  Additive Manufacturing (AM) is a manufacturing paradigm that builds
three-dimensional objects from a computer-aided design model by successively
adding material layer by layer. AM has become very popular in the past decade
due to its utility for fast prototyping such as 3D printing as well as
manufacturing functional parts with complex geometries using processes such as
laser metal deposition that would be difficult to create using traditional
machining. As the process for creating an intricate part for an expensive metal
such as Titanium is prohibitive with respect to cost, computational models are
used to simulate the behavior of AM processes before the experimental run.
However, as the simulations are computationally costly and time-consuming for
predicting multiscale multi-physics phenomena in AM, physics-informed
data-driven machine-learning systems for predicting the behavior of AM
processes are immensely beneficial. Such models accelerate not only multiscale
simulation tools but also empower real-time control systems using in-situ data.
In this paper, we design and develop essential components of a scientific
framework for developing a data-driven model-based real-time control system.
Finite element methods are employed for solving time-dependent heat equations
and developing the database. The proposed framework uses extremely randomized
trees - an ensemble of bagged decision trees as the regression algorithm
iteratively using temperatures of prior voxels and laser information as inputs
to predict temperatures of subsequent voxels. The models achieve mean absolute
percentage errors below 1% for predicting temperature profiles for AM
processes. The code is made available for the research community at
https://github.com/paularindam/ml-iter-additive.


  In the study of long-time correlations extremely long orbits must be
calculated. This may be accomplished much more reliably using fixed-point
arithmetic. Use of this arithmetic on the Cray-1 computer is illustrated.


  We prove the Plancherel formula for Whittaker functions on a reductive p-adic
group. This a sequel to our work on Paley-Wiener theorem. Our proof is close to
the proof written by Waldspurger of the Harish-Chandra Plancherel formula for
smooth functions on the group and use many of his results. One simplification
is the easy proof of the Fourier transfom, which follows from a result of
Joseph Bernstein.


  Quantum open systems are described in the Markovian limit by master equations
in Lindblad form. I argue that common ``quantum trajectory'' techniques
corresponding to continuous measurement schemes, which solve the master
equation by unraveling its evolution into stochastic trajectories in Hilbert
space, correspond closely to particular sets of decoherent (or consistent)
histories. This is illustrated by a simple model of photon counting. An
equivalence is shown for these models between standard quantum jumps and the
orthogonal jumps of Di\'osi, which have already been shown to correspond to
decoherent histories. This correspondence is compared to simple treatments of
trajectories based on repeated or continuous measurements.


  The exploration of sentiment analysis in low-resource languages, such as
Marathi, has been limited due to the availability of suitable datasets. In this
work, we present L3Cube-MahaSent-MD, a multi-domain Marathi sentiment analysis
dataset, with four different domains - movie reviews, general tweets, TV show
subtitles, and political tweets. The dataset consists of around 60,000 manually
tagged samples covering 3 distinct sentiments - positive, negative, and
neutral. We create a sub-dataset for each domain comprising 15k samples. The
MahaSent-MD is the first comprehensive multi-domain sentiment analysis dataset
within the Indic sentiment landscape. We fine-tune different monolingual and
multilingual BERT models on these datasets and report the best accuracy with
the MahaBERT model. We also present an extensive in-domain and cross-domain
analysis thus highlighting the need for low-resource multi-domain datasets. The
data and models are available at https://github.com/l3cube-pune/MarathiNLP .


  It has been known for some time now that error correction plays a fundamental
role in the determining the emergence of semiclassical geometry in quantum
gravity. In this work I connect several different lines of reasoning to argue
that this should indeed be the case. The kinematic data which describes the
scattering of $ N $ massless particles in flat spacetime can put in one-to-one
correspondence with coherent states of quantum geometry. These states are
labeled by points in the Grassmannian $ Gr_{2,n} $, which can be viewed as
labeling the code-words of a quantum error correcting code. The condition of
Lorentz invariance of the background geometry can then be understood as the
requirement that co-ordinate transformations should leave the code subspace
unchanged. In this essay I show that the language of subsystem (or operator)
quantum error correcting codes provides the proper framework for understanding
these aspects of particle scattering and quantum geometry.


  We examine the optical properties of two different configurations of a
cylindrical device made from a hyperbolic metamaterial with optical axis
defined by circular and radial director fields. The hyperbolic metamaterial is
an uniaxial anisotropic medium for which the ratio between ordinary and
extraordinary permittivities is negative, leading to a particular effective
geometry with two timelike coordinates in the metric (Kleinian signature). By
using differential geometry tools we are able to perform a comparison between a
simple geometrical optics treatment and the wave formalism that shows the
concentration of light along the cylinder axis for the case of the circular
field configuration, whatever the injection conditions are.


  It is well known that in Zermelo-Fraenkel (ZF) set theory any finite set is
decidable. In this paper we discuss an extension of ZF where this result is no
longer valid. Such an extension is quasi-set theory and it has its origin on
problems motivated by quantum mechanics.


  For three nebulae that have early-WN Wolf-Rayet exciting stars, NGC 6888, WR
8 and Abell 48, we have obtained Herschel-PACS line scans of the [N III] 57 um
and [O III] 88 micron lines, along with the 122 and 205 micron lines of [N II].
From the former two lines we have derived N$^{2+}$/O$^{2+}$ abundance ratios,
equal to the overall N/O ratio under a wide range of nebular conditions. We
find that all of the nebulae observed possess significant nitrogen enrichment,
with derived N/O ratios greater than solar. The two nebulae with massive
Wolf-Rayet exciting stars, NGC 6888 and WR8 are found to have N/O ratios that
are enhanced by factors of 7 - 10 relative to the solar N/O ratio, consistent
with an origin as material ejected just before the onset of the Wolf-Rayet
phase. The other nebula, Abell 48, has recently been reclassified as a member
of the rare class of three planetary nebulae that have early-WN central stars
and are not of Peimbert Type I. We derive a nebular N/O ratio for it that is a
factor of 4 enhanced relative to solar and slightly above the range of N/O
values that have been measured for the other three members of its [WN]
planetary nebula class.


  The baryon-number-two (B=2) solution based on the SU(2) chiral quark soliton
model ($\chi$QSM) is solved numerically, including fully the sea quark degrees
of freedom. We confirm that the axially symmetric meson configurations yield
the energy minimum for the B=2 state in the $\chi$QSM when taking into account
quark dynamics. Due to the axially symmetric meson fields, six valence quarks
occupy the lowest energy level, consistent with the Pauli exclusion principle.
The minimal-energy of the entire system is obtained within the framework of a
symmetric ansatz. The fermion determinant with axially symmetric meson fields
is calculated by diagonalizing the corresponding Dirac hamiltonian in a
non-perterbative way, using a cylindrical Dirac basis. The baryon number
density, calculated with quark fields corresponding to a soliton, is toroidal
in shape. We also calculate the mean radius of the toroid from the quark
fields. These results are closely related to Skyrme model calculations based
upon pion degrees of freedom. Our model calculations clarify the underlying
dynamical structure of the baryons at the quark level.


  This paper proposes a learning-from-demonstration method using probability
densities on the workspaces of robot manipulators. The method, named
"PRobabilistically-Informed Motion Primitives (PRIMP)", learns the probability
distribution of the end effector trajectories in the 6D workspace that includes
both positions and orientations. It is able to adapt to new situations such as
novel via poses with uncertainty and a change of viewing frame. The method
itself is robot-agnostic, in which the learned distribution can be transferred
to another robot with the adaptation to its workspace density. The learned
trajectory distribution is then used to guide an optimization-based motion
planning algorithm to further help the robot avoid novel obstacles that are
unseen during the demonstration process. The proposed methods are evaluated by
several sets of benchmark experiments. PRIMP runs more than 5 times faster
while generalizing trajectories more than twice as close to both the
demonstrations and novel desired poses. It is then combined with our robot
imagination method that learns object affordances, illustrating the
applicability of PRIMP to learn tool use through physical experiments.


  In nearly AdS2 gravity the Einstein-Hilbert term is supplemented by the
Jackiw-Teitelboim action. Integrating out the bulk metric gives rise to the
Schwarzian action for the boundary curve. In the present note, we show how the
extension to supergravity leads to the super-Schwarzian action for the
superspace boundary.


  The critical properties characterizing the formation of the Floquet time
crystal in the prethermal phase are investigated analytically in the
periodically driven $O(N)$ model. In particular, we focus on the critical line
separating the trivial phase with period synchronized dynamics and absence of
long-range spatial order from the non-trivial phase where long-range spatial
order is accompanied by period-doubling dynamics. In the vicinity of the
critical line, with a combination of dimensional expansion and exact solution
for $N\to\infty$, we determine the exponent $\nu$ that characterizes the
divergence of the spatial correlation length of the equal-time correlation
functions, the exponent $\beta$ characterizing the growth of the amplitude of
the order-parameter, as well as the initial-slip exponent $\theta$ of the aging
dynamics when a quench is performed from deep in the trivial phase to the
critical line. The exponents $\nu, \beta, \theta$ are found to be identical to
those in the absence of the drive. In addition, the functional form of the
aging is found to depend on whether the system is probed at times that are
small or large compared to the drive period. The spatial structure of the
two-point correlation functions, obtained as a linear response to a perturbing
potential in the vicinity of the critical line, is found to show algebraic
decays that are longer ranged than in the absence of a drive, and besides being
period-doubled, are also found to oscillate in space at the wave-vector
$\omega/(2 v)$, $v$ being the velocity of the quasiparticles, and $\omega$
being the drive frequency.


  We propose a neutrino model based on a $\Delta(54)$ flavor symmetry suitable
for explaining the current neutrino oscillation data. Neutrino masses arise
from the type II seesaw mechanism where the $\Delta(54)$ field assignments has
led to a simple neutrino mass matrix with one texture zero and which satisfies
the magic symmetry consistent with the well-known trimaximal mixing matrix. We
found interesting predictions concerning neutrino masses and mixing. In
particular, only the normal neutrino mass hierarchy and the lower octant of the
atmospheric angles are allowed in this model. The model predicts as well that
the $CP$ conserving values for the Dirac $CP$ phase $\delta _{CP}$ are not
allowed and thus, $CP$ is always violated in the neutrino sector. We have also
investigated the sum of absolute neutrino masses from cosmological
observations, the effective Majorana mass $m_{\beta \beta }$\ from neutrinoless
double beta decay experiments, and the electron neutrino mass $m_{\beta }$\
from beta decays where we found that the obtained range of $m_{\beta \beta }$\
can be tested by several experiments in the near future.


  The presence of turbulent phenomena in the outer solar atmosphere is a given.
However, because we are reduced to remotely sensing the atmosphere of a star
with instruments of limited spatial and/or spectral resolution, we can only
infer the physical progression from macroscopic to microscopic phenomena. Even
so, we know that many, if not all, of the turbulent phenomena that pervade
interplanetary space have physical origins at the Sun and so in this brief
article we consider some recent measurements which point to sustained potential
source(s) of heliospheric turbulence in the magnetic and thermal domains. In
particular, we look at the scales of magnetism that are imprinted on the outer
solar atmosphere by the relentless magneto-convection of the solar interior and
combine state-of-the-art observations from the Solar Dynamics Observatory (SDO)
and the Coronal Multi-channel Polarimeter (CoMP) which are beginning to hint at
the origins of the wave/plasma interplay prevalent closer to the Earth. While
linking these disparate scales of observation and understanding of their
connection is near to impossible, it is clear that the constant evolution of
subsurface magnetism on a host of scales guides and governs the flow of mass
and energy at the smallest scales. In the near future significant progress in
this area will be made by linking observations from high resolution platforms
like the Interface Region Imaging Spectrograph (IRIS) and Advanced Technology
Solar Telescope (ATST) with full-disk synoptic observations such as those
presented herein.


  We show existence of ancient solutions to the rescaled mean curvature flow
starting from a given asymptotically conical self-expander. These are examples
of mean curvature flows coming out of cones that are not self-similar. We also
show a strong uniqueness theorem when the cone is generic and use it to
classify mean curvature flows coming out of generic cones of small entropy in
low dimensions.


  We describe the Cool Opacity-sampling Dynamic EXtended (CODEX) atmosphere
models of Mira variable stars, and examine in detail the physical and numerical
approximations that go in to the model creation. The CODEX atmospheric models
are obtained by computing the temperature and the chemical and radiative states
of the atmospheric layers, assuming gas pressure and velocity profiles from
Mira pulsation models, which extend from near the H-burning shell to the outer
layers of the atmosphere. Although the code uses the approximation of Local
Thermodynamic Equilibrium (LTE) and a grey approximation in the dynamical
atmosphere code, many key observable quantities, such as infrared diameters and
low-resolution spectra, are predicted robustly in spite of these
approximations. We show that in visible light, radiation from Mira variables is
dominated by fluorescence scattering processes, and that the LTE approximation
likely under-predicts visible-band fluxes by a factor of two.


  The $L_p$-discrepancy is a quantitative measure for the irregularity of
distribution of an $N$-element point set in the $d$-dimensional unit cube,
which is closely related to the worst-case error of quasi-Monte Carlo
algorithms for numerical integration. Its inverse for dimension $d$ and error
threshold $\varepsilon \in (0,1)$ is the minimal number of points in $[0,1)^d$
such that the minimal normalized $L_p$-discrepancy is less or equal
$\varepsilon$. It is well known, that the inverse of $L_2$-discrepancy grows
exponentially fast with the dimension $d$, i.e., we have the curse of
dimensionality, whereas the inverse of $L_{\infty}$-discrepancy depends exactly
linearly on $d$. The behavior of inverse of $L_p$-discrepancy for general $p
\not\in \{2,\infty\}$ has been an open problem for many years. In this paper we
show that the $L_p$-discrepancy suffers from the curse of dimensionality for
all $p$ in $(1,2]$ which are of the form $p=2 \ell/(2 \ell -1)$ with $\ell \in
\mathbb{N}$.
  This result follows from a more general result that we show for the
worst-case error of numerical integration in an anchored Sobolev space with
anchor 0 of once differentiable functions in each variable whose first
derivative has finite $L_q$-norm, where $q$ is an even positive integer
satisfying $1/p+1/q=1$.


  Given a permutation $\pi$ chosen uniformly from $S_n$, we explore the joint
distribution of $\pi(1)$ and the number of descents in $\pi$. We obtain a
formula for the number of permutations with $\des(\pi)=d$ and $\pi(1)=k$, and
use it to show that if $\des(\pi)$ is fixed at $d$, then the expected value of
$\pi(1)$ is $d+1$. We go on to derive generating functions for the joint
distribution, show that it is unimodal if viewed correctly, and show that when
$d$ is small the distribution of $\pi(1)$ among the permutations with $d$
descents is approximately geometric. Applications to Stein's method and the
Neggers-Stanley problem are presented.


  Parity-violating (PV) gravity has recently attracted interest in several
aspects. One of them is the axion-graviton coupling to test the axion-dark
matter model. Moreover, by extending Chern-Simons (CS) gravity to include
derivatives of a scalar field up to the second order, a more general class of
PV gravity theory, which we call the CNCL model, has been proposed~[M.
Crisostomi {\it et al.}, Phys. Rev. D, {\bf 97}, 044034 (2018)]. The model can
be further extended by including even higher derivatives of the scalar field
and/or higher curvature terms. In this paper, we discuss the effect of parity
violation in the gravitational sector on the propagation of gravitational waves
from binary coalescence by introducing a model-independent parametrization of
modification. Our parametrization includes the CNCL model as well as CS
gravity. The effect of parity violation on the gravitational waveform is
maximum when the source binary orientation to our line of sight is edge-on,
while the modified waveform reduces to the parity-symmetric one when the source
is face-on. We perform a search for the signature of such modification by using
the LIGO/Virgo O1/O2 catalog. We find that the catalog data is consistent with
general relativity and obtain constraints on parity violation in gravity for
various post-Newtonian order modifications for the first time. The obtained
constraint on CS gravity is consistent with the results in previous works. On
the other hand, the constraint on the CNCL model that we obtain is tighter than
the previous results by roughly 7 orders of magnitude.


  We prove that the modified Benjamin-Ono equation is globally wellposed in
$H^s$ for $s\ge 1/2$.


  The paper provides a comprehensive overview of Neural Architecture Search
(NAS), emphasizing its evolution from manual design to automated,
computationally-driven approaches. It covers the inception and growth of NAS,
highlighting its application across various domains, including medical imaging
and natural language processing. The document details the shift from
expert-driven design to algorithm-driven processes, exploring initial
methodologies like reinforcement learning and evolutionary algorithms. It also
discusses the challenges of computational demands and the emergence of
efficient NAS methodologies, such as Differentiable Architecture Search and
hardware-aware NAS. The paper further elaborates on NAS's application in
computer vision, NLP, and beyond, demonstrating its versatility and potential
for optimizing neural network architectures across different tasks. Future
directions and challenges, including computational efficiency and the
integration with emerging AI domains, are addressed, showcasing NAS's dynamic
nature and its continued evolution towards more sophisticated and efficient
architecture search methods.


  We consider the penetration length $l$ of random walkers diffusing in a
medium of perfect or imperfect absorbers of number density $\rho$. We solve
this problem on a lattice and in the continuum in all dimensions $D$, by means
of a mean-field renormalization group. For a homogeneous system in $D>2$, we
find that $l\sim \max(\xi,\rho^{-1/2})$, where $\xi$ is the absorber density
correlation length. The cases of D=1 and D=2 are also treated. In the presence
of long-range correlations, we estimate the temporal decay of the density of
random walkers not yet absorbed. These results are illustrated by exactly
solvable toy models, and extensive numerical simulations on directed
percolation, where the absorbers are the active sites. Finally, we discuss the
implications of our results for diffusion limited aggregation (DLA), and we
propose a more effective method to measure $l$ in DLA clusters.


  The magnetic shielding $\sigma$ of $^3$He is studied. The complete
relativistic corrections of order $O(\alpha^2)$, leading QED corrections of
order $O(\alpha^3 \ln\alpha)$, and finite nuclear mass effects of order
$O(m/m_{\rm N})$ are calculated with high numerical precision. The resulting
theoretical predictions for $\sigma = 59.967~43(10)\cdot 10^{-6}$ are the most
accurate to date among all elements and support the use of $^3$He as a NMR
standard.


  Collaborative Filtering is largely applied to personalize item recommendation
but its performance is affected by the sparsity of rating data. In order to
address this issue, recent systems have been developed to improve
recommendation by extracting latent factors from the rating matrices, or by
exploiting trust relations established among users in social networks. In this
work, we are interested in evaluating whether other sources of preference
information than ratings and social ties can be used to improve recommendation
performance. Specifically, we aim at testing whether the integration of
frequently co-occurring interests in information search logs can improve
recommendation performance in User-to-User Collaborative Filtering (U2UCF). For
this purpose, we propose the Extended Category-based Collaborative Filtering
(ECCF) recommender, which enriches category-based user profiles derived from
the analysis of rating behavior with data categories that are frequently
searched together by people in search sessions. We test our model using a big
rating dataset and a log of a largely used search engine to extract the
co-occurrence of interests. The experiments show that ECCF outperforms U2UCF
and category-based collaborative recommendation in accuracy, MRR, diversity of
recommendations and user coverage. Moreover, it outperforms the SVD++ Matrix
Factorization algorithm in accuracy and diversity of recommendation lists.


  The massless superfield content of four-dimensional compactifications of
closed superstrings with extended (N=2, 3, or 4) supersymmetry is derived by
multiplying two (N=0, 1, or 2) Yang-Mills multiplets. In some cases these
superfields are known, and the low-energy actions are determined from the fact
that the compensator (dilaton) supermultiplets occur quadratically classically.
In the other cases these superfields suggest new formulations of extended
superspace theories.


  Dogru and Tabachnikov in 2003 explored the polygonal outer billiard map in
the hyperbolic plane and introduced a class of convex polygons called 'large'.
They particularly sought conditions for a triangle to be classified as large.
For a large triangle, there exist two triangles that are circumscribed around
it and inscribed within the unit circle. In the Klein-Beltrami model of
hyperbolic geometry, we reformulate the conditions for a triangle to be
classified as 'large' in a more Euclidean geometric manner. A proposed measure
of its Euclidean geometric size when the triangle is considered 'large' is
introduced, and an evaluation of this measure is conducted. We also provide an
explicit formula for an isosceles triangle.


  We introduce a finitely presented prop $\mathcal{S} = \{\mathcal{S}(n,m)\}$
in the category of differential graded modules whose associated operad
$U(\mathcal{S})=\{\mathcal{S}(1,m)\}$ is a model for the $E_\infty$-operad.
This finite presentation allows us to describe a natural $E_\infty$-coalgebra
structure on the chains of any simplicial set in terms of only three maps: the
Alexander-Whitney diagonal, the augmentation map, and an algebraic version of
the join of simplices. The first appendix connects our construction to the
Surjection operad of McClure-Smith and Berger-Fresse. The second establishes a
duality between the join and AW maps for augmented and non-augmented simplicial
sets. A follow up paper constructs a prop corresponding to $\mathcal{S}$ in the
category of $CW$-complexes.


  Test-time domain adaptation effectively adjusts the source domain model to
accommodate unseen domain shifts in a target domain during inference. However,
the model performance can be significantly impaired by continuous distribution
changes in the target domain and non-independent and identically distributed
(non-i.i.d.) test samples often encountered in practical scenarios. While
existing memory bank methodologies use memory to store samples and mitigate
non-i.i.d. effects, they do not inherently prevent potential model degradation.
To address this issue, we propose a resilient practical test-time adaptation
(ResiTTA) method focused on parameter resilience and data quality.
Specifically, we develop a resilient batch normalization with estimation on
normalization statistics and soft alignments to mitigate overfitting and model
degradation. We use an entropy-driven memory bank that accounts for timeliness,
the persistence of over-confident samples, and sample uncertainty for
high-quality data in adaptation. Our framework periodically adapts the source
domain model using a teacher-student model through a self-training loss on the
memory samples, incorporating soft alignment losses on batch normalization. We
empirically validate ResiTTA across various benchmark datasets, demonstrating
state-of-the-art performance.


  Current research in eSports lacks the tools for proper game practising and
performance analytics. The majority of prior work relied only on in-game data
for advising the players on how to perform better. However, in-game mechanics
and trends are frequently changed by new patches limiting the lifespan of the
models trained exclusively on the in-game logs. In this article, we propose the
methods based on the sensor data analysis for predicting whether a player will
win the future encounter. The sensor data were collected from 10 participants
in 22 matches in League of Legends video game. We have trained machine learning
models including Transformer and Gated Recurrent Unit to predict whether the
player wins the encounter taking place after some fixed time in the future. For
10 seconds forecasting horizon Transformer neural network architecture achieves
ROC AUC score 0.706. This model is further developed into the detector capable
of predicting that a player will lose the encounter occurring in 10 seconds in
88.3% of cases with 73.5% accuracy. This might be used as a players' burnout or
fatigue detector, advising players to retreat. We have also investigated which
physiological features affect the chance to win or lose the next in-game
encounter.


  We propose an optical single-photon switch based on Rydberg atoms that
interact through van der Waals interactions. A weak coherent field probes the
atomic cloud continuously, and when a single photon excites a Rydberg state, it
breaks the conditions for electromagnetically induced transparency, altering
the reflection/transmission. Two versions of the device are proposed, one in a
single-sided cavity and the other in free space. The proposed device extends
the toolkit for quantum light manipulation and photon readout, and represents a
continuous wave version of previously demonstrated single-photon transistors.


  In Bayesian networks, a Most Probable Explanation (MPE) is a complete
variable instantiation with a highest probability given the current evidence.
In this paper, we discuss the problem of finding robustness conditions of the
MPE under single parameter changes. Specifically, we ask the question: How much
change in a single network parameter can we afford to apply while keeping the
MPE unchanged? We will describe a procedure, which is the first of its kind,
that computes this answer for each parameter in the Bayesian network variable
in time O(n exp(w)), where n is the number of network variables and w is its
treewidth.


  Model-based methods and deep neural networks have both been tremendously
successful paradigms in machine learning. In model-based methods, problem
domain knowledge can be built into the constraints of the model, typically at
the expense of difficulties during inference. In contrast, deterministic deep
neural networks are constructed in such a way that inference is
straightforward, but their architectures are generic and it is unclear how to
incorporate knowledge. This work aims to obtain the advantages of both
approaches. To do so, we start with a model-based approach and an associated
inference algorithm, and \emph{unfold} the inference iterations as layers in a
deep network. Rather than optimizing the original model, we \emph{untie} the
model parameters across layers, in order to create a more powerful network. The
resulting architecture can be trained discriminatively to perform accurate
inference within a fixed network size. We show how this framework allows us to
interpret conventional networks as mean-field inference in Markov random
fields, and to obtain new architectures by instead using belief propagation as
the inference algorithm. We then show its application to a non-negative matrix
factorization model that incorporates the problem-domain knowledge that sound
sources are additive. Deep unfolding of this model yields a new kind of
non-negative deep neural network, that can be trained using a multiplicative
backpropagation-style update algorithm. We present speech enhancement
experiments showing that our approach is competitive with conventional neural
networks despite using far fewer parameters.


  We observe the statistical properties of blogs that are expected to reflect
social human interaction. Firstly, we introduce a basic normalization
preprocess that enables us to evaluate the genuine word frequency in blogs that
are independent of external factors such as spam blogs, server-breakdowns,
increase in the population of bloggers, and periodic weekly behaviors. After
this process, we can confirm that small frequency words clearly follow an
independent Poisson process as theoretically expected. Secondly, we focus on
each blogger's basic behaviors. It is found that there are two kinds of
behaviors of bloggers. Further, Zipf's law on word frequency is confirmed to be
universally independent of individual activity types.


  A simple model for electromagnetic wave propagation through zero-temperature
plasma is analyzed. Many of the complexities of the plasma state are present
even under these idealized conditions, and a number of mathematical
difficulties emerge. In particular, boundary value problems formulated on the
basis of conventional electromagnetic theory turn out to be ill-posed in this
context. However, conditions may be prescribed under which solutions to the
Dirichlet problem exist in an appropriately weak sense. In addition to its
physical interest, analysis of the cold plasma model illuminates generic
difficulties in formulating and solving boundary value problems for mixed
elliptic-hyperbolic partial differential equations.


  Explaining the internal distribution and motions of stars and gas in galaxies
is a key aspect in understanding their evolution. In previous work we
identified five well resolved galaxies with atypical kinematics from a
cosmological simulation; two had kinematically distinct cores (KDCs), and three
had counter-rotating gas and stars (CRGD). In this paper, we show that i) the
KDC galaxies have flattening of stellar [O/Fe] at large galacto-centric radii
due to the minor mergers that gave rise to the KDCs, and ii) the CRGD galaxies
have an abrupt transition in the gas metallicity maps, from high metallicity in
the centre to very low metallicity further out. These galaxies are embedded in
dark matter filaments where there is a ready supply of near-pristine gas to
cause this effect. The non-linear increase in gas metallicity is also seen in
the radial profiles, but when the metallicity gradients are measured, the
difference is buried in the scatter of the relation. We also find that all five
galaxies are fairly compact, with small effective radii given their stellar
masses. This is because they have not experienced major mergers that
kinematically heat the stars, and would have destroyed their unusual
kinematics. In order to detect these signatures of minor mergers or accretion,
the galaxy scaling relations or radial metallicity profiles are not enough, and
it is necessary to obtain the 2D maps with integral field spectroscopy
observations.


  We present an approach to matching images of objects in fine-grained datasets
without using part annotations, with an application to the challenging problem
of weakly supervised single-view reconstruction. This is in contrast to prior
works that require part annotations, since matching objects across class and
pose variations is challenging with appearance features alone. We overcome this
challenge through a novel deep learning architecture, WarpNet, that aligns an
object in one image with a different object in another. We exploit the
structure of the fine-grained dataset to create artificial data for training
this network in an unsupervised-discriminative learning approach. The output of
the network acts as a spatial prior that allows generalization at test time to
match real images across variations in appearance, viewpoint and articulation.
On the CUB-200-2011 dataset of bird categories, we improve the AP over an
appearance-only network by 13.6%. We further demonstrate that our WarpNet
matches, together with the structure of fine-grained datasets, allow
single-view reconstructions with quality comparable to using annotated point
correspondences.


  We study supervised learning problems that have significant effects on
individuals from two demographic groups, and we seek predictors that are fair
with respect to a group fairness criterion such as statistical parity (SP). A
predictor is SP-fair if the distributions of predictions within the two groups
are close in Kolmogorov distance, and fairness is achieved by penalizing the
dissimilarity of these two distributions in the objective function of the
learning problem. In this paper, we identify conditions under which hard SP
constraints are guaranteed to improve predictive accuracy. We also showcase
conceptual and computational benefits of measuring unfairness with integral
probability metrics (IPMs) other than the Kolmogorov distance. Conceptually, we
show that the generator of any IPM can be interpreted as a family of utility
functions and that unfairness with respect to this IPM arises if individuals in
the two demographic groups have diverging expected utilities. We also prove
that the unfairness-regularized prediction loss admits unbiased gradient
estimators, which are constructed from random mini-batches of training samples,
if unfairness is measured by the squared $\mathcal L^2$-distance or by a
squared maximum mean discrepancy. In this case, the fair learning problem is
susceptible to efficient stochastic gradient descent (SGD) algorithms.
Numerical experiments on synthetic and real data show that these SGD algorithms
outperform state-of-the-art methods for fair learning in that they achieve
superior accuracy-unfairness trade-offs -- sometimes orders of magnitude
faster.


  We use the lightcurve inversion method to derive new shape models and spin
states of asteroids from the sparse-in-time photometry compiled in the Lowell
Photometric Database. To speed up the time-consuming process of scanning the
period parameter space through the use of convex shape models, we use the
distributed computing project Asteroids@home, running on the Berkeley Open
Infrastructure for Network Computing (BOINC) platform. This way, the
period-search interval is divided into hundreds of smaller intervals. These
intervals are scanned separately by different volunteers and then joined
together. We also use an alternative, faster, approach when searching the
best-fit period by using a model of triaxial ellipsoid. By this, we can
independently confirm periods found with convex models and also find rotation
periods for some of those asteroids for which the convex-model approach gives
too many solutions. From the analysis of Lowell photometric data of the first
100,000 numbered asteroids, we derived 328 new models. This almost doubles the
number of available models. We tested the reliability of our results by
comparing models that were derived from purely Lowell data with those based on
dense lightcurves, and we found that the rate of false-positive solutions is
very low. We also present updated plots of the distribution of spin obliquities
and pole ecliptic longitudes that confirm previous findings about a non-uniform
distribution of spin axes. However, the models reconstructed from noisy sparse
data are heavily biased towards more elongated bodies with high lightcurve
amplitudes.


  We consider an online preemptive scheduling problem where jobs with deadlines
arrive sporadically. A commitment requirement is imposed such that the
scheduler has to either accept or decline a job immediately upon arrival. The
scheduler's decision to accept an arriving job constitutes a contract with the
customer; if the accepted job is not completed by its deadline as promised, the
scheduler loses the value of the corresponding job and has to pay an additional
penalty depending on the amount of unfinished workload. The objective of the
online scheduler is to maximize the overall profit, i.e., the total value of
the admitted jobs completed before their deadlines less the penalty paid for
the admitted jobs that miss their deadlines. We show that the maximum
competitive ratio is $3-2\sqrt{2}$ and propose a simple online algorithm to
achieve this competitive ratio. The optimal scheduling includes a threshold
admission and a greedy scheduling policies. The proposed algorithm has direct
applications to the charging of plug-in hybrid electrical vehicles (PHEV) at
garages or parking lots.


  I considered solving of the system of linear equations
$$a^1_{1s0}x^1a^1_{1s1}+...+a^1_{ns0}x^na^1_{ns1}=b^1$$ $$...$$
$$a^n_{1s0}x^1a^n_{1s1}+...+a^n_{ns0}x^na^n_{ns1}=b^n$$ over non-commutative
associative algebra. I considered examples in quaternion algebra. I considered
also Newton's method to solve the equation $$f(x)=a$$ over non-commutative
associative algebra.


  We have obtained Finslerian Ressiner-Nordstrom solution where it is
asymptotic to a Finsler spacetime with constant flag curvature while
$r\rightarrow\infty$. The covariant derivative of modified Einstein tensor in
Finslerian gravitational field equation for this solution is conserved. The
symmetry of the special Finslerian Ressiner-Nordstrom spacetime, namely,
Finsler spacetime with constant flag curvature, has been investigated. It
admits four independent Killing vectors. The Finslerian Ressiner-Nordstrom
solution differs from Ressiner-Nordstrom metric only in two dimensional
subspace. And our solution requires that its two dimensional subspace have
constant flag curvature. We have obtained eigenfunction of Finslerian Laplace
operator of "Finslerian sphere", namely, a special subspace with positive
constant flag curvature. The eigenfunction is of the form
$\bar{Y}_l^m=Y_l^m+\epsilon^2(C_{l+2}^m Y_{l+2}^m+C_{l-2}^m Y_{l-2}^m)$ in
powers of Finslerian parameter $\epsilon$, where $C_{l+2}^m$ and $C_{l-2}^m$
are constant. However, the eigenvalue depends on both $l$ and $m$. The
eigenvalues corresponded to $Y_1^0$ remain the same with Riemannian Laplace
operator and the eigenvalues corresponded to $Y_1^{\pm1}$ are different. This
fact just reflect the symmetry of "Finslerian sphere", which admits a $z$-axis
rotational symmetry and breaks other symmetry of Riemannian sphere. The
eigenfunction of Finslerian Laplace operator implies that monopolar and dipolar
terms of multipole expansion of gravitational potential are unchanged and other
multipole terms are changed.


  Numerical relativity has recently yielded a plethora of results about kicks
from spinning mergers which has, in turn, vastly increased our knowledge about
the spin interactions of black hole systems. In this work we use black hole
perturbation theory to calculate accurately the gravitational waves emanating
from the end of the plunging stage of an extreme mass ratio merger in order to
further understand this phenomenon. This study focuses primarily on spin
induced effects with emphasis on the maximally spinning limit and the
identification of possible causes of generic behavior.
  We find that gravitational waves emitted during the plunging phase exhibit
damped oscillatory behavior, corresponding to a coherent excitation of
quasi-normal modes by the test particle. This feature is universal in the sense
that the frequencies and damping time do not depend on the orbital parameters
of the plunging particle. Furthermore, the observed frequencies are distinct
from those associated with the usual free quasi-normal ringing. Our calculation
suggests that a maximum in radiated energy and momentum occurs at spin
parameters equal to $a/M=0.86$ and $a/M=0.81$, respectively for the plunge
stage of a polar orbit. The dependence of linear momentum emission on the angle
at which a polar orbit impacts the horizon is quantified. One of the advantages
of the perturbation approach adopted here is that insight into the actual
mechanism of radiation emission and its relationship to black hole ringing is
obtained by carefully identifying the dominant terms in the expansions used.


  We consider a transmission problem where a structurally damped plate equation
is coupled with a damped or undamped wave equation by transmission conditions.
We show that exponential stability holds in the damped-damped situation and
polynomial stability (but no exponential stability) holds in the
damped-undamped case. Additionally, we show that the solutions first defined by
the weak formulation, in fact have higher Sobolev space regularity.


  We propose State Matching Offline DIstribution Correction Estimation
(SMODICE), a novel and versatile regression-based offline imitation learning
(IL) algorithm derived via state-occupancy matching. We show that the SMODICE
objective admits a simple optimization procedure through an application of
Fenchel duality and an analytic solution in tabular MDPs. Without requiring
access to expert actions, SMODICE can be effectively applied to three offline
IL settings: (i) imitation from observations (IfO), (ii) IfO with dynamics or
morphologically mismatched expert, and (iii) example-based reinforcement
learning, which we show can be formulated as a state-occupancy matching
problem. We extensively evaluate SMODICE on both gridworld environments as well
as on high-dimensional offline benchmarks. Our results demonstrate that SMODICE
is effective for all three problem settings and significantly outperforms prior
state-of-art.


  Properties of relative traces and symmetrizing forms on chains of cyclotomic
and affine Hecke algebras are studied. The study relies on a use of bases of
these algebras which generalize a normal form for elements of the complex
reflection groups $G(m,1,n)$, $m=1,2,\dots,\infty$, constructed by a recursive
use of the Coxeter--Todd algorithm. Formulas for inducing, from representations
of an algebra in the chain, representations of the next member of the chain are
presented.


  In this paper, we present a novel reconstruction method for diffuse optical
spectroscopic imaging with a commonly used tissue model of optical absorption
and scattering. It is based on linearization and group sparsity, which allows
recovering the diffusion coefficient and absorption coefficient simultaneously,
provided that their spectral profiles are incoherent and a sufficient number of
wavelengths are judiciously taken for the measurements. We also discuss the
reconstruction for imperfectly known boundary and show that with the
multi-wavelength data, the method can reduce the influence of modelling errors
and still recover the absorption coefficient. Extensive numerical experiments
are presented to support our analysis.


  Air traffic control (ATC) is a safety-critical service system that demands
constant attention from ground air traffic controllers (ATCos) to maintain
daily aviation operations. The workload of the ATCos can have negative effects
on operational safety and airspace usage. To avoid overloading and ensure an
acceptable workload level for the ATCos, it is important to predict the ATCos'
workload accurately for mitigation actions. In this paper, we first perform a
review of research on ATCo workload, mostly from the air traffic perspective.
Then, we briefly introduce the setup of the human-in-the-loop (HITL)
simulations with retired ATCos, where the air traffic data and workload labels
are obtained. The simulations are conducted under three Phoenix approach
scenarios while the human ATCos are requested to self-evaluate their workload
ratings (i.e., low-1 to high-7). Preliminary data analysis is conducted. Next,
we propose a graph-based deep-learning framework with conformal prediction to
identify the ATCo workload levels. The number of aircraft under the
controller's control varies both spatially and temporally, resulting in
dynamically evolving graphs. The experiment results suggest that (a) besides
the traffic density feature, the traffic conflict feature contributes to the
workload prediction capabilities (i.e., minimum horizontal/vertical separation
distance); (b) directly learning from the spatiotemporal graph layout of
airspace with graph neural network can achieve higher prediction accuracy,
compare to hand-crafted traffic complexity features; (c) conformal prediction
is a valuable tool to further boost model prediction accuracy, resulting a
range of predicted workload labels. The code used is available at
\href{https://github.com/ymlasu/para-atm-collection/blob/master/air-traffic-prediction/ATC-Workload-Prediction/}{$\mathsf{Link}$}.


  Through an appropriate election of the molecular orbital basis, we show
analytically that the molecular dissociation occurring in a Heyrovsky reaction
can be interpreted as a Quantum Dynamical Phase Transition, i.e., an analytical
discontinuity in the molecular energy spectrum induced by the catalyst. The
metallic substrate plays the role of an environment that produces an energy
uncertainty on the adatom. This broadening induces a critical behavior not
possible in a quantum closed system. We use suitable approximations on
symmetry, together with both Lanczos and canonical transformations, to give
analytical estimates for the critical parameters of molecular dissociation.
This occurs when the bonding to the surface is (\sqrt{2}) times the molecular
bonding. This value is slightly weakened for less symmetric situations. However
simple, this conclusion involves a high order perturbative solution of the
molecule-catalyst system. This model is further simplified to discuss how an
environment-induced critical phenomenon can be evaluated through an idealized
perturbative tunneling microscopy set-up. In this case, the energy
uncertainties in one or both atoms are either Lorentzian or Gaussian. The
former results from the Fermi Golden Rule, i.e., a Markovian approximation. The
Gaussian uncertainty, associated with non-Markovian decoherent processes,
requires the introduction of a particular model of a spin bath. The partially
coherent tunneling current is obtained from the Generalized Landauer-B\"uttiker
Equations. The resonances observed in these transport parameters reflect, in
many cases, the critical properties of the resonances in the molecular
spectrum.


  Clustering is a fundamental data mining tool that aims to divide data into
groups of similar items. Generally, intuition about clustering reflects the
ideal case -- exact data sets endowed with flawless dissimilarity between
individual instances.
  In practice however, these cases are in the minority, and clustering
applications are typically characterized by noisy data sets with approximate
pairwise dissimilarities. As such, the efficacy of clustering methods in
practical applications necessitates robustness to perturbations.
  In this paper, we perform a formal analysis of perturbation robustness,
revealing that the extent to which algorithms can exhibit this desirable
characteristic is inherently limited, and identifying the types of structures
that allow popular clustering paradigms to discover meaningful clusters in
spite of faulty data.


  This is the third in a sequence of four papers, where we prove the arithmetic
Siegel--Weil formula in co-rank $1$ for Kudla--Rapoport special cycles on
exotic smooth integral models of unitary Shimura varieties of arbitrarily large
even arithmetic dimension. Our arithmetic Siegel--Weil formula implies that
degrees of Kudla--Rapoport arithmetic special $1$-cycles are encoded in the
first derivatives of unitary Eisenstein series Fourier coefficients.
  In this paper, we finish the reduction process from global arithmetic
intersection numbers for special cycles to the local geometric quantities in
our companion papers.
  Building on our previous companion papers, we also propose a construction for
arithmetic special cycle classes associated to possibly singular matrices of
arbitrary co-rank.


  Sound absorption at low frequencies still remains a challenge in both
scientific research and engineering practice. Natural porous materials are
ineffective in this frequency range, as well as acoustic resonators which
present too narrow bandwidth of absorption, thus requiring alternative
solutions based on active absorption techniques. In the present work, we
propose an active control framework applied on a closed-box loudspeaker to
enable the adjustment of the acoustic impedance at the loudspeaker diaphragm.
More specifically, based on the proportionality between the pressure inside the
enclosure and the axial displacement of the loudspeaker diaphragm at low
frequencies, we demonstrate both analytically and experimentally that a
PID-like feedback control approach allows tuning independently the compliance,
the resistance and the moving mass of the closed-box loudspeaker to implement a
prescribed impedance of a single-degree-of-freedom resonator. By considering
different control combinations to tailor the resonator characteristics, a
perfect absorption (with absorption coefficient equal to 1) is achievable at
the target resonance frequency, while enlarging the effective absorption
bandwidth. Moreover, the proposed feedback control strategy shows an excellent
control accuracy, especially compared to the feedforward-based control formerly
reported in the literature. The mismatches between the performance of
experimental prototype and the model, likely to result from the control time
delay and the inaccuracy in estimating the loudspeaker parameters, can be
compensated directly by tuning the control parameters in the control platform.
The active resonators implemented through the reported control scheme can be
used to build more complex acoustic devices/structures to enable
high-efficiency broadband sound absorption or other types of acoustic phenomena
such as wavefront shaping.


  6-d polyhedral models give a periodic description of aperiodic quasicrystals.
There are powerful tools to describe their structural surface properties. Basis
of the model for icosahedral quasicrystals are given. This description is
further used to interpret high resolution STM images of the surface of i-AlPdMn
which surface preparation was followed by He diffraction. It is found that both
terrace structure and step-terrace height profiles in STM images can be
consistently interpreted by the described model.


  Dwarf galaxies are excellent cosmological probes, because their shallow
potential wells make them very sensitive to the key processes that drive galaxy
evolution, including baryonic feedback, tidal interactions, and ram pressure
stripping. However, some of the key parameters of dwarf galaxies, which help
trace the effects of these processes, are still debated, including the
relationship between their sizes and masses. We re-examine the Fornax Cluster
dwarf population from the point of view of isomass-radius--stellar mass
relations (IRSMRs) using the Fornax Deep Survey Dwarf galaxy Catalogue, with
the centrally located (among dwarfs) $3.63 \mathcal{M}_{\odot}$~pc$^{-2}$
isodensity radius defining our fiducial relation. This relation is a powerful
diagnostic tool for identifying dwarfs with unusual structure, as dwarf
galaxies' remarkable monotonicity in light profile shapes, as a function of
stellar mass, reduces the relation's scatter tremendously. By examining how
different dwarf properties (colour, tenth-nearest-neighbour distance, etc.)
correlate with distance from our fiducial relation, we find a significant
population of structural outliers with comparatively lower central mass surface
density and larger half-light-radii, residing in locally denser regions in the
cluster, albeit with similar red colours. We propose that these faint, extended
outliers likely formed through tidal disturbances, which make the dwarfs more
diffuse, but with little mass loss. Comparing these outliers with ultra-diffuse
galaxies (UDGs), we find that the term UDG lacks discriminatory power; UDGs in
the Fornax Cluster lie both on and off of IRSMRs defined at small radii, while
IRSMR outliers with masses below $\sim 10^{7.5} \mathcal{M}_{\odot}$ are
excluded from the UDG classification due to their small effective radii.


  Recently, patch-wise contrastive learning is drawing attention for the image
translation by exploring the semantic correspondence between the input and
output images. To further explore the patch-wise topology for high-level
semantic understanding, here we exploit the graph neural network to capture the
topology-aware features. Specifically, we construct the graph based on the
patch-wise similarity from a pretrained encoder, whose adjacency matrix is
shared to enhance the consistency of patch-wise relation between the input and
the output. Then, we obtain the node feature from the graph neural network, and
enhance the correspondence between the nodes by increasing mutual information
using the contrastive loss. In order to capture the hierarchical semantic
structure, we further propose the graph pooling. Experimental results
demonstrate the state-of-art results for the image translation thanks to the
semantic encoding by the constructed graphs.


  In the present paper a lattice Boltzmann scheme is presented which exhibits
an increased stability and accuracy with respect to standard single- or
multi-relaxation-time (MRT) approaches. The scheme is based on a
single-relaxation-time model where a special regularization procedure is
applied. This regularization is based on the fact that, for a-thermal flows,
there exists a recursive way to express the velocity distribution function at
any order (in the Hermite series sense) in terms of the density, velocity, and
stress tensor. A linear stability analysis is conducted which shows enhanced
dispersion/dissipation relations with respect to existing models. The model is
then validated on two (one 2D and one 3D) moderately high Reynolds number
simulations ($\mathrm{Re}\sim 1000$) at moderate Mach numbers ($\mathrm{Ma}\sim
0.5$). In both cases the results are compared with an MRT model and an enhanced
accuracy and stability is shown by the present model.


  Lattice networks are indispensable to study heterogeneous materials such as
concrete or rock as well as textiles and woven fabrics. Due to the discrete
character of lattices, they quickly become computationally intensive. The
QuasiContinuum (QC) Method resolves this challenge by interpolating the
displacement of the underlying lattice with a coarser finite element mesh and
sampling strategies to accelerate the assembly of the resulting system of
governing equations. In lattices with complex heterogeneous microstructures
with a high number of randomly shaped inclusions the QC leads to an almost
fully-resolved system due to the many interfaces. In the present study the QC
Method is expanded with enrichment strategies from the eXtended Finite Element
Method (XFEM) to resolve material interfaces using nonconforming meshes. The
goal of this contribution is to bridge this gap and improve the computational
efficiency of the method. To this end, four different enrichment strategies are
compared in terms of their accuracy and convergence behavior. These include the
Heaviside, absolute value, modified absolute value and the corrected XFEM
enrichment. It is shown that the Heaviside enrichment is the most accurate and
straightforward to implement. A first-order interaction based summation rule is
applied and adapted for the extended QC for elements intersected by a material
interface to complement the Heaviside enrichment. The developed methodology is
demonstrated by three numerical examples in comparison with the standard QC and
the full solution. The extended QC is also able to predict the results with 5
percent error compared to the full solution, while employing almost one order
of magnitude fewer degrees of freedom than the standard QC and even more
compared to the fully-resolved system.


  Utilizing quantum coherence monotone, we reexamine the thermal nature of the
Unruh effect of an accelerating detector. We consider an UDW detector coupling
to a n-dimensional conformal field in Minkowski spacetime, whose response
spectrum generally exhibits an intermediate statistics of (1+1) anyon field. We
find that the thermal nature of the Unruh effect guaranteed by KMS condition is
characterized by a vanishing asymptotic quantum coherence. We show that the
time-evolution of coherence monotone can distinguish the different thermalizing
ways of the detector, which depends on the scaling dimension of the conformal
primary field. In particular, for the conformal background with certain scaling
dimension, we demonstrate that at fixed proper time a revival of coherence can
occur even for growing Unruh decoherence. Finally, we show that coherence
monotone has distinct dynamics under the Unruh decoherence and a thermal bath
for a static observer.


  We investigate moduli of planar circular quadrilaterals symmetric with
respect to both the coordinate axes. First we develop an analytic approach
which reduces this problem to ODEs and devise a numeric method to find out the
accessory parameters. This method uses the Schwarz equation to determine
conformal mapping of the unit disk onto a given circular quadrilateral. We also
give an example of a circular quadrilateral for which the value of the
conformal modulus can be found in the analytic form; this example is used to
validate the numeric calculations. We also use another method, so called hpFEM,
for the numeric calculation of the moduli. These two different approaches
provide results agreeing with high accuracy.


  We studied numerically electromagnetic response of the finite periodic
structure consisting of the ${\cal{PT}}$ dipoles represented by two infinitely
long, parallel cylinders with the opposite sign of the imaginary part of a
refractive index which are centered at the positions of two-dimensional
honeycomb lattice. We observed that the total scattered energy reveals series
of sharp resonances at which the energy increases by two orders of magnitude
and an incident wave is scattered only in a few directions given by spatial
symmetry of periodic structure. We explain this behavior by analysis of the
complex frequency spectra associated with an infinite honeycomb array of the
${\cal{PT}}$ dipoles and identify the lowest resonance with the broken
${\cal{PT}}$-symmetry mode formed by a doubly degenerate pair with complex
conjugate eigenfrequencies corresponding to the $K$-point of the reciprocal
lattice.


  Applying probabilistic techniques we study regularity properties of quantum
master equations (QMEs) in the Lindblad form with unbounded coefficients; a
density operator is regular if, roughly speaking, it describes a quantum state
with finite energy. Using the linear stochastic Schr\"{o}dinger equation we
deduce that solutions of QMEs preserve the regularity of the initial states
under a general nonexplosion condition. To this end, we develop the
probabilistic representation of QMEs, and we prove the uniqueness of solutions
for adjoint quantum master equations. By means of the nonlinear stochastic
Schr\"{o}dinger equation, we obtain the existence of regular stationary
solutions for QMEs, under a Lyapunov-type condition.


  The demand for mobile robots has rapidly increased in recent years due to the
flexibility and high variety of application fields comparing to static robots.
To deal with complex tasks such as navigation, they work with high amounts of
different sensor data making it difficult to operate with for non-experts. To
enhance user understanding and human robot interaction, we propose an approach
to visualize the navigation stack within a cutting edge 3D Augmented Reality
device -- the Microsoft Hololens. Therefore, relevant navigation stack data
including laser scan, environment map and path planing data are visualized in
3D within the head mounted device. Based on that prototype, we evaluate the
Hololens in terms of computational capabilities and limitations for dealing
with huge amount of real-time data. Results show that the Hololens is capable
of a proper visualization of huge amounts of sensor data. We demonstrate a
proper visualization of navigation stack data in 3D within the Hololens.
However, there are limitations when transferring and displaying different kinds
of data simultaneously.


  We prove several universal properties of charge transport in generic CFTs
holographic to nonminimal extensions of four-dimensional Einstein-Maxwell
theory with exact electromagnetic duality invariance. First, we explicitly
verify that the conductivity of these theories at zero momentum is a universal
frequency-independent constant. Then, we derive their analytical expressions
for non-zero momentum in any holographic duality-invariant theory for large
frequencies and in the limit of small frequencies and momenta. Next, in the
absence of terms that couple covariant derivatives of the curvature to gauge
field strengths, two universal features are proven. On the one hand, it is
shown that for a general-relativity neutral black-hole background the
conductivities at any frequency and momentum are independent of the choice of
duality-invariant theory, thus coinciding with those in the Einstein-Maxwell
case. On the other hand, if higher-curvature terms affect the gravitational
background, the conductivities get modified, but the contributions from
nonminimal couplings of the gauge field to gravity are subleading. We
illustrate this feature with an example.


  We investigate the performance of parallel and adaptive quantum channel
discrimination strategies for a finite number of channel uses. It has recently
been shown that, in the asymmetric setting with asymptotically vanishing type I
error probability, adaptive strategies are asymptotically not more powerful
than parallel ones. We extend this result to the non-asymptotic regime with
finitely many channel uses, by explicitly constructing a parallel strategy for
any given adaptive strategy, and bounding the difference in their performances,
measured in terms of the decay rate of the type II error probability per
channel use. We further show that all parallel strategies can be optimized over
in time polynomial in the number of channel uses, and hence our result can also
be used to obtain a poly-time-computable asymptotically tight upper bound on
the performance of general adaptive strategies.


  ALMA will revolutionize our understanding of star formation within our
galaxy, but before we can use ALMA we need to know where to look. The
Millimeter Astronomy Legacy Team 90 GHz (MALT90) Survey is a large
international project to map the molecular line emission of over 2,000 dense
clumps in the Galactic plane. MALT90 serves as a pathfinder for ALMA, providing
a large public database of dense molecular clumps associated with high-mass
star formation. In this proceedings, we describe the survey parameters and
share early science highlights from the survey, including (1) a comparison
between galactic and extragalactic star formation relations, (2) chemical
trends in MALT90 clumps, (3) the distribution of high-mass star formation in
the Milky Way, and (4) a discussion of the Brick, the target of successful ALMA
Cycle 0 and Cycle 1 proposals.


  We report the results of 67h of CCD photometry of the recently discovered
dwarf nova SDSS J210014.12+004446.0. The data were obtained on 24 nights
spanning a month. During this time we observed four ordinary outbursts lasting
about 2-3 days and reaching an amplitude of ~1.7 mag. On all nights our light
curve revealed persistent modulation with the stable period of 0.081088(3)
days. These humps were already observed on one night by Tramposch et al.
(2005), who additionally observed superhumps during a superoutburst.
Remarkably, from scant evidence at their disposal they were able to discern
them as negative and positive (common) superhumps, respectively. Our period in
quiescence clearly different from their superhump period confirmed this. Our
discovery of an additional modulation, attributed by us to the orbital wave,
completes the overall picture. Lack of superhumps in our data indicates that
all eruptions we observed were ordinary outbursts. The earlier observation of
the superhumps combined with the presence of the ordinary outbursts in our data
enables classification of SDSS J2100 as an active SU UMa dwarf nova.
Additionally, we have promoted SDSS J2100 to the group of cataclysmic variables
exhibiting three periodic modulations of light from their accretion discs. We
updated available information on positive and negative superhumps and thus
provided enhanced evidence that their properties are strongly correlated
mutually as well as with the orbital period. By recourse to these relations we
were able to remove an alias ambiguity and to identify the orbital period of
SDSS J2100 of 0.083304(6) days. SDSS J21000 is only third SU UMa dwarf nova
showing both positive and negative superhumps. Their respective period excess
and deficit equal to 4.99(3)% and -2.660(8)%, yielding the mass ratio q=0.24.


  In a series of papers we study the stellar dynamics of the grand design
barred-spiral galaxy NGC~1300. In the first paper of this series we estimate
the gravitational potential and we give it in a form suitable to be used in
dynamical studies. The estimation is done directly from near-infrared
observations. Since the 3D distribution of the luminous matter is unknown, we
construct three different general models for the potential corresponding to
three different assumptions for the geometry of the system, representing
limiting cases. A pure 2D disc, a cylindrical geometry (thick disc) and a third
case, where a spherical geometry is assumed to apply for the major part of the
bar. For the potential of the disc component on the galactic plane a Fourier
decomposition method is used, that allows us to express it as a sum of
trigonometric terms. Both even and odd components are considered, so that the
estimated potential accounts also for the observed asymmetries in the
morphology. For the amplitudes of the trigonometric terms a smoothed cubic
interpolation scheme is used. The total potential in each model may include two
additional terms (Plummer spheres) representing a central mass concentration
and a dark halo component, respectively. In all examined models, the relative
force perturbation points to a strongly nonlinear gravitational field, which
ranges from 0.45 to 0.8 of the axisymmetric background with the pure 2D being
the most nonlinear one. We present the topological distributions of the stable
and unstable Lagrangian points as a function of the pattern speed $(\Omega_p)$.
In all three models there is a range of $\Omega_p$ values, where we find
multiple stationary points whose stability affects the overall dynamics of the
system.


  This is the first in a series of papers on the construction and validation of
a three-dimensional code for general relativistic hydrodynamics, and its
application to general relativistic astrophysics. This paper studies the
consistency and convergence of our general relativistic hydrodynamic treatment
and its coupling to the spacetime evolutions described by the full set of
Einstein equations with a perfect fluid source. The numerical treatment of the
general relativistic hydrodynamic equations is based on high resolution shock
capturing schemes. These schemes rely on the characteristic information of the
system. A spectral decomposition for general relativistic hydrodynamics
suitable for a general spacetime metric is presented. Evolutions based on three
different approximate Riemann solvers coupled to four different discretizations
of the Einstein equations are studied and compared. The coupling between the
hydrodynamics and the spacetime (the right and left hand side of the Einstein
equations) is carried out in a treatment which is second order accurate in {\it
both} space and time. Convergence tests for all twelve combinations with a
variety of test beds are studied, showing consistency with the differential
equations and correct convergence properties. The test-beds examined include
shocktubes, Friedmann-Robertson-Walker cosmology tests, evolutions of
self-gravitating compact (TOV) stars, and evolutions of relativistically
boosted TOV stars. Special attention is paid to the numerical evolution of
strongly gravitating objects, e.g., neutron stars, in the full theory of
general relativity, including a simple, yet effective treatment for the surface
region of the star (where the rest mass density is abruptly dropping to zero).


  The spatially distributed reaction networks are indispensable for the
understanding of many important phenomena concerning the development of
organisms, coordinated cell behavior, and pattern formation. The purpose of
this brief discussion paper is to point out some open problems in the theory of
PDE and compartmental ODE models of balanced reaction-diffusion networks.


  We compile a new sample of 115 nearby, non-Seyfert galaxies spanning a wide
range of star formation activities, from starburst to nearly dormant, based on
ultraviolet (UV) observations with various satellites. We combine these
observations with infrared (IR) observations to study the relation between
ratio of total far-IR to UV luminosities and UV spectral slope (the `IRX-UV'
relation). We show that, at fixed UV spectral slope, quiescent star-forming
galaxies in our sample have systematically lower ratio of total far-IR to UV
luminosities than starburst galaxies. The strengths of spectral indices
sensitive to star formation history, such as the 4000 A break and EW(Ha),
correlate well with distance from the mean relation for starburst galaxies in
the IRX-UV diagram, while there is little or no correlation between the
dust-sensitive Ha/Hb ratio and this distance. This is strong observational
evidence that the star formation history is relevant to the `second parameter'
affecting the IRX-UV relation. We show that these results can be understood in
the framework of the simple model of Charlot & Fall 2000 for the transfer of
starlight through the ISM in galaxies. We confirm that, for starburst galaxies,
the tight IRX-UV relation can be understood most simply as a sequence in
overall dust content. In addition, we find that the broadening of the relation
for quiescent star-forming galaxies can be understood most simply as a sequence
in the ratio of present to past-averaged star formation rates. We provide
simple formulae for estimating the UV attenuation as a function of either the
ratio of far-IR to UV luminosities or the UV spectral slope and show that the
accuracy of these estimates can be improved if some constraints are available
on the ratio of present to past-averaged star formation rates [abridged].


  An aspatial version for the famous Schelling's segregation model has recently
been proposed, which, called two-room model, is still in an agent-based format
like the original Schelling model. In the present study, we propose a new,
state equation version of the Schelling model. The new equation is based on the
two-room model and is derived in terms of a set of discrete maps. Fixed point
solutions for the new equation are found analytically and confirmed
numerically. Especially, we show that the extremely simple state equations can
reasonably reveal the essence of the Schelling dynamics: integration,
segregation and tipping. In addition to the fixed point solutions, periodic
solutions are identified and conditions of the limit cycles are derived
analytically.


  This paper proposes a novel approach to phase-noise compensation. The basic
idea is to approximate the phase-noise statistics by a finite number of
realizations, i.e., a phase-noise codebook. The receiver then uses an augmented
received signal model, where the codebook index is estimated along with other
parameters. The realization of the basic idea depends on the details of the air
interface, the phase-noise statistics, the propagation scenario and the
computational constraints. In this paper, we will focus on a MQAM-OFDM system
with pilot sub-carriers within each OFDM symbol. The channel is frequency
selective, fading and unknown. A decision-feedback method is employed to
further enhance performance of the system. Simulation results are shown for
uncoded and coded systems to illustrate the performance of the algorithm, which
is also compared with previously employed methods. Our simulations show that
for a 16-QAM coded OFDM system over a frequency selective Rayleigh fading
channel affected by phase noise with root-mean-square (RMS) of 14.4 degrees per
OFDM symbol, the proposed algorithm is 1.5dB from the ideal phase-noise free
case at a BER of $10^{-4}$. The performance of the best reference scheme is
2.5dB from the ideal case at BER of $10^{-4}$. The proposed scheme is also
computationally attractive.


  While image manipulation achieves tremendous breakthroughs (e.g., generating
realistic faces) in recent years, video generation is much less explored and
harder to control, which limits its applications in the real world. For
instance, video editing requires temporal coherence across multiple clips and
thus poses both start and end constraints within a video sequence. We introduce
point-to-point video generation that controls the generation process with two
control points: the targeted start- and end-frames. The task is challenging
since the model not only generates a smooth transition of frames, but also
plans ahead to ensure that the generated end-frame conforms to the targeted
end-frame for videos of various length. We propose to maximize the modified
variational lower bound of conditional data likelihood under a skip-frame
training strategy. Our model can generate sequences such that their end-frame
is consistent with the targeted end-frame without loss of quality and
diversity. Extensive experiments are conducted on Stochastic Moving MNIST,
Weizmann Human Action, and Human3.6M to evaluate the effectiveness of the
proposed method. We demonstrate our method under a series of scenarios (e.g.,
dynamic length generation) and the qualitative results showcase the potential
and merits of point-to-point generation. For project page, see
https://zswang666.github.io/P2PVG-Project-Page/


  We report on an on-going analysis of high-resolution UV spectra of hot
hydrogen-rich central stars of planetary nebulae (CSPN), obtained with the
Hubble Space Telescope and FUSE. Since UV spectra of many CSPN are dominated by
Fe and Ni lines, we intend to use them as temperature indicators to check the
CSPN temperature scale we have derived earlier from CNO ionization balances.
Furthermore, the observed line strengths of heavy metals show large variations
between different objects suggesting a possible spread in abundances. We will
determine abundances of iron group elements by quantitative spectral analyses
with non-LTE model atmospheres.


  We study Markovian symmetry and non-symmetry random evolutions in
$\mathbf{R}^n$. Weak convergence of Markovian symmetry random evolution to
Wiener process and of Markovian non-symmetry random evolution to a diffusion
process with drift is proved using problems of singular perturbation for the
generators of evolutions. Relative compactness in
$\mathbf{D}_{\mathbf{R}^n\times\Theta}[0,\infty)$ of the families of Markovian
random evolutions is also shown.


  Semilinear stochastic partial differential equations on bounded domains
$\mathscr{D}$ are considered. The semilinear term may have arbitrary polynomial
growth as long as it is continuous and monotone except perhaps near the origin.
Typical examples are the stochastic Allen--Cahn and Ginzburg--Landau equations.
The first main result of this article are $L^p$-estimates for such equations.
The $L^p$-estimates are subsequently employed in obtaining higher regularity.
This is motivated by ongoing work to obtain rate of convergence estimates for
numerical approximations to such equations. It is shown, under appropriate
assumptions, that the solution is continuous in time with values in the Sobolev
space $H^2(\mathscr{D}')$ and $\ell^2$-integrable with values in
$H^3(\mathscr{D}')$, for any compact $\mathscr{D}' \subset \mathscr{D}$. Using
results from $L^p$-theory of SPDEs obtained by Kim~\cite{kim04} we get
analogous results in weighted Sobolev spaces on the whole $\mathscr{D}$.
Finally it is shown that the solution is H\"older continuous in time of order
$\frac{1}{2} - \frac{2}{q}$ as a process with values in a weighted $L^q$-space,
where $q$ arises from the integrability assumptions imposed on the initial
condition and forcing terms.


  Attention operators have been widely applied in various fields, including
computer vision, natural language processing, and network embedding learning.
Attention operators on graph data enables learnable weights when aggregating
information from neighboring nodes. However, graph attention operators (GAOs)
consume excessive computational resources, preventing their applications on
large graphs. In addition, GAOs belong to the family of soft attention, instead
of hard attention, which has been shown to yield better performance. In this
work, we propose novel hard graph attention operator (hGAO) and channel-wise
graph attention operator (cGAO). hGAO uses the hard attention mechanism by
attending to only important nodes. Compared to GAO, hGAO improves performance
and saves computational cost by only attending to important nodes. To further
reduce the requirements on computational resources, we propose the cGAO that
performs attention operations along channels. cGAO avoids the dependency on the
adjacency matrix, leading to dramatic reductions in computational resource
requirements. Experimental results demonstrate that our proposed deep models
with the new operators achieve consistently better performance. Comparison
results also indicates that hGAO achieves significantly better performance than
GAO on both node and graph embedding tasks. Efficiency comparison shows that
our cGAO leads to dramatic savings in computational resources, making them
applicable to large graphs.


  We present methods for calculating a measure of phonotactic complexity---bits
per phoneme---that permits a straightforward cross-linguistic comparison. When
given a word, represented as a sequence of phonemic segments such as symbols in
the international phonetic alphabet, and a statistical model trained on a
sample of word types from the language, we can approximately measure bits per
phoneme using the negative log-probability of that word under the model. This
simple measure allows us to compare the entropy across languages, giving
insight into how complex a language's phonotactics are. Using a collection of
1016 basic concept words across 106 languages, we demonstrate a very strong
negative correlation of -0.74 between bits per phoneme and the average length
of words.


  Recently, there has been focus on determining the conditions under which the
data processing inequality for quantum relative entropy is satisfied with
approximate equality. The solution of the exact equality case is due to Petz,
who showed that the quantum relative entropy between two quantum states stays
the same after the action of a quantum channel if and only if there is a
\textit{reversal channel} that recovers the original states after the channel
acts. Furthermore, this reversal channel can be constructed explicitly and is
now called the \textit{Petz recovery map}. Recent developments have shown that
a variation of the Petz recovery map works well for recovery in the case of
approximate equality of the data processing inequality. Our main contribution
here is a proof that bosonic Gaussian states and channels possess a particular
closure property, namely, that the Petz recovery map associated to a bosonic
Gaussian state $\sigma$ and a bosonic Gaussian channel $\mathcal{N}$ is itself
a bosonic Gaussian channel. We furthermore give an explicit construction of the
Petz recovery map in this case, in terms of the mean vector and covariance
matrix of the state $\sigma$ and the Gaussian specification of the channel
$\mathcal{N}$.


  Let G be a complex semisimple group and U its maximal unipotent subgroup. We
study the algebra D(G/U) of algebraic differential operators on G/U and also
its quasi-classical counterpart: the algebra of regular functions on the
cotangent bundle. A long time ago, Gelfand and Graev have constructed an action
of the Weyl group on D(G/U) by algebra automorphisms. The Gelfand-Graev
construction was not algebraic, it involved analytic methods in an essential
way. We give a new algebraic construction of the Gelfand-Graev action, as well
as its quasi-classical counterpart. Our approach is based on Hamiltonian
reduction and involves the ring of Whittaker differential operators on G/U, a
twisted analogue of D(G/U). Our main result has an interpretation, via
geometric Satake, in terms of spherical perverse sheaves on the affine
Grassmanian for the Langlands dual group.


  Homeostasis is a regulatory mechanism that keeps a specific variable close to
a set value as other variables fluctuate. The notion of homeostasis can be
rigorously formulated when the model of interest is represented as an
input-output network, with distinguished input and output nodes, and the
dynamics of the network determines the corresponding input-output function of
the system. In this context, homeostasis can be defined as an 'infinitesimal'
notion, namely, the derivative of the input-output function is zero at an
isolated point. Combining this approach with graph-theoretic ideas from
combinatorial matrix theory provides a systematic framework for calculating
homeostasis points in models and classifying the different homeostasis types in
input-output networks. In this paper we extend this theory by introducing the
notion of a homeostasis pattern, defined as a set of nodes, in addition to the
output node, that are simultaneously infinitesimally homeostatic. We prove that
each homeostasis type leads to a distinct homeostasis pattern. Moreover, we
describe all homeostasis patterns supported by a given input-output network in
terms of a combinatorial structure associated to the input-output network. We
call this structure the homeostasis pattern network.


  We prove two main results on how arbitrary linear threshold functions $f(x) =
\sign(w\cdot x - \theta)$ over the $n$-dimensional Boolean hypercube can be
approximated by simple threshold functions.
  Our first result shows that every $n$-variable threshold function $f$ is
$\eps$-close to a threshold function depending only on $\Inf(f)^2 \cdot
\poly(1/\eps)$ many variables, where $\Inf(f)$ denotes the total influence or
average sensitivity of $f.$ This is an exponential sharpening of Friedgut's
well-known theorem \cite{Friedgut:98}, which states that every Boolean function
$f$ is $\eps$-close to a function depending only on $2^{O(\Inf(f)/\eps)}$ many
variables, for the case of threshold functions. We complement this upper bound
by showing that $\Omega(\Inf(f)^2 + 1/\epsilon^2)$ many variables are required
for $\epsilon$-approximating threshold functions.
  Our second result is a proof that every $n$-variable threshold function is
$\eps$-close to a threshold function with integer weights at most $\poly(n)
\cdot 2^{\tilde{O}(1/\eps^{2/3})}.$ This is a significant improvement, in the
dependence on the error parameter $\eps$, on an earlier result of
\cite{Servedio:07cc} which gave a $\poly(n) \cdot 2^{\tilde{O}(1/\eps^{2})}$
bound. Our improvement is obtained via a new proof technique that uses strong
anti-concentration bounds from probability theory. The new technique also gives
a simple and modular proof of the original \cite{Servedio:07cc} result, and
extends to give low-weight approximators for threshold functions under a range
of probability distributions beyond just the uniform distribution.


  Control barrier functions (CBFs) and safety-critical control have seen a
rapid increase in popularity in recent years, predominantly applied to systems
in aerospace, robotics and neural network controllers. Control barrier
functions can provide a computationally efficient method to monitor arbitrary
primary controllers and enforce state constraints to ensure overall system
safety. One area that has yet to take advantage of the benefits offered by CBFs
is the field of finance and economics. This manuscript re-introduces three
applications of traditional control to economics, and develops and implements
CBFs for such problems. We consider the problem of optimal advertising for the
deterministic and stochastic case and Merton's portfolio optimization problem.
Numerical simulations are used to demonstrate the effectiveness of using
traditional control solutions in tandem with CBFs and stochastic CBFs to solve
such problems in the presence of state constraints.


  Decanol droplets in a thin layer of sodium decanoate with sodium chloride
exhibit bifurcation branching growth due to interplay between osmotic pressure,
diffusion and surface tension. We aimed to evaluate if morphology of the
branching droplets changes when the droplets are subject to electrical
potential difference. We analysed graph-theoretic structure of the droplets and
applied several complexity measures. We found that, in overall, the current
increases complexity of the branching droplets in terms of number of connected
components and nodes in their graph presentations, morphological complexity and
compressibility.


  A broadcast on a connected graph G with vertex set V(G) is a function
$f:V(G)\rightarrow \{0, 1, ..., \text{diam}(G)\}$ such that $f(v)\leq e(v)$
(the eccentricity of $v$) for all $v\in V$. A vertex $v$ is said to be
broadcasting if $f(v)>0$, with the set of all such vertices denoted $V_f^+$. A
vertex $u$ hears $f$ from $v\in V_f^+$ if $d_G(u, v)\leq f(v)$. The broadcast
$f$ is hearing independent if no broadcasting vertex hears another. If, in
addition, any vertex $u$ that hears $f$ from multiple broadcasting vertices
satisfies $f(v)\leq d_G(u, v)$ for all $v\in V_f^+$, the broadcast is said to
be boundary independent.
  The cost of $f$ is $\sigma(f)=\sum_{v\in V(G)}f(v)$. The minimum cost of a
maximal boundary independent broadcast on G, called the lower bn-independence
number, is denoted $i_{bn}(G)$. The lower h-independence number $i_h(G)$ is
defined analogously for hearing independent broadcasts. We prove that
$i_{bn}(G)\leq i_h(G)$ for all G and show that $i_h(G)/i_{bn}(G)$ is bounded.
For both parameters, we show that the lower bn-independence number
(h-independence number) of a connected graph G equals the minimum lower
bn-independence number (h-independence number) among those of its spanning
trees.
  We further study the maximum cost of boundary independent broadcasts, denoted
$\alpha_{bn}(G)$. We show $\alpha_{bn}(G)$ can be bounded in terms of the
independence number $\alpha(G)$, and prove that the maximum bn-independent
broadcast problem is NP-hard by a reduction from the independent set problem to
an instance of the maximum bn-independent broadcast problem.
  With particular interest in caterpillars, we investigate bounds on
$\alpha_{bn}(T)$ when T is a tree in terms of its order and the number of
vertices of degree at least 3, known as the branch vertices of T. We conclude
by describing a polynomial-time algorithm to determine $\alpha_{bn}(T)$ for a
given tree T.


  A new class of noncommutative $k$-algebras (for $k$ an algebraically closed
field) is defined and shown to contain some important examples of quantum
groups. To each such algebra, a first order theory is assigned describing
models of a suitable corresponding geometric space. Model-theoretic results for
these geometric structures are established (uncountable categoricity,
quantifier elimination to the level of existential formulas) and that an
appropriate dimension theory exists, making them Zariski structures.


  We review the construction of the tensorial structure of the graviton
propagator in the context of loop quantum gravity and spinfoam formalism. The
main result of this analysis is that applying the same strategy used to compute
the diagonal terms, the Barrett-Crane vertex is unable to yield the correct
propagator in the long distance limit. The problem is in the
intertwiner-independence of the Barrett-Crane vertex. We also review the
asymptotic behavior of an alternative vertex that is able to give the correct
propagator.


  Between early 1997 and late 2002, the HEGRA collaboration operated a
stereoscopic system of 4 (later 5) imaging atmospheric Cherenkov telescopes. In
this paper we present the calibration schemes which were developed for the
system, and report on the performance of the detector over the years. In
general, the telescope system was very well understood, regarding both the
absolute calibration and the slight changes in performance over the years. The
system had an energy threshold of 500 GeV for observations at zenith and under
optimum detector conditions. With the corresponding calibration schemes, a
systematic accuracy of 15 percent on the absolute energy scale has been
achieved. The continuous sensitivity monitoring provided a relative accuracy of
a few percent, and showed that the threshold did not exceed 600 GeV throughout
the entire operation time. The readout electronics and the imaging quality of
the dishes were well monitored and stable. The absolute pointing had an
accuracy of at least 25 arcsec; this number was guaranteed throughout the whole
lifetime of the experiment.


  Muons comprise an important contribution of the natural radiation dose in air
(approx. 30 nSv/h of a total dose rate of 65-130 nSv/h), as well as in
underground sites even when the flux and relative contribution are
significantly reduced. The flux of the muons observed in underground can be
used as an estimator for the depth in mwe (meter water equivalent) of the
underground site. The water equivalent depth is an important information to
devise physics experiments feasible for a specific site. A mobile detector for
performing measurements of the muon's flux was developed in IFIN-HH, Bucharest.
Consisting of 2 scintillator plates (approx. 0.9 m2) which measure in
coincidence, the detector is installed on a van which facilitates measurements
at different locations at surface or underground. The detector was used to
determine muon fluxes at different sites in Romania. In particular, data were
taken and the values of meter water equivalents were assessed for several
locations from the salt mine from Slanic Prahova, Romania. The measurements
have been performed in 2 different galleries of the Slanic mine at different
depths. In order to test the stability of the method, also measure- ments of
the muon flux at surface at different elevations were performed. The results
were compared with predictions of Monte-Carlo simulations using the CORSIKA and
MUSIC codes.


  In this paper, we propose a novel single-group multicasting relay beamforming
scheme. We assume a source that transmits common messages via multiple
amplify-and-forward relays to multiple destinations. To increase the number of
degrees of freedom in the beamforming design, the relays process two received
signals jointly and transmit the Alamouti space-time block code over two
different beams. Furthermore, in contrast to the existing relay multicasting
scheme of the literature, we take into account the direct links from the source
to the destinations. We aim to maximize the lowest received quality-of-service
by choosing the proper relay weights and the ideal distribution of the power
resources in the network. To solve the corresponding optimization problem, we
propose an iterative algorithm which solves sequences of convex approximations
of the original non-convex optimization problem. Simulation results demonstrate
significant performance improvements of the proposed methods as compared with
the existing relay multicasting scheme of the literature and an algorithm based
on the popular semidefinite relaxation technique.


  The interacting boson-fermion model (IBFM), with parameters determined from
the microscopic Hartree-Fock-Bogoliubov (HFB) approximation, based on the
parametrization D1M of the Gogny energy density functional (EDF), is employed
to study the structural evolution in odd-mass $\gamma$-soft nuclei. The
deformation energy surfaces of even-even nuclei, single-particle energies and
occupation probabilities of the corresponding odd-mass systems have been
obtained within the constrained HFB approach. Those building blocks are then
used as a microscopic input to build the IBFM Hamiltonian. The coupling
constants of the boson-fermion interaction terms are taken as free parameters,
fitted to reproduce experimental low-lying spectra. The diagonalization of the
IBFM Hamiltonian provides the spectroscopic properties for the studied odd-mass
nuclei. The procedure has been applied to compute low-energy excitation spectra
and electromagnetic transition rates, in the case of the $\gamma$-soft odd-mass
systems $^{129-137}$Ba, $^{127-135}$Xe, $^{129-137}$La and $^{127-135}$Cs. The
calculations provide a reasonable agreement with the available experimental
data and agree well with previous results based on the relativistic mean-field
approximation.


  Let $G$ be a simple graph with no even cycle, called an odd-cycle graph.
Cavers et al. [Cavers et al. Skew-adjacency matrices of graphs, Linear Algebra
Appl. 436(2012), 4512--1829] showed that the spectral radius of $G^\sigma$ is
the same for every orientation $\sigma$ of $G$, and equals the maximum matching
root of $G$. They proposed a conjecture that the graphs which attain the
maximum skew spectral radius among the odd-cycle graphs $G$ of order $n$ are
isomorphic to the odd-cycle graph with one vertex degree $n-1$ and size
$m=\lfloor 3(n-1)/2\rfloor$. This paper, by using the Kelmans transformation,
gives a proof of the conjecture. Moreover, sharp upper bounds of the maximum
matching roots of the odd-cycle graphs with given order $n$ and size $m$ are
given and extremal graphs are characterized.


  In this paper we discuss the recent finalized analyses by the KLOE experiment
at DA$\Phi$NE: the CPT and Lorentz invariance test with entangled $K^0
\bar{K}^0$ pairs, and the precision measurement of the branching fraction of
the decay ${ K^+} \rightarrow \pi^+\pi^-\pi^+(\gamma)$. We also present the
status of an ongoing analysis aiming to precisely measure the $K^{\pm} $ mass.


  This is a self-contained review about ferromagnetism in the Hubbard model,
which should be accessible to readers with various backgrounds who are new to
the field.
  We describe Nagaoka's ferromagnetism and flat-band ferromagnetism in detail,
giving all necessary backgrounds as well as complete (but elementary)
mathematical proofs. By studying an intermediate model called long-range
hopping model, we also demonstrate that there is indeed a deep relation between
these two seemingly different approaches to ferromagnetism.
  We further discuss some attempts to go beyond these approaches. We briefly
discuss recent rigorous example of ferromagnetism in the Hubbard model which
has neither infinitely large parameters nor completely flat bands. We give
preliminary discussions about possible experimental realizations of the
(nearly-)flat-band ferromagnetism. Finally we focus on some theoretical
attempts to understand metallic ferromagnetism. We discuss three artificial
one-dimensional models in which the existence of metallic ferromagnetism can be
easily proved.


  We perform three-dimensional relativistic hydrodynamical calculations of
neutron star mergers to assess the reliability of an approximate treatment of
thermal effects in such simulations by combining an ideal-gas component with
zero-temperature, micro-physical equations of state. To this end we compare the
results of simulations that make this approximation to the outcome of models
with a consistent treatment of thermal effects in the equation of state. In
particular we focus on the implications for observable consequences of merger
events like the gravitational-wave signal. It is found that the characteristic
gravitational-wave oscillation frequencies of the post-merger remnant differ by
about 50 to 250 Hz (corresponding to frequency shifts of 2 to 8 per cent)
depending on the equation of state and the choice of the characteristic index
of the ideal-gas component. In addition, the delay time to black hole collapse
of the merger remnant as well as the amount of matter remaining outside the
black hole after its formation are sensitive to the description of thermal
effects.