  A new formulation of the Phase Field Crystal model is presented that is
consistent with the necessary microscopic independence between the phase field,
reflecting the broken symmetry of the phase, and both mass density and elastic
distortion. Although these quantities are related in equilibrium through a
macroscopic equation of state, they are independent variables in the free
energy, and can be independently varied in evaluating the dissipation
functional that leads to the model governing equations. The equations obtained
describe dislocation motion in an elastically stressed solid, and serve as an
extension of the equations of plasticity to the Phase Field Crystal setting.
Both finite and small deformation theories are considered, and the
corresponding kinetic equations for the fields derived.


  In this note it is shown that in his ``Comments'', Tsallis did not point out
any flaws in the main criticism of my paper, namely, that the nonextensive
q-entropy formalism fails to satisfy the zeroth law of thermodynamics. Details
are also given of a rigorous thermodynamic proof which demonstrates that,
contrary to Tsallis's assertion, the application of a nonextensive formalism to
black-body radiation does not lead to the well known $T^4$ Stefan-Boltzman law.


  We introduce the Koenigs lattice, which is a new integrable reduction of the
quadrilateral lattice (discrete conjugate net) and provides natural integrable
discrete analogue of the Koenigs net. We construct the Darboux-type
transformations of the Koenigs lattice and we show permutability of
superpositions of such transformations, thus proving integrability of the
Koenigs lattice. We also investigate the geometry of the discrete Koenigs
transformation. In particular we characterize the Koenigs transformation in
terms of an involution determined by a congruence conjugate to the lattice.


  This paper proposes a new machine learning based system for forest fire
earlier detection in a low-cost and accurate manner. Accordingly, it is aimed
to bring a new and definite perspective to visual detection in forest fires. A
drone is constructed for this purpose. The microcontroller in the system has
been programmed by training with deep learning methods, and the unmanned aerial
vehicle has been given the ability to recognize the smoke, the earliest sign of
fire detection. The common problem in the prevalent algorithms used in fire
detection is the high false alarm and overlook rates. Confirming the result
obtained from the visualization with an additional supervision stage will
increase the reliability of the system as well as guarantee the accuracy of the
result. Due to the mobile vision ability of the unmanned aerial vehicle, the
data can be controlled from any point of view clearly and continuously. System
performance are validated by conducting experiments in both simulation and
physical environments.


  We present an algorithm for multi-hop routing and scheduling of requests in
wireless networks in the \sinr\ model. The goal of our algorithm is to maximize
the throughput or maximize the minimum ratio between the flow and the demand.
  Our algorithm partitions the links into buckets. Every bucket consists of a
set of links that have nearly equivalent reception powers. We denote the number
of nonempty buckets by $\sigdiv$. Our algorithm obtains an approximation ratio
of $O(\sigdiv \cdot \log n)$, where $n$ denotes the number of nodes. For the
case of linear powers $\sigdiv =1$, hence the approximation ratio of the
algorithm is $O(\log n)$. This is the first practical approximation algorithm
for linear powers with an approximation ratio that depends only on $n$ (and not
on the max-to-min distance ratio).
  If the transmission power of each link is part of the input (and arbitrary),
then $\sigdiv = O(\log\Gamma + \log \Delta)$, where $\Gamma$ denotes the ratio
of the max-to-min power, and $\Delta$ denotes the ratio of the max-to-min
distance. Hence, the approximation ratio is $O(\log n \cdot (\log\Gamma + \log
\Delta))$.
  Finally, we consider the case that the algorithm needs to assign powers to
each link in a range $[\pmin,\pmax]$. An extension of the algorithm to this
case achieves an approximation ratio of $O[(\log n + \log \log \Gamma) \cdot
(\log\Gamma + \log \Delta)]$.


  We consider the problem of reconstructing two signals from the
autocorrelation and cross-correlation measurements. This inverse problem is a
fundamental one in signal processing, and arises in many applications,
including phase retrieval and blind channel estimation. In a typical phase
retrieval setup, only the autocorrelation measurements are obtainable. We show
that, when the measurements are obtained using three simple "masks", phase
retrieval reduces to the aforementioned reconstruction problem.
  The classic solution to this problem is based on finding common factors
between the $z$-transforms of the autocorrelation and cross-correlation
vectors. This solution has enjoyed limited practical success, mainly due to the
fact that it is not sufficiently stable in the noisy setting. In this work,
inspired by the success of convex programming in provably and stably solving
various quadratic constrained problems, we develop a semidefinite
programming-based algorithm and provide theoretical guarantees. In particular,
we show that almost all signals can be uniquely recovered by this algorithm (up
to a global phase). Comparative numerical studies demonstrate that the proposed
method significantly outperforms the classic method in the noisy setting.


  We adopt a statistical point of view on the conjecture of Lang which predicts
a lower bound for the canonical height of non-torsion rational points on
elliptic curves defined over $\mathbb{Q}$. More specifically, we prove that
among the family of all elliptic curves defined over $\mathbb{Q}$ and having
positive rank, there is a density one subfamily of curves which satisfy a
strong form of Lang's conjecture.


  The main concepts of general relativistic thermodynamics and general
relativistic statistical mechanics are reviewed. The main building block of the
proper relativistic extension of the classical thermodynamics laws is the
four-temperature vector \beta, which plays a major role in the quantum
framework and defines a very convenient hydrodynamic frame. The general
relativistic thermodynamic equilibrium condition demands \beta to be a Killing
vector field. We show that a remarkable consequence is that all Lie derivatives
of all physical observables along the four-temperature flow must then vanish.


  We propose a framework for robust and efficient training of Dense Object Nets
(DON) with a focus on multi-object robot manipulation scenarios. DON is a
popular approach to obtain dense, view-invariant object descriptors, which can
be used for a multitude of downstream tasks in robot manipulation, such as,
pose estimation, state representation for control, etc.. However, the original
work focused training on singulated objects, with limited results on
instance-specific, multi-object applications. Additionally, a complex data
collection pipeline, including 3D reconstruction and mask annotation of each
object, is required for training. In this paper, we further improve the
efficacy of DON with a simplified data collection and training regime, that
consistently yields higher precision and enables robust tracking of keypoints
with less data requirements. In particular, we focus on training with
multi-object data instead of singulated objects, combined with a well-chosen
augmentation scheme. We additionally propose an alternative loss formulation to
the original pixelwise formulation that offers better results and is less
sensitive to hyperparameters. Finally, we demonstrate the robustness and
accuracy of our proposed framework on a real-world robotic grasping task.


  In this paper we consider the potential benefits of adopting a binary
symmetric broadcast channel paradigm for multi-destination aggregation in
802.11 WLANs, as opposed to a more conventional packet erasure channel
paradigm. We propose two approaches for multi-destination aggregation, i.e.
superposition coding and a simpler time-sharing coding. Theoretical and
simulation results for both unicast and multicast traffic demonstrate that
increases in network throughput of more than 100% are possible over a wide
range of network conditions and that the much simpler time-sharing scheme
yields most of these gains and have minimal loss of performance. Importantly,
these performance gains are achieved exclusively through software rather than
hardware changes.


  A major experimental program is presently underway worldwide to determine the
fundamental non-perturbative functions, the Sivers, Boer-Mulders and
transversity distributions, which are vital for an understanding of the
internal structure of the nucleon. However, at present, many simplifying
assumptions are used in extracting these functions from the data. We
demonstrate that if the binning of the data in Q^2 is small enough so that
Q^2-evolution can be neglected inside a bin, then one can obtain stringent
tests of these assumptions. Failure to satisfy these tests implies that the
presently extracted non-perturbative functions are unreliable.
  To this end we consider the measurement of the Sivers, Boer-Mulders and
transversity difference asymmetries for hadrons with opposite charges in SIDIS
reactions with unpolarized and transversely polarized deuteron and proton
targets: l+N\to l'+h+X, h=\pi^\pm ,K^\pm ,h^\pm. Utilizing only charge and
isospin invariance, and applying the above mentioned simplifying assumptions we
obtain several testable relations amongst the measured asymmetries. If these
tests are satisfied then the measured asymmetries determine two different
combinations of the valence-quark transverse momentum dependent distributions,
which can be determined separately without any contributions from the strange
and other sea-quarks.


  We introduce a modification to the patchy method of Navasca and Krener for
solving the stationary Hamilton Jacobi Bellman equation. The numerical solution
that we generate is a set of polynomials that approximate the optimal cost and
optimal control on a partition of the state space. We derive an error bound for
our numerical method under the assumption that the optimal cost is a smooth
strict Lyupanov function. The error bound is valid when the number of subsets
in the partition is not too large.


  In this paper, we consider the meta learning problem for estimating the
graphs associated with high-dimensional Ising models, using the method of
$\ell_1$-regularized logistic regression for neighborhood selection of each
node. Our goal is to use the information learned from the auxiliary tasks in
the learning of the novel task to reduce its sufficient sample complexity. To
this end, we propose a novel generative model as well as an improper estimation
method. In our setting, all the tasks are \emph{similar} in their \emph{random}
model parameters and supports. By pooling all the samples from the auxiliary
tasks to \emph{improperly} estimate a single parameter vector, we can recover
the true support union, assumed small in size, with a high probability with a
sufficient sample complexity of $\Omega(1) $ per task, for $K = \Omega(d^3 \log
p ) $ tasks of Ising models with $p$ nodes and a maximum neighborhood size $d$.
Then, with the support for the novel task restricted to the estimated support
union, we prove that consistent neighborhood selection for the novel task can
be obtained with a reduced sufficient sample complexity of $\Omega(d^3 \log
d)$.


  Over two hundred years ago Capt. James Cook sailed up Whitsunday Passage,
just a few miles where we now sit, on a voyage of astronomical observation and
discovery that remains an inspiration to us all. Since the prospects of our
visiting planets beyond our solar system are slim, we will have to content
ourselves with searching for life using remote sensing, not sailing ships.
Fortunately, a recently completed NASA study has concluded that a Terrestrial
Planet Finder could be launched within a decade to detect terrestrial planets
around nearby stars. A visible light coronagraph using an 8-10 m telescope, or
an infrared nulling interferometer, operated on either a $\sim40$ m structure
or separated spacecraft, could survey over 150 stars, looking for habitable
planets and signs of primitive life. Such a mission, complemented by projects
(Kepler and Eddington) that will provide statistical information on the
frequency of Earth-sized planets in the habitable zone, will determine key
terms in the ``Drake equation'' that describes the number of intelligent
civilizations in the Universe.


  In a previous paper, we presented solution to the Slavnov--Taylor identity
for the QCD effective action, and argued that the action terms containing
(anti)ghost fields are unique. These terms have the same form as those in the
classical action, but the gluon and (anti)ghost effective fields are convoluted
with gluon and ghost dressing functions G_A and G_c, the latter containing
perturbative and nonperturbative effects (but not including the soliton-like
vacuum effects). In the present work we show how the perturbative QCD (pQCD)
can be incorporated into the framework of this action, and we present explicit
one-loop pQCD expressions for G_A and G_c. We then go on to check the
consistency of the obtained results by considering an antighost
Dyson--Schwinger equation (DSE). By solving the relations that result from the
Legendre transformation leading to the effective action, we obtain the
effective fields as power expansions of sources. We check explicitly that the
aforementioned one-loop functions G_A and G_c fulfil the antighost DSE at the
linear source level. We further explicitly check that these one-loop G_A and
G_c have the regularization-scale and momentum dependence consistent with the
antighost DSE at the quadratic source level. These checks suggest that the the
effective action with dressing functions represents a consistent framework for
treating QCD, at least at the one-loop level.


  The phase-field method is used as a basis to develop a strictly mass
conserving, yet simple, model for simulation of two-phase flow. The model is
aimed to be applied for the study of structure evolution in metallic foams. In
this regard, the critical issue is to control the rate of bubble coalescence
compared to concurrent processes such as their rearrangement due to fluid
motion. In the present model, this is achieved by tuning the interface energy
as a free parameter. The model is validated by a number of benchmark tests.
First, stability of a two dimensional bubble is investigated by the
Young-Laplace law for different values of the interface energy. Then, the
coalescence of two bubbles is simulated until the system reaches equilibrium
with a circular shape. To address the major capability of the present model for
the formation of foam structure, the bubble coalescence is simulated for
various values of interface energy in order to slow down the merging process.
These simulations are repeated in the presence of a rotational flow to
highlight the fact that the model allows to suppress the coalescence process
compared to the motion of bubbles relative to each other.


  Minimum Cost Polygon Overlay (MCPO) is a unique two-dimensional optimization
problem that involves the task of covering a polygon shaped area with a series
of rectangular shaped panels. This has a number of applications in the
construction industry. This work examines the MCPO problem in order to
construct a model that captures essential parameters of the problem to be
solved automatically using numerical optimization algorithms. Three algorithms
have been implemented of the actual optimization task: the greedy search, the
Monte Carlo (MC) method, and the Genetic Algorithm (GA). Results are presented
to show the relative effectiveness of the algorithms. This is followed by
critical analysis of various findings of this research.


  We show here the global, in time, regularity of the three dimensional viscous
Camassa-Holm (Lagrangian Averaged Navier-Stokes-alpha) equations. We also
provide estimates, in terms of the physical parameters of the equations, for
the Hausdorff and fractal dimensions of their global attractor. In analogy with
the Kolmogorov theory of turbulence, we define a small spatial scale,
\ell_{\epsilon}, as the scale at which the balance occurs in the mean rates of
nonlinear transport of energy and viscous dissipation of energy. Furthermore,
we show that the number of degrees of freedom in the long-time behavior of the
solutions to these equations is bounded from above by (L/\ell_{epsilon})^3,
where L is a typical large spatial scale (e.g., the size of the domain). This
estimate suggests that the Landau-Lifshitz classical theory of turbulence is
suitable for interpreting the solutions of the NS-alpha equations. Hence, one
may consider these equations as a closure model for the Reynolds averaged
Navier-Stokes equations (NSE). We study this approach, further, in other
related papers. Finally, we discuss the relation of the NS-alpha model to the
NSE by proving a convergence theorem, that as the length scale alpha tends to
zero a subsequence of solutions of the NS-alpha equations converges to a weak
solution of the three dimensional NSE.


  I describe a mathematical framework for the efficient processing of the very
large sets of Feynman diagrams contributing to the scattering of many
particles. I reexpress the established numerical methods for the recursive
construction of scattering elements as operations on compact abstract data
types. This allows efficient perturbative computations in arbitrary models, as
long as they can be described by an effective, not necessarily local,
Lagrangian.


  Reconfigurable intelligent surface (RIS) is a promising technology for RF
wireless power transfer (WPT) as it is capable of beamforming and beam focusing
without using active and power-hungry components. In this paper, we propose a
multi-tile RIS beam scanning (MTBS) algorithm for powering up
internet-of-things (IoT) devices. Considering the hardware limitations of the
IoT devices, the proposed algorithm requires only power information to enable
the beam focusing capability of the RIS. Specifically, we first divide the RIS
into smaller RIS tiles. Then, all RIS tiles and the phased array transmitter
are iteratively scanned and optimized to maximize the receive power. We
elaborately analyze the proposed algorithm and build a simulator to verify it.
Furthermore, we have built a real-life testbed of RIS-aided WPT systems to
validate the algorithm. The experimental results show that the proposed MTBS
algorithm can properly control the transmission phase of the transmitter and
the reflection phase of the RIS to focus the power at the receiver.
Consequently, after executing the algorithm, about 20 dB improvement of the
receive power is achieved compared to the case that all unit cells of the RIS
are in OFF state. By experiments, we confirm that the RIS with the MTBS
algorithm can greatly enhance the power transfer efficiency.


  In this paper, we propose a novel deep learning architecture to improving
word-level lip-reading. On the one hand, we first introduce the multi-scale
processing into the spatial feature extraction for lip-reading. Specially, we
proposed hierarchical pyramidal convolution (HPConv) to replace the standard
convolution in original module, leading to improvements over the model's
ability to discover fine-grained lip movements. On the other hand, we merge
information in all time steps of the sequence by utilizing self-attention, to
make the model pay more attention to the relevant frames. These two advantages
are combined together to further enhance the model's classification power.
Experiments on the Lip Reading in the Wild (LRW) dataset show that our proposed
model has achieved 86.83% accuracy, yielding 1.53% absolute improvement over
the current state-of-the-art. We also conducted extensive experiments to better
understand the behavior of the proposed model.


  We derive analytically the scaling behavior in the thermodynamic limit of the
number of nonfrozen and relevant nodes in the most general class of critical
Kauffman networks for any number of inputs per node, and for any choice of the
probability distribution for the Boolean functions. By defining and analyzing a
stochastic process that determines the frozen core we can prove that the mean
number of nonfrozen nodes in any critical network with more than one input per
node scales with the network size $N$ as $N^{2/3}$, with only $N^{1/3}$
nonfrozen nodes having two nonfrozen inputs and the number of nonfrozen nodes
with more than two inputs being finite in the thermodynamic limit. Using these
results we can conclude that the mean number of relevant nodes increases for
large $N$ as $N^{1/3}$, with only a finite number of relevant nodes having two
relevant inputs, and a vanishing fraction of nodes having more than three of
them. It follows that all relevant components apart from a finite number are
simple loops, and that the mean number and length of attractors increases
faster than any power law with network size.


  We consider the dynamics of dark matter solitons moving through non-uniform
cigar-shaped Bose-Einstein condensates described by the mean field
Gross-Pitaevskii equation with generalized nonlinearities, in the case when the
condition for the modulation stability of the Bose-Einstein condensate is
fulfilled. The analytical expression for the frequency of the oscillations of a
deep dark soliton is derived for nonlinearities which are arbitrary functions
of the density, while specific results are discussed for the physically
relevant case of a cubic-quintic nonlinearity modeling two- and three-body
interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation
for which the frequencies of the oscillations are known to be independent of
background density and interaction strengths, we find that in the presence of a
cubic-quintic nonlinearity an explicit dependence of the oscillations frequency
on the above quantities appears. This dependence gives rise to the possibility
of measuring these quantities directly from the dark soliton dynamics, or to
manage the oscillation via the changes of the scattering lengths by means of
Feshbach resonance. A comparison between analytical results and direct
numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good
agreement which confirms the validity of our approach.


  Interactions between galaxies leave distinguishable imprints in the form of
tidal features which hold important clues about their mass assembly.
Unfortunately, these structures are difficult to detect because they are low
surface brightness features so deep observations are needed. Upcoming surveys
promise several orders of magnitude increase in depth and sky coverage, for
which automated methods for tidal feature detection will become mandatory. We
test the ability of a convolutional neural network to reproduce human visual
classifications for tidal detections. We use as training $\sim$6000 simulated
images classified by professional astronomers. The mock Hyper Suprime Cam
Subaru (HSC) images include variations with redshift, projection angle and
surface brightness ($\mu_{lim}$ =26-35 mag arcsec$^{-2}$). We obtain
satisfactory results with accuracy, precision and recall values of Acc=0.84,
P=0.72 and R=0.85, respectively, for the test sample. While the accuracy and
precision values are roughly constant for all surface brightness, the recall
(completeness) is significantly affected by image depth. The recovery rate
shows strong dependence on the type of tidal features: we recover all the
images showing shell features and 87% of the tidal streams; these fractions are
below 75% for mergers, tidal tails and bridges. When applied to real HSC
images, the performance of the model worsens significantly. We speculate that
this is due to the lack of realism of the simulations and take it as a warning
on applying deep learning models to different data domains without prior
testing on the actual data.


  Designs generated by density-based topology optimization (TO) exhibit jagged
and/or smeared boundaries, which forms an obstacle to their integration with
existing CAD tools. Addressing this problem by smoothing or manual design
adjustments is time-consuming and affects the optimality of TO designs. This
paper proposes a fully automated procedure to obtain unambiguous, accurate and
optimized geometries from arbitrary 3D TO results. It consists of a geometry
extraction stage using a level-set-based design description involving radial
basis functions, followed by a shape optimization stage involving local
analysis refinements near the structural boundary using the Finite Cell Method.
Well-defined bounds on basis function weights ensure that sufficient
sensitivity information is available throughout the shape optimization process.
Our approach results in highly smooth and accurate optimized geometries, and
its effectiveness is illustrated by 2D and 3D examples.


  We show there is a positivity property for Wightman functions which is
analogous to the reflection positivity for the euclidean ones. The role of
euclidean time reflections is played here by the wedge reflections, which
change the sign of the time and one of the spatial coordinates.


  The Dirac semimetal PdTe${}_2$ becomes superconducting at a temperature
$T_{c}=1.6$~K. Thermodynamic and muon spin rotation experiments support type-I
superconductivity, which is unusual for a binary compound. A key property of a
type-I superconductor is the intermediate state which presents a coexistence of
superconducting and normal domains (flux structures) at magnetic fields lower
than the thermodynamic critical field $H_{c}$. By means of scanning SQUID
microscopy (SSM) we observe flux structures in the superconducting state of
PdTe${}_2$. The flux structures are strongly history dependent with a
transition from round shapes to laminar shapes as the magnetic field is more
and more increased. The field amplitudes measured at the surface are indicative
for the presence of Landau branching. The domain wall width in the intermediate
state has been determined.


  Given a prime q and a negative discriminant D, the CM method constructs an
elliptic curve E/\Fq by obtaining a root of the Hilbert class polynomial H_D(X)
modulo q. We consider an approach based on a decomposition of the ring class
field defined by H_D, which we adapt to a CRT setting. This yields two
algorithms, each of which obtains a root of H_D mod q without necessarily
computing any of its coefficients. Heuristically, our approach uses
asymptotically less time and space than the standard CM method for almost all
D. Under the GRH, and reasonable assumptions about the size of log q relative
to |D|, we achieve a space complexity of O((m+n)log q) bits, where mn=h(D),
which may be as small as O(|D|^(1/4)log q). The practical efficiency of the
algorithms is demonstrated using |D| > 10^16 and q ~ 2^256, and also |D| >
10^15 and q ~ 2^33220. These examples are both an order of magnitude larger
than the best previous results obtained with the CM method.


  We study the dynamical properties of the bosonic quantum East model at low
temperature. We show that a naive generalization of the corresponding spin-1/2
quantum East model does not posses analogous slow dynamical properties. In
particular, conversely to the spin case, the bosonic ground state turns out to
be not localized. We restore localization by introducing a repulsive
interaction term. The bosonic nature of the model allows us to construct rich
families of many-body localized states, including coherent, squeezed and cat
states. We formalize this finding by introducing a set of superbosonic
creation-annihilation operators which satisfy the bosonic commutation relations
and, when acting on the vacuum, create excitations exponentially localized
around a certain site of the lattice. Given the constrained nature of the
model, these states retain memory of their initial conditions for long times.
Even in the presence of dissipation, we show that quantum information remains
localized within decoherence times tunable with the parameters of the system.
We propose an implementation of the bosonic quantum East model based on
state-of-the-art superconducting circuits, which could be used in the near
future to explore dynamical properties of kinetically constrained models in
modern platforms.


  Holographic particle image velocimetry allows tracking particle trajectories
in time and space by means of holography. However, the drawback of the
technique is that in the three-dimensional particle distribution reconstructed
from a hologram, the individual particles can hardly be resolved due to the
superimposed out-of-focus signal from neighboring particles. We demonstrate
here a three-dimensional volumetric deconvolution applied to the reconstructed
wavefront which results in resolving all particles simultaneously in
three-dimensions. Moreover, we apply the three-dimensional volumetric
deconvolution to reconstructions of a time-dependent sequence of holograms of
an ensemble of polystyrene spheres moving in water. From each hologram we
simultaneously resolve all particles in the ensemble in three dimensions and
from the sequence of holograms we obtain the time-resolved trajectories of
individual polystyrene spheres.


  We study the gravitational wave (GW) phase shift arising from R{\o}mer delay
in binary black hole (BBH) mergers formed dynamically in three-body systems,
where both the inner orbit of the merging binary and the outer orbit are
eccentric. We provide a semi-analytical model and several analytical
approximations that allow for fast evaluation of both the temporal evolution
and the maximum value of the phase shift. The highest phase shifts occur when
the binary merges close to the pericentre of the outer orbit, and can in this
case be orders-of-magnitude larger compared to the circular limit. At high
outer orbit eccentricities, the orbital curvature leaves distinct imprints onto
the phase shift if the binary passes the outer pericentre during its inspiral.
By comparing with phase-shifts measured in numerical chaotic 3-body
scatterings, we show that our model accurately describes the observed phase of
dynamically assembled binary systems in realistic astrophysical scenarios,
providing a way to directly determine their formation channel via single GW
observations.


  We consider partial supersymmetry breaking in ${\cal N}=2$ supergravity
coupled to a single vector and a single hypermultiplet. This breaking pattern
is in principle possible if the quaternion-K\"ahler space of the hypermultiplet
admits (at least) one pair of commuting isometries. For this class of
manifolds, explicit metrics exist and we analyse a generic electro-magnetic
(dyonic) gauging of the isometries. An example of partial breaking in Minkowski
spacetime has been found long ago by Ferrara, Girardello and Porrati, using the
gauging of two translation isometries on $SO(4,1)/SO(4)$. We demonstrate that
no other example of partial breaking of ${\cal N}=2$ supergravity in Minkowski
spacetime exists. We also examine partial-breaking vacua in anti-de Sitter
spacetime that are much less constrained and exist generically even for
electric gaugings. On $SO(4,1)/SO(4)$, we construct the partially-broken
solution and its global limit which is the Antoniadis-Partouche-Taylor model.


  In the swiftly expanding domain of Natural Language Processing (NLP), the
potential of GPT-based models for the financial sector is increasingly evident.
However, the integration of these models with financial datasets presents
challenges, notably in determining their adeptness and relevance. This paper
introduces a distinctive approach anchored in the Instruction Tuning paradigm
for open-source large language models, specifically adapted for financial
contexts. Through this methodology, we capitalize on the interoperability of
open-source models, ensuring a seamless and transparent integration. We begin
by explaining the Instruction Tuning paradigm, highlighting its effectiveness
for immediate integration. The paper presents a benchmarking scheme designed
for end-to-end training and testing, employing a cost-effective progression.
Firstly, we assess basic competencies and fundamental tasks, such as Named
Entity Recognition (NER) and sentiment analysis to enhance specialization.
Next, we delve into a comprehensive model, executing multi-task operations by
amalgamating all instructional tunings to examine versatility. Finally, we
explore the zero-shot capabilities by earmarking unseen tasks and incorporating
novel datasets to understand adaptability in uncharted terrains. Such a
paradigm fortifies the principles of openness and reproducibility, laying a
robust foundation for future investigations in open-source financial large
language models (FinLLMs).


  We calibrate and then use the relation between equivalent width (EW) and
full-width-half-maximum (FWHM) of metallic absorption lines in the spectra of
RR Lyrae stars to estimate a new upper limit of Vrot sini less than or equal to
6 km/s on their axial equatorial rotational velocities, and to derive the
variations of macroturbulent velocities in their atmospheres during pulsation
cycles. Finally, we present a simple way to estimate macroturbulent/rotational
velocity from FWHM of the cross-correlation function.


  Nigerian Pidgin is an English-derived contact language and is traditionally
an oral language, spoken by approximately 100 million people. No orthographic
standard has yet been adopted, and thus the few available Pidgin datasets that
exist are characterised by noise in the form of orthographic variations. This
contributes to under-performance of models in critical NLP tasks. The current
work is the first to describe various types of orthographic variations commonly
found in Nigerian Pidgin texts, and model this orthographic variation. The
variations identified in the dataset form the basis of a phonetic-theoretic
framework for word editing, which is used to generate orthographic variations
to augment training data. We test the effect of this data augmentation on two
critical NLP tasks: machine translation and sentiment analysis. The proposed
variation generation framework augments the training data with new orthographic
variants which are relevant for the test set but did not occur in the training
set originally. Our results demonstrate the positive effect of augmenting the
training data with a combination of real texts from other corpora as well as
synthesized orthographic variation, resulting in performance improvements of
2.1 points in sentiment analysis and 1.4 BLEU points in translation to English.


  Given their capability of spreading active chemical species and collecting
electricity, porous media made of carbon fibers are extensively used as
diffusion layers in energy storage systems, such as redox flow batteries. In
spite of this, the dispersion dynamics of species inside porous media is still
not well understood and often lends itself to different interpretations.
Actually, the microscopic design of efficient porous media which can
potentially and effectively improve the performances of flow batteries, is a
still open challenge. The present study aims to investigate the effect of
fibrous media micro-structure on dispersion, in particular the effect of fiber
orientation on drag and dispersion dynamics. Several Lattice-Boltzmann
simulations of {flows through} differently-oriented fibrous media coupled with
Lagrangian simulations of particle tracers have been performed. Results show
that orienting fibers preferentially along the streamwise direction minimizes
the drag and maximizes the dispersion, which is the most desirable condition
for diffusion layers in flow batteries applications.


  Learning to predict scene depth from RGB inputs is a challenging task both
for indoor and outdoor robot navigation. In this work we address unsupervised
learning of scene depth and robot ego-motion where supervision is provided by
monocular videos, as cameras are the cheapest, least restrictive and most
ubiquitous sensor for robotics.
  Previous work in unsupervised image-to-depth learning has established strong
baselines in the domain. We propose a novel approach which produces higher
quality results, is able to model moving objects and is shown to transfer
across data domains, e.g. from outdoors to indoor scenes. The main idea is to
introduce geometric structure in the learning process, by modeling the scene
and the individual objects; camera ego-motion and object motions are learned
from monocular videos as input. Furthermore an online refinement method is
introduced to adapt learning on the fly to unknown domains.
  The proposed approach outperforms all state-of-the-art approaches, including
those that handle motion e.g. through learned flow. Our results are comparable
in quality to the ones which used stereo as supervision and significantly
improve depth prediction on scenes and datasets which contain a lot of object
motion. The approach is of practical relevance, as it allows transfer across
environments, by transferring models trained on data collected for robot
navigation in urban scenes to indoor navigation settings. The code associated
with this paper can be found at https://sites.google.com/view/struct2depth.


  We prove the equivalence of the two important facts about finite metric
spaces and universal Urysohn metric spaces $\Bbb U$, namely theorem A and
theorem B below: Theorem A (Approximation): The group of isometry $ISO(\Bbb U)$
contains everywhere dense locally finite subgroup; Theorem G(Globalization):
For each finite metric space $F$ there exists another finite metric space $\bar
F$ and isometric imbedding $j$ of $F$ to $\bar F$ such that isometry $j$
induces the imbedding of the group monomorphism of the group of isometries of
the space $F$ to the group of isometries of space $\bar F$ and each partial
isometry of $F$ can be extended up to global isometry in $\bar F$. The fact
that theorem $G$, is true was announced in 2005 by author without proof, and
was proved by S.Solecki in \cite{Sol} (see also \cite{P,P1}) based on the
previous complicate results of other authors. The theorem is generalization of
the Hrushevski's theorem about the globalization of the partial isomorphisms of
finite graphs. We intend to give a constructive proof in the same spirit for
metric spaces elsewhere. We also give the strengthening of homogeneity of
Urysohn space and in the last paragraph we gave a short survey of the various
constructions of Urysohn space including the new proof of the construction of
shift invariant universal distance matrix from \cite{CV}.


  Product cannibalisation is a well-known phenomenon in marketing and
technological research and describes the case when a new product steals sales
from another product under the same brand. A very special case of
cannibalisation may occur when the older product react to the competitive
strength of the newer one, absorbing the corresponding market shares. Given its
special character, we call this phenomenon inverse product cannibalisation. We
suppose that a case of inverse cannibalisation is observed between two products
of Apple Inc., the iPhone and the more recent iPad, and the first has been able
to succeed at the expense of the second. To explore this hypothesis, within a
diffusion of innovations perspective, we propose a modified Lotka-Volterra
model for mean trajectories in asymmetric competition, allowing us to test the
presence and the extent of the inverse cannibalisation phenomenon. A SARMAX
refinement integrates the short term predictions with seasonal and
autodependent components. A non-dimensional representation of the proposed
model shows that the penetration of the second technology has been beneficial
for the first, both in terms of market size and life cycle length.


  We study the effect of Zn alloying on the hydrogen desorption properties of
Mg(BH$_4$)$_2$ using $\it{ab\ initio}$ simulations. In particular, we
investigate formation/reaction enthalpies/entropies for a number of compounds
and reactions at a wide range of temperatures and Zn concentrations in
Mg$_{1-x}$Zn$_x$(BH$_4$)$_2$. Our results show that the thermodynamic stability
of the resulting material can be significantly lowered through Zn alloying. We
find that e.g. the solid solution Mg$_{2/3}$Zn$_{1/3}$(BH$_4$)$_2$ has a
reaction enthalpy for the complete hydrogen desorption of only 25.3 kJ/mol
H$_2$$-$a lowering of 15 kJ/mol H$_2$ compared to the pure phase and a
corresponding lowering in critical temperature of 123 K. In addition, we find
that the enthalpy of mixing is rather small and show that the decrease in
reaction enthalpy with Zn concentration is approximately linear.


  Beam dump experiments provide a distinctive opportunity to search for dark
photons, which are compelling candidates for dark matter with low mass. In this
study, we propose the application of Graph Neural Networks (GNN) in tracking
reconstruction with beam dump experiments to obtain high resolution in both
tracking and vertex reconstruction. Our findings demonstrate that in a typical
3-track scenario with the visible decay mode, the GNN approach significantly
outperforms the traditional approach, improving the 3-track reconstruction
efficiency by up to 88% in the low mass region. Furthermore, we show that
improving the minimal vertex detection distance significantly impacts the
signal sensitivity in dark photon searches with the visible decay mode. By
reducing the minimal vertex distance from 5 mm to 0.1 mm, the exclusion upper
limit on the dark photon mass ($m_A\prime$) can be improved by up to a factor
of 3.


  By means of an analogy with Classical Mechanics and Geometrical Optics, we
are able to reduce Lagrangians to a kinetic term only. This form enables us to
examine the extended solution set of field theories by finding the geodesics of
this kinetic term's metric. This new geometrical standpoint sheds light on some
foundational issues of QFT and brings to the forefront core aspects of field
theory.


  Using Pathak and Pathak techniques, the basic function $D^\alpha(u,v,w)$
associated with general novel fractional wavelet transform (GNFrWT)is defined
and its properties are investigated. By using basic function $D^\alpha(u,v,w)$
translation and convolution associated with GNFrWT are defined and certain
existence theorems are proved for basic function and associated convolution.


  The problem of accretion in the Trojan 1:1 resonance is akin to the standard
problem of planet formation, transplanted from a star-centered disk to a disk
centered on the Lagrange point. The newly discovered class of Neptune Trojans
promises to test theories of planet formation by coagulation. Neptune Trojans
resembling the prototype 2001 QR322 (``QR'')--whose radius of ~100 km is
comparable to that of the largest Jupiter Trojan--may outnumber their Jovian
counterparts by a factor of ~10. We discover that seeding the 1:1 resonance
with debris from planetesimal collisions and having the seed particles accrete
in situ naturally reproduces the inferred number of QR-sized Trojans. We
analyze accretion in the Trojan sub-disk by applying the two-groups method,
accounting for kinematics specific to the resonance. We find that a Trojan
sub-disk comprising decimeter-sized seed particles and having a surface density
1e-3 that of the local minimum-mass disk produces ~10 QR-sized objects in ~1
Gyr, in accord with observation. Further growth is halted by collisional
diffusion of seed particles out of resonance. In our picture, the number and
sizes of the largest Neptune Trojans represent the unadulterated outcome of
dispersion-dominated, oligarchic accretion. Large Neptune Trojans, perhaps the
most newly accreted objects in our Solar System, may today have a dispersion in
orbital inclination of less than ~10 degrees, despite the existence of niches
of stability at higher inclinations. Such a vertically thin disk, born of a
dynamically cold environment necessary for accretion, and raised in minimal
contact with external perturbations, contrasts with the thick disks of other
minor body belts.


  A heat flux in a high-$\beta$ plasma with low collisionality triggers the
whistler instability. Quasilinear theory predicts saturation of the instability
in a marginal state characterized by a heat flux that is fully controlled by
electron scattering off magnetic perturbations. This marginal heat flux does
not depend on the temperature gradient and scales as $1/\beta$. We confirm this
theoretical prediction by performing numerical particle-in-cell simulations of
the instability. We further calculate the saturation level of magnetic
perturbations and the electron scattering rate as functions of $\beta$ and the
temperature gradient to identify the saturation mechanism as quasilinear.
Suppression of the heat flux is caused by oblique whistlers with
magnetic-energy density distributed over a wide range of propagation angles.
This result can be applied to high-$\beta$ astrophysical plasmas, such as the
intracluster medium, where thermal conduction at sharp temperature gradients
along magnetic-field lines can be significantly suppressed. We provide a
convenient expression for the amount of suppression of the heat flux relative
to the classical Spitzer value as a function of the temperature gradient and
$\beta$. For a turbulent plasma, the additional independent suppression by the
mirror instability is capable of producing large total suppression factors
(several tens in galaxy clusters) in regions with strong temperature gradients.


  The Large Hadron Collider is currently undergoing its High Luminosity
upgrade, which is set to increase the instantaneous luminosity by about a
factor of five. Consequently, the Compact Muon Solenoid experiment is upgrading
its muon spectrometer to cope with the increased muon flux in the forward
region. The GE2/1 triple-Gas Electron Multiplier detector, which has recently
entered the mass production phase, and the ME0 triple-GEM detector system,
which is in the late prototyping phase, are undergoing electronics integration.
These proceedings briefly discuss the frontend electronics for the GE2/1 and
ME0 detector systems, the electronics integration testing process, and the
future plans for the frontend electronics of these two detector systems by the
CMS GEM Collaboration.


  All of the 14 subfields of the Kepler field have been observed at least once
with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST,
Xinglong Observatory, China) during the 2012-2014 observation seasons. There
are 88,628 reduced spectra with SNR$_g$ (signal-to-noise ratio in g band)
$\geq$ 6 after the first round (2012-2014) of observations for the
LAMOST-Kepler project (LK-project). By adopting the upgraded version of the
LAMOST Stellar Parameter pipeline (LASP), we have determined the atmospheric
parameters ($T_{\rm eff}$ , $\log g$, and $\rm [Fe/H]$) and heliocentric radial
velocity $v_{\rm rad}$ for 51,406 stars with 61,226 spectra. Compared with
atmospheric parameters derived from both high-resolution spectroscopy and
asteroseismology method for common stars in Huber et al. (2014), an external
calibration of LASP atmospheric parameters was made, leading to the
determination of external errors for the giants and dwarfs, respectively.
Multiple spectroscopic observations for the same objects of the LK-project were
used to estimate the internal uncertainties of the atmospheric parameters as a
function of SNR$_g$ with the unbiased estimation method. The LASP atmospheric
parameters were calibrated based on both the external and internal
uncertainties for the giants and dwarfs, respectively. A general statistical
analysis of the stellar parameters leads to discovery of 106 candidate
metal-poor stars, 9 candidate very metal-poor stars, and 18 candidate
high-velocity stars. Fitting formulae were obtained segmentally for both the
calibrated atmospheric parameters of the LK-project and the KIC parameters with
the common stars. The calibrated atmospheric parameters and radial velocities
of the LK-project will be useful for studying stars in the Kepler field.


  We construct a series of C^2-Morse functions on the Deligne-Mumford
compactification M_{g,n} bar of the moduli space of genus g Riemann/hyperbolic
surfaces with n punctures. This series of functions converges to the systole
function, which is topologically Morse. We will show that the critical points
of our functions approach those of systole sublinearly, stratum-wise, and with
the same indices. These functions might be the first explicit examples of
C^2-Morse functions on M_{g,n} bar, and the Morse handle decomposition may give
rise to the first example of a natural cell decomposition of M_{g,n} bar, that
works no matter if n is positive or equal to 0.


  We review our recent proposals for the on-demand generation of entangled
few-electron states using dynamic single-electron sources. The generation of
entanglement can be traced back to the single-electron entanglement produced by
quantum point contacts acting as electronic beam splitters. The coherent
partitioning of a single electron leads to entanglement between the two
outgoing arms of the quantum point contact. We describe our various approaches
for generating and certifying entanglement in dynamic electronic conductors and
we quantify the influence of detrimental effects such as finite electronic
temperatures and other dephasing mechanisms. The prospects for future
experiments are discussed and possible avenues for further developments are
identified.


  This paper focuses on the estimation of the concentration curve of a finite
population, when data are collected according to a complex sampling design with
different inclusion probabilities. A (design-based) Hajek type estimator for
the Lorenz curve is proposed, and its asymptotic properties are studied. Then,
a resampling scheme able to approximate the asymptotic law of the Lorenz curve
estimator is constructed. Applications are given to the construction of (i) a
confidence band for the Lorenz curve, (ii) confidence intervals for the Gini
concentration ratio, and (iii) a test for Lorenz dominance. The merits of the
proposed resampling procedure are evaluated through a simulation study.


  The expected level of linkage disequilibrium (LD) in a finite ideal
population at equilibrium is of relevance for many applications in population
and quantitative genetics. Several recursion formulae have been proposed during
the last decades, whose derivations mostly contain heuristic parts and
therefore remain mathematically questionable. We propose a more justifiable
approach, including an alternative recursion formula for the expected LD. Since
the exact formula depends on the distribution of allele frequencies in a very
complicated manner, we suggest an approximate solution and analyze its validity
extensively in a simulation study. Compared to the widely used formula of Sved,
the proposed formula performs better for all parameter constellations
considered. We then analyze the expected LD at equilibrium using the theory on
discrete-time Markov chains based on the linear recursion formula, with
equilibrium being defined as the steady-state of the chain, which finally leads
to a formula for the effective population size N_e. An additional analysis
considers the effect of non-exactness of a recursion formula on the
steady-state, demonstrating that the resulting error in expected LD can be
substantial. In an application to the HapMap data of two human populations we
illustrate the dependency of the N_e-estimate on the distribution of minor
allele frequencies (MAFs), showing that the estimated N_e can vary by up to 30%
when a uniform instead of a skewed distribution of MAFs is taken as a basis to
select SNPs for the analyses. Our analyses provide new insights into the
mathematical complexity of the problem studied.


  Flow cytometry (FCM) is an analytic technique that is capable of detecting
and recording the emission of fluorescence and light scattering of cells or
particles (that are collectively called "events") in a population. A typical
FCM experiment can produce a large array of data making the analysis
computationally intensive. Current FCM data analysis platforms (FlowJo, etc.),
while very useful, do not allow interactive data processing online due to the
data size limitations. Here we report a more effective way to analyze FCM data.
Freecyto is a free, easy-to-learn, Python-flask-based web application that uses
a weighted k-means clustering algorithm to facilitate the interactive analysis
of flow cytometry data. A key limitation of web browsers is their inability to
interactively display large amounts of data. Freecyto addresses this bottleneck
through the use of the k-means algorithm to quantize the data, allowing the
user to access a representative set of data points for interactive
visualization of complex datasets. Moreover, Freecyto enables the interactive
analyses of large complex datasets while preserving the standard FCM
visualization features, such as the generation of scatterplots (dotplots),
histograms, heatmaps, boxplots, as well as a SQL-based sub-population gating
feature. We also show that Freecyto can be applied to the analysis of various
experimental setups that frequently require the use of FCM. Finally, we
demonstrate that the data accuracy is preserved when Freecyto is compared to
conventional FCM software.


  We derive necessary conditions for the spinorial Witten-Nester energy to be
well-defined for asymptotically locally AdS spacetimes. We find that the
conformal boundary should admit a spinor satisfying certain differential
conditions and in odd dimensions the boundary metric should be conformally
Einstein. We show that these conditions are satisfied by asymptotically AdS
spacetimes. The gravitational energy (obtained using the holographic stress
energy tensor) and the spinorial energy are equal in even dimensions and differ
by a bounded quantity related to the conformal anomaly in odd dimensions.


  Subwavelength gratings, with period shorter than the incident wavelength,
have garnered significant attention in the fields of photonics,
optoelectronics, and image sensor technology. In this research, we delve into
the scattering characteristics of these gratings by employing the 2-dimensional
point dipole approximation. Additionally, we propose a version of perturbation
theory that relies on Fourier decomposition to obtain analytical expressions
for the near-field behavior. We validate our models using numerical techniques
such as boundary and finite element analysis. Notably, we explore how
parameters like the grating period and slit width affect field enhancements. We
demonstrate that our models produce qualitatively accurate results even for
narrow slits.


  Existing works address the problem of generating high frame-rate sharp videos
by separately learning the frame deblurring and frame interpolation modules.
Most of these approaches have a strong prior assumption that all the input
frames are blurry whereas in a real-world setting, the quality of frames
varies. Moreover, such approaches are trained to perform either of the two
tasks - deblurring or interpolation - in isolation, while many practical
situations call for both. Different from these works, we address a more
realistic problem of high frame-rate sharp video synthesis with no prior
assumption that input is always blurry. We introduce a novel architecture,
Adaptive Latent Attention Network (ALANET), which synthesizes sharp high
frame-rate videos with no prior knowledge of input frames being blurry or not,
thereby performing the task of both deblurring and interpolation. We
hypothesize that information from the latent representation of the consecutive
frames can be utilized to generate optimized representations for both frame
deblurring and frame interpolation. Specifically, we employ combination of
self-attention and cross-attention module between consecutive frames in the
latent space to generate optimized representation for each frame. The optimized
representation learnt using these attention modules help the model to generate
and interpolate sharp frames. Extensive experiments on standard datasets
demonstrate that our method performs favorably against various state-of-the-art
approaches, even though we tackle a much more difficult problem.


  Giant impacts refer to collisions between two objects each of which is
massive enough to be considered at least a planetary embryo. The putative
collision suffered by the proto-Earth that created the Moon is a prime example,
though most Solar System bodies bear signatures of such collisions. Current
planet formation models predict that an epoch of giant impacts may be
inevitable, and observations of debris around other stars are providing
mounting evidence that giant impacts feature in the evolution of many planetary
systems. This chapter reviews giant impacts, focussing on what we can learn
about planet formation by studying debris around other stars. Giant impact
debris evolves through mutual collisions and dynamical interactions with
planets. General aspects of this evolution are outlined, noting the importance
of the collision-point geometry. The detectability of the debris is discussed
using the example of the Moon-forming impact. Such debris could be detectable
around another star up to 10Myr post-impact, but model uncertainties could
reduce detectability to a few 100yr window. Nevertheless the 3% of young stars
with debris at levels expected during terrestrial planet formation provide
valuable constraints on formation models; implications for super-Earth
formation are also discussed. Variability recently observed in some bright
disks promises to illuminate the evolution during the earliest phases when
vapour condensates may be optically thick and acutely affected by the
collision-point geometry. The outer reaches of planetary systems may also
exhibit signatures of giant impacts, such as the clumpy debris structures seen
around some stars.


  The analysis and prediction of visual attention have long been crucial tasks
in the fields of computer vision and image processing. In practical
applications, images are generally accompanied by various text descriptions,
however, few studies have explored the influence of text descriptions on visual
attention, let alone developed visual saliency prediction models considering
text guidance. In this paper, we conduct a comprehensive study on text-guided
image saliency (TIS) from both subjective and objective perspectives.
Specifically, we construct a TIS database named SJTU-TIS, which includes 1200
text-image pairs and the corresponding collected eye-tracking data. Based on
the established SJTU-TIS database, we analyze the influence of various text
descriptions on visual attention. Then, to facilitate the development of
saliency prediction models considering text influence, we construct a benchmark
for the established SJTU-TIS database using state-of-the-art saliency models.
Finally, considering the effect of text descriptions on visual attention, while
most existing saliency models ignore this impact, we further propose a
text-guided saliency (TGSal) prediction model, which extracts and integrates
both image features and text features to predict the image saliency under
various text-description conditions. Our proposed model significantly
outperforms the state-of-the-art saliency models on both the SJTU-TIS database
and the pure image saliency databases in terms of various evaluation metrics.
The SJTU-TIS database and the code of the proposed TGSal model will be released
at: https://github.com/IntMeGroup/TGSal.


  Rigorous implementation of the effects of collisions in modeling the
formation of the polarized solar lines is of utmost importance in order to
realistically analyze the available, highly sensitive solar spectropolarimetric
observations. Indeed, even when an observation seems to fit well with theory,
one can misinterpret results if important effects due to collisions are not
correctly implemented in the modeling process. We point out inconsistencies in
the models adopted to implement the Paschen Back effect together with
collisional effects on the solar linear polarization formed by scattering of
anisotropic radiation. Because the significance of these inconsistencies
increases as polarization becomes increasingly responsive to collisions, we
investigate the range of hydrogen densities $n_\text{H}$ to which the
polarization is sensitive. We used the density matrix formalism in the
tensorial irreducible basis, which was developed within the theory of
atom-radiation interaction and of atomic collisions. We solved the statistical
equilibrium equations for multi-level atoms with hyperfine structure (HFS) in
order to evaluate the collisional depolarization of levels of the D1-D2 lines
of the K I atom. We find that collisions play a prominent role, particularly at
hydrogen densities of between 10$^{13}$ and 10$^{16}$ cm$^{-3}$. So far,
analyses of polarized lines formed in the presence of solar magnetic field have
incorporated, if at all, collisional rates calculated assuming zero magnetic
field. This could be a good approximation in the Hanle regime but not in the
Paschen Back regime. For typical quiet Sun magnetic fields, the latter regime
could be reached, and level-crossing takes place in several atomic systems.
Therefore, one must be careful when using collisional rates calculated in the
zero-field case to interpret linear polarization formed in magnetized media.


  Let $\Bbbk$ be a field and let $I$ be a monomial ideal in the polynomial ring
$Q=\Bbbk[x_1,\ldots,x_n]$. In her thesis, Taylor introduced a complex which
provides a finite free resolution for $Q/I$ as a $Q$-module. Later, Gemeda
constructed a differential graded structure on the Taylor resolution. More
recently, Avramov showed that this differential graded algebra admits divided
powers. We generalize each of these results to monomial ideals in a skew
polynomial ring $R$. Under the hypothesis that the skew commuting parameters
defining $R$ are roots of unity, we prove as an application that as $I$ varies
among all ideals generated by a fixed number of monomials of degree at least
two in $R$, there is only a finite number of possibilities for the Poincar\'{e}
series of $\Bbbk$ over $R/I$ and for the isomorphism classes of the homotopy
Lie algebra of $R/I$ in cohomological degree larger or equal to two.


  Let $U\subset \mathbb P^N$ be a projective variety which is not a cone and
whose hyperplane sections are smooth Enriques surfaces. We prove that the
degree of a $U$ is at most 32 and the bound is sharp.


  Multinomial logistic regression models allow one to predict the risk of a
categorical outcome with more than 2 categories. When developing such a model,
researchers should ensure the number of participants (n) is appropriate
relative to the number of events (E.k) and the number of predictor parameters
(p.k) for each category k. We propose three criteria to determine the minimum n
required in light of existing criteria developed for binary outcomes. The first
criteria aims to minimise the model overfitting. The second aims to minimise
the difference between the observed and adjusted R2 Nagelkerke. The third
criterion aims to ensure the overall risk is estimated precisely. For criterion
(i), we show the sample size must be based on the anticipated Cox-snell R2 of
distinct one-to-one logistic regression models corresponding to the sub-models
of the multinomial logistic regression, rather than on the overall Cox-snell R2
of the multinomial logistic regression. We tested the performance of the
proposed criteria (i) through a simulation study, and found that it resulted in
the desired level of overfitting. Criterion (ii) and (iii) are natural
extensions from previously proposed criteria for binary outcomes. We illustrate
how to implement the sample size criteria through a worked example considering
the development of a multinomial risk prediction model for tumour type when
presented with an ovarian mass. Code is provided for the simulation and worked
example. We will embed our proposed criteria within the pmsampsize R library
and Stata modules.


  The classical Eisenhart lift is a method by which the dynamics of a classical
system subject to a potential can be recreated by means of a free system
evolving in a higher-dimensional curved manifold, known as the lifted manifold.
We extend the formulation of the Eisenhart lift to quantum systems, and show
that the lifted manifold recreates not only the classical effects of the
potential, but also its quantum mechanical effects. In particular, we find that
the solutions of the Schrodinger equations of the lifted system reduce to those
of the original system after projecting out the new degrees of freedom. In this
context, we identify a conserved quantum number, which corresponds to the
lifted momentum of the classical system. We further apply the Eisenhart lift to
Quantum Field Theory (QFT). We show that a lifted field space manifold is able
to recreate both the classical and quantum effects of a scalar field potential.
We find that, in the case of QFT, the analogue of the lifted momentum is a
quantum charge that is conserved not only in time, but also in space. The
different possible values for this charge label an ensemble of Fock spaces that
are all disjoint from one another. The relevance of these extended Fock spaces
to the cosmological constant and gauge hierarchy problems is considered.


  A key challenge in systems biology is the elucidation of the underlying
principles, or fundamental laws, which determine the cellular phenotype.
Understanding how these fundamental principles are altered in diseases like
cancer is important for translating basic scientific knowledge into clinical
advances. While significant progress is being made, with the identification of
novel drug targets and treatments by means of systems biological methods, our
fundamental systems level understanding of why certain treatments succeed and
others fail is still lacking. We here advocate a novel methodological framework
for systems analysis and interpretation of molecular omic data, which is based
on statistical mechanical principles. Specifically, we propose the notion of
cellular signalling entropy (or uncertainty), as a novel means of analysing and
interpreting omic data, and more fundamentally, as a means of elucidating
systems-level principles underlying basic biology and disease. We describe the
power of signalling entropy to discriminate cells according to differentiation
potential and cancer status. We further argue the case for an empirical
cellular entropy-robustness correlation theorem and demonstrate its existence
in cancer cell line drug sensitivity data. Specifically, we find that high
signalling entropy correlates with drug resistance and further describe how
entropy could be used to identify the achilles heels of cancer cells. In
summary, signalling entropy is a deep and powerful concept, based on rigorous
statistical mechanical principles, which, with improved data quality and
coverage, will allow a much deeper understanding of the systems biological
principles underlying normal and disease physiology.


  By means of identical cubic elements, we generate a partition of a volume in
which a particle-based cosmological simulation is carried out. In each cubic
element, we determine the gas particles with a normalized density greater than
an arbitrarily chosen density threshold. By using a proximity parameter, we
calculate the neighboring cubic elements and generate a list of neighbors. By
imposing dynamic conditions on the gas particles, we identify gas clumps and
their neighbors, so that we calculate and fit some properties of the groups so
identified, including the mass, size and velocity dispersion, in terms of their
multiplicity (here defined simply as the number of member galaxies). Finally,
we report the value of the ratio of kinetic energy to gravitational energy of
such dense gas clumps, which will be useful as initial conditions in
simulations of gravitational collapse of gas clouds and clusters of gas clouds.


  We will give new applications of quantum groups to the study of spherical
Whittaker functions on the metaplectic $n$-fold cover of $GL(r,F)$, where $F$
is a nonarchimedean local field. Earlier Brubaker, Bump, Friedberg, Chinta and
Gunnells had shown that these Whittaker functions can be identified with the
partition functions of statistical mechanical systems. They postulated that a
Yang-Baxter equation underlies the properties of these Whittaker functions. We
confirm this, and identify the corresponding Yang-Baxter equation with that of
the quantum affine Lie superalgebra
$U_{\sqrt{v}}(\widehat{\mathfrak{gl}}(1|n))$, modified by Drinfeld twisting to
introduce Gauss sums. (The deformation parameter $v$ is specialized to the
inverse of the residue field cardinality.) For principal series representations
of metaplectic groups, the Whittaker models are not unique. The scattering
matrix for the standard intertwining operators is vector valued. For a simple
reflection, it was computed by Kazhdan and Patterson, who applied it to
generalized theta series. We will show that the scattering matrix on the space
of Whittaker functions for a simple reflection coincides with the twisted
$R$-matrix of the quantum group $U_{\sqrt{v}}(\widehat{\mathfrak{gl}}(n))$.
This is a piece of the twisted $R$-matrix for
$U_{\sqrt{v}}(\widehat{\mathfrak{gl}}(1|n))$, mentioned above.


  A new method for constructing a Hamiltonian for configuration interaction
calculations with constraints to energies of spherical configurations obtained
with energy-density-functional (EDF) methods is presented. This results in a
unified model that reproduced the EDF binding-energy in the limit of
single-Slater determinants, but can also be used for obtaining energy spectra
and correlation energies with renormalized nucleon-nucleon interactions. The
three-body and/or density-dependent terms that are necessary for good nuclear
saturation properties are contained in the EDF. Applications to binding
energies and spectra of nuclei in the region above 208Pb are given.


  We unveil a topological phase of interacting fermions on a two-leg ladder of
unequal parity orbitals, derived from the experimentally realized double-well
lattices by dimension reduction. $Z_2$ topological invariant originates simply
from the staggered phases of $sp$-orbital quantum tunneling, requiring none of
the previously known mechanisms such as spin-orbit coupling or artificial gauge
field. Another unique feature is that upon crossing over to two dimensions with
coupled ladders, the edge modes from each ladder form a parity-protected flat
band at zero energy, opening the route to strongly correlated states controlled
by interactions. Experimental signatures are found in density correlations and
phase transitions to trivial band and Mott insulators.


  Periodic solutions of the planar $N$-body problem determine braids through
the trajectory of $N$ bodies. Braid types can be used to classify periodic
solutions. According to the Nielsen-Thurston classification of surface
automorphisms, braids fall into three types: periodic, reducible and
pseudo-Anosov. To a braid of pseudo-Anosov type, there is an associated stretch
factor greater than 1, and this is a conjugacy invariant of braids. In 2006,
the third author discovered a family of multiple choreographic solutions of the
planar $2n$-body problem. We prove that braids obtained from the solutions in
the family are of pseudo-Anosov type, and their stretch factors are expressed
in metallic ratios. New numerical periodic solutions of the planar $2n$-body
problem are also provided.


  Variational quantum algorithms are the centerpiece of modern quantum
programming. These algorithms involve training parameterized quantum circuits
using a classical co-processor, an approach adapted partly from classical
machine learning. An important subclass of these algorithms, designed for
combinatorial optimization on currrent quantum hardware, is the quantum
approximate optimization algorithm (QAOA). It is known that problem density - a
problem constraint to variable ratio - induces under-parametrization in fixed
depth QAOA. Density dependent performance has been reported in the literature,
yet the circuit depth required to achieve fixed performance (henceforth called
critical depth) remained unknown. Here, we propose a predictive model, based on
a logistic saturation conjecture for critical depth scaling with respect to
density. Focusing on random instances of MAX-2-SAT, we test our predictive
model against simulated data with up to 15 qubits. We report the average
critical depth, required to attain a success probability of 0.7, saturates at a
value of 10 for densities beyond 4. We observe the predictive model to describe
the simulated data within a $3\sigma$ confidence interval. Furthermore, based
on the model, a linear trend for the critical depth with respect problem size
is recovered for the range of 5 to 15 qubits.


  In this work, we propose a self-supervised learning method for affine image
registration on 3D medical images. Unlike optimisation-based methods, our
affine image registration network (AIRNet) is designed to directly estimate the
transformation parameters between two input images without using any metric,
which represents the quality of the registration, as the optimising function.
But since it is costly to manually identify the transformation parameters
between any two images, we leverage the abundance of cheap unlabelled data to
generate a synthetic dataset for the training of the model. Additionally, the
structure of AIRNet enables us to learn the discriminative features of the
images which are useful for registration purpose. Our proposed method was
evaluated on magnetic resonance images of the axial view of human brain and
compared with the performance of a conventional image registration method.
Experiments demonstrate that our approach achieves better overall performance
on registration of images from different patients and modalities with 100x
speed-up in execution time.


  We use methods of approximation theory to find the absolute minima on the
sphere of the potential of spherical $(2m-3)$-designs with a non-trivial index
$2m$ that are contained in a union of $m$ parallel hyperplanes, $m\geq 2$,
whose locations satisfy certain additional assumptions. The interaction between
points is described by a function of the dot product, which has positive
derivatives of orders $2m-2$, $2m-1$, and $2m$. This includes the case of the
classical Coulomb, Riesz, and logarithmic potentials as well as a completely
monotone potential of the distance squared. We illustrate this result by
showing that the absolute minimum of the potential of the set of vertices of
the icosahedron on the unit sphere $S^2$ in $\mathbb R^3$ is attained at the
vertices of the dual dodecahedron and the one for the set of vertices of the
dodecahedron is attained at the vertices of the dual icosahedron. The absolute
minimum of the potential of the configuration of $240$ minimal vectors of $E_8$
root lattice normalized to lie on the unit sphere $S^7$ in $\mathbb R^8$ is
attained at a set of $2160$ points on $S^7$ which we describe.


  Phonon-phonon interaction is systematically studied by nonequilibrium Green's
function (NEGF) formulism in momentum space at finite temperatures. Within the
quasi-particle approximation, phonon frequency shift and lifetime are obtained
from the retarded self-energy. The lowest order NEGF provides the same phonon
lifetime as Fermi's golden rule. Thermal conductance is predicted by the
Landauer formula with a phenomenological transmission function. The main
advantage of our method is that it covers both ballistic and diffusive limits
and thermal conductance of different system sizes can be easily obtained once
the mode-dependent phonon mean free path is calculated by NEGF. As an
illustration, the method is applied to two one-dimensional atom chain models
(the FPU-\beta model and the \phi^4 model) with an additional harmonic on-site
potential. The obtained thermal conductance is compared with that from a
quasi-classical molecular dynamics method. The harmonic on-site potential is
shown to remove the divergence of thermal conductivity in the FPU-\beta model.


  We consider a 5D BPS dilatonic two brane model which reduces to the
Randall-Sundrum model or the Horava-Witten theory for a particular choice of
parameters. Recently new dynamical solutions were found by Chen et al., which
describe a moduli instability of the warped geometry. Using a 4D effective
theory derived by solving the 5D equations of motion, based on the gradient
expansion method, we show that the exact solution of Chen et. al. can be
reproduced within the 4D effective theory and we identify the origin of the
moduli instability. We revisit the gradient expansion method with a new metric
ansatz to clarify why the 4D effective theory solution can be lifted back to an
exact 5D solution. Finally we argue against a recent claim that the 4D
effective theory allows a much wider class of solutions than the 5D theory and
provide a way to lift solutions in the 4D effective theory to 5D solutions
perturbatively in terms of small velocities of the branes.


  Recent surveys show that wide ($>10^4$ AU) binaries and triples are abundant
in the field. We study the long-term evolution of wide hierarchical triple
systems and the role played by the Galactic tidal (GT) field. We find that when
the timescales of the secular von-Ziepel-Lidov-Kozai and the GT oscillations
are comparable, triple evolution becomes chaotic which leads to extreme
eccentricities. Consequently, the close pericentre approaches of the
inner-binary components lead to strong interactions, mergers and collisions. We
use a novel secular evolution code to quantify the key parameters and carry out
a population-synthesis study of low and intermediate-mass wide-orbit triples.
We find that in $\sim9\%$ of low-mass wide-triples the inner main-sequence
binaries collide or tidally-inspiral within $10\ \rm Gyr$, with direct
collisions are $6$ times more likely to occur. For the intermediate-mass
sample, $\sim7.6\%$ of the systems merge or inspiral with roughly equal
probabilities. We discuss the relative fractions of different stellar
merger/inspiral outcomes as a function of their evolutionary stage
(Main-Sequence, MS; Red-Giant, RG; or White-Dwarf, WD), their transient
electromagnetic signatures and the final products of the merger/inspiral. In
particular, the rate of WD-WD direct-collisions that lead to type-Ia Supernovae
is comparable to other dynamical channels and accounts for at most $0.1\%$ of
the observed rate. RG inspirals provide a novel channel for the formation of
eccentric common-envelope-evolution binaries. The catalysis of
mergers/collisions in triples due to GT could explain a significant fraction,
or even the vast majority, of blue-stragglers in the field, produce progenitors
for cataclysmic-variables, and give-rise to mergers/collisions of double-RG
binaries.


  We construct an N=2 supersymmetric generalization of the N=1 supercurrent
formalism of Komargodski and Seiberg (KS) and use it to show that N=2 theories
with linear superconformal anomalies cannot break SUSY under certain broad
assumptions. This result suggests that there are no metastable SUSY breaking
vacua in a large class of theories that includes N=2 Super Yang-Mills (SYM).


  The spread of new products in a networked population is often modeled as an
epidemic. However, in the case of `complex' contagion, these models {do not
capture nuanced, dynamic social reinforcement effects in adoption behavior}. In
this paper, we investigate a model of complex contagion which allows a
coevolutionary interplay between adoption, modeled as an SIS epidemic spreading
process, and social reinforcement effects, modeled as consensus opinion
dynamics. Asymptotic stability analysis of the all-adopt as well as the
none-adopt equilibria of the combined opinion-adoption model is provided
through the use of Lyapunov arguments. In doing so, sufficient conditions are
provided which determine the stability of the `flop' state, where no one adopts
the product and everyone's opinion of the product is least favorable, and the
`hit' state, where everyone adopts and their opinions are most favorable. These
conditions are shown to extend to the bounded confidence opinion dynamic under
a stronger assumption on the model parameters. To conclude, numerical
simulations demonstrate behavior of the model which reflect findings from the
sociology literature on adoption behavior.


  We show how the character tables of the groups $E_6(q)_{\text{ad}}$ and
${^2\!E}_6(q)_{\text{ad}}$ can be constructed, where $q$ is a power of~$2$.
(Partial results are also obtained for any $q$ not divisible by~$3$.) This is
based on previous work by Hetz, Lusztig, Malle, Mizuno and Shoji, plus
computations using Michel's version of {\sf CHEVIE}. We also need some general
results that are specific to semisimple groups which are not of simply
connected type. A further crucial ingredient is the determination of the values
of the unipotent characters on unipotent elements for groups of type $D_4$ and
$D_5$ (in characteristic~$2$).


  The total energy of a quasi-one-dimensional electron system is calculated
using density functional theory. It is shown that spontaneous ferromagnetic
state in quantum wire occurs at low one-dimensional electron density. The
critical electron density below which electrons are in spin-polarized state is
estimated analytically.


  We examine an unexplored quantum phenomenon we call oscillatory localization,
where a discrete-time quantum walk with Grover's diffusion coin jumps back and
forth between two vertices. We then connect it to the power dissipation of a
related electric network. Namely, we show that there are only two kinds of
oscillating states, called uniform states and flip states, and that the
projection of an arbitrary state onto a flip state is bounded by the power
dissipation of an electric circuit. By applying this framework to states along
a single edge of a graph, we show that low effective resistance implies
oscillatory localization of the quantum walk. This reveals that oscillatory
localization occurs on a large variety of regular graphs, including
edge-transitive, expander, and high degree graphs. As a corollary, high
edge-connectivity also implies localization of these states, since it is
closely related to electric resistance.


  Let $q$ be an odd prime power. Combining the discussion of Varnavides and a
recent theorem of Ellenberg and Gijswijt, we show that a subset
$A\subset{\mathbb F}_q^n$ will contain many non-trivial three-term arithmetic
progressions, whenever $|A|\geq (c_q q)^n$ for some constant $c_q>0$. After the
first version of our manuscript was uploaded in the arXiv, we learned from
Professors Jacob Fox and Terence Tao that our result is a special case of a
result of Fox and Lovasz [1, Theorem 3]. In fact, [1, Theorem 3] gives a much
better bound than ours. For example, when $q=3$, the lower bound given by Fox
and Lovasz is $|A|^{2}\cdot (|A|q^{-n})^{11.901}$, while our bound is
$|A|^{2}\cdot (|A|q^{-n})^{25.803}$. We thank Professors Jacob Fox and Terence
Tao for their helpful comments on our manuscript. [1] Jacob Fox, L\'aszl\'o
Mikl\'os Lov\'asz, A tight bound for Green's arithmetic triangle removal lemma
in vector spaces, preprint, arXiv:1606.01230.


  Taking photographs ''in-the-wild'' is often hindered by fence obstructions
that stand between the camera user and the scene of interest, and which are
hard or impossible to avoid. De-fencing is the algorithmic process of
automatically removing such obstructions from images, revealing the invisible
parts of the scene. While this problem can be formulated as a combination of
fence segmentation and image inpainting, this often leads to implausible
hallucinations of the occluded regions. Existing multi-frame approaches rely on
propagating information to a selected keyframe from its temporal neighbors, but
they are often inefficient and struggle with alignment of severely obstructed
images. In this work we draw inspiration from the video completion literature
and develop a simplified framework for multi-frame de-fencing that computes
high quality flow maps directly from obstructed frames and uses them to
accurately align frames. Our primary focus is efficiency and practicality in a
real-world setting: the input to our algorithm is a short image burst (5
frames) - a data modality commonly available in modern smartphones - and the
output is a single reconstructed keyframe, with the fence removed. Our approach
leverages simple yet effective CNN modules, trained on carefully generated
synthetic data, and outperforms more complicated alternatives real bursts, both
quantitatively and qualitatively, while running real-time.


  We study the problem of learning unknown parameters in stochastic interacting
particle systems with polynomial drift, interaction and diffusion functions
from the path of one single particle in the system. Our estimator is obtained
by solving a linear system which is constructed by imposing appropriate
conditions on the moments of the invariant distribution of the mean field limit
and on the quadratic variation of the process. Our approach is easy to
implement as it only requires the approximation of the moments via the ergodic
theorem and the solution of a low-dimensional linear system. Moreover, we prove
that our estimator is asymptotically unbiased in the limits of infinite data
and infinite number of particles (mean field limit). In addition, we present
several numerical experiments that validate the theoretical analysis and show
the effectiveness of our methodology to accurately infer parameters in systems
of interacting particles.


  We discuss the clusters of resources that emerge when upper-division students
write about electromagnetic fields in linear materials. The data analyzed for
this paper comes from students' written tests in an upper-division electricity
and magnetism course. We examine how these clusters change with time and
context. The evidence shows that students benefit from activating resources
related to the internal structure of the atom when thinking about electric
fields and their effect on materials. We argue that facilitating activation of
certain resources by the instructor in the classroom can affect the plasticity
of those resources in the student, making them more solid and easily activated.
We find that the wording of the questions posed to students affects which
resources are activated, and that students often fill in resources to link
known phenomena to phenomena described by the question when lacking detailed
mental models.


  We explicitly construct a supersymmetric $so(n)$ spin-Calogero model with an
arbitrary even number $\cal N$ of supersymmetries. It features
$\frac{1}{2}{\cal N}n(n{+}1)$ rather than ${\cal N}n$ fermionic coordinates and
a very simple structure of the supercharges and the Hamiltonian. The latter,
together with additional conserved currents, form an $osp({\cal N}|2)$
superalgebra. We provide a superspace description for the simplest case, namely
${\cal N}{=}2$ supersymmetry. The reduction to an $\cal N$-extended
supersymmetric goldfish model is also discussed.


  Horn functions form a subclass of Boolean functions possessing interesting
structural and computational properties. These functions play a fundamental
role in algebra, artificial intelligence, combinatorics, computer science,
database theory, and logic.
  In the present paper, we introduce the subclass of hypergraph Horn functions
that generalizes matroids and equivalence relations. We provide multiple
characterizations of hypergraph Horn functions in terms of implicate-duality
and the closure operator, which are respectively regarded as generalizations of
matroid duality and Mac Lane-Steinitz exchange property of matroid closure. We
also study algorithmic issues on hypergraph Horn functions, and show that the
recognition problem (i.e., deciding if a given definite Horn CNF represents a
hypergraph Horn function) and key realization (i.e., deciding if a given
hypergraph is realized as a key set by a hypergraph Horn function) can be done
in polynomial time, while implicate sets can be generated with polynomial
delay.


  We show that the Bousfield-Kan spectral sequence which computes the rational
homotopy groups of the space of long knots in ${\mathbb R}^d$, where $d\ge 4$,
collapses at the $E^2$ page. The main ingredients in the proof are Sinha's
cosimplicial model for the space of long knots and a coformality result for the
little balls operad.


  The inclusive production of the omega(782) vector meson in hadronic Z decays
is measured and compared to model predictions. The analysis is based on 4
million hadronic Z decays recorded by the ALEPH detector between 1991 and 1995.
The production rate for x_p = p_meson/p_beam > 0.05 is measured in the omega ->
pi^+ pi^- pi^0 decay mode and found to be 0.585 +- 0.019_stat +- 0.033_sys per
event. Inclusive eta meson production is also measured in the same decay
channel for x_p > 0.10, obtaining 0.355 +- 0.011_stat +- 0.024_sys per event.
The branching ratio for omega -> mu^+ mu^- is investigated. A total of 18.1 +-
5.9 events are observed, from which the muonic branching ratio is measured for
the first time to be BR(omega -> mu^+ mu^-) = (9.0 +- 2.9_stat +-
1.1_sys)*10^-5.


  The $b$ ghost, or $b$ operator, used for fixing Siegel gauge in the pure
spinor superfield formalism, is a composite operator of negative ghost number,
satisfying $\{q,b\}=\square$, where $q$ is the pure spinor differential (BRST
operator). It is traditionally constructed using non-minimal variables.
However, since all cohomology has minimal representatives, it seems likely that
there should be versions of physically meaningful operators, also with negative
ghost number, using only minimal variables. The purpose of this letter is to
demonstrate that this statement holds by providing a concrete construction in
$D=10$ super-Yang-Mills theory, and to argue that it is a general feature in
the pure spinor superfield formalism.


  This article reports on the confluence of two streams of research, one
emanating from the fields of numerical analysis and scientific computation, the
other from topology and geometry. In it we consider the numerical
discretization of partial differential equations that are related to
differential complexes so that de Rham cohomology and Hodge theory are key
tools for the continuous problem. After a brief introduction to finite element
methods, the discretization methods we consider, we develop an abstract Hilbert
space framework for analyzing stability and convergence. In this framework, the
differential complex is represented by a complex of Hilbert spaces and
stability is obtained by transferring Hodge theoretic structures from the
continuous level to the discrete. We show stable discretization is achieved if
the finite element spaces satisfy two hypotheses: they form a subcomplex and
there exists a bounded cochain projection from the full complex to the
subcomplex. Next, we consider the most canonical example of the abstract
theory, in which the Hilbert complex is the de Rham complex of a domain in
Euclidean space. We use the Koszul complex to construct two families of finite
element differential forms, show that these can be arranged in subcomplexes of
the de Rham complex in numerous ways, and for each construct a bounded cochain
projection. The abstract theory therefore applies to give the stability and
convergence of finite element approximations of the Hodge Laplacian. Other
applications are considered as well, especially to the equations of elasticity.
Background material is included to make the presentation self-contained for a
variety of readers.


  Sum-of-norms clustering is a clustering formulation based on convex
optimization that automatically induces hierarchy. Multiple algorithms have
been proposed to solve the optimization problem: subgradient descent by Hocking
et al., ADMM and ADA by Chi and Lange, stochastic incremental algorithm by
Panahi et al. and semismooth Newton-CG augmented Lagrangian method by Sun et
al. All algorithms yield approximate solutions, even though an exact solution
is demanded to determine the correct cluster assignment. The purpose of this
paper is to close the gap between the output from existing algorithms and the
exact solution to the optimization problem. We present a clustering test that
identifies and certifies the correct cluster assignment from an approximate
solution yielded by any primal-dual algorithm. Our certification validates
clustering for both unit and multiplicative weights. The test may not succeed
if the approximation is inaccurate. However, we show the correct cluster
assignment is guaranteed to be certified by a primal-dual path following
algorithm after sufficiently many iterations, provided that the model parameter
$\lambda$ avoids a finite number of bad values. Numerical experiments are
conducted on Gaussian mixture and half-moon data, which indicate that carefully
chosen multiplicative weights increase the recovery power of sum-of-norms
clustering.


  Billey and Braden defined maps on flag manifolds that are the geometric
counterpart of permutation patterns. A section of their pattern map is an
embedding of the flag manifold of a Levi subgroup into the full flag manifold.
We give two expressions for the induced map on cohomology. One is in terms of
generators and the other is in terms of the Schubert basis. We show that the
coefficients in the second expression are naturally Schubert structure
constants and therefore positive. These formulas also hold for K-theory, and
generalize known formulas in type A for cohomology and K-theory.


  Building segmentation is of great importance in the task of remote sensing
imagery interpretation. However, the existing semantic segmentation and
instance segmentation methods often lead to segmentation masks with blurred
boundaries. In this paper, we propose a novel instance segmentation network for
building segmentation in high-resolution remote sensing images. More
specifically, we consider segmenting an individual building as detecting
several keypoints. The detected keypoints are subsequently reformulated as a
closed polygon, which is the semantic boundary of the building. By doing so,
the sharp boundary of the building could be preserved. Experiments are
conducted on selected Aerial Imagery for Roof Segmentation (AIRS) dataset, and
our method achieves better performance in both quantitative and qualitative
results with comparison to the state-of-the-art methods. Our network is a
bottom-up instance segmentation method that could well preserve geometric
details.


  We employ Hamiltonian light-front quantum field theory in a basis function
approach to solve the non-perturbative problem of an electron in a strong
scalar transverse confining potential. We evaluate both the invariant mass
spectra and the anomalous magnetic moment of the lowest state for this
two-scale system. The weak external field limit of the anomalous magnetic
moment agrees with the result of QED perturbation theory within the anticipated
accuracy.


  In this paper, we develop the theory of contractive Markov systems initiated
in \cite{Wer1}.
  We construct a coding map for such systems and investigate some of its
properties.


  We study the equation of state in two-flavor QCD at finite temperature and
density. Simulations are made with the RG-improved gluon action and the
clover-improved Wilson quark action. Along the lines of constant physics for
$m_{\rm PS}/m_{\rm V} = 0.65$ and 0.80, we compute the derivatives of the quark
determinant with respect to the quark chemical potential $\mu_q$ up to the
fourth order at $\mu_q=0$. We adopt several improvement techniques in the
evaluation. We study thermodynamic quantities and quark number susceptibilities
at finite $\mu_q$ using these derivatives. We find enhancement of the quark
number susceptibility at finite $\mu_q$, in accordance with previous
observations using staggered-type quarks. This suggests the existence of a
nearby critical point.


  We report the enhanced superconducting properties of double-chain based
superconductor Pr$_{2}$Ba$_{4}$Cu$_{7}$O$_{15-\delta}$ synthesized by the
citrate pyrolysis technique.
  %In spite of the polycrystalline bulk samples, we obtained the higher
residual resistivity ratios (10-12).
  The reduction heat treatment in vacuum results in the appearance of
superconducting state with $T_\mathrm{c}$=22-24 K, accompanied by the higher
residual resistivity ratios. The superconducting volume fractions are estimated
from the ZFC data to be 50$\sim55\%$, indicating the bulk superconductivity. We
evaluate from the magneto-transport data the temperature dependence of the
superconducting critical field, to establish the superconducting phase diagram.
The upper critical magnetic field is estimated to be about 35 T at low
temperatures from the resistive transition data using the
Werthamer-Helfand-Hohenberg formula. The Hall coefficient $R_{H}$ of the
48-h-reduced superconducting sample is determined to be -0.5$\times10^{-3}$
cm$^{3}$/C at 30 K, suggesting higher electron concentration. These findings
have a close relationship with homogeneous distributions of the superconducting
grains and improved weak links between their superconducting grains in the
present synthesis process.


  We report the incorporation of the Wiimote, a light-tracking remote control
device, into two undergraduate-level experiments. We provide an overview of the
Wiimote's basic functions and a systematic analysis of its motion tracking
capabilities. We describe the Wiimote's use in measuring conservation of linear
and angular momentum on an air table, and measuring the gravitational constant
with the classic Cavendish torsion pendulum. Our results show that Wiimote is a
simple and affordable way to streamline the data acquisition process and
produce results that are generally superior to those obtained with conventional
techniques.