  In this paper, we use a new method to obtain the necessary and sufficient
condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality
for the generalized upper Sugeno integral in the case of functions belonging to
a wider class than the comonotone functions. As a by-product, we show that the
Minkowski type inequality for seminormed fuzzy integral presented by Daraby and
Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy
integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not
true. Next, we study the Minkowski-H\"{o}lder inequality for the lower Sugeno
integral and the class of $\mu$-subadditive functions introduced in On
Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and
Systems 244 (2014) 51--62. The results are applied to derive new metrics on the
space of measurable functions in the setting of nonadditive measure theory. We
also give a partial answer to the open problem 2.22 posed by
Borzov\'a-Moln\'arov\'a and et al in The smallest semicopula-based universal
integrals I: Properties and characterizations, Fuzzy Sets and Systems 271
(2015) 1--17.


  In our previous work, it was shown that the topology of an event horizon (EH)
is determined by the past endpoints of the EH. A torus EH (the collision of two
EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In
the present article, we examine the stability of the topology of the EH. We see
that a simple case of a single spherical EH is unstable. Furthermore, in
general, an EH with handles (a torus, a double torus, ...) is structurally
stable in the sense of catastrophe theory.


  Simply and reliably detecting and quantifying entanglement outside laboratory
conditions will be essential for future quantum information technologies. Here
we address this issue by proposing a method for generating expressions which
can perform this task between two parties who do not share a common reference
frame. These reference frame independent expressions only require simple local
measurements, which allows us to experimentally test them using an
off-the-shelf entangled photon source. We show that the values of these
expressions provide bounds on the concurrence of the state, and demonstrate
experimentally that these bounds are more reliable than values obtained from
state tomography since characterizing experimental errors is easier in our
setting. Furthermore, we apply this idea to other quantities, such as the Renyi
and von Neumann entropies, which are also more reliably calculated directly
from the raw data than from a tomographically reconstructed state. This
highlights the relevance of our approach for practical quantum information
applications that require entanglement.


  When parsing morphologically-rich languages with neural models, it is
beneficial to model input at the character level, and it has been claimed that
this is because character-level models learn morphology. We test these claims
by comparing character-level models to an oracle with access to explicit
morphological analysis on twelve languages with varying morphological
typologies. Our results highlight many strengths of character-level models, but
also show that they are poor at disambiguating some words, particularly in the
face of case syncretism. We then demonstrate that explicitly modeling
morphological case improves our best model, showing that character-level models
can benefit from targeted forms of explicit morphological modeling.


  In gamma ray astronomy muon events have a distinct feature of casting
ring-like images on the sensor plane, thus forming a well known signal class
for Cherenkov telescopes. These ring-like images can then be used to deduce the
optical point spread function (PSF) which is an important measure of the
optical quality of the imaging-reflector. In this thesis the observed
'fuzziness' of muon rings is used as a measure to infer the PSF. However to
have a good estimate for this 'fuzziness' parameter, the reconstruction of the
ring center and ring radius itself needs to be accurate, so different methods
of ring feature extraction are studied. To check for the accuracy of the
methods a simulation and analysis is performed. Measuring the evolution of the
PSF over time allows to identify its effects and take them into account for the
reconstruction of gamma-rays postliminary. As a further benefit of the methods
presented here no additional observations are needed to measure the PSF nor any
human activity on site is required. The accuracy of the method, and the PSF of
FACT vs. time are presented.


  Image registration and in particular deformable registration methods are
pillars of medical imaging. Inspired by the recent advances in deep learning,
we propose in this paper, a novel convolutional neural network architecture
that couples linear and deformable registration within a unified architecture
endowed with near real-time performance. Our framework is modular with respect
to the global transformation component, as well as with respect to the
similarity function while it guarantees smooth displacement fields. We evaluate
the performance of our network on the challenging problem of MRI lung
registration, and demonstrate superior performance with respect to state of the
art elastic registration methods. The proposed deformation (between inspiration
& expiration) was considered within a clinically relevant task of interstitial
lung disease (ILD) classification and showed promising results.


  This paper aims to compare different regularization strategies to address a
common phenomenon, severe overfitting, in embedding-based neural networks for
NLP. We chose two widely studied neural models and tasks as our testbed. We
tried several frequently applied or newly proposed regularization strategies,
including penalizing weights (embeddings excluded), penalizing embeddings,
re-embedding words, and dropout. We also emphasized on incremental
hyperparameter tuning, and combining different regularizations. The results
provide a picture on tuning hyperparameters for neural NLP models.


  We present a solution to egocentric 3D body pose estimation from monocular
images captured from downward looking fish-eye cameras installed on the rim of
a head mounted VR device. This unusual viewpoint leads to images with unique
visual appearance, with severe self-occlusions and perspective distortions that
result in drastic differences in resolution between lower and upper body. We
propose an encoder-decoder architecture with a novel multi-branch decoder
designed to account for the varying uncertainty in 2D predictions. The
quantitative evaluation, on synthetic and real-world datasets, shows that our
strategy leads to substantial improvements in accuracy over state of the art
egocentric approaches. To tackle the lack of labelled data we also introduced a
large photo-realistic synthetic dataset. xR-EgoPose offers high quality
renderings of people with diverse skintones, body shapes and clothing,
performing a range of actions. Our experiments show that the high variability
in our new synthetic training corpus leads to good generalization to real world
footage and to state of theart results on real world datasets with ground
truth. Moreover, an evaluation on the Human3.6M benchmark shows that the
performance of our method is on par with top performing approaches on the more
classic problem of 3D human pose from a third person viewpoint.


  We advocate a novel perspective on the phenomenology of a framework with
spacetime noncommutativity which is of established relevance for string theory.
Our analysis applies to cases in which the noncommutativity parameters are
arranged according to the criteria of "light-like noncommutativity" and
ultraviolet supersymmetry is assumed, so that the implications of the
characteristic mechanism of ultraviolet/infrared mixing are relatively soft. We
also observe that an analogous case of soft ultraviolet-infrared mixing is
present in a previously-proposed Loop-quantum-gravity-inspired description of
quantum spacetime. And we show that soft ultraviolet-infrared mixing produces
an anomaly for the nonrelativistic de Broglie relation $\lambda v = h/m$, with
correction term governed by a single (but particle-dependent) parameter $\chi$.
We test this hypothesis by comparing a determination of the fine structure
constant that relies on the de Broglie relation for nonrelativistic neutrons to
other independent determinations of the fine structure constant, and we obtain
an estimate of $\chi$ that differs from 0 with four-standard-deviation
significance.


  In this note, we investigate the possibility of avoiding the Big Bang
singularity with a single scalar field which couples non-minimally to gravity.
We show that in the case that gravity couples linearly to the field, some
severe conditions on the field's potential have to be imposed. However, in
non-linear case, it is quite generic to avoid the singularity with single
scalar field.


  In this paper we generalize some classical birational transformations to the
non-commutative case. In particular we show that 3-dimensional quadratic
Sklyanin algebras (non-commutative projective planes) and 3-dimensional cubic
Sklyanin algebras (non-commutative quadrics) have the same function field. In
the same vein we construct and analogue of the Cremona transform for
non-commutative projective planes.


  Global deformations of surfaces, immersed into the Euclidean 3-space, by
using the modified Novikov--Veselov equation are investigated. relation to the
theory of the Willmore functional is discussed


  Stably-stratified layers may be present at the top of the
electrically-conducting fluid layers of many planets either because the
temperature gradient is locally subadiabatic or because a stable composition
gradient is maintained by the segregation of chemical elements. Here we study
the double-diffusive processes taking place in such a stable layer, considering
the case of Mercury's core where the temperature gradient is stable but the
composition gradient is unstable over a 800km-thick layer. The large difference
in the molecular diffusivities leads to the development of buoyancy-driven
instabilities that drive radial flows known as fingering convection. We model
fingering convection using hydrodynamical simulations in a rotating spherical
shell and varying the rotation rate and the stratification strength. For small
Rayleigh numbers (i.e. weak background temperature and composition gradients),
fingering convection takes the form of columnar flows aligned with the rotation
axis and with an azimuthal size comparable with the layer thickness. For larger
Rayleigh numbers, the flows retain a columnar structure but the azimuthal size
is drastically reduced leading to thin sheet-like structures that are elongated
in the meridional direction. The azimuthal length decreases when the thermal
stratification increases, following closely the scaling law expected from the
linear non-rotating planar theory (Stern, 1960). We find that the radial flows
always remain laminar with local Reynolds number of order 1-10.
Equatorially-symmetric zonal flows form due to latitudinal variations of the
axisymmetric composition. The zonal velocity exceeds the non-axisymmetric
velocities at the largest Rayleigh numbers. We discuss plausible implications
for planetary magnetic fields.


  Our surrounding environment impacts our cognitive-emotional processes on a
daily basis and shapes our physical, psychological and social wellbeing.
Although the effects of the built environment on our psycho-physiological
processes are well studied, virtual environment design with a potentially
similar impact on the user, has received limited attention. Based on the
influence of space design on a user and combining that with the dynamic
affordances of virtual spaces, we present the idea of adaptive virtual
neuroarchitecture (AVN), where virtual environments respond to the user and the
user's real world context while simultaneously influencing them both in
realtime. To show how AVN has been explored in current research, we present a
sampling of recent work that demonstrates reciprocal relationships using
physical affordances (space, objects), the user's state (physiological,
cognitive, emotional), and the virtual world used in the design of novel
virtual reality experiences. We believe AVN has the potential to help us learn
how to design spaces and environments that can enhance the wellbeing of their
inhabitants.


  Due to the high quality constraints available for the Sun, we can carry out
combined analyses using neutrino, spectroscopic and helioseismic observations.
Such studies lay the ground for future improvements of key physical components
of solar and stellar models, such as the equation of state, radiative opacities
or prescriptions for macroscopic transport processes of chemicals which are
then used to study other stars in the Universe. We study the existing
degeneracies in solar models using the recent high-metallicity spectroscopic
abundances by comparing them to helioseismic and neutrino data and discuss how
their properties are impacted by changes in various physical ingredients. We
carry out a detailed study of solar models computed with a high-metallicity
composition from the literature based on averaged-3D models that was claimed to
solve the solar problem. The properties of the solar models are significantly
affected by using the recent OPLIB opacities and the inclusion of macroscopic
transport. The properties of the standard solar models computed using the OPAL
opacities are similar to those using the OP opacities. We show that a modifying
the temperature gradient just below the base of the convective zone is required
to erase the discrepancies in solar models, particularly in the presence of
macroscopic mixing. This can be simulated by a local increase of opacity of a
few percent. We conclude that the existing degeneracies and issues in solar
modelling are not erased by an increase in the solar metallicity in
contradiction to was suggested in recent papers. Therefore, standard solar
models cannot be used as an argument for a high metallicity composition. While
further work is required to improve solar models, we note that direct
helioseismic inversions indicate a low metallicity in the convective envelope,
in agreement with spectroscopic analyses based on full 3D models.


  Wireless communication faces adversities due to noise, fading, and path loss.
Multiple-Input Multiple-Output (MIMO) systems are used to overcome individual
fading effect by employing transmit diversity. Duo to user single-antenna,
Cooperation between at least two users is able to provide spatial diversity.
This paper presents the evaluation of the performances of the Amplify and
Forward (AF) cooperative system for different relay positions using several
network topologies over Rayleigh and Rician fading channel. Furthermore, we
present the performances of AF cooperative system with various power
allocation. The results show that cooperative communication with convolutional
coding shows an outperformance compared to the non-convolutional, which is a
promising solution for high data-rate networks such as (WSN), Ad hoc, (IoT),
and even mobile networks. When topologies are compared, the simulation shows
that, linear topology offers the best BER performance, in contrast when the
relay acts as source and the source take the relay place, the analysis result
shows that, equilateral triangle topology has the best BER performance and
stability, and the system performance with inter-user Rician fading channel is
better than the performance of the system with inter-user Rayleigh fading
channel.


  This paper studies the Sobolev regularity estimates for weak solutions of a
class of degenerate, and singular quasi-linear elliptic problems of the form
$\text{div}[\mathbf{A}(x,u, \nabla u)]= \text{div}[\mathbf{F}]$ with
non-homogeneous Dirichlet boundary conditions over bounded non-smooth domains.
The coefficients $\mathbf{A}$ could be be singular, and degenerate or both in
$x$ in the sense that they behave like some weight function $\mu$, which is in
the $A_2$ class of Muckenhoupt weights. Global and interior weighted
$W^{1,p}(\Omega, \omega)$-regularity estimates are established for weak
solutions of these equations with some other weight function $\omega$. The
results obtained are even new for the case $\mu =1$ because of the dependence
on the solution $u$ of $\mathbf{A}$. In case of linear equations, our
$W^{1,p}$-regularity estimates can be viewed as the Sobolev's counterpart of
the H\"{o}lder's regularity estimates established by B. Fabes, C. E. Kenig, and
R. P. Serapioni.


  The relative center-of-mass energy spread at $e^+e^-$ colliders is about
$10^{-3}$, which is much larger than the widths of narrow resonances produced
in the s-channel in $e^+e^-$ collisions. This circumstance greatly lowers the
resonance production rates of J/Psi, Upsilon(1S), Upsilon(2S), Upsilon(3S) and
makes it extremely difficult to observe resonance production of the Higgs
boson. Thus, a significant reduction of the center-of-mass energy spread would
open up great opportunities in the search for new physics in rare decays of
narrow resonances, the search for new narrow states with small
$\Gamma_{e^+e^-}$, the study of true muonium and tauonium, etc. The existing
monochromatization scheme is only suitable for head-on collisions, while
$e^+e^-$ colliders with crossing angles (the so-called Crab Waist collision
scheme) can provide significantly higher luminosity due to reduced collision
effects. In this paper, we propose a new monochromatization method for
colliders with a large crossing angle. The contribution of the beam energy
spread to the spread of the center-of-mass energy is canceled by introducing an
appropriate energy-angle correlation at the interaction point; $\sigma_W/W \sim
(3-5)10^{-6}$ appears possible. Limitations of the proposed method are also
considered.


  An architecture for a quantum computer is presented in which spins associated
with donors in silicon function as qubits. Quantum operations on the spins are
performed using a combination of voltages applied to gates adjacent to the
spins and radio frequency applied magnetic fields resonant with spin
transitions. Initialization and measurement of electron spins is made by
electrostatic probing of a two electron system, whose orbital configuration
must depend on the spin states of the electrons because of the Pauli Principle.
Specific devices will be discussed which perform all the necessary operations
for quantum computing, with an emphasis placed on the qualitative principles
underlying their operation.
  The likely impediments to achieving large-scale quantum computation using
this architecture will be addressed: the computer must operate at extremely low
temperature, must be fabricated from devices built with near atomic precision,
and will require extremely accurate gating operations in order to perform
quantum logic. Refinements to the computer architecture will be presented which
could remedy each of these deficiencies. I will conclude by discussing a
specific realization of the computer using Si/SiGe heterostructures into which
donors are deposited using a low energy focused ion beam.


  Beyond the scope of space-coding metasurfaces, space-time digital
metasurfaces can substantially expand the application scope of digital
metamaterials in which simultaneous manipulation of electromagnetic waves in
both space and frequency domains would be feasible. In this paper, by adopting
a superposition operation of terms with unequal coefficient, Huygens principle,
and a proper time-varying biasing mechanism, some useful closed-form formulas
in the class of large digital metasurfaces were presented for predicting the
absolute directivity of scatted beams. Moreover, in the harmonic beam steering
scheme, by applying several suitable assumptions, we have derived two separate
expressions for calculating the exact total radiated power at harmonic
frequencies and total radiated power for scattered beams located at the
end-fire direction. Despite the simplifying assumptions we have applied, we
have proved that the provided formulas can still be a good and fast estimate
for developing a large digital metasurface with a predetermined power intensity
pattern. The effect of quantization level and metasurface dimensions on the
performance of power manipulating as well as the limitation on the maximum scan
angle in harmonic beam steering have been addressed. Several demonstrative
examples numerically demonstrated through MATLAB software and the good
agreement between simulations and theoretical predictions have been observed.
By considering the introduced restrictions in the manuscript, this method can
be implemented in any desired frequency just by employing phase-only
meta-particles as physical coding elements. The author believes that the
proposed straightforward approach discloses a new opportunity for various
applications such as multiple-target radar systems and THz communication.


  We study curves of marginal stability (CMS) in five-dimensional N=1 E_N
theories compactified on a circle using the D3-brane probe realization. In this
realization, BPS states correspond to string webs in the affine E_N 7-brane
background and junction positions of the webs deteremine CMS. We find that
there exist string webs involving infinitely many junctions. Consequently the
E_N theories have infinitely many CMS. We also find that there exists a
transition from open strings to string webs involving loops. The transition
describes a new phenomenon occurring on CMS.


  We apply the relative weights method to SU(3) gauge theory with staggered
fermions of mass 695 MeV at a set of temperatures in the range $151 \le T \le
267$ MeV, to obtain an effective Polyakov line action at each temperature. We
then apply a mean-field method to search for phase transitions in the effective
theory at finite densities. The result is a transition line in the plane of
temperature and chemical potential, with an endpoint at high temperature, as
expected, but also a second endpoint at a lower temperature. We cannot rule out
the possibilities that a transition line reappears at temperatures lower than
the range investigated, or that the second endpoint is absent for light quarks.


  We calculate the subjet rates for jets produced in hadron collisions. The kt
algorithm is used to define the jets and allows the theoretical calculation to
sum both the leading and next-to-leading logarithms in the resolution variable,
ycut. We also ensure that our calculation matches exactly the leading order in
alpha_s result and has sensible behaviour near thresholds.


  We survey key techniques and results from approximation theory in the context
of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We
then present a selection of results demonstrating how such approximations can
be used to speed up primitives crucial for the design of fast algorithms for
problems such as simulating random walks, graph partitioning, solving linear
system of equations, computing eigenvalues and combinatorial approaches to
solve semi-definite programs.


  We synthesize and study single crystals of the layered honeycomb lattice Mott
insulators Na2RuO3 and Li2RuO3 with magnetic Ru4+(4d4) ions. The newly found
Na2RuO3 features a nearly ideal honeycomb lattice and orders
antiferromagnetically at 30 K. Single-crystals of Li2RuO3 adopt a honeycomb
lattice with either C2/m or more distorted P21/m below 300 K, depending on
detailed synthesis conditions. We find that Li2RuO3 in both structures hosts a
well-defined magnetic state, in contrast to the singlet ground state found in
polycrystalline Li2RuO3. A phase diagram generated based on our results
uncovers a new, direct correlation between the magnetic ground state and
basal-plane distortions in the honeycomb ruthenates.


  In this paper, we consider the symmetric multi-type non-negative matrix
tri-factorization problem (SNMTF), which attempts to factorize several
symmetric non-negative matrices simultaneously. This can be considered as a
generalization of the classical non-negative matrix tri-factorization problem
and includes a non-convex objective function which is a multivariate sixth
degree polynomial and a has convex feasibility set. It has a special importance
in data science, since it serves as a mathematical model for the fusion of
different data sources in data clustering.
  We develop four methods to solve the SNMTF. They are based on four
theoretical approaches known from the literature: the fixed point method (FPM),
the block-coordinate descent with projected gradient (BCD), the gradient method
with exact line search (GM-ELS) and the adaptive moment estimation method
(ADAM). For each of these methods we offer a software implementation: for the
former two methods we use Matlab and for the latter Python with the TensorFlow
library.
  We test these methods on three data-sets: the synthetic data-set we
generated, while the others represent real-life similarities between different
objects.
  Extensive numerical results show that with sufficient computing time all four
methods perform satisfactorily and ADAM most often yields the best mean square
error ($\mathrm{MSE}$). However, if the computation time is limited, FPM gives
the best $\mathrm{MSE}$ because it shows the fastest convergence at the
beginning.
  All data-sets and codes are publicly available on our GitLab profile.


  I demonstrate that a very simple and safe change to the planning software
filter assignment algorithm for the Ultraviolet/Optical Telescope (UVOT)
onboard the Neil Gehrels Swift Observatory can reduce the number of filter
wheel rotations by $>10\%$, and its adoption is thus likely to significantly
extend the usable lifetime of the UVOT instrument. I recommend that such a
scheme be implemented.


  We study the maximum modulus set, $\mathcal{M}(p)$, of a polynomial $p$. We
are interested in constructing $p$ so that $\mathcal{M}(p)$ has certain
exceptional features. Jassim and London gave a cubic polynomial $p$ such that
$\mathcal{M}(p)$ has one discontinuity, and Tyler found a quintic polynomial
$\tilde{p}$ such that $\mathcal{M}(\tilde{p})$ has one singleton component.
These are the only results of this type, and we strengthen them considerably.
In particular, given a finite sequence $a_1, a_2, \ldots, a_n$ of distinct
positive real numbers, we construct polynomials $p$ and $\tilde{p}$ such that
$\mathcal{M}(p)$ has discontinuities of modulus $a_1, a_2, \ldots, a_n$, and
$\mathcal{M}(\tilde{p})$ has singleton components at the points $a_1, a_2,
\ldots, a_n$.
  Finally we show that these results are strong, in the sense that it is not
possible for a polynomial to have infinitely many discontinuities in its
maximum modulus set.


  We evaluated all two loop conformal integrals appearing in five point
correlation functions of protected operators of $\mathcal{N} = 4$ Super
Yang-Mills in several kinematical regimes. Starting from the correlation
function of the lightest operators of the theory, we were able to extract
structure constants of up to two spinning operators for small and large values
of polarizations and spin. We conjectured an universal all loop behaviour for
the large spin small polarization structure constants and comment on the
subtleties of analytically continuing it from finite to large spin. We also
consider correlation functions of heavier operators that get factorized in the
more fundamental object called decagon. We fixed this object at two loops in
general kinematics and studied its physical properties under OPE and null
limits.


  Recent deep-learning models have achieved impressive prediction performance,
but often sacrifice interpretability and computational efficiency.
Interpretability is crucial in many disciplines, such as science and medicine,
where models must be carefully vetted or where interpretation is the goal
itself. Moreover, interpretable models are concise and often yield
computational efficiency. Here, we propose adaptive wavelet distillation (AWD),
a method which aims to distill information from a trained neural network into a
wavelet transform. Specifically, AWD penalizes feature attributions of a neural
network in the wavelet domain to learn an effective multi-resolution wavelet
transform. The resulting model is highly predictive, concise, computationally
efficient, and has properties (such as a multi-scale structure) which make it
easy to interpret. In close collaboration with domain experts, we showcase how
AWD addresses challenges in two real-world settings: cosmological parameter
inference and molecular-partner prediction. In both cases, AWD yields a
scientifically interpretable and concise model which gives predictive
performance better than state-of-the-art neural networks. Moreover, AWD
identifies predictive features that are scientifically meaningful in the
context of respective domains. All code and models are released in a
full-fledged package available on Github
(https://github.com/Yu-Group/adaptive-wavelets).


  In this paper, we set up two surgery theories and two kinds of Whitehead
torsion for foliations. First, we construct a bounded surgery theory and
bounded Whitehead torsion for foliations, which correspond to the Connes'
foliation algebra in the K-theory of operator algebras, in the sense that there
is an analogy between surgery theory and index theory, and a Novikov Conjecture
for bounded surgery on foliations in analogy with the foliated Novikov
conjecture of P.Baum and A.Connes in operator theory. This surgery theory
classifies the leaves topologically. Secondly, we construct a bounded geometry
surgery for foliations, which is a generalization of blocked surgery, and a
bounded geometry Whitehead torsion. The classifications in this surgery theory
include the specification of the Riemannian metrics of the leaves up to
quasi=isometry. We state Borel conjectures for foliations, which solves a
problem posed by S.Weinberger \cite{Wein}, and verify these in some cases of
geometrical interest.


  We study generalized gauge theories engineered by taking the low energy limit
of the $Dp$ branes wrapping $X \times T^{p-3}$, with $X$ a possibly singular
surface in a Calabi-Yau fourfold $Z$. For toric $Z$ and $X$ the partition
function can be computed by localization, making it a statistical mechanical
model, called the gauge origami. The random variables are the ensembles of
Young diagrams. The building block of the gauge origami is associated with a
tetrahedron, whose edges are colored by vector spaces. We show the properly
normalized partition function is an entire function of the Coulomb moduli, for
generic values of the $\Omega$-background parameters. The orbifold version of
the theory defines the $qq$-character operators, with and without the surface
defects. The analytic properties are the consequence of a relative compactness
of the moduli spaces $M({\vec n}, k)$ of crossed and spiked instantons,
demonstrated in arXiv:1608.07272.


  Based on the relativistic mean-field effective interactions theory, and Lai
dong model \citep{b37, b38, b39}, we discuss the influences of superstrong
magnetic fields (SMFs) on electron Fermi energy, nuclear blinding energy, and
single-particle level structure in magnetars surface. By using the method of
Shell-Model Monte Carlo (SMMC), and the Random Phase Approximation (RPA)
theory, we detailed analyze the neutrino energy loss rates(NELRs) by electron
capture (EC) for iron group nuclei in SMFs.


  We propose a fully automatic method for fitting a 3D morphable model to
single face images in arbitrary pose and lighting. Our approach relies on
geometric features (edges and landmarks) and, inspired by the iterated closest
point algorithm, is based on computing hard correspondences between model
vertices and edge pixels. We demonstrate that this is superior to previous work
that uses soft correspondences to form an edge-derived cost surface that is
minimised by nonlinear optimisation.


  The volatile transition from quiescent laminar to strongly fluctuating
turbulent dynamics in shear flows remains only poorly understood despite its
practical importance and more than a century of intense research. The
theoretical understanding of the transition process has been complicated by the
lack of a linear instability mechanism and additionally by a catastrophic
collapse of turbulence which can occur after extremely long lifetimes.
Turbulence close to onset is investigated experimentally in three different
geometries: pipe, duct and channel flow. The reverse transition from turbulent
to laminar flow is observed to be a general feature of shear flows. A critical
point is uncovered at slightly higher flow rates, where the nature of the flow
changes abruptly to the generic case of expanding turbulence. The critical
exponent associated with this phase transition is found to be universal. This
confirms a conjecture made over 20 years ago based on an analogy between fluid
turbulence and discrete models in statistical physics.


  In recent years a large literature on deep learning based methods for the
numerical solution partial differential equations has emerged; results for
integro-differential equations on the other hand are scarce. In this paper we
study deep neural network algorithms for solving linear and semilinear
parabolic partial integro-differential equations with boundary conditions in
high dimension. To show the viability of our approach we discuss several case
studies from insurance and finance.


  A central challenge to many fields of science and engineering involves
minimizing non-convex error functions over continuous, high dimensional spaces.
Gradient descent or quasi-Newton methods are almost ubiquitously used to
perform such minimizations, and it is often thought that a main source of
difficulty for these local methods to find the global minimum is the
proliferation of local minima with much higher error than the global minimum.
Here we argue, based on results from statistical physics, random matrix theory,
neural network theory, and empirical evidence, that a deeper and more profound
difficulty originates from the proliferation of saddle points, not local
minima, especially in high dimensional problems of practical interest. Such
saddle points are surrounded by high error plateaus that can dramatically slow
down learning, and give the illusory impression of the existence of a local
minimum. Motivated by these arguments, we propose a new approach to
second-order optimization, the saddle-free Newton method, that can rapidly
escape high dimensional saddle points, unlike gradient descent and quasi-Newton
methods. We apply this algorithm to deep or recurrent neural network training,
and provide numerical evidence for its superior optimization performance.


  We calculate the partial decay widths of the W boson at one loop in the
standard model using the on-shell renormalization scheme endowed with a
gauge-independent definition of the Cabibbo-Kobayashi-Maskawa (CKM) mixing
matrix. We work in $R_\xi$ gauge and explicitly verify that the final
expressions are independent of the gauge parameters. Furthermore, we establish
the relationship between the on-shell and $\bar{\mathrm{MS}}$ definitions of
the CKM matrix, both in its generic form and in the Wolfenstein
parameterization. As a by-product of our analysis, we recover the beta function
of the CKM matrix.


  There are serious discussions for building a muon collider with
$\mu^{+}\mu^{-}$ collisions at c.o.m. energies up to 4 TeV. We point out that
the bileptonic gauge bosons predicted in some extensions of the Standard Model
would be readily discernable from the backward scattering cross-section, for
bilepton masses up to a substantial fraction of the c.o.m. energy.


  We solve the generalized Langevin equation driven by a stochastic force with
power-law autocorrelation function. A stationary Markov process has been
applied as a model of the noise. However, the resulting velocity variance does
not stabilizes but diminishes with time. It is shown that algebraic
distributions can induce such non-stationary affects. Results are compared to
those obtained with a deterministic random force. Consequences for the
diffusion process are also discussed.


  Regularity and uniqueness of weak solution of the compressible isentropic
Navier-Stokes equations is proven for small time in dimension $N=2,3$ under
periodic boundary conditions. In this paper, the initial density is not
required to have a positive lower bound and the pressure law is assumed to
satisfy a condition that reduces to $\gamma>1$ when $N=2,3$ and
$P(\rho)=a\rho^{\gamma}$. In a second part we prove a condition of blow-up in
slightly subcritical initial data when $\rho\in L^{\infty}$. We finish by
proving that weak solutions in $\T^{N}$ turn out to be smooth as long as the
density remains bounded in $L^{\infty}(L^{(N+1+\e)\gamma})$ with $\e>0$
arbitrary small.


  We study the problem of resolving a perhaps misspelled address of a location
into geographic coordinates of latitude and longitude. Our data structure
solves this problem within a few milliseconds even for misspelled and
fragmentary queries. Compared to major geographic search engines such as Google
or Bing we achieve results of significantly better quality.


  The infall of the Large Magellanic Cloud (LMC) is predicted to displace the
inner Milky Way (MW), imprinting an apparent 'reflex motion' on the observed
velocities of distant halo stars. We construct the largest all-sky
spectroscopic dataset of luminous red giant stars from $50-160$ kpc, including
a new survey of the southern celestial hemisphere. We fit the full 6D
kinematics of our data to measure the amplitude and direction of the inner MW's
motion towards the outer halo. The observed velocity grows with distance such
that, relative to halo stars at $100$ kpc, the inner MW is lurching at $\approx
40$ km s$^{-1}$ towards a recent location along the LMC's past orbit. Our
measurements align with N-body simulations of the halo's response to a $1.8
\times 10^{11} M_\odot$ LMC on first infall, suggesting that the LMC is at
least 15% as massive as the MW. Our findings highlight the dramatic
disequilibrium of the MW outskirts, and will enable more accurate measurements
of the total mass of our Galaxy.


  The Gas Slit Camera (GSC) is an X-ray instrument on the MAXI (Monitor of
All-sky X-ray Image) mission on the International Space Station. It is designed
to scan the entire sky every 92-minute orbital period in the 2--30 keV band and
to achieve the highest sensitivity among the X-ray all-sky monitors ever flown
so far. The GSC employs large-area position-sensitive proportional counters
with the total detector area of 5350 cm$^2$. The on-board data processor has
functions to format telemetry data as well as to control the high voltage of
the proportional counters to protect them from the particle irradiation. The
paper describes the instruments, on-board data processing, telemetry data
formats, and performance specifications expected from the ground calibration
tests.


  Let h be a probability measure on the nodes and arcs of a network Q, viewed
either as the location of a hidden object to be found or as the continuous
distribution of customers receiving packages. We wish to find a trajectory
starting from a specified root, or depot O that minimizes the expected search
or delivery time. We call such a trajectory optimal. When Q is a tree, we ask
for which h there is an optimal trajectory that is depth-first, and we find
sufficient conditions and in some cases necessary and sufficient conditions on
h. A consequence of our analysis is a determination of the optimal depot
location in the Delivery Man Problem, correcting an error in the literature. We
concentrate mainly on the search problem, with the Delivery Man Problem arising
as a special case.


  In this paper we discuss the notion of research data for the field of
mathematics and report on the status quo of research-data management and
planning. A number of decentralized approaches are presented and compared to
needs and challenges faced in three use cases from different mathematical
subdisciplines. We highlight the importance of tailoring research-data
management plans to mathematicians' research processes and discuss their usage
all along the data life cycle.


  Given a consistent choice of conformally invariant boundary conditions in a
two dimensional conformal field theory, one can construct new consistent
boundary conditions by deforming with a relevant boundary operator and flowing
to the infrared, or by a marginal deformation. Open string field theory
provides a very universal tool to discover and study such new boundary
theories. Surprisingly, it also allows one to go in the reverse direction and
to uncover solutions with higher boundary entropy. We will illustrate our
results on the well studied example of Ising model.


  We present the first unbiased determination of spin-dependent, or polarized,
Parton Distribution Functions (PDFs) of the proton. A statistically sound
representation of the corresponding uncertainties is achieved by means of the
NNPDF methodology: this was formerly developed for unpolarized distributions
and is now generalized to the polarized here for the first time. The features
of the procedure, based on robust statistical tools (Monte Carlo sampling for
error propagation, neural networks for PDF parametrization, genetic algorithm
for their minimization, and possibly reweighting for including new data samples
without refitting), are illustrated in detail. Different sets of polarized PDFs
are obtained at next-to-leading order accuracy in perturbative quantum
chromodynamics, based on both fixed-target inclusive deeply-inelastic
scattering data and the most recent polarized collider data. A quantitative
appraisal on the potential role of future measurements at an Electron-Ion
Collider is also presented. We study the stability of our results upon the
variation of several theoretical and methodological assumptions and we present
a detailed investigation of the first moments of our polarized PDFs, compared
to other recent analyses. We find that the uncertainty on the gluon
distribution from available data was substantially underestimated in previous
determinations; in particular, we emphasize that a large contribution to the
gluon may arise from the unmeasured small-x region, against the common belief
that this is actually rather small. We demonstrate that an Electron-Ion
Collider would provide evidence for a possible large gluon contribution to the
nucleon spin, though with a sizable residual uncertainty.


  For a tripartite pure state of three qubits, it is well known that there are
two inequivalent classes of genuine tripartite entanglement, namely the
GHZ-class and the W-class. Any two states within the same class can be
transformed into each other with stochastic local operations and classical
communication (SLOCC) with a non-zero probability. The optimal conversion
probability, however, is only known for special cases. Here, we derive new
lower and upper bounds for the optimal probability of transformation from a
GHZ-state to other states of the GHZ-class. A key idea in the derivation of the
upper bounds is to consider the action of the LOCC protocol on a different
input state, namely $1/\sqrt{2} [\ket{000} - \ket{111}]$, and demand that the
probability of an outcome remains bounded by 1. We also find an upper bound for
more general cases by using the constraints of the so-called interference term
and 3-tangle. Moreover, we generalize some of our results to the case where
each party holds a higher-dimensional system. In particular, we found that the
GHZ state generalized to three qutrits, i.e., $\ket{\mathrm{GHZ}_3} =
1/\sqrt{3} [ \ket{000} + \ket{111} + \ket{222} ] $, shared among three parties
can be transformed to {\it any} tripartite 3-qubit pure state with probability
1 via LOCC. Some of our results can also be generalized to the case of a
multipartite state shared by more than three parties.


  Adding domain knowledge to a learning system is known to improve results. In
multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior.
On the other hand, various model parameters can have different learning rates
in real-world problems, especially with skewed data. Two often-faced challenges
in Operation Management and Management Science applications are the absence of
informative priors, and the inability to control parameter learning rates. In
this study, we propose a hierarchical Empirical Bayes approach that addresses
both challenges, and that can generalize to any Bayesian framework. Our method
learns empirical meta-priors from the data itself and uses them to decouple the
learning rates of first-order and second-order features (or any other given
feature grouping) in a Generalized Linear Model. As the first-order features
are likely to have a more pronounced effect on the outcome, focusing on
learning first-order weights first is likely to improve performance and
convergence time. Our Empirical Bayes method clamps features in each group
together and uses the deployed model's observed data to empirically compute a
hierarchical prior in hindsight. We report theoretical results for the
unbiasedness, strong consistency, and optimal frequentist cumulative regret
properties of our meta-prior variance estimator. We apply our method to a
standard supervised learning optimization problem, as well as an online
combinatorial optimization problem in a contextual bandit setting implemented
in an Amazon production system. Both during simulations and live experiments,
our method shows marked improvements, especially in cases of small traffic. Our
findings are promising, as optimizing over sparse data is often a challenge.


  Let $G=C_n\oplus C_n$ and let $k\in [0,n-1]$. We study the structure of
sequences of terms from $G$ with maximal length $|S|=2n-2+k$ that fail to
contain a nontrivial zero-sum subsequence of length at most $2n-1-k$. For
$k\leq 1$, this is the inverse question for the Davenport Constant. For
$k=n-1$, this is the inverse question for the $\eta(G)$ invariant concerning
short zero-sum subsequences. The structure in both these cases (known
respectively as Property B and Property C) was established in a two-step
process: first verifying the multiplicative property that, if the structural
description holds when $n=n_1$ and $n=n_2$, then it holds when $n=n_1n_2$, and
then resolving the case $n$ prime separately. When $n$ is prime, the structural
characterization for $k\in [2,\frac{2n+1}{3}]$ was recently established,
showing $S$ must have the form $S=e_1^{[n-1]}\boldsymbol{\cdot}e_2^{[n
-1]}\boldsymbol{\cdot} (e_1+e_2)^{[k]}$ for some basis $(e_1,e_2)$ for $G$. It
was conjectured that this also holds for $k\in [2,n-2]$ (when $n$ is prime). In
this paper, we extend this conjecture by dropping the restriction that $n$ be
prime and establish the following multiplicative result. Suppose $k=k_mn+k_n$
with $k_m\in [0,m-1]$ and $k_n\in [0,n-1]$. If the conjectured structure holds
for $k_m$ in $C_m\oplus C_m$ and for $k_n$ in $C_n\oplus C_n$, then it holds
for $k$ in $C_{mn}\oplus C_{mn}$. This reduces the full characterization
question for $n$ and $k$ to the prime case. Combined with known results, this
unconditionally establishes the structure for extremal sequences in
$G=C_{n}\oplus C_{n}$ in many cases, including when $n$ is only divisible by
primes at most $7$, when $n\geq 2$ is a prime power and $k\leq \frac{2n+1}{3}$,
or when $n$ is composite and $k=n-d-1$ or $n-2d+1$ for a proper, nontrivial
divisor $d\mid n$.


  Feature selection and regularization are becoming increasingly prominent
tools in the efforts of the reinforcement learning (RL) community to expand the
reach and applicability of RL. One approach to the problem of feature selection
is to impose a sparsity-inducing form of regularization on the learning method.
Recent work on $L_1$ regularization has adapted techniques from the supervised
learning literature for use with RL. Another approach that has received renewed
attention in the supervised learning community is that of using a simple
algorithm that greedily adds new features. Such algorithms have many of the
good properties of the $L_1$ regularization methods, while also being extremely
efficient and, in some cases, allowing theoretical guarantees on recovery of
the true form of a sparse target function from sampled data. This paper
considers variants of orthogonal matching pursuit (OMP) applied to
reinforcement learning. The resulting algorithms are analyzed and compared
experimentally with existing $L_1$ regularized approaches. We demonstrate that
perhaps the most natural scenario in which one might hope to achieve sparse
recovery fails; however, one variant, OMP-BRM, provides promising theoretical
guarantees under certain assumptions on the feature dictionary. Another
variant, OMP-TD, empirically outperforms prior methods both in approximation
accuracy and efficiency on several benchmark problems.


  We propose a level-set approach to characterize the region occupied by the
solid in Stefan problems with and without surface tension, based on their
recent probabilistic reformulation. The level-set function is parameterized by
a feed-forward neural network, whose parameters are trained using the
probabilistic formulation of the Stefan growth condition. The algorithm can
handle Stefan problems where the liquid is supercooled and can capture surface
tension effects through the simulation of particles along the moving boundary
together with an efficient approximation of the mean curvature. We demonstrate
the effectiveness of the method on a variety of examples with and without
radial symmetry.


  We study a generalization of the problem of online learning in adversarial
linear contextual bandits by incorporating loss functions that belong to a
reproducing kernel Hilbert space, which allows for a more flexible modeling of
complex decision-making scenarios. We propose a computationally efficient
algorithm that makes use of a new optimistically biased estimator for the loss
functions and achieves near-optimal regret guarantees under a variety of
eigenvalue decay assumptions made on the underlying kernel. Specifically, under
the assumption of polynomial eigendecay with exponent $c>1$, the regret is
$\widetilde{O}(KT^{\frac{1}{2}(1+\frac{1}{c})})$, where $T$ denotes the number
of rounds and $K$ the number of actions. Furthermore, when the eigendecay
follows an exponential pattern, we achieve an even tighter regret bound of
$\widetilde{O}(\sqrt{T})$. These rates match the lower bounds in all special
cases where lower bounds are known at all, and match the best known upper
bounds available for the more well-studied stochastic counterpart of our
problem.


  The quasi-two-dimensional nickel chalcogenides $TlNi_2Se_2$ is a newly
discovered superconductor. We have performed optical spectroscopy study on
$TlNi_2Se_2$ single crystals over a broad frequency range at various
temperatures. The overall optical reflectance spectra are similar to those
observed in its isostructure $BaNi_2As_2$. Both the suppression in $R(\omega)$
and the peaklike feature in $\sigma_1(\omega)$ suggest the progressive
formation of a pseudogap feature in the midinfrared range with decreasing
temperatures, which might be originated from the dynamic local fluctuation of
charge-density-wave (CDW) instability. We propose that the CDW instability in
$TlNi_2Se_2$ is driven by the saddle points mechanism, due to the existence of
van Hove singularity very close to the Fermi energy.


  In this paper we apply second order stochastic dominance (SSD) to the problem
of enhanced indexation with asset subset (sector) constraints. The problem we
consider is how to construct a portfolio that is designed to outperform a given
market index whilst having regard to the proportion of the portfolio invested
in distinct market sectors. In our approach, subset SSD, the portfolio
associated with each sector is treated in a SSD manner. In other words in
subset SSD we actively try to find sector portfolios that SSD dominate their
respective sector indices. However the proportion of the overall portfolio
invested in each sector is not pre-specified, rather it is decided via
optimisation. Computational results are given for our approach as applied to
the S\&P~500 over the period $29^{\text{th}}$ August 2018 to $29^{\text{th}}$
December 2023. This period, over 5 years, includes the Covid pandemic, which
had a significant effect on stock prices. Our results indicate that the scaled
version of our subset SSD approach significantly outperforms the S\&P~500 over
the period considered. Our approach also outperforms the standard SSD based
approach to the problem.


  We summarize new RXTE observations to search for millisecond X-ray
variability from the bright Galactic bulge source GX 3+1. During a short 2 ksec
observation we did not detect kilohertz (kHz) quasiperiodic oscillations (QPO).
We place an upper limit of about 1 % (rms) on the amplitude of such
oscillations.


  Permutation Pattern Matching (or PPM) is a decision problem whose input is a
pair of permutations $\pi$ and $\tau$, represented as sequences of integers,
and the task is to determine whether $\tau$ contains a subsequence
order-isomorphic to $\pi$. Bose, Buss and Lubiw proved that PPM is NP-complete
on general inputs.
  We show that PPM is NP-complete even when $\pi$ has no decreasing subsequence
of length 3 and $\tau$ has no decreasing subsequence of length 4. This provides
the first known example of PPM being hard when one or both of $\pi$ and
$\sigma$ are restricted to a proper hereditary class of permutations.
  This hardness result is tight in the sense that PPM is known to be polynomial
when both $\pi$ and $\tau$ avoid a decreasing subsequence of length 3, as well
as when $\pi$ avoids a decreasing subsequence of length 2. The result is also
tight in another sense: we will show that for any hereditary proper subclass C
of the class of permutations avoiding a decreasing sequence of length 3, there
is a polynomial algorithm solving PPM instances where $\pi$ is from C and
$\tau$ is arbitrary.
  We also obtain analogous hardness and tractability results for the class of
so-called skew-merged patterns.
  From these results, we deduce a complexity dichotomy for the PPM problem
restricted to $\pi$ belonging to $Av(\rho)$, where $Av(\rho)$ denotes the class
of permutations avoiding a permutation $\rho$. Specifically, we show that the
problem is polynomial when $\rho$ is in the set {1, 12, 21, 132, 213, 231,
312}, and it is NP-complete for any other $\rho$.


  In their Comment, Park, Park and Kim claimed that the approach devised in our
work Phys.Rev.Lett. {\bf 83}, 5214 (1999) reproduces the correct long-time
behaviour of the density and correlation functions of the model under
consideration because of the {\it irrelevance} of the quartic term. Park,Park
and Kim also claimed that the approach devised in Phys.Rev.Lett. {\bf 83}, 5214
(1999) is a traditional Hartree-Fock approach.
  In this Reply we argue that the results obtained with our approach are in
agreement (also the subdominant corrections) with previous numerical
calculations and are therefore beyond traditional approximative
  (e.g. Hartree-Fock) schemes. Such a striking agreement cannot, in our
opinion, be explained only by the {\it eventual} irrelevance of a quartic term.


  We propose Functional Flow Matching (FFM), a function-space generative model
that generalizes the recently-introduced Flow Matching model to operate in
infinite-dimensional spaces. Our approach works by first defining a path of
probability measures that interpolates between a fixed Gaussian measure and the
data distribution, followed by learning a vector field on the underlying space
of functions that generates this path of measures. Our method does not rely on
likelihoods or simulations, making it well-suited to the function space
setting. We provide both a theoretical framework for building such models and
an empirical evaluation of our techniques. We demonstrate through experiments
on several real-world benchmarks that our proposed FFM method outperforms
several recently proposed function-space generative models.


  We describe a fast and accurate method for estimation of the cosmic microwave
background (CMB) anisotropy angular power spectrum --- Monte Carlo Apodised
Spherical Transform EstimatoR. Originally devised for use in the interpretation
of the Boomerang experimental data, MASTER is both a computationally efficient
method suitable for use with the currently available CMB data sets (already
large in size, despite covering small fractions of the sky, and affected by
inhomogeneous and correlated noise), and a very promising application for the
analysis of very large future CMB satellite mission products.


  The fusion rules in $\mathrm{Rep}_f D(G)$ for a finite group $G$ can be
computed in terms of character inner products. Using an explicit formula for
these fusion rules, we show that $\mathrm{Rep}_f D(G)$ is multiplicity free for
two infinite families of finite groups: the Dihedral groups and the Dicyclic
groups. In fact, we will compute all fusion rules in these categories.
Multiplicity freeness is a desired property for modular tensor categories,
since it greatly simplifies the computation of $F$-matrices. Furthermore, we
observe that the fusion rules for Dihedral groups $D_{2n}$ with $n$ odd are
extremely similar to the fusion rules of Type $B$ level $2$ fusion algebras of
Wess-Zumino-Witten conformal field theories. Moreover, we give a proof of the
fusion rule formula by using Mackey theory.


  An exact map was established by Lacroix-A-Chez-Toine, Majumdar, and Schehr in
[44] between the $N$ complex eigenvalues of complex non-Hermitian random
matrices from the Ginibre ensemble, and the positions of $N$ non-interacting
Fermions in a rotating trap in the ground state. An important quantity is the
statistics of the number of Fermions $\mathcal{N}_a$ in a disc of radius $a$.
Extending the work [44] covering Gaussian and rotationally invariant potentials
$Q$, we present a rigorous analysis in planar complex and symplectic ensembles,
which both represent 2D Coulomb gases. We show that the variance of
$\mathcal{N}_a$ is universal in the large-$N$ limit, when measured in units of
the mean density proportional to $\Delta Q$, which itself is non-universal.
This holds in the large-$N$ limit in the bulk and at the edge, when a finite
fraction or almost all Fermions are inside the disc. In contrast, at the
origin, when few eigenvalues are contained, it is the singularity of the
potential that determines the universality class. We present three explicit
examples from the Mittag-Leffler ensemble, products of Ginibre matrices, and
truncated unitary random matrices. Our proofs exploit the integrable structure
of the underlying determinantal respectively Pfaffian point processes and a
simple representation of the variance in terms of truncated moments at
finite-$N$.


  We prove a fractional version of Poincar\'e inequalities in the context of
$\R^n$ endowed with a fairly general measure. Namely we prove a control of an
$L^2$ norm by a non local quantity, which plays the role of the gradient in the
standard Poincar\'e inequality. The assumption on the measure is the fact that
it satisfies the classical Poincar\'e inequality, so that our result is an
improvement of the latter inequality. Moreover we also quantify the tightness
at infinity provided by the control on the fractional derivative in terms of a
weight growing at infinity. The proof goes through the introduction of the
generator of the Ornstein-Uhlenbeck semigroup and some careful estimates of its
powers. To our knowledge this is the first proof of fractional Poincar\'e
inequality for measures more general than L\'evy measures.


  The noisy dynamics of chemical systems is commonly studied using either the
chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE).
The latter is a continuum approximation of the discrete CME approach. We here
show that the CFPE may fail to capture the CME's prediction of noise-induced
multistability. In particular we find a simple chemical system for which the
CME's marginal probability distribution changes from unimodal to multimodal as
the system-size decreases below a critical value, while the CFPE's marginal
probability distribution is unimodal for all physically meaningful system
sizes.


  The purpose of this paper is to establish analogues of the classical
Lefschetz Section Theorem for smooth tropical varieties. More precisely, we
prove tropical analogues of the section theorems of Lefschetz,
Andreotti-Frankel, Bott-Milnor-Thom, Hamm-L\^e and Kodaira-Spencer, and the
vanishing theorems of Andreotti-Frankel and Akizuki-Kodaira-Nakano.
  We start the paper by resolving a conjecture of Mikhalkin and Ziegler (2008)
concerning the homotopy types of certain filtrations of geometric lattices,
generalizing several known properties of full geometric lattices. This
translates to a crucial index estimate for the stratified Morse data at
critical points of the tropical variety; it can also by itself be interpreted
as a Lefschetz-type theorem for matroids.


  Token dropping is a recently-proposed strategy to speed up the pretraining of
masked language models, such as BERT, by skipping the computation of a subset
of the input tokens at several middle layers. It can effectively reduce the
training time without degrading much performance on downstream tasks. However,
we empirically find that token dropping is prone to a semantic loss problem and
falls short in handling semantic-intense tasks. Motivated by this, we propose a
simple yet effective semantic-consistent learning method (ScTD) to improve the
token dropping. ScTD aims to encourage the model to learn how to preserve the
semantic information in the representation space. Extensive experiments on 12
tasks show that, with the help of our ScTD, token dropping can achieve
consistent and significant performance gains across all task types and model
sizes. More encouragingly, ScTD saves up to 57% of pretraining time and brings
up to +1.56% average improvement over the vanilla token dropping.


  For many emerging optoelectronic materials, heteroepitaxial growth techniques
do not offer the same high material quality afforded by bulk, single-crystal
growth. However, the need for optical, electrical, or mechanical isolation at
the nanoscale level often necessitates the use of a dissimilar substrate, upon
which the active device layer stands. Faraday cage angled-etching (FCAE)
obviates the need for these planar, thin-film technologies by enabling in-situ
device release and isolation through an angled-etching process. By placing a
Faraday cage around the sample during inductively-coupled plasma reactive ion
etching (ICP-RIE), the etching plasma develops an equipotential at the cage
surface, directing ions normal to its face. In this Article, the effects
Faraday cage angle, mesh size, and sample placement have on etch angle,
uniformity, and mask selectivity are investigated within a silicon etching
platform. Simulation results qualitatively confirm experiments and help to
clarify the physical mechanisms at work. These results will help guide FCAE
process design across a wide range of material platforms.


  The DUNE IDR describes the proposed physics program and technical designs of
the DUNE far detector modules in preparation for the full TDR to be published
in 2019. It is intended as an intermediate milestone on the path to a full TDR,
justifying the technical choices that flow down from the high-level physics
goals through requirements at all levels of the Project. These design choices
will enable the DUNE experiment to make the ground-breaking discoveries that
will help to answer fundamental physics questions. Volume 2 describes the
single-phase module's subsystems, the technical coordination required for its
design, construction, installation, and integration, and its organizational
structure.


  Pervasive computing appears like a new computing era based on networks of
objects and devices evolving in a real world, radically different from
distributed computing, based on networks of computers and data storages.
Contrary to most context-aware approaches, we work on the assumption that
pervasive software must be able to deal with a dynamic software environment
before processing contextual data. After demonstrating that SOA (Service
oriented Architecture) and its numerous principles are well adapted for
pervasive computing, we present our extended SOA model for pervasive computing,
called Service Lightweight Component Architecture (SLCA). SLCA presents various
additional principles to meet completely pervasive software constraints:
software infrastructure based on services for devices, local orchestrations
based on lightweight component architecture and finally encapsulation of those
orchestrations into composite services to address distributed composition of
services. We present a sample application of the overall approach as well as
some relevant measures about SLCA performances.


  We introduce a new algorithm for approximate inference that combines
reparametrization, Markov chain Monte Carlo and variational methods. We
construct a very flexible implicit variational distribution synthesized by an
arbitrary Markov chain Monte Carlo operation and a deterministic transformation
that can be optimized using the reparametrization trick. Unlike current methods
for implicit variational inference, our method avoids the computation of log
density ratios and therefore it is easily applicable to arbitrary continuous
and differentiable models. We demonstrate the proposed algorithm for fitting
banana-shaped distributions and for training variational autoencoders.


  We present a measurement of the muon charge asymmetry from W boson decays
using 0.3 fb^{-1} of data collected at \sqrt{s}=1.96 GeV between 2002 and 2004
with the D0 detector at the Fermilab Tevatron ppbar Collider. We compare our
findings with expectations from next-to-leading-order calculations performed
using the CTEQ6.1M and MRST04 NLO parton distribution functions. Our findings
can be used to constrain future parton distribution function fits.


  We study the consequences of superconducting quark cores in neutron stars for
the magnetic fields of pulsars. We find that within recent nonperturbative
approaches to the effective quark interaction the diquark condensate forms a
superconductor of second kind whereas previously quark matter was considered as
a first kind superconductor. In both cases the magnetic field which is
generated in the surrounding hadronic shell of superfluid neutrons and
superconducting protons can penetrate into the quark matter core since it is
concentrated in neutron vortices where the field strength exceeds the critical
value. Therefore the magnetic field will not be expelled from the
superconducting quark core with the consequence that there is no decay of the
magnetic fields of pulsars. Thus we conclude that the occurence of a
superconducting quark matter core in pulsars does not contradict the
observational data which indicate that magnetic fields of pulsars have life
times larger than $10^7$ years.


  We present a clock-driven Spiking Neural Network simulator which is up to 3x
faster than the state of the art while, at the same time, being more general
and requiring less programming effort on both the user's and maintainer's side.
This is made possible by designing our pipeline around "work queues" which act
as interfaces between stages and greatly reduce implementation complexity. We
evaluate our work using three well-established SNN models on a series of
benchmarks.


  The need for appropriate ways to measure the distance or similarity between
data is ubiquitous in machine learning, pattern recognition and data mining,
but handcrafting such good metrics for specific problems is generally
difficult. This has led to the emergence of metric learning, which aims at
automatically learning a metric from data and has attracted a lot of interest
in machine learning and related fields for the past ten years. This survey
paper proposes a systematic review of the metric learning literature,
highlighting the pros and cons of each approach. We pay particular attention to
Mahalanobis distance metric learning, a well-studied and successful framework,
but additionally present a wide range of methods that have recently emerged as
powerful alternatives, including nonlinear metric learning, similarity learning
and local metric learning. Recent trends and extensions, such as
semi-supervised metric learning, metric learning for histogram data and the
derivation of generalization guarantees, are also covered. Finally, this survey
addresses metric learning for structured data, in particular edit distance
learning, and attempts to give an overview of the remaining challenges in
metric learning for the years to come.


  Estimation of a conditional mean (linking a set of features to an outcome of
interest) is a fundamental statistical task. While there is an appeal to
flexible nonparametric procedures, effective estimation in many classical
nonparametric function spaces (e.g., multivariate Sobolev spaces) can be
prohibitively difficult -- both statistically and computationally -- especially
when the number of features is large. In this paper, we present (penalized)
sieve estimators for regression in nonparametric tensor product spaces: These
spaces are more amenable to multivariate regression, and allow us to, in-part,
avoid the curse of dimensionality. Our estimators can be easily applied to
multivariate nonparametric problems and have appealing statistical and
computational properties. Moreover, they can effectively leverage additional
structures such as feature sparsity. In this manuscript, we give theoretical
guarantees, indicating that the predictive performance of our estimators scale
favorably in dimension. In addition, we also present numerical examples to
compare the finite-sample performance of the proposed estimators with several
popular machine learning methods.


  We investigate the problem of percolation of words in a random environment.
To each vertex, we independently assign a letter $0$ or $1$ according to
Bernoulli r.v.'s with parameter $p$. The environment is the resulting graph
obtained from an independent long-range bond percolation configuration on
$\mathbb{Z}^{d-1} \times \mathbb{Z}$, $d\geq 3$, where each edge parallel to
$\mathbb{Z}^{d-1}$ has length one and is open with probability $\epsilon$,
while edges of length $n$ parallel to $\mathbb{Z}$ are open with probability
$p_n$. We prove that if the sum of $p_n$ diverges, then for any $\epsilon$ and
$p$, there is a $K$ such that all words are seen from the origin with
probability close to $1$, even if all connections with length larger than $K$
are suppressed.


  We examine the role of environment on the in situ star formation (SF) hosted
by the progenitors of the most massive galaxies in the present-day universe,
the brightest cluster galaxies (BCGs), from $z \sim 3$ to present in the COSMOS
field. Progenitors are selected from the COSMOS field using a stellar mass cut
motivated by the evolving cumulative comoving number density of progenitors
within the Illustris simulation, as well as the Millennium-II simulation and a
constant comoving number density method for comparison. We characterize each
progenitor using far-ultraviolet--far-infrared observations taken from the
COSMOS field and fitting stellar, dust, and active galactic nucleus components
to their spectral energy distributions. Additionally, we compare the SF rates
of our progenitor sample to the local density maps of the COSMOS field to
identify the effects of environment. We find that BCG progenitors evolve in
three stages, starting with an in situ SF dominated phase ($z > 2.25$). This is
followed by a phase until $z \sim 1.25$ where mass growth is driven by in situ
SF and stellar mass deposited by mergers (both gas rich and poor) on the same
order of magnitude independent of local environment. Finally, at low redshift
dry mergers are the dominant stellar mass generation process. We also identify
this final transition period as the time when progenitors quench, exhibiting
quiescent NUV\emph{rJ} colors.


  Many new physics models, e.g., leptoquarks, extra dimensions, extended Higgs
sectors, supersymmetric theories, and dark sector extensions, are expected to
manifest themselves in the final states with hadronic jets. Novel experimental
techniques, including a dedicated scouting trigger stream and advanced machine
learning techniques can be employed to identify such signals. This talk
presents searches in CMS for new phenomena in the final states that include
jets, focusing on the most recent results obtained using the full Run-II
data-set collected at the LHC.


  The Higgs mixing term coefficient $\mu_{eff}$ is calculated in the scalar
potential in supergravity theories with string origin, in a model independent
approach. A general low energy effective expression is derived, where new
contributions are included which depend on the modular weights $q_{1,2}$ of the
Higgs superfields, the moduli and derivative terms. We find that in a class of
models obtained in the case of compactifications of the heterotic superstring,
the derivative terms are identically zero. Further, the total $\mu_{eff}$-term
vanishes identically if the sum of the two modular weights $q_1+q_2$ is equal
to two. Subleading $\mu$- corrections, in the presence of intermediate gauge
symmetries predicted in viable string scenarios, are also discussed.


  We discuss some special classes of canonical transformations of the extended
phase space, which relate integrable systems with a common Lagrangian
submanifold. Various parametric forms of trajectories are associated with
different integrals of motion, Lax equations, separated variables and
action-angles variables. In this review we will discuss namely these induced
transformations instead of the various parametric form of the geometric
objects.


  Ionization of acetylene by linearly-polarized, vacuum ultraviolet (VUV) laser
pulses is modelled using time-dependent density functional theory. Several
laser wavelengths are considered including one that produces direct ionization
to the first excited cationic state while another excites the molecules to a
Rydberg series incorporating an autoionizing state. We show that for the
wavelengths and intensities considered, ionization is greatest whenever the
molecule is aligned along the laser polarization direction. By considering high
harmonic generation we show that populating excited states can lead to a large
enhancement in the harmonic yield. Lastly, angularly-resolved photoelectron
spectra are calculated which show how the energy profile of the emitted
electrons significantly changes in the presence of these excited states.


  Robustness of convolutional neural networks (CNNs) has gained in importance
on account of adversarial examples, i.e., inputs added as well-designed
perturbations that are imperceptible to humans but can cause the model to
predict incorrectly. Recent research suggests that the noises in adversarial
examples break the textural structure, which eventually leads to wrong
predictions. To mitigate the threat of such adversarial attacks, we propose
defective convolutional networks that make predictions relying less on textural
information but more on shape information by properly integrating defective
convolutional layers into standard CNNs. The defective convolutional layers
contain defective neurons whose activations are set to be a constant function.
As defective neurons contain no information and are far different from standard
neurons in its spatial neighborhood, the textural features cannot be accurately
extracted, and so the model has to seek other features for classification, such
as the shape. We show extensive evidence to justify our proposal and
demonstrate that defective CNNs can defense against black-box attacks better
than standard CNNs. In particular, they achieve state-of-the-art performance
against transfer-based attacks without any adversarial training being applied.


  Topology optimization is widely used by engineers during the initial product
development process to get a first possible geometry design. The
state-of-the-art is the iterative calculation, which requires both time and
computational power. Some newly developed methods use artificial intelligence
to accelerate the topology optimization. These require conventionally
pre-optimized data and therefore are dependent on the quality and number of
available data. This paper proposes an AI-assisted design method for topology
optimization, which does not require pre-optimized data. The designs are
provided by an artificial neural network, the predictor, on the basis of
boundary conditions and degree of filling (the volume percentage filled by
material) as input data. In the training phase, geometries generated on the
basis of random input data are evaluated with respect to given criteria. The
results of those evaluations flow into an objective function which is minimized
by adapting the predictor's parameters. After the training is completed, the
presented AI-assisted design procedure supplies geometries which are similar to
the ones generated by conventional topology optimizers, but requires a small
fraction of the computational effort required by those algorithms. We
anticipate our paper to be a starting point for AI-based methods that requires
data, that is hard to compute or not available.


  The centerpoint theorem is a well-known and widely used result in discrete
geometry. It states that for any point set $P$ of $n$ points in $\mathbb{R}^d$,
there is a point $c$, not necessarily from $P$, such that each halfspace
containing $c$ contains at least $\frac{n}{d+1}$ points of $P$. Such a point
$c$ is called a centerpoint, and it can be viewed as a generalization of a
median to higher dimensions. In other words, a centerpoint can be interpreted
as a good representative for the point set $P$. But what if we allow more than
one representative? For example in one-dimensional data sets, often certain
quantiles are chosen as representatives instead of the median. We present a
possible extension of the concept of quantiles to higher dimensions. The idea
is to find a set $Q$ of (few) points such that every halfspace that contains
one point of $Q$ contains a large fraction of the points of $P$ and every
halfspace that contains more of $Q$ contains an even larger fraction of $P$.
This setting is comparable to the well-studied concepts of weak
$\varepsilon$-nets and weak $\varepsilon$-approximations, where it is stronger
than the former but weaker than the latter.


  We investigate regular elliptic boundary-value problems in bounded domains
and show the Fredholm property for the related operators in an extended scale
formed by inner product Sobolev spaces (of arbitrary real orders) and
corresponding interpolation Hilbert spaces. In particular, we can deal with
boundary data with arbitrary low regularity. In addition, we show interpolation
properties for the extended scale, embedding results, and global and local a
priori estimates for solutions to the problems under investigation. The results
are applied to elliptic problems with homogeneous right-hand side and to
elliptic problems with rough boundary data in Nikoskii spaces, which allows us
to treat some cases of white noise on the boundary.


  Open cell foams have diverse industrial applications e.g. heat exchangers,
structured reactors, filtration due to their unique properties such as high
porosity and high specific surface area. In order to theoretically determine
the geometric specific surface area and relationships between geometrical
parameters of isotropic open cell foams, a generalized mathematical correlation
was developed. For this purpose the tetrakaidecahedron geometry was used and
different shapes of strut cross-sections of foam structures were taken
explicitly into account. The derived correlation to predict geometrical
properties can be easily extended to different strut shapes. 3-D numerical
simulations at pore scale were performed to study the pressure drop
characteristics and effective thermal conductivity. Fluid flow through open
cell foam was performed in three different regimes: Darcy regime, transition
regime and inertia regime. Importance of geometrical properties on fluid flow
characteristics and their inclusion in the proposed correlations for predicting
pressure drop is discussed. Can Ergun parameters have constant numerical values
or not is also extensively discussed. Three different correlations were derived
to predict the effective thermal conductivity for both, isotropic and
anisotropic open cell foams. Geometrical parameters of foam matrix were
introduced in the correlations to predict effective thermal conductivity.


  We present a formalism to solve the Bethe-Goldstone scattering equation
without the use of partial wave expansion which is alternative to the one we
developed in a previous work. The present approach is more suitable for the
calculation of in-medium nucleon-nucleon cross sections, which are the focal
point of this paper. The impact of removing the spherical approximation on the
angle and energy dependence of, particularly, in-medium proton-proton and
proton-neutron differential cross sections is discussed along with its
potential implication.


  Let $u$ and $v$ be harmonic in $ \Omega \subset \mathbb{R}^n$ functions with
the same zero set $Z$. We show that the ratio $f$ of such functions is always
well-defined and is real analytic. Moreover it satisfies the maximum and
minimum principles. For $n=3$ we also prove the Harnack inequality and the
gradient estimate for the ratios of harmonic functions, namely ${
\sup\limits_{K} |f| \leq C \inf\limits_{K}| f| \quad \& \quad \sup\limits_{K}
|\nabla f| \leq C \inf\limits_{K}| f| }$ for any compact subset $K$ of
$\Omega$, where the constant $C$ depends on $K$, $Z$, $\Omega$ only. In
dimension two the first inequality follows from the boundary Harnack principle
and the second from the gradient estimate recently obtained by Mangoubi. It is
an open question whether these inequalities remain true in higher dimensions
($n \geq 4$).


  We present near-infrared (NIR) spectroscopic observations of the blue compact
dwarf (BCD) galaxy Mrk 59, obtained with the TripleSpec spectrograph mounted on
the 3.5m APO telescope. The NIR spectrum of Mrk 59, which covers the 0.90 -
2.40 micron wavelength range, shows atomic hydrogen, molecular hydrogen,
helium, sulfur and iron emission lines. The NIR data have been supplemented by
a SDSS optical spectrum. We found extinction in the BCD to be low [A(V)=0.24
mag] and to be the same in both the optical and NIR ranges. The NIR light does
not reveal hidden star formation. The H2 emission comes from dense clumps and
the H2 vibrational emission line intensities can be accounted for by photon
excitation. No shock excitation is needed. A CLOUDY photoinization model of Mrk
59 reproduces well the observed optical and NIR emission line fluxes. There is
no need to invoke sources of ionization other than stellar radiation.The [FeII]
1.257 and 1.643 micron emission lines, often used as supernova shock indicators
in low-excitation high-metallicity starburst galaxies, cannot play such a role
in high-excitation low-metallicity HII regions such as Mrk 59.


  The Ebola virus and the disease in effect tend to randomly move individuals
in the population around susceptible, infected, quarantined, hospitalized,
recovered, and dead sub-population. Motivated by the effectiveness in
propagating the disease through the virus, a new bio-inspired and
population-based optimization algorithm is proposed. This paper presents a
novel metaheuristic algorithm named Ebola optimization algorithm (EOSA). To
correctly achieve this, this study models the propagation mechanism of the
Ebola virus disease, emphasising all consistent states of the propagation. The
model was further represented using a mathematical model based on first-order
differential equations. After that, the combined propagation and mathematical
models were adapted for developing the new metaheuristic algorithm. To evaluate
the proposed method's performance and capability compared with other
optimization methods, the underlying propagation and mathematical models were
first investigated to determine how they successfully simulate the EVD.
Furthermore, two sets of benchmark functions consisting of forty-seven (47)
classical and over thirty (30) constrained IEEE CEC-2017 benchmark functions
are investigated numerically. The results indicate that the performance of the
proposed algorithm is competitive with other state-of-the-art optimization
methods based on scalability analysis, convergence analysis, and sensitivity
analysis. Extensive simulation results indicate that the EOSA outperforms other
state-of-the-art popular metaheuristic optimization algorithms such as the
Particle Swarm Optimization Algorithm (PSO), Genetic Algorithm (GA), and
Artificial Bee Colony Algorithm (ABC) on some shifted, high dimensional and
large search range problems.


  This paper is related to our previous works [1][2] on the error estimate of
the averaging technique, for systems with one fast angular variable. In the
cited references, a general method (of mixed analytical and numerical type) has
been introduced to obtain precise, fully quantitative estimates on the
averaging error. Here, this procedure is applied to the motion of a satellite
in a polar orbit around an oblate planet, retaining only the J_2 term in the
multipole expansion of the gravitational potential. To exemplify the method,
the averaging errors are estimated for the data corresponding to two Earth
satellites; for a very large number of orbits, computation of our estimators is
much less expensive than the direct numerical solution of the equations of
motion.


  Non-minimally coupled curvature-matter gravity models are an interesting
alternative to the Theory of General Relativity and to address the dark energy
and dark matter cosmological problems. These models have complex field
equations that prevent a full analytical study. Nonetheless, in a particular
limit, the behavior of a matter distribution can, in these models, be described
by a Schr\"odinger-Newton system. In nonlinear optics, the Schr\"odinger-Newton
system can be used to tackle a wide variety of relevant situations and several
numerical tools have been developed for this purpose. Interestingly, these
methods can be adapted to study General Relativity problems as well as its
extensions. In this work, we report the use of these numerical tools to study a
particular non-minimal coupling model that introduces two new potentials, an
attractive Yukawa potential and a repulsive potential proportional to the
energy density. Using the imaginary-time propagation method we have shown that
stationary solutions arise even at low energy density regimes.


  We give a new elementary proof of existence and uniqueness of a solution to
the Sylvester equation $AX-XB=Y$


  I propose a paradigm for scientific progress in NLP centered around
developing scalable, data-driven theories of linguistic structure. The idea is
to collect data in tightly scoped, carefully defined ways which allow for
exhaustive annotation of behavioral phenomena of interest, and then use machine
learning to construct explanatory theories of these phenomena which can form
building blocks for intelligible AI systems. After laying some conceptual
groundwork, I describe several investigations into data-driven theories of
shallow semantic structure using Question-Answer driven Semantic Role Labeling
(QA-SRL), a schema for annotating verbal predicate-argument relations using
highly constrained question-answer pairs. While this only scratches the surface
of the complex language behaviors of interest in AI, I outline principles for
data collection and theoretical modeling which can inform future scientific
progress. This note summarizes and draws heavily on my PhD thesis.


  We show that the Fe (VII-XII) M-shell unresolved transition array (UTA) in
the NGC 3783 900 ks Chandra HETGS observation clearly changes in opacity in a
timescale of 31 days responding to a factor of 2 change in the ionizing
continuum. The opacity variation is observed at a level >10 sigma. There is
also evidence for variability in the O VI K edge (at 3 sigma level). The
observed changes are consistent with the gas producing these absorption
features (the low ionization component) being close to photoionization
equilibrium. The gas responsible for the Fe (XVII-XXII) L-shell absorption (the
high ionization component), does not seem to be responding as expected in
photoionization equilibrium. The observed change in opacity for the UTA implies
a density >1E4 cm-3, and so locates the gas within 6 pc of the X-ray source.
The scenario in which the gas is composed of a continuous radial range of
ionization structures is ruled out, as in such scenario, no opacity variations
are expected. Rather, the structure of the absorber is likely composed by
heavily clumped gas.


  Partitions, the partition function $p(n)$, and the hook lengths of their
Ferrers-Young diagrams are important objects in combinatorics, number theory
and representation theory. For positive integers $n$ and $t$, we study
$p_t^e(n)$ (resp. $p_t^o(n)$), the number of partitions of $n$ with an even
(resp. odd) number of $t$-hooks. We study the limiting behavior of the ratio
$p_t^e(n)/p(n)$, which also gives $p_t^o(n)/p(n)$ since $p_t^e(n) + p_t^0(n) =
p(n)$. For even $t$, we show that $$\lim\limits_{n \to \infty}
\dfrac{p_t^e(n)}{p(n)} = \dfrac{1}{2},$$ and for odd $t$ we establish the
non-uniform distribution $$\lim\limits_{n \to \infty} \dfrac{p^e_t(n)}{p(n)} =
\begin{cases} \dfrac{1}{2} + \dfrac{1}{2^{(t+1)/2}} & \text{if } 2 \mid n, \\
\\ \dfrac{1}{2} - \dfrac{1}{2^{(t+1)/2}} & \text{otherwise.} \end{cases}$$
Using the Rademacher circle method, we find an exact formula for $p_t^e(n)$ and
$p_t^o(n)$, and this exact formula yields these distribution properties for
large $n$. We also show that for sufficiently large $n$, the signs of $p_t^e(n)
- p_t^o(n)$ are periodic.


  The generalized constrained search formalism is used to address the issues
concerning density-to-potential mapping for excited states in time-independent
density-functional theory. The multiplicity of potentials for any given density
and the uniqueness in density-to-potential mapping are explained within the
framework of unified constrained search formalism for excited-states due to
G\"orling, Levy-Nagy, Samal-Harbola and Ayers-Levy. The extensions of
Samal-Harbola criteria and it's link to the generalized constrained search
formalism are revealed in the context of existence and unique construction of
the density-to-potential mapping. The close connections between the proposed
criteria and the generalized adiabatic connection are further elaborated so as
to keep the desired mapping intact at the strictly correlated regime.
Exemplification of the unified constrained search formalism is done through
model systems in order to demonstrate that the seemingly contradictory results
reported so far are neither the true confirmation of lack of Hohenberg-Kohn
theorem nor valid representation of violation of Gunnarsson-Lundqvist theorem
for excited states. Hence the misleading interpretation of subtle differences
between the ground and excited state density functional formalism are
exemplified.


  The name "Ultra-Compact Dwarf Galaxy" (UCD) was invented for a new type of
astronomical object that has been discovered in cores of nearby galaxy clusters
a decade ago. UCDs resemble globular clusters, but are up to 100 times more
massive and slightly more extended. Their luminosities are comparable to those
of nuclei of the most massive dwarf ellipticals or late-type spirals. Various
formation scenarios have been brought forward to explain the origin and
evolution of UCDs. Two of them seem to be most promising: first, UCDs might be
the remnant nuclei of galaxies that have been disrupted in the cluster
environment. Second, UCDs might have formed from the agglomeration of many
young, massive star clusters that were created during ancient merger events. In
this contribution, I review the discovery history of UCDs, summarize their
observational properties in the fundamental plane of stellar systems and
discuss the implications for the different formation scenarios based on our
current knowledge about these enigmatic objects.


  We present a detailed study of D-brane superpotentials depending on several
open and closed-string deformations. The relative cohomology group associated
with the brane defines a generalized hypergeometric GKZ system which determines
the off-shell superpotential and its analytic properties under deformation.
Explicit expressions for the N=1 superpotential for families of type
II/F-theory compactifications are obtained for a list of multi-parameter
examples. Using the Hodge theoretic approach to open-string mirror symmetry, we
obtain new predictions for integral disc invariants in the A model instanton
expansion. We study the behavior of the brane vacua under extremal transitions
between different Calabi-Yau spaces and observe that the web of Calabi-Yau
vacua remains connected for a particular class of branes.


  We localize the entropy functionals of G. Perelman and generalize his
no-local-collapsing theorem and pseudo-locality theorem.
  Our generalization is technically inspired by further development of Li-Yau
estimate along the Ricci flow.
  It can be used to show the Gromov-Hausdorff convergence of the K\"ahler Ricci
flow on each minimal projective manifold of general type.


  With the potential prospects of the ${\Upsilon}(nS)$ at high-luminosity
dedicated heavy-flavor factories, the color-favored ${\Upsilon}(nS)$ ${\to}$
$B_{c}{\pi}$, $B_{c}K$ weak decays are studied with the pQCD approach. It is
found that branching ratios for the ${\Upsilon}(nS)$ ${\to}$ $B_{c}{\pi}$ decay
are as large as the order of ${\cal O}(10^{-11})$, which might be measured
promisingly by the future experiments.


  We present an architecture for arbitrarily scalable boson-sampling using two
nested fiber loops. The architecture has fixed experimental complexity,
irrespective of the size of the desired interferometer, whose scale is limited
only by fiber and switch loss rates. The architecture employs time-bin
encoding, whereby the incident photons form a pulse train, which enters the
loops. Dynamically controlled loop coupling ratios allow the construction of
the arbitrary linear optics interferometers required for boson-sampling. The
architecture employs only a single point of interference and may thus be easier
to stabilize than other approaches. The scheme has polynomial complexity and
could be realized using demonstrated present-day technologies.


  Newtonian physics is based on Newtonian calculus applied to Newtonian
dynamics. New paradigms such as MOND change the dynamics, but do not alter the
calculus. Calculus is dependent on arithmetic, e.g. in special relativity we
add and subtract velocities by means of addition $\beta_1\oplus
\beta_2=\tanh\big(\tanh^{-1}(\beta_1)+\tanh^{-1}(\beta_2)\big)$, although
multiplication $\beta_1\odot
\beta_2=\tanh\big(\tanh^{-1}(\beta_1)\cdot\tanh^{-1}(\beta_2)\big)$ does not
seem to appear in the literature. The map
$f_\mathbb{X}(\beta)=\tanh^{-1}(\beta)$ defines an isomorphism of the
arithmetic in $\mathbb{X}=(-1,1)$ with the standard one in $\mathbb{R}$. The
new arithmetic is non-Diophantine in the sense of Burgin. Velocity of light
plays a role of non-Diophantine infinity. The new arithmetic allows us to
define the corresponding derivative and integral, and thus a new calculus which
is non-Newtonian in the sense of Grossman and Katz. Treating he above example
as a paradigm, we ask what can be said about the set $\mathbb{X}$ and the
isomorphism $f_{\mathbb{X}}:\mathbb{X}\to \mathbb{R}$, if we assume the
standard form of Newtonian mechanics and general relativity (formulated by
means of the new calculus) but demand agreement with astrophysical
observations. It turns out that for $f_\mathbb{X}(t/t_H)\approx 0.8\sinh
(t-t_1)/(0.8\, t_H)$ the resulting non-Newtonian Friedman equation with
$\Omega_\Lambda=0$ is exactly quivalent to the standard Newtonian one with
$\Omega_\Lambda=0.7$, $\Omega_M=0.3$. Asymptotically flat rotation curves are
obtained if `zero', the neutral element of addition, is nonzero from the point
of view of the standard arithmetic of $\mathbb{R}$. We do not yet know if the
proposed generalization ultimately removes any need of dark matter, but it will
certainly change estimates of its parameters.


  We investigate Lepton Flavor Violation (LFV) in the general extension of the
Standard Model parametrized by the gauge invariant operators of dimension-6. We
discuss 3-body charged lepton decays and decay of $Z$ boson to lepton pair and
compare the obtained analytical expression with the current experimental
results. We derive the numerical bounds on the size of the Wilson coefficients
parameterizing the allowed size of New Physics effects.


  We study color superconductivity with $N_f=1,2,$ and 3 massless flavors of
quarks. We present a general formalism to derive and solve the gap equations
for condensation in the even-parity channel. This formalism shows that the
leading-order contribution to the gap equation is unique for all color
superconductors studied here, and that differences arise solely at the
subleading order. We discuss a simple method to compute subleading
contributions from the integration over gluon momenta in the gap equation.
Subleading contributions enter the prefactor of the color-superconducting gap
parameter. In the case of color-flavor and color-spin locking we identify
further corrections to this prefactor arising from the two-gap structure of the
quasiparticle excitations. Computing the transition temperature, $T_c$, where
the color-superconducting condensate melts, we find that these contributions
lead to deviations from the BCS behavior $T_c\simeq 0.57 \phi_0$, where
$\phi_0$ is the magnitude of the zero-temperature gap at the Fermi surface.


  A classical result in risk measure theory states that every coherent risk
measure has a dual representation as the supremum of certain expected value
over a risk envelope. We study this topic in more detail. The related issues
include: 1. Set operations of risk envelopes and how they change the risk
measures, 2. The structure of risk envelopes of popular risk measures, 3.
Aversity of risk measures and its impact to risk envelopes, and 4. A connection
between risk measures in stochastic optimization and uncertainty sets in robust
optimization.