  This paper proposes a new channel modelling method for powerline
communications networks based on the multipath profile in the time domain. The
new channel model is developed to be applied in a range of Powerline
Communications (PLC) research topics such as impulse noise modelling,
deployment and coverage studies, and communications theory analysis. To develop
the methodology, channels are categorised according to their propagation
distance and power delay profile. The statistical multipath parameters such as
path arrival time, magnitude and interval for each category are analyzed to
build the model. Each generated channel based on the proposed statistical model
represents a different realisation of a PLC network. Simulation results in
similar the time and frequency domains show that the proposed statistical
modelling method, which integrates the impact of network topology presents the
PLC channel features as the underlying transmission line theory model.
Furthermore, two potential application scenarios are described to show the
channel model is applicable to capacity analysis and correlated impulse noise
modelling for PLC networks.


  In this paper we present our work on a case study on Statistical Machine
Translation (SMT) and Rule based machine translation (RBMT) for translation
from English to Malayalam and Malayalam to English. One of the motivations of
our study is to make a three way performance comparison, such as, a) SMT and
RBMT b) English to Malayalam SMT and Malayalam to English SMT c) English to
Malayalam RBMT and Malayalam to English RBMT. We describe the development of
English to Malayalam and Malayalam to English baseline phrase based SMT system
and the evaluation of its performance compared against the RBMT system. Based
on our study the observations are: a) SMT systems outperform RBMT systems, b)
In the case of SMT, English - Malayalam systems perform better than that of
Malayalam - English systems, c) In the case RBMT, Malayalam to English systems
are performing better than English to Malayalam systems. Based on our
evaluations and detailed error analysis, we describe the requirements of
incorporating morphological processing into the SMT to improve the accuracy of
translation.


  The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell
electrodynamics in presence of electrical sources and arbitrary media is
investigated within the matrix formalism. The symmetry of the matrix Maxwell
equation under transformations of the complex rotation group SO(3.C) is
demonstrated explicitly. In vacuum case, the matrix form includes four real $4
\times 4$ matrices $\alpha^{b}$. In presence of media matrix form requires two
sets of $4 \times 4$ matrices, $\alpha^{b}$ and $\beta^{b}$ -- simple and
symmetrical realization of which is given. Relation of $\alpha^{b}$ and
$\beta^{b}$ to the Dirac matrices in spinor basis is found. Minkowski
constitutive relations in case of any linear media are given in a short
algebraic form based on the use of complex 3-vector fields and complex
orthogonal rotations from SO(3.C) group. The matrix complex formulation in the
Esposito's form,based on the use of two electromagnetic 4-vectors,
$e^{\alpha}(x) = u_{\beta} F^{\alpha \beta}(x), b^{\alpha} (x) = u_{\beta}
\tilde{F}^{\alpha \beta}(x) $ is studied and discussed. It is argued that
Esposito form is achieved trough the use of a trivial identity
$I=U^{-1}(u)U(u)$ in the Maxwell equation.


  The dissociative adsorption of methane on variously oxidized Pd, Pt and Pd-Pt
surfaces is investigated using density-functional theory, as a step towards
understanding the combustion of methane on these materials. For Pd-Pt alloys,
models of surface oxide structures are built on the basis of known oxides on Pd
and Pt. The methane adsorption energy presents large variations depending on
the oxide structure and composition. Adsorption is endothermic on the bare
Pd(111) metal surface as well as on stable thin layer oxide structures such as
the ($\sqrt{5}\times\sqrt{5}$) surface oxide on Pd(100) and the PtO$_2$-like
oxide on Pt(111). Instead, large adsorption energies are obtained for the (100)
surface of bulk PdO, for metastable mixed Pd$_{1-x}$Pt$_x$O$_{4/3}$ oxide
layers on Pt(100), and for Pd-Pt(111) surfaces covered with one oxygen
monolayer. In the latter case, we find a net thermodynamic preference for a
direct conversion of methane to methanol, which remains adsorbed on the
oxidized metal substrates via weak hydrogen-bond interactions.


  Tamil language has an agglutinative, diglossic, alpha-syllabary structure
which provides a significant combinatorial explosion of morphological forms all
of which are effectively used in Tamil prose, poetry from antiquity to the
modern age in an unbroken chain of continuity. However, for the language
understanding, spelling correction purposes some of these present challenges as
out-of-dictionary words. In this paper the authors propose algorithmic
techniques to handle specific problems of conjoined-words (out-of-dictionary)
(transliteration)[thendRalkattRu] = [thendRal]+[kattRu] when parts are alone
present in word-list in efficient way. Morphological structure of Tamil makes
it necessary to depend on synthesis-analysis approach and dictionary lists will
never be sufficient to truly capture the language. In this paper we have
attempted to make a summary of various known algorithms for specific classes of
Tamil spelling errors. We believe this collection of suggestions to improve
future spelling checkers. We also note do not cover many important techniques
like affix removal and other such techniques of key importance in rule-based
spell checkers.


  This paper considers safe robot mission planning in uncertain dynamical
environments. This problem arises in applications such as surveillance,
emergency rescue, and autonomous driving. It is a challenging problem due to
modeling and integrating dynamical uncertainties into a safe planning
framework, and finding a solution in a computationally tractable way. In this
work, we first develop a probabilistic model for dynamical uncertainties. Then,
we provide a framework to generate a path that maximizes safety for complex
missions by incorporating the uncertainty model. We also devise a Monte Carlo
method to obtain a safe path efficiently. Finally, we evaluate the performance
of our approach and compare it to potential alternatives in several case
studies.


  Fine-grained 3D shape classification is important for shape understanding and
analysis, which poses a challenging research problem. However, the studies on
the fine-grained 3D shape classification have rarely been explored, due to the
lack of fine-grained 3D shape benchmarks. To address this issue, we first
introduce a new 3D shape dataset (named FG3D dataset) with fine-grained class
labels, which consists of three categories including airplane, car and chair.
Each category consists of several subcategories at a fine-grained level.
According to our experiments under this fine-grained dataset, we find that
state-of-the-art methods are significantly limited by the small variance among
subcategories in the same category. To resolve this problem, we further propose
a novel fine-grained 3D shape classification method named FG3D-Net to capture
the fine-grained local details of 3D shapes from multiple rendered views.
Specifically, we first train a Region Proposal Network (RPN) to detect the
generally semantic parts inside multiple views under the benchmark of generally
semantic part detection. Then, we design a hierarchical part-view attention
aggregation module to learn a global shape representation by aggregating
generally semantic part features, which preserves the local details of 3D
shapes. The part-view attention module hierarchically leverages part-level and
view-level attention to increase the discriminability of our features. The
part-level attention highlights the important parts in each view while the
view-level attention highlights the discriminative views among all the views of
the same object. In addition, we integrate a Recurrent Neural Network (RNN) to
capture the spatial relationships among sequential views from different
viewpoints. Our results under the fine-grained 3D shape dataset show that our
method outperforms other state-of-the-art methods.


  When an initial failure of nodes occurs in interdependent networks, a cascade
of failure between the networks occurs. Earlier studies focused on random
initial failures. Here we study the robustness of interdependent networks under
targeted attack on high or low degree nodes. We introduce a general technique
and show that the {\it targeted-attack} problem in interdependent networks can
be mapped to the {\it random-attack} problem in a transformed pair of
interdependent networks. We find that when the highly connected nodes are
protected and have lower probability to fail, in contrast to single scale free
(SF) networks where the percolation threshold $p_c=0$, coupled SF networks are
significantly more vulnerable with $p_c$ significantly larger than zero. The
result implies that interdependent networks are difficult to defend by
strategies such as protecting the high degree nodes that have been found useful
to significantly improve robustness of single networks.


  In this paper, we develop a neural attentive interpretable recommendation
system, named NAIRS. A self-attention network, as a key component of the
system, is designed to assign attention weights to interacted items of a user.
This attention mechanism can distinguish the importance of the various
interacted items in contributing to a user profile. Based on the user profiles
obtained by the self-attention network, NAIRS offers personalized high-quality
recommendation. Moreover, it develops visual cues to interpret recommendations.
This demo application with the implementation of NAIRS enables users to
interact with a recommendation system, and it persistently collects training
data to improve the system. The demonstration and experimental results show the
effectiveness of NAIRS.


  Thin films of perovskite manganite La_{0.7}Ca_{0.3}MnO_{3} were grown
epitaxially on SrTiO_3(100), MgO(100) and LaAlO_3(100) substrates by the pulsed
laser deposition method. Microscopic structures of these thin film samples as
well as a bulk sample were fully determined by x-ray diffraction measurements.
The unit cells of the three films have different shapes, i.e., contracted
tetragonal, cubic, and elongated tetragonal for SrTiO_3, MgO, and LaAlO_3
cases, respectively, while the unit cell of the bulk is cubic. It is found that
the samples with cubic unit cell show smaller peak magnetoresistance than the
noncubic ones do. The present result demonstrates that the magnetoresistance of
La_{0.7}Ca_{0.3}MnO_{3} can be controlled by lattice distortion via externally
imposed strains.


  We have analyzed the effects of the addition of external noise to
non-dynamical systems displaying intrinsic noise, and established general
conditions under which stochastic resonance appears. The criterion we have
found may be applied to a wide class of non-dynamical systems, covering
situations of different nature. Some particular examples are discussed in
detail.


  Survival Analysis (SA) constitutes the default method for time-to-event
modeling due to its ability to estimate event probabilities of sparsely
occurring events over time. In this work, we show how to improve the training
and inference of SA models by decoupling their full expression into (1) an
aggregated baseline hazard, which captures the overall behavior of a given
population, and (2) independently distributed survival scores, which model
idiosyncratic probabilistic dynamics of its given members, in a fully
parametric setting. The proposed inference method is shown to dynamically
handle right-censored observation horizons, and to achieve competitive
performance when compared to other state-of-the-art methods in a variety of
real-world datasets, including computationally inefficient Deep Learning-based
SA methods and models that require MCMC for inference. Nevertheless, our method
achieves robust results from the outset, while not being subjected to
fine-tuning or hyperparameter optimization.


  We focus on the high-dimensional linear regression problem, where the
algorithmic goal is to efficiently infer an unknown feature vector
$\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$
of samples. Unlike most of the literature, we make no sparsity assumption on
$\beta^*$, but instead adopt a different regularization: In the noiseless
setting, we assume $\beta^*$ consists of entries, which are either rational
numbers with a common denominator $Q\in\mathbb{Z}^+$ (referred to as
$Q$-rationality); or irrational numbers supported on a rationally independent
set of bounded cardinality, known to learner; collectively called as the
mixed-support assumption. Using a novel combination of the PSLQ integer
relation detection, and LLL lattice basis reduction algorithms, we propose a
polynomial-time algorithm which provably recovers a $\beta^*\in\mathbb{R}^p$
enjoying the mixed-support assumption, from its linear measurements
$Y=X\beta^*\in\mathbb{R}^n$ for a large class of distributions for the random
entries of $X$, even with one measurement $(n=1)$. In the noisy setting, we
propose a polynomial-time, lattice-based algorithm, which recovers a
$\beta^*\in\mathbb{R}^p$ enjoying $Q$-rationality, from its noisy measurements
$Y=X\beta^*+W\in\mathbb{R}^n$, even with a single sample $(n=1)$. We further
establish for large $Q$, and normal noise, this algorithm tolerates
information-theoretically optimal level of noise. We then apply these ideas to
develop a polynomial-time, single-sample algorithm for the phase retrieval
problem. Our methods address the single-sample $(n=1)$ regime, where the
sparsity-based methods such as LASSO and Basis Pursuit are known to fail.
Furthermore, our results also reveal an algorithmic connection between the
high-dimensional linear regression problem, and the integer relation detection,
randomized subset-sum, and shortest vector problems.


  The low brightness dust emission at high Galactic latitude is of interest to
study the interplay between physical processes in shaping the structure of the
interstellar medium (ISM), as well as to statistically characterize dust
emission as a foreground to the Cosmic Microwave Background (CMB). Progress in
this avenue of research have been hampered by the difficulty of separating the
dust emission from the Cosmic Infrared Background (CIB). We demonstrate that
dust and CIB may be effectively separated based on their different structure on
the sky and use the separation to characterize the structure of diffuse dust
emission on angular scales where CIB is a significant component in terms of
power. We use scattering transform statistics, the Wavelet Phase Harmonics
(WPH), to perform a statistical component separation using Herschel SPIRE
observations. This component separation is done only from observational data
using non-Gaussian properties as a lever arm, and is done at a single 250
microns frequency. This method, that we validate on mock data, gives us access
to non-Gaussian statistics of the interstellar dust and an output dust map
essentially free from CIB contamination. Our statistical modelling
characterizes the non-Gaussian structure of the diffuse ISM down to the
smallest scales observed by Herschel. We recover the power-law shape of the
dust power spectrum up to a wavenumber of 2 arcmin$^{-1}$ where the dust signal
represents 2 percent of the total power. The output dust map reveals coherent
structures at the smallest scales which were hidden by the CIB anisotropies. It
opens new observational perspectives on the formation of structure in the
diffuse ISM which we discuss with reference to past work. We have succeeded to
perform a statistical separation from observational data only at a single
frequency by using non-Gaussian statistics.


  High dimensional case control studies are ubiquitous in the biological
sciences, particularly genomics. To maximise power while constraining cost and
to minimise type-1 error rates, researchers typically seek to replicate
findings in a second experiment on independent cohorts before proceeding with
further analyses.
  This paper presents a method in which control (or case) samples from the
discovery cohort are re-used in the replication study. The theoretical
implications of this method are discussed and simulations used to compare
performance against the standard method in a range of circumstances. In several
common study designs, a shared-control method allows a substantial improvement
in power while retaining type-1 error rate control.
  An important area of potential application arises when control samples are
difficult to recruit or ascertain; for example in inter-disease comparisons, or
studies on degenerative diseases. Using similar methods, a procedure is
proposed for `partial replication' using a new independent cohort consisting of
only controls. This methods can be used to provide some validation of findings
when a full replication procedure is not possible.
  The new method has differing sensitivity to confounding in study cohorts
compared to the standard procedure, which must be considered in its
application. Type-1 error rates in these scenarios are analytically and
empirically derived, and an online tool for comparing power and error rates is
provided.
  Although careful consideration must be made of all necessary assumptions,
this method can enable more efficient use of data in genome-wide association
studies (GWAS) and other applications.


  The use of Aloha-based Random Access protocols is interesting when channel
sensing is either not possible or not convenient and the traffic from terminals
is unpredictable and sporadic. In this paper an analytic model for packet
interference calculation in asynchronous Random Access protocols using
diversity is presented. The aim is to provide a tool that avoids time-consuming
simulations to evaluate packet loss and throughput in case decodability is
still possible when a certain interference threshold is not exceeded. Moreover
the same model represents the groundbase for further studies in which iterative
Interference Cancellation is applied to received frames.


  Thermodynamic uncertainty relations (TURs) relate precision to the
dissipation rate, yet the inequalities can be far from saturation. Indeed, in
catenane molecular motor simulations, we record precision far below the TUR
limit. We further show that this inefficiency can be anticipated by four
physical parameters: the thermodynamic driving force, fuel decomposition rate,
coupling between fuel decomposition and motor motion, and rate of undriven
motor motion. The physical insights might assist in designing molecular motors
in the future.


  White dwarfs with helium-dominated atmospheres comprise approximately 20% of
all white dwarfs. Among the open questions are the total masses and the origin
of the hydrogen traces observed in a large number and the nature of the deficit
of DBs in the range from 30000 - 45000K. We use the largest-ever sample (by a
factor of 10) provided by the Sloan Digital Sky Survey (SDSS) to study these
questions. The photometric and spectroscopic data of 1107 helium-rich objects
from the SDSS are analyzed using theoretical model atmospheres. Along with the
effective temperature and surface gravity, we also determine hydrogen and
calcium abundances or upper limits for all objects. The atmosphere models are
extended with envelope calculations to determine the extent of the helium
convection zones and thus the total amount of hydrogen and calcium present.
When accounting for problems in determining surface gravities at low Teff, we
find an average mass for helium-dominated white dwarfs of 0.606+-0.004 Msun,
which is very similar to the latest determinations for DAs. There are 32% of
the sample with detected hydrogen, but this increases to 75% if only the
objects with the highest signal-to-noise ratios are considered. In addition,
10-12% show traces of calcium, which must come from an external source. The
interstellar medium (ISM) is ruled out by the fact that all polluted objects
show a Ca/H ratio that is much larger than solar. We also present arguments
that demonstrate that the hydrogen is very likely not accreted from the ISM but
is the result of convective mixing of a residual thin hydrogen layer with the
developing helium convection zone. It is very important to carefully consider
the bias from observational selection effects when drawing these conclusions.


  We obtain the frequency and temperature dependence of the conductivity for
(disordered) solids, where the temperature dependence is defined in terms of
the related thermodynamic state function in exponential (or power law, etc.)
forms. The model is applied to n-type Si with various donor and acceptor
impurities and several concentrations at T about 0 Kelvin and sodium borate
glasses and mixed alkalis with various compositions (x) in all at T about 500
Kelvin. The results are found in good agreement with experiments.


  In order to obtain a comprehensive understanding of both thermodynamics and
kinetics of water dissociation on TiO2, the reactions between liquid water and
perfect and defective rutile TiO2 (110) surfaces were investigated using ab
initio molecular dynamics simulations. The results showed that the free-energy
barrier (~ 4.4 kcal/mol) is too high for a spontaneous dissociation of water on
the perfect rutile (110) surface at a low temperature. The most stable oxygen
vacancy (Vo1) on the rutile (110) surface cannot promote the dissociation of
water, while other unstable oxygen vacancies can significantly enhance the
water dissociation rate. This is opposite to the general understanding that Vo1
defects are active sites for water dissociation. Furthermore, we reveal that
water dissociation is an exothermic reaction, which demonstrates that the
dissociated state of the adsorbed water is thermodynamically favorable for both
perfect and defective rutile (110) surfaces. The dissociation adsorption of
water can also increase the hydrophilicity of TiO2.


  The oscillation of a Laplacian eigenfunction gives a great deal of
information about the manifold on which it is defined. This oscillation can be
encoded in the nodal deficiency, an important geometric quantity that is
notoriously hard to compute, or even estimate. Here we compare two recently
obtained formulas for the nodal deficiency, one in terms of an energy
functional on the space of equipartitions of the manifold, and the other in
terms of a two-sided Dirichlet-to-Neumann map defined on the nodal set. We
relate these two approaches by giving an explicit formula for the Hessian of
the equipartition energy in terms of the Dirichlet-to-Neumann map. This allows
us to compute Hessian eigenfunctions, and hence directions of steepest descent,
for the equipartition energy in terms of the corresponding Dirichlet-to-Neumann
eigenfunctions. Our results do not assume bipartiteness, and hence are relevant
to the study of spectral minimal partitions.


  We analyze the stress-energy tensor for the self-coupled Maxwell-Dirac system
in the bilinear current formalism, using two independent approaches. The first
method used is that attributed to Belinfante: starting from the spinor form of
the action, the well-known canonical stress-energy tensor is augmented, by
extending the Noether symmetry current to include contributions from the
Lorentz group, to a manifestly symmetric form. This form admits a transcription
to bilinear current form. The second method used is the variational derivation
based on the covariant coupling to general relativity. The starting point here
at the outset is the transcription of the action using, as independent field
variables, both the bilinear currents, together with a gauge invariant vector
field (a proxy for the electromagnetic vector potential). A central feature of
the two constructions is that they both involve the mapping of the Dirac
contribution to the stress-energy from the spinor fields to the equivalent set
of bilinear tensor currents, through the use of appropriate Fierz identities.
Although this mapping is done at quite different stages, nonetheless we find
that the two forms of the bilinear stress-energy tensor agree. Finally, as an
application, we consider the reduction of the obtained stress-energy tensor in
bilinear form, under the assumption of spherical symmetry.


  We demonstrate theoretically the parametric oscillator behavior of a
two-level quantum system with broken inversion symmetry exposed to a strong
electromagnetic field. A multitude of resonance frequencies and additional
harmonics in the scattered light spectrum as well as altered Rabi frequency are
predicted to be inherent to such systems. In particular, dipole radiation at
the Rabi frequency appears to be possible. Since the Rabi frequency is
controlled by the strength of coupling electromagnetic field, the effect can
serve for the frequency-tuned parametric amplification and generation of
electromagnetic waves. Manifestation of the effect is discussed for III-nitride
quantum dots with strong build-in electric field breaking the inversion
symmetry. Terahertz emission from arrays of such quantum dots is shown to be
experimentally observable.


  Chrysotile asbestos is formed by densely packed bundles of multiwall hollow
nanotubes. Each wall in the nanotubes is a cylindrically wrapped layer of $Mg_3
Si_2 O_5 (OH)_4$. We show by experiment and theory that the infrared spectrum
of chrysotile presents multiple plasmon resonances in the Si-O stretching
bands. These collective charge excitations are universal features of the
nanotubes that are obtained by cylindrically wrapping an anisotropic material.
The multiple plasmons can be observed if the width of the resonances is
sufficiently small as in chrysotile.


  We present results from a fully relativistic Monte Carlo simulation of
diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses
a single algorithmic sequence to smoothly span the range from nonrelativistic
speeds to fully relativistic shocks of arbitrary obliquity, providing a
powerful consistency check. While known results are obtained for
nonrelativistic and ultra-relativistic parallel shocks, new results are
presented for the less explored trans- relativistic regime and for oblique,
fully relativistic shocks. We find, for a wide trans-relativistic range
extending to shock Lorentz factors >30, that the particle spectrum produced by
DSA varies strongly from the canonical f(p) proportional to p^{-4.23} spectrum
known to result in ultra-relativistic shocks. Trans- relativistic shocks may
play an important role in gamma-ray bursts and other sources and most
relativistic shocks will be highly oblique.


  This paper summarizes the observations which provide the best evidence for
the presence of black holes in active galactic nuclei. This includes: X-ray
variability; kinematical studies using optical emission lines as well as the
distribution of megamaser spots; and the shape of the Fe K$\alpha$ X-ray
emission line. It also presents the current status of our understanding of
jet-dominated active galaxies (blazars), and briefly reviews the currently
popular AGN ``Unification Schemes.''


  It is argued that a dual symmetry is needed to naturally explain experimental
limits on color confinement. Since color is an exact symmetry the only
possibility is that this symmetry be a dual symmetry, related to non trivial
spatial homotopy. The sphere at infinity of 3-dimensional space being
2-dimensional, the relevant homotopy is $\Pi_2$, the corresponding
configurations monopoles, and the mechanism dual superconductivity. The
consistency of the order-disorder nature of the deconfining transition is
compared with lattice data . It is also shown that the only dual quantum number
is magnetic charge and the key quantity is 't Hooft tensor, independent of the
gauge group. The general form of the 't Hooft tensor is computed.


  We have studied self-sustained, deformable, rotating liquid He cylinders of
infinite length. In the normal fluid $^3$He case, we have employed a classical
model where only surface tension and centrifugal forces are taken into account,
as well as the Density Functional Theory (DFT) approach in conjunction with a
semi-classical Thomas-Fermi approximation for the kinetic energy. In both
approaches, if the angular velocity is sufficiently large, it is energetically
favorable for the $^3$He cylinder to undergo a shape transition, acquiring an
elliptic-like cross section which eventually becomes two-lobed. In the $^4$He
case, we have employed a DFT approach that takes into account its superfluid
character, limiting the description to vortex-free configurations where angular
momentum is exclusively stored in capillary waves on a deformed cross section
cylinder. The calculations allow us to carry out a comparison between the
rotational behavior of a normal, rotational fluid ($^3$He) and a superfluid,
irrotational fluid ($^4$He).


  In quantum field theories with massless particles, states carrying a
nontrivial superselection charge may have very poor localisation properties
when compared to the vacuum. In this case, replacing the vacuum with a suitable
``infravacuum'' state can improve the localisability of the charges in such a
way that the Doplicher-Haag-Roberts (DHR) theory of superselection sectors is
applicable.
  As an explicit example for this phenomenon, we consider a certain class of
sectors of the free massless scalar field. These sectors carry a charge of
electric type, and the corresponding infravacuum background may be interpreted
as a cloud of infrared radiation.
  Motivated by this situation, we propose a model-independent definition of
infravacuum representations and derive some of their properties. We analyse in
particular their role as reference representations for DHR theory and
investigate to what an extent the absence of a translation invariant vector
affects the results of the DHR analysis. Special emphasis is put on the
functorial aspects of the theory and on the description of the covariance and
the spectral properties of charged sectors in terms of so-called charge
transporting cocycles.


  The treewidth of control flow graphs arising from structured programs is
known to be at most six. However, as a control flow graph is inherently
directed, it makes sense to consider a measure of width for digraphs instead.
We use the so-called DAG-width and show that the DAG-width of control flow
graphs arising from structured (goto-free) programs is at most three.
Additionally, we also give a linear time algorithm to compute the DAG
decomposition of these control flow graphs. One consequence of this result is
that parity games (and hence the $\mu$-calculus model checking problem), which
are known to be tractable on graphs of bounded DAG-width, can be solved
efficiently in practice on control flow graphs.


  We present new XMM-Newton results on the field around the NGC346 star cluster
in the SMC. This continues and extends previously published work on Chandra
observations of the same field. The two XMM-Newton observations were obtained,
respectively, six months before and six months after the previously published
Chandra data. Of the 51 X-ray sources detected with XMM-Newton, 29 were already
detected with Chandra. Comparing the properties of these X-ray sources in each
of our three datasets has enabled us to investigate their variability on times
scales of a year. Changes in the flux levels and/or spectral properties were
observed for 21 of these sources. In addition, we discovered long-term
variations in the X-ray properties of the peculiar system HD5980, a luminous
blue variable star, that is likely to be a colliding wind binary system, which
displayed the largest luminosity during the first XMM-Newton observation.


  We initiate the study of boundary Vertex Operator Algebras (VOAs) of
topologically twisted 3d $\mathcal{N}=4$ rank-0 SCFTs. This is a recently
introduced class of $\mathcal{N}=4$ SCFTs that by definition have
zero-dimensional Higgs and Coulomb branches. We briefly explain why it is
reasonable to obtain rational VOAs at the boundary of their topological twists.
When a rank-0 SCFT is realized as the IR fixed point of a $\mathcal{N}=2$
Lagrangian theory, we propose a technique for the explicit construction of its
topological twists and boundary VOAs based on deformations of the
holomorphic-topological twist of the $\mathcal{N}=2$ microscopic description.
We apply this technique to the $B$ twist of a newly discovered family of 3d
$\mathcal{N}=4$ rank-0 SCFTs ${\mathcal T}_r$ and argue that they admit the
simple affine VOAs $L_r(\mathfrak{osp}(1|2))$ at their boundary. In the
simplest case, this leads to a novel level-rank duality between
$L_1(\mathfrak{osp}(1|2))$ and the minimal model $M(2,5)$. As an aside, we
present a TQFT obtained by twisting a 3d $\mathcal{N}=2$ QFT that admits the
$M(3,4)$ minimal model as a boundary VOA and briefly comment on the classical
freeness of VOAs at the boundary of 3d TQFTs.


  It is shown how to write the Kirkwood-Rihaczec quasiprobability distribution
as an expectation value of the vacuum state. We do this, by writing the
position eigenstates as a "displacment" of the vacumm. We also give a relation
between the Glauber-Sudarshan and Kirkwood-Rihaczec quasiprobability
distributions.


  The complex range of interactions between electrons and electromagnetic
fields gave rise to countless scientific and technological advances. A prime
example is photon-induced nearfield electron microscopy (PINEM), enabling the
detection of confined electric fields in illuminated nanostructures with
unprecedented spatial resolution. However, PINEM is limited by its dependence
on strong fields, making it unsuitable for sensitive samples, and its inability
to resolve complex phasor information. Here, we leverage the nonlinear,
over-constrained nature of PINEM to present an algorithmic microscopy approach,
achieving far superior nearfield imaging capabilities. Our algorithm relies on
free-electron Ramsey-type interferometry to produce orders-of-magnitude
improvement in sensitivity and ambiguity-immune nearfield phase reconstruction,
both of which are optimal when the electron exhibits a fully quantum behavior.
Our results demonstrate the potential of combining algorithmic approaches with
novel modalities in electron microscopy, and may lead to various applications
from imaging sensitive biological samples to performing full-field tomography
of confined light.


  The origins of enhanced piezoelectric coupling along nonpolar
crystallographic directions in ferroelectric BaTiO3 are investigated using in
situ neutron spectroscopy. It is observed that an electric field applied away
from the equilibrium polarization direction causes changes in the phonon
spectra that lead to an increase in the interaction between the transverse
acoustic and transverse optic branches (TA-TO) near the Brillouin zone center.
This provides a direct lattice dynamics mechanism for enhanced
electromechanical coupling, and could act as a guide for designing improved
piezoelectric materials.


  How to make a model of a non-Fermi-liquid metal with efficient current
dissipation is a long-standing problem. Results from holographic duality
suggest a framework where local critical fermionic degrees of freedom provide
both a source of decoherence for the Landau quasiparticle, and a sink for its
momentum. This leads us to study a Kondo lattice type model with SYK models in
place of the spin impurities. We find evidence for a stable phase at
intermediate couplings.


  We have investigated a group of stars known to have low chromospheric ages,
but high kinematical ages. Isochrone, chemical and lithium ages are estimated
for them. The majority of stars in this group show lithium abundances much
smaller than expected for their chromospheric ages, which is interpreted as an
indication of their old age. Radial velocity measurements in the literature
also show that they are not close binaries. The results suggest that they can
be formed from the coalescence of short-period binaries. Coalescence rates,
calculated taking into account several observational data and a maximum
theoretical time scale for contact, in a short-period pair, predict a number of
coalesced stars similar to what we have found in the solar neighbourhood.


  The electroproduction of selected $p$- and $sd$-shell hypernuclei was studied
within a many-body approach using realistic interactions between the
constituent baryons. The cross sections were computed in distorted-wave impulse
approximation using two elementary amplitudes for the electroproduction of the
$\Lambda$ hyperon. The structure of the hypernuclei was investigated within the
framework of the self-consistent $\Lambda$-nucleon Tamm-Dancoff approach and
its extension known as the $\Lambda$-nucleon equation of motion phonon method.
Use was made of the NNLOsat chiral potential plus the effective Nijmegen-F YN
interaction. The method was first implemented on light nuclei for studying the
available experimental data and establishing a relation to other approaches.
After this proof test, it was adopted for predicting the electroproduction
cross section of the hypernuclei $^{40}_{~\Lambda}$K and $^{48}_{~\Lambda}$K in
view of the E12-15-008 experiment in preparation at JLab. On the ground of
these predictions, appreciable effects on the spectra are expected to be
induced by the YN interaction.


  In this paper we will examine the consequence of a canonical theory of
quantum dust collapse in 2+1 dimensions. The solution of the WDW equation
describing the collapse indicates that collapsing shells outside the apparent
horizon are accompanied by outgoing shells within the apparent horizon during
their collapse phase and stop collapsing once they reach the apparent horizon.
Taking this picture of quantum collapse seriously, we determine a static
solution with energy density corresponding to a dust ball whose collapse has
terminated at the apparent horizon. We show that the boundary radius of the
ball is larger than the BTZ radius confirming that no event horizon is formed.
The ball is sustained by radial pressure which we determine and which we
attribute to the Unruh radiation within it.


  The Far-Infrared Surveyor (FIS) is one of two focal plane instruments on the
AKARI satellite. FIS has four photometric bands at 65, 90, 140, and 160 um, and
uses two kinds of array detectors. The FIS arrays and optics are designed to
sweep the sky with high spatial resolution and redundancy. The actual scan
width is more than eight arcmin, and the pixel pitch is matches the diffraction
limit of the telescope. Derived point spread functions (PSFs) from observations
of asteroids are similar to the optical model. Significant excesses, however,
are clearly seen around tails of the PSFs, whose contributions are about 30% of
the total power. All FIS functions are operating well in orbit, and its
performance meets the laboratory characterizations, except for the two longer
wavelength bands, which are not performing as well as characterized.
Furthermore, the FIS has a spectroscopic capability using a Fourier transform
spectrometer (FTS). Because the FTS takes advantage of the optics and detectors
of the photometer, it can simultaneously make a spectral map. This paper
summarizes the in-flight technical and operational performance of the FIS.


  One dimensional S=1 antiferromagnetic Heisenberg chains with bond alternation
and uniaxial single-ion-type anisotropy are studied by numerical exact
diagonalization of finite size systems. We calculate the ground state phase
diagram using the twisted boundary condition method for $D\geq 0$. The ground
states of this model contain the Haldane state, large-D state and the dimer
state. Using conformal field theory and the level spectroscopy method, we
calculate the D and $\delta$-dependence of the Luttinger liquid paraments K and
the critical exponent $\nu$ of the energy gap.


  A new scheme of realizing the nonadiabatic conditional geometric phase shift
via a noncoplanar (and coiled) fiber system is presented in this Letter. It is
shown that the effective Hamiltonian that describes the interaction of
polarized photons with the fiber medium is just the Wang-Keiji type of
Hamiltonian. This, therefore, means that the coiled fiber system may be an
ideal implementation of realizing the nonadiabatic geometric phase gates for
the topological quantum computation. The remarkable feature of the present
method is that it can automatically meet the conditions and requirements
proposed in the Wang-Keiji scheme: (i) in the coiled fiber system, the
dynamical phase of photon wavefunction caused by the interaction Hamiltonian
automatically vanishes; (ii) the Wang-Keiji requirement for the parameters in
the Wang-Keiji Hamiltonian can be exactly satisfied automatically in the fiber
system; (iii) the conditional initial state can be easily achieved by
manipulating the initial wave vector of polarized photons. Due to these three
advantages, the coiled fiber system may be a potentially practical way of
achieving the nonadiabatic conditional geometric phase shift (and hence the
nonadiabatic geometric quantum gates).


  We present a permanent magnet arrangement that can achieve a tuneable axial
magnetic field from 1.80(8)-2.67(2) kG along the z-axis, where (x,y) = (0,0),
with a rms field variation of less than 1% over a length of 25 mm. The
instrument consists of an arrangement of off-the-shelf N42 neodymium-iron-boron
(NdFeB) axially magnetized ring magnets, of varying outer and inner diameters.
The magnets are organized into four cylindrical brass holders, whose relative
separation can be manipulated to achieve the desired magnetic field strength
and homogeneity over the region of interest. We present magnetic field
computations and Marquardt-Levenberg fits to experimental data and demonstrate
excellent agreement between theory and experiment. The apparatus has been
designed to accommodate a cylindrical atomic vapor cell of length 25 mm and
diameter 25 mm to lie within the bore of the ring magnets. The design has a
clear aperture of 20 mm in the x-y plane along the z-axis, which opens up new
avenues for imaging exploration in atomic spectroscopy.


  We study the thermodynamic behavior of attractive binary Bose mixtures using
exact path-integral Monte-Carlo methods. Our focus is on the regime of
interspecies interactions where the ground state is in a self-bound liquid
phase, stabilized by beyond mean-field effects. We calculate the isothermal
curves in the pressure vs density plane for different values of the attraction
strength and establish the extent of the coexistence region between liquid and
vapor using the Maxwell construction. Notably, within the coexistence region,
Bose-Einstein condensation occurs in a discontinuous way as the density jumps
from the normal gas to the superfluid liquid phase. Furthermore, we determine
the critical point where the line of first-order transition ends and
investigate the behavior of the density discontinuity in its vicinity. We also
point out that the density discontinuity at the transition could be observed in
experiments of mixtures in traps.


  A systematic analysis of the multifragmentation (MF) in fully reconstructed
events from 1A GeV Au, La and Kr collisions with C has been performed. This
data is used to provide a definitive test of the variable volume version of the
statistical multifragmentation model (SMM). A single set of SMM parameters
directly determined by the data and the semi-empiricalmass formula are used
after the adjustable inverse level density parameter, $\epsilon_{o}$ is
determined by the fragment distributions. The results from SMM for second stage
multiplicity, size of the biggest fragment and the intermediate mass fragments
are in excellent agreement with the data. Multifragmentation thresholds have
been obtained for all three systems using SMM prior to secondary decay. The
data indicate that both thermal excitation energy $E_{th}^{*}$ and the isotope
ratio temperature $T_{He-DT}$ decrease with increase in system size at the
critical point. The breakup temperature obtained from SMM also shows the same
trend as seen in the data. The SMM model is used to study the nature of the MF
phase transition. The caloric curve for Kr exhibits back-bending (finite latent
heat) while the caloric curves for Au and La are consistent with a continuous
phase transition (nearly zero latent heat) and the values of the critical
exponents $\tau$, $\beta$ and $\gamma$, both from data and SMM, are close to
those for a 'liquid-gas' system for Au and La. We conclude that the larger
Coulomb expansion energy in Au and La reduces the latent heat required for MF
and changes the nature of the phase transition. Thus the Coulomb energy plays a
major role in nuclear MF.


  A first comprehensive treatment on complex eigenmodes is presented for
general lossy traveling-wave electromagnetic structures where the per unit
length propagation phase shift ($\beta$) dependent complex eigenfrequencies
$\Omega(\beta)$ are mapped to the frequency dependent complex propagation
constant $\gamma(\omega_0)$ for variety of electromagnetic structures. Rigorous
procedures are presented to first compute the complex eigenmodes of both
uniform and periodic electromagnetic structures which are confirmed using
full-wave simulations and known analytical results. Two mapping procedures are
further presented for arbitrary uniform and periodic structures, where the
known $\{\Omega-\beta\}$ relationship is expressed using polynomial and Fourier
series expansions, respectively. Consequently replacing $\{\Omega,~j\beta\}$
with $\{\omega_0, \gamma\}$ in the known $\{\Omega-\beta\}$ relation, a
characteristic equation is formed which is then numerically solved for the two
unknowns, representing the physical dispersion relation $\omega_0(\beta)$ and
the frequency dependent propagation loss $\alpha(\omega_0)$ of the structure.
The mapping procedure is demonstrated for variety of cases including unbounded
uniform media, rectangular waveguide, Drude dispersive metamaterial and a
periodic dielectric stack, where exact propagation characteristics have been
successfully retrieved in all cases across both passbands and stopbands across
frequency.


  In this paper we adapt the notion of the nucleus defined by Benson, Carlson,
and Robinson to compact Lie groups in non-modular characteristic. We show that
it describes the singularities of the projective scheme of the cohomology of
its classifying space. A notion of support for singularity categories of ring
spectra (in the sense of Greenlees and Stevenson) is established, and is shown
to be precisely the nucleus in this case, consistent with a conjecture of
Benson and Greenlees for finite groups.


  We analyze a whispering gallery mode biosensor with a metallic nanorod bound
to its surface. It is found that a localized surface plasmon resonance in the
nanorod can reduce the optical mode volume of the resonator by as much as four
orders of magnitude via a local enhancement of the electric field, thus
improving the detection sensitivity. Optical frequency shifts as large as 15
MHz are predicted for typical proteins and, for typical experimental
parameters, the biosensor is predicted to be limited by laser frequency noise,
leading to a minimum detectable polarizability on the order of 10 cubic
angstroms.


  High-harmonic generation (HHG) from a compact, solid-state medium is highly
desirable for applications such as coherent attosecond pulse generation and
extreme ultra-violet (EUV) spectroscopy, yet the typically weak conversion of
pump light to HHG can largely hinder its applications. Here, we use a material
operating in its epsilon-near-zero (ENZ) region, where the real part of its
permittivity vanishes, to greatly boost the efficiency of the HHG process at
the microscopic level. In experiments, we report high-harmonic emission up to
the 9th order directly from a low-loss, solid-state ENZ medium: indium-doped
cadmium oxide, with an excitation intensity at the GW cm-2 level. Furthermore,
the observed HHG signal exhibits a pronounced spectral red-shift as well as
linewidth broadening, resulting from the photo-induced electron heating and the
consequent time-dependent resonant frequency of the ENZ film. Our results
provide a novel nanophotonic platform for strong field physics, reveal new
degrees of freedom for spectral and temporal control of HHG, and open up
possibilities of compact solid-state attosecond light sources.


  The solution existence of finite horizon optimal economic growth problems is
studied by invoking Filippov's Existence Theorem for optimal control problems
with state constraints of the Bolza type from the monograph of L. Cesari
[Optimization Theory and Applications, Springer-Verlag, New York, 1983]. Our
results are obtained not only for general problems but also for typical ones
with the production function and the utility function being either the AK
function or the Cobb--Douglas one. Some open questions and conjectures about
the regularity of the global solutions of finite horizon optimal economic
growth problems are formulated in this paper.


  We investigate the dust energy balance for the edge-on galaxy IC 2531, one of
the seven galaxies in the HEROES sample. We perform a state-of-the-art
radiative transfer modelling based, for the first time, on a set of optical and
near-infrared galaxy images. We show that taking into account near-infrared
imaging in the modelling significantly improves the constraints on the
retrieved parameters of the dust content. We confirm the result from previous
studies that including a young stellar population in the modelling is important
for explaining the observed stellar energy distribution. However, the
discrepancy between the observed and modelled thermal emission at far-infrared
wavelengths, the so-called dust energy balance problem, is still present: the
model underestimates the observed fluxes by a factor of about two. We compare
two different dust models, and find that dust parameters and thus the spectral
energy distribution in the infrared domain are sensitive to the adopted dust
model. In general, the THEMIS model reproduces the observed emission in the
infrared wavelength domain better than the popular Zubko et al. BARE-GR-S
model. Our study of IC 2531 is a pilot case for detailed and uniform radiative
transfer modelling of the entire HEROES sample, which will shed more light on
the strength and origins of the dust energy balance problem.


  Eisenbud and Harris conjectured in 1982 that an algebraic curve of high genus
lies on a surface of low degree (which they proved for curves of very large
degree). They observed constraints on the Hilbert function of a general
hyperplane section which imply that the hyperplane section lies on a curve of
low degree. We investigate this situation under deformation. Given a set of
sufficiently many points (as postulated by the conjecture) on a linearly normal
curve, we show that if the number of conditions on quadrics remains constant,
then for every deformation of the points the curve deforms along with them.


  We obtain, by extensive direct numerical simulations, time-dependent and
equal-time structure functions for the vorticity, in both quasi-Lagrangian and
Eulerian frames, for the direct-cascade regime in two-dimensional fluid
turbulence with air-drag-induced friction. We show that differ- ent ways of
extracting time scales from these time-dependent structure functions lead to
different dynamic-multiscaling exponents, which are related to equal-time
multiscaling exponents by different classes of bridge relations; for a
representative value of the friction we verify that, given our error bars,
these bridge relations hold.


  New cells are generated throughout life and integrate into the hippocampus
via the process of adult neurogenesis. Epileptogenic brain injury induces many
structural changes in the hippocampus, including the death of interneurons and
altered connectivity patterns. The pathological neurogenic niche is associated
with aberrant neurogenesis, though the role of the network-level changes in
development of epilepsy is not well understood. In this paper, we use
computational simulations to investigate the effect of network environment on
structural and functional outcomes of neurogenesis. We find that small-world
networks with external stimulus are able to be augmented by activity-seeking
neurons in a manner that enhances activity at the stimulated sites without
altering the network as a whole. However, when inhibition is decreased or
connectivity patterns are changed, new cells are both less responsive to
stimulus and the new cells are more likely to drive the network into bursting
dynamics. Our results suggest that network-level changes caused by
epileptogenic injury can create an environment where neurogenic reorganization
can induce or intensify epileptic dynamics and abnormal integration of new
cells.


  This letter provides evidence of complexity-volume and complexity-action
conjectures by examining the structure of a black hole, which comprises a
horizon linked to the singularity through a wormhole. In this situation, the
shape of the black hole's geometry resembles that of Gabriel's horn. In
essence, our results indicate that the information paradox is merely the
painter's paradox.


  High resolution (R > 40 000) and high S/N spectra have been acquired with
UVES on the VLT-Kueyen (Paranal Observatory, ESO Chile) for several main
sequence turnoff stars (V ~ 17 mag) and subgiants at the base of the Red Giant
Branch (V ~ 16 mag) in three globular clusters (NGC 6397, NGC 6752 and 47
Tuc/NGC 104) at different metallicities (respectively [Fe/H] = -2.0; -1.5;
-0.7$). Spectra for a sample of 25 field halo subdwarves have also been taken
with equal resolution, but higher S/N. These data have been used to determine
the abundances of several neutron-capture elements in these three clusters:
strontium, yttrium, barium and europium. This is the first abundance
determination of these heavy elements for such unevolved stars in these three
globular clusters. These values, together with the [Ba/Eu] and [Sr/Ba]
abundance ratios, have been used to test the self-enrichment scenario. A
comparison is done with field halo stars and other well known Galactic globular
clusters in which heavy elements have already been measured in the past, at
least in bright giants (V > 11-12 mag). Our results show clearly that globular
clusters have been uniformly enriched by r- and s-process syntheses, and that
most of them seem to follow exactly the same abundance patterns as field halo
stars, which discards the ``classical'' self-enrichment scenario for the origin
of metallicities and heavy elements in globular clusters.


  The JUNO mission to Jupiter is planned to measure the water abundance in
Jupiter's atmosphere below the cloud layer. This measurement is important
because it can be used to reveal valuable information on Jupiter's origin and
its composition. In this paper we discuss the importance of this measurement,
the challenges in its interpretation, and address how it can be connected to
interior and formation models of Jupiter.


  The question of global existence or non-existence of solution to a given
stochastic partial differential equation under some non-linear conditions
always comes to mind. To show that our weak-predictable random field solutions
do not have global existence for all time , it requires that we first establish
that the solutions exhibit continuity in time property. The results discuss the
mean-square and mean continuity in time of a class of jump-discontinuous heat
equations perturbed by compensated and non-compensated Poisson random noises
respectively; and we showed that our mild solutions are mean and mean-square
continuous in time for any time interval ; better put, our solutions have
continuous versions or modifications for any time interval.


  Consider a measured equivalence relation acting on a bundle of hyperbolic
metric spaces by isometries. We prove that every aperiodic hyperfinite
subequivalence relation is contained in a {\em unique} maximal hyperfinite
subequivalence relation. We classify elements of the full group according to
their action on fields on boundary measures (extending earlier results of
Kaimanovich), study the existence and residuality of different types of
elements and obtain an analogue of Tits' alternative.


  In this paper, we prove that the semigroups of invertible matrices with
nonnegative elements over linearly oredered associative rings are elementarily
equivalent if and only if the matrices have the same dimension and the rings
are elementarily equivalent as ordered rings.


  This paper deals with a remarkable integrable discretization of the so(3)
Euler top introduced by Hirota and Kimura. Such a discretization leads to an
explicit map, whose integrability has been understood by finding two
independent integrals of motion and a solution in terms of elliptic functions.
Our goal is the construction of its Hamiltonian formulation. After giving a
simplified and streamlined presentation of their results, we provide a
bi-Hamiltonian structure for this discretization, thus proving its
integrability in the standard Liouville-Arnold sense.


  This paper presents a method that leverages vehicle motion constraints to
refine data associations in a point-based radar odometry system. By using the
strong prior on how a non-holonomic robot is constrained to move smoothly
through its environment, we develop the necessary framework to estimate
ego-motion from a single landmark association rather than considering all of
these correspondences at once. This allows for informed outlier detection of
poor matches that are a dominant source of pose estimate error. By refining the
subset of matched landmarks, we see an absolute decrease of 2.15% (from 4.68%
to 2.53%) in translational error, approximately halving the error in odometry
(reducing by 45.94%) than when using the full set of correspondences. This
contribution is relevant to other point-based odometry implementations that
rely on a range sensor and provides a lightweight and interpretable means of
incorporating vehicle dynamics for ego-motion estimation.


  We establish some upper and lower bounds for the number of rational points of
Prym varieties over finite fields.


  Magnetic B-type stars exhibit photometric variability due to diverse causes,
and consequently on a variety of timescales. In this paper we describe
interpretation of BRITE photometry and related ground-based observations of 4
magnetic B-type systems: $\epsilon$ Lupi, $\tau$ Sco, a Cen and $\epsilon$ CMa.


  Quantum fluctuations of local quantities can be a direct signature of
entanglement in an extended quantum many-body system. Hence they may serve as a
theoretical (as well as an experimental) tool to detect the spatial properties
of the entanglement entropy of a subsystem. In the ground state of quantum
many-body systems, its scaling is typically linear in the boundary of the
subsystem (area law). Here we propose a microscopic insight into the spatial
structure of entanglement and fluctuations using the concept of \emph{contour},
recently introduced to decompose the bipartite entanglement entropy of lattice
free fermions between two extended regions $A$ and $B$ into contributions from
single sites in $A$. We generalize the notion of contour to the entanglement of
any quadratic (bosonic or fermionic) lattice Hamiltonian, as well as to
particle-number fluctuations. The entanglement and fluctuations contours are
found to generally decay when moving away from the boundary between $A$ and
$B$. We show that in the case of free fermions the decay of the entanglement
contour follows closely that of the fluctuation contour. In the case of
Bose-condensed interacting bosons, treated via the Bogoliubov and spin-wave
approximations, such a link cannot be established -- fluctuation and
entanglement contours are found to be radically different, as they lead to a
logarithmically violated area law for fluctuations, and to a strict area law of
entanglement. Analyzing in depth the role of the zero-energy Goldstone mode of
spin-wave theory, and of the corresponding lowest-energy mode in the
entanglement spectrum, we unveil a subtle interplay between the special contour
and energy scaling of the latter, and universal additive logarithmic
corrections to entanglement area law discussed extensively in the recent
literature.


  We explore the potential of CNN-based models for gallbladder cancer (GBC)
detection from ultrasound (USG) images as no prior study is known. USG is the
most common diagnostic modality for GB diseases due to its low cost and
accessibility. However, USG images are challenging to analyze due to low image
quality, noise, and varying viewpoints due to the handheld nature of the
sensor. Our exhaustive study of state-of-the-art (SOTA) image classification
techniques for the problem reveals that they often fail to learn the salient GB
region due to the presence of shadows in the USG images. SOTA object detection
techniques also achieve low accuracy because of spurious textures due to noise
or adjacent organs. We propose GBCNet to tackle the challenges in our problem.
GBCNet first extracts the regions of interest (ROIs) by detecting the GB (and
not the cancer), and then uses a new multi-scale, second-order pooling
architecture specializing in classifying GBC. To effectively handle spurious
textures, we propose a curriculum inspired by human visual acuity, which
reduces the texture biases in GBCNet. Experimental results demonstrate that
GBCNet significantly outperforms SOTA CNN models, as well as the expert
radiologists. Our technical innovations are generic to other USG image analysis
tasks as well. Hence, as a validation, we also show the efficacy of GBCNet in
detecting breast cancer from USG images. Project page with source code, trained
models, and data is available at https://gbc-iitd.github.io/gbcnet


  We present a modification of the so-called Parrondo's paradox where one is
allowed to choose in each turn the game that a large number of individuals
play. It turns out that, by choosing the game which gives the highest average
earnings at each step, one ends up with systematic loses, whereas a periodic or
random sequence of choices yields a steadily increase of the capital. An
explanation of this behavior is given by noting that the short-range
maximization of the returns is "killing the goose that laid the golden eggs". A
continuous model displaying similar features is analyzed using dynamic
programming techniques from control theory.


  The WFIRST-AFTA 2.4 m telescope will provide in the next decade the
opportunity to host a coronagraph for the imaging and spectroscopy of planets
and disks. The telescope, however, is not ideal, given its obscured aperture.
Only recently have coronagraph designs been thoroughly investigated that can
efficiently work with this configuration. Three coronagraph designs, the hybrid
Lyot, the shaped pupil, and the phase-induced amplitude-apodization complex
mask coronagraph (PIAA-CMC) have been selected for further development by the
AFTA project. Real-world testbed demonstrations of these have just begun, so
for now the most reliable means of evaluating their potential performance comes
from numerical modeling incorporating diffraction propagation, realistic system
models, and simulated wavefront sensing and control. Here we present the
methods of performance evaluation and results for the current coronagraph
designs.


  As one of the most intriguing intrinsic properties of quantum world, quantum
superposition provokes great interests in its own generation. Oszmaniec [Phys.
Rev. Lett. 116, 110403 (2016)] have proven that though a universal quantum
machine that creates superposition of arbitrary two unknown states is
physically impossible, a probabilistic protocol exists in the case of two input
states have nonzero overlaps with the referential state. Here we report a
heralded quantum machine realizing superposition of arbitrary two unknown
photonic qubits as long as they have nonzero overlaps with the horizontal
polarization state $|H\rangle$. A total of 11 different qubit pairs are chosen
to test this protocol by comparing the reconstructed output state with
theoretical expected superposition of input states. We obtain the average
fidelity as high as 0.99, which shows the excellent reliability of our
realization. This realization not only deepens our understanding of quantum
superposition but also has significant applications in quantum information and
quantum computation, e.g., generating non-classical states in the context of
quantum optics and realizing information compression by coherent superposition
of results of independent runs of subroutines in a quantum computation.


  The second-generation interferometric gravitational wave detectors currently
under construction are expected to make their first detections within this
decade. This will firmly establish gravitational wave physics as an empirical
science and will open up a new era in astrophysics, cosmology, and fundamental
physics. Already with the first detections, we will be able to, among other
things, establish the nature of short-hard gamma ray bursts, definitively
confirm the existence of black holes, measure the Hubble constant in a
completely independent way, and for the first time gain access to the genuinely
strong-field dynamics of gravity. Hence it is timely to consider the
longer-term future of this new field. The Einstein Telescope (ET) is a concrete
conceptual proposal for a third-generation gravitational wave observatory,
which will be ~10 times more sensitive in strain than the second-generation
detectors. This will give access to sources at cosmological distances, with a
correspondingly higher detection rate. I give an overview of the science case
for ET, with a focus on what can be learned from signals emitted by coalescing
compact binaries. Third-generation observatories will allow us to map the
coalescence rate out to redshifts z ~ 3, determine the mass functions of
neutron stars and black holes, and perform precision measurements of the
neutron star equation of state. ET will enable us to study the large-scale
structure and evolution of the Universe without recourse to a cosmic distance
ladder. Finally, I discuss how it will allow for high-precision measurements of
strong-field, dynamical gravity.


  We describe cosmological galaxy formation simulations with the adaptive mesh
refinement code Enzo that incorporate a star formation prescription regulated
by the local abundance of molecular hydrogen. We show that this H2-regulated
prescription leads to a suppression of star formation in low mass halos (M_h <
~10^10 M_sun) at z>4, alleviating some of the dwarf galaxy problems faced by
theoretical galaxy formation models. H2 regulation modifies the efficiency of
star formation of cold gas directly, rather than indirectly reducing the cold
gas content with "supernova feedback". We determine the local H2 abundance in
our most refined grid cells (76 proper parsec in size at z=4) by applying the
model of Krumholz, McKee, & Tumlinson, which is based on idealized 1D radiative
transfer calculations of H2 formation-dissociation balance in ~100 pc
atomic--molecular complexes. Our H2-regulated simulations are able to reproduce
the empirical (albeit lower z) Kennicutt-Schmidt relation, including the low
Sigma_gas cutoff due to the transition from atomic to molecular phase and the
metallicity dependence thereof, without the use of an explicit density
threshold in our star formation prescription. We compare the evolution of the
luminosity function, stellar mass density, and star formation rate density from
our simulations to recent observational determinations of the same at z=4-8 and
find reasonable agreement between the two.


  In multicomponent superfluids and superconductors, co- and counter-flows of
components have in general different properties. It was discussed in 1975 by
Andreev and Bashkin, in the context of He$^3$/He$^4$ superfluid mixtures, that
inter-particle interactions produce a dissipationless drag. The drag can be
understood as a superflow of one component induced by phase gradients of the
other component. Importantly the drag can be both positive (entrainment) and
negative (counter-flow). The effect is known to be of crucial importance for
many properties of diverse physical systems ranging from the dynamics of
neutron stars, rotational responses of Bose mixtures of ultra-cold atoms to
magnetic responses of multicomponent superconductors. Although there exists a
substantial literature that includes the drag interaction phenomenologically,
much fewer regimes are covered by quantitative studies of the microscopic
origin of the drag and its dependence on microscopic parameters. Here we study
the microscopic origin and strength of the drag interaction in a quantum system
of two-component bosons on a lattice with short-range interaction. By
performing quantum Monte-Carlo simulations of a two-component Bose-Hubbard
model we obtain dependencies of the drag strength on the boson-boson
interactions and properties of the optical lattice. Of particular interest are
the strongly-correlated regimes where the ratio of co-flow and counter-flow
superfluid stiffnesses can diverge, corresponding to the case of saturated
drag.


  We study states on the universal noncommutative *-algebra generated by the
coefficients of a unitary matrix, or equivalently states on the unitary dual
group. Its structure of dual group in the sense of Voiculescu allows to define
five natural convolutions. We prove that there exists no Haar state for those
convolutions. However, we prove that there exists a weaker form of absorbing
state, that we call Haar trace, for the free and the tensor convolutions. We
show that the free Haar trace is the limit in distribution of the blocks of a
Haar unitary matrix when the dimension tends to infinity. Finally, we study a
particular class of free L\'evy processes on the unitary dual group which are
also the limit of the blocks of random matrices on the classical unitary group
when the dimension tends to infinity.


  We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus
on the easiest case of virtually Abelian groups, and introduce a technique to
reduce the quantum walk to an equivalent one on an Abelian group with coin
system having larger dimension. We apply the technique in the case of two
quantum walks on virtually Abelian groups with planar Cayley graphs, finding
the exact solution.


  To achieve propulsion at low Reynolds number, a swimmer must deform in a way
that is not invariant under time-reversal symmetry; this result is known as the
scallop theorem. We show here that there is no many-scallop theorem. We
demonstrate that two active particles undergoing reciprocal deformations can
swim collectively; moreover, polar particles also experience effective
long-range interactions. These results are derived for a minimal dimers model,
and generalized to more complex geometries on the basis of symmetry and scaling
arguments. We explain how such cooperative locomotion can be realized
experimentally by shaking a collection of soft particles with a homogeneous
external field.


  Using standard methods (due to Janson, Stein-Chen, and Talagrand) from
probabilistic combinatorics, we explore the following general theme: As one
progresses from each member of a family of objects ${\cal A}$ being "covered"
by at most one object in a random collection ${\cal C}$, to being covered at
most $\lambda$ times, to being covered at least once, to being covered at least
$\lambda$ times, a hierarchy of thresholds emerge. We will then see how such
results vary according to the context, and level of dependence introduced.
Examples will be from extremal set theory, combinatorics, and additive number
theory.


  We demonstrate the manipulation of transmitted light through an optical
Fabry-Perot cavity, built around a spectroscopy cell containing enriched
rubidium vapor. Light resonant with the $^{87}$Rb D$_{2}$ ($F=2/F=1$)
$\leftrightarrow F'$ manifold, is controlled by transverse intersection of the
cavity mode by another resonant light beam. The cavity transmission can be
suppressed or enhanced depending on the coupling of atomic states due to the
intersecting beams. The extreme manifestation of cavity mode control is the
precipitious destruction (negative logic switching) or buildup (positive logic
switching) of the transmitted light intensity, on intersection of the
transverse control beam with the cavity mode. Both the steady state and
transient response are experimentally investigated. The mechanism behind the
change in cavity transmission is discussed in brief.


  The large majority of extinction sight lines in our Galaxy obey a simple
relation depending on one parameter, the total-to-selective extinction
coefficient, Rv. Different values of Rv are able to match the whole extinction
curve through different environments so characterizing normal extinction
curves. In this paper more than sixty curves with large ultraviolet deviations
from their best-fit one parameter curve are analyzed. These curves are fitted
with dust models to shed light into the properties of the grains, the processes
affecting them, and their relations with the environmental characteristics. The
extinction curve models are reckoned by following recent prescriptions on grain
size distributions able to describe one parameter curves for Rv values from 3.1
to 5.5. Such models, here extended down to Rv=2.0, allow us to compare the
resulting properties of our deviating curves with the same as normal curves in
a self-consistent framework, and thus to recover the relative trends overcoming
the modeling uncertainties. Such curves represent the larger and homogeneous
sample of anomalous curves studied so far with dust models. Results show that
the ultraviolet deviations are driven by a larger amount of small grains than
predicted for lines of sight where extinction depends on one parameter only.
Moreover, the dust-to-gas ratios of anomalous curves are lower than the same
values for no deviating lines of sight. Shocks and grain-grain collisions
should both destroy dust grains, so reducing the amount of the dust trapped
into the grains, and modify the size distribution of the dust, so increasing
the small-to-large grain size ratio. Therefore, the extinction properties
derived should arise along sight lines where shocks and high velocity flows
perturb the physical state of the interstellar medium living their signature on
the dust properties. (Abridged version)


  In this paper, we investigate the boundedness of Toeplitz product
$T_{f}T_{g}$ and Hankel product $H_{f}^{*} H_{g}$ on Fock-Sobolev space for two
polynomials $f$ and $g$ in $z,\overline{z}\in\mathbb{C}^{n}$. As a result, the
boundedness of Toeplitz operator $T_{f}$ and Hankel operator $H_{f}$ with the
polynomial symbol $f$ in $z,\overline{z}\in\mathbb{C}^{n}$ is characterized.


  We use M\"obius inversion and the Bernoulli polynomials to prove inequalities
between the logarithmic summatory function of the M\"obius function and
weighted averages of its ordinary summatory function.


  We investigate gene interaction networks in various cancer cells by spectral
analysis of the adjacency matrices. We observe localization of the networks on
hub genes which have extraordinarily many links. The eigenvector centralities
take finite values only on special nodes when the hub degree exceeds a critical
value $d_c \simeq 40$. The degree correlation function shows the disassortative
behavior in the large degrees, and the nodes whose degrees $d \gtrsim 40$ have
tendencies to link to small degree nodes. The communities of the gene networks
centered at the hub genes are extracted by the amount of node degree
discrepancies between linked nodes. We verify the Wigner-Dyson distribution of
the nearest neighbor eigenvalues spacing distribution $P(s)$ in the small
degree discrepancy communities, and the Poisson $P(s)$ in the communities of
large degree discrepancies including the hubs.


  Radiative transfer effects due to overlapping X-ray lines in a
high-temperature, optically-thick, highly-ionized medium are investigated. One
particular example, where the O VIII Ly-alpha doublet coincide in frequency
with the N VII Ly-zeta lines is studied in detail to illustrate the effects on
the properties of the emergent line spectrum. We solve the radiative transfer
equation to study the energy transport of resonance line radiation in a static,
infinite, plane-parallel geometry, which is used to compute the
destruction/escape probabilities for each of the lines for various total
optical thicknesses of the medium, as well as destruction probabilities by
sources of underlying photoelectric opacity. It is found that a large fraction
of the O VIII Ly-alpha line radiation can be destroyed by N VII, which can
result in an reversal of the O VIII Ly-alpha/N VII Ly-alpha line intensity
ratio similar to what may be seen under non-solar abundances. Photoelectric
absorption by ionized carbon and nitrogen can also subsequently increase the
emission line intensities of these ions. We show that line ratios, which are
directly proportional to the abundance ratios in optically thin plasmas, are
not good indicators of the true CNO abundances. Conversely, global spectral
modeling that assumes optically thin conditions may yield incorrect abundance
estimates when compared to observations, especially if the optical depth is
large. Other potentially important overlapping lines and continua in the X-ray
band are also identified and their possible relevance to recent high resolution
spectroscopic observations with Chandra and XMM-Newton are briefly discussed.


  We analyze the dynamic aspect of the chiral phase transition. We apply the
mode coupling theory to the linear sigma model and derive the kinetic equation
for the chiral phase transition. We challenge Hohenberg and Halperin's
classification scheme of dynamic critical phenomena in which the dynamic
universality class of the chiral phase transition has been identified with that
of the antiferromagnet. We point out a crucial difference between the chiral
dynamics and the antiferromagnet system. We also calculate the dynamic critical
exponent for the chiral phase transition. Our result is $z=1-\eta/2\cong 0.98$
which is contrasted with $z=d/2=1.5$ of the antiferromagnet.


  Robotic manipulation relies on analytical or learned models to simulate the
system dynamics. These models are often inaccurate and based on offline
information, so that the robot planner is unable to cope with mismatches
between the expected and the actual behavior of the system (e.g., the presence
of an unexpected obstacle). In these situations, the robot should use
information gathered online to correct its planning strategy and adapt to the
actual system response. We propose a sampling-based motion planning approach
that uses an estimate of the model error and online observations to correct the
planning strategy at each new replanning. Our approach adapts the cost function
and the sampling bias of a kinodynamic motion planner when the outcome of the
executed transitions is different from the expected one (e.g., when the robot
unexpectedly collides with an obstacle) so that future trajectories will avoid
unreliable motions. To infer the properties of a new transition, we introduce
the notion of context-awareness, i.e., we store local environment information
for each executed transition and avoid new transitions with context similar to
previous unreliable ones. This is helpful for leveraging online information
even if the simulated transitions are far (in the state-and-action space) from
the executed ones. Simulation and experimental results show that the proposed
approach increases the success rate in execution and reduces the number of
replannings needed to reach the goal.


  We consider scattering by general compactly supported semi-classical
perturbations of the Euclidean Laplace-Beltrami operator. We show that if the
suitably cut-off resolvent of the Hamiltonian quantizes a Lagrangian relation
on the product cotangent bundle, the scattering amplitude quantizes the natural
scattering relation. In the case when the resolvent is tempered, which is true
under some non-resonance assumptions, and when we work microlocally near a
non-trapped ray, our result implies that the scattering amplitude defines a
semiclassical Fourier integral operator associated to the scattering relation
in a neighborhood of that ray. Compared to previous work we allow this relation
to have more general geometric structure.


  We derive X-ray mass, luminosity, and temperature profiles for 45 galaxy
clusters to explore relationships between halo mass, AGN feedback, and central
cooling time. We find that radio--mechanical feedback power (referred to here
as "AGN power") in central cluster galaxies correlates with halo mass as
P$_{\rm mech}$ $\propto$ M$^{1.55\pm0.26}$, but only in halos with central
atmospheric cooling times shorter than 1 Gyr. The trend of AGN power with halo
mass is consistent with the scaling expected from a self-regulating AGN
feedback loop, as well as with galaxy and central black hole co-evolution along
the $M_{\rm BH} - \sigma$ relation. AGN power in clusters with central
atmospheric cooling times longer than $\sim 1$ Gyr typically lies two orders of
magnitude below those with shorter central cooling times. Galaxies centred in
clusters with long central cooling times nevertheless experience ongoing and
occasionally powerful AGN outbursts. We further investigate the impact of
feedback on cluster scaling relations. We find $L-T$, and $M-T$ relations in
clusters with direct evidence of feedback which are steeper than self-similar,
but not atypical compared to previous studies of the full cluster population.
While the gas mass rises, the stellar mass remains nearly constant with rising
total mass, consistent with earlier studies. This trend is found regardless of
central cooling time, implying tight regulation of star formation in central
galaxies as their halos grew, and long-term balance between AGN heating and
atmospheric cooling. Our scaling relations are presented in forms that can be
incorporated easily into galaxy evolution models.


  We present exploratory results for the hadron mass spectrum and pseudoscalar
meson decay constants using mixed actions. We use improved staggered sea quarks
and HYP-smeared overlap valence quarks. We obtain good signals on 10
configurations at one lattice spacing and two different sets of sea quark
masses.


  The detection of gravitational waves has opened a new era for astronomy,
allowing for the combined use of gravitational wave and electromagnetic
emissions to directly probe the physics of compact objects, still poorly
understood. So far, the theoretical modelling of these sources has mainly
relied on standard numerical techniques as grid-based methods or smoothed
particle hydrodynamics, with only a few recent attempts at using new techniques
as moving-mesh schemes. Here, we introduce a general relativistic extension to
the mesh-less hydrodynamic schemes in the code GIZMO, which benefits from the
use of Riemann solvers and at the same time perfectly conserves angular
momentum thanks to a generalised leap-frog integration scheme. We benchmark our
implementation against many standard tests for relativistic hydrodynamics,
either in one or three dimensions, and also test the ability to preserve the
equilibrium solution of a Tolman-Oppenheimer-Volkoff compact star. In all the
presented tests, the code performs extremely well, at a level at least
comparable to other numerical techniques.


  We propose EXAMS -- a new benchmark dataset for cross-lingual and
multilingual question answering for high school examinations. We collected more
than 24,000 high-quality high school exam questions in 16 languages, covering 8
language families and 24 school subjects from Natural Sciences and Social
Sciences, among others.
  EXAMS offers a fine-grained evaluation framework across multiple languages
and subjects, which allows precise analysis and comparison of various models.
We perform various experiments with existing top-performing multilingual
pre-trained models and we show that EXAMS offers multiple challenges that
require multilingual knowledge and reasoning in multiple domains. We hope that
EXAMS will enable researchers to explore challenging reasoning and knowledge
transfer methods and pre-trained models for school question answering in
various languages which was not possible before. The data, code, pre-trained
models, and evaluation are available at https://github.com/mhardalov/exams-qa.


  This paper reports the track multiplicity and kinematics of muons, charged
pions, and protons from charged-current inclusive $\bar{\nu}_{\mu}$ and
$\nu_{\mu}$ interactions on a water target, measured using a nuclear emulsion
detector in the NINJA experiment. A 3-kg water target was exposed to the T2K
antineutrino-enhanced beam with a mean energy of 1.3 GeV. Owing to the
high-granularity of the nuclear emulsion, protons with momenta down to 200
MeV/$c$ from the neutrino-water interactions were detected. We find good
agreement between the observed data and model predictions for all kinematic
distributions other than the number of charged pions. These results demonstrate
the capability of measurements with nuclear emulsion to improve neutrino
interaction models.


  Nonlinearity of rotation symmetric Boolean functions is an important topic on
cryptography algorithm. Let $e\ge 1$ be any given integer. In this paper, we
investigate the following question: Is the nonlinearity of the quartic rotation
symmetric Boolean function generated by the monomial $x_0x_ex_{2e}x_{3e}$ equal
to its weight? We introduce some new simple sub-functions and develop new
technique to get several recursive formulas. Then we use these recursive
formulas to show that the nonlinearity of the quartic rotation symmetric
Boolean function generated by the monomial $x_0x_ex_{2e}x_{3e}$ is the same as
its weight. So we answer the above question affirmatively. Finally, we
conjecture that if $l\ge 4$ is an integer, then the nonlinearity of the
rotation symmetric Boolean function generated by the monomial
$x_0x_ex_{2e}...x_{le}$ equals its weight.


  We investigate the dynamics of the sine-Gordon solitons perturbed by
spatiotemporal external forces. We prove the existence of internal (shape)
modes of sine-Gordon solitons when they are in the presence of inhomogeneous
space-dependent external forces, provided some conditions (for these forces)
hold. Additional periodic time-dependent forces can sustain oscillations of the
soliton width. We show that, in some cases, the internal mode even can become
unstable, causing the soliton to decay in an antisoliton and two solitons. In
general, in the presence of spatiotemporal forces the soliton behaves as a
deformable (non-rigid) object. A soliton moving in an array of inhomogeneities
can also present sustained oscillations of its width. There are very important
phenomena (like the soliton-antisoliton collisions) where the existence of
internal modes plays a crucial role.


  The scalar and vectorial self energies obtained through QCD sum rules are
introduced in the Quantum Hadrodynamics (QHD) equations. This QHD and QCD
mixing show us that the effect of the density on the coupling constants is very
small.


  (ABRIDGED) We present a new Schwarzschild orbit-superposition code designed
to model discrete datasets composed of velocities of individual kinematic
tracers in a dynamical system. This constitutes an extension of previous
implementations that can only address continuous data in the form of (the
moments of) velocity distributions, thus avoiding potentially important losses
of information due to data binning. Furthermore, the code can handle any
combination of available velocity components, i.e., only line-of-sight
velocities, only proper motions, or a combination of both. It can also handle a
combination of discrete and continuous data. The code finds the distribution
function (DF, a function of the three integrals of motion E, Lz, and I3) that
best reproduces the available kinematic and photometric observations in a given
axisymmetric gravitational potential. The fully numerical approach ensures
considerable freedom on the form of the DF f(E,Lz,I3). This allows a very
general modeling of the orbital structure, thus avoiding restrictive
assumptions about the degree of (an)isotropy of the orbits. We describe the
implementation of the discrete code and present a series of tests of its
performance based on the modeling of simulated datasets generated from a known
DF. We find that the discrete Schwarzschild code recovers the original orbital
structure, M/L ratios, and inclination of the input datasets to satisfactory
accuracy, as quantified by various statistics. The code will be valuable, e.g.,
for modeling stellar motions in Galactic globular clusters, and those of
individual stars, planetary nebulae, or globular clusters in nearby galaxies.
This can shed new light on the total mass distributions of these systems, with
central black holes and dark matter halos being of particular interest.


  Two recently discovered very luminous supernovae (SNe) present stimulating
cases to explore the extents of the available theoretical models. SN 2011kl
represents the first detection of a supernova explosion associated with an
ultra-long duration gamma ray burst. ASASSN-15lh was even claimed as the most
luminous SN ever discovered, challenging the scenarios so far proposed for
stellar explosions. Here we use our radiation hydrodynamics code in order to
simulate magnetar powered SNe. To avoid explicitly assuming neutron star
properties we adopt the magnetar luminosity and spin-down timescale as free
parameters of the model. We find that the light curve (LC) of SN 2011kl is
consistent with a magnetar power source, as previously proposed, but we note
that some amount of 56^Ni (> 0.08 M_sun) is necessary to explain the low
contrast between the LC peak and tail. For the case of ASASSN-15lh we find
physically plausible magnetar parameters that reproduce the overall shape of
the LC provided the progenitor mass is relatively large (a mass of the ejecta
approx 6 M_sun). The ejecta hydrodynamics of this event is dominated by the
magnetar input, while the effect is more moderate for SN 2011kl. We conclude
that a magnetar model may be used for the interpretation of these events and
that the hydrodynamic modeling is necessary to derive the properties of
powerful magnetars and their progenitors.


  Let $X$ be a compact complex manifold which admits a hermitian metric
satisfying a curvature condition introduced by Guan-Li. Given a semipositive
form $\theta$ with positive volume, we define the Monge-Amp\`ere operator for
unbounded $\theta$-psh functions and prove that it is continuous with respect
to convergence in capacity. We then develop pluripotential tools to study
degenerate complex Monge-Amp\`ere equations in this context, extending recent
results of Tosatti-Weinkove, Kolodziej-Nguyen, Guedj-Lu and many others who
treat bounded solutions.


  We consider a cooperative multiplayer bandit learning problem where the
players are only allowed to agree on a strategy beforehand, but cannot
communicate during the learning process. In this problem, each player
simultaneously selects an action. Based on the actions selected by all players,
the team of players receives a reward. The actions of all the players are
commonly observed. However, each player receives a noisy version of the reward
which cannot be shared with other players. Since players receive potentially
different rewards, there is an asymmetry in the information used to select
their actions. In this paper, we provide an algorithm based on upper and lower
confidence bounds that the players can use to select their optimal actions
despite the asymmetry in the reward information. We show that this algorithm
can achieve logarithmic $O(\frac{\log T}{\Delta_{\bm{a}}})$ (gap-dependent)
regret as well as $O(\sqrt{T\log T})$ (gap-independent) regret. This is
asymptotically optimal in $T$. We also show that it performs empirically better
than the current state of the art algorithm for this environment.


  Previous critiques of the Drake Equation have highlighted its deterministic
nature, implying that the number of civilizations is the same at all times.
Here, I build upon earlier work and present a stochastic formulation. The birth
of civilizations within the galaxy is modeled as following a uniform rate
(Poisson) stochastic process, with a mean rate of $\lambda_C$. Each then
experiences a constant hazard rate of collapse, which defines an exponential
distribution with rate parameter $\lambda_L$. Thus, the galaxy is viewed as a
frothing landscape of civilization birth and collapse. Under these assumptions,
I show that N in the Drake Equation must follow another Poisson distribution,
with a mean rate $(\lambda_C/\lambda_L)$. This is then used to rigorously
demonstrate why the Copernican Principle does not allow one to infer N, as well
evaluating the algebraic probability of being alone in the galaxy.


  We study kink-antikink scattering in a one-parameter variant of the $\phi^4$
theory where the model parameter controls the static intersoliton force. We
interpolate between the limit of no static force (BPS limit) and the regime
where the static interaction is small (non-BPS). This allows us to study the
impact of the strength of the intersoliton static force on the soliton
dynamics.
  In particular, we analyze how the transition of a bound mode through the mass
threshold affects the soliton dynamics in a generic process, i.e., when a
static intersoliton force shows up. We show that the thin, precisely localized
spectral wall which forms in the limit of no static force, broadens in a
well-defined manner when a static force is included, giving rise to what we
will call a thick spectral wall. This phenomenon just requires that a discrete
mode crosses into the continuum at some intermediate stage of the dynamics and,
therefore, should be observable in many soliton-antisoliton collisions.


  The study of combinatorial games is intimately tied to the study of graphs,
as any game can be realized as a directed graph in which players take turns
traversing the edges until reaching a sink. However, there have heretofore been
few efforts towards analyzing game graphs using graph theoretic metrics and
techniques. A set $S$ of vertices in a graph $G$ resolves $G$ if every vertex
in $G$ is uniquely determined by the vector of its distances from the vertices
in $S$. A metric basis of $G$ is a smallest resolving set and the metric
dimension is the cardinality of a metric basis. In this article we examine the
metric dimension of the graphs resulting from some rulesets, including both
short games (those which are sure to end after finitely many turns) and loopy
games (those games for which the associated graph contains cycles).


  Class incremental learning approaches are useful as they help the model to
learn new information (classes) sequentially, while also retaining the
previously acquired information (classes). However, it has been shown that such
approaches are extremely vulnerable to the adversarial backdoor attacks, where
an intelligent adversary can introduce small amount of misinformation to the
model in the form of imperceptible backdoor pattern during training to cause
deliberate forgetting of a specific task or class at test time. In this work,
we propose a novel defensive framework to counter such an insidious attack
where, we use the attacker's primary strength-hiding the backdoor pattern by
making it imperceptible to humans-against it, and propose to learn a
perceptible (stronger) pattern (also during the training) that can overpower
the attacker's imperceptible (weaker) pattern. We demonstrate the effectiveness
of the proposed defensive mechanism through various commonly used Replay-based
(both generative and exact replay-based) class incremental learning algorithms
using continual learning benchmark variants of CIFAR-10, CIFAR-100, and MNIST
datasets. Most noteworthy, our proposed defensive framework does not assume
that the attacker's target task and target class is known to the defender. The
defender is also unaware of the shape, size, and location of the attacker's
pattern. We show that our proposed defensive framework considerably improves
the performance of class incremental learning algorithms with no knowledge of
the attacker's target task, attacker's target class, and attacker's
imperceptible pattern. We term our defensive framework as Adversary Aware
Continual Learning (AACL).


  We study the module of Koszul cycles $Z_t(I,M)$ of a homogeneous ideal $I$ in
a polynomial ring $S$ with respect to a graded module $M$. Under mild
assumptions on the base field we prove that the regularity of $Z_t(I,S)$ is a
subadditive function of the homological position t when I is 0-dimensional. For
Borel-fixed ideals $I$ and $J$ we prove that the regularity of $Z_t(I,S/J)$ is
bounded above by $t(1+\reg I)+\reg S/J$.


  The growth of the Internet and its associated technologies; including digital
services have tremendously impacted our society. However, scholars have noted a
trend in data flow and collection; and have alleged mass surveillance and
digital supremacy. To this end therefore, nations of the world such as Russia,
China, Germany, Canada, France and Brazil among others have taken steps toward
changing the narrative. The question now is, should Africans join these giants
in this school of thought on digital sovereignty or fold their hands to remain
on the other side of the divide? This question among others are the main
reasons that provoked the thoughts of putting this paper together. This is with
a view to demystifying the strategies to reconfigure data infrastructure in the
context of Africa. It also highlights the benefits of digital technologies and
its propensity to foster all round development in the continent as it relates
to economic face-lift, employment creation, national security, among others.
There is therefore a need for African nations to design appropriate blueprint
to ensure security of her digital infrastructure and the flow of data within
her cyber space. In addition, a roadmap in the immediate, short- and long-term
in accordance with the framework of African developmental goals should be put
in place to guide the implementation.