  The equation of state of the partially polarized two component Fermi gas at
zero temperature in the unitary limit is computed by {\it ab initio} auxiliary
field Monte Carlo method. We obtain the critical ratio of the chemical
potentials $\mu_\downarrow/\mu_\uparrow$ at the phase transitions. The value of
$\mu_\downarrow/\mu_\uparrow$ at the transition between the fully paired
superfluid and the partially polarized phase is 0.11 while the critical value
for the phase transition between the partially polarized phase and the fully
polarized normal fluid is -0.59. We also determine the radial boundaries of the
phase transitions of the Fermi gas in the harmonic trap as function of the
total polarization. We find that beyond the critical polarization 0.65, the
fully paired superfluid core disappears in the trapped Fermi gas.


  We study a collapsing system attracted by a spherically symmetric
gravitational source, with an increasing mass, that generates back-reaction
effects that are the source of space-time waves. As an example, we consider an
exponential collapse and the space-time waves emitted during this collapse due
to the back-reaction effects, originated by geometrical deformation driven by
the increment of the gravitational attracting mass during the collapse.


  An improved version of the PNJL model is used to calculate various
thermodynamical quantities, {\it viz.}, quark number susceptibility, isospin
susceptibility, specific heat, speed of sound and conformal measure. Comparison
with Lattice data is found to be encouraging.


  Let $\Gamma_{g}$ be the fundamental group of a closed connected orientable
surface of genus $g\geq2$. We develop a new method for integrating over the
representation space $\mathbb{X}_{g,n}=\mathrm{Hom}(\Gamma_{g},S_{n})$ where
$S_{n}$ is the symmetric group of permutations of $\{1,\ldots,n\}$.
Equivalently, this is the space of all vertex-labeled, $n$-sheeted covering
spaces of the the closed surface of genus $g$.
  Given $\phi\in\mathbb{X}_{g,n}$ and $\gamma\in\Gamma_{g}$, we let
$\mathsf{fix}_{\gamma}(\phi)$ be the number of fixed points of the permutation
$\phi(\gamma)$. The function $\mathsf{fix}_{\gamma}$ is a special case of a
natural family of functions on $\mathbb{X}_{g,n}$ called Wilson loops. Our new
methodology leads to an asymptotic formula, as $n\to\infty$, for the
expectation of $\mathsf{fix}_{\gamma}$ with respect to the uniform probability
measure on $\mathbb{X}_{g,n}$, which is denoted by
$\mathbb{E}_{g,n}[\mathsf{fix}_{\gamma}]$. We prove that if
$\gamma\in\Gamma_{g}$ is not the identity, and $q$ is maximal such that
$\gamma$ is a $q$th power in $\Gamma_{g}$, then \[
\mathbb{E}_{g,n}[\mathsf{fix}_{\gamma}]=d(q)+O(n^{-1}) \] as $n\to\infty$,
where $d\left(q\right)$ is the number of divisors of $q$. Even the weaker
corollary that $\mathbb{E}_{g,n}[\mathsf{fix}_{\gamma}]=o(n)$ as $n\to\infty$
is a new result of this paper. We also prove that if $\gamma$ is not the
identity then $\mathbb{E}_{g,n}[\mathsf{fix}_{\gamma}]$ can be approximated to
any order $O(n^{-M})$ by a polynomial in $n^{-1}$.


  A new formulation of the Hamiltonian dynamics of the gravitational field
interacting with(non-dissipative) thermo-elastic matter is discussed. It is
based on a gauge condition which allows us to encode the six degrees of freedom
of the ``gravity + matter''-system (two gravitational and four
thermo-mechanical ones), together with their conjugate momenta, in the
Riemannian metric q_{ij} and its conjugate ADM momentum P^{ij}. These variables
are not subject to constraints. We prove that the Hamiltonian of this system is
equal to the total matter entropy. It generates uniquely the dynamics once
expressed as a function of the canonical variables. Any function U obtained in
this way must fulfil a system of three, first order, partial differential
equations of the Hamilton-Jacobi type in the variables (q_{ij},P^{ij}). These
equations are universal and do not depend upon the properties of the material:
its equation of state enters only as a boundary condition. The well posedness
of this problem is proved. Finally, we prove that for vanishing matter density,
the value of U goes to infinity almost everywhere and remains bounded only on
the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on
constraints and infinity elsewhere) can be obtained as the limit of a ``deep
potential well'' corresponding to non-vanishing matter. This unconstrained
description of Hamiltonian General Relativity can be useful in numerical
calculations as well as in the canonical approach to Quantum Gravity.


  Treebanks are valuable linguistic resources that include the syntactic
structure of a language sentence in addition to POS-tags and morphological
features. They are mainly utilized in modeling statistical parsers. Although
the statistical natural language parser has recently become more accurate for
languages such as English, those for the Arabic language still have low
accuracy. The purpose of this paper is to construct a new Arabic dependency
treebank based on the traditional Arabic grammatical theory and the
characteristics of the Arabic language, to investigate their effects on the
accuracy of statistical parsers. The proposed Arabic dependency treebank,
called I3rab, contrasts with existing Arabic dependency treebanks in two main
concepts. The first concept is the approach of determining the main word of the
sentence, and the second concept is the representation of the joined and covert
pronouns. To evaluate I3rab, we compared its performance against a subset of
Prague Arabic Dependency Treebank that shares a comparable level of details.
The conducted experiments show that the percentage improvement reached up to
7.5% in UAS and 18.8% in LAS.


  For large volumes of text data collected over time, a key knowledge discovery
task is identifying and tracking clusters. These clusters may correspond to
emerging themes, popular topics, or breaking news stories in a corpus.
Therefore, recently there has been increased interest in the problem of
clustering dynamic data. However, there exists little support for the
interactive exploration of the output of these analysis techniques,
particularly in cases where researchers wish to simultaneously explore both the
change in cluster structure over time and the change in the textual content
associated with clusters. In this paper, we propose a model for tracking
dynamic clusters characterized by the evolutionary events of each cluster.
Motivated by this model, the TextLuas system provides an implementation for
tracking these dynamic clusters and visualizing their evolution using a metro
map metaphor. To provide overviews of cluster content, we adapt the tag cloud
representation to the dynamic clustering scenario. We demonstrate the TextLuas
system on two different text corpora, where they are shown to elucidate the
evolution of key themes. We also describe how TextLuas was applied to a problem
in bibliographic network research.


  For any group $G$, let $nacent(G)$ denote the set of all nonabelian
centralizers of $G$. Amiri and Rostami in (Publ. Math. Debrecen 87/3-4 (2015),
429-437) put forward the following question:
  Let H and G be finite simple groups. Is it true that if $|nacent(H)| =
|nacent(G)|$, then $G$ is isomorphic to $H$?
  In this paper, among other things, we give a negative answer to this
question.


  Topological data analysis is a powerful framework for extracting useful
topological information from complex datasets. Recent work has shown its
application for the dynamical analysis of classical dissipative systems through
a topology-preserving embedding method that allows reconstructing dynamical
attractors, the topologies of which can be used to identify chaotic behaviour.
Open quantum systems can similarly exhibit non-trivial dynamics, but the
existing toolkit for classification and quantification are still limited,
particularly for experimental applications. In this work, we present a
topological pipeline for characterizing quantum dynamics, which draws
inspiration from the classical approach by using single quantum trajectory
unravelings of the master equation to construct analogue 'quantum attractors'
and extracting their topology using persistent homology. We apply the method to
a periodically modulated Kerr-nonlinear cavity to discriminate parameter
regimes of regular and chaotic phase using limited measurements of the system.


  Using the COVID-19 Trends and Impact survey, we find that COVID-19
vaccinations reduced the prevalence of self-reported feelings of depression and
anxiety, isolation, and worries about health among vaccine-accepting
respondents in February 2021 by 3.7, 3.3, and 4.3 percentage points,
respectively, with particularly large reductions among respondents aged 18 and
24 years old. We show that interventions targeting social isolation account for
39.1\% of the total effect of COVID-19 vaccinations on depression, while
interventions targeting worries about health can account for 8.3\%. This
suggests that social isolation is a stronger mediator of the effect of COVID-19
vaccinations on depression than worries about health. We caution that these
causal interpretations rely on strong assumptions.


  The gender bias present in the data on which language models are pre-trained
gets reflected in the systems that use these models. The model's intrinsic
gender bias shows an outdated and unequal view of women in our culture and
encourages discrimination. Therefore, in order to establish more equitable
systems and increase fairness, it is crucial to identify and mitigate the bias
existing in these models. While there is a significant amount of work in this
area in English, there is a dearth of research being done in other gendered and
low resources languages, particularly the Indian languages. English is a
non-gendered language, where it has genderless nouns. The methodologies for
bias detection in English cannot be directly deployed in other gendered
languages, where the syntax and semantics vary. In our paper, we measure gender
bias associated with occupations in Hindi language models. Our major
contributions in this paper are the construction of a novel corpus to evaluate
occupational gender bias in Hindi, quantify this existing bias in these systems
using a well-defined metric, and mitigate it by efficiently fine-tuning our
model. Our results reflect that the bias is reduced post-introduction of our
proposed mitigation techniques. Our codebase is available publicly.


  Standard few-shot benchmarks are often built upon simplifying assumptions on
the query sets, which may not always hold in practice. In particular, for each
task at testing time, the classes effectively present in the unlabeled query
set are known a priori, and correspond exactly to the set of classes
represented in the labeled support set. We relax these assumptions and extend
current benchmarks, so that the query-set classes of a given task are unknown,
but just belong to a much larger set of possible classes. Our setting could be
viewed as an instance of the challenging yet practical problem of extremely
imbalanced K-way classification, K being much larger than the values typically
used in standard benchmarks, and with potentially irrelevant supervision from
the support set. Expectedly, our setting incurs drops in the performances of
state-of-the-art methods. Motivated by these observations, we introduce a
PrimAl Dual Minimum Description LEngth (PADDLE) formulation, which balances
data-fitting accuracy and model complexity for a given few-shot task, under
supervision constraints from the support set. Our constrained MDL-like
objective promotes competition among a large set of possible classes,
preserving only effective classes that befit better the data of a few-shot
task. It is hyperparameter free, and could be applied on top of any base-class
training. Furthermore, we derive a fast block coordinate descent algorithm for
optimizing our objective, with convergence guarantee, and a linear
computational complexity at each iteration. Comprehensive experiments over the
standard few-shot datasets and the more realistic and challenging i-Nat dataset
show highly competitive performances of our method, more so when the numbers of
possible classes in the tasks increase. Our code is publicly available at
https://github.com/SegoleneMartin/PADDLE.


  Energy transport in one-dimensional chains of particles with three
conservation laws is generically anomalous and belongs to the
Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples
where an apparent normal heat diffusion is found over a large range of length
scales were reported. We propose a novel physical explanation of these
intriguing observations. We develop a scaling analysis which explains how this
may happen in the vicinity of an integrable limit, such as, but not only, the
famous Toda model. In this limit, heat transport is mostly supplied by
quasi-particles with a very large mean free path $\ell$. Upon increasing the
system size $L$, three different regimes can be observed: a ballistic one, an
intermediate diffusive range, and, eventually, the crossover to the anomalous
(hydrodynamic) regime. Our theoretical considerations are supported by
numerical simulations of a gas of diatomic hard-point particles for almost
equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case
of the perturbed harmonic chain, which exhibits a yet different scenario.


  An alternative method to the density matrix formalism for the derivation of
general expressions of the interaction of polarized atoms with polarized
photons and electrons is presented. The expression for the cross-section
describing the polarization states of all particles taking part in the process
are obtained in the form of an expansion via irreducible tensors that have the
most simplest possible behaviour under changes of directions. The ways of the
application of the general expressions suitable for the specific experimental
conditions are outlined by deriving asymmetry parameters of the angular
distributions of photoelectrons and Auger electrons following photoionization
as well as the parameters of the angular correlations between photo- and Auger
electrons.


  We derive abundances of Fe, Na, O, and s-elements from GIRAFFE@VLT spectra
for more than 200 red giant stars in the Milky Way satellite Omega Centauri.
Our preliminary results are that: (i) we confirm that Omega Centauri exibiths
large star-to-star metallicity variations ($\sim$ 1.4 dex); (ii) the
metallicity distribution reveals the presence of at least five stellar
populations with different [Fe/H]; (iii) a clear Na-O anticorrelation is
clearly observed for the metal-poor and metal-intermediate populations while
apparently the anticorrelation disappears for the most metal-rich populations.
Interestingly the Na level grows with iron.


  The sensitivity of NMR and MRI can be boosted via hyperpolarization of
nuclear spins. However, current methods are costly, polarization is relatively
low, or applicability is limited. Here, we report a new hyperpolarization
method combining the low-cost, high polarization of hydrogenative
parahydrogen-induced polarization (PHIP) with the flexibility of polarization
transfer via proton exchange. The new method can be used to polarize various
molecules, including alcohols, water, lactate, and pyruvate. On average, only
$\approx$3 mM of a hyperpolarized transfer agent was sufficient to
significantly enhance the signal of $\approx$100 mM of target molecules via
proton exchange. Thus, hydrogenative parahydrogen-induced hyperpolarization
with proton exchange (PHIP-X) provides a new avenue for NMR applications beyond
the limits imposed by thermal polarization.


  We consider the problem of designing a revenue-optimal mechanism in the
two-item, single-buyer, unit-demand setting when the buyer's valuations, $(z_1,
z_2)$, are uniformly distributed in an arbitrary rectangle
$[c,c+b_1]\times[c,c+b_2]$ in the positive quadrant. We provide a complete and
explicit solution for arbitrary nonnegative values of $(c,b_1,b_2)$. We
identify five simple structures, each with at most five (possibly stochastic)
menu items, and prove that the optimal mechanism has one of the five
structures. We also characterize the optimal mechanism as a function of $b_1,
b_2$, and $c$. When $c$ is low, the optimal mechanism is a posted price
mechanism with an exclusion region; when $c$ is high, it is a posted price
mechanism without an exclusion region. Our results are the first to show the
existence of optimal mechanisms with no exclusion region, to the best of our
knowledge.


  Gravitational wave astronomy relies on the use of multiple detectors, so that
coincident detections may distinguish real signals from instrumental artifacts,
and also so that relative timing of signals can provide the sky position of
sources. We show that the comparison of instantaneous time-frequency and time-
amplitude maps provided by the Hilbert-Huang Transform (HHT) can be used
effectively for relative signal timing of common signals, to discriminate
between the case of identical coincident signals and random noise coincidences,
and to provide a classification of signals based on their time-frequency
trajectories. The comparison is done with a chi-square goodness-of-fit method
which includes contributions from both the instantaneous amplitude and
frequency components of the HHT to match two signals in the time domain. This
approach naturally allows the analysis of waveforms with strong frequency
modulation.


  Designing 3D scenes is currently a creative task that requires significant
expertise and effort in using complex 3D design interfaces. This effortful
design process starts in stark contrast to the easiness with which people can
use language to describe real and imaginary environments. We present SceneSeer:
an interactive text to 3D scene generation system that allows a user to design
3D scenes using natural language. A user provides input text from which we
extract explicit constraints on the objects that should appear in the scene.
Given these explicit constraints, the system then uses a spatial knowledge base
learned from an existing database of 3D scenes and 3D object models to infer an
arrangement of the objects forming a natural scene matching the input
description. Using textual commands the user can then iteratively refine the
created scene by adding, removing, replacing, and manipulating objects. We
evaluate the quality of 3D scenes generated by SceneSeer in a perceptual
evaluation experiment where we compare against manually designed scenes and
simpler baselines for 3D scene generation. We demonstrate how the generated
scenes can be iteratively refined through simple natural language commands.


  We experimentally study the dynamics of granular media in a discharging
hopper. In such flows, there often appears to be a critical outlet size $D_c$
such that the flow never clogs for $D > D_c$. We report on the time-averaged
velocity distributions, as well as temporal intermittency in the
ensemble-averaged velocity of grains in a viewing window, for both $D < D_c$
and $D > D_c$, near and far from the outlet. We characterize the velocity
distributions by the standard deviation and the skewness of the distribution of
vertical velocities. We propose a measure for intermittency based on the
two-sample Kolmogorov-Smirnov $D_{KS}$-statistic for the velocity distributions
as a function of time. We find that there is no discontinuity or kink in these
various measures as a function of hole size. This result supports the
proposition that there is no well-defined $D_c$ and that clogging is always
possible. Furthermore, the intermittency time scale of the flow is set by the
speed of the grains at the hopper exit. This latter finding is consistent with
a model of clogging as the independent sampling for stable configurations at
the exit with a rate set by the exiting grain speed [Thomas and Durian, Phys.
Rev. Lett. (2015)].


  It has been a half-decade since the first direct detection of gravitational
waves, which signifies the coming of the era of the gravitational-wave
astronomy and gravitational-wave cosmology. The increasing number of the
detected gravitational-wave events has revealed the promising capability of
constraining various aspects of cosmology, astronomy, and gravity. Due to the
limited space in this review article, we will briefly summarize the recent
progress over the past five years, but with a special focus on some of our own
work for the Key Project ``Physics associated with the gravitational waves''
supported by the National Natural Science Foundation of China. In particular,
(1) we have presented the mechanism of the gravitational-wave production during
some physical processes of the early Universe, such as inflation, preheating
and phase transition, and the cosmological implications of gravitational-wave
measurements; (2) we have put constraints on the neutron star maximum mass
according to GW170817 observations; (3) we have developed a numerical
relativity algorithm based on the finite element method and a waveform model
for the binary black hole coalescence along an eccentric orbit.


  We present the results of Monte Carlo simulations of two different Potts
glass models with short range random interactions. In the first model a \pm
J-distribution of the bonds is chosen, in the second model a Gaussian
distribution. In both cases the first two moments of the distribution are
chosen to be J_0=-1, Delta J=+1, so that no ferromagnetic ordering of the Potts
spins can occur. We find that for all temperatures investigated the spin glass
susceptibility remains finite, the spin glass order parameter remains zero, and
that the specific heat has only a smooth Schottky-like peak. These results can
be understood quantitatively by considering small but independent clusters of
spins. Hence we have evidence that there is no static phase transition at any
nonzero temperature. Consistent with these findings, only very minor size
effects are observed, which implies that all correlation lengths of the models
remain very short. We also compute for both models the time auto-correlation
function C(t) of the Potts spins. While in the Gaussian model C(t) shows a
smooth uniform decay, the correlator for the \pm J model has several distinct
steps. These steps correspond to the breaking of bonds in small clusters of
ferromagnetically coupled spins (dimers, trimers, etc.). The relaxation times
follow simple Arrhenius laws, with activation energies that are readily
interpreted within the cluster picture, giving evidence that the system does
not have a dynamic transition at a finite temperature. Hence we find that for
the present models all the transitions known for the mean-field version of the
model are completely wiped out. Finally we also determine the time
auto-correlation functions of individual spins, and show that the system is
dynamically very heterogeneous.


  We present the analysis and results of recent high-energy gamma-ray
observations of the BL Lac object 3C 66A conducted with the Solar Tower
Atmospheric Cherenkov Effect Experiment (STACEE). During the 2003-2004
observing season, STACEE extensively observed 3C 66A as part of a
multiwavelength campaign on the source. A total of 33.7 hours of data was taken
on the source, plus an equivalent-duration background observation. After
cleaning the data set a total of 16.3 hours of live time remained, and a net
on-source excess of 1134 events was seen against a background of 231742 events.
At a significance of 2.2 standard deviations this excess is insufficient to
claim a detection of 3C 66A, but is used to establish flux upper limits for the
source.


  We initiate the study of general neighborhood growth dynamics on two
dimensional Hamming graphs. The decision to add a point is made by counting the
currently occupied points on the horizontal and the vertical line through it,
and checking whether the pair of counts lies outside a fixed Young diagram. We
focus on two related extremal quantities. The first is the size of the smallest
set that eventually occupies the entire plane. The second is the minimum of an
energy-entropy functional that comes from the scaling of the probability of
eventual full occupation versus the density of the initial product measure
within a rectangle. We demonstrate the existence of this scaling and study
these quantities for large Young diagrams.


  From different public and private instances, mechanisms have been set in
action that allow for companies to obtain information in order to make
decisions with a stronger foundation. This article is focused on the
description of an entire information system for the business world, developed
in the realm of the Chambers of Commerce of Spain, which have given rise to the
creation of an authentic network of inter-chamber information.
  In Spain, the obligatory membership of businesses to the Chambers of Commerce
in their geographic areas, and therefore the compulsory payment of member
quotas, has traditionally generated some polemics, above all because many firms
have not perceived a material usefulness of the services offered by these
Chambers.
  Notwithstanding, the 85 Chambers currently existing in Spain, as well as the
organism that coordinates them -the Upper Council or Consejo Superior de
Camaras de Comercio- and the company created expressly to commercialize
informational services online, Camerdata, have developed genuinely informative
tools that cover a good part of the informational demands that a business might
claim, described here.


  For a driven-dissipative quantum many-body system prepared in a spontaneous
broken-symmetry steady state, in addition to the Goldstone mode the soft
fluctuation modes provide important insight into the system's dynamics. Using a
microscopic polariton laser theory, we find a rich transformation behavior of
discrete and continuum soft modes in a two parameter (pump density and cavity
dissipation rate) space. In addition to finding exceptional-point Goldstone
companion modes, our theory yields a unified picture of a variety of seemingly
disconnected physical concepts including Mott transition, Mollow spectra or
relaxation oscillations, and polaritonic Bardeen-Cooper-Schrieffer gaps.


  We consider the canonical symplectic form for sine-Gordon evaluated
explicitly on the solitons of the model. The integral over space in the form,
which arises because the canonical argument uses the Lagrangian density, is
done explicitly in terms of functions arising in the group doublecrossproduct
formulation of the inverse scattering procedure, and we are left with a simple
expression given by two boundary terms. The expression is then evaluated
explicitly in terms of the changes in the positions and momenta of the
solitons, and we find agreement with a result of Babelon and Bernard who have
evaluated the form using a different argument, where it is diagonal in terms of
`in' or `out' co-ordinates. Using the result, we also investigate the higher
conserved charges within the inverse scattering framework, check that they
Poisson commute and evaluate them on the soliton solutions.


  (abridged) We present a comprehensive comparison of the X-ray properties of a
sample of eight dwarf starburst galaxies observed with Chandra (I Zw 18, VII Zw
403, NGC 1569, NGC 3077, NGC 4214, NGC 4449, NGC 5253, He 2-10). In Paper I we
presented in detail the data reduction and analysis of the individual galaxies.
For the unresolved X-ray sources we find the following: point sources are in
general located close to bright HII regions, rims of superbubbles, or young
stellar clusters. The number of X-ray point sources appears to be a function of
the current star formation rate and the blue luminosity of the hosts.
Ultraluminous X-ray sources are only found in those dwarf galaxies which are
currently interacting. The power law index of the combined cumulative X-ray
point source luminosity function is alpha=0.24+/-0.06, shallower than that of
more massive starburst galaxies (alpha=0.4-0.8) and of non-starburst galaxies
(alpha~1.2). For those galaxies showing extended X-ray emission (6 out of the 8
galaxies), we derive the following: Superwinds develop along the steepest
gradient of the HI distribution with volume densities of 0.02-0.06 cm^-3,
pressures of 1-3x10^5 K cm^-3, thermal energies of 2-30x10^54 erg, and hot gas
masses of 2-20x10^6 Mo (~1 per cent of the HI masses). The mechanical
luminosities of the developing superwinds are energetic enough to overcome the
gravitational potentials of their host galaxies. This scenario is supported by
the overpressures of the hot gas compared to the ambient ISM. Extended HI
envelopes such as tidal tails, however, may delay outflows on timescales
exceeding those of the cooling time of the hot gas.


  We present the first non-trivial online algorithms for the non-uniform,
multicommodity buy-at-bulk (MC-BB) network design problem in undirected and
directed graphs. Our competitive ratios qualitatively match the best known
approximation factors for the corresponding offline problems. The main engine
for our results is an online reduction theorem of MC-BB problems to their
single-sink (SS-BB) counterparts. We use the concept of junction-tree solutions
(Chekuri et al., FOCS 2006) that play an important role in solving the offline
versions of the problem via a greedy subroutine -- an inherently offline
procedure. Our main technical contribution is in designing an online algorithm
using only the existence of good junction-trees to reduce an MC-BB instance to
multiple SS-BB sub-instances. Along the way, we also give the first non-trivial
online node-weighted/directed single-sink buy-at-bulk algorithms. In addition
to the new results, our generic reduction also yields new proofs of recent
results for the online node-weighted Steiner forest and online group Steiner
forest problems.


  The exact degeneracies of quarter-BPS dyons in Type II string theory on $K3
\times T^2$ are given by Fourier coefficients of the inverse of the Igusa cusp
form. For a fixed magnetic charge invariant $m$, the generating function of
these degeneracies naturally decomposes as a sum of two parts, which are
supposed to account for single-centered black holes, and two-centered black
hole bound states, respectively. The decomposition is such that each part is
separately modular covariant but neither is holomorphic, calling for a physical
interpretation of the non-holomorphy. We resolve this puzzle by computing the
supersymmetric index of the quantum mechanics of two-centered half-BPS
black-holes, which we model by geodesic motion on Taub-NUT space subject to a
certain potential. We compute a suitable index using localization methods, and
find that it includes both a temperature-independent contribution from BPS
bound states, as well as a temperature-dependent contribution due to a spectral
asymmetry in the continuum of scattering states. The continuum contribution
agrees precisely with the non-holomorphic completion term required for the
modularity of the generating function of two-centered black hole bound states.


  In the minimal supersymmetric standard model extended by including
right-handed neutrinos with see-saw mechanism, the neutrino Yukaka couplings
can be as large as the top-quark Yukawa couplings and thus the
neutrino/sneutrino may cause sizable effects in Higgs boson self-energy loops.
Our explicit one-loop calculations show that the neutrino/sneutrino effects may
have an opposite sign to top/stop effects and thus lighten the lightest Higgs
boson. If the soft-breaking mass of the right-handed neutrino is very large (at
the order of Majorana mass scale), such as in the split-SUSY scenario, the
effects can lower the lightest Higgs boson mass by a few tens of GeV. So the
Higgs mass bound of about 150 GeV in split-SUSY may be lowered significantly if
right-handed neutrinos come into play with see-saw mechanism.


  Aims: In light of recent discoveries of pulsating ULXs and recently
introduced models, that propose neutron stars (NSs) as the central engines of
ULXs, we revisit the (XMM-Newton and NuSTAR) spectra of eighteen well known
ULXs, in search of indications that favor this new hypothesis. Results: We
confirm the, previously noted, presence of the low energy (<6 keV) spectral
rollover and argue that it could be interpreted as thermal emission. The
spectra are well described by a double thermal model consisting of a "hot" (>1
keV) and a "cool" (<0.7 keV) multicolor black body (MCB). Under the assumption
that the "cool" MCD emission originates in a disk truncated at the NS
magnetosphere, we find that all ULXs in our sample are consistent with
accretion onto a highly magnetized (B>10^12G) NS. We note a strong correlation
between the strength of the magnetic field, the temperature of the "hot"
thermal component and the total unabsorbed luminosity. Examination of the
NuSTAR data supported this interpretation and confirmed the presence of a weak,
high energy (>15 keV) tail, most likely the result of modification of the MCB
emission by inverse Compton scattering. We also note that the apparent high
energy tail, may simply be the result of mis-modeling of MCB emission with an
atypical temperature (T) vs radius (r) gradient, using a standard MCD model
with a fixed gradient of T~r^-0.75. Conclusions: We have offered a new physical
interpretation for the dual-thermal spectra of ULXs. We find that the best-fit
derived parameters, are in excellent agreement with recent predictions that
favor super-critically accreting NSs as the engines of a large fraction of
ULXs. Nevertheless, the considerable degeneracy between models and the lack of
unequivocal evidence cannot rule out other equally plausible interpretations.
Our results warrant further exploration of this new framework.


  For an integer $n\geq 2$, let $X_n$ be the Cayley graph on the symmetric
group $S_n$ generated by the set of transpositions ${(1 2),(1 3),...,(1 n)}$.
It is shown that the spectrum of $X_n$ contains all integers from $-(n-1)$ to
$n-1$ (except 0 if $n=2$ or $n=3$).


  Recent neural sequence to sequence models have provided feasible solutions
for abstractive summarization. However, such models are still hard to tackle
long text dependency in the summarization task. A high-quality summarization
system usually depends on strong encoder which can refine important information
from long input texts so that the decoder can generate salient summaries from
the encoder's memory. In this paper, we propose an aggregation mechanism based
on the Transformer model to address the challenge of long text representation.
Our model can review history information to make encoder hold more memory
capacity. Empirically, we apply our aggregation mechanism to the Transformer
model and experiment on CNN/DailyMail dataset to achieve higher quality
summaries compared to several strong baseline models on the ROUGE metrics.


  Should students be used as experimental subjects in software engineering?
Given that students are in many cases readily available and cheap it is no
surprise that the vast majority of controlled experiments in software
engineering use them. But they can be argued to constitute a convenience sample
that may not represent the target population (typically "real" developers),
especially in terms of experience and proficiency. This causes many researchers
(and reviewers) to have reservations about the external validity of
student-based experiments, and claim that students should not be used. Based on
an extensive review of published works that have compared students to
professionals, we find that picking on "students" is counterproductive for two
main reasons. First, classifying experimental subjects by their status is
merely a proxy for more important and meaningful classifications, such as
classifying them according to their abilities, and effort should be invested in
defining and using these more meaningful classifications. Second, in many cases
using students is perfectly reasonable, and student subjects can be used to
obtain reliable results and further the research goals. In particular, this
appears to be the case when the study involves basic programming and
comprehension skills, when tools or methodologies that do not require an
extensive learning curve are being compared, and in the initial formative
stages of large industrial research initiatives -- in other words, in many of
the cases that are suitable for controlled experiments of limited scope.


  Adopting an accurate kinetic energy density functional (KEDF) to characterize
the noninteracting kinetic energy within the framework of orbital-free density
functional theory (OFDFT) is challenging. We propose a new form of the
non-local KEDF with a real-space truncation cutoff that satisfies the uniform
electron gas limit and design KEDFs for simple metals and silicon. The new
KEDFs are obtained by minimizing a residual function, which contains the
differences in the total energy and charge density of several representative
systems with respect to the Kohn-Sham DFT results. By systematically testing
different cutoffs of the new KEDFs, we find that the cutoff plays a crucial
role in determining the properties of metallic Al and semiconductor Si systems.
We conclude that the new KEDF with a sufficiently long cutoff performs even
better than some representative non-local KEDFs in some aspects, which sheds
new light on optimizing the KEDFs in OFDFT to achieve better accuracy.


  Using the stationary formulation of the toroidally compactified heterotic
string theory in terms of a pair of matrix Ernst potentials we consider the
four-dimensional truncation of this theory with no U(1) vector fields excited.
Imposing one time-like Killing vector permits us to express the stationary
effective action as a model in which gravity is coupled to a matrix Ernst
potential which, under certain parametrization, allows us to interpret the
matter sector of this theory as a double Ernst system. We generate a web of
string vacua which are related to each other via a set of discrete symmetries
of the effective action (some of them involve S-duality transformations and
possess non-perturbative character). Some physical implications of these
discrete symmetries are analyzed and we find that, in some particular cases,
they relate rotating black holes coupled to a dilaton with no Kalb--Ramond
field, static black holes with non-trivial dilaton and antisymmetric tensor
fields, and rotating and static naked singularities. Further, by applying a
nonlinear symmetry, namely, the so-called normalized Harrison transformation,
on the seed field configurations corresponding to these neutral backgrounds, we
recover the U(1)^n Abelian vector sector of the four-dimensional action of the
heterotic string, charging in this way the double Ernst system which
corresponds to each one of the neutral string vacua, i.e., the stationary and
the static black holes and the naked singularities.


  A new operational, ensemble-based search and rescue model for the Norwegian
Sea and the North Sea is presented. The stochastic trajectory model computes
the net motion of a range of search and rescue objects. A new, robust
formulation for the relation between the wind and the motion of the drifting
object (termed the leeway of the object) is employed. Empirically derived
coefficients for 63 categories of search objects compiled by the US Coast Guard
are ingested to estimate the leeway of the drifting objects. A Monte Carlo
technique is employed to generate an ensemble that accounts for the
uncertainties in forcing fields (wind and current), leeway drift properties,
and the initial position of the search object. The ensemble yields an estimate
of the time-evolving probability density function of the location of the search
object, and its envelope defines the search area. Forcing fields from the
operational oceanic and atmospheric forecast system of The Norwegian
Meteorological Institute are used as input to the trajectory model. This allows
for the first time high-resolution wind and current fields to be used to
forecast search areas up to 60 hours into the future. A limited set of field
exercises show good agreement between model trajectories, search areas, and
observed trajectories for liferafts and other search objects. Comparison with
older methods shows that search areas expand much more slowly using the new
ensemble method with high resolution forcing fields and the new leeway
formulation. It is found that going to higher-order stochastic trajectory
models will not significantly improve the forecast skill and the rate of
expansion of search areas.


  In this paper, we consider the fifth-order modified Korteweg-de Vries
(modified KdV) equation under the periodic boundary condition. We prove the
local well-posedness in $H^s(\mathbb T)$, $s > 2$, via the energy method. The
main tool is the short-time Fourier restriction norm method, which was first
introduced in its current form by Ionescu, Kenig and Tataru [Global
well-posedness of the KP-I initial-value problem in the energy space, Invent.
Math. 173 (2) (2008) 265--304]. Besides, we use the frequency localized
modified energy to control the high-low interaction component in the energy
estimate. We remark that under the periodic setting, the integrable structure
is very useful (but not necessary) to remove harmful terms in the nonlinearity
and this work is the first low regularity well-posedness result for the
fifth-order modified KdV equation.


  We prove that etale morphisms of schemes yield separable extensions of
derived categories. We then generalize the Neeman-Thomason Localization Theorem
to separable extensions of triangulated categories.


  Deep Neural Networks are generally trained using iterative gradient updates.
Magnitudes of gradients are affected by many factors, including choice of
activation functions and initialization. More importantly, gradient magnitudes
can greatly differ across layers, with some layers receiving much smaller
gradients than others. causing some layers to train slower than others and
therefore slowing down the overall convergence. We analytically explain this
disproportionality. Then we propose to explicitly train all layers at the same
speed, by scaling the gradient w.r.t. every trainable tensor to be proportional
to its current value. In particular, at every batch, we want to update all
trainable tensors, such that the relative change of the L1-norm of the tensors
is the same, across all layers of the network, throughout training time.
Experiments on MNIST show that our method appropriately scales gradients, such
that the relative change in trainable tensors is approximately equal across
layers. In addition, measuring the test accuracy with training time, shows that
our method trains faster than other methods, giving higher test accuracy given
same budget of training steps.


  Mixed-criticality real-time scheduling has been developed to improve resource
utilization while guaranteeing safe execution of critical applications. These
studies use optimistic resource reservation for all the applications to improve
utilization, but prioritize critical applications when the reservations become
insufficient at runtime. Many of them however share an impractical assumption
that all the critical applications will simultaneously demand additional
resources. As a consequence, they under-utilize resources by penalizing all the
low-criticality applications. In this paper we overcome this shortcoming using
a novel mechanism that comprises a parameter to model the expected number of
critical applications simultaneously demanding more resources, and an execution
strategy based on the parameter to improve resource utilization. Since most
mixed-criticality systems in practice are component-based, we design our
mechanism such that the component boundaries provide the isolation necessary to
support the execution of low-criticality applications, and at the same time
protect the critical ones. We also develop schedulability tests for the
proposed mechanism under both a flat as well as a hierarchical scheduling
framework. Finally, through simulations, we compare the performance of the
proposed approach with existing studies in terms of schedulability and the
capability to support low-criticality applications.


  This thesis investigates the use of problem-specific knowledge to enhance a
genetic algorithm approach to multiple-choice optimisation problems. It shows
that such information can significantly enhance performance, but that the
choice of information and the way it is included are important factors for
success.


  Side-informed steganography has always been among the most secure approaches
in the field. However, a majority of existing methods for JPEG images use the
side information, here the rounding error, in a heuristic way. For the first
time, we show that the usefulness of the rounding error comes from its
covariance with the embedding changes. Unfortunately, this covariance between
continuous and discrete variables is not analytically available. An estimate of
the covariance is proposed, which allows to model steganography as a change in
the variance of DCT coefficients. Since steganalysis today is best performed in
the spatial domain, we derive a likelihood ratio test to preserve a model of a
decompressed JPEG image. The proposed method then bounds the power of this test
by minimizing the Kullback-Leibler divergence between the cover and stego
distributions. We experimentally demonstrate in two popular datasets that it
achieves state-of-the-art performance against deep learning detectors.
Moreover, by considering a different pixel variance estimator for images
compressed with Quality Factor 100, even greater improvements are obtained.


  We introduce a scheme to reconstruct arbitrary states of networks composed of
quantum oscillators--e.g., the motional state of trapped ions or the radiation
state of coupled cavities. The scheme uses minimal resources, in the sense that
it i) requires only the interaction between one-qubit probe and one constituent
of the network; ii) provides the reconstructed state directly from the data,
avoiding any tomographic transformation; iii) involves the tuning of only one
coupling parameter. In addition, we show that a number of quantum properties
can be extracted without full reconstruction of the state. The scheme can be
used for probing quantum simulations of anharmonic many-body systems and
quantum computations with continuous variables. Experimental implementation
with trapped ions is also discussed and shown to be within reach of current
technology.


  Given any two classical codes with parameters $[n_1,k,d_1]$ and
$[n_2,k,d_2]$, we show how to construct a quantum subsystem code in
2-dimensions with parameters $[[N,K,D]]$ satisfying $N\le 2n_1n_2$, $K=k$, and
$D=\min(d_1,d_2)$. These quantum codes are in the class of generalized
Bacon-Shor codes introduced by Bravyi. We note that constructions of good
classical codes can be used to construct quantum codes that saturate Bravyi's
bound $KD=O(N)$ on the code parameters of 2-dimensional subsystem codes. One of
these good constructions uses classical expander codes. This construction has
the additional advantage of a linear time quantum decoder based on the
classical Sipser-Spielman flip decoder. Finally, while the subsystem codes we
create do not have asymptotic thresholds, we show how they can be gauge-fixed
to certain hypergraph product codes that do.


  We consider an axisymmetric, freely suspended fluid drop with surface
tension, whose viscosity is so large that both inertia and forcing by an
external fluid can be ignored. We show that whatever be the initial condition,
pinchoff can never occur.


  A brief overview is given of the phenomenology of particle dark matter and
the properties of some of the most widely studied dark matter candidates.
Recent developments in direct and indirect dark matter searches are discussed.


  We study the effective radius of weakly self-avoiding star polymers in one,
two, and three dimensions. Our model includes $N$ Brownian motions up to time
$T$, started at the origin and subject to exponential penalization based on the
amount of time they spend close to each other, or close to themselves. The
effective radius measures the typical distance from the origin. Our main result
gives estimates for the effective radius where in two and three dimensions we
impose the restriction that $T \leq N$. One of the highlights of our results is
that in two dimensions, we find that the radius is proportional to $T^{3/4}$,
up to logarithmic corrections.


  Successful assembly of suspended nanoscale rod-like particles depends on
fundamental phenomena controlling rotational and translational diffusion.
Despite the significant developments in fluidic fabrication of nanostructured
materials, the ability to quantify the dynamics in processing systems remains
challenging. Here we demonstrate an experimental method for characterization of
the orientation dynamics of nanorod suspensions in assembly flows using
birefringence relaxation. The methodology is illustrated using nanocelluloses
(cellulose nanocrystals and nanofibrils) as model systems, where the coupling
of rotational diffusion coefficients to particle size distributions as well as
flow-induced orientation mechanisms are elucidated. Our observations advance
the knowledge on key fundamental nanoscale mechanisms governing the dynamics of
nanotubes and nanorods allowing bottom-up assembly into hierarchical
superstructures.


  We investigate the existence of two nontrivial solutions for a poly-Laplacian
system involving concave-convex nonlinearities and parameters with Dirichlet
boundary condition on locally finite graphs. By using the mountain pass theorem
and Ekeland's variational principle, we obtain that system has at least one
nontrivial solution of positive energy and one nontrivial solution of negative
energy, respectively. We also obtain an estimate about semi-trivial solutions.
Moreover, by using a result in [4] which is based on the fibering method and
Nehari manifold, we obtain the existence of ground state solution to the single
equation corresponding to poly-Laplacian system. Especially, we present some
ranges of parameters in all of results.


  High-energy photons emitted by flaring active galactic nuclei (AGNs) have
been used for many years to constrain modified dispersion relations in vacuum
encountered in the context of quantum gravity phenomenology. In such studies,
done in the GeV-TeV range, energy-dependent delays (spectral lags) are searched
for, usually neglecting any source-intrinsic time delay. With the aim being to
distinguish lorentz invariance violation (LIV) effects from lags generated at
the sources themselves, a detailed investigation into intrinsic spectral lags
in flaring AGNs above 100 GeV is presented in the frame of
synchrotron-self-Compton (SSC) scenarios for their very-high-energy (VHE)
emission. A simple model of VHE flares in blazars is proposed, allowing to
explore the influence of the main physical parameters describing the emitting
zones on intrinsic delays. For typical conditions expected in TeV blazars,
significant intrinsic lags are obtained, which can dominate over LIV effects,
especially at low redshifts, and should therefore be carefully disentangled
from any extrinsic lags. Moreover, two main regimes are identified with
characteristic spectral lags, corresponding to long-lasting and fast particle
acceleration. Such intrinsic spectral lags should be detected with
new-generation instruments at VHE such as the Cherenkov Telescope Array which
begins operation in a few years. This will provide original constraints on AGN
flare models and open a new era for LIV searches in the photon sector.


  Without doubt, mass transfer in close binary systems contributes to the
populations of Wolf-Rayet (WR) stars in the Milky Way and the Magellanic
Clouds. However, the binary formation channel is so far not well explored. We
want to remedy this by exploring large grids of detailed binary and single star
evolution models computed with the publicly available MESA code, for a
metallicity appropriate for the Large Magellanic Cloud (LMC). The binary models
are calculated through Roche-lobe overflow and mass transfer, until the
initially more massive star exhausts helium in its core. We distinguish models
of WR and helium stars based on the estimated stellar wind optical depth. We
use these models to build a synthetic WR population, assuming constant star
formation. Our models can reproduce the WR population of the LMC to significant
detail, including the number and luminosity functions of the main WR subtypes.
We find that for binary fractions of 100% (50%), all LMC WR stars below
$10^6\,L_{\odot}$ ($10^{5.7}\,L_{\odot}$) are stripped binary mass donors. We
also identify several insightful mismatches. With a single star fraction of
50\%, our models produce too many yellow supergiants, calling either for a
larger initial binary fraction, or for enhanced mass-loss near the
Humphreys-Davidson limit. Our models predict more long-period WR binaries than
observed, arguably due to an observational bias towards short periods. Our
models also underpredict the shortest-period WR binaries, which may have
implications for understanding the progenitors of double black hole mergers.
The fraction of binary produced WR stars may be larger than often assumed, and
outline the risk to mis-calibrate stellar physics when only single star models
are used to reproduce the observed WR stars.


  We present a new strategy for gap estimation in randomized algorithms for
multiarmed bandits and combine it with the EXP3++ algorithm of Seldin and
Slivkins (2014). In the stochastic regime the strategy reduces dependence of
regret on a time horizon from $(\ln t)^3$ to $(\ln t)^2$ and eliminates an
additive factor of order $\Delta e^{1/\Delta^2}$, where $\Delta$ is the minimal
gap of a problem instance. In the adversarial regime regret guarantee remains
unchanged.


  Random boolean cellular automata are investigated, where each gate has two
randomly chosen inputs and is randomly assigned a boolean function of its
inputs. The effect of non-uniform distributions on the choice of the boolean
functions is considered. The main results are that if the gates are more likely
to be assigned constant functions than non-canalyzing functions, then with very
high probability, the automaton will exhibit very stable behavior: most of the
gates will stabilize, and the state cycles will be bounded in size.


  The renormalization group (RG) approach is largely responsible for the
considerable success which has been achieved in developing a quantitative
theory of phase transitions. This work treats the rigorous definition of the RG
map for classical Ising-type lattice systems in the infinite volume limit at
high temperature. A cluster expansion is used to justify the existence of the
partial derivatives of the renormalized interaction with respect to the
original interaction. This expansion is derived from the formal expressions,
but it is itself well-defined and convergent. Suppose in addition that the
original interaction is finite-range and translation-invariant. We will show
that the matrix of partial derivatives in this case displays an approximate
band property. This in turn gives an upper bound for the RG linearization.


  In this paper we present a new characterization of Pareto distribution and
consider goodness of fit tests based on it. We provide an integral and
Kolmogorov- Smirnov type statistics based on U-statistics and we calculate
Bahadur efficiency for various alternatives. We find locally optimal
alternatives for those tests. For small sample sizes we compare the power of
those tests with some common goodness of fit tests.


  In this paper, we show how to construct examples of closed manifolds with
explicitly computed irrational, even transcendental L2 Betti numbers, defined
via the universal covering.
  We show that every non-negative real number shows up as an L2-Betti number of
some covering of a compact manifold, and that many computable real numbers
appear as an L2-Betti number of a universal covering of a compact manifold
(with a precise meaning of computable given below).
  In algebraic terms, for many given computable real numbers (in particular for
many transcendental numbers) we show how to construct a finitely presented
group and an element in the integral group ring such that the L2-dimension of
the kernel is the given number.
  We follow the method pioneered by Austin in "Rational group ring elements
with kernels having irrational dimension" arXiv:0909.2360) but refine it to get
very explicit calculations which make the above statements possible.


  A novel general approximation scheme (NGAS) proposed earlier (ref.2-3) is
applied to the problem of the quartic anharmonic (QAHO) and the
double-well-oscillator (QDWO) in quantum theory by choosing the infinite
square-well-potential in one dimension as the input approximation. The leading
order (LO) results obtained for the energy eigen-values are uniformly accurate
to within a few percent of the exact results for $arbitrary$ values of the
quartic coupling: $\lambda > 0$ and the level-index $n_s$. These results are
shown to be non-perturbative in the LO and reproduce the known analytic and
scaling properties of energy as a function of the coupling $\lambda$ and $n_s$.
The LO-results are further improved in accuracy by including the
perturbative-correction at the next non-trivial order of an improved
perturbation theory (IPT) based upon NGAS. The method can be trivially extended
to other cases of higher anharmonicity.


  We perform simulations of the capabilities of the next generation Very Large
Array to image stellar radio photospheres. For very large (in angle) stars,
such as red supergiants within a few hundred parsecs, good imaging fidelity
results can be obtained on radio photospheric structures at 38 GHz employing
standard techniques, such as disk model fitting and subtraction, with hundreds
of resolution elements over the star, even with just the ngVLA-classic
baselines to 1000 km. Using the ngVLA Rev B plus long baseline configuration
(with baselines out to 9000 km, August 2018), we find for main sequence stars
within $\sim$ 10 pc, the photospheres can be easily resolved at 85 GHz, with
accurate measures of the mean brightness and size, and possibly imaging large
surface structures, as might occur on e.g., active M dwarf stars. For more
distant main sequence stars, we find that measurements of sizes and
brightnesses can be made using disk model fitting to the u,v-data down to
stellar diameters $\sim$ 0.4 mas in a few hours. This size would include M0 V
stars to a distance of 15 pc, A0 V stars to 60 pc, and Red Giants to 2.4 kpc.
Based on the Hipparcos catalog, we estimate that there are at least 10,000
stars that will be resolved by the ngVLA. While the vast majority of these
(95\%) are giants or supergiants, there are still over 500 main sequence stars
that can be resolved, with $\sim$ 50 to 150 in each spectral type (besides O
stars). Note that these are lower limits, since radio photospheres can be
larger than optical, and the Hipparcos catalog might not be complete. Our
initial look into the Gaia catalog suggests these numbers might be pessimistic
by a factor few.


  Laser scanning can provide timely assessments of mine sites despite adverse
challenges in the operational environment. Although there are several published
articles on laser scanning, there is a need to review them in the context of
underground mining applications. To this end, a holistic review of laser
scanning is presented including progress in 3D scanning systems, data
capture/processing techniques and primary applications in underground mines.
Laser scanning technology has advanced significantly in terms of mobility and
mapping, but there are constraints in coherent and consistent data collection
at certain mines due to feature deficiency, dynamics, and environmental
influences such as dust and water. Studies suggest that laser scanning has
matured over the years for change detection, clearance measurements and
structure mapping applications. However, there is scope for improvements in
lithology identification, surface parameter measurements, logistic tracking and
autonomous navigation. Laser scanning has the potential to provide real-time
solutions but the lack of infrastructure in underground mines for data
transfer, geodetic networking and processing capacity remain limiting factors.
Nevertheless, laser scanners are becoming an integral part of mine automation
thanks to their affordability, accuracy and mobility, which should support
their widespread usage in years to come.


  The Spectral and Photometric Imaging Receiver (SPIRE) on the European Space
Agency's Herschel Space Observatory utilizes a pioneering design for its
imaging spectrometer in the form of a Fourier Transform Spectrometer (FTS). The
standard FTS data reduction and calibration schemes are aimed at objects with
either a spatial extent much larger than the beam size or a source that can be
approximated as a point source within the beam. However, when sources are of
intermediate spatial extent, neither of these calibrations schemes is
appropriate and both the spatial response of the instrument and the source's
light profile must be taken into account and the coupling between them
explicitly derived. To that end, we derive the necessary corrections using an
observed spectrum of a fully extended source with the beam profile and the
source's light profile taken into account. We apply the derived correction to
several observations of planets and compare the corrected spectra with their
spectral models to study the beam coupling efficiency of the instrument in the
case of partially extended sources. We find that we can apply these correction
factors for sources with angular sizes up to \theta_{D} ~ 17". We demonstrate
how the angular size of an extended source can be estimated using the
difference between the sub-spectra observed at the overlap bandwidth of the two
frequency channels in the spectrometer, at 959<\nu<989 GHz. Using this
technique on an observation of Saturn, we estimate a size of 17.2", which is 3%
larger than its true size on the day of observation. Finally, we show the
results of the correction applied on observations of a nearby galaxy, M82, and
the compact core of a Galactic molecular cloud, Sgr B2.


  We present methods for detecting entanglement around symmetric Dicke states.
In particular, we consider N-qubit symmetric Dicke states with N/2 excitations.
In the first part of the paper we show that for large N these states have the
smallest overlap possible with states without genuine multi-partite
entanglement. Thus these states are particulary well suited for the
experimental examination of multi-partite entanglement. We present
fidelity-based entanglement witness operators for detecting multipartite
entanglement around these states. In the second part of the paper we consider
entanglement criteria, somewhat similar to the spin squeezing criterion, based
on the moments or variances of the collective spin operators. Surprisingly,
these criteria are based on an upper bound for variances for separable states.
We present both criteria detecting entanglement in general and criteria
detecting only genuine multi-partite entanglement. The collective operator
measured for our criteria is an important physical quantity: Its expectation
value essentially gives the intensity of the radiation when a coherent atomic
cloud emits light.


  We study a massive vector tensor theory that acquires mass via a standard
Proca term but also via a higher order term containing an explicit coupling to
curvature. We find static solutions that are asymptotically flat, adS or
Lifshitz black holes. Since the higher order term regularizes the effect of the
Proca mass term, generically solutions are asymptotically regular for arbitrary
couplings. This is true in particular for asymptotically flat black holes. For
a particular coupling we find particle like solitons that have a regular and
non trivial geometry everywhere. In all adS solutions the Proca mass term plays
the role of an effective cosmological constant distinctly different from the
bare cosmological constant.


  We calculate the production and decay rates of the Higgs boson at the LHC in
the context of general 5 dimensional (5D) warped scenarios with a spacetime
background modified from the usual $AdS_5$, with SM fields propagating in the
bulk. We extend previous work by considering the full flavor structure of the
SM, and thus including all possible flavor effects coming from mixings with
heavy fermions. We proceed in three different ways, first by only including two
complete Kaluza-Klein (KK) levels ($15\times15$ fermion mass matrices), then
including three complete KK levels ($21\times21$ fermion mass matrices) and
finally we compare with the effect of including the infinite (full) KK towers.
We present numerical results for the Higgs production cross section via gluon
fusion and Higgs decay branching fractions in both the modified metric scenario
and in the usual Randall-Sundrum metric scenario.


  We apply 3D hydrodynamical simulations to study the rotational aspect of gas
flow patterns around eccentric companions embedded in an accretion disk around
its primary host. We sample a wide range of companion mass ratio q and disk
aspect ratio h, and confirm a generic transition from prograde (steady tidal
interaction dominated) to retrograde (background Keplerian shear dominated)
circum-companion flow when orbital eccentricity exceeds a critical value et. We
find et \sim h for sub-thermal companions while et \sim (q/h)^1/3 for
super-thermal companions, and propose an empirical formula to unify the two
scenarios. Our results also suggest that et is insensitive to modest levels of
turbulence, modeled in the form of a kinematic viscosity term. In the context
of stellar-mass Black Holes (sBHs) embedded in AGN accretion disks, the
bifurcation of their circum-stellar disk (CSD) rotation suggest the formation
of a population of nearly anti-aligned sBHs, whose relevance to low spin
gravitational waves (GW) events can be probed in more details with future
population models of sBH evolution in AGN disks, making use of our quantitative
scaling for et; In the context of circum-planetary disks (CPDs), our results
suggest the possibility of forming retrograde satellites in-situ in retrograde
CPDs around eccentric planets.


  Personalized medicine is expected to maximize the intended drug effects and
minimize side effects by treating patients based on their genetic profiles.
Thus, it is important to generate drugs based on the genetic profiles of
diseases, especially in anticancer drug discovery. However, this is challenging
because the vast chemical space and variations in cancer properties require a
huge time resource to search for proper molecules. Therefore, an efficient and
fast search method considering genetic profiles is required for de novo
molecular design of anticancer drugs. Here, we propose a faster molecular
generative model with genetic algorithm and tree search for cancer samples
(FasterGTS). FasterGTS is constructed with a genetic algorithm and a Monte
Carlo tree search with three deep neural networks: supervised learning,
self-trained, and value networks, and it generates anticancer molecules based
on the genetic profiles of a cancer sample. When compared to other methods,
FasterGTS generated cancer sample-specific molecules with general chemical
properties required for cancer drugs within the limited numbers of samplings.
We expect that FasterGTS contributes to the anticancer drug generation.


  N44 is the second active site of high mass star formation next to R136 in the
Large Magellanic Cloud (LMC). We carried out a detailed analysis of HI at 60
arcsec resolution by using the ATCA & Parkes data. We presented decomposition
of the HI emission into two velocity components (the L- and D-components) with
the velocity separation of 60 km s$^{-1}$. In addition, we newly defined the
I-component whose velocity is intermediate between the L- and D-components. The
D-component was used to derive the rotation curve of the LMC disk, which is
consistent with the stellar rotation curve (Alves et al. 2000). Toward the
active cluster forming region of LHA 120-N 44, the three velocity components of
HI gas show signatures of dynamical interaction including bridges and
complementary spatial distributions. We hypothesize that the L- and
D-components have been colliding with each other since 5 Myrs ago and the
interaction triggered formation of the O and early B stars ionizing N44. In the
hypothesis the I-component is interpreted as decelerated gas in terms of
momentum exchange in the collisional interaction of the L- and D-components. In
the N44 region the Planck sub-mm dust optical depth is correlated with the HI
intensity, which is well approximated by a linear regression. We found that the
N44 region shows a significantly steeper regression line than in the Bar region
indicating less dust abundance in the N44 region, which is ascribed to the
tidal interaction between the LMC with the SMC 0.2 Gyrs ago.


  We present a comprehensive analysis of form factors for two light
pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The
theoretical framework is based on a combination of unitarized chiral
perturbation theory and dispersion relations. The low-energy constants in
chiral perturbation theory are fixed by a global fit to the available data of
the two-meson scattering phase shifts. Each form factor derived from unitarized
chiral perturbation theory is improved by iteratively applying a dispersion
relation. This study updates the existing results in the literature and
explores those that have not been systematically studied previously, in
particular the two-meson tensor form factors within unitarized chiral
perturbation theory. We also discuss the applications of these form factors as
mandatory inputs for low-energy phenomena, such as the semi-leptonic decays
$B_s\to \pi^+\pi^-\ell^+\ell^-$ and the $\tau$ lepton decay
$\tau\rightarrow\pi^{-}\pi^{0}\nu_{\tau}$, in searches for physics beyond the
Standard Model.


  For a nonlinear equation with several variable delays $$
\dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where
the functions $f_k$ increase in some variables and decrease in the others, we
obtain conditions when a positive solution exists on $[0, \infty)$, as well as
explore boundedness and persistence of solutions. Finally, we present
sufficient conditions when a solution is unbounded. Examples include the
Mackey-Glass equation with non-monotone feedback and two variable delays; its
solutions can be neither persistent nor bounded, unlike the well studied case
when these two delays coincide.


  With HST, colour-magnitude diagrams (CMDs) can be obtained for young star
clusters well beyond the Local Group. Such data can help constrain cluster ages
and metallicities, and also provide a reference against which intermediate- and
high mass stellar models can be compared. Here, CMDs are presented for two
massive (>10^5 Msun) clusters and compared with Padua and Geneva isochrones.
The problem of the ratio of blue to red supergiants is also addressed.


  We study the quantum fluctuations of scalar fields with a variable effective
mass during an inflationary phase. We consider the situation where the
effective mass depends on a background scalar field, which evolves during
inflation from being frozen into a damped oscillatory phase when the Hubble
parameter decreases below its mass. We find power spectra with suppressed
amplitude on large scales, similar to the standard massless spectrum on small
scales, and affected by modulations on intermediate scales. We stress the
analogies and differences with the parametric resonance in the preheating
scenario. We also discuss some potentially observable consequences when the
scalar field behaves like a curvaton.


  The problem of constructing a perfect cuboid is related to a certain class of
univariate polynomials with three integer parameters $a$, $b$, and $u$. Their
irreducibility over the ring of integers under certain restrictions for $a$,
$b$, and $u$ would mean the non-existence of perfect cuboids. This
irreducibility is conjectured and then verified numerically for approximately
10000 instances of $a$, $b$, and $u$.


  The existence of a solution, convergence and stability of the penalty method
for variational inequalities with nonsmooth unbounded uniformly and properly
monotone operators in Banach spase $B$ are investigated. All the objects of the
inequality - the operator A, "the right-hand part" $f$ and the set of
constrains $\Omega $ - are to be perturbed. The stability theorems are
formulated in terms of geometric characteristics of the spaces $B$ and $B^*$.
The results of this paper are continuity and generalization of the Lions' ones,
published earlier in \cite{l}. They are new even in Hilbert spaces.


  WASP-12b was the first planet reported to have a carbon-to-oxygen ratio (C/O)
greater than one in its dayside atmosphere. However, recent work to further
characterize its atmosphere and confirm its composition has led to incompatible
measurements and divergent conclusions. Additionally, the recent discovery of
stellar binary companions ~1" from WASP-12 further complicates the analyses and
subsequent interpretations. We present a uniform analysis of all available
Hubble and Spitzer Space Telescope secondary-eclipse data, including
previously-unpublished Spitzer measurements at 3.6 and 4.5 microns. The primary
controversy in the literature has centered on the value and interpretation of
the eclipse depth at 4.5 microns. Our new measurements and analyses confirm the
shallow eclipse depth in this channel, as first reported by Campo and
collaborators and used by Madhusudhan and collaborators to infer a carbon-rich
composition. To explain WASP-12b's observed dayside emission spectrum, we
implemented several recent retrieval approaches. We find that when we exclude
absorption due to C2H2 and HCN, which are not universally considered in the
literature, our models require implausibly large atmospheric CO2 abundances,
regardless of the C/O. By including C2H2 and HCN in our models, we find that a
physically-plausible carbon-rich solution achieves the best fit to the
available photometric and spectroscopic data. In comparison, the best-fit
oxygen-rich models have abundances that are inconsistent with the chemical
equilibrium expectations for hydrogen-dominated atmospheres and are 670 times
less probable. Our best-fit solution is also 7.3*10^{6} times more probable
than an isothermal blackbody model.


  Carbon radio recombination lines (RRLs) at low frequencies (<=500 MHz) trace
the cold, diffuse phase of the interstellar medium, which is otherwise
difficult to observe. We present the detection of carbon RRLs in absorption in
M82 with LOFAR in the frequency range of 48-64 MHz. This is the first
extragalactic detection of RRLs from a species other than hydrogen, and below 1
GHz. Since the carbon RRLs are not detected individually, we cross-correlated
the observed spectrum with a template spectrum of carbon RRLs to determine a
radial velocity of 219 +- 9 km/s . Using this radial velocity, we stack 22
carbon-{\alpha} transitions from quantum levels n = 468-508 to achieve an 8.5
sigma detection. The absorption line profile exhibits a narrow feature with
peak optical depth of 0.003 and FWHM of 31 km/s. Closer inspection suggests
that the narrow feature is superimposed on a broad, shallow component. The
total line profile appears to be correlated with the 21 cm H I line profile
reconstructed from H I absorption in the direction of supernova remnants in the
nucleus. The narrow width and centroid velocity of the feature suggests that it
is associated with the nuclear starburst region. It is therefore likely that
the carbon RRLs are associated with cold atomic gas in the direction of the
nucleus of M82.


  PSR B1259-63 is in a highly eccentric 3.4 yr orbit around the Be-star SS2883.
The system is located in the direction of the Sagittarius-Carina spiral arm at
a distance of $\sim$1.5 kpc. We have made scintillation observations of the
pulsar far from periastron at 4.8 GHz and 8.4 GHz, determining the diffractive
bandwidth, $\Delta \nu_{\rm d}$, and timescale, $\Delta t_{\rm d}$, at both
frequencies. We find no dependency on orbital phase until within 30 days of
periastron. The data indicate that the scintillation is caused, not by the
circumstellar environment, but by an HII region within the Sagittarius-Carina
spiral arm located at least three-quarters of the way to the pulsar. Close to
periastron, when the line-of-sight to the pulsar intersects the disk of the Be
star, the electron densities within the disk are sufficient to overcome the
`lever-arm effect' and produce a reduction in the scintillation bandwidth by
six orders of magnitude.


  The electronic structure and thermopower ($\alpha$) behavior of LaFeO$_{3}$
compound were investigated by combining the ab-initio electronic structures and
Boltzmann transport calculations. LSDA plus Hubbard U (U = 5 eV) calculation on
G-type anti-ferromagnetic (AFM) configuration gives an energy gap of $\sim$2
eV, which is very close to the experimentally reported energy gap. The
calculated values of effective mass of holes (m$^{*}$$_{h}$) in valance band
(VB) are found $\sim$4 times that of the effective mass of electrons
(m$^{*}$$_{e}$) in conduction band (CB). The large effective masses of holes
are responsible for the large and positive thermopower exhibited by this
compound. The calculated values of $\alpha$ using BoltzTraP code are found to
be large and positive in the 300-1200 K temperature range, which is in
agreement with the experimentally reported data.


  We extend several known results on solvability in the Sobolev spaces
$W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in divergence form in $\bR^{d}_{+}$ to
equations having coefficients which are discontinuous in the space variable.


  Using Polyakov's functional integral approach with the Liouville action
functional defined in \cite{ZT2} and \cite{LTT}, we formulate quantum Liouville
theory on a compact Riemann surface X of genus g > 1. For the partition
function <X> and for the correlation functions with the stress-energy tensor
components $<\prod_{i=1}^{n}T(z_{i})\prod_{k=1}^{l}\bar{T}(\w_{k})X>$, we
describe Feynman rules in the background field formalism by expanding
corresponding functional integrals around a classical solution - the hyperbolic
metric on X. Extending analysis in \cite{LT1,LT2,LT-Varenna,LT3}, we define the
regularization scheme for any choice of global coordinate on X, and for
Schottky and quasi-Fuchsian global coordinates we rigorously prove that one-
and two-point correlation functions satisfy conformal Ward identities in all
orders of the perturbation theory. Obtained results are interpreted in terms of
complex geometry of the projective line bundle $\cE_{c}=\lambda_{H}^{c/2}$ over
the moduli space $\mathfrak{M}_{g}$, where c is the central charge and
$\lambda_{H}$ is the Hodge line bundle, and provide Friedan-Shenker \cite{FS}
complex geometry approach to CFT with the first non-trivial example besides
rational models.


  Monocular depth estimation and semantic segmentation are two fundamental
goals of scene understanding. Due to the advantages of task interaction, many
works study the joint task learning algorithm. However, most existing methods
fail to fully leverage the semantic labels, ignoring the provided context
structures and only using them to supervise the prediction of segmentation
split, which limit the performance of both tasks. In this paper, we propose a
network injected with contextual information (CI-Net) to solve the problem.
Specifically, we introduce self-attention block in the encoder to generate
attention map. With supervision from the ideal attention map created by
semantic label, the network is embedded with contextual information so that it
could understand scene better and utilize correlated features to make accurate
prediction. Besides, a feature sharing module is constructed to make the
task-specific features deeply fused and a consistency loss is devised to make
the features mutually guided. We evaluate the proposed CI-Net on the
NYU-Depth-v2 and SUN-RGBD datasets. The experimental results validate that our
proposed CI-Net could effectively improve the accuracy of semantic segmentation
and depth estimation.


  As a first step to analyze the electromagnetic meson production reactions in
the nucleon resonance region, the parameters of the hadronic interactions of a
dynamical coupled-channel model, developed in {\it Physics Reports 439, 193
(2007)}, are determined by fitting the $\pi N$ scattering data. The channels
included in the calculations are $\pi N$, $\eta N$ and $\pi\pi N$ which has
$\pi\Delta$, $\rho N$, and $\sigma N$ resonant components. The non-resonant
meson-baryon interactions of the model are derived from a set of Lagrangians by
using a unitary transformation method. One or two bare excited nucleon states
in each of $S$, $P$, $D$, and $F$ partial waves are included to generate the
resonant amplitudes in the fits. The parameters of the model are first
determined by fitting as much as possible the empirical $\pi N$ elastic
scattering amplitudes of SAID up to 2 GeV. We then refine and confirm the
resulting parameters by directly comparing the predicted differential cross
section and target polarization asymmetry with the original data of the elastic
$\pi^{\pm} p \to \pi^{\pm} p$ and charge-exchange $\pi^- p \to \pi^0 n$
processes. The predicted total cross sections of $\pi N$ reactions and $\pi
N\to \eta N$ reactions are also in good agreement with the data. Applications
of the constructed model in analyzing the electromagnetic meson production data
as well as the future developments are discussed.


  We present a variational method for deriving relativistic two-fermion wave
equations in a Hamiltonian formulation of QED. A reformulation of QED is
performed, in which covariant Green functions are used to solve for the
electromagnetic field in terms of the fermion fields. The resulting modified
Hamiltonian contains the photon propagator directly. The reformulation permits
one to use a simple Fock-space variational trial state to derive relativistic
fermion-antifermion wave equations from the corresponding quantum field theory.
We verify that the energy eigenvalues obtained from the wave equation agree
with known results for positronium.


  With deep neural network based solution more readily being incorporated in
real-world applications, it has been pressing requirement that predictions by
such models, especially in safety-critical environments, be highly accurate and
well-calibrated. Although some techniques addressing DNN calibration have been
proposed, they are only limited to visual classification applications and
in-domain predictions. Unfortunately, very little to no attention is paid
towards addressing calibration of DNN-based visual object detectors, that
occupy similar space and importance in many decision making systems as their
visual classification counterparts. In this work, we study the calibration of
DNN-based object detection models, particularly under domain shift. To this
end, we first propose a new, plug-and-play, train-time calibration loss for
object detection (coined as TCD). It can be used with various
application-specific loss functions as an auxiliary loss function to improve
detection calibration. Second, we devise a new implicit technique for improving
calibration in self-training based domain adaptive detectors, featuring a new
uncertainty quantification mechanism for object detection. We demonstrate TCD
is capable of enhancing calibration with notable margins (1) across different
DNN-based object detection paradigms both in in-domain and out-of-domain
predictions, and (2) in different domain-adaptive detectors across challenging
adaptation scenarios. Finally, we empirically show that our implicit
calibration technique can be used in tandem with TCD during adaptation to
further boost calibration in diverse domain shift scenarios.


  We explore the minimax optimal error associated with a demographic
parity-constrained regression problem within the context of a linear model. Our
proposed model encompasses a broader range of discriminatory bias sources
compared to the model presented by Chzhen and Schreuder (2022). Our analysis
reveals that the minimax optimal error for the demographic parity-constrained
regression problem under our model is characterized by $\Theta(\frac{dM}{n})$,
where $n$ denotes the sample size, $d$ represents the dimensionality, and $M$
signifies the number of demographic groups arising from sensitive attributes.
Moreover, we demonstrate that the minimax error increases in conjunction with a
larger bias present in the model.


  Assuming the Dirac-type neutrino masses m_D are related to quark or charged
lepton masses, neutrino oscillation data indicate that right handed neutrino
masses are in general strongly hierarchical. In particular, if m_D is similar
to the up-type quark masses, the mass of the lightest right handed neutrino
M_1<~10^6 GeV. We show that non-thermal leptogenesis by inflaton decay can
yield sufficient baryon asymmetry despite this constraint, and discuss how the
asymmetry is correlated with the low energy neutrino masses and CP-violating
phases.


  We show remnants of chiral symmetry breaking in the center-projected theory.
We construct and study an unambiguous definition of center vortices.


  We study the effects of gluon radiation on top production and decay processes
at an $e^+e^-$ collider.The matrix elements are computed without any
approximations, using spinor techniques. We use a Monte Carlo event generator
which takes into account the infrared singularity due to soft gluons and
differences in kinematics associated with radiation in the production versus
decay process. The calculation is illustrated for several strategies of top
mass reconstruction.


  We investigate dark-bright vector solitary wave solutions to the coupled
non-linear Schr\"odinger equations which describe an inhomogeneous two-species
Bose-Einstein condensate. While these structures are well known in non-linear
fiber optics, we show that spatial inhomogeneity strongly affects their motion,
stability, and interaction, and that current technology suffices for their
creation and control in ultracold trapped gases. The effects of controllably
different interparticle scattering lengths, and stability against
three-dimensional deformations, are also examined.


  In this paper, we concentrate on the MF property of reduced free products of
unital C*-algebras with amalgamation over finite dimensional C*-algebras. More
specifically, we give a necessary and sufficient condition for a reduced free
product of two UHF algebras amalgamated over a finite-dimensional C*-algebra
with respect to trace preserving conditional expectations to be MF.


  We present a practical guide for the analysis of regression discontinuity
(RD) designs in biomedical contexts. We begin by introducing key concepts,
assumptions, and estimands within both the continuity-based framework and the
local randomization framework. We then discuss modern estimation and inference
methods within both frameworks, including approaches for bandwidth or local
neighborhood selection, optimal treatment effect point estimation, and robust
bias-corrected inference methods for uncertainty quantification. We also
overview empirical falsification tests that can be used to support key
assumptions. Our discussion focuses on two particular features that are
relevant in biomedical research: (i) fuzzy RD designs, which often arise when
therapeutic treatments are based on clinical guidelines but patients with
scores near the cutoff are treated contrary to the assignment rule; and (ii) RD
designs with discrete scores, which are ubiquitous in biomedical applications.
We illustrate our discussion with three empirical applications: the effect of
CD4 guidelines for anti-retroviral therapy on retention of HIV patients in
South Africa, the effect of genetic guidelines for chemotherapy on breast
cancer recurrence in the United States, and the effects of age-based patient
cost-sharing on healthcare utilization in Taiwan. We provide replication
materials employing publicly available statistical software in Python, R and
Stata, offering researchers all necessary tools to conduct an RD analysis.


  We introduce a class of metrics on gauge theoretic moduli spaces. These
metrics are made out of the universal matrix that appears in the universal
connection construction of M. S. Narasimhan and S. Ramanan. As an example we
construct metrics on the c_{2}=1 SU(2) moduli space of instantons on R^4 for
various universal matrices.


  The use of nuclear magnetic resonance (NMR) to carry out quantum information
processing (QIP) often requires the preparation, transformation, and detection
of pseudopure states. In our previous work, it was shown that the use of pairs
of pseudopure states (POPS) as a basis for QIP is very convenient because of
the simplicity in experimental execution. It is now further demonstrated that
the product of the NMR spectra corresponding to two sets of POPS that share a
common pseudopure state has the same peak frequencies as those of the common
(single) pseudopure state. Examples of applying two different quantum logic
gates to a 5-qubit system are given.


  We present a new extended resolution clause learning (ERCL) algorithm,
implemented as part of a conflict-driven clause-learning (CDCL) SAT solver,
wherein new variables are dynamically introduced as definitions for {\it Dual
Implication Points} (DIPs) in the implication graph constructed by the solver
at runtime. DIPs are generalizations of unique implication points and can be
informally viewed as a pair of dominator nodes, from the decision variable at
the highest decision level to the conflict node, in an implication graph. We
perform extensive experimental evaluation to establish the efficacy of our ERCL
method, implemented as part of the MapleLCM SAT solver and dubbed xMapleLCM,
against several leading solvers including the baseline MapleLCM, as well as
CDCL solvers such as Kissat 3.1.1, CryptoMiniSat 5.11, and SBVA+CaDiCaL, the
winner of SAT Competition 2023. We show that xMapleLCM outperforms these
solvers on Tseitin and XORified formulas. We further compare xMapleLCM with
GlucoseER, a system that implements extended resolution in a different way, and
provide a detailed comparative analysis of their performance.


  State-of-the-art machine learning models often learn spurious correlations
embedded in the training data. This poses risks when deploying these models for
high-stake decision-making, such as in medical applications like skin cancer
detection. To tackle this problem, we propose Reveal to Revise (R2R), a
framework entailing the entire eXplainable Artificial Intelligence (XAI) life
cycle, enabling practitioners to iteratively identify, mitigate, and
(re-)evaluate spurious model behavior with a minimal amount of human
interaction. In the first step (1), R2R reveals model weaknesses by finding
outliers in attributions or through inspection of latent concepts learned by
the model. Secondly (2), the responsible artifacts are detected and spatially
localized in the input data, which is then leveraged to (3) revise the model
behavior. Concretely, we apply the methods of RRR, CDEP and ClArC for model
correction, and (4) (re-)evaluate the model's performance and remaining
sensitivity towards the artifact. Using two medical benchmark datasets for
Melanoma detection and bone age estimation, we apply our R2R framework to VGG,
ResNet and EfficientNet architectures and thereby reveal and correct real
dataset-intrinsic artifacts, as well as synthetic variants in a controlled
setting. Completing the XAI life cycle, we demonstrate multiple R2R iterations
to mitigate different biases. Code is available on
https://github.com/maxdreyer/Reveal2Revise.


  Nonlinear mode coupling in a coaxial waveguide filled with Faraday material
has been considered. The picture of mode interaction is shown to resemble
Coulomb interaction of charges: higher modes with nonzero angular momentum
interact like effective charges via exchange of zero angular momentum quanta of
the fundamental mode. Thus, at large distances this interaction becomes the
dominant mechanism of mode coupling. The developed model may be used in
designing coaxial photonic crystal fibers with strong tailored mode
interaction.


  The replacement closeout convention has drawn more and more attention since
the 2008 financial crisis. Compared with the conventional risk-free closeout,
the replacement closeout convention incorporates the creditworthiness of the
counterparty and thus providing a more accurate estimate of the Mark-to-market
value of a financial claim. In contrast to the risk-free closeout, the
replacement closeout renders a nonlinear valuation system, which constitutes
the major difficulty in the valuation of the counterparty credit risk.
  In this paper, we show how to address the nonlinearity attributed to the
replacement closeout in the theoretical and computational analysis. In the
theoretical part, we prove the unique solvability of the nonlinear valuation
system and study the impact of the replacement closeout on the credit valuation
adjustment. In the computational part, we propose a neural network-based
algorithm for solving the (high dimensional) nonlinear valuation system and
effectively alleviating the curse of dimensionality. We numerically compare the
computational cost for the valuations with risk-free and replacement closeouts.
The numerical tests confirm both the accuracy and the computational efficiency
of our proposed algorithm for the valuation of the replacement closeout.


  One of the fundamental results in computability is the existence of
well-defined functions that cannot be computed. In this paper we study the
effects of data representation on computability; we show that, while for each
possible way of representing data there exist incomputable functions, the
computability of a specific abstract function is never an absolute property,
but depends on the representation used for the function domain. We examine the
scope of this dependency and provide mathematical criteria to favour some
representations over others. As we shall show, there are strong reasons to
suggest that computational enumerability should be an additional axiom for
computation models. We analyze the link between the techniques and effects of
representation changes and those of oracle machines, showing an important
connection between their hierarchies. Finally, these notions enable us to gain
a new insight on the Church-Turing thesis: its interpretation as the underlying
algebraic structure to which computation is invariant.


  We calculate the one-loop quantum contributions to soft supersymmetry
breaking terms in the scalar potential in supergravity theories regulated \`a
la Pauli-Villars. We find ``universal'' contributions, independent of the
regulator masses and tree level soft supersymmetry breaking, that contribute
gaugino masses and A-terms equal to the ``anomaly mediated'' contributions
found in analyses using spurion techniques, as well as a scalar mass term not
identified in those analyses. The universal terms are in general modified --
and in some cases canceled -- by model-dependent terms. Under certain
restrictions on the couplings we recover the one-loop results of previous
``anomaly mediated'' supersymmetry breaking scenarios. We emphasize the model
dependence of loop-induced soft terms in the potential, which are much more
sensitive to the details of Planck scale physics then are the one-loop
contributions to gaugino masses. We discuss the relation of our results to
previous analyses.


  A multi-stream instability is observed experimentally in a longitudinally
expanding electron beam in a storage ring. The instability is observed when the
beam expands such that its length is several times the circumference of the
ring, and portions of the beam overlap. While portions of the beam overlap in
physical space, due to the nature of the expansion process, the portions form
multiple streams and remain separate in velocity space. The streams become
unstable as their number increases and their separation in velocity decreases.
An analytical theory predicts the onset of the instability, consistent with
simulations and measurements, over a wide range of peak line-charge densities
and bunch lengths. This work extends previous calculations to include the
dynamic non-linear elongation of the bunch, with a given initial length, and
defines an onset criterion for the filament velocity separation.


  We study the following two fixed-cardinality optimization problems (a
maximization and a minimization variant). For a fixed $\alpha$ between zero and
one we are given a graph and two numbers $k \in \mathbb{N}$ and $t \in
\mathbb{Q}$. The task is to find a vertex subset $S$ of exactly $k$ vertices
that has value at least (resp. at most for minimization) $t$. Here, the value
of a vertex set computes as $\alpha$ times the number of edges with exactly one
endpoint in $S$ plus $1-\alpha$ times the number of edges with both endpoints
in $S$. These two problems generalize many prominent graph problems, such as
Densest $k$-Subgraph, Sparsest $k$-Subgraph, Partial Vertex Cover, and Max
($k$,$n-k$)-Cut.
  In this work, we complete the picture of their parameterized complexity on
several types of sparse graphs that are described by structural parameters. In
particular, we provide kernelization algorithms and kernel lower bounds for
these problems. A somewhat surprising consequence of our kernelizations is that
Partial Vertex Cover and Max $(k,n-k)$-Cut not only behave in the same way but
that the kernels for both problems can be obtained by the same algorithms.