  The Human Genome Project (HGP) provides researchers with the data of nearly
all human genes and the challenge to use this information for elucidating the
etiology of common disorders. A secondary Darwinian method was applied to HGP
and other research data to approximate and possibly unravel the etiology of
schizophrenia. The results indicate that genetic and epigenetic variants of
genes involved in signal transduction, transcription and translation -
converging at the protein-synthesis rate (PSR) as common final pathway - might
be responsible for the genetic susceptibility to schizophrenia. Environmental
(e.g. viruses)and/or genetic factors can lead to cerebral PSR (CPSR)
deficiency. The CPSR hypothesis of schizophrenia and antipsychotic mechanism
explains 96% of the major facts of schizophrenia, reveals links between
previously unrelated facts, integrates many hypotheses, and implies that
schizophrenia should be easily preventable and treatable, partly by
immunization against neurotrophic viruses and partly by the development of new
drugs which selectively increase CPSR. Part of the manuscript has been
published in a modified form as "The glial growth factors deficiency and
synaptic destabilization hypothesis of schizophrenia" in BMC Psychiatry
available online at http://www.biomedcentral.com/1471-244X/2/8/


  We use former results on geometric local $\varepsilon$-factors over curves in
order to prove a factorization result for the determinant of the cohomology of
an $\ell$-adic sheaf over an arbitrary proper scheme over a perfect field of
positive characteristic $p$ distinct from $\ell$. The local contributions are
constructed by iterating vanishing cycle functors as well as certain "refined
Artin conductors", the latter being exact additive functors which can be
considered as linearized versions of Artin conductors and local
$\varepsilon$-factors. We provide several applications of our higher
dimensional product formula, such as twist formulas for global
$\varepsilon$-factors.


  Many matrices that arise in the solution of signal processing problems have a
special displacement structure. For example, adaptive filtering and
direction-of-arrival estimation yield matrices of Toeplitz type. A recent
method of Gohberg, Kailath and Olshevsky (GKO) allows fast Gaussian elimination
with partial pivoting for such structured matrices. In this paper, a rounding
error analysis is performed on the Cauchy and Toeplitz variants of the GKO
method. It is shown the error growth depends on the growth in certain auxiliary
vectors, the generators, which are computed by the GKO algorithms. It is also
shown that in certain circumstances, the growth in the generators can be large,
and so the error growth is much larger than would be encountered with normal
Gaussian elimination with partial pivoting. A modification of the algorithm to
perform a type of row-column pivoting is proposed; it may ameliorate this
problem.


  Superradiance and subradiance concerning enhanced and inhibited collective
radiation of an ensemble of atoms have been a central topic in quantum optics.
However, precise generation and control of these states remain challenging.
Here we deterministically generate up to 10-qubit superradiant and 8-qubit
subradiant states, each containing a single excitation, in a superconducting
quantum circuit with multiple qubits interconnected by a cavity resonator. The
$\sqrt{N}$-scaling enhancement of the coupling strength between the
superradiant states and the cavity is validated. By applying appropriate phase
gate on each qubit, we are able to switch the single collective excitation
between superradiant and subradiant states. While the subradiant states
containing a single excitation are forbidden from emitting photons, we
demonstrate that they can still absorb photons from the resonator. However, for
even number of qubits, a singlet state with half of the qubits being excited
can neither emit nor absorb photons, which is verified with 4 qubits. This
study is a step forward in coherent control of collective radiation and has
promising applications in quantum information processing.


  We describe an implicit prediction of the accretion disk models constructed
by Wardle and Konigl (1990) for the circumnuclear disk (CND) of gas and dust
near the Galactic center: supersonic ambipolar diffusion, an essential
dynamical ingredient of the Wardle-Konigl disks, will cause the alignment of
dust grains due to a process described by Roberge, Hanany, & Messinger (1995).
We calculate synthetic maps of the polarized thermal emission which would be
caused by ambipolar alignment in the preferred Wardle-Konigl model. Our maps
are in reasonable agreement with 100 micron polarimetry of the CND if we assume
that the grains have shapes similar to those of grains in nearby molecular
clouds and that the CND contains a disordered magnetic field in energy
equipartition with its ordered field.


  A quadrupole topological insulator, being one higher-order topological
insulator with nontrivial quadrupole quantization, has been intensely
investigated very recently. However, the tight-binding model proposed for such
emergent topological insulators demands both positive and negative hopping
coefficients, which imposes an obstacle in practical realizations. Here we
introduce a feasible approach to design the sign of hopping in acoustics, and
construct the first acoustic quadrupole topological insulator that stringently
emulates the tight-binding model. The inherent hierarchy quadrupole topology
has been experimentally confirmed by detecting the acoustic responses at the
bulk, edge and corner of the sample. Potential applications can be anticipated
for the topologically robust in-gap states, such as acoustic sensing and energy
trapping.


  There are currently two singularity-free universal expressions for the
topological susceptibility in QCD, one based on the Yang-Mills gradient flow
and the other on density-chain correlation functions. While the latter link the
susceptibility to the anomalous chiral Ward identities, the gradient flow
permits the emergence of the topological sectors in lattice QCD to be
understood. Here the two expressions are shown to coincide in the continuum
theory, for any number of quark flavours in the range where the theory is
asymptotically free.


  We discuss the ill-posed Cauchy problem for elliptic equations, which is
pervasive in inverse boundary value problems modeled by elliptic equations. We
provide essentially optimal stability results, in wide generality and under
substantially minimal assumptions. As a general scheme in our arguments, we
show that all such stability results can be derived by the use of a single
building brick, the three-spheres inequality.


  Let $A$ be an abelian variety over a $p$-adic field $K$ and $L$ an algebraic
infinite extension over $K$. We consider the finiteness of the torsion part of
the group of rational points $A(L)$ under some assumptions. In 1975, Hideo Imai
proved that such a group is finite if $A$ has good reduction and $L$ is the
cyclotomic $\mathbb{Z}_p$-extension of $K$. In this talk, first we show a
generalization of Imai's result in the case where $A$ has ordinary good
reduction. Next we give some finiteness results when $A$ is an elliptic curve
and $L$ is the field generated by the $p$-power torsion of an elliptic curve.


  Quasicrystals exhibit long-range order but lack translational symmetry. When
grown as single crystals, they possess distinctive and unusual properties owing
to the absence of grain boundaries. Unfortunately, conventional methods such as
bulk crystal growth or thin film deposition only allow us to synthesize either
polycrystalline quasicrystals or quasicrystals that are at most a few
centimeters in size. Here, we reveal through real-time and 3D imaging the
formation of a single decagonal quasicrystal arising from a hard collision
between multiple growing quasicrystals in an Al-Co-Ni liquid. Through
corresponding molecular dynamics simulations, we examine the underlying
kinetics of quasicrystal coalescence and investigate the effects of initial
misorientation between the growing quasicrystalline grains on the formation of
grain boundaries. At small misorientation, coalescence occurs following rigid
rotation that is facilitated by phasons. Our joint experimental-computational
discovery paves the way toward fabrication of single, large-scale quasicrystals
for novel applications.


  A generalized continuity equation extending the ordinary continuity equation
has been found using quanternions. It is shown to be compatible with Dirac,
Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is
Lorentz invariant. The transport properties of electrons are found to be
governed by Schrodinger-like equation and not by the diffusion equation.


  We prove that for every $T_0$ space $X$, there is a well-filtered space
$W(X)$ and a continuous mapping $\eta_X: X\lra W(X)$ such that for any
well-filtered space $Y$ and any continuous mapping $f: X\lra Y$ there is a
unique continuous mapping $\hat{f}: W(X)\lra Y$ such that $f=\hat{f}\circ
\eta_X$. Such a space $W(X)$ will be called the well-filterification of $X$.
This result gives a positive answer to one of the major open problems on
well-filtered spaces. Another result on well-filtered spaces we will prove is
that the product of two well-filtered spaces is well-filtered.


  Pseudorange errors are the root cause of localization inaccuracy in GPS.
Previous data-driven methods regress and eliminate pseudorange errors using
handcrafted intermediate labels. Unlike them, we propose an end-to-end GPS
localization framework, E2E-PrNet, to train a neural network for pseudorange
correction (PrNet) directly using the final task loss calculated with the
ground truth of GPS receiver states. The gradients of the loss with respect to
learnable parameters are backpropagated through a differentiable nonlinear
least squares optimizer to PrNet. The feasibility is verified with GPS data
collected by Android phones, showing that E2E-PrNet outperforms the
state-of-the-art end-to-end GPS localization methods.


  Significant insights for critical current density (Jc) improvement in Bi-2212
super- conductor wires can be obtained by an accurate analysis of the
structural and mi- crostructural properties evolving during the so-called
partial-melt process, a heat treatment needed to improve grain connectivity and
therefore gain high Jc. Here, we report an in-situ analysis by means of
synchrotron X-ray and neutron diffraction performed, for the first time, during
the heat treatment carried out with the very same temperature profile and
reacting oxygen atmosphere in which the Bi-2212 wires are usually treated for
practical applications. The obtained results show the thermal evolution of the
Bi-2212 structure, focusing in particular on texturing and secondary phases
formation. The role of the oxygen is discussed as well. Hence, the present
investigation marks a significant advance for the comprehension of the
phenomena involved in the wire fabrication process and provides useful insights
for the process optimization as well.


  We review the use of the path integral Monte Carlo (PIMC) methodology to the
study of finite-size quantum clusters, with particular emphasis on recent
applications to pure and impurity-doped He clusters. We describe the principles
of PIMC, the use of the multilevel Metropolis method for sampling particle
permutations, and the methods used to accurately incorporate anisotropic
molecule-helium interactions into the path integral scheme. Applications to
spectroscopic studies of embedded atoms and molecules are summarized, with
discussion of the new concepts of local and nanoscale superfluidity that have
been generated by recent PIMC studies of the impurity-doped He clusters.


  In general, the solution to a regression problem is the minimizer of a given
loss criterion, and depends on the specified loss function. The nonparametric
isotonic regression problem is special, in that optimal solutions can be found
by solely specifying a functional. These solutions will then be minimizers
under all loss functions simultaneously as long as the loss functions have the
requested functional as the Bayes act. For the functional, the only requirement
is that it can be defined via an identification function, with examples
including the expectation, quantile, and expectile functionals. Generalizing
classical results, we characterize the optimal solutions to the isotonic
regression problem for such functionals, and extend the results from the case
of totally ordered explanatory variables to partial orders. For total orders,
we show that any solution resulting from the pool-adjacent-violators algorithm
is optimal. It is noteworthy, that simultaneous optimality is unattainable in
the unimodal regression problem, despite its close connection.


  A curious property of randomized log-space search algorithms is that their
outputs are often longer than their workspace. This leads to the question: how
can we reproduce the results of a randomized log space computation without
storing the output or randomness verbatim? Running the algorithm again with new
random bits may result in a new (and potentially different) output.
  We show that every problem in search-RL has a randomized log-space algorithm
where the output can be reproduced. Specifically, we show that for every
problem in search-RL, there are a pair of log-space randomized algorithms A and
B where for every input x, A will output some string t_x of size O(log n), such
that B when running on (x, t_x) will be pseudo-deterministic: that is, running
B multiple times on the same input (x, t_x) will result in the same output on
all executions with high probability. Thus, by storing only O(log n) bits in
memory, it is possible to reproduce the output of a randomized log-space
algorithm.
  An algorithm is reproducible without storing any bits in memory (i.e.,
|t_x|=0) if and only if it is pseudo-deterministic. We show
pseudo-deterministic algorithms for finding paths in undirected graphs and
Eulerian graphs using logarithmic space. Our algorithms are substantially
faster than the best known deterministic algorithms for finding paths in such
graphs in log-space.
  The algorithm for search-RL has the additional property that its output, when
viewed as a random variable depending on the randomness used by the algorithm,
has entropy O(log n).


  In recent years fairness in machine learning (ML) has emerged as a highly
active area of research and development. Most define fairness in simple terms,
where fairness means reducing gaps in performance or outcomes between
demographic groups while preserving as much of the accuracy of the original
system as possible. This oversimplification of equality through fairness
measures is troubling. Many current fairness measures suffer from both fairness
and performance degradation, or "levelling down," where fairness is achieved by
making every group worse off, or by bringing better performing groups down to
the level of the worst off. When fairness can only be achieved by making
everyone worse off in material or relational terms through injuries of stigma,
loss of solidarity, unequal concern, and missed opportunities for substantive
equality, something would appear to have gone wrong in translating the vague
concept of 'fairness' into practice. This paper examines the causes and
prevalence of levelling down across fairML, and explore possible justifications
and criticisms based on philosophical and legal theories of equality and
distributive justice, as well as equality law jurisprudence. We find that
fairML does not currently engage in the type of measurement, reporting, or
analysis necessary to justify levelling down in practice. We propose a first
step towards substantive equality in fairML: "levelling up" systems by design
through enforcement of minimum acceptable harm thresholds, or "minimum rate
constraints," as fairness constraints. We likewise propose an alternative
harms-based framework to counter the oversimplified egalitarian framing
currently dominant in the field and push future discussion more towards
substantive equality opportunities and away from strict egalitarianism by
default. N.B. Shortened abstract, see paper for full abstract.


  People with some kind of disability face a high level of difficulty for
everyday tasks because, in many cases, accessibility was not considered
necessary when the task or process was designed. An example of this scenario is
a computer's BIOS configuration screens, which do not consider the specific
needs, such as screen readers, of visually impaired people. This paper proposes
the idea that it is possible to make the pre-operating system environment
accessible to visually impaired people. We report our work-in-progress in
creating a screen reader prototype, accessing audio cards compatible with the
High Definition Audio specification in systems running UEFI compliant firmware.


  The Numerical Renormalization Group method (NRG) has been developed by Wilson
in the 1970's to investigate the Kondo problem. The NRG allows the
non-perturbative calculation of static and dynamic properties for a variety of
impurity models. In addition, this method has been recently generalized to
lattice models within the Dynamical Mean Field Theory. This paper gives a brief
historical overview of the development of the NRG and discusses its application
to the Hubbard model; in particular the results for the Mott metal-insulator
transition at low temperatures.


  In this paper, we study the maximum loads of explicit hash families in the
$d$-choice schemes when allocating sequentially $n$ balls into $n$ bins. We
consider the \emph{Uniform-Greedy} scheme, which provides $d$ independent bins
for each ball and places the ball into the bin with the least load, and its
non-uniform variant --- the \emph{Always-Go-Left} scheme introduced by
V\"ocking. We construct a hash family with $O(\log n \log \log n)$ random bits
based on the previous work of Celis et al. and show the following results.
  1. With high probability, this hash family has a maximum load of $\frac{\log
\log n}{\log d} + O(1)$ in the \emph{Uniform-Greedy} scheme.
  2. With high probability, it has a maximum load of $\frac{\log \log n}{d \log
\phi_d} + O(1)$ in the \emph{Always-Go-Left} scheme for a constant
$\phi_d>1.61$.
  The maximum loads of our hash family match the maximum loads of a perfectly
random hash function in the \emph{Uniform-Greedy} and \emph{Always-Go-Left}
scheme separately, up to the low order term of constants. Previously, the best
known hash families matching the same maximum loads of a perfectly random hash
function in $d$-choice schemes were $O(\log n)$-wise independent functions,
which needs $\Theta(\log^2 n)$ random bits.


  At a quantum critical point (QCP) -- a zero-temperature singularity in which
a line of continuous phase transition terminates -- quantum fluctuations
diverge in space and time, leading to exotic phenomena that can be observed at
non-zero temperatures. Using a quantum antiferromagnet, we present calorimetric
evidence that nuclear spins frozen in a high-temperature metastable state by
temperature quenching are annealed by quantum fluctuations near the QCP. This
phenomenon, with readily detectable heat release from the nuclear spins as they
are annealed, serves as an excellent marker of a quantum critical region around
the QCP and provides a probe of the dynamics of the divergent quantum
fluctuations.


  Model-based reinforcement learning is an appealing framework for creating
agents that learn, plan, and act in sequential environments. Model-based
algorithms typically involve learning a transition model that takes a state and
an action and outputs the next state---a one-step model. This model can be
composed with itself to enable predicting multiple steps into the future, but
one-step prediction errors can get magnified, leading to unacceptable
inaccuracy. This compounding-error problem plagues planning and undermines
model-based reinforcement learning. In this paper, we address the
compounding-error problem by introducing a multi-step model that directly
outputs the outcome of executing a sequence of actions. Novel theoretical and
empirical results indicate that the multi-step model is more conducive to
efficient value-function estimation, and it yields better action selection
compared to the one-step model. These results make a strong case for using
multi-step models in the context of model-based reinforcement learning.


  Recent research has demonstrated the ability to estimate gaze on mobile
devices by performing inference on the image from the phone's front-facing
camera, and without requiring specialized hardware. While this offers wide
potential applications such as in human-computer interaction, medical diagnosis
and accessibility (e.g., hands free gaze as input for patients with motor
disorders), current methods are limited as they rely on collecting data from
real users, which is a tedious and expensive process that is hard to scale
across devices. There have been some attempts to synthesize eye region data
using 3D models that can simulate various head poses and camera settings,
however these lack in realism.
  In this paper, we improve upon a recently suggested method, and propose a
generative adversarial framework to generate a large dataset of high resolution
colorful images with high diversity (e.g., in subjects, head pose, camera
settings) and realism, while simultaneously preserving the accuracy of gaze
labels. The proposed approach operates on extended regions of the eye, and even
completes missing parts of the image. Using this rich synthesized dataset, and
without using any additional training data from real users, we demonstrate
improvements over state-of-the-art for estimating 2D gaze position on mobile
devices. We further demonstrate cross-device generalization of model
performance, as well as improved robustness to diverse head pose, blur and
distance.


  We consider a class of stochastic evolution equations that include in
particular the stochastic Camassa--Holm equation. For the initial value problem
on a torus, we first establish the local existence and uniqueness of pathwise
solutions in the Sobolev spaces $H^s$ with $s>3/2$. Then we show that strong
enough nonlinear noise can prevent blow-up almost surely. To analyze the
effects of weaker noise, we consider a linearly multiplicative noise with
non-autonomous pre-factor. Then, we formulate precise conditions on the inital
data that lead to global existence of strong solutions or to blow-up. The
blow-up occurs as wave breaking. For blow-up with positive probability, we
derive lower bounds for these probabilities. Finally, the blow-up rate of these
solutions is precisely analyzed.


  It is shown that the minimal Higgs sector of a generic N=2 supergravity
theory with unbroken N=1 supersymmetry must contain a Higgs hypermultiplet and
a vector multiplet. When the multiplets parametrize the quaternionic manifold
SO(4,1)/SO(4), and the special Kahler manifold SU(1,1)/U(1), respectively, a
vanishing vacuum energy with a sliding massive spin 3/2 multiplet is obtained.
Potential applications to N=2 low energy effective actions of superstrings are
briefly discussed.


  A subgroup of the automorphism group of a graph acts {\em
half-arc-transitively} on the graph if it acts transitively on the vertex-set
and on the edge-set of the graph but not on the arc-set of the graph. If the
full automorphism group of the graph acts half-arc-transitively, the graph is
said to be {\em half-arc-transitive}.
  In 1994 Gardiner and Praeger introduced two families of tetravalent
arc-transitive graphs, called the $C^{\pm 1}$ and the $C^{\pm \varepsilon}$
graphs, that play a prominent role in the characterization of the tetravalent
graphs admitting an arc-transitive group of automorphisms with a normal
elementary abelian subgroup such that the corresponding quotient graph is a
cycle. All of the Gardiner-Praeger graphs are arc-transitive but admit a
half-arc-transitive group of automorphisms. Quite recently, Poto\v cnik and
Wilson introduced the family of CPM graphs, which are generalizations of the
Gardiner-Praeger graphs. Most of these graphs are arc-transitive, but some of
them are half-arc-transitive. In fact, at least up to order $1000$, each
tetravalent half-arc-transitive loosely-attached graph of odd radius having
vertex-stabilizers of order greater than $2$ is isomorphic to a CPM graph.
  In this paper we determine the automorphism group of the CPM graphs and
investigate isomorphisms between them. Moreover, we determine which of these
graphs are $2$-arc-transitive, which are arc-transitive but not
$2$-arc-transitive, and which are half-arc-transitive.


  The secant varieties of Severi varieties provide special examples of
(singular) cubic hypersurfaces. An interesting question asks when a given cubic
hypersurface is projectively equivalent to a secant cubic hypersurface.
Inspired by the ''geometric'' Torelli theorem for smooth cubic hypersurfaces
due to F. Charles, we study the geometry of lines on secant cubics and describe
the Fano variety of lines. Then we verify the ''geometric'' Torelli theorem for
the case of secant cubics. Namely, a cubic hypersurface is isomorphic to a
secant cubic if and only if their Fano varieties of lines are isomorphic.


  Understanding the physics of phase transitions in two-dimensional (2D)
systems underpins the research in diverse fields including statistical
mechanics, quantum systems, nanomagnetism, and soft condensed matter. However,
many fundamental aspects of 2D phase transitions are still not well understood,
including the effects of interparticle potential, polydispersity, and particle
shape. Magnetic skyrmions, which are non-trivial chiral spin structures, can be
considered as quasi-particles that form two-dimensional lattices. Here we show,
by real-space imaging using in situ cryo-Lorentz transmission electron
microscopy coupled with machine learning, the ordering behavior of N\'eel
skyrmion lattices in van der Waals Fe3GeTe2. We demonstrate a distinct change
in the skyrmion size distribution during field-cooling, which leads to a loss
of lattice order and an evolution of the skyrmion liquid phase. Remarkably, the
lattice order is restored during field heating and demonstrates a thermal
hysteresis. Our quantitative analysis explains this behavior based on the
energy landscape of skyrmions and demonstrates the potential to control the
lattice order in 2D phase transitions.


  The yield of the $^{16}$O$(\gamma ,\pi^{+} p)$ reaction has been measured in
the region of the excitation of the $\Delta(1232)$ isobar at high momentum
transfers to the residual nuclear system. The experimental data are interpreted
within the model taking into account of isobar configurations in the ground
state of the $^{16}$O nucleus. Direct and exchange mechanisms of the production
of pions with emission of one and two nucleons, which follow from the
structures of the density matrices for these reactions, have been considered.
The probability of the production of the $\Delta$ isobar in the ground state of
the $^{16}$O nucleus has been empirically estimated as $P_ {\Delta} = 0.019 \pm
0.003 \pm 0.003$.


  We present novel statistical tools to cross-correlate frequency cleaned
thermal Sunyaev-Zel'dovich (tSZ) maps and tomographic weak lensing (wl)
convergence maps. Moving beyond the lowest order cross-correlation, we
introduce a hierarchy of mixed higher-order statistics, the cumulants and
cumulant correlators, to analyze non-Gaussianity in real space, as well as
corresponding polyspectra in the harmonic domain. Using these moments, we
derive analytical expressions for the joint two-point probability distribution
function (2PDF) for smoothed tSZ (y_s) and convergence (\kappa_s) maps. The
presence of tomographic information allows us to study the evolution of higher
order {\em mixed} tSZ-weak lensing statistics with redshift. We express the
joint PDFs p_{\kappa y}(\kappa_s,y_s) in terms of individual one-point PDFs
(p_{\kappa}(\kappa_s), p_y(y_s)) and the relevant bias functions
(b_{\kappa}(\kappa_s), b_y(y_s)). Analytical results for two different regimes
are presented that correspond to the small and large angular smoothing scales.
Results are also obtained for corresponding {\em hot spots} in the tSZ and
convergence maps. In addition to results based on hierarchical techniques and
perturbative methods, we present results of calculations based on the lognormal
approximation. The analytical expressions derived here are generic and
applicable to cross-correlation studies of arbitrary tracers of large scale
structure including e.g. that of tSZ and soft X-ray background.


  In this work, we present our generic framework to construct, simulate, and
calibrate dynamical systems in Python 3. Its goal is to reduce the time it
takes to implement a dynamical system with $n$-dimensional states represented
by coupled ordinary differential equations (ODEs), simulate the system
deterministically or stochastically, and, calibrate the system using
n-dimensional data. We demonstrate our code's capabilities by building three
models in the context of two case studies. First, we forecast the yields of the
enzymatic esterification reaction of D-glucose and lauric acid, performed in a
continuous-flow, packed-bed reactor. The model yields a satisfactory
description of the reaction yields under different flow rates and can be
applied to design a viable process. Second, we build a stochastic,
age-stratified model to make forecasts on the evolution of influenza in Belgium
during the 2017-2018 season. Using only limited data, our simple model was able
to make a fairly accurate assessment of the future course of the epidemic. By
presenting real-world case studies from two scientific disciplines, we
demonstrate our code's applicability across domains.


  We consider the three-dimensional Dirac equation in spherical coordinates
with coupling to static electromagnetic potential. The space components of the
potential have angular (non-central) dependence such that the Dirac equation is
separable in all coordinates. We obtain exact solutions for the case where the
potential satisfies the Lorentz gauge fixing condition and its time component
is the Coulomb potential. The relativistic energy spectrum and corresponding
spinor wavefunctions are obtained. The Aharonov-Bohm and magnetic monopole
potentials are included in these solutions. The conventional relativistic
units, $\hbar$ = c = 1, are used.


  In this work, we apply self-supervised learning with instance differentiation
to learn a robust, multi-purpose representation for image analysis of resolved
extragalactic continuum images. We train a multi-use model which compresses our
unlabelled data into a structured, low dimensional representation which can be
used for a variety of downstream tasks (e.g. classification, similarity
search). We exceed baseline supervised Fanaroff-Riley classification
performance by a statistically significant margin, with our model reducing the
test set error by up to half. Our model is also able to maintain high
classification accuracy with very few labels, with only 7.79% error when only
using 145 labels. We further demonstrate that by using our foundation model,
users can efficiently trade off compute, human labelling cost and test set
accuracy according to their respective budgets, allowing for efficient
classification in a wide variety of scenarios. We highlight the
generalizability of our model by showing that it enables accurate
classification in a label scarce regime with data from the new MIGHTEE survey
without any hyper-parameter tuning, where it improves upon the baseline by ~8%.
Visualizations of our labelled and un-labelled data show that our model's
representation space is structured with respect to physical properties of the
sources, such as angular source extent. We show that the learned representation
is scientifically useful even if no labels are available by performing a
similarity search, finding hybrid sources in the RGZ DR1 data-set without any
labels. We show that good augmentation design and hyper-parameter choice can
help achieve peak performance, while emphasising that optimal hyper-parameters
are not required to obtain benefits from self-supervised pre-training.


  Experimental data on fragmentation channels in peripheral interactions of
$^8$B nuclei in nuclear track emulsions are presented. A detailed analysis made
it possible to justify selections of events of the electromagnetic-dissociation
process $^8$B $\to^7$Be + \emph{p} and to estimate its cross section. Events of
$^{10}$C peripheral dissociation that were observed in the same exposure are
described.


  We report on the broadband transient optical response from anisotropic
nanobrick amorphous silicon particles, exhibiting Mie-type resonances. A
quantitative model is developed to identify and disentangle the three physical
processes that govern the ultrafast changes of the nanobrick optical
properties, namely two-photon absorption, free-carrier relaxation, and lattice
heating. We reveal a set of operating windows where ultrafast all-optical
modulation of transmission is achieved with full return to zero in 20 ps. This
is made possible due to the interplay between the competing nonlinear processes
and despite the slow (nanosecond) internal lattice dynamics. The observed
ultrafast switching behavior can be independently engineered for both or-
thogonal polarizations using the large anisotropy of nanobricks thus allowing
ultrafast anisotropy control. Our results categorically ascertain the potential
of all-dielectric resonant nanophotonics as a platform for ultrafast optical
devices, and reveal the pos- sibility for ultrafast polarization-multiplexed
displays and polarization rotators.


  The nonlinear wave and Schrodinger equations on Euclidean space of any
dimension, with general power nonlinearity and with both the focusing and
defocusing signs, are proved to be ill-posed in the Sobolev space of index s
whenever the exponent s is lower than that predicted by scaling or Galilean
invariances, or when the regularity is too low to support distributional
solutions. This extends previous work of the authors, which treated the
one-dimensional cubic nonlinear Schrodinger equation. In the defocusing case
soliton or blowup examples are unavailable, and a proof of ill-posedness
requires the construction of other solutions. In earlier work this was achieved
using certain long-time asymptotic behavior which occurs only for low power
nonlinearities. Here we analyze instead a class of solutions for which the
zero-dispersion limit provides a good approximation.


  In this paper we study the asymptotic behavior of the principal eigenvalues
associated to the Pucci operator in bounded domain $\Omega$ with Neumann/Robin
boundary condition i.e. $\partial_n u=\alpha u$ when $\alpha$ tends to
infinity. This study requires Lipschitz estimates up to the boundary that are
interesting in their own rights.


  Autonomous nano-drones (~10 cm in diameter), thanks to their ultra-low power
TinyML-based brains, are capable of coping with real-world environments.
However, due to their simplified sensors and compute units, they are still far
from the sense-and-act capabilities shown in their bigger counterparts. This
system paper presents a novel deep learning-based pipeline that fuses
multi-sensorial input (i.e., low-resolution images and 8x8 depth map) with the
robot's state information to tackle a human pose estimation task. Thanks to our
design, the proposed system -- trained in simulation and tested on a real-world
dataset -- improves a state-unaware State-of-the-Art baseline by increasing the
R^2 regression metric up to 0.10 on the distance's prediction.


  Artificial intelligence is being utilized in many domains as of late, and the
legal system is no exception. However, as it stands now, the number of
well-annotated datasets pertaining to legal documents from the Supreme Court of
the United States (SCOTUS) is very limited for public use. Even though the
Supreme Court rulings are public domain knowledge, trying to do meaningful work
with them becomes a much greater task due to the need to manually gather and
process that data from scratch each time. Hence, our goal is to create a
high-quality dataset of SCOTUS court cases so that they may be readily used in
natural language processing (NLP) research and other data-driven applications.
Additionally, recent advances in NLP provide us with the tools to build
predictive models that can be used to reveal patterns that influence court
decisions. By using advanced NLP algorithms to analyze previous court cases,
the trained models are able to predict and classify a court's judgment given
the case's facts from the plaintiff and the defendant in textual format; in
other words, the model is emulating a human jury by generating a final verdict.


  Accurate and efficient models for rainfall runoff (RR) simulations are
crucial for flood risk management. Most rainfall models in use today are
process-driven; i.e. they solve either simplified empirical formulas or some
variation of the St. Venant (shallow water) equations. With the development of
machine-learning techniques, we may now be able to emulate rainfall models
using, for example, neural networks. In this study, a data-driven RR model
using a sequence-to-sequence Long-short-Term-Memory (LSTM) network was
constructed. The model was tested for a watershed in Houston, TX, known for
severe flood events. The LSTM network's capability in learning long-term
dependencies between the input and output of the network allowed modeling RR
with high resolution in time (15 minutes). Using 10-years precipitation from
153 rainfall gages and river channel discharge data (more than 5.3 million data
points), and by designing several numerical tests the developed model
performance in predicting river discharge was tested. The model results were
also compared with the output of a process-driven model Gridded Surface
Subsurface Hydrologic Analysis (GSSHA). Moreover, physical consistency of the
LSTM model was explored. The model results showed that the LSTM model was able
to efficiently predict discharge and achieve good model performance. When
compared to GSSHA, the data-driven model was more efficient and robust in terms
of prediction and calibration. Interestingly, the performance of the LSTM model
improved (test Nash-Sutcliffe model efficiency from 0.666 to 0.942) when a
selected subset of rainfall gages based on the model performance, were used as
input instead of all rainfall gages.


  Firstly, we generalize a semi-classical limit of open strings on D-branes in
group manifolds. The limit gives rise to rigid open strings, whose dynamics can
efficiently be described in terms of a matrix algebra. Alternatively, the
dynamics is coded in group theory coefficients whose properties are translated
in a diagrammatical language. In the case of compact groups, it is a simplified
version of rational boundary conformal field theories, while for non-compact
groups, the construction gives rise to new associative products. Secondly, we
argue that the intuitive formalism that we provide for the semi-classical
limit, extends to the case of quantum groups. The associative product we
construct in this way is directly related to the boundary vertex operator
algebra of open strings on symmetry preserving branes in WZW models, and
generalizations thereof, e.g. to non-compact groups. We treat the groups SU(2)
and SL(2,R) explicitly. We also discuss the precise relation of the
semi-classical open string dynamics to Berezin quantization and to star product
theory.


  The imbalance of an edge $e=\{u,v\}$ in a graph is defined as
$i(e)=|d(u)-d(v)|$, where $d(\cdot)$ is the vertex degree. The irregularity
$I(G)$ of $G$ is then defined as the sum of imbalances over all edges of $G$.
This concept was introduced by Albertson who proved that $I(G) \leq
\frac{n^{3}}{27}$ (where $n=|V(G)|$) and obtained stronger bounds for bipartite
and triangle-free graphs. Since then a number of additional bounds were given
by various authors. In this paper we prove a new upper bound, which improves a
bound found by Zhou and Luo in 2011. Our bound involves the Laplacian spectral
radius $\lambda$.


  Using density functional perturbation theory (DFPT) we computed the phonon
frequencies, Raman and IR activities of hafnia polymorphs (P4$_{2}$nmc,
Pca2$_{1}$, Pmn2$_{1}$, Pbca OI, brookite, and baddeleyite) for phase
identification. We investigated the evolution of Raman and IR activities with
respect to epitaxial strain and provide plots of frequency differences as a
function of strain for experimental calibration and identification of the
strain state of the sample. We found Raman signatures of different hafnia
polymorphs: $\omega(A_{1g})=300$ cm$^{-1}$ for P4$_{2}$nmc, $\omega(A_{1})=343$
cm$^{-1}$ for Pca2$_{1}$, $\omega(B_{2})=693$ cm$^{-1}$ for Pmn2$_{1}$,
$\omega(A_{g})=513$ cm$^{-1}$ for Pbca (OI), $\omega(A_{g})=384$ cm$^{-1}$ for
brookite, and $\omega (A_{g}) = 496$ cm$^{-1}$ for baddeleyite. We also
identified the Raman $B_{1g}$ mode, an anti-phase vibration of dipole moments,
( $\omega(B_{1g}) = 758$ cm$^{-1}$ for OI, $\omega (B_{1g})= 784$ cm$^{-1}$ for
brookite) as the Raman signature of antipolar Pbca structures. We calculated a
large splitting between longitudinal optical (LO) and transverse optical (TO)
modes ($\Delta{\omega_{\text{LO-TO}}(A^{z}_{1})}=255$ cm$^{-1}$ in Pca2$_{1}$,
and $\Delta{\omega_{\text{LO-TO}}(A_{1})}=263$ cm$^{-1}$ in Pmn2$_{1}$) to the
same order as those observed in perovskite ferroelectrics, and related them to
the anomalously large Born effective charges of Hf atoms ($Z^{*}(\text{Hf}) =
5.54$).


  This paper explores the application of the multiscale finite element method
(MsFEM) to address steady-state Stokes-Darcy problems with BJS interface
conditions in highly heterogeneous porous media. We assume the existence of
multiscale features in the Darcy region and propose an algorithm for the
multiscale Stokes-Darcy model. During the offline phase, we employ MsFEM to
construct permeability-dependent offline bases for efficient coarse-grid
simulation, with this process conducted in parallel to enhance its efficiency.
In the online phase, we use the Robin-Robin algorithm to derive the model's
solution. Subsequently, we conduct error analysis based on $L^2$ and $H^1$
norms, assuming certain periodic coefficients in the Darcy region. To validate
our approach, we present extensive numerical tests on highly heterogeneous
media, illustrating the results of the error analysis.


  I review various ideas on MOND cosmology and structure formation beginning
with non-relativistic models in analogy with Newtonian cosmology. I discuss
relativistic MOND cosmology in the context of Bekenstein's theory and propose
an alternative biscalar effective theory of MOND in which the acceleration
parameter is identified with the cosmic time derivative of a matter coupling
scalar field. Cosmic CDM appears in this theory as scalar field oscillations of
the auxiliary "coupling strength" field.


  Human society is an open system that evolves by coupling with various known
and unknown (energy) fluxes. How do these dynamics precisely unfold? Energetics
may provide further insights. We expand on Navier Stokes' approach to study
non-equilibrium dynamics in a field that evolves with time. Based on the social
field theory, an induction of the classical field theories, we define social
force, social energy and Hamiltonian of an individual in a society. The
equations for the evolution of an individual and society are sketched based on
the time-dependent Hamiltonian that includes power dynamics. In this paper, we
will demonstrate that Lotka-Volterra type equations can be derived from the
Hamiltonian equation in the social field.


  This paper investigates the utility of the weighted Birkhoff average (WBA)
for distinguishing between regular and chaotic orbits of flows, extending
previous results that applied the WBA to maps. It is shown that the WBA can be
super-convergent for flows when the dynamics and phase space function are
smooth, and the dynamics is conjugate to a rigid rotation with Diophantine
rotation vector. The dependence of the accuracy of the average on orbit length
and width of the weight function width are investigated. In practice, the
average achieves machine precision of the rotation frequency of quasiperiodic
orbits for an integration time of O(10^3) periods. The contrasting, relatively
slow convergence for chaotic trajectories allows an efficient discrimination
criterion. Three example systems are studied: a two-wave Hamiltonian system, a
quasiperiodically forced, dissipative system that has a strange attractor with
no positive Lyapunov exponents, and a model for magnetic field line flow.


  We revise imposition of various constraints in spin foam models of
4-dimensional general relativity. We argue that the usual simplicity constraint
must be supplemented by a constraint on holonomies and together they must be
inserted explicitly into the discretized path integral. At the same time, the
closure constraint must be relaxed so that the new constraint expresses
covariance of intertwiners assigned to tetrahedra by spin foam quantization. As
a result, the spin foam boundary states are shown to be realized in terms of
projected spin networks of the covariant loop approach to quantum gravity.


  The last two decades witnessed tremendous advances in the Information and
Communications Technologies. Beside improvements in computational power and
storage capacity, communication networks carry nowadays an amount of data which
was not envisaged only few years ago. Together with their pervasiveness,
network complexity increased at the same pace, leaving operators and
researchers with few instruments to understand what happens in the networks,
and, on the global scale, on the Internet. Fortunately, recent advances in data
science and machine learning come to the rescue of network analysts, and allow
analyses with a level of complexity and spatial/temporal scope not possible
only 10 years ago. In my thesis, I take the perspective of an Internet Service
Provider (ISP), and illustrate challenges and possibilities of analyzing the
traffic coming from modern operational networks. I make use of big data and
machine learning algorithms, and apply them to datasets coming from passive
measurements of ISP and University Campus networks. The marriage between data
science and network measurements is complicated by the complexity of machine
learning algorithms, and by the intrinsic multi-dimensionality and variability
of this kind of data. As such, my work proposes and evaluates novel techniques,
inspired from popular machine learning approaches, but carefully tailored to
operate with network traffic.


  The self consistent version of the density functional theory (DFT) is
presented, which allows to calculate the ground state and dynamic properties of
finite multi-electron systems such as atoms, molecules and clusters. The exact
functional equation for the effective interaction, using which one can
construct the action functional, density functional, the response functions,
and excitation spectra of the considered systems, are discussed. We have also
related the eigenvalues of the single-particle Kohn-Sham equations to the real
single-particle spectra. We begin with the standard action functional and show
that it is useful in calculating the linear response functions via which all
physical characteristics of a many-body system can be expressed. It is shown,
that function can be causal (retarded), noncausal and advanced ones. This
resolves the well known paradox related to the causality and symmetry
properties of the response functions and the effective interaction.


  Energetic H$_2^+$ ions are formed as a result of intra-molecular
rearrangement during fragmentation of linear alcohols (methanol, ethanol,
propanol, hexanol, and dodecanol) induced by intense optical fields produced by
100 fs long, infrared, laser pulses of peak intensity 8$\times10^{15}$ W
cm$^{-2}$. Polarization dependent measurements show, counterintuitively, that
rearrangement is induced by the strong optical field within a single laser
pulse, and that it occurs before Coulomb explosion of the field-ionized
multiply charged alcohols.


  Graph randomization techniques play a crucial role in network analysis,
allowing researchers to assess the statistical significance of observed network
properties and distinguish meaningful patterns from random fluctuations. In
this survey we provide an overview of the graph randomization methods available
in the most popular software tools for network analysis. We propose a
comparative analysis of popular software tools to highlight their
functionalities and limitations. Through case studies involving diverse graph
types, we demonstrate how different randomization methods can lead to divergent
conclusions, emphasizing the importance of careful method selection based on
the characteristics of the observed network and the research question at hand.
This survey proposes some guidelines for researchers and practitioners seeking
to understand and utilize graph randomization techniques effectively in their
network analysis projects.


  A covering system is a finite collection of arithmetic progressions whose
union is the set of integers. The study of covering systems with distinct
moduli was initiated by Erd\H{o}s in 1950, and over the following decades
numerous problems were posed regarding their properties. One particularly
notorious question, due to Erd\H{o}s, asks whether there exist covering systems
whose moduli are distinct and all odd. We show that if in addition one assumes
the moduli are square-free, then there must be an even modulus.


  We study the effect that the temperature structure has on the determination
of the primordial helium abundance, Yp. We provide an equation linking T(OIII),
the temperature derived from the [OIII] lines, and T(HeII), the temperature of
the He I lines, both for HII regions with O++ only and for HII regions where a
fraction of O+ is present. By means of T(HeII), which is always smaller than
T(OIII), we derive the helium abundances of 5 objects with low and very low
metallicity (NGC 346, NGC 2363, Haro29, SBS 0335-052, and I Zw 18); these
objects were selected from the literature because they include the 3 low
metallicity objects with the best line determinations and the 2 objects with
the lowest metallicity. From these abundances we obtain that
Yp(nHc)=0.2356+-0.0020, a value 0.0088 lower than that derived by using
T(OIII). We call this determination Yp(nHc) because the collisional
contribution to the Balmer line intensities has not been taken into account.
All the recent Yp determinations in the literature have not taken into account
the collisional contribution to the Balmer line intensities. By considering the
collisional contribution to the Balmer line intensities of these five objects
we derive that Yp(+Hc)=0.2384+-0.0025.


  The study of Weyl points in electronic systems has inspired many recent
researches in classical systems such as photonic and acoustic lattices. Here we
show how the Weyl physics can also inspire the design of novel elastic
structures. We construct a single-phase 3D structure, an analogue of the
AA-stacked honeycomb lattice, and predict the existence of Weyl points with
opposite topological charges (${\pm 1}$), elastic Fermi arcs, and the
associated gapless topologically protected surface states. We employ full-scale
numerical simulations on the elastic 3D structure, and present a clear
visualization of topological surface states that are directional and robust.
Such designed lattices can pave the way for novel vibration control and energy
harvesting on structures that are ubiquitous in many engineering applications.


  The illegal disposal of trash is a major public health and environmental
concern. Disposing of trash in unplanned places poses serious health and
environmental risks. We should try to restrict public trash cans as much as
possible. This research focuses on automating the penalization of litterbugs,
addressing the persistent problem of littering in public places. Traditional
approaches relying on manual intervention and witness reporting suffer from
delays, inaccuracies, and anonymity issues. To overcome these challenges, this
paper proposes a fully automated system that utilizes surveillance cameras and
advanced computer vision algorithms for litter detection, object tracking, and
face recognition. The system accurately identifies and tracks individuals
engaged in littering activities, attaches their identities through face
recognition, and enables efficient enforcement of anti-littering policies. By
reducing reliance on manual intervention, minimizing human error, and providing
prompt identification, the proposed system offers significant advantages in
addressing littering incidents. The primary contribution of this research lies
in the implementation of the proposed system, leveraging advanced technologies
to enhance surveillance operations and automate the penalization of litterbugs.


  Estimating 3D human poses from a monocular video is still a challenging task.
Many existing methods' performance drops when the target person is occluded by
other objects, or the motion is too fast/slow relative to the scale and speed
of the training data. Moreover, many of these methods are not designed or
trained under severe occlusion explicitly, making their performance on handling
occlusion compromised. Addressing these problems, we introduce a
spatio-temporal network for robust 3D human pose estimation. As humans in
videos may appear in different scales and have various motion speeds, we apply
multi-scale spatial features for 2D joints or keypoints prediction in each
individual frame, and multi-stride temporal convolutional networks (TCNs) to
estimate 3D joints or keypoints. Furthermore, we design a spatio-temporal
discriminator based on body structures as well as limb motions to assess
whether the predicted pose forms a valid pose and a valid movement. During
training, we explicitly mask out some keypoints to simulate various occlusion
cases, from minor to severe occlusion, so that our network can learn better and
becomes robust to various degrees of occlusion. As there are limited 3D
ground-truth data, we further utilize 2D video data to inject a semi-supervised
learning capability to our network. Moreover, we observe that there is a
discrepancy between 3D pose prediction and 2D pose estimation due to different
pose variations between video and image training datasets. We, therefore
propose a confidence-based inference stage optimization to adaptively enforce
3D pose projection to match 2D pose estimation to further improve final pose
prediction accuracy. Experiments on public datasets validate the effectiveness
of our method, and our ablation studies show the strengths of our network's
individual submodules.


  We present a new group law defined on a subset of the projective plane
$\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to
applications in Public Key Cryptography, in particular to a Diffie-Hellman-like
key agreement protocol. We analyze the computational difficulty of solving the
mathematical problem underlying the proposed Abelian group law and we prove
that the security of our proposal is equivalent to the discrete logarithm
problem in the multiplicative group of the cubic extension of the finite field
considered. Finally, we present a variant of the proposed group law but over
the ring $\mathbb{Z}/pq\mathbb{Z}$, and explain how the security becomes
enhanced, though at the cost of a longer key length.


  We study the automorphism group of the algebraic closure of a substructure A
of a pseudo-finite field F, or more generally, of a bounded PAC field F. This
paper answers some of the questions of [1], and in particular that any finite
group which is geometrically represented in a pseudo-finite field must be
abelian.


  A novel general purpose Finite Element framework is presented to study
small-scale metal plasticity. A distinct feature of the adopted distortion
gradient plasticity formulation, with respect to strain gradient plasticity
theories, is the constitutive inclusion of the plastic spin, as proposed by
Gurtin (2004) through the prescription of a free energy dependent on Nye's
dislocation density tensor. The proposed numerical scheme is developed by
following and extending the mathematical principles established by Fleck and
Willis (2009). The modeling of thin metallic foils under bending reveals a
significant influence of the plastic shear strain and spin due to a mechanism
associated with the higher-order boundary conditions allowing dislocations to
exit the body. This mechanism leads to an unexpected mechanical response in
terms of bending moment versus curvature, dependent on the foil length, if
either viscoplasticity or isotropic hardening are included in the model. In
order to study the effect of dissipative higher-order stresses, the mechanical
response under non-proportional loading is also investigated.


  We present a scheme to establish non-classical correlations in the motion of
two macroscopically separated massive particles without resorting to
entanglement in their internal degrees of freedom. It is based on the
dissociation of a diatomic molecule with two temporally separated Feshbach
pulses generating a motional state of two counter-propagating atoms that is
capable of violating a Bell inequality by means of correlated single particle
interferometry. We evaluate the influence of dispersion on the Bell
correlation, showing it to be important but manageable in a proposed
experimental setup. The latter employs a molecular BEC of fermionic Lithium
atoms, uses laser-guided atom interferometry, and seems to be within the reach
of present-day technology.


  We study the possibility to bind eight quarks in a molecular hadronic system
composed of two nucleons and an antikaon, with the quantum numbers of a
hexaquark flavour, in particular with strangeness -1, isospin 1/2, parity -,
baryonic number 2 and two possible spins, 0 or 1. These exotic hadrons are
motivated by the deuteron, a proton-neutron boundstate, and by the model of the
Lambda(1405) as an antikaon proton boundstate. We discuss the possible
production of this hadron in the experiments which are presently investigating
hot topics like the Theta+ pentaquark or the K- deeply bound in nuclei. The K-
N interactions and the coupling to other channels are computed microscopically
from a confining and chiral invariant quark model resulting in local plus
separable Gaussian potentials. The N N interactions used here are the state of
the art Nijmegen potentials. The binding energy and the decay rate of the K- N
and K- N N systems are computed with configuration space variational methods.
The only systems that bind with our microscopic interaction are the K- N in the
I=0 channel and the K- N N in the S=0 channel.


  We propose a four-point effective action for the graviton, antisymmetric
two-forms, dilaton and axion of type IIB superstring in ten dimensions. It is
explicitly SL(2,Z)-invariant and reproduces the known tree-level results.
Perturbatively, it has only one-loop corrections for the NS-NS sector,
generalizing the non-renormalization theorem of the R^4 term. Finally, the
non-perturbative corrections are of the expected form, namely, they can be
interpreted as arising from single D-instantons of multiple charge.


  We present infrared (IR) and optical echelle spectra of the Classical T Tauri
star TW Hydrae. Using the optical data, we perform detailed spectrum synthesis
to fit atomic and molecular absorption lines and determine key stellar
parameters: Teff = 4126 \pm 24 K, log g = 4.84 \pm 0.16, [M/H] = -0.10 \pm
0.12, vsini = 5.8 \pm 0.6 km/s. The IR spectrum is used to look for Zeeman
broadening of photospheric absorption lines. We fit four Zeeman sensitive Ti I
lines near 2.2 microns and find the average value of the magnetic field over
the entire surface is 2.61 \pm 0.23 kG. In addition, several nearby
magnetically insensitive CO lines show no excess broadening above that produced
by stellar rotation and instrumental broadening, reinforcing the magnetic
interpretation for the width of the Ti I lines. We carry out extensive tests to
quantify systematic errors in our analysis technique which may result from
inaccurate knowledge of the effective temperature or gravity, finding that
reasonable errors in these quantities produce a 10% uncertainty in the mean
field measurement.


  The size of vision models has grown exponentially over the last few years,
especially after the emergence of Vision Transformer. This has motivated the
development of parameter-efficient tuning methods, such as learning adapter
layers or visual prompt tokens, which allow a tiny portion of model parameters
to be trained whereas the vast majority obtained from pre-training are frozen.
However, designing a proper tuning method is non-trivial: one might need to try
out a lengthy list of design choices, not to mention that each downstream
dataset often requires custom designs. In this paper, we view the existing
parameter-efficient tuning methods as "prompt modules" and propose Neural
prOmpt seArcH (NOAH), a novel approach that learns, for large vision models,
the optimal design of prompt modules through a neural architecture search
algorithm, specifically for each downstream dataset. By conducting extensive
experiments on over 20 vision datasets, we demonstrate that NOAH (i) is
superior to individual prompt modules, (ii) has a good few-shot learning
ability, and (iii) is domain-generalizable. The code and models are available
at https://github.com/Davidzhangyuanhan/NOAH.


  We give a short proof that Strassen's asymptotic rank conjecture implies that
for every $\varepsilon > 0$ there exists a $(3/2^{2/3} + \varepsilon)^n$-time
algorithm for set cover on a universe of size $n$ with sets of bounded size.
This strengthens and simplifies a recent result of Bj\"orklund and Kaski that
Strassen's asymptotic rank conjecture implies that the set cover conjecture is
false. From another perspective, we show that the set cover conjecture implies
that a particular family of tensors $T_n \in \mathbb{C}^N \otimes \mathbb{C}^N
\otimes \mathbb{C}^N$ has asymptotic rank greater than $N^{1.08}$. Furthermore,
if one could improve a known upper bound of $\frac{1}{2}8^n$ on the tensor rank
of $T_n$ to $\frac{2}{9 \cdot n}8^n$ for any $n$, then the set cover conjecture
is false.


  We have obtained deep optical, long-slit spectrophotometry of the Galactic
HII regions M 17, NGC 3576 and of the Magellanic Cloud HII regions 30 Doradus,
LMC N11B and SMC N66, recording the optical recombination lines (ORLs) of CII,
NII and OII. Temperature-insensitive ORL C2+/O2+ and N2+/O2 ratios are obtained
for all nebulae except SMC N66. The ORL C2+/O2+ ratios show remarkable
agreement within each galactic system, while also being in agreement with the
corresponding CEL ratios. For all five nebulae, the O2+/H+ abundance derived
from multiple OII ORLs is found to be higher than the corresponding value
derived from the strong [OIII] 4959, 5007A CELs, by factors of 1.8--2.7 for
four of the nebulae. The LMC N11B nebula exhibits a more extreme discrepancy
factor for the O2+ ion, ~5. Thus these HII regions exhibit ORL/CEL abundance
discrepancy factors that are similar to those previously encountered amongst
planetary nebulae.
  Our optical CEL O2+/H+ abundances agree to within 20-30 per cent with
published O2+/H+ abundances that were obtained from observations of infrared
fine-structure lines. Since the low excitation energies of the latter make them
insensitive to variations about typical nebular temperatures, fluctuations in
temperature are ruled out as the cause of the observed ORL/CEL O2+ abundance
discrepancies. We present evidence that the observed OII ORLs from these HII
regions originate from gas of very similar density (<3500 cm-3) to that
emitting the observed heavy-element optical and infrared CELs, ruling out
models that employ high-density ionized inclusions in order to explain the
abundance discrepancy. We consider a scenario whereby much of the heavy-element
ORL emission originates from cold (<=500 K) metal-rich ionized regions.


  For A a category with finite colimits, we show that the embedding of A into
the category of arrows Arr(A) determined by the initial object is the
completion of A under strong homotopy cokernels. The nullhomotopy structure of
Arr(A) (needed in order to express the notion of homotopy cokernel) is the
usual one induced by the canonical string of adjunctions between A and Arr(A).


  Half-dozen of extreme representatives of void dwarf galaxy population were
found in our study of evolutionary status of a hundred galaxies in the nearby
Lynx-Cancer void. They are very gas-rich, extremely low-metallicity [7.0 <
12+log(O/H)< ~7.3] objects, with blue colours of outer parts. The colours
indicate the ages of the oldest visible stellar population of one to a few Gyr.
They all are intrinsically faint, mostly Low Surface Brightness dwarfs, with
M_B range of -9.5 to -14 mag. Thus, their finding is a subject of the severe
observational selection. The recent advancement in search for such objects in
other nearby voids resulted in doubled their total number. We summarize all
available data on this group of unusual void dwarf galaxies and discuss them in
the general context of very low metallicity galaxies and their possible
formation and evolutionary scenarios.


  Based on numbers of stars, supernova rates, and metallicity, a prior study
(Dayal et al. 2015) concluded that large elliptical galaxies contain up to
10,000 times more habitable planets than the Milky Way and are thus the
"cradles of life". Using the results of their model and taking into account
galactic number distributions and supernova rates I argue here that this result
constitutes a violation of the Principle of Mediocrity as applied to the
reference class of all extant technological species. Assuming that we are a
typical technological species in the attribute of inhabiting a relatively large
disk-dominated galaxy, I outline two hypotheses that could significantly limit
the habitability of large elliptical galaxies: (1) massive galactic
sterilization events associated with quasar/AGN activity and starburst
supernovae that occurred when the antecedents of today's large elliptical
galaxies were much more compact; and (2) the probability of habitable planet
formation in large elliptical galaxies may be small since a disproportionately
larger number of gaseous planets are expected to form as a result of the
generally higher metallicity in large elliptical galaxies. Consequently, fewer
habitable planets will accrete if the gaseous planets inward migrations are
sufficiently slow. The sterilization events of Hypothesis (1) occurred at
earlier epochs (z $\geq$ 1) and so they must be effectively permanent, implying
two possible scenarios regarding the origin and evolution of life. In
connection with one of these scenarios, independent applications of the
Principle of Mediocrity suggest that M-dwarf stars are not significant hosts of
technological life.


  We prove that every lattice with more than one element has a proper
congruence-preserving extension.


  We present an example of a generically forbidden phase transition in 1d at
finite temperature -- stress induced and thermally assisted roughening of a
superclimbing dislocation in a Peierls potential. We also argue that such
roughening is behind the strong suppression of the superflow through solid \he4
in a narrow temperature range recently observed by Ray and Hallock (Phys.Rev.
Lett. {\bf 105}, 145301 (2010)).


  We have grown underdoped (x = 0.11, 0.12) and optimally doped (x = 0.16)
La2-xSrxCuO4 (LSCO) crystals by traveling-solvent floating-zone (TSFZ)
technique. In order to obtain LSCO single crystals of high quality, we have
made much effort to optimize the preparation procedures. For example, we have
adopted sol-gel route to prepare highly fine and homogeneous LSCO precursor
powder, and used quite slow growth rate. The sizable grown crystal ingots are
typically about 6.6 mm in diameter and 100 mm in length, and no impurity phases
were detected. The high quality of grown crystals has been verified by
double-crystal x-ray rocking curves, with full-width-at-half-maximum (FWHM)
being only 113 ~ 150 arcseconds (or 0.03 deg - 0.04 deg), which are the best
data reported so far for LSCO crystals. The superconducting critical
temperatures (TC's) of the cuprate crystals are 30 K for x = 0.11, 31 K for x =
0.12 and 38.5 K for x = 0.16 samples according to magnetic measurements.


  Partial quorum systems are widely used in distributed key-value stores due to
their latency benefits at the expense of providing weaker consistency
guarantees. The probabilistically bounded staleness framework (PBS) studied the
latency-consistency trade-off of Dynamo-style partial quorum systems through
Monte Carlo event-based simulations. In this paper, we study the
latency-consistency trade-off for such systems analytically and derive a
closed-form expression for the inconsistency probability. Our approach allows
fine-tuning of latency and consistency guarantees in key-value stores, which is
intractable using Monte Carlo event-based simulations.


  We report on the performance of a compact photon pair source that was
recovered intact from a failed space launch. The source had been embedded in a
nanosatellite and was designed to perform pathfinder experiments leading to
global quantum communication networks using spacecraft. Despite the launch
vehicle explosion soon after takeoff?, the nanosatellite was successfully
retrieved from the accident site and the source within it was found to be fully
operational. We describe the assembly technique for the rugged source.
Post-recovery data is compared to baseline measurements collected before the
launch attempt and no degradation in brightness or polarization correlation was
observed. The survival of the source through an extreme environment provides
strong evidence that it is possible to engineer rugged quantum optical systems.


  The contextual linear bandit is an important online learning problem where
given arm features, a learning agent selects an arm at each round to maximize
the cumulative rewards in the long run. A line of works, called the clustering
of bandits (CB), utilize the collaborative effect over user preferences and
have shown significant improvements over classic linear bandit algorithms.
However, existing CB algorithms require well-specified linear user models and
can fail when this critical assumption does not hold. Whether robust CB
algorithms can be designed for more practical scenarios with misspecified user
models remains an open problem. In this paper, we are the first to present the
important problem of clustering of bandits with misspecified user models
(CBMUM), where the expected rewards in user models can be perturbed away from
perfect linear models. We devise two robust CB algorithms, RCLUMB and RSCLUMB
(representing the learned clustering structure with dynamic graph and sets,
respectively), that can accommodate the inaccurate user preference estimations
and erroneous clustering caused by model misspecifications. We prove regret
upper bounds of $O(\epsilon_*T\sqrt{md\log T} + d\sqrt{mT}\log T)$ for our
algorithms under milder assumptions than previous CB works (notably, we move
past a restrictive technical assumption on the distribution of the arms), which
match the lower bound asymptotically in $T$ up to logarithmic factors, and also
match the state-of-the-art results in several degenerate cases. The techniques
in proving the regret caused by misclustering users are quite general and may
be of independent interest. Experiments on both synthetic and real-world data
show our outperformance over previous algorithms.


  We show that generically, the degeneracies of a family of Hermitian matrices
depending on three parameters have a conical structure. Our result applies to
the study of topological phases of matter. It implies that adiabatic
deformations of two-dimensional topological insulators come generically with
Dirac-like propagating currents, whose total conductivity equals the chiral
number of conical points.


  The type and distribution of oxygen functional groups in graphene oxide (GO)
and reduced graphene oxide (RGO) remain still a subject of great debate. Local
analytic techniques are required to access the chemistry of these materials at
a nanometric scale. Electron energy loss spectroscopy in a scanning
transmission electron microscope can provide the suitable resolution, but GO
and RGO are extremely sensitive to electron irradiation. In this work we employ
a dedicated experimental setup to reduce electron illumination below damage
limit. GO oxygen maps obtained at a few nanometers scale show separated domains
with different oxidation levels. The C/O ratio varies from about 4:1 to 1:1,
the latter corresponding to a complete functionalization of the graphene
flakes. In RGO the residual oxygen concentrates mostly in regions few tens
nanometers wide. Specific energy-loss near-edge structures are observed for
different oxidation levels. By combining these findings with first-principles
simulations we propose a model for the highly oxidized domains where graphene
is fully functionalized by hydroxyl groups forming a 2D-sp$^3$ carbon network
analogous to that of graphane.


  Relying on the known two-term quasiclassical asymptotic formula for the trace
of the function $f(A)$ of a Wiener-Hopf type operator $A$ in dimension one, in
1982 H. Widom conjectured a multi-dimensional generalization of that formula
for a pseudo-differential operator $A$ with a symbol $a(\bx, \bxi)$ having jump
discontinuities in both variables. In 1990 he proved the conjecture for the
special case when the jump in any of the two variables occurs on a hyperplane.
The present paper gives a proof of Widom's Conjecture under the assumption that
the symbol has jumps in both variables on arbitrary smooth bounded surfaces.


  We study the isotropic elastic wave equation in a bounded domain with
boundary with coefficients having jumps at a nested set of interfaces
satisfying the natural transmission conditions there. We analyze in detail the
microlocal behavior of such solution like reflection, transmission and mode
conversion of S and P waves, evanescent modes, Rayleigh and Stoneley waves. In
particular, we recover Knott's equations in this setting. We show that
knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the
P and the S waves if there is a strictly convex foliation with respect to them,
under an additional condition of lack of full internal reflection of some of
the waves.


  The notion of completely positive invariant conjugate-bilinear map in a
partial *-algebra is introduced and a generalized Stinespring theorem is
proven. Applications to the existence of integrable extensions of
*-representations of commutative, locally convex quasi*-algebras are also
discussed.


  The present paper explores the synchronization scenario of hyperchaotic
time-delayed electronic oscillators coupled indirectly via a common
environment. We show that depending upon the coupling parameters a hyperchaotic
time-delayed system can show in-phase or complete synchronization, and also
inverse-phase or anti-synchronization. This paper reports the first
experimental confirmation of synchronization of hyperchaos in time-delayed
electronic oscillators coupled indirectly through a common environment. We
confirm the occurrence of in-phase and inverse-phase synchronization phenomena
in the coupled system through the dynamical measures like generalized
autocorrelation function, correlation of probability of recurrence, and the
concept of localized sets computed directly from the experimental time-series
data. We also present a linear stability analysis of the coupled system. The
experimental and analytical results are further supported by the detailed
numerical analysis of the coupled system. Apart from the above mentioned
measures, we numerically compute another quantitative measure, namely, Lyapunov
exponent spectrum of the coupled system that confirms the transition from the
in-phase (inverse-phase) synchronized state to the complete (anti-)
synchronized state with the increasing coupling strength.


  Self-training approach recently secures its position in domain adaptive
semantic segmentation, where a model is trained with target domain
pseudo-labels. Current advances have mitigated noisy pseudo-labels resulting
from the domain gap. However, they still struggle with erroneous pseudo-labels
near the boundaries of the semantic classifier. In this paper, we tackle this
issue by proposing a dual-level interaction for domain adaptation (DIDA) in
semantic segmentation. Explicitly, we encourage the different augmented views
of the same pixel to have not only similar class prediction (semantic-level)
but also akin similarity relationship with respect to other pixels
(instance-level). As it's impossible to keep features of all pixel instances
for a dataset, we, therefore, maintain a labeled instance bank with dynamic
updating strategies to selectively store the informative features of instances.
Further, DIDA performs cross-level interaction with scattering and gathering
techniques to regenerate more reliable pseudo-labels. Our method outperforms
the state-of-the-art by a notable margin, especially on confusing and
long-tailed classes. Code is available at
\href{https://github.com/RainJamesY/DIDA}


  Initial-boundary value problems for nonlinear dispersive equations of
evolution of order $2l+1,\;l\in\mathbb{N}$ with a convective term of the form
$u^ku_x,\;k\in\mathbb{N}$ have been considered on intervals $(0,L),\;L\in
(0,+\infty)$. The existence and uniqueness of local regular solutions have been
established.


  We report on observation of ferroelastic domain structure in single crystals
of multiferroic CaMn$_7$O$_{12}$ at room temperature. Two types of ferroelastic
domain wall are found, consistent with the material's rhombohedral symmetry
that is reduced from cubic symmetry at higher temperatures. Using Raman
spectroscopy along with other measurements, we develop a systematic method to
determine the microscopic domain orientation. Moreover, we find a switching
behavior of the domains, which allows us to detwin the crystals conveniently at
room temperature using a moderate uniaxial compression. Our result paves the
way for further spectroscopic study and domain engineering in CaMn$_7$O$_{12}$.


  A sequential fourth generation is known to be excluded because the
non-decoupling contribution to $\kappa_g$, the Higgs coupling modifier with a
gluon pair, is unacceptably large. Recently a new way to save the model was
suggested in the Type-II two Higgs doublet model: if the Yukawa couplings of
down-type fermions have wrong-sign, the contributions from $t'$ and $b'$ to
$\kappa_g$ are cancelled. We study the theoretical and experimental constraints
on this model, focusing on the heavy Higgs bosons. Two constraining features
are pointed out. First the exact wrong-sign limit does not allow the alignment,
which makes the perturbative unitarity for the scalar-scalar scattering put the
upper bounds on the heavy Higgs boson masses like $M_H, M_A \lesssim 920$ GeV
and $M_{H^\pm} \lesssim 620$ GeV. Secondly, the Yukawa couplings of the fourth
generation fermions to the heavy Higgs bosons are generically large as being
proportional to the heavy fermion mass and, for the down-type fermions, to
$\tan\beta$ as well. The gluon fusion productions of $H$ and $A$ through the
fourth generation quark loops become significant. We found that the current LHC
data on $pp \to Z Z$ for $H$ along with the theoretical and indirect
constraints exclude the model at leading order.


  The multiplication of a matrix by its transpose, $A^T A$, appears as an
intermediate operation in the solution of a wide set of problems. In this
paper, we propose a new cache-oblivious algorithm (ATA) for computing this
product, based upon the classical Strassen algorithm as a sub-routine. In
particular, we decrease the computational cost to $\frac{2}{3}$ the time
required by Strassen's algorithm, amounting to $\frac{14}{3}n^{\log_2 7}$
floating point operations. ATA works for generic rectangular matrices, and
exploits the peculiar symmetry of the resulting product matrix for saving
memory. In addition, we provide an extensive implementation study of ATA in a
shared memory system, and extend its applicability to a distributed
environment. To support our findings, we compare our algorithm with
state-of-the-art solutions specialized in the computation of $A^T A$. Our
experiments highlight good scalability with respect to both the matrix size and
the number of involved processes, as well as favorable performance for both the
parallel paradigms and the sequential implementation, when compared with other
methods in the literature.


  Evolutionary algorithms solve problems by simulating the evolution of a
population of candidate solutions. We focus on evolving permutations for
ordering problems like the traveling salesperson problem (TSP), as well as
assignment problems like the quadratic assignment problem (QAP) and largest
common subgraph (LCS). We propose cycle mutation, a new mutation operator whose
inspiration is the well known cycle crossover operator, and the concept of a
permutation cycle. We use fitness landscape analysis to explore the problem
characteristics for which cycle mutation works best. As a prerequisite, we
develop new permutation distance measures: cycle distance, $k$-cycle distance,
and cycle edit distance. The fitness landscape analysis predicts that cycle
mutation is better suited for assignment and mapping problems than it is for
ordering problems. We experimentally validate these findings showing cycle
mutation's strengths on problems like QAP and LCS, and its limitations on
problems like the TSP, while also showing that it is less prone to local optima
than commonly used alternatives. We integrate cycle mutation into the
open-source Chips-n-Salsa library, and the new distance metrics into the
open-source JavaPermutationTools library.


  An analytical model for the self-modulation instability of a long
relativistic proton bunch propagating in uniform plasmas is developed. The
self-modulated proton bunch resonantly excites a large amplitude plasma wave
(wake field), which can be used for acceleration of plasma electrons.
Analytical expressions for the linear growth rate and the number of
exponentiations are given. We use the full three-dimensional particle-in-cell
(PIC) simulations to study the beam self-modulation and the transition to the
nonlinear stage. It is shown that the self-modulation of the proton bunch
competes with the hosing instability which tends to destroy the plasma wave. A
method is proposed and studied through PIC simulations to circumvent this
problem which relies on the seeding of the self-modulation instability in the
bunch.


  Semi-supervised video object segmentation (VOS) refers to segmenting the
target object in remaining frames given its annotation in the first frame,
which has been actively studied in recent years. The key challenge lies in
finding effective ways to exploit the spatio-temporal context of past frames to
help learn discriminative target representation of current frame. In this
paper, we propose a novel Siamese network with a specifically designed
interactive transformer, called SITVOS, to enable effective context propagation
from historical to current frames. Technically, we use the transformer encoder
and decoder to handle the past frames and current frame separately, i.e., the
encoder encodes robust spatio-temporal context of target object from the past
frames, while the decoder takes the feature embedding of current frame as the
query to retrieve the target from the encoder output. To further enhance the
target representation, a feature interaction module (FIM) is devised to promote
the information flow between the encoder and decoder. Moreover, we employ the
Siamese architecture to extract backbone features of both past and current
frames, which enables feature reuse and is more efficient than existing
methods. Experimental results on three challenging benchmarks validate the
superiority of SITVOS over state-of-the-art methods.


  In order to measure the radial displacements of facets on surface of a
growing spherical Cu_{2-\delta}Se crystal with sub-nanometer resolution, we
have investigated the reliability and accuracy of standard method of Fourier
analysis of fringes obtained applying digital laser interferometry method.
Guided by the realistic experimental parameters (density and orientation of
fringes), starting from 2-dimensional model interferograms and using
unconventional custom designed Gaussian filtering window and unwrapping
procedure of the retrieved phase, we have demonstrated that for considerable
portion of parameter space the non-negligible inherent phase retrieval error is
present solely due to non-integer number of fringes within the digitally
recorded image (using CCD camera). Our results indicate the range of
experimentally adjustable parameters for which the generated error is
acceptably small. We also introduce a modification of the (last part) of the
usual phase retrieval algorithm which significantly reduces the error in the
case of small fringe density.


  The equilibration of two coupled reservoirs is studied using a Green function
approach which is suitable for future development with the closed time path
method. The problem is solved in two parameterizations, in order to demonstrate
the non-trivial issues of parameterization in both the intermediate steps and
the interpretation of physical quantities. We use a covariant approach to find
self-consistent solutions for the statistical distributions as functions of
time. We show that by formally introducing covariant connections, one can
rescale a slowly varying non-equilibrium theory so that it appears to be an
equilibrium one, for the purposes of calculation. We emphasize the importance
of properly tracking variable redefinitions in order to correctly interpret
physical quantities.


  Image retrieval has become an increasingly appealing technique with broad
multimedia application prospects, where deep hashing serves as the dominant
branch towards low storage and efficient retrieval. In this paper, we carried
out in-depth investigations on metric learning in deep hashing for establishing
a powerful metric space in multi-label scenarios, where the pair loss suffers
high computational overhead and converge difficulty, while the proxy loss is
theoretically incapable of expressing the profound label dependencies and
exhibits conflicts in the constructed hypersphere space. To address the
problems, we propose a novel metric learning framework with Hybrid Proxy-Pair
Loss (HyP$^2$ Loss) that constructs an expressive metric space with efficient
training complexity w.r.t. the whole dataset. The proposed HyP$^2$ Loss focuses
on optimizing the hypersphere space by learnable proxies and excavating
data-to-data correlations of irrelevant pairs, which integrates sufficient data
correspondence of pair-based methods and high-efficiency of proxy-based
methods. Extensive experiments on four standard multi-label benchmarks justify
the proposed method outperforms the state-of-the-art, is robust among different
hash bits and achieves significant performance gains with a faster, more stable
convergence speed. Our code is available at
https://github.com/JerryXu0129/HyP2-Loss.


  Multilayer neural networks set the current state of the art for many
technical classification problems. But, these networks are still, essentially,
black boxes in terms of analyzing them and predicting their performance. Here,
we develop a statistical theory for the one-layer perceptron and show that it
can predict performances of a surprisingly large variety of neural networks
with different architectures. A general theory of classification with
perceptrons is developed by generalizing an existing theory for analyzing
reservoir computing models and connectionist models for symbolic reasoning
known as vector symbolic architectures. Our statistical theory offers three
formulas leveraging the signal statistics with increasing detail. The formulas
are analytically intractable, but can be evaluated numerically. The description
level that captures maximum details requires stochastic sampling methods.
Depending on the network model, the simpler formulas already yield high
prediction accuracy. The quality of the theory predictions is assessed in three
experimental settings, a memorization task for echo state networks (ESNs) from
reservoir computing literature, a collection of classification datasets for
shallow randomly connected networks, and the ImageNet dataset for deep
convolutional neural networks. We find that the second description level of the
perceptron theory can predict the performance of types of ESNs, which could not
be described previously. The theory can predict deep multilayer neural networks
by being applied to their output layer. While other methods for prediction of
neural networks performance commonly require to train an estimator model, the
proposed theory requires only the first two moments of the distribution of the
postsynaptic sums in the output neurons. The perceptron theory compares
favorably to other methods that do not rely on training an estimator model.


  A new nonlocality experiment with moving beam-splitters is proposed. The
experiment is analysed according to conventional quantum mechanics, and to an
alternative nonlocal description in which superposition depends not only on
indistinguishability but also on the timing of the impacts at the
beam-splitters.


  This article introduces strongly near proximity, which represents a new kind
of proximity called \emph{almost proximity}. A main result in this paper is the
introduction of a hit-and-miss topology on ${CL}(X)$, the hyperspace of
nonempty closed subsets of $X$, based on the strongly near proximity.


  Lithium and zirconium abundances (the latter taken as representative for
s-process enrichment) are determined for a large sample of massive Galactic
O-rich AGB stars, for which high resolution optical spectroscopy has been
obtained (R=40,000-50,000). This is done by computing synthetic spectra based
on classical hydrostatic model atmospheres for cool stars using extensive line
lists. The results obtained are discussed in the framework of hot bottom
burning (HBB) and nucleosynthesis models. The complete sample is studied
attending to various observational properties such as the position of the stars
in the IRAS two-colour diagram ([12]-[25] vs [25]-[60]), Galactic distribution,
expansion velocity (derived from the OH maser emission) and period of
variability (when available). We conclude that a considerable fraction of the
sources observed are actually massive AGB stars (M > 3-4 solar masses)
experiencing HBB, as deduced from the strong Li overabundances found. A
comparison of our results with similar studies carried out in the past for the
Magellanic Clouds (MCs) reveals that, in contrast to MC AGB stars, our Galactic
sample does not show any indication of s-process element enrichment. The
differences observed are explained as a consequence of metallicity effects.
Finally, we discuss the results obtained in the framework of stellar evolution
by comparing our results with the data available in the literature for Galactic
post-AGB stars and PNe.


  Robins 1997 introduced marginal structural models (MSMs), a general class of
counterfactual models for the joint effects of time-varying treatment regimes
in complex longitudinal studies subject to time-varying confounding. In his
work, identification of MSM parameters is established under a sequential
randomization assumption (SRA), which rules out unmeasured confounding of
treatment assignment over time. We consider sufficient conditions for
identification of the parameters of a subclass, Marginal Structural Mean Models
(MSMMs), when sequential randomization fails to hold due to unmeasured
confounding, using instead a time-varying instrumental variable. Our
identification conditions require that no unobserved confounder predicts
compliance type for the time-varying treatment. We describe a simple weighted
estimator and examine its finite-sample properties in a simulation study. We
apply the proposed estimator to examine the effect of delivery hospital on
neonatal survival probability.


  Let $G$ be a $p$-divisible group over the ring of integers of $\mathbb{C}_p$,
and assume that it is endowed with an action of the ring of integers of a
finite unramified extension $F$ of $\mathbb{Q}_p$. Let us fix the type $\mu$ of
this action on the sheaf of differentials $\omega_G$. V. Hernandez, following a
construction of Goldring and Nicole, defined partial Hasse invariants for $G$.
The product of these invariants is the $\mu$-ordinary Hasse invariant, and it
is non-zero if and only if the $p$-divisible group is $\mu$-ordinary (i.e. the
Newton polygon is minimal given the type of the action). \\ We show that if the
valuation of the $\mu$-ordinary Hasse invariant is small enough, then each of
these partial Hasse invariants is a product of other sections, the refined
partial Hasse invariants. We also give a condition for the construction of
these invariants over an arbitrary scheme of characteristic $p$. We then give a
simple, natural and elegant proof of the compatibility with duality for the
classical Hasse invariant, and show how to adapt it to the case of the refined
partial Hasse invariants. Finally, we show how these invariants allow us to
compute the partial degrees of the canonical filtration (if it exists).


  We present a simple lattice model showing a glassy behavior. $R$ matrix
analysis predicts critical termination of the super-cooled fluid branch at
density $\rho_g=0.1717$. This prediction is confirmed by dynamical numerical
simulations, showing power-law divergences of relaxation time $\tau_{1/2}$, as
well as the 4-susceptibility $\chi_4$ peak's location and height exactly at the
predicted density. The power-law divergence of $\chi_4$ continues up to
$\chi_4$ as high as $10^4$. Finite-size scaling study reveals divergence of
correlation length accompanying the transition.


  Binding of acridine derivative quinacrine (QA) to chicken erythrocyte DNA was
studied by methods of absorption and polarized fluorescent spectroscopy.
Measurements were carried out in aqueous buffered solutions (pH 6.9) of
different dye concentrations (QA concentration range from $10^{-6}$ till
$10^{-4}$ M) and ionic strengths ($Na^{+}$ concentration rang from $10^{-3}$
till 0.15 M) in a wide range of phosphate-to-dye molar ratios ($P/D$). It is
established that the minimum of fluorescent titration curve plotted as relative
fluorescence intensity $vs$ $P/D$ is conditioned by the competition between the
two types of QA binding to DNA which posses by different emission parameters:
(i) intercalative one dominating under high $P/D$ values, and (ii) outside
electrostatic binding dominating under low $P/D$ values, which is accompanied
by the formation of non-fluorescent dye associates on the DNA backbone.
Absorption and fluorescent characteristics of complexes formed were determined.
The method of calculation of different binding modes contribution to the
complex formation depending on $P/D$ value is presented. It was shown that the
size of binding site measured as the number of DNA base pairs per one QA
molecule bound in the case of the electrostatic interaction is 8 times less
than that for the intercalative one that determines the competitive ability of
the outside binding against the stronger intercalative binding mode.


  We study a layered three-dimensional heterostructure in which two types of
Kondo insulators are stacked alternatingly. One of them is the topological
Kondo insulator SmB 6 , the other one an isostructural Kondo insulator AB 6 ,
where A is a rare-earth element, e.g., Eu, Yb, or Ce. We find that if the
latter orders ferromagnetically, the heterostructure generically becomes a
magnetic Weyl Kondo semimetal, while antiferromagnetic order can yield a
magnetic Dirac Kondo semimetal. We detail both scenarios with general symmetry
considerations as well as concrete tight-binding calcu-lations and show that
type-I as well as type-II magnetic Weyl/Dirac Kondo semimetal phases are
possible in these heterostructures. Our results demonstrate that Kondo
insulator heterostructures are a versatile platform for design of strongly
correlated topological semimetals.


  We present results from a comprehensive lensing analysis in HST data, of the
complete CLASH cluster sample. We identify new multiple-images previously
undiscovered allowing improved or first constraints on the cluster inner mass
distributions and profiles. We combine these strong-lensing constraints with
weak-lensing shape measurements within the HST FOV to jointly constrain the
mass distributions. The analysis is performed in two different common
parameterizations (one adopts light-traces-mass for both galaxies and dark
matter while the other adopts an analytical, elliptical NFW form for the dark
matter), to provide a better assessment of the underlying systematics - which
is most important for deep, cluster-lensing surveys, especially when studying
magnified high-redshift objects. We find that the typical (median), relative
systematic differences throughout the central FOV are $\sim40\%$ in the
(dimensionless) mass density, $\kappa$, and $\sim20\%$ in the magnification,
$\mu$. We show maps of these differences for each cluster, as well as the mass
distributions, critical curves, and 2D integrated mass profiles. For the
Einstein radii ($z_{s}=2$) we find that all typically agree within $10\%$
between the two models, and Einstein masses agree, typically, within
$\sim15\%$. At larger radii, the total projected, 2D integrated mass profiles
of the two models, within $r\sim2\arcmin$, differ by $\sim30\%$. Stacking the
surface-density profiles of the sample from the two methods together, we obtain
an average slope of $d\log (\Sigma)/d\log(r)\sim-0.64\pm0.1$, in the radial
range [5,350] kpc. Lastly, we also characterize the behavior of the average
magnification, surface density, and shear differences between the two models,
as a function of both the radius from the center, and the best-fit values of
these quantities.


  We compute the monodromy group of irreducible holomorphic symplectic
manifolds of OG10 type, confirming a conjecture of Markman.