  Fusion of two deuterons of room temperature energy is studied. The nuclei are
in vacuum with no connection to any external source (electric or magnetic
field, illumination, surrounding matter, traps, etc.) which may accelerate
them. The energy of the two nuclei is conserved and remains small during the
motion through the Coulomb barrier. The penetration through this barrier, which
is the main obstacle for low-energy fusion, strongly depends on a form of the
incident flux on the Coulomb center at large distances from it. In contrast to
the usual scattering, the incident wave is not a single plane wave but the
certain superposition of plane waves of the same energy and various directions,
for example, a convergent conical wave. As a result of interference, the wave
function close to the Coulomb center is determined by a cusp caustic which is
probed by de Broglie waves. The particle flux gets away from the cusp and moves
to the Coulomb center providing a not small probability of fusion (cusp driven
tunneling). Getting away from a caustic cusp also occurs in optics and
acoustics.


  Skyrmions are vortex-like textures of magnetic moments found in some
magnetically ordered materials. Here we describe the origin of the skyrmion and
discuss the experimental realization of skyrmions in magnetic materials, the
dynamic properties of the skyrmion and the potentially useful interaction of
skyrmions with electrons. Our discussion is based on the physics of fields and
allows us to touch on notions from field theory and topology that illustrate
how skyrmions can be understood as part of a family of defects in an ordered
field, and hint at other topological objects that await our discovery.


  We consider a noncommutative standard model with a minimal coupling scalar
field and a dynamical deformation between the canonical momenta of its scale
factor and scalar field, and a chameleon model with a non-minimally coupling
scalar field. We indicate that there is a correspondence between these two
models, more specific, actually between the noncommutative parameter and the
chameleon coupling strength, and also between the matter density of the
chameleon model and the noncommutative geometry. In addition, the analogy
constrains the type of the matter field in the chameleon model to be nearly a
cosmic string-like during the inflation. Thus, the scenario enables the
evolution of the universe being described by one single scalar field. That is,
the effects of the chameleon and the inflaton can be described by one single
scalar field which plays the role of inflaton in the very early universe and
then, acts as a chameleon field. Moreover, the proposed correspondence
procedure not~only sets some constraints on the noncommutative parameter and
the chameleon coupling constant, but also nearly specifies functions of the
scalar field and its potential.


  We identify the leading term describing the behavior at large distances of
the steady state solutions of the Navier-Stokes equations in 3D exterior
domains with vanishing velocity at the spatial infinity.


  Let $\mathcal{G}$ be a connected reductive almost simple group over the Witt
ring $W(\mathbb{F})$ for $\mathbb{F}$ a finite field of characteristic $p$. Let
$R$ and $R'$ be complete noetherian local $W(\mathbb{F})$ -algebras with
residue field $\mathbb{F}$. Under a mild condition on $p$ in relation to
structural constants of $\mathcal{G}$, we show the following results: (1) Every
closed subgroup $H$ of $\mathcal{G}(R)$ with full residual image
$\mathcal{G}(\mathbb{F})$ is a conjugate of a group $\mathcal{G}(A)$ for
$A\subset R$ a closed subring that is local and has residue field $\mathbb{F}$
. (2) Every surjective homomorphism $\mathcal{G}(R)\to\mathcal{G}(R')$ is, up
to conjugation, induced from a ring homomorphism $R\to R'$. (3) The identity
map on $\mathcal{G}(R)$ represents the universal deformation of the
representation of the profinite group $\mathcal{G}(R)$ given by the reduction
map $\mathcal{G}(R)\to\mathcal{G}(\mathbb{F})$. This generalizes results of
Dorobisz and Eardley-Manoharmayum and of Manoharmayum, and in addition provides
an abstract classification result for closed subgroups of $\mathcal{G}(R)$ with
residually full image.
  We provide an axiomatic framework to study this type of question, also for
slightly more general $\mathcal{G}$, and we study in the case at hand in great
detail what conditions on $\mathbb{F}$ or on $p$ in relation to $\mathcal{G}$
are necessary for the above results to hold.


  The statistics of low-lying zeros of quadratic Dirichlet L-functions were
conjectured by Katz and Sarnak to be given by the scaling limit of eigenvalues
from the unitary symplectic ensemble. The n-level densities were found to be in
agreement with this in a certain neighborhood of the origin in the Fourier
domain by Rubinstein in his Ph.D. thesis in 1998. An attempt to extend the
neighborhood was made in the Ph.D. thesis of Peng Gao (2005), who under GRH
gave the density as a complicated combinatorial factor, but it remained open
whether it coincides with the Random Matrix Theory factor. For n at most 7 this
was recently confirmed by Levinson and Miller. We resolve this problem for all
n, not by directly doing the combinatorics, but by passing to a function field
analogue, of L-functions associated to hyper-elliptic curves of given genus g
over a field of q elements. We show that the answer in this case coincides with
Gao's combinatorial factor up to a controlled error. We then take the limit of
large finite field size q to infinity and use the Katz-Sarnak equidistribution
theorem, which identifies the monodromy of the Frobenius conjugacy classes for
the hyperelliptic ensemble with the group USp(2g). Further taking the limit of
large genus g to infinity allows us to identify Gao's combinatorial factor with
the RMT answer.


  In this work we study the competition and correspondence between the
classical and quantum routes to intramolecular vibrational energy
redistribution (IVR) in a three degrees of freedom model effective Hamiltonian.
Specifically, we focus on the classical and the quantum dynamics near the
resonance junctions on the Arnold web that are formed by intersection of
independent resonances. The regime of interest models the IVR dynamics from
highly excited initial states near dissociation thresholds of molecular systems
wherein both classical and purely quantum, involving dynamical tunneling,
routes to IVR coexist. In the vicinity of a resonance junction classical chaos
is inevitably present and hence one expects the quantum IVR pathways to have a
strong classical component as well. We show that with increasing resonant
coupling strengths the classical component of IVR leads to a transition from
coherent dynamical tunneling to incoherent dynamical tunneling. Furthermore, we
establish that the quantum IVR dynamics can be predicted based on the
structures on the classical Arnold web. In addition, we investigate the nature
of the highly excited eigenstates in order to identify the quantum signatures
of the multiplicity-2 junctions. For the parameter regimes studies herein, by
projecting the eigenstates onto the Arnold web, we find that eigenstates in the
vicinity of the junctions are primarily delocalized due to dynamical tunneling.


  The well-known Kalman filters model dynamical systems by relying on
state-space representations with the next state updated, and its uncertainty
controlled, by fresh information associated with newly observed system outputs.
This paper generalizes, for the first time in the literature, Kalman and
extended Kalman filters to discrete-time settings where inputs, states, and
outputs are represented as attributed graphs whose topology and attributes can
change with time. The setup allows us to adapt the framework to cases where the
output is a vector or a scalar too (node/graph level tasks). Within the
proposed theoretical framework, the unknown state-transition and the readout
functions are learned end-to-end along with the downstream prediction task.


  We derive an explicit manifestly covariant expression for the most general
positive-definite and Lorentz-invariant inner product on the space of solutions
of the Klein-Gordon equation. This expression involves a one-parameter family
of conserved current densities J_a^\mu, with a\in(-1,1), that are analogous to
the chiral current density for spin half fields. The conservation of J_a^\mu is
related to a global gauge symmetry of the Klein-Gordon fields whose gauge group
is U(1) for rational a and the multiplicative group of positive real numbers
for irrational a. We show that the associated gauge symmetry is responsible for
the conservation of the total probability of the localization of the field in
space. This provides a simple resolution of the paradoxical situation resulting
from the fact that the probability current density for free scalar fields is
neither covariant nor conserved. Furthermore, we discuss the implications of
our approach for free real scalar fields offering a direct proof of the
uniqueness of the relativistically invariant positive-definite inner product on
the space of real Klein-Gordon fields. We also explore an extension of our
results to scalar fields minimally coupled to an electromagnetic field.


  Choosing a normal crossings anticanonical divisor of $\mathbb{P}^2$ leads to
four log Calabi-Yau surfaces, three of which are Looijenga pairs. In this
survey article, I describe how to count rational curves in these that intersect
each component of the divisor in one point of maximal tangency.


  With the growing technological advances in autonomous driving, the transport
industry and research community seek to determine the impact that autonomous
vehicles (AV) will have on consumers, as well as identify the different factors
that will influence their use. Most of the research performed so far relies on
laboratory-controlled conditions using driving simulators, as they offer a safe
environment for testing advanced driving assistance systems (ADAS). In this
study we analyze the behavior of drivers that are placed in control of an
automated vehicle in a real life driving environment. The vehicle is equipped
with advanced autonomy, making driver control of the vehicle unnecessary in
many scenarios, although a driver take over is possible and sometimes required.
In doing so, we aim to determine the impact of such a system on the driver and
their driving performance. To this end road users' behavior from naturalistic
driving data is analyzed focusing on awareness and diagnosis of the road
situation. Results showed that the road features determined the level of visual
attention and trust in the automation. They also showed that the activities
performed during the automation affected the reaction time to take over the
control of the vehicle.


  The minimal supersymmetric SO(10) model, in which not only the gauge but also
the third generation fermion Yukawa couplings are unified, provides a simple
and highly predictive theoretical scenario for the understanding of the origin
of the low energy gauge interactions and fermion masses. In the framework of
the MSSM, with universal soft supersymmetry breaking parameters at the grand
unification scale, large values of the universal gaugino mass $M_{1/2}\geq 300$
GeV are needed in order to induce a proper breakdown of the electroweak
symmetry. In addition, in order to obtain acceptable experimental values for
both the pole bottom mass and the $b\rightarrow s\gamma$ decay rate, even
larger values of the gaugino masses are required. The model is strongly
constrained by theoretical and phenomenological requirements and a heavy top
quark, with mass $M_t\geq 170$ GeV, is hard to accomodate within this scheme.
However, we show that to accommodate a top quark mass $M_t\simeq180$ GeV, it is
sufficient to relax the condition of universality of the scalar soft SUSY
breaking parameters at the grand unification scale. Still, the requirement of a
heavy top quark demands a very heavy squark spectrum, unless specific relations
between the soft SUSY breaking parameters are fulfilled.


  The many genres of narrative visualization (e.g. data comics, data videos)
each offer a unique set of affordances and constraints. To better understand a
genre that we call cinematic visualizations-3D visualizations that make highly
deliberate use of a camera to convey a narrative-we gathered 50 examples and
analyzed their traditional cinematic aspects to identify the benefits and
limitations of the form. While the cinematic visualization approach can violate
traditional rules of visualization, we find that through careful control of the
camera, cinematic visualizations enable immersion in data-driven,
anthropocentric environments, and can naturally incorporate in-situ narrators,
concrete scales, and visual analogies. Our analysis guides our design of a
series of cinematic visualizations, created for NASA's Earth Science
Communications team. We present one as a case study to convey design guidelines
covering cinematography, lighting, set design, and sound, and discuss
challenges in creating cinematic visualizations.


  We study the 3D Hubbard model with anisotropic nearest neighbor tunneling
amplitudes using the dynamical cluster approximation and compare the results
with a quantum simulation experiment using ultracold fermions in an optical
lattice, focussing on magnetic correlations. We find that the short-range spin
correlations are significantly enhanced in the direction with stronger
tunneling amplitudes. Our results agree with the experimental observations and
show that the experimental temperature is lower than the strong tunneling
amplitude. We characterize the system by examining the spin correlations beyond
neighboring sites and determine the distribution of density, entropy and spin
correlation in the trapped system. We furthermore investigate the dependence of
the critical entropy at the N\'eel transition on anisotropy.


  Interest in components with detailed structures increased with the progress
in advanced manufacturing techniques in recent years. Parts with graded lattice
elements can provide interesting mechanical, thermal, and acoustic properties
compared to parts where only coarse features are included. One of these
improvements is better global buckling resistance of the component. However,
thin features are prone to local buckling. Normally, analyses with high
computational effort are conducted on high-resolution finite element meshes to
optimize parts with good global and local stability. Until recently, works
focused only on either global or local buckling behavior. We use two-scale
optimization based on asymptotic homogenization of elastic properties and local
buckling behavior to reduce the effort of full-scale analyses. For this, we
present an approach for concurrent local and global buckling optimization of
parameterized graded lattice structures. It is based on a worst-case model for
the homogenized buckling load factor, which acts as a safeguard against pure
local buckling. Cross-modes residing on both scales are not detected. We
support our theory with numerical examples and validations on dehomogenized
designs, which show the capabilities of our method, and discuss the advantages
and limitations of the worst-case model.


  We apply Velocity Channel Gradients (VChGs) and Reduced Velocity Centroids
Gradients (RVCGs) to H I data (the LAB survey), obtaining the plane-of-sky
component (POS) of the magnetic field as a function of the relative velocity.
Assuming a galactic rotation curve, we transformed the relative velocities to
distances, constructing the first map of the POS magnetic field at every point
of the celestial sphere as a function of the distance. To test the accuracy of
our 3D distribution, we used a set of stars with known distances from the
stellar polarization catalog. We compared the polarization directions that we
obtain with the VChGs and RVCGs against the starlight polarization directions.
We find a good correspondence between the derived magnetic field and measured
polarization directions, which testifies to the accuracy of this new way of
probing the 3D galactic POS magnetic field structure.


  Sentiment analysis can be regarded as a relation extraction problem in which
the sentiment of some opinion holder towards a certain aspect of a product,
theme or event needs to be extracted. We present a novel neural architecture
for sentiment analysis as a relation extraction problem that addresses this
problem by dividing it into three subtasks: i) identification of aspect and
opinion terms, ii) labeling of opinion terms with a sentiment, and iii)
extraction of relations between opinion terms and aspect terms. For each
subtask, we propose a neural network based component and combine all of them
into a complete system for relational sentiment analysis. The component for
aspect and opinion term extraction is a hybrid architecture consisting of a
recurrent neural network stacked on top of a convolutional neural network. This
approach outperforms a standard convolutional deep neural architecture as well
as a recurrent network architecture and performs competitively compared to
other methods on two datasets of annotated customer reviews. To extract
sentiments for individual opinion terms, we propose a recurrent architecture in
combination with word distance features and achieve promising results,
outperforming a majority baseline by 18% accuracy and providing the first
results for the USAGE dataset. Our relation extraction component outperforms
the current state-of-the-art in aspect-opinion relation extraction by 15%
F-Measure.


  Factorized in the lifting structure, the wavelet transform can easily be
extended by arbitrary compensation methods. Thereby, the transform can be
adapted to displacements in the signal without losing the ability of perfect
reconstruction. This leads to an improvement of scalability. In temporal
direction of dynamic medical 3-D+t volumes from Computed Tomography,
displacement is mainly given by expansion and compression of tissue. We show
that these smooth movements can be well compensated with a mesh-based method.
We compare the properties of triangle and quadrilateral meshes. We also show
that with a mesh-based compensation approach coding results are comparable to
the common slice wise coding with JPEG 2000 while a scalable representation in
temporal direction can be achieved.


  How structures, e.g., magnetic loops, in the upper atmosphere, i.e., the
transition region and corona, are heated and sustained is one of the major
unresolved issues in solar and stellar physics. Various theoretical and
observational studies on the heating of coronal loops have been undertaken. The
heating of quiescent loops caused by eruptions is, however, rarely observed. In
this study, employing data from the Solar Dynamics Observatory (SDO) and Solar
Upper Transition Region Imager (SUTRI), we report the heating of quiescent
loops associated with nearby eruptions. In active regions (ARs) 13092 and
13093, a long filament and a short filament, and their overlying loops are
observed on 2022 September 4. In AR 13093, a warm channel erupted toward the
northeast, whose material moved along its axis toward the northwest under the
long filament, turned to the west above the long filament, and divided into two
branches falling to the solar surface. Subsequently, the short filament erupted
toward the southeast. Associated with these two eruptions, the quiescent loops
overlying the long filament appeared in SDO/Atmospheric Imaging Assembly (AIA)
high-temperature images, indicating the heating of loops. During the heating,
signature of magnetic reconnection between loops is identified, including the
inflowing motions of loops, and the formation of X-type structures and newly
reconnected loops. The heated loops then cooled down. They appeared
sequentially in AIA and SUTRI lower-temperature images. All the results suggest
that the quiescent loops are heated by reconnection between loops caused by the
nearby warm channel and filament eruptions.


  We review arguments that the cosmological constant (c.c.) should not be
thought of as a local contribution to the energy density, but rather as an
infrared boundary condition specifying particular models of quantum gravity.


  I present an extensible experimental design for optical continuous-variable
cluster states of arbitrary size using four offline (vacuum) squeezers and six
beamsplitters. This method has all the advantages of a temporal-mode encoding
[Phys. Rev. Lett. 104, 250503], including finite requirements for coherence and
stability even as the computation length increases indefinitely, with none of
the difficulty of inline squeezing. The extensibility stems from a construction
based on Gaussian projected entangled pair states (GPEPS). The potential for
use of this design within a fully fault tolerant model is discussed.


  We present a study of the distribution of asymptotic burst oscillation
periods for a sample of 26 bursts from 4U 1636-53 observed with the Rossi X-ray
Timing Explorer (RXTE). The burst sample includes both archival and proprietary
data and spans more than 4.5 years. We also present new optical light curves of
V801 Arae, the optical counterpart of 4U 1636-53, obtained during 1998-2001. We
use these optical data to refine the binary period measured by Augusteijn et
al. (1998) to 3.7931206(152) hours. We show that a subset of ~70% of the bursts
form a tightly clustered distribution of asymptotic periods consistent with a
period stability of ~ 1/10,000. The tightness of this distribution, made up of
bursts spanning more than 4 years in time, suggests that the underlying period
is highly stable, with a time to change the period of ~30,000 years, comparable
to similar numbers derived for X-ray pulsars. We investigate the period and
orbital phase data for our burst sample and show that it is consistent with
binary motion of the neutron star with v sin i < 55 km/sec at 90% confidence.
We use this limit as well as previous radial velocity data to constrain the
binary geometry and component masses in 4U 1636-53.


  We introduce variational sequential Optimal Experimental Design (vsOED), a
new method for optimally designing a finite sequence of experiments under a
Bayesian framework and with information-gain utilities. Specifically, we adopt
a lower bound estimator for the expected utility through variational
approximation to the Bayesian posteriors. The optimal design policy is solved
numerically by simultaneously maximizing the variational lower bound and
performing policy gradient updates. We demonstrate this general methodology for
a range of OED problems targeting parameter inference, model discrimination,
and goal-oriented prediction. These cases encompass explicit and implicit
likelihoods, nuisance parameters, and physics-based partial differential
equation models. Our vsOED results indicate substantially improved sample
efficiency and reduced number of forward model simulations compared to previous
sequential design algorithms.


  We analyze Implicit Repeated Squaring ($\textbf{IRS}$) -- an algorithm that
implicitly computes $(A^{-1}B)^{2^p}$ for $A,B \in {\mathbb C}^{n \times n}$
and $p \in {\mathbb N}_+$. Originating with inverse-free divide-and-conquer
eigensolvers, this routine uses only matrix multiplication and QR to produce
$A_p$ and $B_p$ satisfying $A_p^{-1}B_p = (A^{-1}B)^{2^p}$. By offering the
choice to work with $A_p$ and $B_p$ individually or form $A_p^{-1}B_p$,
$\textbf{IRS}$ is applicable to both implicit and explicit computations
involving $(A^{-1}B)^{2^p}$. Moreover, it exhibits stability. In this paper, we
present the first rigorous and general analysis of the algorithm, showing that
a finite-arithmetic implementation of $\textbf{IRS}$ -- using any fast matrix
multiplication routine -- satisfies a mixed forward/backward stability bound
provided $O(\log(1/\epsilon) + \log(\mu(n)) + (p-1)
\log(\kappa_\text{IRS}(A,B,p)))$ bits of precision are used, where $\epsilon$
is the desired (sufficiently small) forward error, $\mu(n)$ is a polynomial in
$n$, and $\kappa_{\text{IRS}}$ is an appropriately chosen condition number.
Hence, fast $\textbf{IRS}$ is stable in relatively modest precision when $p$ is
logarithmic in $n$ or smaller. We also demonstrate on a handful of examples
that $\textbf{IRS}$ offers improved accuracy over a naive algorithm that
explicitly forms and squares $A^{-1}B$. Along the way, we develop a spectral
norm perturbation bound for full QR that may be of independent interest.


  Performance appraisal (PA) is an important HR process to periodically measure
and evaluate every employee's performance vis-a-vis the goals established by
the organization. A PA process involves purposeful multi-step multi-modal
communication between employees, their supervisors and their peers, such as
self-appraisal, supervisor assessment and peer feedback. Analysis of the
structured data and text produced in PA is crucial for measuring the quality of
appraisals and tracking actual improvements. In this paper, we apply text
mining techniques to produce insights from PA text. First, we perform sentence
classification to identify strengths, weaknesses and suggestions of
improvements found in the supervisor assessments and then use clustering to
discover broad categories among them. Next we use multi-class multi-label
classification techniques to match supervisor assessments to predefined broad
perspectives on performance. Finally, we propose a short-text summarization
technique to produce a summary of peer feedback comments for a given employee
and compare it with manual summaries. All techniques are illustrated using a
real-life dataset of supervisor assessment and peer feedback text produced
during the PA of 4528 employees in a large multi-national IT company.


  Active stabilisation of a quantum system is the active suppression of noise
(such as decoherence) in the system, without disrupting its unitary evolution.
Quantum error correction suggests the possibility of achieving this, but only
if the recovery network can suppress more noise than it introduces. A general
method of constructing such networks is proposed, which gives a substantial
improvement over previous fault tolerant designs. The construction permits
quantum error correction to be understood as essentially quantum state
synthesis. An approximate analysis implies that algorithms involving very many
computational steps on a quantum computer can thus be made possible.


  the storage infrastructure is the foundation on which information relies and
therefore must support a company's business objectives and business model. In
this environment, simply deploying more and faster storage devices is not
enough; a new kind of infrastructure is needed, one that provides more enhanced
network availability, data accessibility, and system manageability than is
provided by today's infrastructure. The SAN meets this challenge. The SAN
liberates the storage device, so it is not on a particular server bus, and
attaches it directly to the network. In other words, storage is externalized
and functionally distributed across the organization. The SAN also enables the
centralizing of storage devices and the clustering of servers, which makes for
easier and less expensive administration. So the idea is to create an
intelligent SAN infrastructure that stretches to meet increased demands, allows
highly available and heterogeneous access to expanding information.


  The re-identification or de-anonymization of users from anonymized data
through matching with publicly available correlated user data has raised
privacy concerns, leading to the complementary measure of obfuscation in
addition to anonymization. Recent research provides a fundamental understanding
of the conditions under which privacy attacks, in the form of database
matching, are successful in the presence of obfuscation. Motivated by
synchronization errors stemming from the sampling of time-indexed databases,
this paper presents a unified framework considering both obfuscation and
synchronization errors and investigates the matching of databases under noisy
entry repetitions. By investigating different structures for the repetition
pattern, replica detection and seeded deletion detection algorithms are devised
and sufficient and necessary conditions for successful matching are derived.
Finally, the impacts of some variations of the underlying assumptions, such as
the adversarial deletion model, seedless database matching, and zero-rate
regime, on the results are discussed. Overall, our results provide insights
into the privacy-preserving publication of anonymized and obfuscated
time-indexed data as well as the closely related problem of the capacity of
synchronization channels.


  The case of Hyperion has been studied excesively due to the fact it is the
largest known celestial body of a highly aspherical shape. It also has a low
mass density and remains in a 4:3 orbital resonance with Titan. Its lightcurve,
obtained through photometric observations by (Klavetter 1989a,b), was initialy
used to show that Hyperion's rotation exhibits no periodicity. Herein it is
analyzed in the means of time series analysis. The Hurst Exponent was estimated
to be H=0.87, indicating a persistent behaviour. The largest Lyapunov Exponent
$\lambda_{max}$ unfortunately could not be given a reliable estimate because of
the shortness of the dataset, consisting 38 observational points. These results
are compared with numerical simulations, which gave a value H=0.88 for the
chaotic zone of the phase space. The Lyapunov time $T_{Lyap}=1/\lambda_{max}$
is about 30 days, which is roughly 1.5 times greater than the orbital period.
By conducting observations over a longer period an insight in the dynamical
features of the present rotational state is possible.


  Let $\Phi$ be an irreducible crystallographic root system with Weyl group $W$
and coroot lattice $\check{Q}$, spanning a Euclidean space $V$. Let $m$ be a
positive integer and $\aA^m_\Phi$ be the arrangement of hyperplanes in $V$ of
the form $(\alpha, x) = k$ for $\alpha \in \Phi$ and $k = 0, 1,...,m$. It is
known that the number $N^+ (\Phi, m)$ of bounded dominant regions of
$\aA^m_\Phi$ is equal to the number of facets of the positive part $\Delta^m_+
(\Phi)$ of the generalized cluster complex associated to the pair $(\Phi, m)$
by S. Fomin and N. Reading.
  We define a statistic on the set of bounded dominant regions of $\aA^m_\Phi$
and conjecture that the corresponding refinement of $N^+ (\Phi, m)$ coincides
with the $h$-vector of $\Delta^m_+ (\Phi)$. We compute these refined numbers
for the classical root systems as well as for all root systems when $m=1$ and
verify the conjecture when $\Phi$ has type $A$, $B$ or $C$ and when $m=1$. We
give several combinatorial interpretations to these numbers in terms of chains
of order ideals in the root poset of $\Phi$, orbits of the action of $W$ on the
quotient $\check{Q} / (mh-1) \check{Q}$ and coroot lattice points inside a
certain simplex, analogous to the ones given by the first author in the case of
the set of all dominant regions of $\aA^m_\Phi$. We also provide a dual
interpretation in terms of order filters in the root poset of $\Phi$ in the
special case $m=1$.


  Exclusive electroproduction of a K or K^* meson on the nucleon can give a
Theta^+ pentaquark in the final state. This reaction offers an opportunity to
investigate the structure of pentaquark baryons at parton level. We discuss the
generalized parton distributions for the N -> Theta^+ transition and give the
leading order amplitude for electroproduction in the Bjorken regime.


  In the framework of the theory of Equilibrium Manifold of a Pure Exchange
Economy, introduced by Balasko, we give a rigorous definition of a crisis
transition and establish some infinitesimal criteria which distinguish
unavoidable crises from other critical equilibria. Our approach builds on the
relationship between the mathematical notions of branching, envelopes, and the
intrinsic derivative.


  We carry out an asymptotic analysis of a thin nematic liquid crystal in which
one elastic constant dominates over the others, namely \begin{align}
\label{energyab} \inf E_\varepsilon(u)\quad\mbox{where}\quad E_\varepsilon(u)
:= \frac{1}{2}\int_\Omega \left\{\varepsilon\,|\nabla u|^2 +
\frac{1}{\varepsilon} \,(|u|^2 - 1)^2 + L \,(\mathrm{div}\,u)^2\right\} \,dx.
\end{align} Here $u: \Omega \to \mathbb R^2$ is a vector field, $0 <
\varepsilon \ll 1 $ is a small parameter, and $L > 0$ is a fixed constant,
independent of $\varepsilon$. We derive the $\Gamma$-limit $E_0$, which is a
sum of a bulk term penalizing divergence and an Aviles-Giga type wall energy
involving the cube of the jump in the tangential component of the
$\mathbb{S}^1$-valued order parameter. We then derive criticality conditions
for $E_0$ and analyze minimization of $E_0$ both rigorously and numerically for
various domains $\Omega$ and a variety of Dirichlet boundary conditions.


  The development of skyrmionic devices requires a suitable tuning of material
parameters in order to stabilize skyrmions and control their density. It has
been demonstrated recently that different skyrmion types can be simultaneously
stabilized at room temperature in heterostructures involving ferromagnets,
ferrimagnets and heavy metals, offering a new platform of coding binary
information in the type of skyrmion instead of the presence/absence of
skyrmions. Here, we tune the energy landscape of the two skyrmion types in such
heterostructures by engineering the geometrical and material parameters of the
individual layers. We find that a fine adjustment of the ferromagnetic layer
thickness and thus its magnetic anisotropy, allows the trilayer system to
support either one of the skyrmion types or the coexistence of both and with
varying densities.


  For linear problems, domain decomposition methods can be used directly as
iterative solvers, but also as preconditioners for Krylov methods. In practice,
Krylov acceleration is almost always used, since the Krylov method finds a much
better residual polynomial than the stationary iteration, and thus converges
much faster. We show in this paper that also for non-linear problems, domain
decomposition methods can either be used directly as iterative solvers, or one
can use them as preconditioners for Newton's method. For the concrete case of
the parallel Schwarz method, we show that we obtain a preconditioner we call
RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is
similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all
components directly defined by the iterative method. This has the advantage
that RASPEN already converges when used as an iterative solver, in contrast to
ASPIN, and we thus get a substantially better preconditioner for Newton's
method. The iterative construction also allows us to naturally define a coarse
correction using the multigrid full approximation scheme, which leads to a
convergent two level non-linear iterative domain decomposition method and a two
level RASPEN non-linear preconditioner. We illustrate our findings with
numerical results on the Forchheimer equation and a non-linear diffusion
problem.


  We survey recent results on the exact dyon spectrum in a class of N=4
supersymmetric string theories, and discuss how the results can be understood
from the macroscopic viewpoint using AdS_2/CFT_1 correspondence. The comparison
between the microscopic and the macroscopic results includes power suppressed
corrections to the entropy, the sign of the index, logarithmic corrections and
also the twisted index measuring the distribution of discrete quantum numbers
among the microstates.


  We study Toeplitz operator theory on the doubling Fock spaces, which are Fock
spaces whose exponential weight is associated to a subharmonic function with
doubling Riesz measure. Namely, we characterize the boundedness, compactness
and membership in the Schatten class of Toeplitz operators on doubling Fock
spaces whose symbol is a positive Radon measure.


  In this paper we will prove a maximum principle for the solutions of linear
parabolic equation on complete non-compact manifolds with a time varying
metric. We will prove the convergence of the Neumann Green function of the
conjugate heat equation for the Ricci flow in $B_k\times (0,T)$ to the minimal
fundamental solution of the conjugate heat equation as $k\to\infty$. We will
prove the uniqueness of the fundamental solution under some exponential decay
assumption on the fundamental solution. We will also give a detail proof of the
convergence of the fundamental solutions of the conjugate heat equation for a
sequence of pointed Ricci flow $(M_k\times (-\alpha,0],x_k,g_k)$ to the
fundamental solution of the limit manifold as $k\to\infty$ which was used
without proof by Perelman in his proof of the pseudolocality theorem for Ricci
flow.


  We study the two-party communication complexity of functions with large
outputs, and show that the communication complexity can greatly vary depending
on what output model is considered. We study a variety of output models,
ranging from the open model, in which an external observer can compute the
outcome, to the XOR model, in which the outcome of the protocol should be the
bitwise XOR of the players' local outputs. This model is inspired by XOR games,
which are widely studied two-player quantum games. We focus on the question of
error-reduction in these new output models. For functions of output size k,
applying standard error reduction techniques in the XOR model would introduce
an additional cost linear in k. We show that no dependency on k is necessary.
Similarly, standard randomness removal techniques, incur a multiplicative cost
of $2^k$ in the XOR model. We show how to reduce this factor to O(k). In
addition, we prove analogous error reduction and randomness removal results in
the other models, separate all models from each other, and show that some
natural problems, including Set Intersection and Find the First Difference,
separate the models when the Hamming weights of their inputs is bounded.
Finally, we show how to use the rank lower bound technique for our weak output
models.


  Recent work has highlighted roles for thermodynamic phase behavior in diverse
cellular processes. Proteins and nucleic acids can phase separate into
three-dimensional liquid droplets in the cytoplasm and nucleus and the plasma
membrane of animal cells appears tuned close to a two-dimensional liquid-liquid
critical point. In some examples, cytoplasmic proteins aggregate at plasma
membrane domains, forming structures such as the post-synaptic density and
diverse signaling clusters. Here we examine the physics of these surface
densities, employing minimal simulations of co-acervating polymers coupled to
an Ising membrane surface in conjunction with a complementary Landau theory. We
argue that these surface densities are a novel phase reminiscent of
pre-wetting, in which a molecularly thin three-dimensional liquid forms on a
usually solid surface. However, in surface densities the solid surface is
replaced by a membrane with an independent propensity to phase separate. We
show that proximity to criticality in the membrane dramatically increases the
parameter regime in which a pre-wetting-like transition occurs, leading to a
broad region where coexisting surface phases can form even when a bulk phase is
unstable. Our simulations naturally exhibit three surface phase coexistence
even though both the membrane and the polymer bulk can only display two phase
coexistence on their own. We argue that the physics of these surface densities
enables diverse functions seen in Eukaryotic cells.


  We study the origin of fifth forces in scalar-tensor theories of gravity in
the so-called Jordan frame, where the modifications to the gravitational sector
are manifest. We focus on theories of Brans-Dicke type in which an additional
scalar field is coupled directly to the Ricci scalar of General Relativity. We
describe how the necessary diffeomorphism invariance of the modified
gravitational sector leads to a modification of the usual gauge fixing term
(for the harmonic gauge), as compared to Einstein gravity. This allows us to
perform a consistent linearization of the gravitational sector in the
weak-field limit, which gives rise to a kinetic mixing between the
non-minimally coupled scalar field and the graviton. It is through this mixing
that a fifth force can arise between matter fields. We are then able to compute
the matrix elements for fifth-force exchanges directly in the Jordan frame,
without the need to perform a conformal transformation to the so-called
Einstein frame, where the gravitational sector is of Einstein-Hilbert form. We
obtain results that are in agreement with the equivalent Einstein-frame
calculations and illustrate, still in the Jordan frame, the pivotal role that
sources of explicit scale symmetry breaking in the matter sector play in
admitting fifth-force couplings.


  It has been proposed that an intermediate mass black hole can produce compact
molecular clouds with large velocity dispersions. This model is called into
question due to the discovery of several such short lived clouds, which
suggests they are common, and hence it is unlikely that their formation
involves an exotic object such as an intermediate mass black hole. In this
paper we propose an alternative model, where supernovae produce such clouds. We
apply our model to a such a cloud called CO-0.40-0.22. A previous work pointed
out the fact that the kinetic energy of this cloud is comparable to that from a
supernova, but disqualified the supernova scenario due to lack of thermal
emission. We explain the lack of thermal emission as a consequence of the large
density of the medium. In such a medium, the supernova shock is radiation
dominated, and hence the initial temperatures are lower by many orders of
magnitude compared with a typical supernova. Finally, we discuss some of the
consequences of having a significant population of intermediate mass black
holes in the galactic centre.


  Reverse H\"{o}lder inequalities for a class of functions on a probability
space constitute an important tool in Analysis in Probability. After revisiting
how a (modified) log-Sobolev inequality can be used to derive reverse
H\"{o}lder inequalities for the class of log-Lipschitz functions, we obtain a
weaker condition using general Transport-Entropy inequalities, which can also
handle approximately log-Lipschitz functions. In its weakest form, the
condition degenerates to the assumption of satisfying a concentration
inequality. We compare this with a scenario in which the underlying space only
satisfies a Poincar\'e inequality.


  We reconsider the dynamical systems approach to analyze inflationary universe
in the Jordan frame models of scalar field nonminimally coupled to curvature.
The adopted set of variables allows us to clearly distinguish between different
asymptotic states in the phase space, including the kinetic and inflationary
regimes. Inflation is realized as a heteroclinic trajectory originating either
at infinity from a nonhyperbolic asymptotic de Sitter point or from a regular
saddle de Sitter point. We also present a comprehensive picture of possible
initial conditions leading to sufficient inflationary expansion and show their
extent on the phase diagrams. In addition we comment on the slow roll
conditions applicable in the Jordan frame and show how they approximate the
leading inflationary "attractor solution". As particular examples we portrait
quadratic and quartic potential models and note that increasing the nonminimal
coupling diminishes the range of good initial conditions in the quadratic case,
but enlarges is in the quartic case.


  Image deraining is an important yet challenging image processing task. Though
deterministic image deraining methods are developed with encouraging
performance, they are infeasible to learn flexible representations for
probabilistic inference and diverse predictions. Besides, rain intensity varies
both in spatial locations and across color channels, making this task more
difficult. In this paper, we propose a Conditional Variational Image Deraining
(CVID) network for better deraining performance, leveraging the exclusive
generative ability of Conditional Variational Auto-Encoder (CVAE) on providing
diverse predictions for the rainy image. To perform spatially adaptive
deraining, we propose a spatial density estimation (SDE) module to estimate a
rain density map for each image. Since rain density varies across different
color channels, we also propose a channel-wise (CW) deraining scheme.
Experiments on synthesized and real-world datasets show that the proposed CVID
network achieves much better performance than previous deterministic methods on
image deraining. Extensive ablation studies validate the effectiveness of the
proposed SDE module and CW scheme in our CVID network. The code is available at
\url{https://github.com/Yingjun-Du/VID}.


  We analyze the thermodynamic limit - modeled as the open-trap limit of an
isotropic harmonic potential - of an ideal, non-relativistic Bose gas with a
special emphasis on the phenomenon of Bose-Einstein condensation. This is
accomplished by the use of an asymptotic expansion of the grand potential,
which is derived by $\zeta$-regularization techniques. Herewith we can show,
that the singularity structure of this expansion is directly interwoven with
the phase structure of the system: In the non-condensation phase the expansion
has a form that resembles usual heat kernel expansions. By this, thermodynamic
observables are directly calculable. In contrast, the expansion exhibits a
singularity of infinite order above a critical density and a renormalization of
the chemical potential is needed to ensure well-defined thermodynamic
observables. Furthermore, the renormalization procedure forces the system to
exhibit condensation. In addition, we show that characteristic features of the
thermodynamic limit, like the critical density or the internal energy, are
entirely encoded in the coefficients of the asymptotic expansion.


  Optically thick energy dominated plasma created in the source of Gamma-Ray
Bursts (GRBs) expands radially with acceleration and forms a shell with
constant width measured in the laboratory frame. When strong Lorentz factor
gradients are present within the shell it is supposed to spread at sufficiently
large radii. There are two possible mechanisms of spreading: hydrodynamical and
thermal ones. We consider both mechanisms evaluating the amount of spreading
that occurs during expansion up to the moment when the expanding shell becomes
transparent for photons. We compute the hydrodynamical spreading of an
ultrarelativistically expanding shell. In the case of thermal spreading we
compute the velocity spread as a function of two parameters: comoving
temperature and bulk Lorentz factor of relativistic Maxwellian distribution.
Based on this result we determine the value of thermal spreading of
relativistically expanding shell. We found that thermal spreading is negligible
for typical GRB parameters. Instead hydrodynamical spreading appears to be
significant, with the shell width reaching $\sim10^{10}$ cm for total energy
$E=10^{54}$ erg and baryonic loading $B=10^{-2}$. Within the fireshell model
such spreading will result in the duration of Proper Gamma-Ray Bursts up to
several seconds.


  The generalized additive Runge-Kutta (GARK) framework provides a powerful
approach for solving additively partitioned ordinary differential equations.
This work combines the ideas of symplectic GARK schemes and multirate GARK
schemes to efficiently solve additively partitioned Hamiltonian systems with
multiple time scales. Order conditions, as well as conditions for symplecticity
and time-reversibility, are derived in the general setting of non-separable
Hamiltonian systems. Investigations of the special case of separable
Hamiltonian systems are also carried out. We show that particular partitions
may introduce stability issues, and discuss partitions that enable an
implicit-explicit integration leading to improved stability properties.
Higher-order symplectic multirate GARK schemes based on advanced composition
techniques are discussed. The performance of the schemes is demonstrated by
means of the Fermi-Pasta-Ulam problem.


  Advances in Tiny Machine Learning (TinyML) have bolstered the creation of
smart industry solutions, including smart agriculture, healthcare and smart
cities. Whilst related research contributes to enabling TinyML solutions on
constrained hardware, there is a need to amplify real-world applications by
optimising energy consumption in battery-powered systems. The work presented
extends and contributes to TinyML research by optimising battery-powered
image-based anomaly detection Internet of Things (IoT) systems. Whilst previous
work in this area has yielded the capabilities of on-device inferencing and
training, there has yet to be an investigation into optimising the management
of such capabilities using machine learning approaches, such as Reinforcement
Learning (RL), to improve the deployment battery life of such systems. Using
modelled simulations, the battery life effects of an RL algorithm are
benchmarked against static and dynamic optimisation approaches, with the
foundation laid for a hardware benchmark to follow. It is shown that using RL
within a TinyML-enabled IoT system to optimise the system operations, including
cloud anomaly processing and on-device training, yields an improved battery
life of 22.86% and 10.86% compared to static and dynamic optimisation
approaches respectively. The proposed solution can be deployed to
resource-constrained hardware, given its low memory footprint of 800 B, which
could be further reduced. This further facilitates the real-world deployment of
such systems, including key sectors such as smart agriculture.


  One of the greatest challenges in interpreting the pulsations of rapidly
rotating stars is mode identification, i.e. correctly matching theoretical
modes to observed pulsation frequencies. Indeed, the latest observations as
well as current theoretical results show the complexity of pulsation spectra in
such stars, and the lack of easily recognisable patterns. In the present
contribution, the latest results on non-adiabatic effects in such pulsations
are described, and we show how these come into play when identifying modes.
These calculations fully take into account the effects of rapid rotation,
including centrifugal distortion, and are based on models from the ESTER
project, currently the only rapidly rotating models in which the energy
conservation equation is satisfied, a prerequisite for calculating
non-adiabatic effects. Non-adiabatic effects determine which modes are excited
and play a key role in the near-surface pulsation-induced temperature
variations which intervene in multi-colour amplitude ratios and phase
differences, as well as line profile variations.


  Using the orthodox Weyl -- Wigner -- Stratonovich -- Cohen (WWSC)
quantization rule we construct a time -- of -- arrival operator for a free
particle on the circle. It is shown that this operator is self -- adjoint but
the careful analysis of its properties suggests that it cannot represent a
`physical' time -- of -- arrival observable. The problem of a time -- of --
arrival observable for the `waiting screen' is also considered. A method of
avoiding the quantum Zeno effect is proposed and the positive operator valued
measure (POV -- measure) or the generalized positive operator valued measure
(GPOV -- measure) describing quantum time -- of -- arrival observable for the
waiting screen are found.


  The study of multi-band superconductivity is relevant for a variety of
systems, from ultra cold atoms with population imbalance to particle physics,
and condensed matter. As a consequence, this problem has been widely
investigated bringing to light many new and interesting phenomena. In this work
we point out and explore a correspondence between a two-band metal with a
$k$-dependent hybridization and a uniformly polarized fermionic system in the
presence of spin-orbit coupling (SOC). We study the ground state phase diagram
of the metal in the presence of an attractive interaction. We find remarkable
superconducting properties whenever hybridization mixes orbitals of different
parities in neighboring sites. We show that this mechanism enhances
superconductivity and drives the crossover from weak to strong coupling in
analogy with SOC in cold atoms. We obtain the quantum phase transitions between
the normal and superfluid states, as the intensity of different parameters
characterizing the metal are varied, including Lifshitz transitions, with no
symmetry breaking, associated with the appearance of soft modes in the Fermi
surface.


  The R\'enyi entropy is a generalization of the Shannon entropy and is widely
used in mathematical statistics and applied sciences for quantifying the
uncertainty in a probability distribution. We consider estimation of the
quadratic R\'enyi entropy and related functionals for the marginal distribution
of a stationary m-dependent sequence. The U-statistic estimators under study
are based on the number of epsilon-close vector observations in the
corresponding sample. A variety of asymptotic properties for these estimators
are obtained (e.g., consistency, asymptotic normality, Poisson convergence).
The results can be used in diverse statistical and computer science problems
whenever the conventional independence assumption is too strong (e.g.,
epsilon-keys in time series databases, distribution identification problems for
dependent samples).


  In this paper, we study Joule-Thomson expansion for Hayward-AdS black hole in
the extended phase space, and obtain a Joule-Thomson expansion formula for the
black hole. We plot the inversion and isenthalpic curves in the T-P plane, and
determine the cooling-heating regions. The intersection points of the
isenthalpic and inversion curves are exactly the inversion points
discriminating the heating process from the cooling one.


  We study the connection between the BCS pairing model and the inhomogeneous
vertex model. The two spectral problems coincide in the quasi-classical limit
of the off-shell Bethe Ansatz of the disordered six vertex model. The latter
problem is transformed into an auxiliary spectral problem which corresponds to
the diagonalization of the integrals of motion of the BCS model. A generating
functional whose quasi classical expansion leads to the constants of motion of
the BCS model and in particular the Hamiltonian, is identified.


  NpT ensemble Monte Carlo simulations were performed for fully flexible
Lennard-Jones chains in the solid phase. The bond length between monomers
within the chains is fixed to $L=\sigma$ and the molecule is free to adopt any
configuration. The solid structure of fully flexible chains is obtained by
randomly locating the bonds of the chain within a face centered cubic close
packed arrangement of atoms. For fully flexible chains it is believed that the
stable solid phase is disordered. Such a solid is considered in this work.
Computer simulations were performed for chains with $m=3, 4$ and 5 monomer
units, and results were obtained for the equation of state and internal energy
of the chains. An extension of Wertheim's TPT1 to the solid phase of
Lennard-Jones chains (C.Vega, F.J.Blas and A.Galindo, J.Chem.Phys.,{\bf
116},7645,2002) has been proposed recently. The simulation results of this work
provide a check on the performance of this theory. It is found that Wertheim's
TPT1 successfully predicts the equation of state and internal energies of fully
flexible LJ chains in the solid phase. Finally, a rigid LJ chain in a linear
configuration has been considered. Computer simulations were also performed for
the rigid chain in an ordered solid structure. It is found that fully flexible
and linear rigid chains present quite different equations of state and
different thermodynamic properties in the solid phase.


  We consider performance enhancement of asymmetrically-clipped optical
orthogonal frequency division multiplexing (ACO-OFDM) and related optical OFDM
schemes, which are variations of OFDM in intensity-modulated optical wireless
communications. Unlike most existing studies on specific designs of improved
receivers, this paper investigates information theoretic limits of all possible
receivers. For independent and identically distributed complex Gaussian inputs,
we obtain an exact characterization of information rate of ACO-OFDM with
improved receivers for all SNRs. It is proved that the high-SNR gain of
improved receivers asymptotically achieve 1/4 bits per channel use, which is
equivalent to 3 dB in electrical SNR or 1.5 dB in optical SNR; as the SNR
decreases, the maximum achievable SNR gain of improved receivers decreases
monotonically to a non-zero low-SNR limit, corresponding to an information rate
gain of 36.3%. For practically used constellations, we derive an upper bound on
the gain of improved receivers. Numerical results demonstrate that the upper
bound can be approached to within 1 dB in optical SNR by combining existing
improved receivers and coded modulation. We also show that our information
theoretic analyses can be extended to Flip-OFDM and PAM-DMT. Our results imply
that, for the considered schemes, improved receivers may reduce the gap to
channel capacity significantly at low-to-moderate SNR.


  We investigate a geometric criterion for a smooth curve $C$ of genus $14$ and
degree $18$ to be described as the zero locus of a section in an Ulrich bundle
of rank $3$ on a del Pezzo threefold $V_5 \subset \mathbb{P}^6$. The main
challenge is to read off the Pfaffian quadrics defining $V_5$ from geometric
structures of $C$. We find that this problem is related to the existence of a
special rank-two vector bundle on $C$ with trivial resonance. This answers a
question posed by Ciliberto-Flamini-Knutsen, in the case of degree $5$ del
Pezzo threefolds. From an explicit calculation of the Betti table of such a
curve, we also deduce the uniqueness of the del Pezzo threefold.


  New solutions of relativistic wave equations are obtained in a unified manner
from generating functions of spinorial variables. The choice of generating
functions as Gaussians leads to representations in the form of generalized
fractional Fourier transforms. Wave functions satisfying the Dirac, Maxwell,
and Weyl equations are constructed by simple differentiations with respect to
spinorial arguments. In the simplest case, one obtains Maxwell and Dirac
hopfion solutions.


  We apply ideas from abstract argumentation theory to study cooperative game
theory. Building on Dung's results in his seminal paper, we further the
correspondence between Dung's four argumentation semantics and solution
concepts in cooperative game theory by showing that complete extensions (the
grounded extension) correspond to Roth's subsolutions (respectively, the
supercore). We then investigate the relationship between well-founded
argumentation frameworks and convex games, where in each case the semantics
(respectively, solution concepts) coincide; we prove that three-player convex
games do not in general have well-founded argumentation frameworks.


  A quandle is an algebraic system which excels at describing limited
symmetries of a space. We introduce the concept of Schl\"{a}fli quandles which
are defined relating to chosen rotational symmetries of regular tessellations.
On the other hand, quandles have a good chemistry with knot theory. Associated
with a knot we have its knot quandle. We show that the knot quandle of the
$m$-twist-spun trefoil is a central extension of the Schl\"{a}fli quandle
related to the regular tessellation $\{ 3, m \}$ in the sense of the
Schl\"{a}fli symbol if $m \geq 3$.


  Secure network coding realizes the secrecy of the message when the message is
transmitted via noiseless network and a part of edges or a part of intermediate
nodes are eavesdropped. In this framework, if the channels of the network has
noise, we apply the error correction to noisy channel before applying the
secure network coding. In contrast, secure physical layer network coding is a
method to securely transmit a message by a combination of coding operation on
nodes when the network is given as a set of noisy channels. In this paper, we
give several examples of network, in which, secure physical layer network
coding has advantage over secure network coding.


  We explore the ideas of resurgence and Pad\'{e}-Borel resummation in the
Euler-Heisenberg Lagrangian of scalar quantum electrodynamics, which has
remained largely unexamined in these contexts. We thereby extend the related
seminal works in spinor quantum electrodynamics, while contrasting the
similarities and differences in the two cases. We investigate in detail the
efficacy of resurgent extrapolations starting from just a finite number of
terms in the weak-field expansions of the 1-loop and 2-loop scalar quantum
electrodynamics Euler-Heisenberg Lagrangian. While we re-derive some of the
well-known 1-loop and 2-loop contributions in representations suitable for
Pad\'{e}-Borel analyses, other contributions have been derived for the first
time. For instance, we find a closed analytic form for the one-particle
reducible contribution at 2-loop, which until recently was thought to be
unimportant. It is pointed out that there could be an interesting interplay
between the one-particle irreducible and one-particle reducible terms in the
strong-field limit. For the 1-loop contribution, the resurgent analysis may be
mapped effectively into two copies of the spinor quantum electrodynamics
weak-field expansions, differing only in their prefactors and masses. This
simple mapping is no longer true at 2-loops. The singularity structures in the
Pad\'{e}-Borel transforms at 1-loop and 2-loop are examined in some detail.
Analytic continuation to the electric field case and the generation of an
imaginary part is also studied. We compare the Pad\'{e}-Borel reconstructions
to closed analytic forms or to numerically computed values in the full theory.
It is seen that Pad\'{e}-Borel resummations based on even a small number of
terms from the weak-field expansions can accurately approximate the
strong-field behaviour.


  We prove a new system of relations in the tautological ring of the moduli
space of curves involving stable rooted trees with level structure decorated by
the top Chern class of the Hodge bundle and $\Omega$-classes and double
ramification structures. In particular, this resolves a recent conjecture on
these relations as well as connects with one of the two sides of the recently
established DR/DZ equivalence between the integrable hierarchies constructions
of Buryak and of Dubrovin--Zhang.


  Software architecture has been a key research area in the software
engineering community due to its significant role in creating high quality
software. The trend of developing product lines rather than single products has
made the software product line a viable option in the industry. Software
product line architecture is regarded as one of the crucial components in the
product lines, since all of the resulting products share this common
architecture. The increased popularity of software product lines demands a
process maturity evaluation methodology. Consequently, this paper presents an
architecture process maturity model for software product line engineering to
evaluate the current maturity of the product line architecture development
process in an organization. Assessment questionnaires and a rating methodology
comprise the framework of this model. The objective of the questionnaires is to
collect information about the software product line architecture development
process. Thus, in general this work contributes towards the establishment of a
comprehensive and unified strategy for the process maturity evaluation of
software product line engineering. Furthermore, we conducted two case studies
and reported the assessment results, which show the maturity of the
architecture development process in two organizations


  As quantum computing progresses steadily from theory into practice,
programmers will face a common problem: How can they be sure that their code
does what they intend it to do? This paper presents encouraging results in the
application of mechanized proof to the domain of quantum programming in the
context of the SQIR development. It verifies the correctness of a range of a
quantum algorithms including Grover's algorithm and quantum phase estimation, a
key component of Shor's algorithm. In doing so, it aims to highlight both the
successes and challenges of formal verification in the quantum context and
motivate the theorem proving community to target quantum computing as an
application domain.


  The low-energy structure and the thermodynamic properties of ferrimagnetic
Heisenberg chains of alternating spins $S$ and $s$ are investigated by the use
of numerical tools as well as the spin-wave theory. The elementary excitations
are calculated through an efficient quantum Monte Carlo technique featuring
imaginary-time correlation functions and are characterized in terms of
interacting spin waves. The thermal behavior is analyzed with particular
emphasis on its ferromagnetic and antiferromagnetic dual aspect. The extensive
numerical and analytic calculations lead to the classification of the
one-dimensional ferrimagnetic behavior according to the constituent spins: the
ferromagnetic ($S>2s$), antiferromagnetic ($S<2s$), and balanced ($S=2s$)
ferrimagnetism.


  Both observations and recent numerical simulations of the circumgalactic
medium (CGM) support the hypothesis that a self-regulating feedback loop
suspends the gas density of the ambient CGM close to the galaxy in a state with
a ratio of cooling time to freefall time >10. This limiting ratio is thought to
arise because circumgalactic gas becomes increasingly susceptible to multiphase
condensation as the ratio declines. If the timescale ratio gets too small, then
cold clouds precipitate out of the CGM, rain into the galaxy, and fuel
energetic feedback that raises the ambient cooling time. The astrophysical
origin of this so-called precipitation limit is not simple but is critical to
understanding the CGM and its role in galaxy evolution. This paper therefore
attempts to interpret its origin as simply as possible, relying mainly on
conceptual reasoning and schematic diagrams. It illustrates how the
precipitation limit can depend on both the global configuration of a galactic
atmosphere and the degree to which dynamical disturbances drive CGM
perturbations. It also frames some tests of the precipitation hypothesis that
can be applied to both CGM observations and numerical simulations of galaxy
evolution.


  Applying the classical Serre-Swan theorem, as this is extended to topological
(non-normed) algebras, one attains a classification of elementary particles via
their spin-structure. In this context, our argument is virtually based on a
``correspondence principle'' of S. A. Selesnick, formulated herewith in a
sheaf-theoretic language, presisely speaking, in terms of vector sheaves. This
then leads directly to second quantization, as well as, to other applications
of geometric (pre)quantization theory.


  We demonstrate a controllable depletion of the nitrogen buffer gas pressure
in a micro-machined cesium (Cs) vapor cell from the dynamic heating of an
alkali dispenser pill. When the alkali source is laser activated, the gettering
compounds within the alkali pill dispenser reduce the nitrogen (N$_2$) content
from the vapor for fine-tuning of the alkali to buffer gas pressure ratio.
Additionally, we decrease the buffer gas pressure below 100$\,$mTorr to
evaluate the presence of other potential broadening mechanisms. Real-time
control of the gas pressure ratio in the vapor cell will have notable benefits
for refining atomic sensor performance and provide a routine to achieve various
target pressures across a wafer bonded with a uniform back-filled buffer gas
pressure.


  Bulk resistivity and point contact spectra of Ni_xNb_{1-x} metallic glasses
have been investigated as functions of temperature (0.3-300K) and magnetic
field (0-12T). Metallic glasses in this family undergo a superconducting phase
transition determined by the Nb concentration. When superconductivity was
suppressed by a strong magnetic field, both the bulk sample R(T) and the point
contact differential resistance curves of Ni_xNb_{1-x} showed logarithmic
behavior at low energies, which is explained by a strong electron - "two level
system" coupling. We studied the temperature, magnetic field and contact
resistance dependence of Ni_{44}Nb_{56} point-contact spectra in the
superconducting state and found telegraph-like fluctuations superimposed on
superconducting characteristics. These R(V) characteristics are extremely
sensitive detectors for slow relaxing "two level system" motion.


  We propose a new method to optically levitate a macroscopic mirror with two
vertical Fabry-P{\'e}rot cavities linearly aligned. This configuration gives
the simplest possible optical levitation in which the number of laser beams
used is the minimum of two. We demonstrate that reaching the standard quantum
limit (SQL) of a displacement measurement with our system is feasible with
current technology. The cavity geometry and the levitated mirror parameters are
designed to ensure that the Brownian vibration of the mirror surface is smaller
than the SQL. Our scheme provides a promising tool for testing macroscopic
quantum mechanics.


  We report the fabrication and characterization of photonic structures using
tapered optical nanofibers. Thanks to the extension of the evanescent
electromagnetic field outside of the nanofiber two types of devices can be
built: a ring interferometer and a knot resonator. We propose a general
approach to predict the properties of these structures using the linear
coupling theory. In addition, we describe a new source of birefringence due to
the ovalization of a nanofiber under strong bending, known in mechanical
engineering as the Brazier effect.


  We use microscopic linear response theory to derive a set of equations that
provide a complete description of coupled spin and charge diffusive transport
in a two-dimensional electron gas (2DEG) with the Rashba spin-orbit (SO)
interaction. These equations capture a number of interrelated effects including
spin accumulation and diffusion, Dyakonov-Perel spin relaxation,
magnetoelectric, and spin-galvanic effects. They can be used under very general
circumstances to model transport experiments in 2DEG systems that involve
either electrical or optical spin injection. We comment on the relationship
between these equations and the exact spin and charge density operator
equations of motion. As an example of the application of our equations, we
consider a simple electrical spin injection experiment and show that a voltage
will develop between two ferromagnetic contacts if a spin-polarized current is
injected into a 2DEG, that depends on the relative magnetization orientation of
the contacts. This voltage is present even when the separation between the
contacts is larger than the spin diffusion length.


  Using a model system, we demonstrate both experimentally and theoretically
that coherent scattering of light can be robust in hot atomic vapors despite a
significant Doppler effect. By operating in a linear regime of far-detuned
light scattering, we also unveil the emergence of interference triggered by
inelastic Stokes and anti-Stokes transitions involving the atomic hyperfine
structure.


  This chapter describes the relationship between low frequency noise and
coherence decay of localized spins in semiconductors. Section 2 establishes a
direct relationship between an arbitrary noise spectral function and spin
coherence as measured by a number of pulse spin resonance sequences. Section 3
describes the electron-nuclear spin Hamiltonian, including isotropic and
anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the
effective Hamiltonian for nuclear-nuclear coupling mediated by the electron
spin hyperfine interaction. Section 4 describes a microscopic calculation of
the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops
with quasiparticle broadening included. Section 5 compares our explicit
numerical results to electron spin echo decay experiments for phosphorus doped
silicon in natural and nuclear spin enriched samples.


  For two correlated graphs which are independently sub-sampled from a common
Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their
\emph{latent} vertex matching from the observation of these two graphs
\emph{without labels}. When $p = n^{-\alpha+o(1)}$ for $\alpha\in (0, 1]$, we
establish a sharp information-theoretic threshold for whether it is possible to
correctly match a positive fraction of vertices. Our result sharpens a constant
factor in a recent work by Wu, Xu and Yu.


  The high redshift radio galaxy 4C41.17 consists of a powerful radio source in
which previous work has shown that there is strong evidence for jet-induced
star formation along the radio axis. We argue that nuclear photoionization is
not responsible for the excitation of the emission line clouds and we construct
a jet-cloud interaction model to explain the major features revealed by the
data. The interaction of a high-powered jet with a dense cloud in the halo of
4C41.17 produces shock-excited emission-line nebulosity through ~1000 km/s
shocks and induces star formation. The CIII to CIV line ratio and the CIV
luminosity emanating from the shock, imply that the pre-shock density in the
line-emitting cloud is high enough (~1-10 cm^-3) that shock initiated star
formation could proceed on a timescale of order a few x 10^6 yrs, well within
the estimated dynamical age of the radio source. Broad (FWHM ~ 100 - 1400 km/s)
emission lines are attributed to the disturbance of the gas cloud by a partial
bow--shock and narrow emission lines (FWHM ~ 500 - 650 km/s) (in particular
CIV) arise in precursor emission in relatively low metallicity gas. The implied
baryonic mass ~ 8 \times 10^{10} solar masses of the cloud is high and implies
that Milky Way size condensations existed in the environments of forming radio
galaxies at a redshift of 3.8. Our interpretation of the data provides a
physical basis for the alignment of the radio, emission-line and UV continuum
images in some of the highest redshift radio galaxies and the analysis
presented here may form a basis for the calculation of densities and cloud
masses in other high redshift radio galaxies.


  This paper introduces the Passive Transformable Omni-Ball (PTOB), an advanced
omnidirectional wheel engineered to enhance step-climbing performance,
incorporate built-in actuators, diminish vibrations, and fortify structural
integrity. By modifying the omni-ball's structure from two to three segments,
we have achieved improved in-wheel actuation and a reduction in vibrational
feedback. Additionally, we have implemented a sliding mechanism in the follower
wheels to boost the wheel's step-climbing abilities. A prototype with a 127 mm
diameter PTOB was constructed, which confirmed its functionality for
omnidirectional movement and internal actuation. Compared to a traditional
omni-wheel, the PTOB demonstrated a comparable level of vibration while
offering superior capabilities. Extensive testing in varied settings showed
that the PTOB can adeptly handle step obstacles up to 45 mm, equivalent to 35
$\%$ of the wheel's diameter, in both the forward and lateral directions. The
PTOB showcased robust construction and proved to be versatile in navigating
through environments with diverse obstacles.


  Structures and properties of many inorganic compounds have been collected
historically. However, it only covers a very small portion of possible
inorganic crystals, which implies the presence of numerous currently unknown
compounds. A powerful machine-learning strategy is mandatory to discover new
inorganic compounds from all chemical combinations. Herein we propose a
descriptor-based recommender-system approach to estimate the relevance of
chemical compositions where stable crystals can be formed [i.e., chemically
relevant compositions (CRCs)]. As well as data-driven compositional similarity
used in the literature, the use of compositional descriptors as a prior
knowledge can accelerate the discovery of new compounds. We validate our
recommender systems in two ways. Firstly, one database is used to construct a
model, while another is used for the validation. Secondly, we estimate the
phase stability for compounds at expected CRCs using density functional theory
calculations.


  In this article we characterize the $\mathrm{L}^\infty$ eigenvalue problem
associated to the Rayleigh quotient $\left.{\|\nabla
u\|_{\mathrm{L}^\infty}}\middle/{\|u\|_\infty}\right.$ and relate it to a
divergence-form PDE, similarly to what is known for $\mathrm{L}^p$ eigenvalue
problems and the $p$-Laplacian for $p<\infty$. Contrary to existing methods,
which study $\mathrm{L}^\infty$-problems as limits of $\mathrm{L}^p$-problems
for $p\to\infty$, we develop a novel framework for analyzing the limiting
problem directly using convex analysis and geometric measure theory. For this,
we derive a novel fine characterization of the subdifferential of the
Lipschitz-constant-functional $u\mapsto\|\nabla u\|_{\mathrm{L}^\infty}$. We
show that the eigenvalue problem takes the form $\lambda \nu u
=-\operatorname{div}(\tau\nabla_\tau u)$, where $\nu$ and $\tau$ are
non-negative measures concentrated where $|u|$ respectively $|\nabla u|$ are
maximal, and $\nabla_\tau u$ is the tangential gradient of $u$ with respect to
$\tau$. Lastly, we investigate a dual Rayleigh quotient whose minimizers solve
an optimal transport problem associated to a generalized
Kantorovich--Rubinstein norm. Our results apply to all stationary points of the
Rayleigh quotient, including infinity ground states, infinity harmonic
potentials, distance functions, etc., and generalize known results in the
literature.


  The antisymmetrized geminal power (AGP) wavefunction has a long history and
is known by different names in various chemical and physical problems. There
has been recent interest in using AGP as a starting point for strongly
correlated electrons. Here, we show that in a seniority-conserving regime,
different AGP based correlator representations based on generators of the
algebra, killing operators, and geminal replacement operators are all
equivalent. We implement one representation that uses number operators as
correlators and has linearly independent curvilinear metrics to distinguish the
regions of Hilbert space. This correlation method called J-CI, provides
excellent accuracy in energies when applied to the pairing Hamiltonian.


  Neutrino interactions recorded in a 5.1 fiducial kiloton-year exposure of the
Soudan-2 iron tracking calorimeter are analyzed for effects of neutrino
oscillations. Using contained single track and single shower events, we update
our measurement of the atmospheric nu_mu/nu_e ratio-of-ratios and find R = 0.68
\pm 0.11 \pm 0.06. Assuming this anomalously low R-value is the result of nu_mu
flavor disappearance via nu_mu to nu_tau oscillation, we select samples of
charged current events which offer good resolution, event-by-event, for L/Enu
reconstruction. Oscillation-weighted Monte Carlo events are fitted to these
data events using a chisq function summed over bins of log(L/E_nu). The region
allowed in the (sin^2 2\theta, \Delta m^2) plane at 90% CL is obtained using
the Feldman-Cousins procedure: 0.46 < sin^2 2\theta < 1.0 and 2.2x10^-4 <
\Delta m^2 < 2.2x10^-2 ev^2. A small but relatively energetic sample of
partially contained nu_mu events has also been isolated. Their distribution in
log(L/E_vis) relative to null oscillation Monte Carlo is compatible with nu_mu
to nu_tau oscillation scenarios within the parameter region allowed by our
contained events.


  We investigate the topology of the space of M\"obius conjugacy classes of
degree $d$ rational maps on the Riemann sphere. We show that it is rationally
acyclic and we compute its fundamental group. As a byproduct, we also obtain
the ranks of some higher homotopy groups of the parameter space of degree $d$
rational maps allowing us to extend the previously known range. Moreover, we
show that this parameter space is not nilpotent.


  The in-plane correlation lengths and magnetic disorder of magnetic domains in
a transition metal multilayer have been studied using neutron scattering
techniques. A new theoretical framework is presented connecting the observed
scattering to the in-plane correlation length and the dispersion of the local
magnetization vector about the mean macroscopic direction. The results
unambiguously show the highly correlated nature of the antiferromagnetically
coupled domain structure vertically throughout the multilayer. We are easily
able to relate the neutron determined magnetic dispersion and domain
correlations to magnetization and magnetotransport experiments.


  When inferring reward functions from human behavior (be it demonstrations,
comparisons, physical corrections, or e-stops), it has proven useful to model
the human as making noisy-rational choices, with a "rationality coefficient"
capturing how much noise or entropy we expect to see in the human behavior.
Prior work typically sets the rationality level to a constant value, regardless
of the type, or quality, of human feedback. However, in many settings, giving
one type of feedback (e.g. a demonstration) may be much more difficult than a
different type of feedback (e.g. answering a comparison query). Thus, we expect
to see more or less noise depending on the type of human feedback. In this
work, we advocate that grounding the rationality coefficient in real data for
each feedback type, rather than assuming a default value, has a significant
positive effect on reward learning. We test this in both simulated experiments
and in a user study with real human feedback. We find that overestimating human
rationality can have dire effects on reward learning accuracy and regret. We
also find that fitting the rationality coefficient to human data enables better
reward learning, even when the human deviates significantly from the
noisy-rational choice model due to systematic biases. Further, we find that the
rationality level affects the informativeness of each feedback type:
surprisingly, demonstrations are not always the most informative -- when the
human acts very suboptimally, comparisons actually become more informative,
even when the rationality level is the same for both. Ultimately, our results
emphasize the importance and advantage of paying attention to the assumed
human-rationality level, especially when agents actively learn from multiple
types of human feedback.


  In this work, we propose a portable, Linux-based emulation framework to
provide an ecosystem for hardware-software co-design of Domain-specific SoCs
(DSSoCs) and enable their rapid evaluation during the pre-silicon design phase.
This framework holistically targets three key challenges of DSSoC design:
accelerator integration, resource management, and application development. We
address these challenges via a flexible and lightweight user-space runtime
environment that enables easy integration of new accelerators, scheduling
heuristics, and user applications, and we illustrate the utility of each
through various case studies. With signal processing (WiFi and RADAR) as the
target domain, we use our framework to evaluate the performance of various
dynamic workloads on hypothetical DSSoC hardware configurations composed of
mixtures of CPU cores and FFT accelerators using a Zynq UltraScale+TM MPSoC. We
show the portability of this framework by conducting a similar study on an
Odroid platform composed of big.LITTLE ARM clusters. Finally, we introduce a
prototype compilation toolchain that enables automatic mapping of unlabeled C
code to DSSoC platforms. Taken together, this environment offers a unique
ecosystem to rapidly perform functional verification and obtain performance and
utilization estimates that help accelerate convergence towards a final DSSoC
design.


  We introduce a micro-macro parareal algorithm for the time-parallel
integration of multiscale-in-time systems. The algorithm first computes a
cheap, but inaccurate, solution using a coarse propagator (simulating an
approximate slow macroscopic model), which is iteratively corrected using a
fine-scale propagator (accurately simulating the full microscopic dynamics).
This correction is done in parallel over many subintervals, thereby reducing
the wall-clock time needed to obtain the solution, compared to the integration
of the full microscopic model. We provide a numerical analysis of the algorithm
for a prototypical example of a micro-macro model, namely singularly perturbed
ordinary differential equations. We show that the computed solution converges
to the full microscopic solution (when the parareal iterations proceed) only if
special care is taken during the coupling of the microscopic and macroscopic
levels of description. The convergence rate depends on the modeling error of
the approximate macroscopic model. We illustrate these results with numerical
experiments.


  A dual pair of supersymmetric string theories that involves an asymmetric
orbifold and an orientifold of Type II is considered. The D-branes of the
orbifold theory (that were recently determined by Gutperle) are all non-BPS and
do not carry any conserved gauge charges. It is shown that they carry
non-trivial K-theory charges, and that they can be understood in terms of
branes wrapping certain homology classes of the M-theory compactification.
Using the adiabatic argument, dual partners of some of these non-BPS D-branes
are proposed. The relations between these dual states are found to be in
agreement with the M-theory description of the D-branes.


  Modern open source software development heavily relies on the issue tracking
systems to manage their feature requests, bug reports, tasks, and other similar
artifacts. Together, those "issues" form a complex network with links to each
other. The heterogeneous character of issues inherently results in varied link
types and therefore poses a great challenge for users to create and maintain
the label of the link manually. The goal of most existing automated issue link
construction techniques ceases with only examining the existence of links
between issues. In this work, we focus on the next important question of
whether we can assess the type of issue link automatically through a
data-driven method. We analyze the links between issues and their labels used
the issue tracking system for 66 open source projects. Using three projects, we
demonstrate promising results when using supervised machine learning
classification for the task of link label recovery with careful model selection
and tuning, achieving F1 scores of between 0.56-0.70 for the three studied
projects. Further, the performance of our method for future link label
prediction is convincing when there is sufficient historical data. Our work
signifies the first step in systematically manage and maintain issue links
faced in practice.


  In this article the author reviews Jos\'e Bioucas-Dias' key contributions to
hyperspectral unmixing (HU), in memory of him as an influential scholar and for
his many beautiful ideas introduced to the hyperspectral community. Our story
will start with vertex component analysis (VCA) -- one of the most celebrated
HU algorithms, with more than 2,000 Google Scholar citations. VCA was
pioneering, invented at a time when HU research just began to emerge, and it
shows sharp insights on a then less-understood subject. Then we will turn to
SISAL, another widely-used algorithm. SISAL is not only a highly successful
algorithm, it is also a demonstration of its inventor's ingenuity on applied
optimization and on smart formulation for practical noisy cases. Our tour will
end with dependent component analysis (DECA), perhaps a less well-known
contribution. DECA adopts a statistical inference framework, and the author's
latest research indicates that such framework has great potential for further
development, e.g., there are hidden connections between SISAL and DECA. The
development of DECA shows foresight years ahead, in that regard.


  We study a current-biased 0-\pi-0 Josephson junction made by high-T_c
superconductors, theoretically. When a length of the \pi junction is large
enough, this junction contains a vortex-antivortex pair at both ends of the \pi
junction. Magnetic flux carried by the vortices is calculated using the
sine-Gordon equation. The result shows that the magnetic flux of the vortices
is suppressed to zero as the distance between the vortices is reduced. By
applying an external current, the orientation of the vortices is reversed, and
a voltage pulse is generated. The current needed for this transition and
generated pulse energy are calculated. Macroscopic quantum tunneling (MQT) in
this transition is also studied. The tunneling rate has been evaluated by an
effective Hamiltonian with one degree of freedom.


  Physics-informed neural network (PINN) has been a prevalent framework for
solving PDEs since proposed. By incorporating the physical information into the
neural network through loss functions, it can predict solutions to PDEs in an
unsupervised manner. However, the design of the neural network structure
basically relies on prior knowledge and experience, which has caused great
trouble and high computational overhead. Therefore, we propose a neural
architecture search-guided method, namely NAS-PINN, to automatically search the
optimum neural architecture for solving certain PDEs. By relaxing the search
space into a continuous one and utilizing masks to realize the addition of
tensors in different shapes, NAS-PINN can be trained through a bi-level
optimization, where the inner loop optimizes the weights and bias of neural
networks and the outer loop the architecture parameters. We verify the ability
of NAS-PINN by several numerical experiments including Poisson, Burgers, and
Advection equations. The characteristics of effective neural architectures for
solving different PDEs are summarized, which can be used to guide the design of
neural networks in PINN. It is found that more hidden layers do not necessarily
mean better performance and sometimes can be harmful. Especially for Poisson
and Advection, a shallow neural network with more neurons is more appropriate
in PINNs. It is also indicated that for complex problems, neural networks with
residual connection can improve the performance of PINNs.


  This investigation covers the effects of variable exchange interactions on
the spin dynamics of the zig-zag honeycomb lattice. Using a Holstein-Primakoff
expansion of the Heisenberg Hamiltonian with easy-axis anisotropy, we
characterize the effects of multiple nearest-neighbor and next-nearest-neighbor
interactions with asymmetry within the context of a frustrated and
non-frustrated zig-zag magnetic configuration. Furthermore, we compare to the
known inelastic neutron scattering data for the proximate quantum spin liquid
$\alpha$-RuCl$_3$, and we provide insight into the evolution of the spin
dynamics, showing that the Heisenberg interaction dominates the majority of the
spin excitation behavior. By analyzing the frustrated system with multiple
interactions, direction-dependent Dirac nodes present themselves, and we can
demonstrate that a standard Heisenberg model can accurately describe the
observed magnon spectra.


  Metasurface optical elements enable wavefront control and polarization
manipulation with subwavelength resolution. Metasurfaces made of linearly
birefringent meta-atoms such as rectangular nano-posts are commonly used to
control phase and polarization, but a single layer of these meta-atoms cannot
implement transformations with elliptically polarized or circularly polarized
eigenstates (i.e., chiral transformations). Here, it is shown that two cascaded
metasurface layers comprising linearly birefringent meta-atoms provide
sufficiently many degrees of freedom to implement arbitrary unitary phase and
polarization transformations. A systematic design method for such
metastructures is described and used to design a bifocal metalens that cannot
be implemented by a single layer of birefringent meta-atoms. The presented
design and implementation techniques introduce a systematic approach for
realizing the most general form of lossless polarization and phase
transformations using metasurfaces with high efficiency.


  Symbolic equations are at the core of scientific discovery. The task of
discovering the underlying equation from a set of input-output pairs is called
symbolic regression. Traditionally, symbolic regression methods use
hand-designed strategies that do not improve with experience. In this paper, we
introduce the first symbolic regression method that leverages large scale
pre-training. We procedurally generate an unbounded set of equations, and
simultaneously pre-train a Transformer to predict the symbolic equation from a
corresponding set of input-output-pairs. At test time, we query the model on a
new set of points and use its output to guide the search for the equation. We
show empirically that this approach can re-discover a set of well-known
physical equations, and that it improves over time with more data and compute.


  HD 19467 B is presently the only directly imaged T dwarf companion known to
induce a measurable Doppler acceleration around a solar type star. We present
spectroscopy measurements of this important benchmark object taken with the
Project 1640 integral field unit at Palomar Observatory. Our high-contrast R~30
observations obtained simultaneously across the $JH$ bands confirm the cold
nature of the companion as reported from the discovery article and determine
its spectral type for the first time. Fitting the measured spectral energy
distribution to SpeX/IRTF T dwarf standards and synthetic spectra from BT-Settl
atmospheric models, we find that HD 19467 B is a T5.5+/-1 dwarf with effective
temperature Teff=$978^{+20}_{-43}$ K. Our observations reveal significant
methane absorption affirming its substellar nature. HD 19467 B shows promise to
become the first T dwarf that simultaneously reveals its mass, age, and
metallicity independent from the spectrum of light that it emits.


  Certain non-asymptotically flat but supersymmetric classical solution of the
type IIA supergravity can be interpreted as the infinitely-boosted version of
the D-particle solution along the M-theory circle. By a chain of T-dual
transformations, this analysis also applies to yield non-asymptotically flat
solutions from the asymptotically flat and (non)-extremal solutions with
intersecting D-strings and D five-branes of the type IIB supergravity
compactified on a five-torus. Under S-duality, the non-asymptotically flat
solutions in this context can in particular be used to describe the
(1+1)-dimensional CGHS type black holes via spontaneous compactifications.


  We use optical tweezers microrheology and fluorescence microscopy to apply
nonlinear microscale strains to entangled and crosslinked actin networks, and
measure the resulting stress and actin filament deformations. We couple
nonlinear stress response and subsequent relaxation to the velocity profiles of
individual fluorescent-labeled actin segments at varying times throughout the
strain and varying distances from the strain path to determine the underlying
molecular dynamics that give rise to the debated nonlinear response and stress
propagation of crosslinked and entangled actin networks at the microscale. We
show that initial stress stiffening arises from acceleration of strained
filaments due to molecular extension along the strain, while softening and
yielding is coupled to filament deceleration, halting and recoil. We
demonstrate a surprising non-monotonic dependence of velocity profiles on
crosslinker concentration. Namely, networks with no crosslinks or substantial
crosslinks both exhibit fast initial filament velocities and reduced molecular
recoil while intermediate crosslinker concentrations display reduced velocities
and increased recoil. We show that these collective results are due to a
balance of network elasticity and transient crosslinker unbinding and
rebinding. We further show that elasticity and relaxation timescales display an
exponential dependence on crosslinker concentration that reveal that crosslinks
dominate entanglement dynamics when the length between crosslinkers becomes
smaller than the length between entanglements. In accord with recent
simulations, our relaxation dynamics demonstrate that post-strain stress can be
long-lived in crosslinked networks by distributing stress to a small fraction
of highly-strained connected filaments that span the network and sustain the
load, thereby allowing the rest of the network to recoil and relax.


  The importance of the excited states of Positronium (Ps) in the formation
cross sections(both differential and total) of the negative hydrogen ion (H^-)
are investigated theoretically for the charge transfer reaction, Ps (n = 1, 2)
+ H --> e+ + H^- for a wide range of incident energies (e. g., threshold - 500
eV) . The calculations are performed in the frame work of a qualitative model,
the post collisional Coulomb Modified Eikonal Approximation (CMEA) . A
comparative study is also made between the capture from ground and excited
states of the Ps. The present CMEA model takes account of higher order effects
which is essential for a rearrangement process where the First Born type
Approximation (Coulomb Born for the ionic case) is not supposed to be adequate.
At low incident energies, the excited states of Ps (2s, 2p) are found to play a
dominant role in the H^- formation cross sections . Significant deviations are
noted between the present CMEA and the Coulomb Born (CBA) results even at very
high incident energies (e.g., Ei = 500 eV), indicating the importance of higher
order effects. At high incident energies the present CMEA differential cross
section (DCS) exhibits a double peak structure which is totally absent in the
CBA and could again be attributed to higher order effects.


  Asteroseismic investigations, particularly based on data on stellar
oscillations from the CoRoT and Kepler space missions, are providing unique
possibilities for investigating the properties of stellar interiors. This
constitutes entirely new ways to study the effects of dynamic phenomena on
stellar structure and evolution. Important examples are the extent of
convection zones and the associated mixing and the direct and indirect effects
of stellar rotation. In addition, the stellar oscillations themselves show very
interesting dynamic behaviour. Here we discuss examples of the results obtained
from such investigations, across the Hertzsprung-Russell diagram.