  Fermi's golden rule applies to a situation in which a single quantum state
$|\psi\rangle$ is coupled to a near-continuum. This "quasi-continuum coupling"
structure results in a rate equation for the population of $|\psi\rangle$. Here
we show that the coupling of a quantum system to the standard model of a
thermal environment, a bath of harmonic oscillators, can be decomposed into a
"cascade" made up of the quasi-continuum coupling structures of Fermi's golden
rule. This clarifies the connection between the physics of the golden rule and
that of a thermal bath, and provides a non-rigorous but physically intuitive
derivation of the Markovian master equation directly from the former. The exact
solution to the Hamiltonian of the golden rule, known as the Bixon-Jortner
model, generalized for an asymmetric spectrum, provides a window on how the
evolution induced by the bath deviates from the master equation as one moves
outside the Markovian regime. Our analysis also reveals the relationship
between the oscillator bath and the "random matrix model" (RMT) of a thermal
bath. We show that the cascade structure is the one essential difference
between the two models, and the lack of it prevents the RMT from generating
transition rates that are independent of the initial state of the system. We
suggest that the cascade structure is one of the generic elements of
thermalizing many-body systems.


  In this article, we show how to transform a colored de Bruijn graph (dBG)
into a practical index for processing massive sets of sequencing reads. Similar
to previous works, we encode an instance of a colored dBG of the set using BOSS
and a color matrix C. To reduce the space requirements, we devise an algorithm
that produces a smaller and more sparse version of C. The novelties in this
algorithm are (i) an incomplete coloring of the graph and (ii) a greedy
coloring approach that tries to reuse the same colors for different strings
when possible. We also propose two algorithms that work on top of the index;
one is for reconstructing reads, and the other is for contig assembly.
Experimental results show that our data structure uses about half the space of
the plain representation of the set (1 Byte per DNA symbol) and that more than
99% of the reads can be reconstructed just from the index.


  We give a geometric characterization of certain hypersurfaces of
cohomogeneity one in the complex projective and hyperbolic planes. We also
obtain some partial classifications of austere hypersurfaces and of Levi-flat
hypersurfaces with constant mean curvature in these spaces.


  We show that below the degenerate temperature the distribution profiles of
strongly interacting anyons in one dimension coincide with the most probable
distributions of ideal particles obeying generalized exclusion statistics
(GES). In the strongly interacting regime the thermodynamics and the local
two-particle correlation function derived from the GES are seen to agree for
low temperatures with the results derived for the anyon model using the
thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a
continuous range of GES, providing a signature of strongly interacting anyons,
including the strongly interacting one-dimensional Bose gas.


  The barrel part of the ATLAS pixel detector will consist of 112 carbon-carbon
structures called "staves" with 13 hybrid detector modules being glued on each
stave. The demands on the glue joints are high, both in terms of mechanical
precision and thermal contact. To achieve this precision a custom-made
semi-automated mounting machine has been constructed in Wuppertal, which
provides a precision in the order of tens of microns. As this is the last stage
of the detector assembly providing an opportunity for stringent tests, a
detailed procedure has been defined for assessing both mechanical and
electrical properties. This note gives an overview of the procedure for
affixation and tests, and summarizes the first results of the production.


  The NuSTEC workshop held at the University of Pittsburgh in October 2019
brought theorists and experimentalists together to discuss the state of
modeling and measurements related to pion production in neutrino-nucleus
scattering in the kinematic region where pions are produced through both
resonant and non-resonant mechanisms. Modeling of this region is of critical
importance to the current and future accelerator- and atmospheric-based
neutrino oscillation experiments. For the benefit of the community, links to
the presentations are accompanied by annotations from the speakers highlighting
significant points made during the presentations and resulting discussions.


  In contrast to a projective quantum measurement in which the system is
projected onto an eigenstate of the measured operator, in a weak measurement
the system is only weakly perturbed while only partial information on the
measured observable is obtained. A full description of such measurement should
describe the measurement protocol and provide an explicit form of the
measurement operator that transform the quantum state to its post measurement
form. A simultaneous measurement of non-commuting observables cannot be
projective, however the strongest possible such measurement can be defined as
providing their values at the smallest uncertainty limit. Starting with the
Arthurs and Kelly (AK) protocol for such measurement of position and momentum,
we derive a systematic extension to a corresponding weak measurement along
three steps: First, a plausible form of the weak measurement operator analogous
to the Gaussian Kraus operator often used to model a weak measurement of a
single observable is obtained by projecting a na\"ive extension (valid for
commuting observable) onto the corresponding Gabor space. Second, we show that
the so obtained set of measurement operators satisfies the normalization
condition for the probability to obtain given values of the position and
momentum in the weak measurement operation, namely that this set constitutes a
positive operator valued measure (POVM) in the position-momentum space.
Finally, we show that the so-obtained measurement operator corresponds to a
generalization of the AK measurement protocol in which the initial detector
wavefunctions is suitable broadened.


  Geographic structure can affect patterns of genetic differentiation and
speciation rates. In this article, we investigate the dynamics of genetic
distances in a geographically structured metapopulation. We model the
metapopulation as a weighted directed graph, with d vertices corresponding to d
subpopulations that evolve according to an individual based model. The dynamics
of the genetic distances is then controlled by two types of transitions
-mutation and migration events. We show that, under a rare mutation - rare
migration regime, intra subpopulation diversity can be neglected and our model
can be approximated by a population based model. We show that under a large
population - large number of loci limit, the genetic distance between two
subpopulations converges to a deterministic quantity that can asymptotically be
expressed in terms of the hitting time between two random walks in the
metapopulation graph. Our result shows that the genetic distance between two
subpopulations does not only depend on the direct migration rates between them
but on the whole metapopulation structure.


  Quantifying the data uncertainty in learning tasks is often done by learning
a prediction interval or prediction set of the label given the input. Two
commonly desired properties for learned prediction sets are \emph{valid
coverage} and \emph{good efficiency} (such as low length or low cardinality).
Conformal prediction is a powerful technique for learning prediction sets with
valid coverage, yet by default its conformalization step only learns a single
parameter, and does not optimize the efficiency over more expressive function
classes.
  In this paper, we propose a generalization of conformal prediction to
multiple learnable parameters, by considering the constrained empirical risk
minimization (ERM) problem of finding the most efficient prediction set subject
to valid empirical coverage. This meta-algorithm generalizes existing conformal
prediction algorithms, and we show that it achieves approximate valid
population coverage and near-optimal efficiency within class, whenever the
function class in the conformalization step is low-capacity in a certain sense.
Next, this ERM problem is challenging to optimize as it involves a
non-differentiable coverage constraint. We develop a gradient-based algorithm
for it by approximating the original constrained ERM using differentiable
surrogate losses and Lagrangians. Experiments show that our algorithm is able
to learn valid prediction sets and improve the efficiency significantly over
existing approaches in several applications such as prediction intervals with
improved length, minimum-volume prediction sets for multi-output regression,
and label prediction sets for image classification.


  We present the spectroscopic characterization of the unusual high-amplitude
very low mass pre-main-sequence periodic variable CHS7797. This study is based
on optical medium-resolution (R=2200) spectroscopy in the 6450-8600 A range,
carried out with GMOS-GEMINI-S in March 2011. Observations of CHS7797 have been
carried out at two distinct phases of the 17.8d period, namely at maximum and
four days before maximum. Four different spectral indices were used for the
spectral classification at these two phases, all of them well-suited for
spectral classification of young and obscured late M dwarfs. In addition, the
gravity-sensitive NaI (8183/8195 A) and KI (7665/7699 A) doublet lines were
used to confirm the young age of CHS7797. From the spectrum obtained at maximum
light we derived a spectral type (SpT) of M6.05, while for the spectrum taken
four days before maximum the derived SpT is M5.75. The derived SpTs confirm
that CHS7797 has a mass in the stellar-substellar boundary mass range. In
addition, the small differences in the derived SpTs at the two observed phases
may provide indirect hints that CHS7797 is a binary system of similar mass
components surrounded by a tilted circumbinary disk, a system similar to KH15D.


  In this work we study a continuous opinion dynamics model considering 3-agent
interactions and group pressure. Agents interact in a fully-connected
population, and two parameters govern the dynamics: the agents' convictions
$\lambda$, that are homogeneous in the population, and the group pressure $p$.
Stochastic parameters also drive the interactions. Our analytical and numerical
results indicate that the model undergoes symmetry-breaking transitions at
distinct critical points $\lambda_{c}$ for any value of $p<p^{*}=2/3$, i.e.,
the transition can be suppressed for sufficiently high group pressure. Such
transition separates two phases: for any $\lambda \leq \lambda_{c}$, the order
parameter $O$ is identically null ($O=0$, a symmetric, absorbing phase), while
for $\lambda>\lambda_{c}$, we have $O>0$, i.e., a symmetry-broken phase
(ferromagnetic). The numerical simulations also reveal that the increase of
group pressure leads to a wider distribution of opinions, decreasing the
extremism in the population.


  In model-driven engineering (MDE), UML class diagrams serve as a way to plan
and communicate between developers. However, it is complex and
resource-consuming. We propose an automated approach for the extraction of UML
class diagrams from natural language software specifications. To develop our
approach, we create a dataset of UML class diagrams and their English
specifications with the help of volunteers. Our approach is a pipeline of steps
consisting of the segmentation of the input into sentences, the classification
of the sentences, the generation of UML class diagram fragments from sentences,
and the composition of these fragments into one UML class diagram. We develop a
quantitative testing framework specific to UML class diagram extraction. Our
approach yields low precision and recall but serves as a benchmark for future
research.


  The plant community composition is an essential indicator of environmental
changes and is, for this reason, usually analyzed in ecological field studies
in terms of the so-called plant cover. The manual acquisition of this kind of
data is time-consuming, laborious, and prone to human error. Automated camera
systems can collect high-resolution images of the surveyed vegetation plots at
a high frequency. In combination with subsequent algorithmic analysis, it is
possible to objectively extract information on plant community composition
quickly and with little human effort. An automated camera system can easily
collect the large amounts of image data necessary to train a Deep Learning
system for automatic analysis. However, due to the amount of work required to
annotate vegetation images with plant cover data, only few labeled samples are
available. As automated camera systems can collect many pictures without
labels, we introduce an approach to interpolate the sparse labels in the
collected vegetation plot time series down to the intermediate dense and
unlabeled images to artificially increase our training dataset to seven times
its original size. Moreover, we introduce a new method we call Monte-Carlo
Cropping. This approach trains on a collection of cropped parts of the training
images to deal with high-resolution images efficiently, implicitly augment the
training images, and speed up training. We evaluate both approaches on a plant
cover dataset containing images of herbaceous plant communities and find that
our methods lead to improvements in the species, community, and segmentation
metrics investigated.


  In this paper we describe all edge-colored graphs that are fully symmetric
with respect to colors and transitive on every set of edges of the same color.
They correspond to fully symmetric homogeneous factorizations of complete
graphs. Our description completes the work done in our previous paper, where we
have shown, in particular, that there are no such graphs with more than 5
colors. Using some recent results, with a help of computer, we settle all the
cases that was left open in the previous paper.


  In this paper we present a new bound obtained with the probabilistic method
for the solution of the Set Covering problem with unit costs. The bound is
valid for problems of fixed dimension, thus extending previous similar
asymptotic results, and it depends only on the number of rows of the
coefficient matrix and the row densities. We also consider the particular case
of matrices that are \textit{almost} block decomposable, and show how the bound
may improve according to the particular decomposition adopted. Such final
result may provide interesting indications for comparing different matrix
decomposition strategies.


  We compare the dynamical masses of dwarf galaxies in the Local Group (LG) to
the predicted masses of halos in the ELVIS suite of $\Lambda$CDM simulations, a
sample of 48 Galaxy-size hosts, 24 of which are in paired configuration similar
to the LG. We enumerate unaccounted-for dense halos ($V_\mathrm{max} \gtrsim
25$ km s$^{-1}$) in these volumes that at some point in their histories were
massive enough to have formed stars in the presence of an ionizing background
($V_\mathrm{peak} > 30$ km s$^{-1}$). Within 300 kpc of the Milky Way, the
number of unaccounted-for massive halos ranges from 2 - 25 over our full
sample. Moreover, this "too big to fail" count grows as we extend our
comparison to the outer regions of the Local Group: within 1.2 Mpc of either
giant we find that there are 12-40 unaccounted-for massive halos. This count
excludes volumes within 300 kpc of both the MW and M31, and thus should be
largely unaffected by any baryonically-induced environmental processes.
According to abundance matching -- specifically abundance matching that
reproduces the Local Group stellar mass function -- all of these missing
massive systems should have been quite bright, with $M_\star > 10^6M_\odot$.
Finally, we use the predicted density structure of outer LG dark matter halos
together with observed dwarf galaxy masses to derive an
$M_\star-V_\mathrm{max}$ relation for LG galaxies that are outside the virial
regions of either giant. We find that there is no obvious trend in the relation
over three orders of magnitude in stellar mass (a "common mass" relation), from
$M_\star \sim 10^8 - 10^5 M_\odot$, in drastic conflict with the tight relation
expected for halos that are unaffected by reionization. Solutions to the too
big to fail problem that rely on ram pressure stripping, tidal effects, or
statistical flukes appear less likely in the face of these results.


  Cooperative trajectory planning methods for automated vehicles can solve
traffic scenarios that require a high degree of cooperation between traffic
participants. However, for cooperative systems to integrate into human-centered
traffic, the automated systems must behave human-like so that humans can
anticipate the system's decisions. While Reinforcement Learning has made
remarkable progress in solving the decision-making part, it is non-trivial to
parameterize a reward model that yields predictable actions. This work employs
feature-based Maximum Entropy Inverse Reinforcement Learning combined with
Monte Carlo Tree Search to learn reward models that maximize the likelihood of
recorded multi-agent cooperative expert trajectories. The evaluation
demonstrates that the approach can recover a reasonable reward model that
mimics the expert and performs similarly to a manually tuned baseline reward
model.


  The large side aperture of the NuSTAR telescope for unfocused photons
(so-called stray light) is a known source of rich astrophysical information. To
support many studies based on the NuSTAR stray light data, we present a fully
automatic method for determining detector area suitable for background analysis
and free from any kind of focused X-ray flux. The method's main idea is `a
trous' wavelet image decomposition, capable of detecting structures of any
spatial scale and shape, which makes the method of general use. Applied to the
NuSTAR data, the method provides a detector image region with the highest
possible statistical quality, suitable for the NuSTAR stray light studies. We
developed an open-source Python nuwavdet package, which implements the
presented method. The package contains subroutines to generate detector image
region for further stray light analysis and/or to produce a list of detector
bad-flagged pixels for processing in the NuSTAR Data Analysis Software for
conventional X-ray analysis.


  We consider several transitions between narrow lines that have an enhanced
sensitivity to a possible variation of the fine structure constant, alpha. This
enhancement may allow a search to be performed with an effective suppression of
the systematic sources of uncertainty that are unavoidable in conventional
high-resolution spectroscopic measurements. In the future this may provide the
strongest laboratory constraints on alpha variation.


  The three open clusters Be 15, Be 80, and NGC 2192 have been observed using
CCD UBV(RI)_C photometry at the San Pedro M\'artir Observatory, M\'exico within
the framework of our open-cluster survey. The fundamental parameters of
interstellar reddening, distance, and age have been derived, and also the
metallicity for NGC 2192 (solar metallicity has been assumed for the other
two). By shifting the colours of Schmidt-Kaler in the (U-B, B-V) two-colour
diagram along the appropriate reddening vector, the interstellar reddenings
have been derived as E(B-V)=0.23+/-0.03 mag for Be 15, 1.31+/-0.05 for Be 80,
and 0.16+/-0.03 for NGC 2192. Evidence is shown for a variable interstellar
extinction across the cluster Be 80. For NGC 2192 a nicely consistent fit is
obtained for both the interstellar reddening and the metallicity ([Fe/H]=-0.31)
using simultaneously the F-type and red-clump stars. By fitting isochrones to
the observed sequences of these three clusters in various colour-magnitude
diagrams of different colour indices, (B-V, V-I, or V-R) the averages of
distance moduli and heliocentric distances ((V-M_V)_o (mag); d(pc)) are the
following: (10.74+/-0.01; 1202) for Be 15, (10.75+/-0.01; 1413) for Be 80, and
(12.7+/-0.01; 3467) for NGC 2192, and the averages of the inferred best ages
(log(age); age (Gyr)) are (8.6+/-0.05; 0.4) for Be 80, and (9.15+/-0.05; 1.4)
for NGC 2192; for Be 15 there are two distinct possibilities for the age fit,
depending on the membership of three brighter stars, (9.35 or 9.95+/-0.05; 2.2
or 8.9). The need for spectroscopic observations in Be 15 is emphasized to
select between alternate reddening and age solutions, and for deeper UBV
observations in Be 80 to study in greater detail the variable interstellar, or
intracluster, reddening across this cluster.


  There is a growing need for anomaly detection methods that can broaden the
search for new particles in a model-agnostic manner. Most proposals for new
methods focus exclusively on signal sensitivity. However, it is not enough to
select anomalous events - there must also be a strategy to provide context to
the selected events. We propose the first complete strategy for unsupervised
detection of non-resonant anomalies that includes both signal sensitivity and a
data-driven method for background estimation. Our technique is built out of two
simultaneously-trained autoencoders that are forced to be decorrelated from
each other. This method can be deployed offline for non-resonant anomaly
detection and is also the first complete online-compatible anomaly detection
strategy. We show that our method achieves excellent performance on a variety
of signals prepared for the ADC2021 data challenge.


  The growing popularity of dynamic applications such as social networks
provides a promising way to detect valuable information in real time. Efficient
analysis over high-speed data from dynamic applications is of great
significance. Data from these dynamic applications can be easily modeled as
streaming graph. In this paper, we study the subgraph (isomorphism) search over
streaming graph data that obeys timing order constraints over the occurrence of
edges in the stream. We propose a data structure and algorithm to efficiently
answer subgraph search and introduce optimizations to greatly reduce the space
cost, and propose concurrency management to improve system throughput.
Extensive experiments on real network traffic data and synthetic social
streaming data confirms the efficiency and effectiveness of our solution.


  We examine the black hole solutions of dS$_3$ gravity by applying the
explicit dS$_3$/CFT$_2$ correspondence. The gravity theory is described by
Chern-Simons theory with complex gauge group SL$(2,\mathbb{C})$, and the
complexified theory is known to have too many saddle points. We determine the
set of "allowable geometry" from dual CFT correlators. Concretely, we classify
the possible complex solutions corresponding to dS$_3$ black holes from
Liouville two-point functions. We extend the analysis to Liouville multi-point
functions and among others we study geometry corresponding to two linked Wilson
loops on $S^3$ by the monodromy matrix of Liouville four-point function. Some
parts of the results were presented in a previous letter but here they are
explained in more details and extended in various ways. In particular, we
generalize the results to the case with higher-spin gravity by focusing the
effects of higher-spin charges.


  Music generation has generally been focused on either creating scores or
interpreting them. We discuss differences between these two problems and
propose that, in fact, it may be valuable to work in the space of direct $\it
performance$ generation: jointly predicting the notes $\it and$ $\it also$
their expressive timing and dynamics. We consider the significance and
qualities of the data set needed for this. Having identified both a problem
domain and characteristics of an appropriate data set, we show an LSTM-based
recurrent network model that subjectively performs quite well on this task.
Critically, we provide generated examples. We also include feedback from
professional composers and musicians about some of these examples.


  For the first time quaternions have been used for real-time frequency
estimation, where the multi-dimensional nature of quaternions allows for the
full characterization of three-phase power systems. This is achieved through
the use of quaternions to provide a unified framework for incorporating voltage
measurements from all the phases of a three-phase system and then employing the
recently introduced HR-calculus to derive a state space estimator based on the
quaternion extended Kalman filter (QEKF). The components of the state space
vector are designed such that they can be deployed for adaptive estimation of
the system phasors. Finally, the proposed algorithm is validated through
simulations using both synthetic and real-world data, which indicate that the
developed quaternion frequency estimator can outperform its complex-valued
counterparts.


  We show that for the Kuramoto model (with identical phase oscillators equally
coupled) its global statistics and size of the basins of attraction can be
estimated through the eigenvalues of all stable (frequency) synchronized
states. This result is somehow unexpected since, by doing that, one could just
use local analysis to obtain global dynamic properties. But recent works based
on Koopman and Perron-Frobenius operators demonstrate that global features of a
nonlinear dynamical system, with some specific conditions, are somehow encoded
in the local eigenvalues of its equilibrium states. Recognized numerical
simulations in the literature reinforce our analytical results.


  A modular tensor category provides the appropriate data for the construction
of a three-dimensional topological field theory. We describe the following
analogue for two-dimensional conformal field theories: a 2-category whose
objects are symmetric special Frobenius algebras in a modular tensor category
and whose morphisms are categories of bimodules. This 2-category provides
sufficient ingredients for constructing all correlation functions of a
two-dimensional rational conformal field theory. The bimodules have the
physical interpretation of chiral data, boundary conditions, and topological
defect lines of this theory.


  The paper contains results in three areas: First we present a general
estimate for tail probabilities of Gaussian quadratic forms with known
expectation and variance. Thereafter we analyze the distribution of norms of
complex Gaussian random fields (with possibly dependent real and complex part)
and derive representation results, which allow to find efficient estimators for
the moments of the associated Gaussian quadratic form. Finally, we apply these
results to sample distance multivariance, which is the test statistic
corresponding to distance multivariance -- a recently introduced multivariate
dependence measure. The results yield new tests for independence of multiple
random vectors. These are less conservative than the classical tests based on a
general quadratic form estimate and they are (much) faster than tests based on
a resampling approach. As a special case this also improves independence tests
based on distance covariance, i.e., tests for independence of two random
vectors.


  In this thesis we study the flat model, the main buidling block for the
spinfoam approach to quantum gravity, with an emphasis on its divergences.
Besides a personal introduction to the problem of quantum gravity, the
manuscript consists in two part. In the first one, we establish an exact
powercounting formula for the bubble divergences of the flat model, using tools
from discrete gauge theory and twisted cohomology. In the second one, we
address the issue of spinfoam continuum limit, both from the lattice field
theory and the group field theory perspectives. In particular, we put forward a
new proof of the Borel summability of the Boulatov-Freidel-Louapre model, with
an improved control over the large-spin scaling behaviour. We conclude with an
outlook of the renormalization program in spinfoam quantum gravity.


  We investigate the excitation spectrum and compressibility of a dipolar
Bose-Einstein condensate in an infinite tube potential in the parameter regime
where the transition between superfluid and supersolid phases occurs. Our study
focuses on the density range in which crystalline order develops continuously
across the transition. Above the transition the superfluid shows a single
gapless excitation band, phononic at small momenta and with a roton at a finite
momentum. Below the transition, two gapless excitations branches (three at the
transition point) emerge in the supersolid. We examine the two gapless
excitation bands and their associated speeds of sound in the supersolid phase.
Our results show that the speeds of sound and the compressibility are
discontinuous at the transition, indicating a second-order phase transition.
These results provide valuable insights into the identification of supersolid
phenomena in dipolar quantum gases and the relationship to supersolidity in
spin-orbit coupled gases.


  A content-addressable-memory compares an input search word against all rows
of stored words in an array in a highly parallel manner. While supplying a very
powerful functionality for many applications in pattern matching and search, it
suffers from large area, cost and power consumption, limiting its use. Past
improvements have been realized by using memristors to replace the
static-random-access-memory cell in conventional designs, but employ similar
schemes based only on binary or ternary states for storage and search.
  We propose a new analog content-addressable-memory concept and circuit to
overcome these limitations by utilizing the analog conductance tunability of
memristors. Our analog content-addressable-memory stores data within the
programmable conductance and can take as input either analog or digital search
values. Experimental demonstrations, scaled simulations and analysis show that
our analog content-addressable-memory can reduce area and power consumption,
which enables the acceleration of existing applications, but also new computing
application areas.


  We focus on the computational aspects of counting interval sizes in the poset
$D_n$, which represents all monotone Boolean functions of $n$ variables. We
present a resource-aware algorithm enabling the calculation of interval sizes
in $D_7$.


  We consider accretion disks consisting of counter-rotating gaseous components
with an intervening shear layer. Configurations of this type may arise from the
accretion of newly supplied counter-rotating gas onto an existing co-rotating
gas disk. For simplicity we consider the case where the gas well above the disk
midplane is rotating with angular rate $+\Omega$ and that well below has the
same properties but is rotating with rate $-\Omega$. Using the Shakura-Sunyaev
alpha turbulence model, we find self-similar solutions where a thin (relative
to the full disk thickness) equatorial layer accretes very rapidly, essentially
at free-fall speed. As a result the accretion speed is much larger than it
would be for an alpha disk rotating in one direction. Counter-rotating
accretion disks may be a transient stage in the formation of counter-rotating
galaxies and in the accretion of matter onto compact objects.


  Arnold introduced invariants $J^+$, $J^-$ and $St$ for generic planar curves.
  It is known that both $J^+ /2 + St$ and $J^- /2 + St$ are invariants for
generic spherical curves.
  Applying these invariants to underlying curves of knot diagrams, we can
obtain lower bounds for the number of Reidemeister moves for uknotting.
  $J^- /2 + St$ works well for unmatched RII moves.
  However, it works only by halves for RI moves.
  Let $w$ denote the writhe for a knot diagram.
  We show that $J^- /2 + St \pm w/2$ works well also for RI moves, and
demonstrate that it gives a precise estimation for a certain knot diagram of
the unknot with the underlying curve $r = 2 + \cos (n \theta/(n+1)),\ (0 \le
\theta \le 2(n+1)\pi$).


  In the two previous papers of this serie, we have created a library, called
Population, dedicated to seeded region growing by pixels aggregation and we
have proposed different growing processes to get a partition with or without a
boundary region to divide the other regions or to get a partition invariant
about the seeded region initialisation order. Using this work, we implement
some algorithms belonging to the field of SRGPA using this library and these
growing processes.


  We point out that the mixed-event method for two-particle acceptance
correction, widely used in particle correlation measurements at RHIC and LHC,
is wrong in cases where the single particle pseudorapidity distribution is
significantly nonuniform. The correct acceptance should be the convolution of
two single-particle efficiency$\times$acceptance functions. The error of the
mixed-event method, which guarantees a uniform $\Delta\eta$ two-particle
combinatorial density, is, however, small in correlation analyses where the two
particles are integrated over an extended pseudorapidity $\eta$ range. With one
particle fixed in $\eta$ and the right acceptance correction, the
background-subtracted correlated pair density may reveal not only a short-range
but also a long-range $\Delta\eta$ dependence. This has important physics
implication, and may provide crucial information to disentangle physics
mechanisms for the recently observed long-range ridge correlation in asymmetric
proton-lead collisions at the LHC.


  Solar activity is an important driver of long-term climate trends and must be
accounted for in climate models. Unfortunately, direct measurements of this
quantity over long periods do not exist. The only observation related to solar
activity whose records reach back to the seventeenth century are sunspots.
Surprisingly, determining the number of sunspots consistently over time has
remained until today a challenging statistical problem. It arises from the need
of consolidating data from multiple observing stations around the world in a
context of low signal-to-noise ratios, non-stationarity, missing data,
non-standard distributions and many kinds of errors. The data from some
stations experience therefore severe and various deviations over time. In this
paper, we propose the first systematic and thorough statistical approach for
monitoring these complex and important series. It consists of three steps
essential for successful treatment of the data: smoothing on multiple
timescales, monitoring using block bootstrap calibrated CUSUM charts and
classifying of out-of-control situations by support vector techniques. This
approach allows us to detect a wide range of anomalies (such as sudden jumps or
more progressive drifts), unseen in previous analyses. It helps us to identify
the causes of major deviations, which are often observer or equipment related.
Their detection and identification will contribute to improve future
observations. Their elimination or correction in past data will lead to a more
precise reconstruction of the world reference index for solar activity: the
International Sunspot Number.


  Subspace-valued functions arise in a wide range of problems, including
parametric reduced order modeling (PROM). In PROM, each parameter point can be
associated with a subspace, which is used for Petrov-Galerkin projections of
large system matrices. Previous efforts to approximate such functions use
interpolations on manifolds, which can be inaccurate and slow. To tackle this,
we propose a novel Bayesian nonparametric model for subspace prediction: the
Gaussian Process Subspace regression (GPS) model. This method is extrinsic and
intrinsic at the same time: with multivariate Gaussian distributions on the
Euclidean space, it induces a joint probability model on the Grassmann
manifold, the set of fixed-dimensional subspaces. The GPS adopts a simple yet
general correlation structure, and a principled approach for model selection.
Its predictive distribution admits an analytical form, which allows for
efficient subspace prediction over the parameter space. For PROM, the GPS
provides a probabilistic prediction at a new parameter point that retains the
accuracy of local reduced models, at a computational complexity that does not
depend on system dimension, and thus is suitable for online computation. We
give four numerical examples to compare our method to subspace interpolation,
as well as two methods that interpolate local reduced models. Overall, GPS is
the most data efficient, more computationally efficient than subspace
interpolation, and gives smooth predictions with uncertainty quantification.


  We present a systematic study of the CP conserving and violating SUSY
contributions to b to s processes in a generic MSSM, considering gluino
exchange contributions. Experimental information on B to Xs gamma, B to Xs l+
l- and the Bs-Bsbar mass difference Delta Ms have been taken into account. We
study the induced correlations among several observables: Delta Ms and the
amount of CP violation in B to phi Ks, Bs to J/psi phi, B to Xs gamma. Our
results show that b to s transitions represent a splendid opportunity to
constrain different MSSM realizations and offer concrete prospects to exhibit
SUSY signals at B factories and hadron colliders.


  We have obtained deep photometry in two 1x1 degree fields covering the close
pair of dwarf spheroidal galaxies (dSph) Leo IV and Leo V and part of the area
in between. We find that both systems are significantly larger than indicated
by previous measurements based on shallower data and also significantly
elongated. With half-light radii of r_h=4'.6 +- 0'.8 (206 +- 36 pc) and
r_h=2'.6 +- 0'.6 (133 +- 31 pc), respectively, they are now well within the
physical size bracket of typical Milky Way dSph satellites. Their ellipticities
of epsilon ~0.5 are shared by many faint (M_V>-8) Milky Way dSphs. The large
spatial extent of our survey allows us to search for extra-tidal features with
unprecedented sensitivity. The spatial distribution of candidate red giant
branch and horizontal branch stars is found to be non-uniform at the ~3 sigma
level. This substructure is aligned along the direction connecting the two
systems, indicative of a possible `bridge' of extra-tidal material. Fitting the
stellar distribution with a linear Gaussian model yields a significance of 4
sigma for this overdensity, a most likely FWHM of ~16 arcmin and a central
surface brightness of ~32 mag arcsec^{-2}. We investigate different scenarios
to explain the close proximity of Leo IV and Leo V and the possible tidal
bridge between them. Orbit calculations demonstrate that they are unlikely to
be remnants of a single disrupted progenitor, while a comparison with
cosmological simulations shows that a chance collision between unrelated
subhalos is negligibly small. Leo IV and Leo V could, however, be a bound
`tumbling pair' if their combined mass exceeds 8 +- 4 x 10^9 M_sun. The
scenario of an internally interacting pair appears to be the most viable
explanation for this close celestial companionship. (abridged)


  We derive an analytical expression for extracting the gravitational waveforms
at null infinity using the Weyl scalar $\psi_4$ measured at a finite radius.
Our expression is based on a series solution in orders of 1/r to the equations
for gravitational perturbations about a spinning black hole. We compute this
expression to order $1/r^2$ and include the spin parameter $a$ of the Kerr
background. We test the accuracy of this extraction procedure by measuring the
waveform for a merging black-hole binary at ten different extraction radii (in
the range r/M=75-190) and for three different resolutions in the convergence
regime. We find that the extraction formula provides a set of values for the
radiated energy and momenta that at finite extraction radii converges towards
the expected values with increasing resolution, which is not the case for the
`raw' waveform at finite radius. We also examine the phase and amplitude errors
in the waveform as a function of observer location and again observe the
benefits of using our extraction formula. The leading corrections to the phase
are ${\cal O}(1/r)$ and to the amplitude are ${\cal O}(1/r^2)$. This method
provides a simple and practical way of estimating the waveform at infinity, and
may be especially useful for scenarios such as well separated binaries, where
the radiation zone is far from the sources, that would otherwise require
extended simulation grids in order to extrapolate the `raw' waveform to
infinity. Thus this method saves important computational resources and provides
an estimate of errors.


  We formally extend the CFT techniques introduced in arXiv:1505.00963, to
$\phi^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-\epsilon$ dimensions and use it to
compute anomalous dimensions near $d_0=3, 4$ in a unified manner. We also do a
similar analysis of the $O(N)$ model in three dimensions by developing a
recursive combinatorial approach for OPE contractions. Our results match
precisely with low loop perturbative computations. Finally, using 3-point
correlators in the CFT, we comment on why the $\phi^3$ theory in $d_0=6$ is
qualitatively different.


  Motivated by personalized healthcare and other applications involving
sensitive data, we study online exploration in reinforcement learning with
differential privacy (DP) constraints. Existing work on this problem
established that no-regret learning is possible under joint differential
privacy (JDP) and local differential privacy (LDP) but did not provide an
algorithm with optimal regret. We close this gap for the JDP case by designing
an $\epsilon$-JDP algorithm with a regret of
$\widetilde{O}(\sqrt{SAH^2T}+S^2AH^3/\epsilon)$ which matches the
information-theoretic lower bound of non-private learning for all choices of
$\epsilon> S^{1.5}A^{0.5} H^2/\sqrt{T}$. In the above, $S$, $A$ denote the
number of states and actions, $H$ denotes the planning horizon, and $T$ is the
number of steps. To the best of our knowledge, this is the first private RL
algorithm that achieves \emph{privacy for free} asymptotically as $T\rightarrow
\infty$. Our techniques -- which could be of independent interest -- include
privately releasing Bernstein-type exploration bonuses and an improved method
for releasing visitation statistics. The same techniques also imply a slightly
improved regret bound for the LDP case.


  Object tracking has important application in assistive technologies for
personalized monitoring. Recent trackers choosing AlexNet as their backbone to
extract features have gained great success. However, AlexNet is too shallow to
form a strong feature representation, the tracker based on the Siamese network
have an accuracy gap compared with state-of-the-art algorithms. To solve this
problem, this paper proposes a tracker called SiamPF. Firstly, the modified
pre-trained VGG16 network is fine-tuned as the backbone. Secondly, an
AlexNet-like branch is added after the third convolutional layer and merged
with the response map of the backbone network to form a preliminary strong
feature representation. And then, a channel attention block is designed to
adaptively select the contribution features. Finally, the APCE is modified to
process the response map to reduce interference and focus the tracker on the
target. Our SiamPF only used ILSVRC2015-VID for training, but it achieved
excellent performance on OTB-2013 / OTB-2015 / VOT2015 / VOT2017, while
maintaining the real-time performance of 41FPS on the GTX 1080Ti.


  A model describing cell membranes as optimal shapes with regard to the
$L^2$-deficit of their mean curvature to a given constant called spontaneous
curvature is considered. It is shown that the corresponding energy functional
is lower semi-continuous with respect to oriented varifold convergence on a
space of surfaces whose second fundamental form is uniformly bounded in $L^2$.
Elementary examples are presented showing that the latter condition is
necessary. As a consequence, smoothly embedded minimisers among surfaces of
higher genus are obtained. Moreover, it is shown that the diameter of a
connected surface is controlled by the $L^1$-deficit of its mean curvature to
the spontaneous curvature leading to an improved condition for the existence of
minimisers. Finally, the diameter bound can be applied to obtain an
isoperimetric inequality.


  A fundamental issue in multiscale materials modeling and design is the
consideration of traction-separation behavior at the interface. By enriching
the deep material network (DMN) with cohesive layers, the paper presents a
novel data-driven material model which enables accurate and efficient
prediction of multiscale responses for heterogeneous materials with interfacial
effect. In the newly invoked cohesive building block, the fitting parameters
have physical meanings related to the length scale and orientation of the
cohesive layer. It is shown that the enriched material network can be
effectively optimized via a multi-stage training strategy, with training data
generated only from linear elastic direct numerical simulation (DNS). The
extrapolation capability of the method to unknown material and loading spaces
is demonstrated through the debonding analysis of a unidirectional
fiber-reinforced composite, where the interface behavior is governed by an
irreversible softening mixed-mode cohesive law. Its predictive accuracy is
validated against the nonlinear path-dependent DNS results, and the reduction
in computational time is particularly significant.


  We study the dynamical behavior of an ensemble of oscillators interacting
through short range bidirectional pulses. The geometry is 1D with periodic
boundary conditions. Our interest is twofold. To explore the conditions
required to reach fully synchronization and to invewstigate the time needed to
get such state. We present both theoretical and numerical results.


  Axions or axion-like particles (ALPs) are one of the most promising
candidates of dark matter (DM). A prevalent method to detect axion-like DM is
to seek the periodic oscillation feature in the polarization angles of linearly
polarized light emitted from astrophysical sources. In this work, we use the
time-resolved polarization measurements of the hyperactive repeating fast radio
burst, FRB 20220912A, detected by the Five-hundred-meter Aperture Spherical
radio Telescope (FAST) to search for extragalactic axion-like DM for the first
time. Given a DM density profile of FRB 20220912A's host, we obtain upper
limits on the ALP-photon coupling constant of $g_{a \gamma}<(2.9 \times
10^{-11}-1.1\times 10^{-9})\,\mathrm{GeV}^{-1}$ for the ALP masses $m_a \sim
(1.4\times10^{-21}-5.2\times10^{-20})$ eV. Persistent polarimetric observations
with FAST would further improve the constraints. We prove that FRBs offer an
alternative way to detect axion-like DM on extragalactic distance scales,
complementary to other galactic DM probes.


  The relationship between mass and radius (M-R relation) is the key for
inferring the planetary compositions and thus valuable for the studies of
formation and migration models. However, the M-R relation alone is not enough
for planetary characterization due to the dependence of it on other confounding
variables. This paper provides a non-trivial extension of the M-R relation by
including the incident flux as an additional variable. By using Bayesian
hierarchical modeling (BHM) that leverages the flexibility of finite mixture
models, a probabilistic mass-radius-flux relationship (M-R-F relation) is
obtained based on a sample of 319 exoplanets. We find that the flux has
nonnegligible impact on the M-R relation, while such impact is strongest for
hot-Jupiters. On the population level, the planets with higher level of flux
tend to be denser, and high flux could trigger significant mass loss for plants
with radii larger than $13R_{\oplus}$. As a result, failing to account for the
flux in mass prediction would cause systematic over or under-estimation. With
the recent advent of computing power, although a lot of complex statistical
models can be fitted using Monte Carlo methods, it has largely remain illusive
how to validate these complex models when the data are observed with large
measurement errors. We present two novel methods to examine model assumptions,
which can be used not only for the models we present in this paper but can also
be adapted for other statistical models.


  We analyze dispersion relations of magnons in ferromagnetic nanostructures
with uniaxial anisotropy taking into account inertial terms, i.e. magnetic
nutation. Inertial effects are parametrized by damping-independent parameter
$\beta$, which allows for an unambiguous discrimination of inertial effects
from Gilbert damping parameter $\alpha$. The analysis of magnon dispersion
relation shows its two branches are modified by the inertial effect, albeit in
different ways. The upper nutation branch starts at $\omega=1/ \beta$, the
lower branch coincides with FMR in the long-wavelength limit and deviates from
the zero-inertia parabolic dependence $\simeq\omega_{FMR}+Dk^2$ of the exchange
magnon. Taking a realistic experimental geometry of magnetic thin films,
nanowires and nanodiscs, magnon eigenfrequencies, eigenvectors and $Q$-factors
are found to depend on the shape anisotropy. The possibility of phase-matched
magneto-elastic excitation of nutation magnons is discussed and the condition
was found to depend on $\beta$, exchange stiffness $D$ and the acoustic
velocity.


  Using two dimensional (2D) N=4 sigma model, with $U(1)^r$ gauge symmetry, and
introducing the ADE Cartan matrices as gauge matrix charges, we build " toric"
hyper-Kahler eight real dimensional manifolds X_8. Dividing by one toric
geometry circle action of X_8 manifolds, we present examples describing
quotients $X_7={X_8\over U(1)}$ of G_2 holonomy. In particular, for the A_r
Cartan matrix, the quotient space is a cone on a $ {S^2}$ bundle over r
intersecting $\bf WCP^2_{(1,2,1)}$ projective spaces according to the A_r
Dynkin diagram.


  Starting from the the Boltzmann equation, we study the center of mass
oscillation of a harmonically trapped normal Fermi gas in the presence of a
one-dimensional periodic potential. We show that for values of the the Fermi
energy above the first Bloch band the center of mass motion is strongly damped
in the collisional regime due to umklapp processes. This should be contrasted
with the behaviour of a superfluid where one instead expects the occurrence of
persistent Josephson-like oscillations.


  Over the past decades, the competition for academic resources has gradually
intensified, and worsened with the current financial crisis. To optimize the
resource allocation, individualized assessment of research results is being
actively studied but the current indices, such as the number of papers, the
number of citations, the h-factor and its variants have limitations, especially
their inability of determining co-authors' credit shares fairly. Here we
establish an axiomatic system and quantify co-authors' relative contributions.
Our methodology avoids subjective assignment of co-authors' credits using the
inflated, fractional or harmonic methods, and provides a quantitative tool for
scientific management such as funding and tenure decisions.


  Facial analysis permits many investigations some of the most important of
which are craniofacial identification, facial recognition, and age and sex
estimation. In forensics, photo-anthropometry describes the study of facial
growth and allows the identification of patterns in facial skull development by
using a group of cephalometric landmarks to estimate anthropological
information. In several areas, automation of manual procedures has achieved
advantages over and similar measurement confidence as a forensic expert. This
manuscript presents an approach using photo-anthropometric indexes, generated
from frontal faces cephalometric landmarks, to create an artificial neural
network classifier that allows the estimation of anthropological information,
in this specific case age and sex. The work is focused on four tasks: i) sex
estimation over ages from 5 to 22 years old, evaluating the interference of age
on sex estimation; ii) age estimation from photo-anthropometric indexes for
four age intervals (1 year, 2 years, 4 years and 5 years); iii) age group
estimation for thresholds of over 14 and over 18 years old; and; iv) the
provision of a new data set, available for academic purposes only, with a large
and complete set of facial photo-anthropometric points marked and checked by
forensic experts, measured from over 18,000 faces of individuals from Brazil
over the last 4 years. The proposed classifier obtained significant results,
using this new data set, for the sex estimation of individuals over 14 years
old, achieving accuracy values greater than 0.85 by the F_1 measure. For age
estimation, the accuracy results are 0.72 for measure with an age interval of 5
years. For the age group estimation, the measures of accuracy are greater than
0.93 and 0.83 for thresholds of 14 and 18 years, respectively.


  An EPW-sextic is a special 4-dimensional hypersurfaces of degree 6 which
comes equipped with a double cover which generically is a Hyperkaehler 4-fold
deformation equivalent to the Hilbert square of a K3 surface. The family of
EPW-sextics is analogous to the family of cubic 4-fold hypersurfaces, more
precisely double EPW-sextics are analogous to varieties of lines on cubic
4-folds. This first paper in a series on moduli and periods of double
EPW-sextics is mainly concerned with the classification of EPW-sextics which
are analogous to cubic 4-folds whose singular locus has strictly positive
dimension.


  To pinpoint the peak location of the synchrotron total intensity emission in
a spiral arm, we use a map of the spiralarm locations (from the observed arm
tangent). Thus In a typical spiral arm in Galactic Quadrant I, we find the peak
of the synchrotron radiation to be located about 220 +/-40 pc away from the
inner arm edge (hot dust lane) inside the spiral arm. While most of the
galactic disk has a clockwise largescale magnetic field, we make a statistical
analysis to delimitate more precisely the smaller reverse annulus wiith a
counterclockwise galactic magnetic field. We find an annulus width of 2.1
+/-0.3 kpc (measured along the Galactic radius), located from 5.5 to 7.6 kpc
from the Galactic Center). The annulus does not overlay with a single spiral
arm -- it encompasses segments of two different spiral arms. Using a recent
delineation of the position of spiral arms, the field-reversed annulus is seen
to encompass the Crux-Centaurus arm (in Galactic Quadrant IV) and the
Sagittarius arm (in Galactic Quadrant I).


  Today's mainstream virtualization systems comprise of two cooperative
components: a kernel-resident driver that accesses virtualization hardware and
a user-level helper process that provides VM management and I/O virtualization.
However, this virtualization architecture has intrinsic issues in both security
(a large attack surface) and performance. While there is a long thread of work
trying to minimize the kernel-resident driver by offloading functions to user
mode, they face a fundamental tradeoff between security and performance: more
offloading may reduce the kernel attack surface, yet increase the runtime ring
crossings between the helper process and the driver, and thus more performance
cost.
  This paper explores a new design called delegated virtualization, which
completely separates the control plane (the kernel driver) from the data plane
(the helper process) and thus eliminates the kernel driver from runtime
intervention. The resulting user-level hypervisor, called DuVisor, can handle
all VM operations without trapping into the kernel once the kernel driver has
done the initialization. DuVisor retrofits existing hardware virtualization
support with a new delegated virtualization extension to directly handle VM
exits, configure virtualization registers, manage the stage-2 page table and
virtual devices in user mode. We have implemented the hardware extension on an
open-source RISC-V CPU and built a Rust-based hypervisor atop the hardware.
Evaluation on FireSim shows that DuVisor outperforms KVM by up to 47.96\% in a
variety of real-world applications and significantly reduces the attack
surface.


  With a view toward a fracton theory in condensed matter, we introduce a
higher-moment polynomial degree-p global symmetry, acting on complex
scalar/vector/tensor fields (e.g., ordinary or vector global symmetry for p$=0$
and p$=1$ respectively). We relate this higher-moment global symmetry of
$n$-dimensional space, to a lower degree (either ordinary or higher-moment,
e.g., degree-(p-$\ell$)) subdimensional or subsystem global symmetry on layers
of $(n-\ell)$-submanifolds. These submanifolds are algebraic affine varieties
(i.e., solutions of polynomials). The structure of layers of submanifolds as
subvarieties can be studied via mathematical tools of embedding, foliation, and
algebraic geometry. We also generalize Noether's theorem for this higher-moment
polynomial global symmetry. We can promote the higher-moment global symmetry to
a local symmetry, and derive a new family of higher-rank-m symmetric tensor
gauge theory by gauging, with m = p$+1$. By further gauging a discrete
$\mathbb{Z}_2^C$ charge conjugation (particle-hole) symmetry, we derive a new
general class of rank-m tensor non-abelian gauge field theory (the gauge
structure is non-commutative thus non-abelian but not an ordinary group): a
hybrid class of (symmetric or non-symmetric) higher-rank-m tensor gauge theory
and anti-symmetric tensor topological field theory, generalizing
[arXiv:1909.13879], interplaying between gapless and gapped sectors.


  We demonstrate the combination of a hemispherical solid immersion lens with a
micro-photoluminescence setup. Two advantages introduced by the SIL, an
improved resolution of 0.4 times the wavelength in vacuum and a 5 times
enhancement of the collection efficiency, make it an ideal system for spatially
resolved spectroscopy applications. The influence of the air gap between the
SIL and the sample surface is investigated in detail. We confirm the tolerance
of the set--up to an air gap of several micrometers. Such a system is proven to
be ideal system in the studies of exciton transport and polarization dependent
single quantum dot spectroscopy.


  A gravitational wave stochastic background of astrophysical origin may have
resulted from the superposition of a large number of unresolved sources since
the beginning of stellar activity. Its detection would put very strong
constrains on the physical properties of compact objects, the initial mass
function or the star formation history. On the other hand, it could be a
'noise' that would mask the stochastic background of cosmological origin. We
review the main astrophysical processes able to produce a stochastic background
and discuss how it may differ from the primordial contribution by its
statistical properties. Current detection methods are also presented.


  Cyber-Physical Systems (CPS) use computational resources to control physical
process and provide critical services. For this reason, an attack in these
systems may have dangerous consequences in the physical world. Hence,
resilience is a fundamental property to ensure the safety of the people, the
environment and the controlled physical process. In this paper, we present
metrics to quantify the resilience level based on the design, structure,
stability, and performance under the attack of a given CPS. The metrics provide
reference points to evaluate whether the system is better prepared or not to
face the adversaries. This way, it is possible to quantify the ability to
recover from an adversary using its mathematical model based on switched linear
systems and actuators saturation. Finally, we validate our approach using a
numeric simulation on the Tennesse Eastman control challenge problem.


  Dielectric nanostructures have demonstrated optical antenna effects due to
Mie resonances. Preliminary investigations on dielectric nanoantennas have been
carried out for a trifecta of enhancements, i.e., simultaneous enhancements in
absorption, emission directionality and radiative decay rates of quantum
emitters. However, these investigations are limited by fragile substrates or
low Purcell factor, which is extremely important for exciting quantum emitters
electrically. In this paper, we present a Si mix antenna array to achieve the
trifecta enhancement of ~1200 fold with a Purcell factor of ~47. The antenna
design incorporates ~10 nm gaps within which fluorescent molecules strongly
absorb the pump laser energy through a resonant mode. In the emission process,
the antenna array increases the radiative decay rates of the fluorescence
molecules via Purcell effect and provides directional emission through a
separate mode. This work could lead to novel CMOS compatible platforms for
enhancing fluorescence for biological and chemical applications.


  Event sensors offer high temporal resolution visual sensing, which makes them
ideal for perceiving fast visual phenomena without suffering from motion blur.
Certain applications in robotics and vision-based navigation require 3D
perception of an object undergoing circular or spinning motion in front of a
static camera, such as recovering the angular velocity and shape of the object.
The setting is equivalent to observing a static object with an orbiting camera.
In this paper, we propose event-based structure-from-orbit (eSfO), where the
aim is to simultaneously reconstruct the 3D structure of a fast spinning object
observed from a static event camera, and recover the equivalent orbital motion
of the camera. Our contributions are threefold: since state-of-the-art event
feature trackers cannot handle periodic self-occlusion due to the spinning
motion, we develop a novel event feature tracker based on spatio-temporal
clustering and data association that can better track the helical trajectories
of valid features in the event data. The feature tracks are then fed to our
novel factor graph-based structure-from-orbit back-end that calculates the
orbital motion parameters (e.g., spin rate, relative rotational axis) that
minimize the reprojection error. For evaluation, we produce a new event dataset
of objects under spinning motion. Comparisons against ground truth indicate the
efficacy of eSfO.


  Electron-defect ($e$-d) interactions govern charge carrier dynamics at low
temperature, where they limit the carrier mobility and give rise to phenomena
of broad relevance in condensed matter physics. Ab initio calculations of $e$-d
interactions are still in their infancy, mainly because they require large
supercells and computationally expensive workflows. Here we develop an
efficient ab initio approach for computing elastic $e$-d interactions, their
associated $e$-d relaxation times (RTs), and the low-temperature defect-limited
carrier mobility. The method is applied to silicon with simple neutral defects,
such as vacancies and interstitials. Contrary to conventional wisdom, the
computed $e$-d RTs depend strongly on carrier energy and defect type, and the
defect-limited mobility is temperature dependent. These results highlight the
shortcomings of widely employed heuristic models of $e$-d interactions in
materials. Our method opens new avenues for studying $e$-d scattering and
low-temperature charge transport from first principles.


  A mixed graph has a set of vertices, a set of undirected egdes, and a set of
directed arcs. A proper coloring of a mixed graph $G$ is a function $c$ that
assigns to each vertex in $G$ a positive integer such that, for each edge $uv$
in $G$, $c(u) \ne c(v)$ and, for each arc $uv$ in $G$, $c(u) < c(v)$. For a
mixed graph $G$, the chromatic number $\chi(G)$ is the smallest number of
colors in any proper coloring of $G$. A directional interval graph is a mixed
graph whose vertices correspond to intervals on the real line. Such a graph has
an edge between every two intervals where one is contained in the other and an
arc between every two overlapping intervals, directed towards the interval that
starts and ends to the right.
  Coloring such graphs has applications in routing edges in layered orthogonal
graph drawing according to the Sugiyama framework; the colors correspond to the
tracks for routing the edges. We show how to recognize directional interval
graphs, and how to compute their chromatic number efficiently. On the other
hand, for mixed interval graphs, i.e., graphs where two intersecting intervals
can be connected by an edge or by an arc in either direction arbitrarily, we
prove that computing the chromatic number is NP-hard.


  The point of this paper is to give an explicit p-adic analytic construction
of two Iwasawa functions L_p^\sharp(f,T) and L_p^\flat(f,T) for a weight two
modular form \sum a_n q^n and a good prime p. This generalizes work of Pollack
who worked in the supersingular case and also assumed a_p=0. The Iwasawa
functions work in tandem to shed some light on the Birch and Swinnerton-Dyer
conjectures in the cyclotomic direction: We bound the rank and estimate the
growth of the Tate-Shafarevich group in the cyclotomic direction analytically,
encountering a new phenomenon for small slopes.


  We present the Next Generation Deep Extragalactic Exploratory Public (NGDEEP)
Survey, a deep slitless spectroscopic and imaging Cycle 1 JWST treasury survey
designed to constrain feedback mechanisms in low-mass galaxies across cosmic
time. NGDEEP targets the Hubble Ultra Deep Field (HUDF) with NIRISS slitless
spectroscopy (f~1.2e-18 erg/s/cm^2, 5sigma) to measure metallicities and
star-formation rates (SFRs) for low-mass galaxies through the peak of the
cosmic SFR density (0.5<z<4). In parallel, NGDEEP targets the HUDF-Par2
parallel field with NIRCam (m=30.6-30.9, 5sigma) to discover galaxies to z>12,
constraining the slope of the faint-end of the rest-ultraviolet luminosity
function. NGDEEP overlaps with the deepest HST ACS optical imaging in the sky:
F435W in the HUDF (m=29.6), and F814W in HUDF-Par2 (m=30), making this a
premier HST+JWST Deep Field. As a treasury survey, NGDEEP data is public
immediately, and we will rapidly release data products and catalogs in the
spirit of previous deep field initiatives. In this paper we present the NGDEEP
survey design, summarize the science goals, and detail plans for the public
release of NGDEEP reduced data products.


  In this paper, two developments, the theory of hierarchical equations of
motion (HEOM) for open quantum dynamics systems and the theory of ultrafast
nonlinear two-dimensional (2D) spectroscopies, are described, following the
history of their founder. The HEOM was discovered by attempting to derive an
equation similar to Kuob's stochastic Liouville equation based on the
system-bath Hamiltonian. The theory of 2D spectroscopy was developed in the
process of investigating the effect of quantum coherence on nonlinear
vibrational spectra based on the Feynman-Vernon influence functional. The paper
also describes the development of these two theories for problems such as
electron and exciton transfer in photosynthetic systems, quantum statistical
thermodynamics, and solid-state physics.


  Paring correlations in weakly bound halo nuclei $^{6}$He and $^{11}$Li are
studied by using a three-body model with a density-dependent contact
interaction. We investigate the spatial structure of two-neutron wave function
in a Borromean nucleus $^{11}$Li.The behavior of the neutron pair at different
densities is simulated by calculating the two-neutron wave function at several
distances between the core nucleus $^9$Li and the center of mass of the two
neutrons. With this representation, a strong concentration of the neutron pair
on the nuclear surface is quantitatively established for neutron-rich nuclei.
Dipole excitations in $^{6}$He and $^{11}$Li are also studied within the same
three-body model and compared with experimental data. The small open angles
between the two neutrons from the core are extracted empirically by the B(E1)
sum rule together with the rms mass radii, indicating the strong di-neutron
correlation in the halo nuclei.


  We present novel coupling schemes for partitioned multi-physics simulation
that combine four important aspects for strongly coupled problems: implicit
coupling per time step, fast and robust acceleration of the corresponding
iterative coupling, support for multi-rate time stepping, and higher-order
convergence in time. To achieve this, we combine waveform relaxation -- a known
method to achieve higher order in applications with split time stepping based
on continuous representations of coupling variables in time -- with interface
quasi-Newton coupling, which has been developed throughout the last decade and
is generally accepted as a very robust iterative coupling method even for
gluing together black-box simulation codes. We show convergence results (in
terms of convergence of the iterative solver and in terms of approximation
order in time) for two academic test cases -- a heat transfer scenario and a
fluid-structure interaction simulation. We show that we achieve the expected
approximation order and that our iterative method is competitive in terms of
iteration counts with those designed for simpler first-order-in-time coupling.


  Three first order magnetic phase transitions (FOMT) have been detected at
TCPr, TNinter and TCinter over the temperature range from 5 K to 340 K at
fields up to 9 T in PrMn1.4Fe0.6Ge2, and the magnetocaloric effect (MCE) around
these transitions evaluated. The MCE of two FOMT from planar antiferromagnetism
(AFl) to c-axis ferromagnetism (Fmc) around 168 K, and from the Fmc state to
the c-axis AFmc state around 157 K have acceptable values compared with those
of existing MCE systems. A giant magnetocaloric effect (GMCE) has been observed
around 25.5 K associated with the field-induced FOMT from the AFmc to the
Fmc+F(Pr) state with an additional Pr magnetic contribution. The MCE value 29.1
J/kg K with field change 7 T is comparable to and even larger than reported
values for the best-performed MCE materials. In particular, the giant MCE value
of 12.3 J/kg K obtained for the relatively small field change from 0 to 1 T is
very beneficial for applications, and this, together with the small magnetic
and thermal hysteresis, suggests that PrMn1.4Fe0.6Ge2 may be a promising
candidate for magnetic refrigeration applications in the hydrogen liquefication
temperature range.


  A multichannel detector has been constructed using a single avalanche
photodiode and a fiber-loop delay line. Detection probabilities of the channels
can be set using a variable-ratio coupler. The performance of the detector is
demonstrated on its capability to distinguish multi-photon states (containing
two or more photons) from the one-photon state and the vacuum state.


  Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we
extend the Kuramoto model to account for confidence bounds, i.e., vanishing
interactions between pairs of oscillators when their phases differ by more than
a certain value. We focus on Kuramoto oscillators with peaked, bimodal
distribution of natural frequencies. We show that, in this case, the
fixed-points for the extended model are made of certain numbers of independent
clusters of oscillators, depending on the length of the confidence bound -- the
interaction range -- and the distance between the two peaks of the bimodal
distribution of natural frequencies. This allows us to construct the phase
diagram of attractive fixed-points for the bimodal Kuramoto model with bounded
confidence and to analytically explain clusterization in dynamical systems with
bounded confidence.


  One strategy for reducing the sign problem in finite-density field theories
is to deform the path integral contour from real to complex fields. If the
deformed manifold is the appropriate combination of Lefschetz thimbles -- or
somewhat close to them -- the sign problem is alleviated. Gauge theories lack a
well-defined thimble decomposition, and therefore it is unclear how to carry
out a generalized thimble method. In this paper we discuss some of the
conceptual issues involved by applying this method to $QED_{1+1}$ at finite
density, showing that the generalized thimble method yields correct results
with less computational effort than standard methods.


  In this paper, we use previously developed exact solutions to present some of
the curious features of a force-free magnetosphere in a Kerr background. More
precisely, we obtain a hitherto unseen timelike current in the force-free
magnetosphere that does not flow along a geodesic. The electromagnetic field in
this case happens to be magnetically dominated. This too is a feature that has
entered the literature for the first time. Changing the sign of a single
parameter in our solutions generates a spacelike current that creates an
electromagnetic field that is electrically dominated.


  We construct a compact metric space that has any other compact metric space
as a tangent, with respect to the Gromov-Hausdorff distance, at all points.
Furthermore, we give examples of compact sets in the Euclidean unit cube, that
have almost any other compact set of the cube as a tangent at all points or
just in a dense sub-set. Here the "almost all compact sets" means that the
tangent collection contains a contracted image of any compact set of the cube
and that the contraction ratios are uniformly bounded. In the Euclidean space,
the distance of sub-sets is measured by the Hausdorff distance. Also the
geometric properties and dimensions of such spaces and sets are studied.


  We consider the effect of spin-orbit coupling on the low energy excitation
spectrum of an Andreev billiard (a quantum dot weakly coupled to a
superconductor), using a dynamical numerical model (the spin Andreev map).
Three effects of spin-orbit coupling are obtained in our simulations: In zero
magnetic field: (1) the narrowing of the distribution of the excitation gap;
(2) the appearance of oscillations in the average density of states. In strong
magnetic field: (3) the appearance of a peak in the average density of states
at zero energy. All three effects have been predicted by random-matrix theory.


  Motivated by the importance of understanding competing mechanisms to
current-induced spin-orbit torque in complex magnets, we develop a unified
theory of current-induced spin-orbital coupled dynamics. The theory describes
angular momentum transfer between different degrees of freedom in solids, e.g.,
the electron orbital and spin, the crystal lattice, and the magnetic order
parameter. Based on the continuity equations for the spin and orbital angular
momenta, we derive equations of motion that relate spin and orbital current
fluxes and torques describing the transfer of angular momentum between
different degrees of freedom. We then propose a classification scheme for the
mechanisms of the current-induced torque in magnetic bilayers. Based on our
first-principles implementation, we apply our formalism to two different
magnetic bilayers, Fe/W(110) and Ni/W(110), which are chosen such that the
orbital and spin Hall effects in W have opposite sign and the resulting spin-
and orbital-mediated torques can compete with each other. We find that while
the spin torque arising from the spin Hall effect of W is the dominant
mechanism of the current-induced torque in Fe/W(110), the dominant mechanism in
Ni/W(110) is the orbital torque originating in the orbital Hall effect of W. It
leads to negative and positive effective spin Hall angles, respectively, which
can be directly identified in experiments. This clearly demonstrates that our
formalism is ideal for studying the angular momentum transfer dynamics in
spin-orbit coupled systems as it goes beyond the "spin current picture" by
naturally incorporating the spin and orbital degrees of freedom on an equal
footing. Our calculations reveal that, in addition to the spin and orbital
torque, other contributions such as the interfacial torque and self-induced
anomalous torque within the ferromagnet are not negligible in both material
systems.


  Energetic (suprathermal) solar particles, accelerated in the interplanetary
medium, contribute to the solar wind pressure, in particular during high solar
activity periods. We estimated the effect of the increase of solar wind
pressure due to suprathermal particles on magnetospheric transmissivity of
galactic cosmic rays in the case of one recent solar event.


  We derive analytical solutions for the uniaxial extension problem for the
relaxed micromorphic continuum and other generalized continua. These solutions
may help in the identification of material parameters of generalized continua
which are able to disclose size-effects.


  The potential of a point charge in a thin semiconducting film with the
thickness below the de Broglie wavelength of the free charge carriers is
calculated with and without the screening.


  We derive here a variant of the 2D Green-Naghdi equations that model the
propagation of two-directional, nonlinear dispersive waves in shallow water.
This new model has the same accuracy as the standard $2D $ Green-Naghdi
equations. Its mathematical interest is that it allows a control of the
rotational part of the (vertically averaged) horizontal velocity, which is not
the case for the usual Green-Naghdi equations. Using this property, we show
that the solution of these new equations can be constructed by a standard
Picard iterative scheme so that there is no loss of regularity of the solution
with respect to the initial condition. Finally, we prove that the new
Green-Naghdi equations conserve the almost irrotationality of the vertically
averaged horizontal component of the velocity.


  Many questions in physical cosmology regarding the thermal and ionization
history of the intergalactic medium are now successfully studied with the help
of cosmological hydrodynamical simulations. Here we present a numerical method
that solves the radiative transfer around point sources within a three
dimensional cartesian grid. The method is energy conserving independently of
resolution: this ensures the correct propagation speeds of ionization fronts.
We describe the details of the algorithm, and compute as first numerical
application the ionized region surrounding a mini-quasar in a cosmological
density field at z=7.


  Efficient treatment of systematic uncertainties that depend on a large number
of nuisance parameters is a persistent difficulty in particle physics
experiments. Where low-level effects are not amenable to simple
parameterization or re-weighting, analyses often rely on discrete simulation
sets to quantify the effects of nuisance parameters on key analysis
observables. Such methods may become computationally untenable for analyses
requiring high statistics Monte Carlo with a large number of nuisance degrees
of freedom, especially in cases where these degrees of freedom parameterize the
shape of a continuous distribution. In this paper we present a method for
treating systematic uncertainties in a computationally efficient and
comprehensive manner using a single simulation set with multiple and
continuously varied nuisance parameters. This method is demonstrated for the
case of the depth-dependent effective dust distribution within the IceCube
Neutrino Telescope.


  We consider a generalization of rational inattention problems by measuring
costs of information through the information radius (Sibson, 1969; Verd\'u,
2015) of statistical experiments. We introduce a notion of attention elasticity
measuring the sensitivity of attention strategies with respect to changes in
incentives. We show how the introduced class of cost functions controls
attention elasticities while the Shannon model restricts attention elasticity
to be unity. We explore further differences and similarities relative to the
Shannon model in relation to invariance, posterior separability, consideration
sets, and the ability to learn events with certainty. Lastly, we provide an
efficient alternating minimization method -- analogous to the Blahut-Arimoto
algorithm -- to obtain optimal attention strategies.


  This PhD thesis is devoted to deterministic study of the turbulence in the
Navier- Stokes equations. The thesis is divided in four independent
chapters.The first chapter involves a rigorous discussion about the energy's
dissipation law, proposed by theory of the turbulence K41, in the deterministic
setting of the homogeneous and incompressible Navier-Stokes equations, with a
stationary external force (the force only depends of the spatial variable) and
on the whole space R3. The energy's dissipation law, also called the
Kolmogorov's dissipation law, characterizes the energy's dissipation rate (in
the form of heat) of a turbulent fluid and this law was developed by A.N.
Kolmogorov in 1941. However, its deduction (which uses mainly tools of
statistics) is not fully understood until our days and then an active research
area consists in studying this law in the rigorous framework of the
Navier-Stokes equations which describe in a mathematical way the fluids motion
and in particular the movement of turbulent fluids. In this setting, the
purpose of this chapter is to highlight the fact that if we consider the
Navier-Stokes equations on R3 then certain physical quantities, necessary for
the study of the Kolmogorov's dissipation law, have no a rigorous definition
and then to give a sense to these quantities we suggest to consider the
Navier-Stokes equations with an additional damping term. In the framework of
these damped equations, we obtain some estimates for the energy's dissipation
rate according to the Kolmogorov's dissipation law.In the second chapter we are
interested in study the stationary solutions of the damped Navier- Stokes
introduced in the previous chapter. These stationary solutions are a particular
type of solutions which do not depend of the temporal variable and their study
is motivated by the fact that we always consider the Navier-Stokes equations
with a stationary external force. In this chapter we study two properties of
the stationary solutions : the first property concerns the stability of these
solutions where we prove that if we have a control on the external force then
all non stationary solution (with depends of both spatial and temporal
variables) converges toward a stationary solution. The second property concerns
the decay in spatial variable of the stationary solutions. These properties of
stationary solutions are a consequence of the damping term introduced in the
Navier-Stokes equations.In the third chapter we still study the stationary
solutions of Navier-Stokes equations but now we consider the classical
equations (without any additional damping term). The purpose of this chapter is
to study an other problem related to the deterministic description of the
turbulence : the frequency decay of the stationary solutions. Indeed, according
to the K41 theory, if the fluid is in a laminar setting then the stationary
solutions of the Navier-Stokes equations must exhibit a exponential frequency
decay which starts at lows frequencies. But, if the fluid is in a turbulent
setting then this exponential frequency decay must be observed only at highs
frequencies. In this chapter, using some Fourier analysis tools, we give a
precise description of this exponential frequency decay in the laminar and in
the turbulent setting.In the fourth and last chapter we return to the
stationary solutions of the classical Navier-Stokes equations and we study the
uniqueness of these solutions in the particular case without any external
force. Following some ideas of G. Seregin, we study the uniqueness of these
solutions first in the framework of Lebesgue spaces of and then in the a
general framework of Morrey spaces.


  We consider the geometry of anti-de-Sitter (AdS) black hole thermodynamics in
four dimensions, where the equation of state in the extended phase space
formalism allows explicit comparison with normal fluid systems. We show that
for the two-dimensional parameter manifolds considered here, the scalar
curvature is proportional to the thermodynamic volume. This allows us to
critically examine the applicability of geometric methods in black hole
thermodynamics in extended phase space. We show how several standard features
that are expected to hold in normal fluid systems impose severe restrictions on
the black hole parameters, leading to the fact that several results in the
current literature on the geometry of thermodynamics in extended phase space
may be physically invalid. These are true for both charged and rotating AdS
black holes. As a by-product of our analysis, we examine a conjecture regarding
the equality of the correlation lengths of co-existing phases near criticality,
in charged AdS black hole backgrounds, and find reasonable validity.


  In this paper I survey some recent results on finite determination,
convergence, and approximation of formal mappings between real submanifolds in
complex spaces. A number of conjectures are also given.


  Supply Chain (SC) modeling is essential to understand and influence SC
behavior, especially for increasingly globalized and complex SCs. Existing
models address various SC notions, e.g., processes, tiers and production, in an
isolated manner limiting enriched analysis granted by integrated information
systems. Moreover, the scarcity of real-world data prevents the benchmarking of
the overall SC performance in different circumstances, especially wrt.
resilience during disruption. We present SENS, an ontology-based
Knowlegde-Graph (KG) equipped with SPARQL implementations of KPIs to
incorporate an end-to-end perspective of the SC including standardized SCOR
processes and metrics. Further, we propose SENS-GEN, a highly configurable data
generator that leverages SENS to create synthetic semantic SC data under
multiple scenario configurations for comprehensive analysis and benchmarking
applications. The evaluation shows that the significantly improved simulation
and analysis capabilities, enabled by SENS, facilitate grasping, controlling
and ultimately enhancing SC behavior and increasing resilience in disruptive
scenarios.


  In the present study we report on properties of ZnCoO films grown at
relatively low temperature by the Atomic Layer Deposition, using two reactive
organic zinc precursors (dimethylzinc and diethylzinc). The use of these
precursors allowed us the significant reduction of a growth temperature to
below 300oC. The influence of growth conditions on the Co distribution in ZnCoO
films, their structure and magnetic properties was investigated using Secondary
Ion Mass Spectroscopy, Scanning Electron Microscopy, Cathodoluminescence,
Energy Dispersive X-ray Spectrometry (EDX), X-ray diffraction and
Superconducting Quantum Interference Device magnetometry. We achieved high
uniformity of the films grown at 160{\deg}C. Such films are paramagnetic. Films
grown at 200{\deg} and at higher temperature are nonuniform. Formation of
foreign phases in such films was detected using high resolution EDX method.
These samples are not purely paramagnetic and show weak ferromagnetic response
at low temperature.


  This paper studies the influence of orienting external fields on pattern
formation, particularly mesoscale turbulence, in microswimmer suspensions. To
this end, we apply a hydrodynamic theory that can be derived from a microscopic
microswimmer model [Phys. Rev. E 97, 022613 (2018)]. The theory combines a
dynamic equation for the polar order parameter with a modified Stokes equation
for the solvent flow. Here, we extend the model by including an external field
that exerts an aligning torque on the swimmers (mimicking the situation in
chemo-, photo-, magneto- or gravitaxis). Compared to the field-free case, the
external field breaks the rotational symmetry of the vortex dynamics and leads
instead to strongly asymmetric, traveling stripe patterns, as demonstrated by
numerical solution and linear stability analysis. We further analyze the
emerging structures using a reduced model which involves only an (effective)
microswimmer velocity field. This model is significantly easier to handle
analytically, but still preserves the main features of the asymmetric pattern
formation. We observe an underlying transition between a square vortex lattice
and a traveling stripe pattern. These structures can be well described in the
framework of weakly nonlinear analysis, provided the strength of nonlinear
advection is sufficiently weak.


  Modified Rayleigh conjecture (MRC) in scattering theory is proposed and
justified. MRC allows one to develop numerical algorithms for solving direct
scattering problems related to acoustic wave scattering by soft and hard
obstacles of arbitrary shapes. It gives an error estimate for solving the
direct scattering problem. It suggests a numerical method for finding the shape
of a starshaped obstacle from the scattering data.


  We investigate the depinning dynamics of two-dimensional dusty plasmas (2DDP)
driven over one-dimensional periodic substrates (1DPS) using Langevin dynamical
simulations. We find that, for a specific range of substrate strengths, as the
external driving force increases from zero, there are three different states,
which are the pinned, the disordered plastic flow, and the moving ordered
states, respectively. These three states are clearly observed using different
diagnostics, including the collective drift velocity, static structural
measures, the particle trajectories, the mean-squared displacements, and the
kinetic temperature. We compare the observed depinning dynamics here with the
depinning dynamics in other systems.


  We consider the perturbative computation of the N-point function of chiral
densities of massive free fermions at finite temperature within the thermofield
dynamics approach. The infinite series in the mass parameter for the N-point
functions are computed in the fermionic formulation and compared with the
corresponding perturbative series in the interaction parameter in the bosonized
thermofield formulation. Thereby we establish in thermofield dynamics the
formal equivalence of the massive free fermion theory with the sine-Gordon
thermofield model for a particular value of the sine-Gordon parameter. We
extend the thermofield bosonization to include the massive Thirring model.


  Let f:{-1,1}^n -> R be a real function on the hypercube, given by its
discrete Fourier expansion, or, equivalently, represented as a multilinear
polynomial. We say that it is Boolean if its image is in {-1,1}.
  We show that every function on the hypercube with a sparse Fourier expansion
must either be Boolean or far from Boolean. In particular, we show that a
multilinear polynomial with at most k terms must either be Boolean, or output
values different than -1 or 1 for a fraction of at least 2/(k+2)^2 of its
domain.
  It follows that given oracle access to f, together with the guarantee that
its representation as a multilinear polynomial has at most k terms, one can
test Booleanity using O(k^2) queries. We show an \Omega(k) queries lower bound
for this problem.
  Our proof crucially uses Hirschman's entropic version of Heisenberg's
uncertainty principle.


  We report the most important results on the parsec-scale properties of a
complete sample of radio galaxies carried out at radio frequencies with the
Global VLBI array and with the VLBA. Relativistic parsec-scale jets are common
both in FRI and FRII radio galaxies, and their orientation to the line of sight
is in agreement with the expectations from the unified schemes for radio loud
AGNs. Proper motion has been detected in a few FRI galaxies in the sample. FRI
and FRII radio galaxies exhibit very similar properties on the parsec-scale.
Finally a few radio sources in the sample show evidence of velocity structure
in the parsec-scale jet, i.e. a central spine with high Lorentz factor $\gamma$
and slower layers.


  Massive black holes (BHs) in dwarf galaxies can provide strong constraints on
BH seeds, however reliably detecting them is notoriously difficult. High
resolution radio observations were recently used to identify accreting massive
BHs in nearby dwarf galaxies, with a significant fraction found to be
non-nuclear. Here we present the first results of our optical follow-up of
these radio-selected active galactic nuclei (AGNs) in dwarf galaxies using
integral field unit (IFU) data from Gemini-North. We focus on the dwarf galaxy
J1220+3020, which shows no clear optical AGN signatures in its nuclear SDSS
spectrum covering the radio source. With our new IFU data, we confirm the
presence of an active BH via the AGN coronal line [Fe X] and enhanced [O I]
emission coincident with the radio source. Furthermore, we detect broad
H$\alpha$ emission and estimate a BH mass of $M_{\rm BH}=10^{4.9}M_\odot$. We
compare the narrow emission line ratios to standard BPT diagnostics and shock
models. Spatially-resolved BPT diagrams show some AGN signatures, particularly
in [O I]/H$\alpha$, but overall do not unambiguously identify the AGN. A
comparison of our data to shock models clearly indicates shocked emission
surrounding the AGN. The physical model most consistent with the data is an
active BH with a radiatively inefficient accretion flow (RIAF) that both
photoionizes and shock-excites the surrounding gas. We conclude that feedback
is important in radio-selected BHs in dwarf galaxies, and that radio surveys
may probe a population of low accretion-rate BHs in dwarf galaxies that cannot
be detected through optical surveys alone.


  In this work, we derive the stellar initial mass function (IMF) from the
superposition of mass distributions of dense cores, generated through
gravoturbulent fragmentation of unstable clumps in molecular clouds (MCs) and
growing through competitive accretion. MCs are formed by the turbulent cascade
in the interstellar medium at scales L from 100 down to ~0.1 pc. Their internal
turbulence is essentially supersonic and creates clumps with a lognormal
distribution of densities n. Our model is based on the assumption of a
power-law relationship between clump mass and clump density: n~m^x, where x is
a scale-free parameter. Gravitationally unstable clumps are assumed to undergo
isothermal fragmentation and produce protostellar cores with a lognormal mass
distribution, centred around the clump Jeans mass. Masses of individual cores
are then assumed to grow further through competitive accretion until the rest
of the gas within the clump is being exhausted. The observed IMF is best
reproduced for a choice of x=0.25, for a characteristic star formation
timescale of ~5 Myr, and for a low star formation efficiency of ~10 %.


  We report on the realization and characterization of a novel magic-wavelength
nanofiber-based two-color optical dipole trap that allows us to generate a
periodic one-dimensional array of trapping sites with a spacing significantly
smaller than half of the resonant wavelength of the cesium D2-line. To this
end, we launch a blue-detuned partial standing wave and two red-detuned light
fields through the nanofiber. We demonstrate the trapping of atoms in the array
and characterize the resulting trap configuration by measuring the trap
frequencies in three directions and observe good agreement with theoretical
predictions. The implementation of this nanofiber-based optical interface with
magic trapping wavelengths and sub-$\lambda/2$ spacing is an important step
towards the exploration of novel collective radiative effects such as selective
radiance in 1D atomic arrays.


  We consider a set of electrostatic problems relevant for determining the
real-space structure and the ground-state energy of a two-dimensional electron
liquid subject to smooth external potentials. Three fundamental geometries are
investigated: an elongated metallic island, an antidot, and a constriction. In
the first two cases complete closed-form analytical solutions are obtained,
despite the absence of rotational or translational symmetries. These solutions
govern the shape and size of large quantum dots, and also the size of the
depletion regions and the density profiles around isolated antidots. For the
constriction, an exact asymptotical formula for boundary shape is derived and
arguments are given in favor of its universality. For the cases where the full
analytical solution cannot be obtained, an approximate method is proposed as an
alternative. Its accuracy is verified against numerical simulations in a
periodic (checkerboard) geometry.


  We present infrared galaxy luminosity functions (LFs) in the AKARI North
Ecliptic Pole (NEP) deep field using recently-obtained, wider CFHT
optical/near-IR images. AKARI has obtained deep images in the mid-infrared
(IR), covering 0.6 deg$^2$ of the NEP deep field. However, our previous work
was limited to the central area of 0.25 deg$^2$ due to the lack of optical
coverage of the full AKARI NEP survey. To rectify the situation, we recently
obtained CFHT optical and near-IR images over the entire AKARI NEP deep field.
These new CFHT images are used to derive accurate photometric redshifts,
allowing us to fully exploit the whole AKARI NEP deep field. AKARI's deep,
continuous filter coverage in the mid-IR wavelengths (2.4, 3.2, 4.1, 7, 9, 11,
15, 18, and 24$\mu$m) exists nowhere else, due to filter gaps of other space
telescopes. It allows us to estimate restframe 8$\mu$m and 12$\mu$m
luminosities without using a large extrapolation based on spectral energy
distribution (SED) fitting, which was the largest uncertainty in previous
studies. Total infrared luminosity (TIR) is also obtained more reliably due to
the superior filter coverage. The resulting restframe 8$\mu$m, 12$\mu$m, and
TIR LFs at $0.15<z<2.2$ are consistent with previous works, but with reduced
uncertainties, especially at the high luminosity-end, thanks to the wide field
coverage. In terms of cosmic infrared luminosity density
($\Omega_{\mathrm{IR}}$), we found that the $\Omega_{\mathrm{IR}}$ evolves as
$\propto (1+z)^{4.2\pm 0.4}$.