the state of the art on this task, and on an alternative
formulation of question-answering on ads. We show additional applications of
our learned representations for matching ads to slogans, and clustering ads
according to their topic, without extra training.


  Computer vision techniques are on the rise for industrial applications, like
process supervision and autonomous agents, e.g., in the healthcare domain and
dangerous environments. While the general usability of these techniques is
high, there are still challenging real-world use-cases. Especially transparent
structures, which can appear in the form of glass doors, protective casings or
everyday objects like glasses, pose a challenge for computer vision methods.
This paper evaluates the combination of transparent objects in conjunction with
(naturally occurring) contamination through environmental effects like hazing.
We introduce a novel publicly available dataset containing 489 images
incorporating three grades of water droplet contamination on transparent
structures and examine the resulting influence on transparency handling. Our
findings show, that contaminated transparent objects are easier to segment and
that we are able to distinguish between different severity levels of
contamination with a current state-of-the art machine-learning model. This in
turn opens up the possibility to enhance computer vision systems regarding
resilience against, e.g., datashifts through contaminated protection casings or
implement an automated cleaning alert.


  This paper describes the approach of the THUIR team at the COLIEE 2023 Legal
Case Entailment task. This task requires the participant to identify a specific
paragraph from a given supporting case that entails the decision for the query
case. We try traditional lexical matching methods and pre-trained language
models with different sizes. Furthermore, learning-to-rank methods are employed
to further improve performance. However, learning-to-rank is not very robust on
this task. which suggests that answer passages cannot simply be determined with
information retrieval techniques. Experimental results show that more
parameters and legal knowledge contribute to the legal case entailment task.
Finally, we get the third place in COLIEE 2023. The implementation of our
method can be found at https://github.com/CSHaitao/THUIR-COLIEE2023.


  Three possibilities for the origin of CP violation are discussed: (1) the
Standard Model in which all CP violation is due to one parameter in the CKM
matrix, (2) the superweak model in which all CP violation is due to new physics
and (3) the Standard Model plus new physics. A major goal of B physics is to
distinguish these possibilities. CP violation implies time reversal violation
(TRV) but direct evidence for TRV is difficult to obtain.


  Policy enforcers are sophisticated runtime components that can prevent
failures by enforcing the correct behavior of the software. While a single
enforcer can be easily designed focusing only on the behavior of the
application that must be monitored, the effect of multiple enforcers that
enforce different policies might be hard to predict. So far, mechanisms to
resolve interferences between enforcers have been based on priority mechanisms
and heuristics. Although these methods provide a mechanism to take decisions
when multiple enforcers try to affect the execution at a same time, they do not
guarantee the lack of interference on the global behavior of the system. In
this paper we present a verification strategy that can be exploited to discover
interferences between sets of enforcers and thus safely identify a-priori the
enforcers that can co-exist at run-time. In our evaluation, we experimented our
verification method with several policy enforcers for Android and discovered
some incompatibilities.


  We present a simple yet accurate method to compute the adjoint double layer
potential, which is used to solve the Neumann boundary value problem for
Laplace's equation in three dimensions. An expansion in curvilinear coordinates
leads us to modify the expression for the adjoint double layer so that the
singularity is reduced when evaluating the integral on the surface. We then
regularize the Green's function, with a radial parameter $\delta$. We show that
a natural regularization has error $O(\delta^3)$, and a simple modification
improves the error to $O(\delta^5)$. The integral is evaluated numerically
without the need of special coordinates. We use this treatment of the adjoint
double layer to solve the classical integral equation for the interior Neumann
problem and evaluate the solution on the boundary. Choosing $\delta =
ch^{4/5}$, we find about $O(h^4)$ convergence in our examples, where $h$ is the
spacing in a background grid.


  The frequency-dependent shot noise in long and narrow mesoscopic diffusive
contacts is numerically calculated. The case of arbitrarily strong
electron-electron scattering and zero temperature of electrodes is considered.
For all voltages, the noise increases with frequency and tends to finite
values. These limiting values are larger than the Poissonian noise and increase
nearly as voltage to power 4/3. This allows one to experimentally determine the
parameters of electron-electron interaction.


  Accurate and comprehensive semantic segmentation of Bird's Eye View (BEV) is
essential for ensuring safe and proactive navigation in autonomous driving.
Although cooperative perception has exceeded the detection capabilities of
single-agent systems, prevalent camera-based algorithms in cooperative
perception neglect valuable information derived from historical observations.
This limitation becomes critical during sensor failures or communication issues
as cooperative perception reverts to single-agent perception, leading to
degraded performance and incomplete BEV segmentation maps. This paper
introduces TempCoBEV, a temporal module designed to incorporate historical cues
into current observations, thereby improving the quality and reliability of BEV
map segmentations. We propose an importance-guided attention architecture to
effectively integrate temporal information that prioritizes relevant properties
for BEV map segmentation. TempCoBEV is an independent temporal module that
seamlessly integrates into state-of-the-art camera-based cooperative perception
models. We demonstrate through extensive experiments on the OPV2V dataset that
TempCoBEV performs better than non-temporal models in predicting current and
future BEV map segmentations, particularly in scenarios involving communication
failures. We show the efficacy of TempCoBEV and its capability to integrate
historical cues into the current BEV map, improving predictions under optimal
communication conditions by up to 2% and under communication failures by up to
19%. The code will be published on GitHub.


  We examine a nonlinear magnetoinductive dimer and compute its linear and
nonlinear symmetric, antisymmetric and asymmetric modes in closed-form, in the
rotating-wave approximation. A linear stability analysis of these modes reveals
that the asymmetric mode is always stable, for any allowed value of the
coupling parameter and for both, hard and soft nonlinearity. A numerical
computation of the dimer dynamics reveals a magnetic energy selftrapping whose
threshold increases for increasing dimer coupling.


  Self-consistent system of spinor, scalar and BI gravitational fields is
considered. Exact solutions to the field equations in terms of volume scale of
the BI metric are obtained. Einstein field equations in account of the
cosmological constant $\Lambda$ and perfect fluid are studied. Oscillatory mode
of expansion of the universe is obtained. It is shown that for the interaction
term being a power function of the invariants of bilinear spinor forms and
$\Lambda > 0$ and given other parameters, e.g., coupling constant, spinor mass
etc., there exists a finite range of integration constant which generates
oscillatory mode of evolution.


  The "zero in the spectrum conjecture" asserted (in its strongest form) that
for any manifold M zero should be in the l2-spectrum of the Laplacian (on
forms) of the universal covering of M, i.e. that at least one (unreduced)
L2-cohomology group of (the universal covering of) M is non-zero.
  Farber and Weinberger gave the first counterexamples to this conjecture. In
this paper, using their fundamental idea to show the following stronger version
of this result:
  Let G be a finitely presented group and suppose that the homology groups
H_k(G,\ell^2(G)) are zero for k=0,1,2. For every dimension n\ge 6 there is a
closed manifold M of dimension n and with fundamental group G such that the
L2-cohomology of (the universal covering of) M vanishes in all degrees.


  The ALICE Collaboration will undertake a major upgrade of the detector
apparatus during the second LHC Long Shutdown LS2 (2019-2020) in view of the
Runs 3 and 4 (2021-2029). The objective of the upgrade is two-fold: i) an
improvement of the tracking precision and efficiency, in particular in the
low-momentum range; ii) an improvement of the readout capabilities of the
experiment, in order to fully exploit the luminosity for heavy ions envisaged
after LS2. The first goal will be achieved by replacing the Inner Tracking
System with a new tracker, composed of seven layers of silicon pixel detectors.
The new tracker will be made up of about 25000 Monolithic Active Pixel Sensors
with fast readout, resulting in a material thickness reduced to 0.3% (inner
layers) - 1% (outer layers) of the radiation length and a granularity of
$28\times28$ $\mu$m$^2$. The second goal will be achieved, among other
measures, by replacing the readout chambers of the 90 m$^3$ Time Projection
Chamber with Micro Pattern Gaseous Detectors. In particular, the new readout
chambers will consist of stacks of 4 Gas Electron Multiplier foils combining
different hole pitches. The upgraded detector will operate continuously without
the use of a triggered gating grid. It will thus be able to record all Pb--Pb
collisions at the LHC interaction rate of 50 kHz.


  We consider a financial market in which traders potentially face restrictions
in trading some of the available securities. Traders are heterogeneous with
respect to their beliefs and risk profiles, and the market is assumed thin:
traders strategically trade against their price impacts. We prove existence and
uniqueness of a corresponding equilibrium, and provide an efficient algorithm
to numerically obtain the equilibrium prices and allocations given market's
inputs. We find that restrictions may increase the market's welfare if traders
have different views regarding the covariance matrix of securities returns. The
latter heterogeneity regarding covariance matrix disagreement is essential in
modelling; for instance, when traders agree on the covariance matrix,
restricting participation in some securities for some traders leaves
equilibrium prices unaltered in the unrestricted securities, a certainly
undesirable model effect.


  We study various methods of constructing fat links based upon the HYP (by
Hasenfratz & Knechtli) and Fat7-bar (by W. Lee) algorithms. We present the
minimum plaquette distribution for these fat links. This enables us to
determine which algorithm is most effective at reducing the spread of plaquette
values.


  I review recent observational progress concerning the evolution of the
morphological distribution of galaxies in the rich cluster environment and in
the faint field population. By coupling HST imagery with ground-based
spectroscopic diagnostics, evidence accumulates that galaxy morphology can be a
transient phenomenon reflecting various changes in the star formation rate.
Possible physical processes responsible for these changes are discussed. Future
progress in understanding them will depend on securing 2-D spectroscopic data
for representative systems.


  Quantum Darwinism describes the proliferation, in the environment, of
multiple records of selected states of a quantum system. It explains how the
fragility of a state of a single quantum system can lead to the classical
robustness of states of their correlated multitude; shows how effective
`wave-packet collapse' arises as a result of proliferation throughout the
environment of imprints of the states of quantum system; and provides a
framework for the derivation of Born's rule, which relates probability of
detecting states to their amplitude. Taken together, these three advances mark
considerable progress towards settling the quantum measurement problem.


  In the framework of the planar and circular restricted three-body problem, we
consider an asteroid that orbits the Sun in quasi-satellite motion with a
planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital
resonance with the planet, characterized by a non zero eccentricity and a
resonant angle that librates around zero. Likewise, in the rotating frame with
the planet it describes the same trajectory as the one of a retrograde
satellite even though the planet acts as a perturbator. In the last few years,
the discoveries of asteroids in this type of motion made the term
"quasi-satellite" more and more present in the literature. However, some
authors rather use the term "retrograde satellite" when referring to this kind
of motion in the studies of the restricted problem in the rotating frame. In
this paper we intend to clarify the terminology to use, in order to bridge the
gap between the perturbative co-orbital point of view and the more general
approach in the rotating frame. Through a numerical exploration of the
co-orbital phase space, we describe the quasi-satellite domain and highlight
that it is not reachable by low eccentricities by averaging process. We will
show that the quasi-satellite domain is effectively included in the domain of
the retrograde satellites and neatly defined in terms of frequencies.
Eventually, we highlight a remarkable high eccentric quasi-satellite orbit
corresponding to a frozen ellipse in the heliocentric frame. We extend this
result to the eccentric case (planet on an eccentric motion) and show that two
families of frozen ellipses originate from this remarkable orbit.


  The transport coefficients of quark gluon plasma are calculated on a lattice
16**3X8, with the pure gauge models. Matsubara Green's functions of energy
momentum tensors have very large fluctuations and about a few million MC sweeps
are needed to reduce the errors reasonably small in the case of the standard
action. They are much suppressed if Iwasaki's improved action is employed.
Preliminary results show that the transport coefficients roughly depend on the
coupling constant as a**(-3)(g) in the case of SU(2).


  In this note we put forward a conjecture on the average optimal length for
bipartite matching with a finite number of elements where the different lengths
are independent one from the others and have an exponential distribution.


  Recently discovered quasi periodic oscillations in the X-ray brightness of
low mass X-ray binaries are used to derive constraints on the mass of the
neutron star component and the equation of state of neutron star matter. The
observations are compared with models of rapidly rotating neutron stars which
are calculated by means of an exact numerical method in full relativity. For
the equations of state we select a broad collection of models representing
different assumptions about the many-body structure and the complexity of the
composition of super dense matter. The mass constraints differ from their
values in the approximate treatment by \sim 10%. Under the assumption that the
maximum frequency of the quasi periodic oscillations originates from the
innermost stable orbit the mass of the neutron star is in the range: $M\sim
1.92-2.25 M_\odot$. Especially the quasi periodic oscillation in the
Atoll-source 4U 1820-30 is only consistent with equations of state which are
rather stiff at high densities which is explainable, so far, only with pure
nucleonic/leptonic composition. This interpretation contradicts the hypothesis
that the protoneutron star formed in SN 1987A collapsed to a black hole, since
this would demand a maximum neutron star mass below $1.6 M_\odot$. The recently
suggested identification of quasi periodic oscillations with frequencies around
10 Hz with the Lense-Thirring precession of the accretion disk is found to be
inconsistent with the models studied in this work, unless it is assumed that
the first overtone of the precession is observed.


  While GPUs are responsible for training the vast majority of state-of-the-art
deep learning models, the implications of their architecture are often
overlooked when designing new deep learning (DL) models. As a consequence,
modifying a DL model to be more amenable to the target hardware can
significantly improve the runtime performance of DL training and inference. In
this paper, we provide a set of guidelines for users to maximize the runtime
performance of their transformer models. These guidelines have been created by
carefully considering the impact of various model hyperparameters controlling
model shape on the efficiency of the underlying computation kernels executed on
the GPU. We find the throughput of models with efficient model shapes is up to
39\% higher while preserving accuracy compared to models with a similar number
of parameters but with unoptimized shapes.


  The rapid development of generative diffusion models has significantly
advanced the field of style transfer. However, most current style transfer
methods based on diffusion models typically involve a slow iterative
optimization process, e.g., model fine-tuning and textual inversion of style
concept. In this paper, we introduce FreeStyle, an innovative style transfer
method built upon a pre-trained large diffusion model, requiring no further
optimization. Besides, our method enables style transfer only through a text
description of the desired style, eliminating the necessity of style images.
Specifically, we propose a dual-stream encoder and single-stream decoder
architecture, replacing the conventional U-Net in diffusion models. In the
dual-stream encoder, two distinct branches take the content image and style
text prompt as inputs, achieving content and style decoupling. In the decoder,
we further modulate features from the dual streams based on a given content
image and the corresponding style text prompt for precise style transfer. Our
experimental results demonstrate high-quality synthesis and fidelity of our
method across various content images and style text prompts. Compared with
state-of-the-art methods that require training, our FreeStyle approach notably
reduces the computational burden by thousands of iterations, while achieving
comparable or superior performance across multiple evaluation metrics including
CLIP Aesthetic Score, CLIP Score, and Preference. We have released the code
anonymously at:
\href{https://anonymous.4open.science/r/FreeStyleAnonymous-0F9B}


  A large part of the workforce, and growing every day, is originally from
India. India one of the second largest populations in the world, they have a
lot to offer in terms of jobs. The sheer number of IT workers makes them a
formidable travelling force as well, easily picking up employment in English
speaking countries. The beginning of the economic crises since 2008 September,
many Indians have return homeland, and this has had a substantial impression on
the Indian Rupee (INR) as liken to the US Dollar (USD). We are using
numerational knowledge based techniques for forecasting has been proved highly
successful in present time. The purpose of this paper is to examine the effects
of several important neural network factors on model fitting and forecasting
the behaviours. In this paper, Artificial Neural Network has successfully been
used for exchange rate forecasting. This paper examines the effects of the
number of inputs and hidden nodes and the size of the training sample on the
in-sample and out-of-sample performance. The Indian Rupee (INR) / US Dollar
(USD) is used for detailed examinations. The number of input nodes has a
greater impact on performance than the number of hidden nodes, while a large
number of observations do reduce forecast errors.


  We analyze new physics contributions to $e^+e^-\to W^+W^-$ at the TeV energy
scale, employing an effective field theory framework. A complete basis of
next-to-leading order operators in the standard model effective Lagrangian is
used, both for the nonlinear and the linear realization of the electroweak
sector. The elimination of redundant operators via equations-of-motion
constraints is discussed in detail. Polarized cross sections for $e^+e^-\to
W^+W^-$ (on-shell) are computed and the corrections to the standard model
results are given in an expansion for large $s/M^2_W$. The dominant relative
corrections grow with $s$ and can be fully expressed in terms of modified
gauge-fermion couplings. These corrections are interpreted in the context of
the Goldstone boson equivalence theorem. Explicit new physics models are
considered to illustrate the generation and the potential size of the
coefficients in the effective Lagrangian. Brief comments are made on the
production of $W^+W^-$ pairs at the LHC.


  We introduce Metric3D v2, a geometric foundation model for zero-shot metric
depth and surface normal estimation from a single image, which is crucial for
metric 3D recovery. While depth and normal are geometrically related and highly
complimentary, they present distinct challenges. SoTA monocular depth methods
achieve zero-shot generalization by learning affine-invariant depths, which
cannot recover real-world metrics. Meanwhile, SoTA normal estimation methods
have limited zero-shot performance due to the lack of large-scale labeled data.
To tackle these issues, we propose solutions for both metric depth estimation
and surface normal estimation. For metric depth estimation, we show that the
key to a zero-shot single-view model lies in resolving the metric ambiguity
from various camera models and large-scale data training. We propose a
canonical camera space transformation module, which explicitly addresses the
ambiguity problem and can be effortlessly plugged into existing monocular
models. For surface normal estimation, we propose a joint depth-normal
optimization module to distill diverse data knowledge from metric depth,
enabling normal estimators to learn beyond normal labels. Equipped with these
modules, our depth-normal models can be stably trained with over 16 million of
images from thousands of camera models with different-type annotations,
resulting in zero-shot generalization to in-the-wild images with unseen camera
settings. Our method enables the accurate recovery of metric 3D structures on
randomly collected internet images, paving the way for plausible single-image
metrology. Our project page is at https://JUGGHM.github.io/Metric3Dv2.


  We report on the investigation of the three-dimensional single-atom-resolved
distributions of bosonic Mott insulators in momentum-space. Firstly, we measure
the two-body and three-body correlations deep in the Mott regime, finding a
perfectly contrasted bunching whose periodicity reproduces the reciprocal
lattice. In addition, we show that the two-body correlation length is inversely
proportional to the in-trap size of the Mott state with a pre-factor in
agreement with the prediction for an incoherent state occupying a uniformly
filled lattice. Our findings indicate that the momentum-space correlations of a
Mott insulator at small tunnelling is that of a many-body ground-state with
Gaussian statistics. Secondly, in the Mott insulating regime with increasing
tunnelling, we extract the spectral weight of the quasi-particles from the
momentum density profiles. On approaching the transition towards a superfluid,
the momentum spread of the spectral weight is found to decrease as a result of
the increased mobility of the quasi-particles in the lattice. While the shapes
of the observed spectral weight agree with the ones predicted by perturbative
many-body calculations, the fitted mobilities are larger than the theoretical
ones. This discrepancy is similar to that previously reported on the
time-of-flight visibility.


  Given a closed contact 3-manifold with a compatible Riemannian metric, we
show that if the sectional curvature is 1/4-pinched, then the contact structure
is universally tight. This result improves the Contact Sphere Theorem in
[EKM12], where a 4/9-pinching constant was imposed. Some tightness results on
positively curved contact open 3-manifold are also discussed.


  The existing reservoirs of neutral atomic hydrogen gas (H$\,$I) in galaxies
are insufficient to have maintained the observed levels of star formation
without some kind of replenishment. {This refuelling of the H$\,$I reservoirs}
is likely to occur at column densities an order of magnitude lower than
previous observational limits (N$_{\rm{H\,I}\, limit} \sim 10^{19}\,$cm$^{-2}$
at 30$''$ resolution over a linewidth of $20\,$km/s). In this paper, we present
recent deep H$\,$I observations of NGC 5068, a nearby isolated star-forming
galaxy observed by MeerKAT as part of the MHONGOOSE survey. With these new
data, we are able to detect low column density H$\,$I around NGC 5068 with a
$3\sigma$ detection limit of N$_{\rm{H\,I}} = 6.4 \times 10^{17}\,$cm$^{-2}$ at
90$''$ resolution over a $20\,$km/s linewidth. The high sensitivity and
resolution of the MeerKAT data reveal a complex morphology of the H$\,$I in
this galaxy -- a regularly rotating inner disk coincident with the main
star-forming disk of the galaxy, a warped outer disk of low column density gas
(N$_{\rm{H\,I}} < 9 \times 10^{19}\,$cm$^{-2}$), in addition to clumps of gas
on the north west side of the galaxy. We employ a simple two disk model that
describe the inner and outer disks, and are able to identify anomalous gas that
deviates from the rotation of the main galaxy. The morphology and the
kinematics of the anomalous gas suggest a possible extra-galactic origin. We
explore a number of possible origin scenarios that may explain the anomalous
gas, and conclude that fresh accretion is the most likely scenario.


  In this paper, we introduce the notion of Rota-Baxter Lie $2$-algebras, which
is a categorification of Rota-Baxter Lie algebras. We prove that the category
of Rota-Baxter Lie $2$-algebras and the category of $2$-term Rota-Baxter
$L_\infty$-algebras are equivalent. We introduce the notion of a crossed module
of Rota-Baxter Lie algebras and show that there is a one-to-one correspondence
between strict $2$-term Rota-Baxter $L_\infty$-algebras and crossed modules of
Rota-Baxter Lie algebras. We give the construction of crossed modules of Lie
algebras from crossed modules of Rota-Baxter Lie algebras.


  A new geometric framework is developed to describe non-conservative classical
field theories, which is based on multisymplectic and contact geometries.
Assuming certain additional conditions and using the forms that define this
multicontact structure, as well as other geometric elements that are derived
from them, we can introduce variational field equations in the multicontact
manifolds. These equations are stated using different geometric tools; namely,
sections, multivector fields and Ehresmann connections in fiber bundles. Then,
this framework can be adapted to the jet bundle description of classical field
theories and the field equations are stated both in the Lagrangian and the
Hamiltonian formalisms, which are discussed in the regular and the singular
cases.


  We discuss a special aspect of agents placed in a social network. If an agent
can be seen as comprising many components, the expressions and interactions
among these components may be crucial. We discuss the role of patterns within
the environment as a mode of expression of these components. The stability and
identity of an agent is derived as a function of component and
component-pattern identity. The agent is then placed in a specific social
network within the environment, and the enigmatic case of altruism is explained
in terms of interacting component identities.


  We study the following repeated non-atomic routing game. In every round,
nature chooses a state in an i.i.d. manner according to a publicly known
distribution, which influences link latency functions. The system planner makes
private route recommendations to participating agents, which constitute a fixed
fraction, according to a publicly known signaling strategy. The participating
agents choose between obeying or not obeying the recommendation according to
cumulative regret of the participating agent population in the previous round.
The non-participating agents choose route according to myopic best response to
a calibrated forecast of the routing decisions of the participating agents. We
show that, for parallel networks, if the planner's signal strategy satisfies
the obedience condition, then, almost surely, the link flows are asymptotically
consistent with the Bayes correlated equilibrium induced by the signaling
strategy.


  We investigate experimentally the plasma dynamics of a centimeter-scale,
laser filamentation-guided spark discharge. Using electrical and optical
diagnostics to study monopolar discharges with varying current pulses we show
that plasma decay is dominated by free electron recombination if the current
decay time is shorter than the recombination characteristic time. In the
opposite case, the plasma electron density closely follows the current
evolution. We demonstrate that this criterion holds true in the case of damped
AC sparks, and that alternative current is the best option to achieve a long
plasma lifetime for a given peak current.


  We numerically and experimentally achieve quasi-bound states in the
continuums (BICs) with high-Q factors in the free-standing metal complementary
periodic cross-shaped resonators (CPCRs) at terahertz (THz) frequencies. Such
induced quasi-BICs arises from the breaking of the mirror symmetry of CPCRs. By
properly tuning the asymmetric factor, the measured Q factor of quasi-BIC can
reach 102, which is lower than the simulated Q factor of 166 due to the limited
system resolutions. We also simulate the electric field magnitude and vector
distributions at the quasi-BICs, where the out-phase alignment between the
electric dipoles is found. The sharp quasi-BICs realized in this thin
free-standing metal structure may immediately boost the performance of filters
and sensors in terahertz wave manipulation or biomolecular sensing.


  This work tackles Weakly Supervised Anomaly detection, in which a predictor
is allowed to learn not only from normal examples but also from a few labeled
anomalies made available during training. In particular, we deal with the
localization of anomalous activities within the video stream: this is a very
challenging scenario, as training examples come only with video-level
annotations (and not frame-level). Several recent works have proposed various
regularization terms to address it i.e. by enforcing sparsity and smoothness
constraints over the weakly-learned frame-level anomaly scores. In this work,
we get inspired by recent advances within the field of self-supervised learning
and ask the model to yield the same scores for different augmentations of the
same video sequence. We show that enforcing such an alignment improves the
performance of the model on XD-Violence.


  A fast and effective motion deblurring method has great application values in
real life. This work presents an innovative approach in which a self-paced
learning is combined with GAN to deblur image. First, We explain that a proper
generator can be used as deep priors and point out that the solution for
pixel-based loss is not same with the one for perception-based loss. By using
these ideas as starting points, a Bi-Skip network is proposed to improve the
generating ability and a bi-level loss is adopted to solve the problem that
common conditions are non-identical. Second, considering that the complex
motion blur will perturb the network in the training process, a self-paced
mechanism is adopted to enhance the robustness of the network. Through
extensive evaluations on both qualitative and quantitative criteria, it is
demonstrated that our approach has a competitive advantage over
state-of-the-art methods.


  We begin a systematic study of the problem of the zero--error capacity of
noisy binary channels with memory and solve some of the non--trivial cases.


  Prior to the 1990s, speculations about the occurrence of planets around other
stars were based only on planet formation theory, observations of circumstellar
disks, and the knowledge that at least one seemingly ordinary star is the host
of four terrestrial planets, two gas giants, and two ice giants. Since then,
Doppler and transit surveys have been exploring the population of planets
around other Sun-like stars, especially those with orbital periods shorter than
a few years. Over the last decade, these surveys have risen to new heights with
Doppler spectrographs with a precision better than 1 m/s precision, and space
telescopes capable of detecting the transits of Earth-sized planets. This
article is a brief introductory review of the knowledge of planet occurrence
that has been gained from these surveys.


  We present a library to automatically embed signal processing and neural
network predictions into the material robots are made of. Deep and shallow
neural network models are first trained offline using state-of-the-art machine
learning tools and then transferred onto general purpose microcontrollers that
are co-located with a robot's sensors and actuators. We validate this approach
using multiple examples: a smart robotic tire for terrain classification, a
robotic finger sensor for load classification and a smart composite capable of
regressing impact source localization. In each example, sensing and computation
are embedded inside the material, creating artifacts that serve as stand-in
replacement for otherwise inert conventional parts. The open source software
library takes as inputs trained model files from higher level learning
software, such as Tensorflow/Keras, and outputs code that is readable in a
microcontroller that supports C. We compare the performance of this approach
for various embedded platforms. In particular, we show that low-cost
off-the-shelf microcontrollers can match the accuracy of a desktop computer,
while being fast enough for real-time applications at different neural network
configurations. We provide means to estimate the maximum number of parameters
that the hardware will support based on the microcontroller's specifications.


  Recent studies have shown that seizures can spread and terminate across brain
areas via a rich diversity of spatiotemporal patterns. In particular, while the
location of the seizure onset area is usually in-variant across seizures in a
same patient, the source of traveling (2-3 Hz) spike-and-wave discharges (SWDs)
during seizures can either move with the slower propagating ictal wavefront or
remain stationary at the seizure onset area. In addition, although most focal
seizures terminate quasi-synchronously across brain areas, some evolve into
distinct ictal clusters and terminate asynchronously. To provide a unifying
perspective on the observed diversity of spatiotemporal dynamics for seizure
spread and termination, we introduce here the Epileptor neural field model. Two
mechanisms play an essential role. First, while the slow ictal wavefront
propagates as a front in excitable neural media, the faster SWDs propagation
results from coupled-oscillator dynamics. Second, multiple time scales interact
during seizure spread, allowing for low-voltage fast-activity (>10 Hz) to
hamper seizure spread and for SWD propagation to affect the way a seizure
terminates. These dynamics, together with variations in short and long-range
connectivity strength, play a central role on seizure spread, maintenance and
termination. We demonstrate how Epileptor field models incorporating the above
mechanisms predict the previously reported diversity in seizure spread
patterns. Furthermore, we confirm the predictions for synchronous or
asynchronous (clustered) seizure termination in human seizures recorded via
stereotactic EEG. Our new insights into seizure spatiotemporal dynamics may
also contribute to the development of new closed-loop neuromodulation therapies
for focal epilepsy.


  In this paper, we settle the problem for time-dependent Hartree equation with
inhomogeneous boundary condition in a bounded Lipschitz domain in
$\mathbb{R}^{N}$. A global existence result is derived.


  Collaboration networks arise when we map the connections between scientists
which are formed through joint publications. These networks thus display the
social structure of academia, and also allow conclusions about the structure of
scientific knowledge. Using the computer science publication database DBLP, we
compile relations between authors and publications as graphs and proceed with
examining and quantifying collaborative relations with graph-based methods. We
review standard properties of the network and rank authors and publications by
centrality. Additionally, we detect communities with modularity-based
clustering and compare the resulting clusters to a ground-truth based on
conferences and thus topical similarity. In a second part, we are the first to
combine DBLP network data with data from the Dagstuhl Seminars: We investigate
whether seminars of this kind, as social and academic events designed to
connect researchers, leave a visible track in the structure of the
collaboration network. Our results suggest that such single events are not
influential enough to change the network structure significantly. However, the
network structure seems to influence a participant's decision to accept or
decline an invitation.


  Let $F_g$ be a closed orientable surface of genus $g$. A set $\Omega = \{
\gamma_1, \dots, \gamma_s\}$ of pairwise non-homotopic simple closed curves on
$F_g$ is called a \emph{filling system} or simply a \emph{filling} of $F_g$, if
$F_g\setminus \Omega$ is a union of $b$ topological discs for some $b\geq 1$. A
filling system is called \emph{minimal}, if $b=1$. The \emph{size} of a filling
is defined as the number of its elements. We prove that the maximum size of a
filling of $F_g$ with $b$ complementary discs is $2g+b-1$. Next, we show that
for $g\geq 2, b\geq 1\text{ with }(g,b)\neq (2,1)$ (resp. $(g,b)=(2,1)$) and
for each $2\leq s\leq 2g+b-1$ (resp. $3\leq s\leq 2g+b-1$), there exists a
filling of $F_g$ of size $s$ with $b$ complementary discs.
  Furthermore, we study geometric intersection number of curves in a minimal
filling. For $g\geq 2$, we show that for a minimal filling $\Omega$ of size
$s$, the \emph{geometric intersection numbers} satisfy $\max \left\lbrace
i(\gamma_i, \gamma_j)| i\neq j\right\rbrace\leq 2g-s+1$, and for each such $s$
there exists a minimal filling $\Omega=\left\lbrace \gamma_1, \dots, \gamma_s
\right\rbrace$ such that $\max\left\lbrace i(\gamma_i, \gamma_j) | i\neq
j\right\rbrace = 2g-s+1$.


  We introduce a differential extension of algebraic K-theory of an algebra
using Karoubi's Chern character. In doing so, we develop a necessary theory of
secondary transgression forms as well as a differential refinement of the
smooth Serre--Swan correspondence. Our construction subsumes the differential
K-theory of a smooth manifold when the algebra is complex-valued smooth
functions. Furthermore, our construction fits into a noncommutative
differential cohomology hexagon diagram.


  Primordial gravitational waves generated during inflation lead to the B-mode
polarization in the cosmic microwave background and a stochastic gravitational
wave background in the Universe. We will explore the current constraint on the
tilt of primordial gravitational-wave spectrum, and forecast how the future
observations can improve the current constraint.


  In order to meet the constantly increasing demand by mobile terminals for
higher data rates with limited wireless spectrum resource, cognitive radio and
spectrum aggregation technologies have attracted much attention due to its
capacity in improving spectrum efficiency. Combing cognitive relay and spectrum
aggregation technologies, in this paper, we propose a dynamic spectrum
aggregation strategy based on the Markov Prediction of the state of spectrum
for the cooperatively relay networks on a multi-user and multi-relay scenario
aiming at ensuring the user channel capacity and maximizing the network
throughput. The spectrum aggregation strategy is executed through two steps.
First, predict the state of spectrum through Markov prediction. Based on the
prediction results of state of spectrum, a spectrum aggregation strategy is
proposed. Simulation results show that the spectrum prediction process can
observably lower the outage rate, and the spectrum aggregation strategy can
greatly improve the network throughput.


  The quantum-Extended Church-Turing thesis is a principle of physics as well
as computer science. It asserts that the laws of physics will prevent the
construction of a machine that can efficiently determine the results of any
calculation which cannot be done efficiently by a quantum Turing machine (or a
universal quantum circuit). In this note I will argue that an observer falling
into a black hole can learn the result of such a calculation in a very short
time, thereby seemingly violating the thesis. A viable reformulation requires
that the thesis only applies to observers who have access to the holographic
boundary of space. The properties of the horizon play a crucial a role in
protecting the thesis. The arguments are closely related to, and were partially
motivated by a recent paper by Bouland, Fefferman, and Vazirani, and by a
question raised by Aaronson.


  Graph neural network (GNN) has been demonstrated to be a powerful model in
many domains for its effectiveness in learning over graphs. To scale GNN
training for large graphs, a widely adopted approach is distributed training
which accelerates training using multiple computing nodes. Maximizing the
performance is essential, but the execution of distributed GNN training remains
preliminarily understood. In this work, we provide an in-depth analysis of
distributed GNN training on GPUs, revealing several significant observations
and providing useful guidelines for both software optimization and hardware
optimization.


  Scaling arguments and precise simulations are used to study the square
lattice $\pm J$ Ising spin glass, a prototypical model for glassy systems.
Droplet theory predicts, and our numerical results show,
entropically-stabilized long range spin glass order at zero temperature. The
low temperature scaling behavior has an important new crossover length scale
that produces a power-law dependence of the heat capacity on temperature.


  Dark matter direct detection experiments have poor sensitivity to a galactic
population of dark matter with mass below the GeV scale. However, such dark
matter can be produced copiously in supernovae. Since this thermally-produced
population is much hotter than the galactic dark matter, it can be observed
with direct detection experiments. In this paper, we focus on a dark sector
with fermion dark matter and a heavy dark photon as a specific example. We
first extend existing supernova cooling constraints on this model to the regime
of strong coupling where the dark matter becomes diffusively trapped in the
supernova. Then, using the fact that even outside these cooling constraints the
diffuse galactic flux of these dark sector particles can still be large, we
show that this flux is detectable in direct detection experiments such as
current and next-generation liquid xenon detectors. As a result, due to
supernova production, light dark matter has the potential to be discovered over
many orders of magnitude of mass and coupling.


  Three-dimensional topological insulators (TIs) exhibit time-reversal symmetry
protected, linearly dispersing Dirac surface states. Band bending at the TI
surface may also lead to coexisting trivial two-dimensional electron gas (2DEG)
states with parabolic energy dispersion that exist as spin-split pairs due to
Rashba spin-orbit coupling (SOC). A bias current is expected to generate spin
polarization in both systems arising from their helical spin-momentum locking.
However, their induced spin polarization is expected to be different in both
magnitude and sign. Here, we compare spin potentiometric measurements of bias
current-generated spin polarization in Bi2Se3(111) films where Dirac surface
states coexist with trivial 2DEG states, with identical measurements on
InAs(001) samples where only trivial 2DEG states are present. We observe spin
polarization arising from spin-momentum locking in both cases, with opposite
signs of the spin voltage. We present a model based on spin dependent
electrochemical potentials to directly derive the signs expected for the TI
surface states, and unambiguously show that the dominant contribution to the
current-generated spin polarization measured in the TI is from the Dirac
surface states. This direct electrical access of the helical spin texture of
Dirac and Rashba 2DEG states is an enabling step towards the electrical
manipulation of spins in next generation TI and SOC based quantum devices.


  We provide further evidence for the nontrivial interplay between geometry and
temperature in the Casimir effect. We investigate the temperature dependence of
the Casimir force between an inclined semi-infinite plate above an infinite
plate in D dimensions using the worldline formalism. Whereas the
high-temperature behavior is always found to be linear in T in accordance with
dimensional-reduction arguments, different power-law behaviors at small
temperatures emerge. Unlike the case of infinite parallel plates, which shows
the well-known T^D behavior of the force, we find a T^{D-1} behavior for
inclined plates, and a ~T^{D-0.3} behavior for the edge effect in the limit
where the plates become parallel. The strongest temperature dependence ~T^{D-2}
occurs for the Casimir torque of inclined plates. Numerical as well as
analytical worldline results are presented.


  The process of opinion depolarization is assumed to be mediated through
social networks, where interacting individuals reciprocally exert social
influence leading to a consensus. While network topology plays a decisive role
in many networked dynamical processes, its effect on depolarization dynamics
remains unclear. Here, we show that, in a recently proposed opinion
depolarization model, the threshold of the transition from correlated and
polarized opinions to consensus can vanish on heterogeneous social networks.
Our theoretical findings are validated by running numerical simulations on both
synthetic and real social networks, confirming that a polarized yet
heterogeneously connected population can reach a consensus even in the presence
of weak social influence.


  Sparse codes in neuroscience have been suggested to offer certain
computational advantages over other neural representations of sensory data. To
explore this viewpoint, a sparse code is used to represent natural images in an
optimal control task solved with neuro-dynamic programming, and its
computational properties are investigated. The central finding is that when
feature inputs to a linear network are correlated, an over-complete sparse code
increases the memory capacity of the network in an efficient manner beyond that
possible for any complete code with the same-sized input, and also increases
the speed of learning the network weights. A complete sparse code is found to
maximise the memory capacity of a linear network by decorrelating its feature
inputs to transform the design matrix of the least-squares problem to one of
full rank. It also conditions the Hessian matrix of the least-squares problem,
thereby increasing the rate of convergence to the optimal network weights.
Other types of decorrelating codes would also achieve this. However, an
over-complete sparse code is found to be approximately decorrelated, extracting
a larger number of approximately decorrelated features from the same-sized
input, allowing it to efficiently increase memory capacity beyond that possible
for any complete code: a 2.25 times over-complete sparse code is shown to at
least double memory capacity compared with a complete sparse code using the
same input. This is used in sequential learning to store a potentially large
number of optimal control tasks in the network, while catastrophic forgetting
is avoided using a partitioned representation, yielding a cost-to-go function
approximator that generalizes over the states in each partition. Sparse code
advantages over dense codes and local codes are also discussed.


  The paper presents StegBlocks, which defines a new concept for performing
undetectable hidden communication. StegBlocks is a general approach for
constructing methods of network steganography. In StegBlocks, one has to
determine objects with defined properties which will be used to transfer hidden
messages. The objects are dependent on a specific network protocol (or
application) used as a carrier for a given network steganography method.
Moreover, the paper presents the approach to perfect undetectability of network
steganography, which was developed based on the rules of undetectability for
general steganography. The approach to undetectability of network steganography
was used to show the possibility of developing perfectly undetectable network
steganography methods using the StegBlocks concept.


  In this paper we employ non equilibrium thermodynamics of fluxes and forces
to describe magnetization and heat transport. By the theory we are able to
identify the thermodynamic driving force of the magnetization current as the
gradient of the effective field $\nabla H^*$. This definition permits to define
the spin Seebeck coefficient $\epsilon_M$ which relates $\nabla H^*$ and the
temperature gradient $\nabla T$. By applying the theory to the geometry of the
longitudinal spin Seebeck effect we are able to obtain the optimal conditions
for generating large magnetization currents. Furthermore, by using the results
of recent experiments, we obtain an order of magnitude for the value of
$\epsilon_{M} \sim 10^{-2}$ TK$^{-1}$ for yttrium iron garnet
(Y$_3$Fe$_5$O$_{12}$).


  Current directed graph embedding methods build upon undirected techniques but
often inadequately capture directed edge information, leading to challenges
such as: (1) Suboptimal representations for nodes with low in/out-degrees, due
to the insufficient neighbor interactions; (2) Limited inductive ability for
representing new nodes post-training; (3) Narrow generalizability, as training
is overly coupled with specific tasks. In response, we propose DUPLEX, an
inductive framework for complex embeddings of directed graphs. It (1) leverages
Hermitian adjacency matrix decomposition for comprehensive neighbor
integration, (2) employs a dual GAT encoder for directional neighbor modeling,
and (3) features two parameter-free decoders to decouple training from
particular tasks. DUPLEX outperforms state-of-the-art models, especially for
nodes with sparse connectivity, and demonstrates robust inductive capability
and adaptability across various tasks. The code is available at
https://github.com/alipay/DUPLEX.


  In this note we disprove a conjecture of Kuzmin and Warmuth claiming that
every family whose VC-dimension is at most d admits an unlabeled compression
scheme to a sample of size at most d. We also study the unlabeled compression
schemes of the joins of some families and conjecture that these give a larger
gap between the VC-dimension and the size of the smallest unlabeled compression
scheme for them.


  Persistent homology and zigzag persistent homology are techniques which track
the homology over a sequence of spaces, outputting a set of intervals
corresponding to birth and death times of homological features in the sequence.
This paper presents a method for choosing a homology class to correspond to
each of the intervals at each time point. For each homology class a specific
representative cycle is stored, with the choice of homology class and
representative cycle being both geometrically relevant and compatible with the
birth-death interval decomposition. After describing the method in detail and
proving its correctness, we illustrate the utility of the method by applying it
to the study of coverage holes in time-varying sensor networks.


  Single Instruction, Multiple Data (SIMD) vectorization is a major driver of
performance in current architectures, and is mandatory for achieving good
performance with codes that are limited by instruction throughput. We
investigate the efficiency of different SIMD-vectorized implementations of the
RabbitCT benchmark. RabbitCT performs 3D image reconstruction by back
projection, a vital operation in computed tomography applications. The
underlying algorithm is a challenge for vectorization because it consists,
apart from a streaming part, also of a bilinear interpolation requiring
scattered access to image data. We analyze the performance of SSE (128 bit),
AVX (256 bit), AVX2 (256 bit), and IMCI (512 bit) implementations on recent
Intel x86 systems. A special emphasis is put on the vector gather
implementation on Intel Haswell and Knights Corner microarchitectures. Finally
we discuss why GPU implementations perform much better for this specific
algorithm.


  The formation of eyes led to the big bang of evolution. The dynamics changed
from a primitive organism waiting for the food to come into contact for eating
food being sought after by visual sensors. The human eye is one of the most
sophisticated developments of evolution, but it still has defects. Humans have
evolved a biological perception algorithm capable of driving cars, operating
machinery, piloting aircraft, and navigating ships over millions of years.
Automating these capabilities for computers is critical for various
applications, including self-driving cars, augmented reality, and architectural
surveying. Near-field visual perception in the context of self-driving cars can
perceive the environment in a range of $0-10$ meters and 360{\deg} coverage
around the vehicle. It is a critical decision-making component in the
development of safer automated driving. Recent advances in computer vision and
deep learning, in conjunction with high-quality sensors such as cameras and
LiDARs, have fueled mature visual perception solutions. Until now, far-field
perception has been the primary focus. Another significant issue is the limited
processing power available for developing real-time applications. Because of
this bottleneck, there is frequently a trade-off between performance and
run-time efficiency. We concentrate on the following issues in order to address
them: 1) Developing near-field perception algorithms with high performance and
low computational complexity for various visual perception tasks such as
geometric and semantic tasks using convolutional neural networks. 2) Using
Multi-Task Learning to overcome computational bottlenecks by sharing initial
convolutional layers between tasks and developing optimization strategies that
balance tasks.


  Context. Small bodies change their brightness due to different motives:
Rotation along their axis or axes, combined with irregular shapes and/or
changing surface properties, or changes in the geometry of observations. In
this work, we tackle the problem of Phase curves, which show the change in
brightness due to changes in the fraction of illuminated surface as seen by the
observer. Aims. We aim to study the effect of the phase curves in the five
wavelengths of the Sloan Digital Sky Survey in scores of objects (several tens
of thousands), focusing particularly on the spectral slopes and the colors and
their changes with phase angle. Methods. We used a Bayesian inference method
and Monte Carlo techniques to retrieve the absolute magnitudes in five
wavelengths, using the results to study the phase coloring effect in different
bins of the semi-major axis. Results. We obtained absolute magnitudes in the
five filters for over 40 000 objects. Although some outliers are identified,
most of the usual color-color space is recovered by the data presented. We also
detect a dual behavior in the spectral slopes, with a change at
${\alpha\approx}$ 5 deg.


  A variety of anomaly detection schemes have been proposed to detect malicious
attacks to Cyber-Physical Systems. Among these schemes, Dynamic Watermarking
methods have been proven highly effective at detecting a wide range of attacks.
Unfortunately, in contrast to other anomaly detectors, no method has been
presented to design a Dynamic Watermarking detector to achieve a user-specified
false alarm rate, or subsequently evaluate the capabilities of an attacker
under such a selection. This paper describes methods to measure the capability
of an attacker, to numerically approximate this metric, and to design a Dynamic
Watermarking detector that can achieve a user-specified rate of false alarms.
The performance of the Dynamic Watermarking detector is compared to three
classical anomaly detectors in simulation and on a real-world platform. These
experiments illustrate that the attack capability under the Dynamic
Watermarking detector is comparable to those of classic anomaly detectors.
Importantly, these experiments also make clear that the Dynamic Watermarking
detector is consistently able to detect attacks that the other class of
detectors are unable to identify.


  Interstellar chemistry in low metallicity environments is crucial to
understand chemical processes in the past metal-poor universe. Recent studies
of interstellar molecules in nearby low-metallicity galaxies have suggested
that the metallicity has a significant effect on chemistry of star-forming
cores. Here we report the first detection of a hot molecular core in the
extreme outer Galaxy, which is an excellent laboratory to study star formation
and interstellar medium in a Galactic low-metallicity environment. The target
star-forming region, WB89-789, is located at the galactocentric distance of 19
kpc. Our ALMA observations in 241-246, 256-261, 337-341, and 349-353 GHz have
detected a variety of carbon-, oxygen-, nitrogen-, sulfur-, and silicon-bearing
species, including complex organic molecules (COMs) containing up to nine
atoms, towards a warm (>100 K) and compact (<0.03 pc) region associated with a
protostar (~8x10^3 L_sun). Deuterated species such as HDO, HDCO, D2CO, and
CH2DOH are also detected. A comparison of fractional abundances of COMs
relative to CH3OH between the outer Galactic hot core and an inner Galactic
counterpart shows a remarkable similarity. On the other hand, the molecular
abundances in the present source do not resemble those of low-metallicity hot
cores in the Large Magellanic Cloud. The results suggest that a great molecular
complexity exists even in a primordial environment of the extreme outer Galaxy.
The detection of another embedded protostar associated with high-velocity SiO
outflows is also reported.


  The AMS-02 collaboration has recently presented measurements of excellent
quality of the cosmic electron and positron fluxes as well as the positron
fraction. We use the measurements of the positron flux to derive, for the first
time, limits on the dark matter annihilation cross section and lifetime for
various final states. Working under the well-motivated assumption that a
background positron flux exists from spallations of cosmic rays with the
interstellar medium and from astrophysical sources, we find strong limits on
the dark matter properties which are competitive, although slightly weaker,
than those derived from the positron fraction. Specifically, for dark matter
particles annihilating only into e+ e- or into mu+ mu-, our limits on the
annihilation cross section are stronger than the thermal value when the dark
matter mass is smaller than 100 GeV or 60 GeV, respectively.


  Despite decreasing cosmic star formation rate density over the last 10 Gyr,
the stellar mass ($M_{*}$) buildups in galaxies were still progressing during
this epoch. About 50\% of the current $M_{*}$ density in the universe was built
over the last $\sim 8.7$ Gyr. In this research, we investigated the stellar
mass buildup and quenching of spatially resolved regions within massive disk
galaxies over the last 10 Gyr. We apply the spectral energy distribution (SED)
fitting method to SEDs of sub-galactic regions in galaxies to derive the
spatially resolved distributions of SFR and $M_{*}$ in the galaxies. This
namely \textit{pixel-to-pixel SED fitting} method is applied to massive disk
galaxies at $0.01<z<0.02$ and $0.8<z<1.8$. We found that massive disk galaxies
tend to build their $M_{*}$ and quench their star formation progressively from
the central region to the outskirts, i.e. \textit{inside-out} stellar mass
buildup and quenching.


  We have shown that the Sun's shadow by high energy cosmic rays moves year by
year and its behavior is correlated with a time variation of the large-scale
structure of the solar and interplanetary magnetic fields. The solar activity
was near minimum in the period from 1996 through 1997. Using the data obtained
with the Tibet air shower array, we examined the shadowing of cosmic rays by
the Sun in this quiet phase of solar cycle, and found that the Sun's shadow was
just in the apparent direction of the Sun, though it was observed at the
position considerably away from the Sun to the south-west in the period between
1990 and 1993. It is known that the magnetic pole of equivalent solar dipole
was reversed during the previous active phase, and near solar minimum the
dipole was aligned with the rotating axis, preserving its N-pole on the north
pole side of the Sun. This causes the solar magnetic field to shift the Sun's
shadow to the east. Thus, the observed results suggest that the shift of the
Sun's shadow due to the solar magnetic field was pushed back by the effect of
the geomagnetic field, since the geomagnetic field always make the shadow shift
to the west. We discuss the Sun's shadow observed during the period near solar
minimum in 1996-1997 and compare it with the simulation results.


  The BaBar measurements of the ratios ${\cal R}(D^{(*)})=\frac{{\cal B}(B \to
D^{(*)} \tau {\bar \nu}_\tau)}{{\cal B}(B \to D^{(*)} \mu {\bar \nu}_\mu)}$
deviate from the standard model expectation, while new results on the purely
leptonic $B \to \tau {\bar \nu}_\tau$ mode show a better consistency with the
standard model, within the uncertainties. In a new physics scenario, one
possibility to accomodate these two experimental facts consists in considering
an additional tensor operator in the effective weak hamiltonian. We study the
effects of such an operator in a set of observables, in semileptonic $B \to
D^{(*)}$ modes as well as in semileptonic $B$ and $B_s$ decays to excited
positive parity charmed mesons.


  We used data from the QUEST-La Silla Active Galactic Nuclei (AGN) variability
survey to construct light curves for 208,583 sources over $\sim 70$ deg$^2$,
with a a limiting magnitude $r \sim 21$. Each light curve has at least 40
epochs and a length of $\geq 200$ days. We implemented a Random Forest
algorithm to classify our objects as either AGN or non-AGN according to their
variability features and optical colors, excluding morphology cuts. We tested
three classifiers, one that only includes variability features (RF1), one that
includes variability features and also $r-i$ and $i-z$ colors (RF2), and one
that includes variability features and also $g-r$, $r-i$, and $i-z$ colors
(RF3). We obtained a sample of high probability candidates (hp-AGN) for each
classifier, with 5,941 candidates for RF1, 5,252 candidates for RF2, and 4,482
candidates for RF3. We divided each sample according to their $g-r$ colors,
defining blue ($g-r\leq 0.6$) and red sub-samples ($g-r>0.6$). We find that
most of the candidates known from the literature belong to the blue
sub-samples, which is not necessarily surprising given that, unlike for many
literature studies, we do not cut our sample to point-like objects. This means
that we can select AGN that have a significant contribution from redshifted
starlight in their host galaxies. In order to test the efficiency of our
technique we performed spectroscopic follow-up, confirming the AGN nature of 44
among 54 observed sources (81.5\% of efficiency). From the campaign we
concluded that RF2 provides the purest sample of AGN candidates.


  In this paper, we extend the idea of "geometric reconstruction" to couple a
nonlocal diffusion model directly with the classical local diffusion in one
dimensional space. This new coupling framework removes interfacial
inconsistency, ensures the flux balance, and satisfies energy conservation as
well as the maximum principle, whereas none of existing coupling methods for
nonlocal-to-local coupling satisfies all of these properties. We establish the
well-posedness and provide the stability analysis of the coupling method. We
investigate the difference to the local limiting problem in terms of the
nonlocal interaction range. Furthermore, we propose a first order finite
difference numerical discretization and perform several numerical tests to
confirm the theoretical findings. In particular, we show that the resulting
numerical result is free of artifacts near the boundary of the domain where a
classical local boundary condition is used, together with a coupled fully
nonlocal model in the interior of the domain.


  In the WKB approximation the $\nabla^2S$ term in Schrodinger's equation is
subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation
in which the $\nabla^2 S$ term dominates (after a guess for S is supplied). Our
approximation produces only the nodeless ground state wavefunction, but it can
be used in potential problems where the potential is not symmetric, and in
problems where there are many degrees of freedom. As a test, we apply the
method to potential problems, including the hydrogen and helium atoms and to
$\phi^4$ field theory.


  We show that spherical truncations of the 1/r interactions in models for
water and acetonitrile yield very accurate results in bulk simulations for all
site-site pair correlation functions as well as dipole-dipole correlation
functions. This good performance in bulk simulations contrasts with the
generally poor results found with the use of such truncations in nonuniform
molecular systems. We argue that Local Molecular Field (LMF) theory provides a
general theoretical framework that gives the necessary corrections to simple
truncations in most nonuniform environments and explains the accuracy of
spherical truncations in uniform environments by showing that these corrections
are very small. LMF theory is derived from the exact Yvon-Born-Green (YBG)
hierarchy by making physically-motivated and well-founded approximations. New
and technically interesting derivations of both the YBG hierarchy and LMF
theory for a variety of site-site molecular models are presented in appendices.
The main paper focuses on understanding the accuracy of these spherical
truncations in uniform systems both phenomenologically and quantitatively using
LMF theory.